Quelle  ctomaxi2.tbl   Sprache: unbekannt

#############################################################################
##
#W  ctomaxi2.tbl                GAP table library               Thomas Breuer
##
##  This file contains the ordinary character tables of maximal subgroups
##  (which are neither ATLAS tables nor tables of Ostermann) of the
##  groups $HS$, $McL$, $He$, $Ru$, $Suz$, $ON$, $HN$, $Ly$, $Th$.
##
#H  ctbllib history
#H  ---------------
#H  $Log: ctomaxi2.tbl,v $
#H  Revision 4.64  2012/06/20 14:45:31  gap
#H  added tables and fusions, as documented in ctbldiff.dat
#H      TB
#H
#H  Revision 4.63  2012/04/23 16:16:11  gap
#H  next step of consolidation:
#H
#H  - removed a few unnecessary duplicate tables,
#H    and changed some related fusions, names of maxes, table constructions
#H  - make sure that duplicate tables arise only via `ConstructPermuted'
#H    constructions
#H  - added some relative names
#H  - added fusions A11.2 -> A12.2, L2(11).2 -> A12.2, D8x2F4(2)'.2 -> B,
#H    L2(41) -> M, (A5xA12):2 -> A17,
#H  - added maxes of A12.2, L6(2), 2.M22.2
#H  - added table of QD16.2,
#H  - fixed the syntax of two `ALN' calls
#H      TB
#H
#H  Revision 4.62  2012/03/02 08:22:00  gap
#H  added fusions 2.A7.2 -> 2.Suz.2, Isoclinic(2.A7.2) -> Isoclinic(2.Suz.2)
#H      TB
#H
#H  Revision 4.61  2012/01/30 08:31:55  gap
#H  removed #H entries from the headers
#H      TB
#H
#H  Revision 4.60  2012/01/26 11:12:59  gap
#H  added tables of the missing maxes of 2.Ru:
#H  2xA8, 2xU3(5).2, L2(25).(2x4), 2x5^2:4S5, 3.A6.(2x4),
#H  Isoclinic(L2(13).2x2)
#H      TB
#H
#H  Revision 4.59  2011/09/28 13:08:35  gap
#H  - removed revision entry and SET_TABLEFILENAME call,
#H  - changed the construction of the table of (3xG2(3)):2,
#H  - added fusions 3.ONM5 -> 3.ON.2M4, 3.3^4.3^2.Q8 -> 3^4:(3^2:Q8),
#H    3.3^4.3^2.Q8 -> 3.McL.2N3,
#H    5^(1+4):2^(1+4).5.4 -> 5^(1+4)_+:(4Y2^(1+4)_-.5.4),
#H    5^2.5.5^2.4A5 -> 5^2.5.5^2.4S5, ONM5 -> (3^2:4xA6).2^2,
#H    5^2.5.5^2.4S5 -> G2(5)
#H      TB
#H
#H  Revision 4.58  2011/02/09 15:58:22  gap
#H  name 2^5.L5(2) for 2^5.psl(5,2), name 7^2:2.L2(7) for 7^2:2psl(2,7)
#H  (used in AtlasRep)
#H      TB
#H
#H  Revision 4.57  2010/12/01 17:47:56  gap
#H  renamed "Sym(4)" to "Symm(4)";
#H  note that the table constructed with `CharacterTable( "Symmetric", 4 )'
#H  gets the identifier `"Sym(4)"', and this table is sorted differently
#H      TB
#H
#H  Revision 4.56  2010/05/05 13:20:05  gap
#H  - added many class fusions,
#H  - changed several class fusions according to consistency conditions,
#H    after systematic checks of consistency
#H    - with Brauer tables w.r.t. the restriction of characters,
#H    - of subgroup fusions with the corresponding subgroup fusions between
#H      proper factors where the factor fusions are stored,
#H    - of subgroup fusions from maximal subgroups with subgroup fusions of
#H      extensions inside automorphic extensions
#H
#H      TB
#H
#H  Revision 4.55  2010/01/19 17:05:33  gap
#H  added several tables of maximal subgroups of central extensions of
#H  simple groups (many of them were contributed by S. Dany)
#H      TB
#H
#H  Revision 4.54  2009/04/27 08:27:23  gap
#H  removed some superfluous explicit <nam>M<n> names,
#H  which are created automatically
#H      TB
#H
#H  Revision 4.53  2009/04/22 12:39:04  gap
#H  added missing maxes of He.2, ON.2, HN.2, Fi24, and B
#H      TB
#H
#H  Revision 4.52  2009/01/12 17:33:57  gap
#H  added missing maxes of Fi22.2 and their fusions
#H      TB
#H
#H  Revision 4.51  2009/01/07 10:19:46  gap
#H  added tables of 2^5.S6, (2xA6.2^2).2, 2^(1+6)_+:S5, 4^3:(L3(2)x2), 5:4xS5
#H  (missing maxes of HS.2), and corresp. fusions
#H      TB
#H
#H  Revision 4.50  2008/06/24 16:24:10  gap
#H  added table of Fi22.2N3B
#H      TB
#H
#H  Revision 4.49  2007/07/03 08:50:15  gap
#H  added fusions,
#H  encoded several tables as index two subdirect products
#H      TB
#H
#H  Revision 4.48  2006/06/07 07:54:27  gap
#H  unified ConstructMixed and ConstructMGA (for better programmatic access)
#H      TB
#H
#H  Revision 4.47  2004/03/12 09:05:13  gap
#H  added two fusions needed for automatic table constructions
#H      TB
#H
#H  Revision 4.46  2004/01/20 10:26:13  gap
#H  added several names of the forms `<name>C<class>', `<name>N<class>'
#H      TB
#H
#H  Revision 4.45  2003/11/14 08:40:19  gap
#H  improved an InfoText
#H      TB
#H
#H  Revision 4.44  2003/10/27 08:58:22  gap
#H  added fusion 2^6.U4(2) -> S8(3)
#H      TB
#H
#H  Revision 4.43  2003/06/20 15:02:58  gap
#H  added several fusions
#H      TB
#H
#H  Revision 4.42  2003/06/10 16:19:08  gap
#H  store in several fusions between character tables to which subgroup number
#H  in the table of marks of the supergroup the subgroup belongs
#H  (in order to make the commutative diagrams testable)
#H      TB
#H
#H  Revision 4.41  2003/05/15 17:38:07  gap
#H  next step towards the closer connection to the library of tables of marks:
#H  added fusions tbl -> tom, adjusted fusions between character tables
#H  in order to make the diagrams commute, adjusted orderings of maxes
#H      TB
#H
#H  Revision 4.40  2003/05/05 14:23:43  gap
#H  adjusted fusion texts (no longer ambiguous when s.c. are used)
#H      TB
#H
#H  Revision 4.39  2003/03/31 16:33:22  gap
#H  added fusions BN31 -> B, L2(31) -> B,
#H  added some names and tables of maxes of 2.B,
#H  added table of 2.(S3xFi22.2) < 2.B (J. An had asked for it)
#H      TB
#H
#H  Revision 4.38  2003/03/07 15:53:35  gap
#H  added tables of `Isoclinic(2.A5.2)' and `L2(125)',
#H  and many `tomidentifier' components (still several are missing)
#H      TB
#H
#H  Revision 4.37  2003/01/29 15:51:51  gap
#H  added admissible names, fusions, tables for certain maxes (which are
#H  available in Rob's ATLAS and thus should be available in the table
#H  library, too)
#H      TB
#H
#H  Revision 4.36  2003/01/24 15:57:31  gap
#H  replaced several fusions by ones that are compatible with Brauer tables
#H      TB
#H
#H  Revision 4.35  2003/01/22 12:31:27  gap
#H  fixed an `InfoText' value
#H      TB
#H
#H  Revision 4.34  2003/01/21 16:25:31  gap
#H  further standardizations of `InfoText' strings,
#H  added and corrected `Maxes' infos,
#H  added some fusions
#H      TB
#H
#H  Revision 4.33  2003/01/14 17:28:49  gap
#H  changed `InfoText' values (for a better programmatic access)
#H  and replaced `ConstructDirectProduct' by `ConstructPermuted' where
#H  there is only one factor (again better programmatic handling)
#H      TB
#H
#H  Revision 4.32  2002/12/02 16:37:06  gap
#H  corrected 2nd power map of `3.3^(1+4):4S5'
#H      TB
#H
#H  Revision 4.31  2002/10/22 12:44:07  gap
#H  added 215 factor fusions for cases <tbl> -> <tbl> / O_{<p>}(<tbl>)
#H  (they make it possible to construct <p>-modular Brauer tables
#H  for tables of the type [p^n].<fact> where the <p>-modular Brauer table
#H  of <fact> is in the library)
#H      TB
#H
#H  Revision 4.30  2002/09/23 14:52:22  gap
#H  changed comment for fusion 2.SuzM4 -> 2.Suz,
#H  corrected table automorphisms of D8xV4 and fusion into HS,
#H  replaced 7:3xL3(2) and S4xL3(2) by ``construction'' tables
#H      TB
#H
#H  Revision 4.29  2002/09/18 15:22:00  gap
#H  changed the `text' components of many fusions,
#H  in order to use them as a status information (for evaluation)
#H      TB
#H
#H  Revision 4.28  2002/07/24 16:40:37  gap
#H  corrected the table automorphisms of 3^(1+6):2^(3+4):3^2:2
#H      TB
#H
#H  Revision 4.27  2002/07/17 15:25:32  gap
#H  added missing table automorphisms
#H      TB
#H
#H  Revision 4.26  2002/07/12 06:45:55  gap
#H  further tidying up: removed `irredinfo' stuff, rearranged constructions
#H      TB
#H
#H  Revision 4.25  2002/07/08 16:06:56  gap
#H  changed `construction' component from function (call) to list of function
#H  name and arguments
#H      TB
#H
#H  Revision 4.24  2002/03/04 17:08:48  gap
#H  added some fusions and admissible names
#H      TB
#H
#H  Revision 4.23  2001/05/04 16:48:06  gap
#H  first revision for ctbllib
#H
#H
#H  tbl history (GAP 4)
#H  -------------------
#H  (Rev. 4.23 of ctbllib coincides with Rev. 4.22 of tbl in GAP 4)
#H  
#H  RCS file: /gap/CVS/GAP/4.0/tbl/ctomaxi2.tbl,v
#H  branch:
#H  locks: strict
#H  access list:
#H  symbolic names:
#H   GAP4R2: 4.11.0.6
#H   GAP4R2PRE2: 4.11.0.4
#H   GAP4R2PRE1: 4.11.0.2
#H   GAP4R1: 4.5.0.2
#H  keyword substitution: kv
#H  total revisions: 29; selected revisions: 29
#H  description:
#H  ----------------------------
#H  revision 4.22
#H  date: 2001/03/12 16:44:58;  author: gap;  state: Exp;  lines: +117 -2
#H  added double cover of ThN2A (computed by Simon Norton)
#H  
#H      TB
#H  ----------------------------
#H  revision 4.21
#H  date: 2000/12/11 15:52:34;  author: gap;  state: Exp;  lines: +3 -2
#H  added a new name for a table (Simon had asked for that)
#H  
#H      TB
#H  ----------------------------
#H  revision 4.20
#H  date: 2000/07/22 09:31:21;  author: gap;  state: Exp;  lines: +90 -84
#H  added tables of missing maxes of 2.HS
#H  (I should have done this a long time ago ...)
#H  
#H      TB
#H  ----------------------------
#H  revision 4.19
#H  date: 2000/07/15 07:55:37;  author: gap;  state: Exp;  lines: +3 -3
#H  typos
#H  
#H      TB
#H  ----------------------------
#H  revision 4.18
#H  date: 2000/07/08 10:07:46;  author: gap;  state: Exp;  lines: +188 -6
#H  added some maxes of 2.HS (not yet complete ...) and corresponding fusions
#H  
#H      TB
#H  ----------------------------
#H  revision 4.17
#H  date: 2000/06/09 17:24:18;  author: gap;  state: Exp;  lines: +128 -38
#H  added 6.SuzM12 (now the maxes of 6.Suz are complete)
#H  
#H      TB
#H  ----------------------------
#H  revision 4.16
#H  date: 2000/05/22 16:54:20;  author: gap;  state: Exp;  lines: +182 -20
#H  added 2.SuzM12 and two more maxes of 6.Suz
#H  
#H      TB
#H  ----------------------------
#H  revision 4.15
#H  date: 2000/05/13 12:15:27;  author: gap;  state: Exp;  lines: +704 -21
#H  added some maxes of 6.Suz: [1,2,4,6,9,10,11,14,16]
#H  
#H      TB
#H  ----------------------------
#H  revision 4.14
#H  date: 2000/04/03 11:06:49;  author: gap;  state: Exp;  lines: +25 -2
#H  added tables of 6.U6(2)M3 and (2^2x3).U6(2)M3 (constructed for Eamonn)
#H  
#H      TB
#H  ----------------------------
#H  revision 4.13
#H  date: 2000/03/27 09:54:44;  author: gap;  state: Exp;  lines: +53 -2
#H  added some tables of maxes of 2.Suz and corresponding fusions,
#H  added table of 3.Fi22M5
#H  
#H      TB
#H  ----------------------------
#H  revision 4.12
#H  date: 2000/03/22 15:12:17;  author: gap;  state: Exp;  lines: +372 -24
#H  added missing tables of maxes of 2.Suz
#H  (contributed by Frank Himstedt)
#H  
#H      TB
#H  ----------------------------
#H  revision 4.11
#H  date: 1999/10/22 13:24:48;  author: gap;  state: Exp;  lines: +3 -2
#H  added maxes of J2.2
#H  
#H      TB
#H  ----------------------------
#H  revision 4.10
#H  date: 1999/10/21 14:15:47;  author: gap;  state: Exp;  lines: +56 -36
#H  added many `tomidentifer' and `tomfusion' values, which yields a better
#H  interface between `tom' and `tbl';
#H  
#H  added maxes of McL.2,
#H  
#H  unified tables `J2.2M4', `2^(2+4):(3x3):2^2', `2^(2+4):(S3xS3)'.
#H  
#H      TB
#H  ----------------------------
#H  revision 4.9
#H  date: 1999/10/04 15:57:14;  author: gap;  state: Exp;  lines: +5 -2
#H  added and corrected several fusions from character tables
#H  to their tables of marks,
#H  unified two instances of the table of (A6xA6):2^2,
#H  corrected the name of the table of marks of 2F4(2).
#H  
#H      TB
#H  ----------------------------
#H  revision 4.8
#H  date: 1999/09/17 14:11:51;  author: gap;  state: Exp;  lines: +642 -15
#H  added maxes of 3.Suz.2
#H  
#H      TB
#H  ----------------------------
#H  revision 4.7
#H  date: 1999/09/14 13:30:11;  author: gap;  state: Exp;  lines: +517 -2
#H  added maxes of 3.Suz
#H  
#H      TB
#H  ----------------------------
#H  revision 4.6
#H  date: 1999/08/31 13:16:14;  author: gap;  state: Exp;  lines: +871 -2
#H  added missing tables and fusions of maximal subgroups of Suz.2
#H  
#H      TB
#H  ----------------------------
#H  revision 4.5
#H  date: 1999/07/14 11:39:39;  author: gap;  state: Exp;  lines: +4 -3
#H  cosmetic changes for the release ...
#H  
#H      TB
#H  ----------------------------
#H  revision 4.4
#H  date: 1999/07/12 14:53:28;  author: gap;  state: Exp;  lines: +4 -4
#H  fixed CAS components of a few tables
#H  (now more restrictive than in GAP 3)
#H  
#H      TB
#H  ----------------------------
#H  revision 4.3
#H  date: 1998/03/11 08:05:34;  author: gap;  state: Exp;  lines: +28 -8
#H  mainly new fusions to tables of marks added
#H  
#H      TB
#H  ----------------------------
#H  revision 4.2
#H  date: 1997/11/25 15:45:00;  author: gap;  state: Exp;  lines: +14 -3
#H  first attempt to link the library of character tables and the
#H      library of tables of marks
#H          TB
#H  ----------------------------
#H  revision 4.1
#H  date: 1997/07/17 15:41:34;  author: fceller;  state: Exp;  lines: +2 -2
#H  for version 4
#H  ----------------------------
#H  revision 1.7
#H  date: 1997/05/22 13:46:13;  author: sam;  state: Exp;  lines: +143 -30
#H  some changes to be able to construct all library tables
#H  ----------------------------
#H  revision 1.6
#H  date: 1997/04/04 17:14:32;  author: sam;  state: Exp;  lines: +3 -3
#H  removed last occurrency of 'CharTable' in the files,
#H  fixed a typo
#H  ----------------------------
#H  revision 1.5
#H  date: 1997/04/01 13:56:55;  author: sam;  state: Exp;  lines: +131 -2
#H  added some tables,
#H  removed superfluous file
#H  ----------------------------
#H  revision 1.4
#H  date: 1997/03/19 11:11:58;  author: sam;  state: Exp;  lines: +145 -2
#H  added table of 2.SuzM4
#H  ----------------------------
#H  revision 1.3
#H  date: 1997/02/01 09:48:33;  author: sam;  state: Exp;  lines: +127 -45
#H  added tables of '2^(2+4):(3x3):2^2', '2^(2+4).S3', '2^(2+4).(S3x2)',
#H  reordered some other (new) tables
#H  ----------------------------
#H  revision 1.2
#H  date: 1996/12/17 16:37:40;  author: sam;  state: Exp;  lines: +7 -7
#H  changed the name of '4.2^4:s5' to '4.2^4.S5' (the extension is non-split!)
#H  ----------------------------
#H  revision 1.1
#H  date: 1996/10/21 15:59:50;  author: sam;  state: Exp;
#H  first proposal of the table library
#H  ==========================================================================
##

MOT("(2^2xSz(8)):3",
[
"origin: CAS library,\n",
"maximal subgroup of Ru,\n",
"source: received from S.Mattarei,\n",
"test: 1.OR, JAMES, JAMES,n=3,\n",
"and restricted characters decompose properly,\n",
"tests: 1.o.r., pow[2,3,5,7,13]"
],
[349440,768,192,192,60,28,52,116480,256,64,64,20,28,28,28,52,52,52,60,12,12,
12,15,60,12,12,12,15],
[,[1,1,2,2,5,6,7,1,1,2,2,5,6,6,6,7,7,7,24,24,25,25,28,19,19,20,20,23],[1,2,4,
3,5,6,7,8,9,11,10,12,15,13,14,17,18,16,1,2,3,4,5,1,2,3,4,5],,[1,2,3,4,1,6,7,8,
9,10,11,8,14,15,13,16,17,18,24,25,26,27,24,19,20,21,22,19],,[1,2,4,3,5,1,7,8,
9,11,10,12,8,8,8,18,16,17,19,20,22,21,23,24,25,27,26,28],,,,,,[1,2,3,4,5,6,1,
8,9,10,11,12,13,14,15,8,8,8,19,20,21,22,23,24,25,26,27,28]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,E(3),E(3),E(3),E(3),E(3),E(3)^2,E(3)^2,E(3)^2,E(3)^2,
E(3)^2],
[TENSOR,[2,2]],[3,3,3,3,3,3,3,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,
0,0,0],[14,-2,2*E(4),-2*E(4),-1,0,1,14,-2,2*E(4),-2*E(4),-1,0,0,0,1,1,1,-1,1,
E(4),-E(4),-1,-1,1,E(4),-E(4),-1],
[TENSOR,[5,2]],
[TENSOR,[5,3]],
[GALOIS,[5,3]],
[TENSOR,[8,2]],
[TENSOR,[8,3]],[42,-6,6*E(4),-6*E(4),-3,0,3,-14,2,-2*E(4),2*E(4),1,0,0,0,-1,
-1,-1,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[11,3]],[64,0,0,0,-1,1,-1,64,0,0,0,-1,1,1,1,-1,-1,-1,4,0,0,0,-1,4,0,0,
0,-1],
[TENSOR,[13,2]],
[TENSOR,[13,3]],[91,-5,-1,-1,1,0,0,91,-5,-1,-1,1,0,0,0,0,0,0,1,1,-1,-1,1,1,1,
-1,-1,1],
[TENSOR,[16,2]],
[TENSOR,[16,3]],[105,9,-3,-3,0,0,1,105,9,-3,-3,0,0,0,0,1,1,1,0,0,0,0,0,0,0,0,
0,0],[105,9,-3,-3,0,0,1,-35,-3,1,1,0,0,0,0,E(13)-E(13)^2-E(13)^3+E(13)^4
 +E(13)^5+E(13)^6+E(13)^7+E(13)^8+E(13)^9-E(13)^10-E(13)^11+E(13)^12,
E(13)+E(13)^2+E(13)^3-E(13)^4+E(13)^5-E(13)^6-E(13)^7+E(13)^8-E(13)^9+E(13)^10
 +E(13)^11+E(13)^12,-E(13)+E(13)^2+E(13)^3+E(13)^4-E(13)^5+E(13)^6+E(13)^7
 -E(13)^8+E(13)^9+E(13)^10+E(13)^11-E(13)^12,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[20,4]],
[GALOIS,[20,2]],[192,0,0,0,-3,3,-3,-64,0,0,0,1,-1,-1,-1,1,1,1,0,0,0,0,0,0,0,0,
0,0],[195,3,3,3,0,-1,0,195,3,3,3,0,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0],[195,3,
3,3,0,-1,0,-65,-1,-1,-1,0,-E(7)+E(7)^2-E(7)^3-E(7)^4+E(7)^5-E(7)^6,
-E(7)-E(7)^2+E(7)^3+E(7)^4-E(7)^5-E(7)^6,E(7)-E(7)^2-E(7)^3-E(7)^4-E(7)^5
 +E(7)^6,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[25,3]],
[GALOIS,[25,2]],[273,-15,-3,-3,3,0,0,-91,5,1,1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0]],
[(19,24)(20,25)(21,26)(22,27)(23,28),(16,17,18),(16,18,17),(13,15,14),( 3, 4)
(10,11)(21,22)(26,27)]);
ARC("(2^2xSz(8)):3","projectives",["2.(2^2xSz(8)):3",[[2,2,2,2,2,2,2,0,0,0,0,
0,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[28,-4,-4*E(4),4*E(4),-2,0,2,0,0,
0,0,0,0,0,0,0,0,0,1,-1,E(4),-E(4),1,1,-1,E(4),-E(4),1],
[GALOIS,[2,3]],[128,0,0,0,-2,2,-2,0,0,0,0,0,0,0,0,0,0,0,-4,0,0,0,1,-4,0,0,0,
1],[182,-10,-2,-2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,1,1,-1,-1,-1,1,1,-1],[210,
18,-6,-6,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[390,6,6,6,0,-2,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]],]);
ALF("(2^2xSz(8)):3","Sz(8).3",[1,2,3,4,5,6,7,1,2,3,4,5,6,6,6,7,7,7,8,10,
14,12,16,9,11,15,13,17]);
ALF("(2^2xSz(8)):3","Ru",[1,2,6,6,10,12,20,3,3,8,8,17,21,23,22,32,33,34,4,
11,19,19,24,4,11,19,19,24],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);

MOT("(3^2:4xa6).2",
[
"origin: CAS library,\n",
"13th maximal subgroup of Suz,\n",
"test: 1.OR, JAMES, JAMES,n=3,\n",
"and restricted characters decompose properly,\n",
"tests: 1.o.r., pow[2,3,5]"
],
[25920,3240,2880,1440,576,72,64,32,648,81,72,36,648,81,72,36,288,36,32,16,180,
45,45,20,20,20,96,96,96,96,16,16,12,12,12,12],
[,[1,2,1,3,1,2,1,3,9,10,9,11,13,14,13,15,5,6,5,7,21,23,22,21,24,24,3,3,3,3,7,
7,11,11,15,15],[1,1,3,4,5,5,7,8,1,1,3,4,1,1,3,4,17,17,19,20,21,21,21,24,25,26,
27,28,29,30,31,32,27,28,29,30],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,
19,20,1,2,2,3,4,4,27,28,29,30,31,32,33,34,35,36]],
0,
[(25,26),(22,23),(22,23)(25,26),(27,28)(29,30)(31,32)(33,34)(35,36),( 9,13)
(10,14)(11,15)(12,16)(27,29)(28,30)(33,35)(34,36)],
["ConstructIndexTwoSubdirectProduct","3^2:4","3^2:Q8","A6","A6.2_1",[51,52,53,
54,55,62,63,64,65,66],(2,5,17,18,22,12,24,20,4,13)(3,9,11,19,23,16,14,6,21,8,
7)(10,15)(28,29,31,35,34,32)(30,33),(1,2)(3,4)(7,11,9)(12,13)(14,15)(18,22,20)
(26,27)(33,34)]);
ARC("(3^2:4xa6).2","projectives",["(3^(1+2):4xA6).2",[[48,0,-16,-16,0,0,0,0,-6
,0,2,2,-6,0,2,2,0,0,0,0,3,0,0,-1,-1,-1,0,0,0,0,0,0,0,0,0,0],[48,0,16,0,0,0,0,0
,-6,0,-2,0,-6,0,-2,0,0,0,0,0,3,0,0,1,-E(20)-E(20)^9+E(20)^13+E(20)^17,
E(20)+E(20)^9-E(20)^13-E(20)^17,0,0,0,0,0,0,0,0,0,0],[30,0,-10,-10,-6,0,2,2,3,
0,-1,-1,3,0,-1,-1,0,0,0,0,0,0,0,0,0,0,-2,2,2,-2,0,0,1,-1,-1,1],[6,0,2,0,6,0,2,
0,6,0,2,0,6,0,2,0,6,0,2,0,6,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0],[15,0,-5,-5,3,0,-1,
-1,6,0,-2,-2,-3,0,1,1,-3,0,1,1,0,0,0,0,0,0,-3,3,1,-1,-1,1,0,0,1,-1],[60,0,20,0
,-12,0,-4,0,6,0,2,0,6,0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[3,0,-1,
-1,3,0,-1,-1,3,0,-1,-1,3,0,-1,-1,3,0,-1,-1,3,0,0,-1,-1,-1,1,-1,1,-1,1,-1,1,-1,
1,-1],[15,0,-5,5,3,0,-1,1,-3,0,1,-1,6,0,-2,2,-3,0,1,-1,0,0,0,0,0,0,1,1,-3,-3,
-1,-1,1,1,0,0],[27,0,-9,-9,3,0,-1,-1,0,0,0,0,0,0,0,0,3,0,-1,-1,-3,0,0,1,1,1,-3
,3,-3,3,1,-1,0,0,0,0],[54,0,18,0,6,0,2,0,0,0,0,0,0,0,0,0,6,0,2,0,-6,0,0,-2,0,0
,0,0,0,0,0,0,0,0,0,0],[30,0,10,0,6,0,2,0,-6,0,-2,0,12,0,4,0,-6,0,-2,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0],[30,0,10,0,6,0,2,0,12,0,4,0,-6,0,-2,0,-6,0,-2,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0]],"(3^2:4x2.A6).2",[[4,4,4,4,0,0,0,0,-2,-2,-2,2,1,1
,1,1,0,0,0,0,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,-E(12)^7+E(12)^11,
-E(12)^7+E(12)^11],[4,4,4,4,0,0,0,0,1,1,1,-1,-2,-2,-2,-2,0,0,0,0,-1,-1,-1,-1,
-1,-1,0,0,0,0,0,0,E(3)-E(3)^2,-E(3)+E(3)^2,0,0],[8,8,-8,0,0,0,0,0,-4,-4,4,0,2,
2,-2,0,0,0,0,0,-2,-2,-2,2,0,0,0,0,0,0,0,0,0,0,0,0],[8,8,-8,0,0,0,0,0,2,2,-2,0,
-4,-4,4,0,0,0,0,0,-2,-2,-2,2,0,0,0,0,0,0,0,0,0,0,0,0],[16,16,16,-16,0,0,0,0,-2
,-2,-2,-2,-2,-2,-2,2,0,0,0,0,1,1,1,1,-1,-1,0,0,0,0,0,0,0,0,0,0],[16,16,-16,0,0
,0,0,0,-2,-2,2,0,-2,-2,2,0,0,0,0,0,1,1,1,-1,-E(20)-E(20)^9+E(20)^13+E(20)^17,
E(20)+E(20)^9-E(20)^13-E(20)^17,0,0,0,0,0,0,0,0,0,0],[20,20,20,-20,0,0,0,0,2,2
,2,2,2,2,2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[20,20,-20,0,0,0,0,0,2,
2,-2,0,2,2,-2,0,0,0,0,-2*E(8)-2*E(8)^3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[32,-4
,0,0,0,0,0,0,-16,2,0,0,8,-1,0,0,0,0,0,0,-8,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0],[32,
-4,0,0,0,0,0,0,8,-1,0,0,-16,2,0,0,0,0,0,0,-8,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0],[
64,-8,0,0,0,0,0,0,-8,1,0,0,-8,1,0,0,0,0,0,0,4,-E(5)+2*E(5)^2+2*E(5)^3-E(5)^4,
2*E(5)-E(5)^2-E(5)^3+2*E(5)^4,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[11,2]],[80,-10,0,0,0,0,0,0,8,-1,0,0,8,-1,0,0,0,-3*E(8)+3*E(8)^3,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[13,3]]],"(3^(1+2):4x2.A6).2",[[12,0,-4,-4,0,0,0,0,3,0,-1,1,-6,0,2,2,
0,0,0,0,-3,0,0,1,1,1,0,0,0,0,0,0,E(3)-E(3)^2,E(3)-E(3)^2,0,0],[12,0,-4,-4,0,0,
0,0,-6,0,2,-2,3,0,-1,-1,0,0,0,0,-3,0,0,1,1,1,0,0,0,0,0,0,0,0,E(12)^7-E(12)^11,
-E(12)^7+E(12)^11],[24,0,8,0,0,0,0,0,-12,0,-4,0,6,0,2,0,0,0,0,0,-6,0,0,-2,0,0,
0,0,0,0,0,0,0,0,0,0],[24,0,8,0,0,0,0,0,6,0,2,0,-12,0,-4,0,0,0,0,0,-6,0,0,-2,0,
0,0,0,0,0,0,0,0,0,0,0],[48,0,-16,-16,0,0,0,0,-6,0,2,-2,-6,0,2,2,0,0,0,0,3,0,0,
-1,-1,-1,0,0,0,0,0,0,0,0,0,0],[48,0,16,0,0,0,0,0,-6,0,-2,0,-6,0,-2,0,0,0,0,0,3
,0,0,1,E(20)+E(20)^9-E(20)^13-E(20)^17,-E(20)-E(20)^9+E(20)^13+E(20)^17,0,0,0,
0,0,0,0,0,0,0],[60,0,-20,-20,0,0,0,0,6,0,-2,2,6,0,-2,-2,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0],[60,0,20,0,0,0,0,0,6,0,2,0,6,0,2,0,0,0,0,-2*E(8)-2*E(8)^3,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]],]);
ALF("(3^2:4xa6).2","3^2:Q8",[1,3,2,4,1,3,2,4,1,3,2,4,1,3,2,4,1,3,2,4,1,3,
3,2,4,4,5,6,5,6,5,6,5,6,5,6]);
ALF("(3^2:4xa6).2","A6.2_1",[1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4,5,5,5,5,6,6,
6,6,6,6,7,7,8,8,9,9,10,10,11,11]);
ALF("(3^2:4xa6).2","Suz",[1,6,2,7,3,17,3,9,5,6,16,28,4,6,13,27,10,30,10,10,11,
35,36,24,40,40,8,8,9,9,10,10,31,31,29,29],[
"fusion is unique up to table automorphisms,\n",
"the representative is compatible with the fusion 2.SuzM13 -> 2.Suz"
]);
ALF("(3^2:4xa6).2","(3^2:8xA6).2",[1,2,3,4,7,22,10,16,11,13,24,31,12,14,
25,32,15,33,17,19,20,35,35,30,36,37,50,50,51,51,52,52,53,53,54,54],[
"fusion map is unique up to table automorphisms"
]);

MOT("(3^2:4x2.A6).2",
[
"13th maximal subgroup of 2.Suz,\n",
"origin: Dixon's Algorithm"
],
[51840,51840,6480,6480,5760,5760,2880,2880,576,72,64,32,1296,1296,162,162,144,
144,72,72,1296,1296,162,162,144,144,72,72,288,72,72,32,32,32,360,360,90,90,90,
90,40,40,40,40,40,40,96,96,96,96,16,16,24,24,24,24,24,24,24,24],
[,[1,1,3,3,1,1,5,5,2,4,2,6,13,13,15,15,13,13,17,17,21,21,23,23,21,21,25,25,9,
10,10,9,11,11,35,35,39,39,37,37,35,35,41,41,41,41,5,5,6,6,11,11,17,17,17,17,26
,26,26,26],[1,2,1,2,5,6,7,8,9,9,11,12,1,2,1,2,5,6,8,7,1,2,1,2,5,6,7,8,29,29,29
,32,33,34,35,36,35,36,35,36,41,42,43,44,45,46,47,48,49,50,51,52,47,47,48,48,49
,49,50,50],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25
,26,27,28,29,31,30,32,34,33,1,2,3,4,3,4,5,6,7,8,7,8,47,48,49,50,51,52,54,53,56
,55,58,57,60,59]],
0,
[(37,39)(38,40),(43,45)(44,46),(53,54)(55,56),(30,31),(33,34),(57,58)(59,60),
(47,48)(49,50)(51,52)(53,55)(54,56)(57,59)(58,60),
( 7, 8)(19,20)(27,28)(43,44)(45,46)(53,54)(57,58)],
["ConstructProj",[["(3^2:4xa6).2",[]],["(3^2:4x2.A6).2",[]]]]);
ALF("(3^2:4x2.A6).2","2.Suz",[1,2,10,11,3,4,12,13,5,29,5,15,8,9,10,11,27,
28,48,47,6,7,10,11,21,22,45,46,16,50,51,16,16,16,17,18,59,60,61,62,40,41,
69,70,69,70,14,14,15,15,16,16,52,53,52,53,49,49,49,49],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("(3^2:4x2.A6).2","(3^2:4xa6).2",[1,1,2,2,3,3,4,4,5,6,7,8,9,9,10,10,11,
11,12,12,13,13,14,14,15,15,16,16,17,18,18,19,20,20,21,21,22,22,23,23,24,24,
25,25,26,26,27,28,29,30,31,32,33,33,34,34,35,35,36,36]);
ALF("(3^2:4x2.A6).2","3^2:Q8",[1,1,3,3,2,2,4,4,1,3,2,4,1,1,3,3,2,2,4,4,1,
1,3,3,2,2,4,4,1,3,3,2,4,4,1,1,3,3,3,3,2,2,4,4,4,4,5,6,5,6,5,6,5,5,6,6,5,5,
6,6]);
ALF("(3^2:4x2.A6).2","2.A6.2_1",[1,2,1,2,1,2,2,1,3,3,3,3,4,5,4,5,4,5,4,5,
6,7,6,7,6,7,7,6,8,8,8,8,8,8,9,10,9,10,9,10,9,10,10,9,10,9,11,11,12,12,13,
13,14,15,14,15,16,17,17,16]);

MOT("(3xG2(3)):2",
[
"origin: computed using GAP,\n",
"5th maximal subgroup of Th"
],
[25474176,12737088,3456,1728,17496,17496,17496,4374,2187,972,486,972,486,288,
288,288,216,216,216,108,54,108,54,42,21,24,24,24,162,81,162,81,162,81,36,36,
36,39,39,39,3024,48,54,36,36,12,12,14,18,18,18],
[,[1,2,1,2,5,7,6,8,9,10,11,12,13,3,4,4,5,7,6,10,11,12,13,24,25,14,16,15,29,30,
33,34,31,32,17,19,18,38,39,40,1,3,8,12,12,20,20,24,29,33,31],[1,1,3,3,1,1,1,1,
1,1,1,1,1,14,14,14,3,3,3,3,3,3,3,24,24,26,26,26,8,8,8,8,8,8,14,14,14,38,38,38,
41,42,41,41,41,42,42,48,43,43,43],,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,
17,18,19,20,21,22,23,1,2,26,27,28,29,30,31,32,33,34,35,36,37,38,40,39,41,42,
43,44,45,47,46,41,49,50,51],,,,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,
18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,1,2,2,41,42,43,44,
45,46,47,48,49,50,51]],
0,
[(46,47),(39,40),(31,33)(32,34)(44,45)(50,51),( 6, 7)(15,16)(18,19)(27,28)
(31,33)(32,34)(36,37)(39,40)(44,45)(46,47)(50,51)],
["ConstructIndexTwoSubdirectProduct","C3","S3","G2(3)","G2(3).2",[74,75,76,77,
78,79,80,81,82,83,84],(2,3,5,10,22,9,20,6,12,26,16,35,32,27,18)(4,8,17,38,37,
36,34,30,23,11,24,13,29,21,7,14,31,25,15,33,28,19),(31,32)(39,40)(41,42)(43,
44)(47,48)]);
ALF("(3xG2(3)):2","G2(3).2",[1,1,2,2,3,3,3,4,4,5,5,6,6,7,7,7,8,8,8,9,9,10,
10,11,11,12,12,12,13,13,14,14,15,15,16,16,16,17,17,17,18,19,20,21,22,23,
24,25,26,27,28]);
ALF("(3xG2(3)):2","S3",[1,2,1,2,1,2,2,1,2,1,2,1,2,1,2,2,1,2,2,1,2,1,2,1,2,
1,2,2,1,2,1,2,1,2,1,2,2,1,2,2,3,3,3,3,3,3,3,3,3,3,3]);
ALF("(3xG2(3)):2","Th",[1,3,2,10,4,3,3,4,3,5,4,3,5,6,19,20,11,10,10,9,11,
10,9,12,31,13,33,32,17,17,17,17,17,17,21,19,20,23,47,48,2,7,11,10,10,22,
22,24,28,28,28],[
"fusion map is unique up to table automorphisms"
]);

MOT("(D10xU3(5)).2",
[
"origin: computed in GAP using tables of D10, 5:4, U3(5), U3(5).2, and HN,\n",
"5th maximal subgroup of HN,\n",
"5A normalizer in HN,\n",
"tests: 1.o.r., pow[2,3,5,7]"
],
[2520000,4800,720,160,5000,500,250,240,70,80,200,630000,1200,180,40,1250,125,
125,125,60,35,35,40,40,50,480,480,24,16,20,24,40,40,504000,960,144,32,1000,
100,50,48,14,16,40,480,480,24,16,20,24,40,40],
[,[1,1,3,2,5,6,7,3,9,4,5,12,12,14,13,16,17,19,18,14,22,21,15,15,16,34,35,36,
37,39,41,44,44,1,1,3,2,5,6,7,3,9,4,5,34,35,36,37,39,41,44,44],[1,2,1,4,5,6,7,
2,9,10,11,12,13,12,15,16,17,19,18,13,21,22,24,23,25,45,46,45,48,49,46,51,52,
34,35,34,37,38,39,40,35,42,43,44,26,27,26,29,30,27,32,33],,[1,2,3,4,1,1,1,8,9,
10,2,1,2,3,4,1,1,1,1,8,9,9,10,10,2,26,27,28,29,26,31,27,27,34,35,36,37,34,34,
34,41,42,43,35,45,46,47,48,45,50,46,46],,[1,2,3,4,5,6,7,8,1,10,11,12,13,14,15,
16,17,19,18,20,12,12,23,24,25,45,46,47,48,49,50,51,52,34,35,36,37,38,39,40,41,
34,43,44,26,27,28,29,30,31,32,33]],
0,
[(32,33)(51,52),(23,24),(23,24)(26,45)(27,46)(28,47)(29,48)(30,49)(31,50)
(32,52)(33,51),(21,22),(18,19)(21,22)(23,24)(32,33)(51,52),(26,45)(27,46)
(28,47)(29,48)(30,49)(31,50)(32,52)(33,51)],
["ConstructIndexTwoSubdirectProduct","D10","5:4","U3(5)","U3(5).2",[50,51,52,
53,54,55,56,57,88,89,90,91,92,93,94,95],(26,34,42,31,39,28,36,44,33,41,30,38,
27,35,43,32,40,29,37),(43,48,46,44,47,45)(49,50)]);
ALF("(D10xU3(5)).2","5:4",[1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,
2,2,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5]);
ALF("(D10xU3(5)).2","U3(5).2",[1,2,3,4,5,6,7,8,9,10,11,1,2,3,4,5,6,7,7,8,
9,9,10,10,11,12,13,14,15,16,17,18,19,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,
16,17,18,19]);
ALF("(D10xU3(5)).2","HN",[1,2,4,7,10,9,13,14,17,18,21,9,22,34,41,9,13,11,
12,48,51,52,53,54,22,7,6,30,18,41,31,39,40,2,3,14,7,21,22,26,15,33,18,23,
7,6,30,18,41,31,40,39],[
"fusion map is unique up to table automorphisms"
]);
ALF("(D10xU3(5)).2","Isoclinic(U3(5).2x2)",[1,3,5,7,9,11,13,15,17,19,21,1,
3,5,7,9,11,13,13,15,17,17,19,19,21,23,25,27,29,31,33,35,37,2,4,6,8,10,12,
14,16,18,20,22,24,26,28,30,32,34,36,38]);
ALF("(D10xU3(5)).2","5:4xU3(5):2",[1,2,3,4,5,6,7,8,9,10,11,20,21,22,23,24,
25,26,26,27,28,28,29,29,30,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,
65,66,67,68,88,89,90,91,92,93,94,95],[
"fusion map is unique up to table aut."
]);
ALN("(D10xU3(5)).2",["HNN5A"]);

MOT("(a4xpsl(3,4)):2",
[
"origin: CAS library,\n",
"8th maximal subgroup of Suz,\n",
"test: 1.OR, JAMES, JAMES,n=3,\n",
"and restricted characters decompose properly.\n",
"tests: 1.o.r., pow[2,3,5,7]"
],
[483840,1536,216,384,384,384,60,84,161280,512,72,128,128,128,20,28,60480,192,
27,48,48,48,15,15,21,21,288,288,32,32,36,36,16,16,16,16,16,16],
[,[1,1,3,2,2,2,7,8,1,1,3,2,2,2,7,8,17,17,19,18,18,18,23,24,26,25,1,9,2,10,3,
11,4,12,5,13,6,14],[1,2,1,4,5,6,7,8,9,10,9,12,13,14,15,16,1,2,1,4,5,6,7,7,8,8,
27,28,29,30,27,28,33,34,35,36,37,38],,[1,2,3,4,5,6,1,8,9,10,11,12,13,14,9,16,
17,18,19,20,21,22,17,17,25,26,27,28,29,30,31,32,33,34,35,36,37,38],,[1,2,3,4,
5,6,7,1,9,10,11,12,13,14,15,9,17,18,19,20,21,22,24,23,17,17,27,28,29,30,31,32,
33,34,35,36,37,38]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,
-1,-1,-1,-1,-1],[2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,-1,-1,-1,-1,-1,-1,-1,-1,-1,
-1,0,0,0,0,0,0,0,0,0,0,0,0],[3,3,3,3,3,3,3,3,-1,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,
0,0,0,0,0,0,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1],
[TENSOR,[4,2]],[20,4,2,0,0,0,0,-1,20,4,2,0,0,0,0,-1,20,4,2,0,0,0,0,0,-1,-1,2,
2,-2,-2,2,2,0,0,0,0,0,0],
[TENSOR,[6,2]],[35,3,-1,3,-1,-1,0,0,35,3,-1,3,-1,-1,0,0,35,3,-1,3,-1,-1,0,0,0,
0,1,1,1,1,1,1,1,1,-1,-1,-1,-1],[35,3,-1,-1,3,-1,0,0,35,3,-1,-1,3,-1,0,0,35,3,
-1,-1,3,-1,0,0,0,0,1,1,1,1,1,1,-1,-1,1,1,-1,-1],[35,3,-1,-1,-1,3,0,0,35,3,-1,
-1,-1,3,0,0,35,3,-1,-1,-1,3,0,0,0,0,1,1,1,1,1,1,-1,-1,-1,-1,1,1],
[TENSOR,[8,2]],
[TENSOR,[9,2]],
[TENSOR,[10,2]],[40,8,4,0,0,0,0,-2,40,8,4,0,0,0,0,-2,-20,-4,-2,0,0,0,0,0,1,1,
0,0,0,0,0,0,0,0,0,0,0,0],[60,12,6,0,0,0,0,-3,-20,-4,-2,0,0,0,0,1,0,0,0,0,0,0,
0,0,0,0,2,-2,-2,2,2,-2,0,0,0,0,0,0],
[TENSOR,[15,2]],[64,0,1,0,0,0,-1,1,64,0,1,0,0,0,-1,1,64,0,1,0,0,0,-1,-1,1,1,8,
8,0,0,-1,-1,0,0,0,0,0,0],
[TENSOR,[17,2]],[70,6,-2,6,-2,-2,0,0,70,6,-2,6,-2,-2,0,0,-35,-3,1,-3,1,1,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0],[70,6,-2,-2,6,-2,0,0,70,6,-2,-2,6,-2,0,0,-35,-3,
1,1,-3,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[70,6,-2,-2,-2,6,0,0,70,6,-2,-2,-2,
6,0,0,-35,-3,1,1,1,-3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[90,-6,0,2,2,2,0,-1,90,
-6,0,2,2,2,0,-1,90,-6,0,2,2,2,0,0,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0],[90,-6,0,2,2,
2,0,-1,90,-6,0,2,2,2,0,-1,-45,3,0,-1,-1,-1,0,0,E(21)^2+E(21)^8+E(21)^10
 +E(21)^11+E(21)^13+E(21)^19,E(21)+E(21)^4+E(21)^5+E(21)^16+E(21)^17+E(21)^20,
0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[23,2]],[105,9,-3,9,-3,-3,0,0,-35,-3,1,-3,1,1,0,0,0,0,0,0,0,0,0,0,0,0,
1,-1,1,-1,1,-1,1,-1,-1,1,-1,1],
[TENSOR,[25,2]],[105,9,-3,-3,9,-3,0,0,-35,-3,1,1,-3,1,0,0,0,0,0,0,0,0,0,0,0,0,
1,-1,1,-1,1,-1,-1,1,1,-1,-1,1],
[TENSOR,[27,2]],[105,9,-3,-3,-3,9,0,0,-35,-3,1,1,1,-3,0,0,0,0,0,0,0,0,0,0,0,0,
1,-1,1,-1,1,-1,-1,1,-1,1,1,-1],
[TENSOR,[29,2]],[126,-2,0,-2,-2,-2,1,0,126,-2,0,-2,-2,-2,1,0,126,-2,0,-2,-2,
-2,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[126,-2,0,-2,-2,-2,1,0,126,-2,0,-2,-2,-2,
1,0,-63,1,0,1,1,1,-E(15)-E(15)^2-E(15)^4-E(15)^8,-E(15)^7-E(15)^11-E(15)^13
 -E(15)^14,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[32,7]],[128,0,2,0,0,0,-2,2,128,0,2,0,0,0,-2,2,-64,0,-1,0,0,0,1,1,-1,
-1,0,0,0,0,0,0,0,0,0,0,0,0],[192,0,3,0,0,0,-3,3,-64,0,-1,0,0,0,1,-1,0,0,0,0,0,
0,0,0,0,0,8,-8,0,0,-1,1,0,0,0,0,0,0],
[TENSOR,[35,2]],[270,-18,0,6,6,6,0,-3,-90,6,0,-2,-2,-2,0,1,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0],[378,-6,0,-6,-6,-6,3,0,-126,2,0,2,2,2,-1,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]],
[(25,26),(23,24),(23,24)(25,26),( 5, 6)(13,14)(21,22)(35,37)(36,38),( 4, 5)
(12,13)(20,21)(33,35)(34,36)]);
ARC("(a4xpsl(3,4)):2","projectives",["(A4x3.L3(4)).2",[[270,-18,0,6,6,6,0,-3,
-90,6,0,-2,-2,-2,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[90,-6,0,2,
2,2,0,-1,90,-6,0,2,2,2,0,-1,90,-6,0,2,2,2,0,0,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0],
[90,-6,0,2,2,2,0,-1,90,-6,0,2,2,2,0,-1,-45,3,0,-1,-1,-1,0,0,E(21)^2+E(21)^8+
E(21)^10+E(21)^11+E(21)^13+E(21)^19,E(21)+E(21)^4+E(21)^5+E(21)^16+E(21)^17+
E(21)^20,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[3,2]],[45,-3,0,9,-3,-3,0,3,-15,1,0,-3,1,1,0,-1,0,0,0,0,0,0,0,0,0,0,
-3,3,1,-1,0,0,-1,1,1,-1,1,-1],[63,15,0,3,3,3,3,0,-21,-5,0,-1,-1,-1,-1,0,0,0,0,
0,0,0,0,0,0,0,-3,3,1,-1,0,0,-1,1,-1,1,-1,1],[15,-1,0,3,-1,-1,0,1,15,-1,0,3,-1,
-1,0,1,15,-1,0,3,-1,-1,0,0,1,1,3,3,-1,-1,0,0,1,1,-1,-1,-1,-1],[21,5,0,1,1,1,1,
0,21,5,0,1,1,1,1,0,21,5,0,1,1,1,1,1,0,0,-3,-3,1,1,0,0,-1,-1,-1,-1,-1,-1],[42,
10,0,2,2,2,2,0,42,10,0,2,2,2,2,0,-21,-5,0,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,
0,0,0,0],[84,4,0,0,0,0,-1,0,84,4,0,0,0,0,-1,0,84,4,0,0,0,0,-1,-1,0,0,6,6,2,2,
0,0,0,0,0,0,0,0],[252,12,0,0,0,0,-3,0,-84,-4,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,
6,-6,2,-2,0,0,0,0,0,0,0,0],[126,-2,0,-2,-2,-2,1,0,126,-2,0,-2,-2,-2,1,0,126,
-2,0,-2,-2,-2,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[378,-6,0,-6,-6,-6,3,0,-126,2,
0,2,2,2,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[30,-2,0,6,-2,-2,0,
2,30,-2,0,6,-2,-2,0,2,-15,1,0,-3,1,1,0,0,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0],[126,
-2,0,-2,-2,-2,1,0,126,-2,0,-2,-2,-2,1,0,-63,1,0,1,1,1,-E(15)-E(15)^2-E(15)^4
-E(15)^8,-E(15)^7-E(15)^11-E(15)^13-E(15)^14,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[15,7]],[168,8,0,0,0,0,-2,0,168,8,0,0,0,0,-2,0,-84,-4,0,0,0,0,1,1,0,0,
0,0,0,0,0,0,0,0,0,0,0,0],[45,-3,0,-3,9,-3,0,3,-15,1,0,1,-3,1,0,-1,0,0,0,0,0,0,
0,0,0,0,-3,3,1,-1,0,0,1,-1,-1,1,1,-1],[15,-1,0,-1,-1,3,0,1,15,-1,0,-1,-1,3,0,
1,15,-1,0,-1,-1,3,0,0,1,1,-3,-3,1,1,0,0,1,1,1,1,-1,-1],[45,-3,0,-3,-3,9,0,3,
-15,1,0,1,1,-3,0,-1,0,0,0,0,0,0,0,0,0,0,-3,3,1,-1,0,0,1,-1,1,-1,-1,1],[15,-1,
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-1,-1,1,1],[30,-2,0,-2,6,-2,0,2,30,-2,0,-2,6,-2,0,2,-15,1,0,1,-3,1,0,0,-1,-1,
0,0,0,0,0,0,0,0,0,0,0,0],[30,-2,0,-2,-2,6,0,2,30,-2,0,-2,-2,6,0,2,-15,1,0,1,1,
-3,0,0,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0]],"2.(A4xL3(4)).2",[[40,8,4,-8,0,0,0,-2,
0,0,0,0,0,0,0,0,-20,4,-2,-4,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0],[40,8,4,-8,0,
0,0,-2,0,0,0,0,0,0,0,0,10,-2,1,2,0,0,0,0,
-E(21)-E(21)^4-E(21)^5-E(21)^16-E(21)^17-E(21)^20,
-E(21)^2-E(21)^8-E(21)^10-E(21)^11-E(21)^13-E(21)^19,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[2,2]],[72,8,0,0,0,0,2,2,0,0,0,0,0,0,0,0,-36,4,0,0,0,0,-1,-1,-1,-1,0,
0,0,0,0,0,0,-2*E(8)+2*E(8)^3,0,0,0,0],[112,-16,4,0,0,0,2,0,0,0,0,0,0,0,0,0,-56
,-8,-2,0,0,0,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[112,-16,4,0,0,0,2,0,0,0,0,0,0
,0,0,0,28,4,1,0,0,0,E(15)^7+E(15)^11+E(15)^13+E(15)^14,
E(15)+E(15)^2+E(15)^4+E(15)^8,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[6,7]],[128,0,2,0,0,0,-2,2,0,0,0,0,0,0,0,0,-64,0,-1,0,0,0,1,1,-1,-1,0
,0,0,0,0,-3*E(8)+3*E(8)^3,0,0,0,0,0,0],[140,-4,-4,-4,0,0,0,0,0,0,0,0,0,0,0,0,
-70,-2,2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,0,-2],[144,16,0,0,0,0,4,4,0,0,0,0
,0,0,0,0,36,-4,0,0,0,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0],[180,4,0,4,0,0,0,-2,0,
0,0,0,0,0,0,0,-90,2,0,2,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,-2,0,2],[256,0,4,0,0,0,
-4,4,0,0,0,0,0,0,0,0,64,0,1,0,0,0,-1,-1,1,1,0,0,0,0,0,0,0,0,0,0,0,0],[280,-8,
-8,-8,0,0,0,0,0,0,0,0,0,0,0,0,70,2,-2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[
360,8,0,8,0,0,0,-4,0,0,0,0,0,0,0,0,90,-2,0,-2,0,0,0,0,-1,-1,0,0,0,0,0,0,0,0,0,
0,0,0]],"6.SuzM8",[[12,-4,0,-4,0,0,2,-2,0,0,0,0,0,0,0,0,-6,-2,0,-2,0,0,-1,-1,1
,1,0,0,0,0,0,0,0,0,0,2,0,2],[24,-8,0,-8,0,0,4,-4,0,0,0,0,0,0,0,0,6,2,0,2,0,0,1
,1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0],[72,8,0,0,0,0,2,2,0,0,0,0,0,0,0,0,-36,4,0,0,
0,0,-1,-1,-1,-1,0,0,0,0,0,0,0,-2*E(8)+2*E(8)^3,0,0,0,0],[144,16,0,0,0,0,4,4,0,
0,0,0,0,0,0,0,36,-4,0,0,0,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0],[168,8,0,-8,0,0,
-2,0,0,0,0,0,0,0,0,0,-84,4,0,-4,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[168,8,0,
-8,0,0,-2,0,0,0,0,0,0,0,0,0,42,-2,0,2,0,0,-E(15)^7-E(15)^11-E(15)^13-E(15)^14,
-E(15)-E(15)^2-E(15)^4-E(15)^8,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[6,7]],[180,4,0,4,0,0,0,-2,0,0,0,0,0,0,0,0,-90,2,0,2,0,0,0,0,1,1,0,0,
0,0,0,0,0,0,0,-2,0,2],[240,-16,0,0,0,0,0,2,0,0,0,0,0,0,0,0,-120,-8,0,0,0,0,0,0
,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0],[240,-16,0,0,0,0,0,2,0,0,0,0,0,0,0,0,60,4,0,0,
0,0,0,0,E(21)^2+E(21)^8+E(21)^10+E(21)^11+E(21)^13+E(21)^19,
E(21)+E(21)^4+E(21)^5+E(21)^16+E(21)^17+E(21)^20,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[10,2]],[360,8,0,8,0,0,0,-4,0,0,0,0,0,0,0,0,90,-2,0,-2,0,0,0,0,-1,-1,
0,0,0,0,0,0,0,0,0,0,0,0]],]);
ALF("(a4xpsl(3,4)):2","L3(4).2_1",[1,2,3,4,5,6,7,8,1,2,3,4,5,6,7,8,1,2,3,
4,5,6,7,7,8,8,9,9,10,10,11,11,12,12,13,13,14,14]);
ALF("(a4xpsl(3,4)):2","Suz",[1,2,6,7,9,9,12,18,3,3,17,9,8,8,25,34,4,13,6,
27,29,29,37,37,41,42,3,10,9,10,17,30,19,21,21,20,21,20],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("(a4xpsl(3,4)):2","s4",[1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,
3,3,3,4,5,4,5,4,5,4,5,4,5,4,5],[
"factor fusion equal to that on the CAS table"
]);
ALF("(a4xpsl(3,4)):2","(A4xL3(4):2_3):2",[1,4,6,8,9,9,12,15,2,5,14,10,11,
11,16,19,3,13,7,17,18,18,20,21,22,22,23,24,25,26,27,32,28,29,30,31,30,31],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);

MOT("2.(A4xL3(4)).2",
[
"8th maximal subgroup of 2.Suz,\n",
"structure (SL(2,3) Y 2.L3(4)).2,\n",
"origin: Dixon's Algorithm"
],
[967680,967680,3072,3072,432,432,768,768,384,384,120,120,168,168,161280,512,72
,128,128,128,20,28,120960,120960,384,384,54,54,96,96,48,48,30,30,30,30,42,42,
42,42,288,288,32,32,36,72,72,16,32,32,16,32,32,16,32,32],
[,[1,1,1,1,5,5,3,3,4,4,11,11,13,13,2,2,6,4,3,3,12,14,23,23,23,23,27,27,26,26,
25,25,33,33,35,35,39,39,37,37,2,15,4,16,6,17,17,7,18,18,9,19,19,10,20,20],[1,2
,3,4,1,2,7,8,9,10,11,12,13,14,15,16,15,18,19,20,21,22,1,2,4,3,1,2,8,7,9,10,11,
12,11,12,13,14,13,14,41,42,43,44,41,42,42,48,50,49,51,52,53,54,55,56],,[1,2,3,
4,5,6,7,8,9,10,1,2,13,14,15,16,17,18,19,20,15,22,23,24,25,26,27,28,29,30,31,32
,23,24,23,24,37,38,39,40,41,42,43,44,45,47,46,48,50,49,51,52,53,54,55,56],,[1,
2,3,4,5,6,7,8,9,10,11,12,1,2,15,16,17,18,19,20,21,15,23,24,25,26,27,28,29,30,
31,32,35,36,33,34,23,24,23,24,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56]
],
0,
[(37,39)(38,40),(33,35)(34,36),(46,47),(52,53)(55,56),(49,50),
( 9,10)(19,20)(31,32)(51,54)(52,55)(53,56)],
["ConstructProj",[["(a4xpsl(3,4)):2",[]],["2.(A4xL3(4)).2",[]]]]);
ALF("2.(A4xL3(4)).2","2.Suz",[1,2,3,4,10,11,12,13,15,15,19,20,30,31,5,5,
29,15,14,14,42,58,6,7,22,21,10,11,46,45,49,49,63,64,63,64,71,72,73,74,5,
16,15,16,29,50,51,32,35,35,35,33,34,35,33,34],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("2.(A4xL3(4)).2","(a4xpsl(3,4)):2",[1,1,2,2,3,3,4,4,5,6,7,7,8,8,9,10,11,
12,13,14,15,16,17,17,18,18,19,19,20,20,21,22,23,23,24,24,25,25,26,26,27,28,29,
30,31,32,32,33,34,34,35,36,36,37,38,38]);

MOT("(a6xa5).2",
[
"origin: CAS library,\n",
"12th maximal subgroup of Suz,\n",
"tests: 1.o.r., pow[2,3,5]"
],
[43200,960,540,480,300,2880,64,36,32,20,2160,48,27,24,15,1800,40,45,45,20,25,
25,24,48,48,8,16,16,12,24,24],
[,[1,1,3,2,5,1,1,3,2,5,11,11,13,12,15,16,16,19,18,17,21,22,2,4,4,7,9,9,12,14,
14],[1,2,1,4,5,6,7,6,9,10,1,2,1,4,5,16,17,16,16,20,21,22,23,24,25,26,27,28,23,
24,25],,[1,2,3,4,1,6,7,8,9,6,11,12,13,14,11,1,2,3,3,4,1,1,23,25,24,26,28,27,
29,31,30]],
0,
[(24,25)(27,28)(30,31),(21,22),(18,19)],
["ConstructIndexTwoSubdirectProduct","A5","A5.2","A6","A6.2_3",[38,39,40,46,
47,48,54,55,56],(),(3,15,26,19,30,24,5,8,21,11,16)(4,27,31,25,6,9,7,20,10,17)
(12,28)(13,29)]);
ARC("(a6xa5).2","projectives",["(A6x2.A5).2",[[4,4,4,4,4,0,0,0,0,0,-2,-2,-2,
-2,-2,-1,1,-1,-1,1,-1,-1,0,0,0,0,0,0,0,0,0],[4,4,4,4,4,0,0,0,0,0,1,1,1,1,1,-1,
1,-1,-1,1,-1,-1,0,0,0,0,0,0,-E(12)^7+E(12)^11,E(12)^7-E(12)^11,
E(12)^7-E(12)^11],[6,6,6,6,6,0,0,0,0,0,0,0,0,0,0,1,-1,1,1,-1,1,1,0,0,0,
-E(8)+E(8)^3,E(8)-E(8)^3,E(8)-E(8)^3,0,0,0],[20,4,2,-4,0,0,0,0,0,0,-10,-2,-1,
2,0,-5,1,-E(5)+2*E(5)^2+2*E(5)^3-E(5)^4,2*E(5)-E(5)^2-E(5)^3+2*E(5)^4,-1,0,0,
0,0,0,0,0,0,0,0,0],
[GALOIS,[4,2]],[32,0,-4,0,2,0,0,0,0,0,-16,0,2,0,-1,-8,0,1,1,0,2,-3,0,0,0,0,0,
0,0,0,0],[32,0,-4,0,2,0,0,0,0,0,-16,0,2,0,-1,-8,0,1,1,0,-3,2,0,0,0,0,0,0,0,0,
0],[36,4,0,4,-4,0,0,0,0,0,-18,-2,0,-2,2,-9,1,0,0,1,1,1,0,0,0,0,0,0,0,0,0],[36,
4,0,4,-4,0,0,0,0,0,9,1,0,1,-1,-9,1,0,0,1,1,1,0,0,0,0,0,0,-E(12)^7+E(12)^11,
-E(12)^7+E(12)^11,-E(12)^7+E(12)^11],[40,8,4,-8,0,0,0,0,0,0,10,2,1,-2,0,-10,2,
-1,-1,-2,0,0,0,0,0,0,0,0,0,0,0],[40,-8,4,0,0,0,0,0,0,0,-20,4,-2,0,0,-10,-2,-1,
-1,0,0,0,0,0,0,0,0,0,0,0,0],[40,-8,4,0,0,0,0,0,0,0,10,-2,1,0,0,-10,-2,-1,-1,0,
0,0,0,0,0,0,0,0,0,-E(24)-E(24)^11+E(24)^17+E(24)^19,E(24)+E(24)^11-E(24)^17
 -E(24)^19],[54,6,0,6,-6,0,0,0,0,0,0,0,0,0,0,9,-1,0,0,-1,-1,-1,0,0,0,
E(8)-E(8)^3,E(8)-E(8)^3,E(8)-E(8)^3,0,0,0],[60,12,6,-12,0,0,0,0,0,0,0,0,0,0,0,
10,-2,1,1,2,0,0,0,0,0,0,0,0,0,0,0],[60,-12,6,0,0,0,0,0,0,0,0,0,0,0,0,10,2,1,1,
0,0,0,0,0,0,0,-2*E(4),2*E(4),0,0,0],[64,0,-8,0,4,0,0,0,0,0,16,0,-2,0,1,-16,0,
2,2,0,-1,-1,0,0,0,0,0,0,0,0,0],[96,0,-12,0,6,0,0,0,0,0,0,0,0,0,0,16,0,-2,-2,0,
1,1,0,0,0,0,0,0,0,0,0]],"(3.A6xA5):2",[[60,-4,0,-4,0,0,0,0,0,0,15,-1,0,-1,0,
-15,1,0,0,1,0,0,2,2,2,0,0,0,-1,-1,-1],[36,4,0,4,-4,0,0,0,0,0,9,1,0,1,-1,-9,-1,
0,0,-1,1,1,2,-2,-2,0,0,0,-1,1,1],[24,-8,0,8,4,0,0,0,0,0,6,-2,0,2,1,-6,2,0,0,
-2,-1,-1,0,0,0,0,0,0,0,0,0],[30,-10,0,10,5,6,-2,0,2,1,-6,2,0,-2,-1,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0],[6,-2,0,2,1,6,-2,0,2,1,6,-2,0,2,1,6,-2,0,0,2,1,1,0,0,0,
0,0,0,0,0,0],[36,12,0,0,6,-12,-4,0,0,-2,0,0,0,0,0,6,2,0,0,0,1,1,0,0,0,0,0,0,0,
0,0],[18,-6,0,6,3,-6,2,0,-2,-1,0,0,0,0,0,3,-1,0,0,1,-2,3,0,0,0,0,0,0,0,0,0],[
24,8,0,0,4,0,0,0,0,0,6,2,0,0,1,-6,-2,0,0,0,-1,-1,0,2*E(8)+2*E(8)^3,
-2*E(8)-2*E(8)^3,0,0,0,0,-E(8)-E(8)^3,E(8)+E(8)^3],[54,6,0,6,-6,-18,-2,0,-2,2,
0,0,0,0,0,9,1,0,0,1,-1,-1,0,0,0,0,0,0,0,0,0],[90,-6,0,-6,0,-30,2,0,2,0,0,0,0,
0,0,15,-1,0,0,-1,0,0,0,0,0,0,0,0,0,0,0],[18,-6,0,6,3,-6,2,0,-2,-1,0,0,0,0,0,3,
-1,0,0,1,3,-2,0,0,0,0,0,0,0,0,0],[6,2,0,0,1,6,2,0,0,1,6,2,0,0,1,6,2,0,0,0,1,1,
0,-E(8)-E(8)^3,E(8)+E(8)^3,0,-E(8)-E(8)^3,E(8)+E(8)^3,0,-E(8)-E(8)^3,
E(8)+E(8)^3],[45,5,0,5,-5,9,1,0,1,-1,-9,-1,0,-1,1,0,0,0,0,0,0,0,1,-1,-1,-1,1,
1,1,-1,-1],[9,1,0,1,-1,9,1,0,1,-1,9,1,0,1,-1,9,1,0,0,1,-1,-1,1,-1,-1,1,-1,-1,
1,-1,-1],[15,-1,0,-1,0,15,-1,0,-1,0,15,-1,0,-1,0,15,-1,0,0,-1,0,0,1,1,1,1,1,1,
1,1,1],[30,10,0,0,5,6,2,0,0,1,-6,-2,0,0,-1,0,0,0,0,0,0,0,0,-E(8)-E(8)^3,
E(8)+E(8)^3,0,E(8)+E(8)^3,-E(8)-E(8)^3,0,-E(8)-E(8)^3,E(8)+E(8)^3],[75,-5,0,
-5,0,15,-1,0,-1,0,-15,1,0,1,0,0,0,0,0,0,0,0,1,1,1,-1,-1,-1,1,1,1]],
"(3.A6x2.A5).2",[[12,-4,0,4,2,0,0,0,0,0,-6,2,0,-2,-1,-3,-1,0,0,1,-3,2,0,0,0,0,
0,0,0,0,0],[12,-4,0,4,2,0,0,0,0,0,-6,2,0,-2,-1,-3,-1,0,0,1,2,-3,0,0,0,0,0,0,0,
0,0],[36,-12,0,12,6,0,0,0,0,0,0,0,0,0,0,6,2,0,0,-2,1,1,0,0,0,0,0,0,0,0,0],[24,
-8,0,8,4,0,0,0,0,0,6,-2,0,2,1,-6,-2,0,0,2,-1,-1,0,0,0,0,0,0,0,0,0],[24,8,0,0,4
,0,0,0,0,0,-12,-4,0,0,-2,-6,2,0,0,0,-1,-1,0,0,0,0,0,0,0,0,0],[60,-4,0,-4,0,0,0
,0,0,0,-30,2,0,2,0,-15,-1,0,0,-1,0,0,0,0,0,0,0,0,0,0,0],[36,4,0,4,-4,0,0,0,0,0
,-18,-2,0,-2,2,-9,1,0,0,1,1,1,0,0,0,0,0,0,0,0,0],[60,-4,0,-4,0,0,0,0,0,0,15,-1
,0,-1,0,-15,-1,0,0,-1,0,0,0,0,0,0,0,0,E(12)^7-E(12)^11,-E(12)^7+E(12)^11,
-E(12)^7+E(12)^11],[36,4,0,4,-4,0,0,0,0,0,9,1,0,1,-1,-9,1,0,0,1,1,1,0,0,0,0,0,
0,E(12)^7-E(12)^11,E(12)^7-E(12)^11,E(12)^7-E(12)^11],[24,8,0,0,4,0,0,0,0,0,6,
2,0,0,1,-6,2,0,0,0,-1,-1,0,0,0,0,0,0,0,E(24)+E(24)^11-E(24)^17-E(24)^19,
-E(24)-E(24)^11+E(24)^17+E(24)^19],[36,12,0,0,6,0,0,0,0,0,0,0,0,0,0,6,-2,0,0,0
,1,1,0,0,0,0,2*E(4),-2*E(4),0,0,0],[54,6,0,6,-6,0,0,0,0,0,0,0,0,0,0,9,-1,0,0,
-1,-1,-1,0,0,0,-E(8)+E(8)^3,-E(8)+E(8)^3,-E(8)+E(8)^3,0,0,0],[90,-6,0,-6,0,0,0
,0,0,0,0,0,0,0,0,15,1,0,0,1,0,0,0,0,0,-E(8)+E(8)^3,E(8)-E(8)^3,E(8)-E(8)^3,0,0
,0]],]);
ALF("(a6xa5).2","A5.2",[1,1,1,1,1,2,2,2,2,2,3,3,3,3,3,4,4,4,4,4,4,4,5,5,5,
6,6,6,7,7,7]);
ALF("(a6xa5).2","A6.2_3",[1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,3,4,5,5,6,7,
8,6,7,8,6,7,8]);
ALF("(a6xa5).2","Suz",[1,2,6,7,12,3,3,17,9,25,4,13,6,27,37,11,24,35,36,40,
12,11,9,19,19,10,21,21,29,43,43],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("(a6xa5).2","(A6:2_2xA5).2",[1,2,3,4,5,6,7,15,10,17,8,14,9,18,20,11,
16,19,19,21,12,13,22,24,24,23,25,25,26,27,27],[
"fusion map is unique up to table automorphisms"
]);

MOT("2.(2^2xSz(8)):3",
[
"origin: computed by J\"urgen M\"uller using GAP,\n",
"3rd maximal subgroup of 2.Ru,"
],
[698880,698880,1536,1536,384,384,384,384,120,120,56,56,104,104,116480,256,64,
64,20,28,28,28,52,52,52,120,120,24,24,24,24,24,24,30,30,120,120,24,24,24,24,
24,24,30,30],
[,[1,1,1,1,3,3,3,3,9,9,11,11,13,13,2,2,4,4,10,12,12,12,14,14,14,36,36,36,36,
38,38,38,38,44,44,26,26,26,26,28,28,28,28,34,34],[1,2,3,4,7,8,5,6,9,10,11,12,
13,14,15,16,18,17,19,22,20,21,24,25,23,1,2,3,4,5,6,7,8,9,10,1,2,3,4,5,6,7,8,9,
10],,[1,2,3,4,5,6,7,8,1,2,11,12,13,14,15,16,17,18,15,21,22,20,23,24,25,36,37,
38,39,40,41,42,43,36,37,26,27,28,29,30,31,32,33,26,27],,[1,2,3,4,7,8,5,6,9,10,
1,2,13,14,15,16,18,17,19,15,15,15,25,23,24,26,27,28,29,32,33,30,31,34,35,36,
37,38,39,42,43,40,41,44,45],,,,,,[1,2,3,4,5,6,7,8,9,10,11,12,1,2,15,16,17,18,
19,20,21,22,15,15,15,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,
45]],
0,
[(26,36)(27,37)(28,38)(29,39)(30,40)(31,41)(32,42)(33,43)(34,44)(35,45),
(23,24,25),(20,22,21),( 5, 7)( 6, 8)(17,18)(30,32)(31,33)(40,42)(41,43)],
["ConstructProj",[["(2^2xSz(8)):3",[]],["2.(2^2xSz(8)):3",[]]]]);
ALF("2.(2^2xSz(8)):3","(2^2xSz(8)):3",[1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,9,10,
11,12,13,14,15,16,17,18,19,19,20,20,21,21,22,22,23,23,24,24,25,25,26,26,
27,27,28,28]);
ALF("2.(2^2xSz(8)):3","2.Ru",[1,2,4,3,10,11,11,10,16,17,20,21,34,35,5,5,
13,13,29,36,38,37,55,56,57,6,7,19,18,33,32,32,33,39,40,6,7,19,18,33,32,32,
33,39,40],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("2.(2^2xSz(8)):3","Sz(8).3",[1,1,2,2,3,3,4,4,5,5,6,6,7,7,1,2,3,4,5,6,
6,6,7,7,7,8,8,10,10,14,14,12,12,16,16,9,9,11,11,15,15,13,13,17,17]);

MOT("2.2.2^4+6:S5",
[
"origin: Dixon's Algorithm,\n",
"6th maximal subgroup of 2.Ru"
],
[491520,491520,491520,491520,48,48,48,48,48,48,96,96,96,96,15360,15360,192,
192,24,24,768,768,32,32,32,32,128,128,1024,32,512,80,80,80,80,32,512,16384,
16384,40,40,40,40,7680,7680,64,2048,2048,256,64,24,24,32,512,256,40,40,64,64,
1024,1024,64,64,512,64,64,1024,1024,128,128,128,128,1024,1024,256,64,512,512,
256,512,512,128],
[,[1,1,1,1,10,10,10,10,14,14,11,11,11,11,4,4,16,16,11,11,1,1,28,28,27,27,29,
29,3,31,4,34,34,34,34,37,39,1,1,32,32,32,32,3,3,47,1,1,2,47,13,13,54,39,38,33,
33,60,60,39,39,64,64,38,67,67,39,39,74,74,74,74,1,1,39,48,38,38,39,38,38,38],[
1,2,3,4,17,18,17,18,15,16,1,2,3,4,15,16,18,17,21,22,21,22,25,26,23,24,28,27,
29,30,31,32,33,34,35,36,37,38,39,42,43,40,41,45,44,46,47,48,49,50,45,44,53,54,
55,56,57,59,58,60,61,63,62,64,66,65,67,68,69,70,71,72,73,74,75,76,78,77,79,81,
80,82],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,
27,28,29,30,31,3,4,1,2,36,37,38,39,44,45,45,44,44,45,46,47,48,49,50,51,52,53,
54,55,15,16,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,
80,81,82]],
0,
[(40,43)(41,42),(19,20)(21,22)(40,41)(42,43)(44,45)(51,52)(69,72)(70,71)
(77,78),(5,7)(6,8),( 5, 8)( 6, 7)(17,18)(23,25)(24,26)(27,28)(40,41)(42,43)
(44,45)(51,52)(58,59)(62,63)(65,66)(77,78)(80,81),(23,24)(25,26)(62,63)(69,71)
(70,72),(23,25)(24,26)(27,28)(58,59)(62,63)(80,81)],
["ConstructProj",[["2.2^4+6:S5",[]],["2.2.2^4+6:S5",[]]]]);
ALF("2.2.2^4+6:S5","2.2^4+6:S5",[1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,9,10,
10,11,11,12,12,13,13,14,14,15,16,17,18,18,19,19,20,21,22,22,23,23,24,24,
25,25,26,27,27,28,29,30,30,31,32,33,34,34,35,35,36,36,37,37,38,39,39,40,
40,41,41,42,42,43,43,44,45,46,46,47,48,48,49]);
ALF("2.2.2^4+6:S5","2.Ru",[1,2,4,3,51,52,53,54,30,31,6,7,19,18,8,9,23,22,
18,19,3,4,41,42,43,44,24,25,12,26,13,28,27,14,15,26,13,4,3,47,48,50,49,10,
11,12,4,3,5,12,32,33,26,13,12,45,46,22,23,9,8,25,24,12,22,23,9,8,13,13,8,
9,4,3,13,13,10,11,13,11,10,12],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("2.2.2^4+6:S5","A5.2",[1,1,1,1,7,7,7,7,3,3,3,3,3,3,1,1,5,5,7,7,5,5,6,
6,6,6,2,2,1,6,2,4,4,4,4,2,1,1,1,4,4,4,4,1,1,2,1,1,2,5,3,3,5,1,2,4,4,2,2,1,
1,6,6,2,6,6,2,2,6,6,6,6,2,2,2,5,2,2,2,2,2,5]);

MOT("2xA8",
[
"8th maximal subgroup of 2.Ru"
],
0,
0,
0,
[(25,27)(26,28),(21,23)(22,24)],
["ConstructDirectProduct",[["A8"],["Cyclic",2]]]);
ALF("2xA8","2.Ru",[1,2,4,3,3,4,6,7,6,7,12,12,13,13,16,17,18,19,19,18,20,
21,20,21,39,40,39,40],[
"fusion map is unique"
]);
ALF("2xA8","A8xS3",[1,3,4,6,7,9,10,12,13,15,16,18,19,21,22,24,25,27,28,30,
31,33,34,36,37,39,40,42],[
"fusion map is unique up to table aut."
]);

MOT("2.2^3+8:L3(2)",
[
"origin: Dixon's Algorithm,\n",
"4th maximal subgroup of 2.Ru,"
],
[688128,688128,98304,98304,4096,4096,1792,1536,1536,3072,3072,1024,512,512,
512,256,56,56,56,56,48,48,48,48,32,32,128,28,28,28,28,28,28,24,24,24,24,256,
256,256,256,32,32,64,32,32,32,32,128,128,64,64,24,24,32],
[,[1,1,1,1,1,1,2,3,3,4,4,3,4,1,1,3,17,17,19,19,21,21,21,21,14,15,5,18,20,20,
18,18,20,23,23,23,23,5,5,5,5,27,27,6,49,49,50,50,12,12,10,10,24,24,13],[1,2,3,
4,5,6,7,9,8,10,11,12,13,14,15,16,19,20,17,18,1,2,3,4,25,26,27,29,31,28,33,30,
32,8,9,8,9,38,39,40,41,43,42,44,47,48,45,46,50,49,52,51,10,11,55],,,,[1,2,3,4,
5,6,7,9,8,10,11,12,13,14,15,16,1,2,1,2,21,22,23,24,25,26,27,7,7,7,7,7,7,35,34,
37,36,38,39,40,41,42,43,44,47,48,45,46,50,49,52,51,53,54,55]],
0,
[(42,43),(34,36)(35,37),(17,19)(18,20)(28,29,31,33,32,30),(14,15)(25,26)
(38,41)(39,40)(45,46)(47,48)(51,52),( 8, 9)(34,35)(36,37)(45,47)(46,48)(49,50)
(51,52),(28,32,31)(29,30,33)],
["ConstructProj",[["2^3+8:L3(2)",[]],["2.2^3+8:L3(2)",[]]]]);
ALF("2.2^3+8:L3(2)","2^3+8:L3(2)",[1,1,2,2,3,3,4,5,5,6,6,7,8,9,9,10,11,11,
12,12,13,13,14,14,15,16,17,18,19,20,21,22,23,24,24,25,25,26,26,27,27,28,
28,29,30,30,31,31,32,32,33,33,34,34,35]);
ALF("2.2^3+8:L3(2)","2.Ru",[1,2,4,3,3,4,5,10,11,9,8,12,13,4,3,12,20,21,20,
21,6,7,19,18,12,13,13,36,37,38,38,37,36,33,32,33,32,8,9,13,13,26,26,12,43,
44,41,42,24,25,22,23,31,30,26],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("2.2^3+8:L3(2)","L3(2)",[1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,5,5,6,6,3,3,
3,3,4,4,2,5,6,6,5,5,6,3,3,3,3,2,2,2,2,4,4,2,4,4,4,4,2,2,2,2,3,3,2]);

MOT("2.2^4+6:S5",
[
"maximal subgroup of Ru,\n",
"normalizer of a 2A involution, tests: 1.o.r., pow[2,3,5]"
],
[245760,245760,24,24,24,48,48,7680,96,12,384,16,16,64,1024,32,512,40,40,32,
512,8192,20,20,3840,64,1024,256,64,12,32,512,256,20,32,512,32,512,32,512,64,
64,512,256,64,256,256,256,128],
[,[1,1,5,5,7,6,6,2,8,6,1,14,14,15,2,17,2,19,19,21,22,1,18,18,2,27,1,1,27,7,32,
22,22,18,36,22,38,22,40,22,43,43,1,22,27,22,22,22,22],[1,2,9,9,8,1,2,8,9,11,
11,13,12,14,15,16,17,18,19,20,21,22,24,23,25,26,27,28,29,25,31,32,33,34,35,36,
37,38,39,40,41,42,43,44,45,46,47,48,49],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,
16,17,2,1,20,21,22,25,25,25,26,27,28,29,30,31,32,33,8,35,36,37,38,39,40,41,42,
43,44,45,46,47,48,49]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1],[1,1,-1,-1,1,1,1,1,-1,-1,-1,-1,-1,1,1,-1,1,1,1,1,1,1,1,
1,1,1,1,1,-1,1,-1,1,1,1,1,1,-1,1,-1,1,-1,-1,1,1,-1,1,1,1,-1],[4,4,-1,-1,1,1,1,
4,2,-1,2,0,0,0,4,0,0,-1,-1,0,4,4,-1,-1,4,0,4,0,2,1,2,4,0,-1,0,4,0,0,0,0,0,0,0,
0,2,0,0,0,2],
[TENSOR,[3,2]],[5,5,-1,-1,-1,-1,-1,5,-1,-1,-1,1,1,1,5,1,1,0,0,1,5,5,0,0,5,1,5,
1,-1,-1,-1,5,1,0,1,5,1,1,1,1,1,1,1,1,-1,1,1,1,-1],
[TENSOR,[5,2]],[6,6,0,0,0,0,0,6,0,0,0,0,0,-2,6,0,-2,1,1,-2,6,6,1,1,6,-2,6,-2,
0,0,0,6,-2,1,-2,6,0,-2,0,-2,0,0,-2,-2,0,-2,-2,-2,0],[6,6,0,0,0,0,0,6,0,0,0,0,
0,2,-2,-2,2,1,1,0,2,6,-1,-1,-6,-2,-2,-2,0,0,0,-2,-2,1,0,2,2,2,-2,2,2,2,2,-2,0,
-2,2,2,0],[6,6,0,0,0,0,0,6,0,0,0,2*E(4),-2*E(4),-2,-2,0,-2,1,1,0,2,6,-1,-1,-6,
2,-2,2,0,0,0,-2,2,1,0,2,0,-2,0,-2,0,0,-2,2,0,2,-2,-2,0],
[TENSOR,[8,2]],
[TENSOR,[9,2]],[10,10,1,1,1,1,1,10,4,-1,-4,0,0,-2,2,0,2,0,0,0,-2,10,0,0,-10,2,
2,-2,0,-1,0,2,-2,0,0,-2,0,2,0,2,0,0,2,-2,0,-2,2,2,-4],
[TENSOR,[12,2]],[10,10,-1,-1,1,1,1,10,2,1,-2,0,0,2,2,0,-2,0,0,0,-2,10,0,0,-10,
-2,2,2,2,-1,-2,2,2,0,0,-2,0,-2,0,-2,0,0,-2,2,2,2,-2,-2,-2],
[TENSOR,[14,2]],[12,12,0,0,0,0,0,-12,0,0,0,0,0,0,4,0,-4,2,2,2,0,12,0,0,0,0,4,
0,0,0,0,-4,0,-2,-2,0,0,4,0,-4,0,0,4,0,0,0,4,-4,0],[12,12,0,0,0,0,0,-12,0,0,0,
0,0,0,4,0,4,2,2,-2,0,12,0,0,0,0,4,0,0,0,0,-4,0,-2,2,0,0,-4,0,4,0,0,-4,0,0,0,
-4,4,0],[15,15,0,0,0,0,0,15,3,0,3,-1,-1,-1,-1,1,3,0,0,-1,-1,15,0,0,15,-1,-1,3,
-1,0,-1,-1,3,0,-1,-1,1,3,1,3,1,1,3,3,-1,3,3,3,3],[15,15,0,0,0,0,0,15,-3,0,-3,
-1,-1,3,-1,1,-1,0,0,-1,-1,15,0,0,15,3,-1,-1,1,0,1,-1,-1,0,-1,-1,1,-1,1,-1,1,1,
-1,-1,1,-1,-1,-1,-3],
[TENSOR,[19,2]],
[TENSOR,[18,2]],[20,20,0,0,-2,2,2,-20,0,0,0,0,0,0,-4,0,4,0,0,2,0,20,0,0,0,0,
-4,0,0,0,0,4,0,0,-2,0,0,-4,0,4,0,0,-4,0,0,0,-4,4,0],[20,20,1,1,-1,-1,-1,20,-2,
-1,2,0,0,0,4,0,0,0,0,0,-4,20,0,0,-20,0,4,0,2,1,-2,4,0,0,0,-4,0,0,0,0,0,0,0,0,
2,0,0,0,2],
[TENSOR,[23,2]],[20,20,0,0,-2,2,2,-20,0,0,0,0,0,0,-4,0,-4,0,0,-2,0,20,0,0,0,0,
-4,0,0,0,0,4,0,0,2,0,0,4,0,-4,0,0,4,0,0,0,4,-4,0],[24,24,0,0,0,0,0,-24,0,0,0,
0,0,0,8,0,0,-1,-1,0,0,24,-E(5)+E(5)^2+E(5)^3-E(5)^4,E(5)-E(5)^2-E(5)^3+E(5)^4,
0,0,8,0,0,0,0,-8,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[26,2]],[24,24,0,0,0,0,0,24,0,0,0,0,0,0,-8,0,0,-1,-1,0,8,24,1,1,-24,0,
-8,0,0,0,0,-8,0,-1,0,8,0,0,0,0,0,0,0,0,0,0,0,0,0],[30,30,0,0,0,0,0,30,0,0,0,0,
0,-2,-2,0,-2,0,0,2,-2,30,0,0,30,-2,-2,-2,0,0,0,-2,-2,0,2,-2,0,-2,0,-2,0,0,-2,
-2,0,-2,-2,-2,0],[40,40,0,0,2,-2,-2,-40,0,0,0,0,0,0,-8,0,0,0,0,0,0,40,0,0,0,0,
-8,0,0,0,0,8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[60,60,0,0,0,0,0,0,0,0,-6,0,0,
0,-4,0,8,0,0,0,-4,-4,0,0,0,0,4,4,2,0,0,0,0,0,0,4,-2,4,0,0,2,2,-4,-4,-2,0,0,-4,
2],[60,60,0,0,0,0,0,0,0,0,-6,0,0,0,-4,0,0,0,0,0,-4,-4,0,0,0,0,4,-4,2,0,0,0,0,
0,0,4,2,-4,0,8,-2,-2,4,4,-2,0,0,-4,2],[60,60,0,0,0,0,0,0,0,0,6,0,0,0,-4,2,4,0,
0,0,4,-4,0,0,0,0,4,0,2,0,0,0,4,0,0,-4,0,0,-2,-4,0,0,8,0,-2,-4,-4,0,-2],
[TENSOR,[31,2]],[60,60,0,0,0,0,0,0,0,0,6,0,0,0,-4,-2,-4,0,0,0,4,-4,0,0,0,0,4,
0,2,0,0,0,-4,0,0,-4,0,8,2,4,0,0,0,0,-2,4,-4,0,-2],
[TENSOR,[33,2]],
[TENSOR,[32,2]],
[TENSOR,[35,2]],[120,120,0,0,0,0,0,0,0,0,0,0,0,0,-8,0,-8,0,0,0,-8,-8,0,0,0,0,
8,0,0,0,0,0,0,0,0,8,0,0,0,-8,0,0,0,0,0,0,0,8,0],[120,120,0,0,0,0,0,0,0,0,0,0,
0,0,8,0,-8,0,0,0,0,-8,0,0,0,0,-8,8,0,0,0,0,0,0,0,0,0,0,0,8,0,0,0,0,0,-8,0,0,
0],[120,120,0,0,0,0,0,0,0,0,0,0,0,0,8,0,0,0,0,0,0,-8,0,0,0,0,-8,0,0,0,0,0,0,0,
0,0,0,-8,0,0,0,0,8,-8,0,8,0,0,0],[120,120,0,0,0,0,0,0,0,0,0,0,0,0,8,0,0,0,0,0,
0,-8,0,0,0,0,-8,-8,0,0,0,0,8,0,0,0,0,8,0,0,0,0,-8,0,0,0,0,0,0],[120,120,0,0,0,
0,0,0,0,0,0,0,0,0,-8,0,0,0,0,0,8,-8,0,0,0,0,8,0,0,0,0,0,0,0,0,-8,0,-8,0,0,0,0,
-8,0,0,0,8,0,0],[120,120,0,0,0,0,0,0,0,0,0,0,0,0,8,0,8,0,0,0,0,-8,0,0,0,0,-8,
0,0,0,0,0,-8,0,0,0,0,0,0,-8,0,0,0,8,0,0,0,0,0],[192,-192,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,-2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-4,4,0,0,0,0,0,0,0],
[TENSOR,[45,2]],[128,-128,0,0,0,-4,4,0,0,0,0,0,0,0,0,0,0,2,-2,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[128,-128,
-E(24)+E(24)^11+E(24)^17-E(24)^19,E(24)-E(24)^11-E(24)^17+E(24)^19,0,2,-2,0,0,
0,0,0,0,0,0,0,0,2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0],
[TENSOR,[48,2]]],
[(41,42),(23,24),(12,13),(3,4),( 3, 4)(12,13)]);
ARC("2.2^4+6:S5","projectives",["2.2.2^4+6:S5",[[12,12,0,0,0,0,0,0,0,0,0,
-1+E(4),-1-E(4),-2*E(4),0,0,0,2,2,0,0,-4,0,0,0,0,-4,0,0,0,0,0,0,0,-2*E(4),-4,
-2*E(4),0,0,0,2,-2,0,0,0,0,0,4*E(4),0],[12,12,0,0,0,0,0,0,0,0,0,1+E(4),1-E(4),
2*E(4),0,0,0,2,2,0,0,-4,0,0,0,0,-4,0,0,0,0,0,0,0,2*E(4),-4,-2*E(4),0,0,0,-2,2,
0,0,0,0,0,-4*E(4),0],[16,-16,-E(4),-E(4),1,1,-1,4,-2*E(4),1,4,0,0,0,0,0,0,-1,
1,0,0,0,-E(4),E(4),4*E(4),0,0,0,0,E(4),0,0,0,-1,0,0,0,0,2*E(4),-4,2,2,-4,0,0,
4*E(4),0,0,0],
[GALOIS,[3,3]],[32,-32,0,0,-2,2,-2,-8,0,0,0,0,0,0,0,0,0,-2,2,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,2,0,0,0,0,0,8,0,0,-8,0,0,0,0,0,0],[48,48,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,-2,-2,0,0,-16,0,0,0,0,-16,0,0,0,0,0,0,0,0,-16,0,0,0,0,0,0,0,0,0,0,0,0,
0],[60,60,0,0,0,0,0,0,0,0,0,1+E(4),1-E(4),2*E(4),0,0,0,0,0,0,0,-20,0,0,0,0,12,
0,0,0,0,0,0,0,-2*E(4),-4,2*E(4),0,0,0,2,-2,0,0,0,0,0,-4*E(4),0],[60,60,0,0,0,
0,0,0,0,0,0,-1+E(4),-1-E(4),-2*E(4),0,0,0,0,0,0,0,-20,0,0,0,0,12,0,0,0,0,0,0,
0,2*E(4),-4,2*E(4),0,0,0,-2,2,0,0,0,0,0,4*E(4),0],[64,-64,-E(4),-E(4),1,1,-1,
16,4*E(4),1,-8,0,0,0,0,0,0,1,-1,0,0,0,E(4),-E(4),16*E(4),0,0,0,0,E(4),0,0,0,1,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[9,3]],[80,-80,-E(4),-E(4),-1,-1,1,20,-2*E(4),1,4,0,0,0,0,0,0,0,0,0,0,
0,0,0,20*E(4),0,0,0,0,-E(4),0,0,0,0,0,0,0,0,-2*E(4),-4,-2,-2,-4,0,0,4*E(4),0,
0,0],
[GALOIS,[11,3]],[96,-96,0,0,0,0,0,24,0,0,0,0,0,0,0,0,0,-1,1,0,0,0,-E(4),E(4),
24*E(4),0,0,0,0,0,0,0,0,-1,0,0,0,0,0,8,0,0,8,0,0,-8*E(4),0,0,0],
[GALOIS,[13,3]],[96,-96,0,0,0,0,0,-24,0,0,0,0,0,0,0,0,0,-1,1,0,0,0,
-E(20)-E(20)^9+E(20)^13+E(20)^17,-E(20)-E(20)^9+E(20)^13+E(20)^17,0,0,0,0,0,0,
0,0,0,1,0,0,0,0,0,-8,0,0,8,0,0,0,0,0,0],
[GALOIS,[15,11]],[120,120,0,0,0,0,0,0,0,0,0,0,0,4*E(4),0,0,0,0,0,0,0,-40,0,0,
0,0,-8,0,0,0,0,0,0,0,0,8,0,0,0,0,0,0,0,0,0,0,0,8*E(4),0],
[GALOIS,[17,3]],[128,-128,0,0,-2,2,-2,-32,0,0,0,0,0,0,0,0,0,2,-2,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[160,160,0,0,0,4,4,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,32,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0],[160,-160,0,0,2,-2,2,-40,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,8,0,0,-8,0,0,0,0,0,0],[160,160,-E(24)-E(24)^11+E(24)^17+E(24)^19,
E(24)+E(24)^11-E(24)^17-E(24)^19,0,-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,32,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]],]);
ALF("2.2^4+6:S5","Ru",[1,2,30,31,18,4,11,5,13,11,2,25,26,14,7,15,8,16,9,
15,8,2,28,29,6,7,2,3,7,19,15,8,7,27,13,5,14,7,13,5,8,5,2,8,8,6,8,6,7],[
"fusion is unique up to table automorphisms"
]);
ALF("2.2^4+6:S5","A5.2",[1,1,7,7,3,3,3,1,5,7,5,6,6,2,1,6,2,4,4,2,1,1,4,4,
1,2,1,2,5,3,5,1,2,4,2,1,6,2,6,2,6,6,2,2,5,2,2,2,5]);
ALN("2.2^4+6:S5",["RuC2A","RuN2A"]);

MOT("2.2^6:u3(3):2",
[
"origin: Dixon's Algorithm,\n",
"2nd maximal subgroup of 2.Ru,"
],
[1548288,1548288,24576,24576,6144,6144,2048,2048,256,432,432,144,144,48,48,
768,768,128,256,256,128,64,48,48,14,14,32,32,32,32,24,24,768,768,768,768,384,
384,128,64,128,24,24,32,32,32,32,24,24,24,24,24,24],
[,[1,1,1,1,1,1,1,1,4,11,11,13,13,13,13,5,5,8,5,5,8,7,11,11,26,26,17,17,18,18,
23,23,1,1,3,3,6,6,4,7,3,13,13,21,21,20,20,14,14,24,24,24,24],[1,2,3,4,5,6,7,8,
9,2,1,2,1,3,4,16,17,18,19,20,21,22,5,6,25,26,28,27,30,29,16,17,33,34,35,36,38,
37,39,40,41,34,33,45,44,46,47,36,35,38,37,38,37],,,,[1,2,3,4,5,6,7,8,9,10,11,
12,13,14,15,16,17,18,19,20,21,22,23,24,2,1,28,27,29,30,31,32,33,34,35,36,38,
37,39,40,41,42,43,44,45,46,47,48,49,51,50,53,52]],
0,
[(50,52)(51,53),(44,45),(29,30),(27,28)(37,38)(50,51)(52,53),(33,34)(35,36)
(37,38)(42,43)(46,47)(48,49)(50,51)(52,53)],
["ConstructProj",[["2^6:u3(3):2",[]],["2.2^6:u3(3):2",[]]]]);
ALF("2.2^6:u3(3):2","2^6:u3(3):2",[1,1,2,2,3,3,4,4,5,6,6,7,7,8,8,9,9,10,
11,11,12,13,14,14,15,15,16,16,17,17,18,18,19,19,20,20,21,21,22,23,24,25,
25,26,26,27,27,28,28,29,29,30,30]);
ALF("2.2^6:u3(3):2","2.Ru",[1,2,3,4,3,4,4,3,12,7,6,7,6,18,19,8,9,13,13,13,
13,12,18,19,21,20,22,23,26,26,30,31,3,4,9,8,10,11,12,12,13,19,18,26,26,26,
26,30,31,32,33,32,33],[
"fusion map is unique up to table automorphisms"
]);
ALF("2.2^6:u3(3):2","U3(3).2",[1,1,1,1,2,2,2,2,2,3,3,4,4,4,4,5,5,5,6,6,6,
6,7,7,8,8,9,9,9,9,10,10,11,11,11,11,12,12,11,12,11,13,13,14,14,14,14,13,
13,15,15,16,16]);

MOT("2.RuM1",
[
"1st maximal subgroup of 2.Ru"
],
0,
0,
0,
[(47,49)(48,50),(35,36)(37,38)(39,40)(41,42)(43,44)(45,46)(47,48)(49,50)(51,
52)(53,54)(55,56)(57,58),(19,21)(20,22)(31,33)(32,34)(35,37)(36,38)(51,53)
(52,54)(55,57)(56,58)],
["ConstructIsoclinic",[["2F4(2)"],["Cyclic",2]],[1,2,3,4,5,6,7,8,9,10,11,12,
13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34]]);
ALF("2.RuM1","2.Ru",[1,2,4,3,3,4,6,7,8,9,12,12,13,13,14,15,18,19,24,25,25,
24,26,26,28,27,30,31,34,35,43,44,41,42,8,9,9,8,10,11,13,13,24,25,22,23,32,
33,32,33,41,42,44,43,45,46,46,45],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("2.RuM1","2F4(2)'.2",[1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,9,10,10,11,11,
12,12,13,13,14,14,15,15,16,16,17,17,18,18,19,19,20,20,21,21,22,22,23,23,
24,24,25,25,26,26,27,27,28,28,29,29]);
ALF("2.RuM1","C4",[1,3,1,3,1,3,1,3,1,3,1,3,1,3,1,3,1,3,1,3,1,3,1,3,1,3,1,
3,1,3,1,3,1,3,2,4,2,4,2,4,2,4,2,4,2,4,2,4,2,4,2,4,2,4,2,4,2,4]);

MOT("2^(1+8).(A5xA5).2",
[
"origin: Dixon's Algorithm,\n",
"4th maximal subgroup of HN,\n",
"table is sorted w.r. to normal series 2.2^8.(A5xA5).2,\n",
"tests: 1.o.r., pow[2,3,5]"
],
[3686400,3686400,30720,24576,15360,3840,256,360,360,600,600,600,600,512,512,
256,128,64,12,20,20,576,576,96,96,96,48,30,30,30,30,100,100,800,800,80,80,80,
100,100,3840,3840,384,192,32,32,16,48,48,24,24,24,20,20,20,20],
[,[1,1,1,1,2,2,4,8,8,12,12,10,10,1,4,4,3,5,9,13,11,22,22,22,22,22,23,30,30,28,
28,39,39,34,34,34,35,35,32,32,1,1,4,3,14,15,17,22,22,24,25,26,32,32,39,39],[1,
2,3,4,5,6,7,1,2,12,13,10,11,14,15,16,17,18,6,21,20,1,2,3,4,4,5,12,13,10,11,39,
40,34,35,36,38,37,32,33,41,42,43,44,45,46,47,42,41,44,43,43,55,56,53,54],,[1,
2,3,4,5,6,7,8,9,1,2,1,2,14,15,16,17,18,19,6,6,22,23,24,26,25,27,8,9,8,9,1,2,1,
2,3,5,5,1,2,41,42,43,44,45,46,47,48,49,50,52,51,42,41,42,41]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
-1,-1,-1,-1],[6,6,6,6,6,2,2,3,3,-4*E(5)-3*E(5)^2-3*E(5)^3-4*E(5)^4,
-4*E(5)-3*E(5)^2-3*E(5)^3-4*E(5)^4,-3*E(5)-4*E(5)^2-4*E(5)^3-3*E(5)^4,
-3*E(5)-4*E(5)^2-4*E(5)^3-3*E(5)^4,-2,-2,-2,-2,-2,-1,E(5)^2+E(5)^3,
E(5)+E(5)^4,0,0,0,0,0,0,-E(5)-E(5)^4,-E(5)-E(5)^4,-E(5)^2-E(5)^3,
-E(5)^2-E(5)^3,-2*E(5)-2*E(5)^4,-2*E(5)-2*E(5)^4,1,1,1,1,1,-2*E(5)^2-2*E(5)^3,
-2*E(5)^2-2*E(5)^3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[3,2]],[8,8,8,8,8,4,4,5,5,3,3,3,3,0,0,0,0,0,1,-1,-1,2,2,2,2,2,2,0,0,0,
0,-2,-2,-2,-2,-2,-2,-2,-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[9,9,9,9,9,-3,
-3,0,0,-3*E(5)-3*E(5)^4,-3*E(5)-3*E(5)^4,-3*E(5)^2-3*E(5)^3,-3*E(5)^2-3*E(5)^3
 ,1,1,1,1,1,0,E(5)+E(5)^4,E(5)^2+E(5)^3,0,0,0,0,0,0,0,0,0,0,
-2*E(5)-E(5)^2-E(5)^3-2*E(5)^4,-2*E(5)-E(5)^2-E(5)^3-2*E(5)^4,-1,-1,-1,-1,-1,
-E(5)-2*E(5)^2-2*E(5)^3-E(5)^4,-E(5)-2*E(5)^2-2*E(5)^3-E(5)^4,-3,-3,-3,-3,1,1,
1,0,0,0,0,0,E(5)+E(5)^4,E(5)+E(5)^4,E(5)^2+E(5)^3,E(5)^2+E(5)^3],
[GALOIS,[6,2]],
[TENSOR,[6,2]],
[TENSOR,[7,2]],[10,10,10,10,10,6,6,4,4,5,5,5,5,2,2,2,2,2,0,1,1,-2,-2,-2,-2,-2,
-2,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[16,16,16,
16,16,0,0,4,4,-4,-4,-4,-4,0,0,0,0,0,0,0,0,1,1,1,1,1,1,-1,-1,-1,-1,1,1,1,1,1,1,
1,1,1,-4,-4,-4,-4,0,0,0,-1,-1,-1,-1,-1,1,1,1,1],
[TENSOR,[11,2]],[18,18,18,18,18,-6,-6,0,0,3,3,3,3,2,2,2,2,2,0,-1,-1,0,0,0,0,0,
0,0,0,0,0,-2,-2,3,3,3,3,3,-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[24,24,24,24,
24,-4,-4,3,3,-E(5)+3*E(5)^2+3*E(5)^3-E(5)^4,-E(5)+3*E(5)^2+3*E(5)^3-E(5)^4,
3*E(5)-E(5)^2-E(5)^3+3*E(5)^4,3*E(5)-E(5)^2-E(5)^3+3*E(5)^4,0,0,0,0,0,-1,1,1,
0,0,0,0,0,0,-E(5)-E(5)^4,-E(5)-E(5)^4,-E(5)^2-E(5)^3,-E(5)^2-E(5)^3,
2*E(5)+2*E(5)^4,2*E(5)+2*E(5)^4,-1,-1,-1,-1,-1,2*E(5)^2+2*E(5)^3,
2*E(5)^2+2*E(5)^3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[14,2]],[25,25,25,25,25,5,5,-5,-5,0,0,0,0,1,1,1,1,1,-1,0,0,1,1,1,1,1,
1,0,0,0,0,0,0,0,0,0,0,0,0,0,-5,-5,-5,-5,-1,-1,-1,1,1,1,1,1,0,0,0,0],
[TENSOR,[16,2]],[30,30,30,30,30,-2,-2,-3,-3,-5*E(5)-5*E(5)^4,-5*E(5)-5*E(5)^4,
-5*E(5)^2-5*E(5)^3,-5*E(5)^2-5*E(5)^3,-2,-2,-2,-2,-2,1,-E(5)-E(5)^4,
-E(5)^2-E(5)^3,0,0,0,0,0,0,E(5)+E(5)^4,E(5)+E(5)^4,E(5)^2+E(5)^3,
E(5)^2+E(5)^3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[18,2]],[40,40,40,40,40,4,4,1,1,-5,-5,-5,-5,0,0,0,0,0,1,-1,-1,-2,-2,
-2,-2,-2,-2,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[60,60,
12,-4,-4,0,0,0,0,0,0,0,0,4,4,-4,0,0,0,0,0,3,3,3,-1,-1,-1,0,0,0,0,0,0,5,5,-3,1,
1,0,0,-10,-10,-2,2,2,-2,0,-1,-1,-1,1,1,0,0,0,0],
[TENSOR,[21,2]],[64,-64,0,0,0,0,0,-2,2,2*E(5)^2+2*E(5)^3,-2*E(5)^2-2*E(5)^3,
2*E(5)+2*E(5)^4,-2*E(5)-2*E(5)^4,0,0,0,0,0,0,0,0,4,-4,0,0,0,0,-E(5)^2-E(5)^3,
E(5)^2+E(5)^3,-E(5)-E(5)^4,E(5)+E(5)^4,-E(5)-2*E(5)^2-2*E(5)^3-E(5)^4,
E(5)+2*E(5)^2+2*E(5)^3+E(5)^4,4,-4,0,0,0,-2*E(5)-E(5)^2-E(5)^3-2*E(5)^4,
2*E(5)+E(5)^2+E(5)^3+2*E(5)^4,-8,8,0,0,0,0,0,2,-2,0,0,0,-E(5)^2-E(5)^3,
E(5)^2+E(5)^3,-E(5)-E(5)^4,E(5)+E(5)^4],
[GALOIS,[23,2]],
[TENSOR,[23,2]],
[TENSOR,[24,2]],[75,75,-5,11,-5,15,-1,0,0,0,0,0,0,3,3,3,-1,-1,0,0,0,6,6,-2,2,
2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,-5,-5,3,-1,-1,-1,1,-2,-2,2,0,0,0,0,0,0],
[TENSOR,[27,2]],[75,75,-5,11,-5,15,-1,0,0,0,0,0,0,3,3,3,-1,-1,0,0,0,-3,-3,1,
-E(3)+3*E(3)^2,3*E(3)-E(3)^2,1,0,0,0,0,0,0,0,0,0,0,0,0,0,-5,-5,3,-1,-1,-1,1,1,
1,-1,-E(3)+E(3)^2,E(3)-E(3)^2,0,0,0,0],
[GALOIS,[29,2]],
[TENSOR,[29,2]],
[TENSOR,[30,2]],[120,120,-8,-8,8,0,0,0,0,0,0,0,0,-8,8,0,0,0,0,0,0,6,6,-2,-2,
-2,2,0,0,0,0,0,0,10,10,2,-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[128,-128,
0,0,0,0,0,-4,4,-2,2,-2,2,0,0,0,0,0,0,0,0,8,-8,0,0,0,0,1,-1,1,-1,-2,2,-12,12,0,
0,0,-2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[225,225,-15,33,-15,-15,1,0,0,0,0,0,
0,1,1,1,5,-3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-15,-15,9,-3,1,1,-1,
0,0,0,0,0,0,0,0,0],
[TENSOR,[35,2]],[240,240,48,-16,-16,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,3,3,3,-1,
-1,-1,0,0,0,0,0,0,-5,-5,3,-1,-1,0,0,-20,-20,-4,4,0,0,0,1,1,1,-1,-1,0,0,0,0],
[TENSOR,[37,2]],[256,-256,0,0,0,0,0,4,-4,-4,4,-4,4,0,0,0,0,0,0,0,0,4,-4,0,0,0,
0,-1,1,-1,1,1,-1,-4,4,0,0,0,1,-1,-16,16,0,0,0,0,0,-2,2,0,0,0,1,-1,1,-1],
[TENSOR,[39,2]],[256,-256,0,0,0,0,0,-2,2,2*E(5)+6*E(5)^2+6*E(5)^3+2*E(5)^4,
-2*E(5)-6*E(5)^2-6*E(5)^3-2*E(5)^4,6*E(5)+2*E(5)^2+2*E(5)^3+6*E(5)^4,
-6*E(5)-2*E(5)^2-2*E(5)^3-6*E(5)^4,0,0,0,0,0,0,0,0,-8,8,0,0,0,0,-E(5)-E(5)^4,
E(5)+E(5)^4,-E(5)^2-E(5)^3,E(5)^2+E(5)^3,-2*E(5)^2-2*E(5)^3,2*E(5)^2+2*E(5)^3,
-4,4,0,0,0,-2*E(5)-2*E(5)^4,2*E(5)+2*E(5)^4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[41,2]],[300,300,60,-20,-20,0,0,0,0,0,0,0,0,4,4,-4,0,0,0,0,0,-3,-3,-3,
1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,-10,-10,-2,2,-2,2,0,-1,-1,-1,1,1,0,0,0,0],
[TENSOR,[43,2]],[360,360,72,-24,-24,0,0,0,0,0,0,0,0,-8,-8,8,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,5,5,-3,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[360,360,-24,
-24,24,0,0,0,0,0,0,0,0,8,-8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,5,5,1,
-E(5)+3*E(5)^2+3*E(5)^3-E(5)^4,3*E(5)-E(5)^2-E(5)^3+3*E(5)^4,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0],
[GALOIS,[46,2]],[384,-384,0,0,0,0,0,-6,6,-2*E(5)+4*E(5)^2+4*E(5)^3-2*E(5)^4,
2*E(5)-4*E(5)^2-4*E(5)^3+2*E(5)^4,4*E(5)-2*E(5)^2-2*E(5)^3+4*E(5)^4,
-4*E(5)+2*E(5)^2+2*E(5)^3-4*E(5)^4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,-1,1,
2*E(5)^2+2*E(5)^3,-2*E(5)^2-2*E(5)^3,4,-4,0,0,0,2*E(5)+2*E(5)^4,
-2*E(5)-2*E(5)^4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[48,2]],[450,450,-30,66,-30,-30,2,0,0,0,0,0,0,2,2,2,-6,2,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[450,450,-30,
66,-30,30,-2,0,0,0,0,0,0,-6,-6,-6,2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[480,480,-32,-32,32,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,6,6,-2,-2,-2,2,0,0,0,0,0,0,-10,-10,-2,2,2,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0],[576,-576,0,0,0,0,0,0,0,6,-6,6,-6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,1,-1,-4,4,0,0,0,1,-1,24,-24,0,0,0,0,0,0,0,0,0,0,1,-1,1,-1],
[TENSOR,[53,2]],[600,600,-40,-40,40,0,0,0,0,0,0,0,0,-8,8,0,0,0,0,0,0,-6,-6,2,
2,2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[768,-768,0,
0,0,0,0,6,-6,-2,2,-2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1,1,-1,-2,2,8,-8,0,0,0,
-2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]],
[(37,38),(25,26)(51,52),(10,12)(11,13)(20,21)(28,30)(29,31)(32,39)(33,40)
(37,38)(53,55)(54,56),(41,42)(48,49)(53,54)(55,56)]);
ALF("2^(1+8).(A5xA5).2","HN",[1,3,2,3,6,8,8,5,16,11,24,12,25,3,6,8,7,19,
32,42,43,4,15,14,15,15,31,35,49,36,50,13,27,10,23,21,39,40,13,28,2,3,6,7,
8,19,18,15,14,30,31,31,27,26,28,26],[
"fusion is unique up to table automorphisms"
]);
ALF("2^(1+8).(A5xA5).2","a5wc2",[1,1,1,1,1,2,2,5,5,8,8,9,9,4,4,4,4,4,13,
16,15,6,6,6,6,6,6,19,19,20,20,10,10,12,12,12,12,12,11,11,3,3,3,3,7,7,7,14,
14,14,14,14,17,17,18,18]);
ALF("2^(1+8).(A5xA5).2","2^(1+8)_+.(A5xA5).2^2",[1,2,3,4,5,9,12,8,18,15,
23,15,23,6,10,11,13,21,27,31,31,7,17,19,20,20,26,28,32,28,32,16,25,14,22,
24,29,30,16,25,33,34,35,36,37,40,41,39,38,44,45,45,42,43,42,43],[
"fusion map is unique up to table aut."
]);
ALN("2^(1+8).(A5xA5).2",["HNC2B","HNN2B"]);

MOT("2^1+6.psl(3,2)",
[
"origin: CAS library,\n",
"maximal subgroup of He,\n",
"test: 1.OR, JAMES, JAMES,n=3,\n",
"and restricted characters decompose properly.\n",
"tests: 1.o.r., pow[2,3,7]"
],
[21504,21504,1536,1536,512,384,256,256,128,128,128,64,64,64,64,32,24,24,12,12,
12,32,32,16,16,16,14,14,14,14],
[,[1,1,1,1,1,2,1,1,1,1,2,3,4,3,4,5,17,17,17,17,18,7,7,9,10,11,27,27,29,29],[1,
2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,1,2,3,4,6,22,23,24,25,26,29,30,27,
28],,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,
1,2,1,2]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[3,3,3,3,3,3,
-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,1,1,1,1,1,E(7)+E(7)^2+E(7)^4,
E(7)+E(7)^2+E(7)^4,E(7)^3+E(7)^5+E(7)^6,E(7)^3+E(7)^5+E(7)^6],
[GALOIS,[2,3]],[6,6,6,6,6,6,2,2,2,2,2,2,2,2,2,2,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,
-1],[7,7,7,7,7,7,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,-1,-1,-1,-1,-1,0,0,0,
0],[8,8,8,8,8,8,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,0,0,0,0,0,1,1,1,1],[7,7,-1,
7,-1,-1,-1,-1,3,-1,3,-1,3,-1,-1,-1,1,1,-1,1,-1,-1,-1,1,-1,1,0,0,0,0],[7,7,-1,
7,-1,-1,3,3,-1,3,-1,-1,-1,-1,3,-1,1,1,-1,1,-1,1,1,-1,1,-1,0,0,0,0],[14,14,-2,
14,-2,-2,2,2,2,2,2,-2,2,-2,2,-2,-1,-1,1,-1,1,0,0,0,0,0,0,0,0,0],[21,21,-3,21,
-3,-3,-3,-3,1,-3,1,1,1,1,-3,1,0,0,0,0,0,1,1,-1,1,-1,0,0,0,0],[21,21,-3,21,-3,
-3,1,1,-3,1,-3,1,-3,1,1,1,0,0,0,0,0,-1,-1,1,-1,1,0,0,0,0],[7,7,7,-1,-1,-1,3,3,
3,-1,-1,3,-1,-1,-1,-1,1,1,1,-1,-1,1,1,1,-1,-1,0,0,0,0],[7,7,7,-1,-1,-1,-1,-1,
-1,3,3,-1,-1,3,-1,-1,1,1,1,-1,-1,-1,-1,-1,1,1,0,0,0,0],[14,14,14,-2,-2,-2,2,2,
2,2,2,2,-2,2,-2,-2,-1,-1,-1,1,1,0,0,0,0,0,0,0,0,0],[21,21,21,-3,-3,-3,1,1,1,
-3,-3,1,1,-3,1,1,0,0,0,0,0,-1,-1,-1,1,1,0,0,0,0],[21,21,21,-3,-3,-3,-3,-3,-3,
1,1,-3,1,1,1,1,0,0,0,0,0,1,1,1,-1,-1,0,0,0,0],[21,21,-3,-3,5,-3,1,1,-3,5,1,1,
1,-3,-3,1,0,0,0,0,0,-1,-1,1,1,-1,0,0,0,0],[21,21,-3,-3,5,-3,5,5,1,1,-3,-3,1,1,
-3,1,0,0,0,0,0,1,1,-1,-1,1,0,0,0,0],[21,21,-3,-3,5,-3,-3,-3,1,1,5,1,-3,-3,1,1,
0,0,0,0,0,1,1,-1,-1,1,0,0,0,0],[21,21,-3,-3,5,-3,1,1,5,-3,1,-3,-3,1,1,1,0,0,0,
0,0,-1,-1,1,1,-1,0,0,0,0],[42,42,-6,-6,10,-6,-2,-2,-2,-2,-2,2,2,2,2,-2,0,0,0,
0,0,0,0,0,0,0,0,0,0,0],[28,28,-4,-4,-4,4,-4,-4,4,4,-4,0,0,0,0,0,1,1,-1,-1,1,0,
0,0,0,0,0,0,0,0],[28,28,-4,-4,-4,4,4,4,-4,-4,4,0,0,0,0,0,1,1,-1,-1,1,0,0,0,0,
0,0,0,0,0],[56,56,-8,-8,-8,8,0,0,0,0,0,0,0,0,0,0,-1,-1,1,1,-1,0,0,0,0,0,0,0,0,
0],[8,-8,0,0,0,0,4,-4,0,0,0,0,0,0,0,0,2,-2,0,0,0,2,-2,0,0,0,1,-1,1,-1],[24,
-24,0,0,0,0,-4,4,0,0,0,0,0,0,0,0,0,0,0,0,0,2,-2,0,0,0,E(7)^3+E(7)^5+E(7)^6,
-E(7)^3-E(7)^5-E(7)^6,E(7)+E(7)^2+E(7)^4,-E(7)-E(7)^2-E(7)^4],
[GALOIS,[26,3]],[48,-48,0,0,0,0,8,-8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,
-1,1],[56,-56,0,0,0,0,-4,4,0,0,0,0,0,0,0,0,2,-2,0,0,0,-2,2,0,0,0,0,0,0,0],[64,
-64,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,2,0,0,0,0,0,0,0,0,1,-1,1,-1]],
[(27,29)(28,30),( 3, 4)( 9,10)(12,15)(13,14)(19,20)(24,25)]);
ARC("2^1+6.psl(3,2)","tomfusion",rec(name:="2^(1+6)+.L3(2)",map:=[1,2,3,4,5,
15,6,7,9,8,32,56,58,61,60,78,10,82,87,84,356,75,76,80,79,333,88,366,88,366],
text:=[
"fusion map is unique up to table autom."
]));
ALF("2^1+6.psl(3,2)","He",[1,3,3,3,2,7,3,2,3,3,8,8,7,7,8,6,5,11,11,11,20,
7,8,8,8,17,15,23,16,24],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("2^1+6.psl(3,2)","2^(1+6)_+.L3(2).2",[1,2,3,3,4,5,6,7,8,8,9,12,11,11,
12,10,13,14,15,15,16,17,18,19,19,20,21,22,21,22],[
"fusion map is unique"
]);
ALF("2^1+6.psl(3,2)","L3(2)",[1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,4,
4,4,4,4,5,5,6,6]);
ALN("2^1+6.psl(3,2)",["2^1+6.L3(2)","HeC2B","HeN2B"]);

MOT("2^1+6.u4q2",
[
"origin: CAS library,\n",
"maximal subgroup of Suz,\n",
"test: 1.OR, JAMES, JAMES,n=3,\n",
"and restricted characters decompose properly,\n",
"tests: 1.o.r., pow[2,3,5]"
],
[3317760,3317760,46080,61440,9216,3072,768,1536,1536,512,512,192,1296,1296,
1296,1296,3456,3456,192,288,432,432,72,384,384,64,32,32,32,32,40,40,20,20,20,
144,144,144,144,144,48,144,48,144,144,24,48,48,24,18,18,18,18,24,24,24,24],
[,[1,1,2,1,1,2,4,4,2,4,1,3,15,15,13,13,17,17,17,18,21,21,22,5,5,6,10,11,9,8,
31,31,32,31,31,15,15,13,13,17,19,17,19,21,21,22,19,18,20,52,52,50,50,39,39,37,
37],[1,2,3,4,5,6,7,8,9,10,11,12,1,2,1,2,1,2,4,3,1,2,3,24,25,26,27,28,29,30,31,
32,33,35,34,5,5,5,5,5,7,5,7,5,5,6,8,9,12,15,16,13,14,25,24,25,24],,[1,2,3,4,5,
6,7,8,9,10,11,12,15,16,13,14,17,18,19,20,21,22,23,24,25,26,27,28,29,30,1,2,3,
4,4,38,39,36,37,42,43,40,41,45,44,46,47,48,49,52,53,50,51,56,57,54,55]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[5,5,5,5,-3,-3,-3,1,1,1,1,1,
E(3)-2*E(3)^2,E(3)-2*E(3)^2,-2*E(3)+E(3)^2,-2*E(3)+E(3)^2,-1,-1,-1,-1,2,2,2,1,
1,1,-1,-1,-1,-1,0,0,0,0,0,E(3)+2*E(3)^2,E(3)+2*E(3)^2,2*E(3)+E(3)^2,
2*E(3)+E(3)^2,-E(3)+E(3)^2,-E(3)+E(3)^2,E(3)-E(3)^2,E(3)-E(3)^2,0,0,0,1,1,1,
-E(3)^2,-E(3)^2,-E(3),-E(3),E(3),E(3),E(3)^2,E(3)^2],
[GALOIS,[2,2]],[6,6,6,6,-2,-2,-2,2,2,2,2,2,-3,-3,-3,-3,3,3,3,3,0,0,0,2,2,2,0,
0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,-2,-2,-2,-1,-1,-1,0,0,0,0,-1,-1,-1,-1],[10,10,
10,10,2,2,2,-2,-2,-2,-2,-2,5*E(3)+2*E(3)^2,5*E(3)+2*E(3)^2,2*E(3)+5*E(3)^2,
2*E(3)+5*E(3)^2,1,1,1,1,1,1,1,2,2,2,0,0,0,0,0,0,0,0,0,E(3)-2*E(3)^2,
E(3)-2*E(3)^2,-2*E(3)+E(3)^2,-2*E(3)+E(3)^2,-1,-1,-1,-1,-1,-1,-1,1,1,1,E(3),
E(3),E(3)^2,E(3)^2,-E(3),-E(3),-E(3)^2,-E(3)^2],
[GALOIS,[5,2]],[15,15,15,15,-1,-1,-1,-1,-1,-1,-1,-1,6,6,6,6,3,3,3,3,0,0,0,3,3,
3,-1,-1,-1,-1,0,0,0,0,0,2,2,2,2,-1,-1,-1,-1,2,2,2,-1,-1,-1,0,0,0,0,0,0,0,0],[
15,15,15,15,7,7,7,3,3,3,3,3,-3,-3,-3,-3,0,0,0,0,3,3,3,-1,-1,-1,1,1,1,1,0,0,0,
0,0,1,1,1,1,-2,-2,-2,-2,1,1,1,0,0,0,0,0,0,0,-1,-1,-1,-1],[20,20,20,20,4,4,4,4,
4,4,4,4,2,2,2,2,5,5,5,5,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,-2,-2,-2,-2,1,1,1,1,
1,1,1,1,1,1,-1,-1,-1,-1,0,0,0,0],[24,24,24,24,8,8,8,0,0,0,0,0,6,6,6,6,0,0,0,0,
3,3,3,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,2,2,2,2,2,2,2,2,-1,-1,-1,0,0,0,0,0,0,0,0,0,
0,0],[30,30,30,30,-10,-10,-10,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,-2,-2,-2,0,0,0,
0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,1,1,1,1],[30,30,
30,30,6,6,6,2,2,2,2,2,6*E(3)-3*E(3)^2,6*E(3)-3*E(3)^2,-3*E(3)+6*E(3)^2,
-3*E(3)+6*E(3)^2,-3,-3,-3,-3,0,0,0,2,2,2,0,0,0,0,0,0,0,0,0,2*E(3)+E(3)^2,
2*E(3)+E(3)^2,E(3)+2*E(3)^2,E(3)+2*E(3)^2,E(3)-E(3)^2,E(3)-E(3)^2,
-E(3)+E(3)^2,-E(3)+E(3)^2,0,0,0,-1,-1,-1,0,0,0,0,-E(3)^2,-E(3)^2,-E(3),-E(3)],
[GALOIS,[12,2]],[40,40,40,40,-8,-8,-8,0,0,0,0,0,2*E(3)+8*E(3)^2,
2*E(3)+8*E(3)^2,8*E(3)+2*E(3)^2,8*E(3)+2*E(3)^2,-2,-2,-2,-2,1,1,1,0,0,0,0,0,0,
0,0,0,0,0,0,-2*E(3),-2*E(3),-2*E(3)^2,-2*E(3)^2,-2*E(3)^2,-2*E(3)^2,-2*E(3),
-2*E(3),1,1,1,0,0,0,E(3),E(3),E(3)^2,E(3)^2,0,0,0,0],
[GALOIS,[14,2]],[45,45,45,45,-3,-3,-3,-3,-3,-3,-3,-3,-9*E(3),-9*E(3),
-9*E(3)^2,-9*E(3)^2,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,3*E(3),3*E(3),
3*E(3)^2,3*E(3)^2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,E(3),E(3),E(3)^2,E(3)^2],
[GALOIS,[16,2]],[60,60,60,60,-4,-4,-4,4,4,4,4,4,6,6,6,6,-3,-3,-3,-3,-3,-3,-3,
0,0,0,0,0,0,0,0,0,0,0,0,2,2,2,2,-1,-1,-1,-1,-1,-1,-1,1,1,1,0,0,0,0,0,0,0,0],[
64,64,64,64,0,0,0,0,0,0,0,0,-8,-8,-8,-8,4,4,4,4,-2,-2,-2,0,0,0,0,0,0,0,-1,-1,
-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,0,0,0,0],[81,81,81,81,9,9,9,-3,
-3,-3,-3,-3,0,0,0,0,0,0,0,0,0,0,0,-3,-3,-3,-1,-1,-1,-1,1,1,1,1,1,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[36,36,-4,4,12,-4,0,8,4,0,-4,0,0,0,0,0,6,6,
-2,2,3,3,-1,0,0,0,2,0,0,-2,1,1,1,-1,-1,0,0,0,0,0,0,0,0,3,3,-1,2,-2,0,0,0,0,0,
0,0,0,0],[36,36,-4,4,-12,4,0,4,8,-4,0,0,0,0,0,0,6,6,-2,2,3,3,-1,0,0,0,0,2,-2,
0,1,1,1,-1,-1,0,0,0,0,0,0,0,0,-3,-3,1,-2,2,0,0,0,0,0,0,0,0,0],[180,180,-20,20,
36,-12,0,4,8,-4,0,0,0,0,0,0,-6,-6,2,-2,6,6,-2,0,0,0,0,-2,2,0,0,0,0,0,0,0,0,0,
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[(34,35),(13,15)(14,16)(36,38)(37,39)(40,42)(41,43)(44,45)(50,52)(51,53)
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ARC("2^1+6.u4q2","projectives",["2.SuzM4",[[4,4,-4,-4,0,0,0,0,0,0,0,0,
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[GALOIS,[30,2]],[240,-240,0,0,40,0,0,-8,0,0,0,0,-3,3,-3,3,-12,12,0,0,6,-6,0,4,
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0,0,0,0,-1,-1,-1,-E(5)+E(5)^2+E(5)^3-E(5)^4,E(5)-E(5)^2-E(5)^3+E(5)^4,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[35,2]],[360,-360,0,0,12,0,0,12,0,0,0,0,9*E(3)^2,-9*E(3)^2,9*E(3),
-9*E(3),0,0,0,0,0,0,0,-2,-2,0,2,0,0,0,0,0,0,0,0,-3*E(3)^2,-3*E(3)^2,-3*E(3),
-3*E(3),0,0,0,0,0,0,0,0,0,0,0,0,0,0,E(3)^2,E(3)^2,-E(3),E(3)],
[GALOIS,[37,2]],[432,432,-48,80,0,0,0,0,0,0,0,0,0,0,0,0,-18,-18,2,-6,0,0,0,0,
0,0,0,0,0,0,2,2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[480,-480,
0,0,16,0,0,-16,0,0,0,0,-6,6,-6,6,12,-12,0,0,-6,6,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,
-2,-2,-2,-2,0,-2,0,-2,-2,0,2,0,0,0,0,0,0,0,0,0,0],[512,-512,0,0,0,0,0,0,0,0,0,
0,8,-8,8,-8,-16,16,0,0,-4,4,0,0,0,0,0,0,0,0,2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,-1,1,-1,1,0,0,0,0],[540,540,-60,100,0,0,0,0,0,0,0,0,0,0,0,0,18,18,-2,6,
0,0,0,-6,6,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[
576,576,64,-64,0,0,0,0,0,0,0,0,0,0,0,0,-12,-12,-4,4,-6,-6,-2,0,0,0,0,0,0,0,1,
1,-1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[648,-648,0,0,-36,0,0,
12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,6,6,0,-2,0,0,0,-2,2,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0],[720,720,80,-80,0,0,0,0,0,0,0,0,0,0,0,0,12,12,4,-4,
6,6,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0]],]);
ALF("2^1+6.u4q2","Suz",[1,2,7,2,2,8,9,7,9,8,3,19,5,14,5,15,4,13,13,27,5,
16,28,7,8,20,20,10,21,19,11,24,40,24,24,15,16,14,16,13,29,13,29,15,14,31,
27,29,43,23,39,22,38,31,28,31,28],[
"fusion determined using U5(2) and U5(2)M1,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("2^1+6.u4q2","2^(1+6)_-.U4(2).2",[1,2,4,3,5,6,7,10,9,11,8,12,13,14,13,
14,15,16,17,18,19,20,21,23,22,24,28,25,27,26,29,30,32,31,31,33,34,33,34,
35,36,35,36,37,37,38,39,40,41,42,43,42,43,45,44,45,44],[
"fusion map is unique"
]);
ALF("2^1+6.u4q2","U4(2)",[1,1,1,1,2,2,2,3,3,3,3,3,4,4,5,5,6,6,6,6,7,7,7,8,
8,8,9,9,9,9,10,10,10,10,10,11,11,12,12,14,14,13,13,15,15,15,16,16,16,18,
18,17,17,19,19,20,20]);
ALN("2^1+6.u4q2",["SuzC2A","SuzN2A"]);

MOT("2.SuzM4",
[
"table of the 4th maximal subgroup of 2.Suz, structure 2.2^(1+6).U4(2),\n",
"constructed by Thomas Breuer 1997/03/17 using the tables of Suz, 2.Suz,\n",
"and SuzM4\n"
],
[6635520,6635520,6635520,6635520,92160,92160,122880,122880,18432,18432,3072,
768,3072,3072,1536,512,512,192,2592,2592,2592,2592,2592,2592,2592,2592,6912,
6912,6912,6912,384,384,576,576,864,864,864,864,144,144,768,768,768,768,128,
128,64,64,32,32,32,80,80,80,80,40,40,40,40,40,40,288,288,288,288,288,288,288,
288,288,288,48,288,288,48,288,288,288,288,48,48,96,96,48,48,48,36,36,36,36,36,
36,36,36,48,48,48,48,48,48,48,48],
[,[1,1,1,1,3,3,1,1,1,1,3,8,7,7,4,7,2,5,23,23,23,23,19,19,19,19,27,27,27,27,27,
27,29,29,35,35,35,35,37,37,9,9,9,9,11,11,16,16,17,15,13,52,52,52,52,54,54,52,
52,52,52,23,23,23,23,19,19,19,19,27,27,32,27,27,32,35,35,35,35,37,37,31,31,30,
33,33,91,91,91,91,87,87,87,87,68,68,68,68,64,64,64,64],[1,2,3,4,5,6,7,8,9,10,
11,12,13,14,15,16,17,18,1,2,3,4,1,2,3,4,1,2,3,4,7,8,5,6,1,2,3,4,5,6,41,42,43,
44,45,46,47,48,49,50,51,52,53,54,55,56,57,60,61,58,59,9,10,9,10,9,10,9,10,9,
10,12,9,10,12,9,10,9,10,11,11,13,14,15,18,18,23,24,25,26,19,20,21,22,43,44,41,
42,44,43,41,42],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,23,24,25,26,19,
20,21,22,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,
50,51,1,2,3,4,5,6,7,8,7,8,66,67,68,69,62,63,64,65,73,74,75,70,71,72,78,79,76,
77,81,80,82,83,84,86,85,91,92,93,94,87,88,89,90,100,99,101,102,96,95,97,98]],
0,
[(85,86),(58,60)(59,61),( 19, 23)( 20, 24)( 21, 25)( 22, 26)( 62, 66)( 63, 67)
( 64, 68)( 65, 69)( 70, 73)( 71, 74)( 72, 75)( 76, 78)( 77, 79)( 80, 81)
( 87, 91)( 88, 92)( 89, 93)( 90, 94)( 95,100)( 96, 99)( 97,101)( 98,102)],
["ConstructProj",[["2^1+6.u4q2",[]],["2.SuzM4",[]]]]);
ALF("2.SuzM4","2.Suz",[1,2,3,4,12,13,3,4,3,4,14,15,12,13,15,14,5,32,8,9,
23,24,8,9,25,26,6,7,21,22,21,22,45,46,8,9,27,28,47,48,12,13,14,14,33,34,
33,34,16,35,32,17,18,40,41,69,70,40,41,40,41,25,26,27,28,23,24,27,28,21,
22,49,21,22,49,25,26,23,24,52,53,45,46,49,75,76,38,39,67,68,36,37,65,66,
52,53,47,48,52,53,47,48],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("2.SuzM4","2^1+6.u4q2",[1,1,2,2,3,3,4,4,5,5,6,7,8,8,9,10,11,12,
13,13,14,14,15,15,16,16,17,17,18,18,19,19,20,20,21,21,22,22,23,23,24,24,
25,25,26,26,27,27,28,29,30,31,31,32,32,33,33,34,34,35,35,36,36,37,37,38,
38,39,39,40,40,41,42,42,43,44,44,45,45,46,46,47,47,48,49,49,50,50,51,51,
52,52,53,53,54,54,55,55,56,56,57,57]);
ALF("2.SuzM4","U4(2)",[1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,4,4,4,4,5,5,5,
5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,9,9,9,9,10,10,10,10,10,10,10,
10,10,10,11,11,11,11,12,12,12,12,14,14,14,13,13,13,15,15,15,15,15,15,16,
16,16,16,16,18,18,18,18,17,17,17,17,19,19,19,19,20,20,20,20]);

MOT("2^1+8.a9",
[
"origin: CAS library,\n",
"maximal subgroup of Th,\n",
"Received from Bielefeld 18.1.1989\n",
"Test: 1.OR, JAMES, JAMES,n=3,\n",
"and restricted characters decompose properly.\n",
"tests: 1.o.r., pow[2,3,5,7]"
],
[92897280,92897280,344064,387072,7680,512,3072,3072,512,384,2160,2160,648,648,
108,1728,1728,288,288,96,96,32,64,64,32,120,120,24,48,48,24,24,24,56,56,28,28,
28,72,72,36,36,36,18,18,20,24,24,30,30,30,30],
[,[1,1,1,2,2,3,3,1,3,4,11,11,14,14,13,16,16,17,17,16,5,6,7,8,9,26,26,12,20,20,
16,19,18,34,34,34,34,35,40,40,39,39,39,44,44,27,28,28,49,49,51,51],[1,2,3,4,5,
6,7,8,9,10,1,2,2,1,4,1,2,4,4,3,21,22,23,24,25,26,27,5,7,7,8,10,10,34,35,37,36,
38,13,14,15,15,15,14,13,46,21,21,26,27,26,27],,[1,2,3,4,5,6,7,8,9,10,11,12,13,
14,15,16,17,19,18,20,21,22,23,24,25,1,2,28,30,29,31,33,32,34,35,37,36,38,39,
40,41,43,42,44,45,5,47,48,11,12,11,12],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,
16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,1,2,3,3,4,39,40,41,42,
43,44,45,46,47,48,51,52,49,50],,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,
19,18,20,21,22,23,24,25,26,27,28,30,29,31,33,32,34,35,36,37,38,39,40,41,43,42,
44,45,46,47,48,51,52,49,50],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,
20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,37,36,38,39,40,41,42,43,44,45,
46,48,47,51,52,49,50],,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,18,20,
21,22,23,24,25,26,27,28,30,29,31,33,32,34,35,37,36,38,39,40,41,43,42,44,45,46,
48,47,49,50,51,52],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,
23,24,25,26,27,28,29,30,31,32,33,34,35,37,36,38,39,40,41,42,43,44,45,46,48,47,
49,50,51,52],,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,18,20,21,22,23,
24,25,26,27,28,30,29,31,33,32,34,35,36,37,38,39,40,41,43,42,44,45,46,48,47,49,
50,51,52],,,,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,18,20,21,22,23,
24,25,26,27,28,30,29,31,33,32,34,35,36,37,38,39,40,41,43,42,44,45,46,47,48,51,
52,49,50],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,
26,27,28,29,30,31,32,33,34,35,37,36,38,39,40,41,42,43,44,45,46,47,48,49,50,51,
52]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1],[8,8,8,8,4,4,0,0,0,0,5,5,-1,-1,-1,2,2,2,2,2,2,2,
0,0,0,3,3,1,0,0,0,0,0,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,0,0,0,0],[21,21,
21,21,1,1,-3,-3,-3,-3,-3,-3,3,3,3,0,0,0,0,0,-1,-1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,1,-1,-1,-E(15)^7-E(15)^11-E(15)^13-E(15)^14,
-E(15)^7-E(15)^11-E(15)^13-E(15)^14,-E(15)-E(15)^2-E(15)^4-E(15)^8,
-E(15)-E(15)^2-E(15)^4-E(15)^8],
[GALOIS,[3,7]],[27,27,27,27,7,7,3,3,3,3,9,9,0,0,0,0,0,0,0,0,1,1,-1,-1,-1,2,2,
1,0,0,0,0,0,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,2,1,1,-1,-1,-1,-1],[28,28,28,28,4,4,
-4,-4,-4,-4,10,10,1,1,1,1,1,1,1,1,0,0,0,0,0,3,3,-2,-1,-1,-1,-1,-1,0,0,0,0,0,1,
1,1,1,1,1,1,-1,0,0,0,0,0,0],[35,35,35,35,-5,-5,3,3,3,3,5,5,-1,-1,-1,2,2,2,2,2,
-1,-1,-1,-1,-1,0,0,1,0,0,0,0,0,0,0,0,0,0,2,2,2,2,2,-1,-1,0,-1,-1,0,0,0,0],[35,
35,35,35,-5,-5,3,3,3,3,5,5,-1,-1,-1,2,2,2,2,2,-1,-1,-1,-1,-1,0,0,1,0,0,0,0,0,
0,0,0,0,0,-1,-1,-1,-1,-1,2,2,0,-1,-1,0,0,0,0],[42,42,42,42,6,6,2,2,2,2,0,0,-3,
-3,-3,3,3,3,3,3,0,0,2,2,2,-3,-3,0,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,
0,0,0,0,0],[48,48,48,48,8,8,0,0,0,0,6,6,3,3,3,0,0,0,0,0,0,0,0,0,0,-2,-2,2,0,0,
0,0,0,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,-2,0,0,1,1,1,1],[56,56,56,56,-4,-4,0,0,0,0,
11,11,2,2,2,2,2,2,2,2,-2,-2,0,0,0,1,1,-1,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,
-1,-1,1,1,1,1,1,1,1],[84,84,84,84,4,4,4,4,4,4,-6,-6,3,3,3,3,3,3,3,3,0,0,0,0,0,
-1,-1,-2,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,-1,-1,-1,-1],[105,105,105,
105,5,5,1,1,1,1,15,15,-3,-3,-3,-3,-3,-3,-3,-3,-1,-1,1,1,1,0,0,-1,1,1,1,1,1,0,
0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,0,0,0,0],[120,120,120,120,0,0,8,8,8,8,0,0,3,3,3,
-3,-3,-3,-3,-3,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,
0,0,0],[162,162,162,162,6,6,-6,-6,-6,-6,0,0,0,0,0,0,0,0,0,0,0,0,-2,-2,-2,-3,
-3,0,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0],[168,168,168,168,4,4,0,
0,0,0,-15,-15,-3,-3,-3,0,0,0,0,0,-2,-2,0,0,0,3,3,1,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,-1,1,1,0,0,0,0],[189,189,189,189,-11,-11,-3,-3,-3,-3,9,9,0,0,0,0,0,0,
0,0,1,1,1,1,1,-1,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,1,-1,-1,-1,-1],[
216,216,216,216,-4,-4,0,0,0,0,-9,-9,0,0,0,0,0,0,0,0,2,2,0,0,0,1,1,-1,0,0,0,0,
0,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,1,-1,-1,1,1,1,1],[128,-128,0,0,0,0,0,0,0,0,-4,
4,-2,2,0,8,-8,0,0,0,0,0,0,0,0,-2,2,0,0,0,0,0,0,2,-2,0,0,0,4,-4,0,0,0,-1,1,0,0,
0,1,-1,1,-1],[128,-128,0,0,0,0,0,0,0,0,-4,4,-2,2,0,8,-8,0,0,0,0,0,0,0,0,-2,2,
0,0,0,0,0,0,2,-2,0,0,0,-2,2,0,0,0,2,-2,0,0,0,1,-1,1,-1],[120,120,-8,8,0,0,8,
-8,0,0,0,0,3,3,-1,6,6,2,2,-2,0,0,0,0,0,0,0,0,2,2,-2,0,0,1,1,-1,-1,1,3,3,-1,-1,
-1,0,0,0,0,0,0,0,0,0],[896,-896,0,0,0,0,0,0,0,0,-16,16,4,-4,0,8,-8,0,0,0,0,0,
0,0,0,-4,4,0,0,0,0,0,0,0,0,0,0,0,-2,2,0,0,0,-1,1,0,0,0,-1,1,-1,1],[960,960,
-64,64,0,0,0,0,0,0,0,0,-3,-3,1,12,12,4,4,-4,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,-1,
-1,1,-3,-3,1,1,1,0,0,0,0,0,0,0,0,0],[2688,-2688,0,0,0,0,0,0,0,0,12,-12,-6,6,0,
0,0,0,0,0,0,0,0,0,0,-2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
-E(15)^7-E(15)^11-E(15)^13-E(15)^14,E(15)^7+E(15)^11+E(15)^13+E(15)^14,
-E(15)-E(15)^2-E(15)^4-E(15)^8,E(15)+E(15)^2+E(15)^4+E(15)^8],[2520,2520,-168,
168,0,0,-24,24,0,0,0,0,9,9,-3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[24,7]],[2560,-2560,0,0,0,0,0,0,0,0,-20,20,-4,4,0,-8,8,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,-2,2,0,0,0,2,-2,0,0,0,1,-1,0,0,0,0,0,0,0],[3240,3240,-216,
216,0,0,24,-24,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,1,1,-1,
0,0,0,0,0,0,0,0,0,0,0,0,0,0],[840,840,-56,56,0,0,-8,8,0,0,0,0,-6,-6,2,6,6,2,2,
-2,0,0,0,0,0,0,0,0,-2,-2,2,0,0,0,0,0,0,0,3,3,-1,-1,-1,0,0,0,0,0,0,0,0,0],[
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1,-1,1,-1],[135,135,7,-9,15,-1,7,7,-1,-1,0,0,0,0,0,9,9,-3,-3,1,3,-1,3,-1,-1,0,
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0,0,0,0],[1890,1890,98,-126,30,-2,10,10,-6,2,0,0,0,0,0,-9,-9,3,3,-1,0,0,-2,-2,
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ARC("2^1+8.a9","projectives",["2^1+8.2.A9",[[8,8,8,8,0,0,0,0,0,0,-4,-4,-1,-1,
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0,0,0,0,0],
[GALOIS,[25,2]],[3240,3240,168,-216,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
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0],[768,-768,0,0,32,0,0,0,0,0,6,-6,6,-6,0,0,0,0,0,0,0,0,0,0,0,-2,2,2,0,0,0,0,0
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4,-4,0,8,-8,0,0,0,-4,0,0,0,0,1,-1,-1,0,0,0,0,0,0,0,0,0,0,-2,2,0,0,0,-1,1,-1,1,
-1,1,-1,1,-1],[1344,-1344,0,0,16,0,16,0,0,0,-6,6,6,-6,0,12,-12,0,0,0,0,0,0,0,0
,-1,1,-2,2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,-1,1,-1,1],[1680,-1680,0,0,
20,0,4,0,0,0,15,-15,-6,6,0,-12,12,0,0,0,-2,0,2,0,0,0,0,-1,2,-2,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,-1,1,0,0,0,0],[1920,-1920,0,0,0,0,32,0,0,0,0,0,6,-6,0,-12,12,
0,0,0,0,0,0,0,0,0,0,0,-2,2,0,0,0,2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[2592
,-2592,0,0,24,0,-24,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-4,0,0,-3,3,0,0,0,0,0,0,2,-2
,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0],[2688,-2688,0,0,16,0,0,0,0,0,-15,15,-6,6,
0,0,0,0,0,0,-4,0,0,0,0,3,-3,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,-1,0,0,0,0
],[3024,-3024,0,0,-44,0,-12,0,0,0,9,-9,0,0,0,0,0,0,0,0,2,0,2,0,0,-1,1,1,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,-1,-1,1,-1,1],[3456,-3456,0,0,-16,0,0,0,0,0,-9
,9,0,0,0,0,0,0,0,0,4,0,0,0,0,1,-1,-1,0,0,0,0,0,-2,2,0,0,0,0,0,0,0,0,0,0,-1,-1,
1,1,-1,1,-1]],]);
ALF("2^1+8.a9","A9",[1,1,1,1,2,2,3,3,3,3,4,4,5,5,5,6,6,6,6,6,7,7,8,8,8,9,
9,10,11,11,11,11,11,12,12,12,12,12,13,13,13,13,13,14,14,15,16,16,17,17,18,
18],[
"factor fusion equal to that on the CAS table"
]);
ALF("2^1+8.a9","Th",[1,2,2,6,7,7,6,2,7,13,5,9,11,4,21,3,10,19,20,10,14,14,
13,7,14,8,18,22,19,20,10,33,32,12,24,24,24,39,27,15,44,45,46,17,28,30,34,
35,25,40,26,41],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALN("2^1+8.a9",["ThC2A","ThN2A"]);

MOT("2^1+8.2.A9",
[
"a double cover of the maximal subgroup 2^1+8.A9 of the Thompson group,\n",
"computed by Simon Norton, Dec. 2000"
],
[185794560,185794560,185794560,185794560,688128,688128,774144,774144,15360,
15360,512,6144,6144,3072,512,768,768,4320,4320,4320,4320,1296,1296,1296,1296,
216,216,3456,3456,3456,3456,576,576,576,576,192,192,192,192,32,128,128,64,32,
240,240,240,240,48,48,96,96,96,96,48,48,48,48,48,48,112,112,112,112,56,56,56,
56,56,56,144,144,144,144,72,72,72,72,72,72,36,36,36,36,40,40,48,48,48,48,60,60
,60,60,60,60,60,60],
[,[1,1,1,1,1,1,3,3,4,4,6,5,5,1,5,7,7,18,18,18,18,24,24,24,24,22,22,28,28,28,28
,30,30,30,30,28,28,9,9,11,12,12,14,15,45,45,45,45,21,21,36,36,36,36,28,28,34,
34,32,32,61,61,61,61,61,61,61,61,63,63,73,73,73,73,71,71,71,71,71,71,81,81,81,
81,48,48,49,49,49,49,91,91,91,91,95,95,95,95],[1,2,3,4,5,6,7,8,9,10,11,12,13,
14,15,16,17,1,2,3,4,3,4,1,2,7,8,1,2,3,4,7,8,7,8,5,6,38,39,40,41,42,43,44,45,46
,47,48,9,10,13,12,12,13,14,14,16,17,16,17,61,62,63,64,67,68,65,66,69,70,22,23,
24,25,26,27,26,27,26,27,24,25,22,23,85,86,39,38,38,39,45,46,47,48,45,46,47,48]
,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,
29,30,31,34,35,32,33,36,37,38,39,40,41,42,43,44,1,2,3,4,49,50,54,53,52,51,56,
55,59,60,57,58,61,62,63,64,67,68,65,66,69,70,71,72,73,74,75,76,79,80,77,78,81,
82,83,84,9,10,87,88,89,90,18,19,20,21,18,19,20,21],,[1,2,3,4,5,6,7,8,9,10,11,
12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,
38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,1,2,3,4,5
,6,5,6,7,8,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,95,96,
97,98,91,92,93,94]],
0,
[(32,34)(33,35)(51,54)(52,53)(55,56)(57,59)(58,60)(77,79)(78,80),
(65,67)(66,68),(87,90)(88,89),(91,95)(92,96)(93,97)(94,98)],
["ConstructProj",[["2^1+8.a9",[]],["2^1+8.2.A9",[]]]]);
ALF("2^1+8.2.A9","2.A9",[1,2,1,2,1,2,1,2,3,3,3,4,4,4,4,4,4,5,6,5,6,7,8,7,8,
7,8,9,10,9,10,9,10,9,10,9,10,11,11,11,12,12,12,12,13,14,13,14,15,15,16,17,
16,17,16,17,16,17,17,16,18,19,18,19,18,19,18,19,18,19,20,21,20,21,20,21,
20,21,20,21,22,23,22,23,24,24,25,26,25,26,27,28,27,28,29,30,29,30]);
ALF("2^1+8.2.A9","2^1+8.a9",[1,1,2,2,3,3,4,4,5,5,6,7,7,8,9,10,10,11,11,12,
12,13,13,14,14,15,15,16,16,17,17,18,18,19,19,20,20,21,21,22,23,23,24,25,
26,26,27,27,28,28,29,29,30,30,31,31,32,32,33,33,34,34,35,35,36,36,37,37,
38,38,39,39,40,40,41,41,42,42,43,43,44,44,45,45,46,46,47,47,48,48,49,49,
50,50,51,51,52,52]);
ALF("2^1+8.2.A9","A9",[1,1,1,1,1,1,1,1,2,2,2,3,3,3,3,3,3,4,4,4,4,5,5,5,5,
5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,8,8,8,8,9,9,9,9,10,10,11,11,11,11,11,11,11,
11,11,11,12,12,12,12,12,12,12,12,12,12,13,13,13,13,13,13,13,13,13,13,14,
14,14,14,15,15,16,16,16,16,17,17,17,17,18,18,18,18]);

MOT("2^2+8(a5xs3)",
[
"origin: CAS library,\n",
"9th maximal subgroup of Suz,\n",
"test: 1.OR, JAMES, JAMES,n=3,\n",
"and restricted characters decompose properly,\n",
"tests: 1.o.r., pow[2,3,5]"
],
[368640,122880,6144,1536,3072,1536,1024,384,256,256,64,64,1152,384,96,96,96,
48,120,40,120,40,180,12,36,12,15,15,3840,3840,384,192,256,256,128,64,64,64,32,
32,48,48,24,24,24,20,20,20,20],
[,[1,1,1,1,2,2,2,1,3,3,5,7,13,13,13,13,14,14,21,21,19,19,23,23,25,25,28,27,1,
2,3,5,1,2,3,5,7,7,6,4,13,14,16,15,17,21,22,19,20],[1,2,3,4,5,6,7,8,9,10,11,12,
1,2,3,3,5,6,21,22,19,20,1,8,1,4,21,19,29,30,31,32,33,34,35,36,37,38,39,40,29,
30,31,31,32,48,49,46,47],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,16,15,17,18,1,2,1,
2,23,24,25,26,23,23,29,30,31,32,33,34,35,36,37,38,39,40,41,42,44,43,45,29,30,
29,30]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1],[3,3,3,3,3,3,3,-1,-1,-1,-1,-1,0,0,0,0,0,0,
-E(5)^2-E(5)^3,-E(5)^2-E(5)^3,-E(5)-E(5)^4,-E(5)-E(5)^4,3,-1,0,0,
-E(5)^2-E(5)^3,-E(5)-E(5)^4,3,3,3,3,-1,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,
-E(5)^2-E(5)^3,-E(5)^2-E(5)^3,-E(5)-E(5)^4,-E(5)-E(5)^4],
[GALOIS,[2,2]],[4,4,4,4,4,4,4,0,0,0,0,0,1,1,1,1,1,1,-1,-1,-1,-1,4,0,1,1,-1,-1,
4,4,4,4,0,0,0,0,0,0,0,0,1,1,1,1,1,-1,-1,-1,-1],[5,5,5,5,5,5,5,1,1,1,1,1,-1,-1,
-1,-1,-1,-1,0,0,0,0,5,1,-1,-1,0,0,5,5,5,5,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,0,0,
0,0],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],
[TENSOR,[2,6]],
[TENSOR,[3,6]],
[TENSOR,[4,6]],
[TENSOR,[5,6]],[2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,-1,-1,-1,-1,-1,-1,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[6,6,6,6,6,6,6,-2,-2,-2,-2,-2,0,0,
0,0,0,0,-2*E(5)^2-2*E(5)^3,-2*E(5)^2-2*E(5)^3,-2*E(5)-2*E(5)^4,
-2*E(5)-2*E(5)^4,-3,1,0,0,E(5)^2+E(5)^3,E(5)+E(5)^4,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0],
[GALOIS,[12,2]],[8,8,8,8,8,8,8,0,0,0,0,0,2,2,2,2,2,2,-2,-2,-2,-2,-4,0,-1,-1,1,
1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[10,10,10,10,10,10,10,2,2,2,2,2,
-2,-2,-2,-2,-2,-2,0,0,0,0,-5,-1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0],[15,15,-1,3,7,-5,-1,3,3,3,-1,-1,6,6,2,2,-2,-2,0,0,0,0,0,0,0,0,0,0,5,5,-3,
1,1,1,1,1,1,1,-1,-1,2,2,0,0,-2,0,0,0,0],[15,15,-1,3,7,-5,-1,3,3,3,-1,-1,-3,-3,
3*E(3)-E(3)^2,-E(3)+3*E(3)^2,1,1,0,0,0,0,0,0,0,0,0,0,5,5,-3,1,1,1,1,1,1,1,-1,
-1,-1,-1,E(3)-E(3)^2,-E(3)+E(3)^2,1,0,0,0,0],
[GALOIS,[17,2]],[45,45,-3,9,21,-15,-3,-3,-3,-3,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,15,15,-9,3,-1,-1,-1,-1,-1,-1,1,1,0,0,0,0,0,0,0,0,0],
[TENSOR,[16,6]],
[TENSOR,[17,6]],
[TENSOR,[18,6]],
[TENSOR,[19,6]],[30,30,14,-6,6,2,-2,6,-2,-2,2,-2,3,3,-1,-1,3,-1,0,0,0,0,0,0,0,
0,0,0,10,10,2,-2,2,2,2,2,-2,-2,0,0,1,1,-1,-1,1,0,0,0,0],[30,30,14,-6,6,2,-2,
-6,2,2,-2,2,3,3,-1,-1,3,-1,0,0,0,0,0,0,0,0,0,0,10,10,2,-2,-2,-2,-2,-2,2,2,0,0,
1,1,-1,-1,1,0,0,0,0],[60,60,28,-12,12,4,-4,0,0,0,0,0,-3,-3,1,1,-3,1,0,0,0,0,0,
0,0,0,0,0,20,20,4,-4,0,0,0,0,0,0,0,0,-1,-1,1,1,-1,0,0,0,0],
[TENSOR,[24,6]],
[TENSOR,[25,6]],
[TENSOR,[26,6]],[60,60,12,8,-12,0,-4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,3,-1,0,
0,0,0,0,0,4,4,-4,0,0,0,2,-2,0,0,0,0,0,0,0,0,0],
[TENSOR,[30,6]],[120,120,24,16,-24,0,-8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-3,
1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[60,60,-20,0,4,8,-4,0,0,0,0,
0,6,6,-2,-2,-2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,4,4,-4,0,0,0,-2,2,0,0,0,0,0,0,0,
0,0],
[TENSOR,[33,6]],[120,120,-40,0,8,16,-8,0,0,0,0,0,-6,-6,2,2,2,-2,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[90,90,-6,-6,-6,-6,10,6,-2,
-2,-2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,4,4,4,-4,0,0,0,0,0,0,0,0,0,0,
0,0,0],[90,90,-6,-6,-6,-6,10,-6,2,2,2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,4,-4,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[36,6]],
[TENSOR,[37,6]],[48,-16,0,0,0,0,0,0,4,-4,0,0,12,-4,0,0,0,0,3,-1,3,-1,0,0,0,0,
0,0,4,-4,0,0,-4,4,0,0,0,0,0,0,-2,2,0,0,0,-1,1,-1,1],[144,-48,0,0,0,0,0,0,-4,4,
0,0,0,0,0,0,0,0,-3*E(5)^2-3*E(5)^3,E(5)^2+E(5)^3,-3*E(5)-3*E(5)^4,E(5)+E(5)^4,
0,0,0,0,0,0,12,-12,0,0,4,-4,0,0,0,0,0,0,0,0,0,0,0,E(5)^2+E(5)^3,
-E(5)^2-E(5)^3,E(5)+E(5)^4,-E(5)-E(5)^4],
[GALOIS,[41,2]],[192,-64,0,0,0,0,0,0,0,0,0,0,12,-4,0,0,0,0,-3,1,-3,1,0,0,0,0,
0,0,16,-16,0,0,0,0,0,0,0,0,0,0,-2,2,0,0,0,1,-1,1,-1],[240,-80,0,0,0,0,0,0,4,
-4,0,0,-12,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,20,-20,0,0,-4,4,0,0,0,0,0,0,2,-2,0,0,
0,0,0,0,0],
[TENSOR,[40,6]],
[TENSOR,[41,6]],
[TENSOR,[42,6]],
[TENSOR,[43,6]],
[TENSOR,[44,6]]],
[(37,38),(19,21)(20,22)(27,28)(46,48)(47,49),(15,16)(43,44)]);
ARC("2^2+8(a5xs3)","projectives",["2.SuzM9",[[12,-4,4,0,4,0,0,0,-4,0,0,-2,-6,2
,2,2,2,0,-3,1,-3,1,0,0,0,0,0,0,-4,-4,0,0,0,0,0,0,-2,2,0,0,-2,2,0,0,0,1,1,1,1],
[32,32,0,0,0,0,0,0,0,0,0,0,-4,-4,0,0,0,0,E(5)^2+E(5)^3,E(5)^2+E(5)^3,
E(5)+E(5)^4,E(5)+E(5)^4,2,0,2,0,E(5)^2+E(5)^3,E(5)+E(5)^4,-8,8,0,0,0,0,0,0,0,0
,0,0,2,2,0,0,0,E(5)^2+E(5)^3,-E(5)^2-E(5)^3,E(5)+E(5)^4,-E(5)-E(5)^4],
[GALOIS,[2,2]],[36,-12,12,0,12,0,0,0,4,0,0,2,0,0,0,0,0,0,3*E(5)^2+3*E(5)^3,
-E(5)^2-E(5)^3,3*E(5)+3*E(5)^4,-E(5)-E(5)^4,0,0,0,0,0,0,-12,-12,0,0,0,0,0,0,2,
-2,0,0,0,0,0,0,0,-E(5)^2-E(5)^3,-E(5)^2-E(5)^3,-E(5)-E(5)^4,-E(5)-E(5)^4],
[GALOIS,[4,2]],[48,-16,16,0,16,0,0,0,0,0,0,0,-6,2,2,2,2,0,3,-1,3,-1,0,0,0,0,0
,0,-16,-16,0,0,0,0,0,0,0,0,0,0,-2,2,0,0,0,-1,-1,-1,-1],[60,-20,20,0,20,0,0,0,
-4,0,0,-2,6,-2,-2,-2,-2,0,0,0,0,0,0,0,0,0,0,0,-20,-20,0,0,0,0,0,0,-2,2,0,0,2,
-2,0,0,0,0,0,0,0],[60,-20,-12,0,4,0,0,0,-4,0,0,2,-12,4,0,0,-4,0,0,0,0,0,0,0,0,
0,0,0,0,0,-4,0,0,0,0,0,-2,-2,0,0,0,0,-2,-2,0,0,0,0,0],[60,-20,-12,0,4,0,0,0,-4
,0,0,2,6,-2,-2*E(3)+2*E(3)^2,2*E(3)-2*E(3)^2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,-4,0,
0,0,0,0,-2,-2,0,0,0,0,-2*E(3)^2,-2*E(3),0,0,0,0,0],
[GALOIS,[9,2]],[64,64,0,0,0,0,0,0,0,0,0,0,4,4,0,0,0,0,-1,-1,-1,-1,4,0,-2,0,-1
,-1,-16,16,0,0,0,0,0,0,0,0,0,0,-2,-2,0,0,0,-1,1,-1,1],[64,64,0,0,0,0,0,0,0,0,0
,0,-8,-8,0,0,0,0,2*E(5)^2+2*E(5)^3,2*E(5)^2+2*E(5)^3,2*E(5)+2*E(5)^4,
2*E(5)+2*E(5)^4,-2,0,-2,0,-E(5)^2-E(5)^3,-E(5)-E(5)^4,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0],
[GALOIS,[12,2]],[96,96,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,6,0,0,0,1,1,
-24,24,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1,1,-1],[128,128,0,0,0,0,0,0,0,0,0,0,8
,8,0,0,0,0,-2,-2,-2,-2,-4,0,2,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
,[180,-60,-36,0,12,0,0,0,4,0,0,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,12,0,0,0
,0,0,-2,-2,0,0,0,0,0,0,0,0,0,0,0],[192,192,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,2
,2,2,-6,0,0,0,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[240,-80,16,0,
-16,0,0,0,0,0,0,0,-12,4,-4,-4,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0],[240,-80,16,0,-16,0,0,0,0,0,0,0,6,-2,2,2,-2,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2*E(12)^7+2*E(12)^11,0,0,0,0]],]);
ALF("2^2+8(a5xs3)","Suz",[1,2,2,3,7,9,8,3,7,8,19,20,4,13,13,13,27,29,11,
24,11,24,6,17,6,17,35,36,2,7,9,19,3,9,8,19,20,20,21,10,13,27,29,29,43,24,
40,24,40],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("2^2+8(a5xs3)","2^(2+8):(S5xS3)",[1,2,3,4,5,6,7,8,11,10,15,16,9,13,14,
14,18,19,12,17,12,17,20,22,21,23,24,24,25,27,28,33,26,29,30,34,36,36,35,
31,32,38,39,39,41,37,40,37,40],[
"fusion map is unique"
]);


MOT("2.SuzM9",
[
"9th maximal subgroup of 2.Suz,\n",
"origin: Dixon's Algorithm"
],
[737280,737280,245760,245760,12288,12288,1536,6144,6144,1536,1024,384,512,512,
256,64,128,128,2304,2304,768,768,192,192,192,192,192,192,48,240,240,80,80,240,
240,80,80,360,360,12,72,72,12,30,30,30,30,7680,7680,7680,7680,768,768,192,256,
256,128,64,128,128,128,128,32,32,96,96,96,96,48,48,48,48,48,48,40,40,40,40,40,
40,40,40],
[,[1,1,1,1,1,1,2,3,3,4,3,2,6,6,6,9,11,11,19,19,19,19,19,19,19,19,21,21,22,34,
34,34,34,30,30,30,30,38,38,39,41,41,42,46,46,44,44,1,1,3,3,5,5,9,2,4,6,9,11,11
,11,11,10,7,19,19,21,21,26,26,24,24,27,27,34,34,36,36,30,30,32,32],[1,2,3,4,5,
6,7,8,9,10,11,12,13,14,15,16,17,18,1,2,3,4,6,5,6,5,9,8,10,34,35,36,37,30,31,32
,33,1,2,12,1,2,7,34,35,30,31,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,
64,49,48,50,51,53,52,53,52,54,54,79,80,81,82,75,76,77,78],,[1,2,3,4,5,6,7,8,9,
10,11,12,13,14,15,16,17,18,19,20,21,22,25,26,23,24,27,28,29,1,2,3,4,1,2,3,4,38
,39,40,41,42,43,38,39,38,39,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64
,65,66,67,68,71,72,69,70,74,73,48,49,50,51,48,49,50,51]],
0,
[(23,25)(24,26)(69,71)(70,72),(52,53)(59,62)(60,61)(69,70)(71,72),(73,74),
(48,49)(50,51)(59,61)(60,62)(65,66)(67,68)(75,76)(77,78)(79,80)(81,82),
(30,34)(31,35)(32,36)(33,37)(44,46)(45,47)(75,79)(76,80)(77,81)(78,82)],
["ConstructProj",[["2^2+8(a5xs3)",[]],["2.SuzM9",[]]]]);
ALF("2.SuzM9","2.Suz",[1,2,3,4,4,3,5,13,12,15,14,5,12,13,14,32,34,33,6,7,
21,22,21,22,21,22,45,46,49,17,18,40,41,17,18,40,41,10,11,29,10,11,29,59,
60,61,62,3,4,12,13,15,15,32,5,15,14,32,34,33,33,34,35,16,22,21,45,46,49,
49,49,49,75,76,40,41,69,70,40,41,69,70],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("2.SuzM9","2^2+8(a5xs3)",[1,1,2,2,3,3,4,5,5,6,7,8,9,9,10,11,12,12,13,13,
14,14,15,15,16,16,17,17,18,19,19,20,20,21,21,22,22,23,23,24,25,25,26,27,27,28,
28,29,29,30,30,31,31,32,33,34,35,36,37,37,38,38,39,40,41,41,42,42,43,43,44,44,
45,45,46,46,47,47,48,48,49,49]);

MOT("(2xL3(3)).2",
[
"14th maximal subgroup of 2.Suz"
],
0,
0,
0,
[(15,17)(16,18),(19,20)(21,22)(23,24)(25,26)(27,28)(29,30),(27,29)(28,30)],
["ConstructIsoclinic",[["L3(3).2"],["Cyclic",2]]]);
ALF("(2xL3(3)).2","2.Suz",[1,2,4,3,8,9,10,11,15,15,28,27,35,35,54,55,56,
57,5,5,14,14,29,29,35,35,52,53,53,52],[
"unique up to table autom., compatible with fusion of factors"
]);
ALF("(2xL3(3)).2","L3(3).2",[1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,9,10,10,
11,11,12,12,13,13,14,14,15,15]);
ALF("(2xL3(3)).2","C4",[1,3,1,3,1,3,1,3,1,3,1,3,1,3,1,3,1,3,2,4,2,4,2,4,2,
4,2,4,2,4]);

MOT("2^2.psl(3,4).s3",
[
"origin: CAS library,\n",
"maximal subgroup of He,\n",
"test: 1.OR, JAMES, JAMES,n=3,\n",
"and restricted characters decompose properly.\n",
"tests: 1.o.r., pow[2,3,5,7]"
],
0,
0,
0,
0,
["ConstructPermuted",["2^2.L3(4).3.2_2"],(20,21)(24,25),(7,15,17,19,12,9)(8,
16,18,11,13,10)(21,23)(22,24)(25,27,26)(32,33)]);
ARC("2^2.psl(3,4).s3","maxes",["2^2.L3(4).3","2^2.L3(4).2_2","2^6:(3xA5):2",
"2^6:(3xA5):2","hed3","7:3xS4"]);
ARC("2^2.psl(3,4).s3","tomfusion",rec(name:="2^2.L3(4).3.2_2",map:=[1,2,3,5,6,
38,28,29,32,125,41,147,41,147,7,8,39,149,149,301,301,4,27,31,30,40,146,119,
119,148,342,148,342],text:=[
"fusion map is unique"
]));
ALF("2^2.psl(3,4).s3","He",[1,2,2,3,4,10,7,8,9,18,12,21,13,22,4,5,10,25,
25,31,30,2,6,6,7,10,19,17,17,21,32,22,33],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("2^2.psl(3,4).s3","L3(4).3.2_2",[1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,9,10,
11,12,14,13,15,15,16,16,17,17,18,18,19,19,20,20]);
ALF("2^2.psl(3,4).s3","2^2.L3(4).D12",[1,2,3,4,5,6,7,8,9,10,11,12,11,12,
20,21,22,23,23,24,24,28,29,31,30,32,33,34,34,35,36,35,36],[
"fusion map is unique"
]);

MOT("2^3+8:L3(2)",
[
"maximal subgroup of Ru,\n",
"origin: computed by K.Lux using Clifford matrices,\n",
"tests: 1.o.r., pow[2,3,7]"
],
[344064,49152,2048,1792,768,1536,1024,512,256,256,28,28,24,24,32,32,128,28,28,
28,28,28,28,12,12,128,128,16,64,16,16,64,32,12,32],
[,[1,1,1,1,2,2,2,2,1,2,11,12,13,13,9,9,3,11,12,12,11,11,12,14,14,3,3,17,3,32,
32,7,6,14,8],[1,2,3,4,5,6,7,8,9,10,12,11,1,2,15,16,17,19,21,18,23,20,22,5,5,
26,27,28,29,31,30,32,33,6,35],,,,[1,2,3,4,5,6,7,8,9,10,1,1,13,14,15,16,17,4,4,
4,4,4,4,24,25,26,27,28,29,31,30,32,33,34,35]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[3,3,
3,3,3,3,3,3,-1,-1,E(7)^3+E(7)^5+E(7)^6,E(7)+E(7)^2+E(7)^4,0,0,1,1,-1,
E(7)^3+E(7)^5+E(7)^6,E(7)+E(7)^2+E(7)^4,E(7)+E(7)^2+E(7)^4,
E(7)^3+E(7)^5+E(7)^6,E(7)^3+E(7)^5+E(7)^6,E(7)+E(7)^2+E(7)^4,0,0,-1,-1,1,-1,1,
1,-1,-1,0,-1],
[GALOIS,[2,3]],[6,6,6,6,6,6,6,6,2,2,-1,-1,0,0,0,0,2,-1,-1,-1,-1,-1,-1,0,0,2,2,
0,2,0,0,2,2,0,2],[7,7,7,7,7,7,7,7,-1,-1,0,0,1,1,-1,-1,-1,0,0,0,0,0,0,1,1,-1,
-1,-1,-1,-1,-1,-1,-1,1,-1],[8,8,8,8,8,8,8,8,0,0,1,1,-1,-1,0,0,0,1,1,1,1,1,1,
-1,-1,0,0,0,0,0,0,0,0,-1,0],[21,21,5,-7,-3,9,-3,1,5,5,0,0,0,0,1,1,5,0,0,0,0,0,
0,0,0,1,1,1,1,-1,-1,-3,-1,0,-1],[21,21,5,-7,-3,9,-3,1,-3,-3,0,0,0,0,1,1,-3,0,
0,0,0,0,0,0,0,1,1,1,1,-1,-1,5,-1,0,-1],[21,21,5,-7,-3,9,-3,1,1,1,0,0,0,0,-1,
-1,1,0,0,0,0,0,0,0,0,5,5,-1,-3,1,1,1,-1,0,-1],[21,21,5,-7,-3,9,-3,1,1,1,0,0,0,
0,-1,-1,1,0,0,0,0,0,0,0,0,-3,-3,-1,5,1,1,1,-1,0,-1],[42,42,10,-14,-6,18,-6,2,
-2,-2,0,0,0,0,0,0,-2,0,0,0,0,0,0,0,0,-2,-2,0,-2,0,0,-2,2,0,2],[42,42,-6,14,-6,
6,2,-2,2,2,0,0,0,0,2,2,2,0,0,0,0,0,0,0,0,-2,-2,-2,-2,0,0,2,0,0,0],[42,42,-6,
14,-6,6,2,-2,-2,-2,0,0,0,0,0,0,-2,0,0,0,0,0,0,0,0,2,2,0,2,-2*E(4),2*E(4),-2,0,
0,0],[42,42,-6,14,-6,6,2,-2,2,2,0,0,0,0,-2,-2,2,0,0,0,0,0,0,0,0,-2,-2,2,-2,0,
0,2,0,0,0],
[GALOIS,[13,3]],[84,84,4,0,12,0,-4,-8,-4,-4,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,-2,0,2],[84,84,4,0,12,0,-4,-8,4,4,0,0,0,0,0,0,-4,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,2,0,-2],[28,28,12,0,-4,-8,4,0,4,4,0,0,1,1,0,0,-4,0,0,0,0,0,0,-1,
-1,0,0,0,0,0,0,0,-2,1,2],[28,28,12,0,-4,-8,4,0,-4,-4,0,0,1,1,0,0,4,0,0,0,0,0,
0,-1,-1,0,0,0,0,0,0,0,2,1,-2],[56,56,24,0,-8,-16,8,0,0,0,0,0,-1,-1,0,0,0,0,0,
0,0,0,0,1,1,0,0,0,0,0,0,0,0,-1,0],[56,56,-8,0,0,-8,-8,8,0,0,0,0,2,2,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,0],[56,56,-8,0,0,-8,-8,8,0,0,0,0,-1,-1,0,0,0,0,
0,0,0,0,0,-E(3)+E(3)^2,E(3)-E(3)^2,0,0,0,0,0,0,0,0,1,0],
[GALOIS,[22,2]],[24,24,-8,-8,0,0,8,0,0,0,E(7)^3+E(7)^5+E(7)^6,
E(7)+E(7)^2+E(7)^4,0,0,0,0,0,E(7)^3-E(7)^5-E(7)^6,-E(7)+E(7)^2-E(7)^4,
E(7)-E(7)^2-E(7)^4,-E(7)^3-E(7)^5+E(7)^6,-E(7)^3+E(7)^5-E(7)^6,
-E(7)-E(7)^2+E(7)^4,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[24,2]],
[GALOIS,[24,4]],
[GALOIS,[24,3]],
[GALOIS,[24,5]],[24,24,-8,-8,0,0,8,0,0,0,3,3,0,0,0,0,0,-1,-1,-1,-1,-1,-1,0,0,
0,0,0,0,0,0,0,0,0,0],
[GALOIS,[24,6]],[112,-16,0,0,0,0,0,0,4,-4,0,0,-2,2,2,-2,0,0,0,0,0,0,0,0,0,-4,
4,0,0,0,0,0,0,0,0],[112,-16,0,0,0,0,0,0,4,-4,0,0,-2,2,-2,2,0,0,0,0,0,0,0,0,0,
4,-4,0,0,0,0,0,0,0,0],[224,-32,0,0,0,0,0,0,8,-8,0,0,2,-2,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0],[336,-48,0,0,0,0,0,0,-4,4,0,0,0,0,2,-2,0,0,0,0,0,0,0,0,
0,4,-4,0,0,0,0,0,0,0,0],[336,-48,0,0,0,0,0,0,-4,4,0,0,0,0,-2,2,0,0,0,0,0,0,0,
0,0,-4,4,0,0,0,0,0,0,0,0]],
[(30,31),(24,25),(15,16)(26,27),(11,12)(18,19,21,23,22,20),(18,22,21)
(19,20,23)]);
ARC("2^3+8:L3(2)","projectives",["2.2^3+8:L3(2)",[[28,-4,4,0,4*E(4),-4,0,0,-4,
0,0,0,1,-1,0,0,0,0,0,0,0,0,0,-E(4),-E(4),4,0,0,0,1-E(4),1+E(4),2*E(4),2*E(4),
-1,0],
[GALOIS,[1,3]],[28,-4,4,0,4*E(4),-4,0,0,4,0,0,0,1,-1,0,0,0,0,0,0,0,0,0,-E(4),
-E(4),0,-4,0,0,-1+E(4),-1-E(4),2*E(4),-2*E(4),-1,0],
[GALOIS,[3,3]],[56,-8,8,0,8*E(4),-8,0,0,0,0,0,0,-1,1,0,0,0,0,0,0,0,0,0,E(4),
E(4),4,-4,0,0,0,0,4*E(4),0,1,0],
[GALOIS,[5,3]],[64,64,0,0,0,0,0,0,0,0,-2*E(7)-2*E(7)^2-2*E(7)^4,
-2*E(7)^3-2*E(7)^5-2*E(7)^6,-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[7,3]],[84,-12,12,0,12*E(4),-12,0,0,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
-4,0,0,0,1-E(4),1+E(4),-2*E(4),-2*E(4),0,0],
[GALOIS,[9,3]],[84,-12,12,0,12*E(4),-12,0,0,-4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,4,0,0,-1+E(4),-1-E(4),-2*E(4),2*E(4),0,0],
[GALOIS,[11,3]],[96,96,0,0,0,0,0,0,0,0,-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
-2*E(8)+2*E(8)^3,0,0,0,0,0,0,0],
[GALOIS,[13,3]],[112,-16,16,0,0,16,0,0,0,0,0,0,-2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,-2,0],[112,-16,16,0,0,16,0,0,0,0,0,0,1,-1,0,0,0,0,0,0,0,0,0,
-E(12)^7+E(12)^11,E(12)^7-E(12)^11,0,0,0,0,0,0,0,0,1,0],
[GALOIS,[16,5]],[128,128,0,0,0,0,0,0,0,0,2,2,2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0],[336,-48,-16,0,0,0,0,0,-8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-4,
-4,0,0,0,0,0,0,0,0],[336,-48,-16,0,0,0,0,0,8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
4,4,0,0,0,0,0,0,0,0]],]);
ALF("2^3+8:L3(2)","Ru",[1,2,2,3,6,5,7,8,2,7,12,12,4,11,7,8,8,21,22,23,23,
22,21,19,19,5,8,15,7,26,25,14,13,18,15],[
"fusion is unique up to table automorphisms"
]);
ALF("2^3+8:L3(2)","L3(2)",[1,1,1,1,1,1,1,1,2,2,5,6,3,3,4,4,2,5,6,6,5,5,6,
3,3,2,2,4,2,4,4,2,2,3,2]);

MOT("2^3.2^2.2^6.(3xL3(2))",
[
"origin: computed by Klaus Lux using Dixon's Algorithm,\n",
"9th maximal subgroup of HN,\n",
"table is sorted w.r. to normal series 2^3.2^2.2^6.3.L3(2),\n",
"tests: 1.o.r., pow[2,3,7]"
],
[1032192,147456,43008,3072,3072,768,4032,4032,576,576,1536,1536,768,128,64,96,
96,96,96,64,48,48,288,72,72,288,72,72,48,48,48,48,48,12,12,96,96,16,24,24,24,
24,84,28,21,21,84,28,21,21],
[,[1,1,1,1,2,2,8,7,8,7,1,1,2,3,4,7,7,8,8,5,9,10,23,25,24,23,25,24,23,23,23,26,
26,27,28,12,11,14,19,18,17,16,43,43,46,45,47,47,50,49],[1,2,3,4,5,6,1,1,2,2,
11,12,13,14,15,11,12,12,11,20,13,13,1,1,1,2,2,2,4,4,3,5,5,6,6,36,37,38,37,36,
36,37,47,48,47,47,43,44,43,43],,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,
18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,1,
3,7,8,1,3,8,7]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1],[3,3,3,3,3,3,3,3,3,3,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,E(7)+E(7)^2+E(7)^4,
E(7)+E(7)^2+E(7)^4,E(7)+E(7)^2+E(7)^4,E(7)+E(7)^2+E(7)^4,E(7)^3+E(7)^5+E(7)^6,
E(7)^3+E(7)^5+E(7)^6,E(7)^3+E(7)^5+E(7)^6,E(7)^3+E(7)^5+E(7)^6],
[GALOIS,[2,3]],[6,6,6,6,6,6,6,6,6,6,2,2,2,2,2,2,2,2,2,2,2,2,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,-1],[7,7,7,7,7,7,7,7,7,7,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,0,0,
0,0,0,0,0,0],[8,8,8,8,8,8,8,8,8,8,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,E(3)^2,E(3),
E(3)^2,E(3),1,1,1,1,1,E(3),E(3),E(3)^2,E(3)^2,1,E(3),E(3)^2,1,E(3)^2,E(3),1,
E(3)^2,E(3),1,1,1,1,1,E(3),E(3)^2,1,1,1,E(3),E(3),E(3)^2,E(3)^2,1,1,E(3)^2,
E(3),1,1,E(3),E(3)^2],
[TENSOR,[7,7]],
[TENSOR,[2,7]],
[TENSOR,[3,7]],
[TENSOR,[2,8]],
[TENSOR,[3,8]],
[TENSOR,[4,7]],
[TENSOR,[4,8]],
[TENSOR,[5,7]],
[TENSOR,[5,8]],
[TENSOR,[6,7]],
[TENSOR,[6,8]],[21,21,21,5,5,-3,0,0,0,0,9,9,9,1,-3,0,0,0,0,1,0,0,3,0,0,3,0,0,
-1,-1,3,-1,-1,0,0,3,3,-1,0,0,0,0,0,0,0,0,0,0,0,0],[21,21,21,5,5,-3,0,0,0,0,-3,
-3,-3,5,1,0,0,0,0,-3,0,0,3,0,0,3,0,0,-1,-1,3,-1,-1,0,0,-3,-3,1,0,0,0,0,0,0,0,
0,0,0,0,0],[42,42,42,10,10,-6,0,0,0,0,6,6,6,6,-2,0,0,0,0,-2,0,0,-3,0,0,-3,0,0,
1,1,-3,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[42,42,42,-6,-6,2,0,0,0,0,6,6,6,
-2,2,0,0,0,0,-2,0,0,0,3,3,0,3,3,0,0,0,0,0,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0],
[TENSOR,[22,7]],
[TENSOR,[22,8]],[63,63,63,15,15,-9,0,0,0,0,3,3,3,-5,-1,0,0,0,0,3,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,-3,-3,1,0,0,0,0,0,0,0,0,0,0,0,0],[63,63,63,15,15,-9,0,0,0,0,
-9,-9,-9,-1,3,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,3,3,-1,0,0,0,0,0,0,0,0,
0,0,0,0],[126,126,126,-18,-18,6,0,0,0,0,-6,-6,-6,2,-2,0,0,0,0,2,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[24,24,-8,-8,8,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,6,0,0,6,0,0,-2,-2,-2,2,2,0,0,0,0,0,0,0,0,0,3,-1,0,0,3,-1,0,
0],[24,24,-8,-8,8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-3,0,0,-3,0,0,1,1,1,
-E(3)+3*E(3)^2,3*E(3)-E(3)^2,0,0,0,0,0,0,0,0,0,3,-1,0,0,3,-1,0,0],
[GALOIS,[29,2]],[72,72,-24,-24,24,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,3*E(7)^3+3*E(7)^5+3*E(7)^6,-E(7)^3-E(7)^5-E(7)^6
 ,0,0,3*E(7)+3*E(7)^2+3*E(7)^4,-E(7)-E(7)^2-E(7)^4,0,0],
[GALOIS,[31,3]],[168,168,-56,8,-8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,6,0,0,6,0,
0,2,2,-2,-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[168,168,-56,8,-8,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,-3,0,0,-3,0,0,3*E(3)-E(3)^2,-E(3)+3*E(3)^2,1,1,1,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[34,2]],[112,-16,0,0,0,0,7,7,-1,-1,12,-4,-4,0,0,3,-1,-1,3,0,-1,-1,4,
-2,-2,-4,2,2,0,0,0,0,0,0,0,2,-2,0,1,-1,-1,1,0,0,0,0,0,0,0,0],[112,-16,0,0,0,0,
7,7,-1,-1,-4,12,-4,0,0,-1,3,3,-1,0,-1,-1,4,-2,-2,-4,2,2,0,0,0,0,0,0,0,-2,2,0,
-1,1,1,-1,0,0,0,0,0,0,0,0],
[TENSOR,[36,7]],
[TENSOR,[36,8]],
[TENSOR,[37,7]],
[TENSOR,[37,8]],[224,-32,0,0,0,0,14,14,-2,-2,8,8,-8,0,0,2,2,2,2,0,-2,-2,-4,2,
2,4,-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[42,7]],
[TENSOR,[42,8]],[336,-48,0,0,0,0,21,21,-3,-3,4,-12,4,0,0,1,-3,-3,1,0,1,1,0,0,
0,0,0,0,0,0,0,0,0,0,0,-2,2,0,-1,1,1,-1,0,0,0,0,0,0,0,0],[336,-48,0,0,0,0,21,
21,-3,-3,-12,4,4,0,0,-3,1,1,-3,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,2,-2,0,1,-1,-1,
1,0,0,0,0,0,0,0,0],
[TENSOR,[45,7]],
[TENSOR,[45,8]],
[TENSOR,[46,7]],
[TENSOR,[46,8]]],
[(43,47)(44,48)(45,50)(46,49),(32,33),(29,30),(11,12)(16,17)(18,19)(36,37)
(39,40)(41,42),( 7, 8)( 9,10)(16,19)(17,18)(21,22)(24,25)(27,28)(29,30)(32,33)
(34,35)(39,42)(40,41)(45,46)(49,50)]);
ALF("2^3.2^2.2^6.(3xL3(2))","HN",[1,3,2,3,6,8,4,4,15,15,2,3,6,7,8,14,15,
15,14,19,31,31,4,5,5,15,16,16,15,15,14,31,31,32,32,6,7,18,30,31,31,30,17,
33,44,44,17,33,44,44],[
"fusion map is unique up to table automorphisms"
]);
ALF("2^3.2^2.2^6.(3xL3(2))","2^3.2^2.2^6.(S3xL3(2))",[1,2,3,4,5,6,26,26,
27,27,7,8,9,10,11,28,29,29,28,12,30,30,13,31,31,14,32,32,16,16,15,17,18,
33,33,19,20,21,34,35,35,34,22,23,36,36,24,25,37,37],[
"fusion map is unique up to table aut."
]);

MOT("2^4+6:3a6",
[
"origin: CAS library,\n",
"7th maximal subgroup of Suz,\n",
"test:     TEST, JAMES, JAMES,n=3,\n",
"and restricted characters decompose properly.\n",
"tests: 1.o.r., pow[2,3,5]"
],
[1105920,73728,3840,3072,3072,17280,1152,17280,1152,1536,512,1536,512,768,256,
64,64,96,96,48,96,96,48,36,12,144,144,144,144,24,24,96,96,32,32,24,24,24,24,
60,20,15,15,60,20,15,15],
[,[1,1,1,2,2,8,8,6,6,1,1,2,2,2,2,4,5,8,9,9,6,7,7,24,24,26,26,26,26,29,29,10,
12,11,13,21,22,18,19,44,44,47,46,40,40,43,42],[1,2,3,4,5,1,2,1,2,10,11,12,13,
14,15,16,17,10,12,14,10,12,14,1,3,1,2,2,2,4,5,32,33,34,35,32,33,32,33,44,45,
44,44,40,41,40,40],,[1,2,3,4,5,8,9,6,7,10,11,12,13,14,15,16,17,21,22,23,18,19,
20,24,25,26,28,27,29,30,31,32,33,34,35,38,39,36,37,1,3,8,6,1,3,8,6]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1],[5,5,5,5,5,5,5,5,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,-1,-1,
-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,0],[5,5,5,5,5,5,5,5,5,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,-1,-1,2,2,2,2,2,2,-1,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,
0],[8,8,8,8,8,8,8,8,8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,-1,0,0,
0,0,0,0,0,0,-E(5)^2-E(5)^3,-E(5)^2-E(5)^3,-E(5)^2-E(5)^3,-E(5)^2-E(5)^3,
-E(5)-E(5)^4,-E(5)-E(5)^4,-E(5)-E(5)^4,-E(5)-E(5)^4],
[GALOIS,[4,2]],[9,9,9,9,9,9,9,9,9,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,
1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1],[10,10,10,10,10,10,10,10,10,-2,-2,-2,
-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0],[3,3,3,3,3,3*E(3),3*E(3),3*E(3)^2,3*E(3)^2,-1,-1,-1,-1,-1,-1,-1,-1,-E(3),
-E(3),-E(3),-E(3)^2,-E(3)^2,-E(3)^2,0,0,0,0,0,0,0,0,1,1,1,1,E(3),E(3),E(3)^2,
E(3)^2,-E(5)^2-E(5)^3,-E(5)^2-E(5)^3,-E(15)^11-E(15)^14,-E(15)-E(15)^4,
-E(5)-E(5)^4,-E(5)-E(5)^4,-E(15)^2-E(15)^8,-E(15)^7-E(15)^13],
[GALOIS,[8,7]],[6,6,6,6,6,6*E(3),6*E(3),6*E(3)^2,6*E(3)^2,2,2,2,2,2,2,2,2,
2*E(3),2*E(3),2*E(3),2*E(3)^2,2*E(3)^2,2*E(3)^2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,1,1,E(3),E(3)^2,1,1,E(3),E(3)^2],[9,9,9,9,9,9*E(3),9*E(3),9*E(3)^2,9*E(3)^2,
1,1,1,1,1,1,1,1,E(3),E(3),E(3),E(3)^2,E(3)^2,E(3)^2,0,0,0,0,0,0,0,0,1,1,1,1,
E(3),E(3),E(3)^2,E(3)^2,-1,-1,-E(3),-E(3)^2,-1,-1,-E(3),-E(3)^2],[15,15,15,15,
15,15*E(3),15*E(3),15*E(3)^2,15*E(3)^2,-1,-1,-1,-1,-1,-1,-1,-1,-E(3),-E(3),
-E(3),-E(3)^2,-E(3)^2,-E(3)^2,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-E(3),-E(3),-E(3)^2,
-E(3)^2,0,0,0,0,0,0,0,0],
[GALOIS,[8,11]],
[GALOIS,[8,2]],
[GALOIS,[10,2]],
[GALOIS,[11,2]],
[GALOIS,[12,2]],[18,18,-6,2,2,0,0,0,0,6,-2,6,-2,6,-2,-2,2,0,0,0,0,0,0,0,0,3,3,
3,3,-1,-1,0,0,0,0,0,0,0,0,3,-1,0,0,3,-1,0,0],[54,54,-18,6,6,0,0,0,0,-6,2,-6,2,
-6,2,2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-3*E(5)^2-3*E(5)^3,
E(5)^2+E(5)^3,0,0,-3*E(5)-3*E(5)^4,E(5)+E(5)^4,0,0],
[GALOIS,[19,2]],[72,72,-24,8,8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,3,3,3,
3,-1,-1,0,0,0,0,0,0,0,0,-3,1,0,0,-3,1,0,0],[90,90,-30,10,10,0,0,0,0,6,-2,6,-2,
6,-2,-2,2,0,0,0,0,0,0,0,0,-3,-3,-3,-3,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[
45,45,5,-3,-3,0,0,0,0,9,1,9,1,9,1,1,-3,0,0,0,0,0,0,3,-1,0,0,0,0,0,0,3,3,-1,-1,
0,0,0,0,0,0,0,0,0,0,0,0],[45,45,5,-3,-3,0,0,0,0,-3,5,-3,5,-3,5,-3,1,0,0,0,0,0,
0,3,-1,0,0,0,0,0,0,-3,-3,1,1,0,0,0,0,0,0,0,0,0,0,0,0],[90,90,10,-6,-6,0,0,0,0,
6,6,6,6,6,6,-2,-2,0,0,0,0,0,0,-3,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0],[135,135,15,-9,-9,0,0,0,0,3,-5,3,-5,3,-5,3,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
-3,-3,1,1,0,0,0,0,0,0,0,0,0,0,0,0],[135,135,15,-9,-9,0,0,0,0,-9,-1,-9,-1,-9,
-1,-1,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,3,3,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0],[60,-4,
0,4,-4,15,-1,15,-1,0,4,8,-4,-4,0,0,0,3,-1,-1,3,-1,-1,0,0,-3,-1,-1,5,1,-1,-2,2,
0,0,1,-1,1,-1,0,0,0,0,0,0,0,0],[60,-4,0,4,-4,15*E(3),-E(3),15*E(3)^2,-E(3)^2,
0,4,8,-4,-4,0,0,0,3*E(3),-E(3),-E(3),3*E(3)^2,-E(3)^2,-E(3)^2,0,0,3,
3*E(3)-E(3)^2,-E(3)+3*E(3)^2,-1,1,-1,-2,2,0,0,E(3),-E(3),E(3)^2,-E(3)^2,0,0,0,
0,0,0,0,0],
[GALOIS,[29,2]],[60,-4,0,4,-4,15,-1,15,-1,8,-4,0,4,-4,0,0,0,-1,3,-1,-1,3,-1,0,
0,-3,-1,-1,5,1,-1,2,-2,0,0,-1,1,-1,1,0,0,0,0,0,0,0,0],[60,-4,0,4,-4,15*E(3),
-E(3),15*E(3)^2,-E(3)^2,8,-4,0,4,-4,0,0,0,-E(3),3*E(3),-E(3),-E(3)^2,3*E(3)^2,
-E(3)^2,0,0,3,3*E(3)-E(3)^2,-E(3)+3*E(3)^2,-1,1,-1,2,-2,0,0,-E(3),E(3),
-E(3)^2,E(3)^2,0,0,0,0,0,0,0,0],
[GALOIS,[32,2]],[120,-8,0,8,-8,30,-2,30,-2,8,0,8,0,-8,0,0,0,2,2,-2,2,2,-2,0,0,
3,1,1,-5,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[120,-8,0,8,-8,30*E(3),-2*E(3),
30*E(3)^2,-2*E(3)^2,8,0,8,0,-8,0,0,0,2*E(3),2*E(3),-2*E(3),2*E(3)^2,2*E(3)^2,
-2*E(3)^2,0,0,-3,-3*E(3)+E(3)^2,E(3)-3*E(3)^2,1,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0],
[GALOIS,[35,2]],[180,-12,0,12,-12,45,-3,45,-3,-8,4,0,-4,4,0,0,0,1,-3,1,1,-3,1,
0,0,0,0,0,0,0,0,2,-2,0,0,-1,1,-1,1,0,0,0,0,0,0,0,0],[180,-12,0,12,-12,45*E(3),
-3*E(3),45*E(3)^2,-3*E(3)^2,-8,4,0,-4,4,0,0,0,E(3),-3*E(3),E(3),E(3)^2,
-3*E(3)^2,E(3)^2,0,0,0,0,0,0,0,0,2,-2,0,0,-E(3),E(3),-E(3)^2,E(3)^2,0,0,0,0,0,
0,0,0],
[GALOIS,[38,2]],[180,-12,0,12,-12,45,-3,45,-3,0,-4,-8,4,4,0,0,0,-3,1,1,-3,1,1,
0,0,0,0,0,0,0,0,-2,2,0,0,1,-1,1,-1,0,0,0,0,0,0,0,0],[180,-12,0,12,-12,45*E(3),
-3*E(3),45*E(3)^2,-3*E(3)^2,0,-4,-8,4,4,0,0,0,-3*E(3),E(3),E(3),-3*E(3)^2,
E(3)^2,E(3)^2,0,0,0,0,0,0,0,0,-2,2,0,0,E(3),-E(3),E(3)^2,-E(3)^2,0,0,0,0,0,0,
0,0],
[GALOIS,[41,2]],[180,-12,0,-4,4,0,0,0,0,-12,0,12,8,0,-4,0,0,0,0,0,0,0,0,0,0,3,
-3,-3,3,-1,1,0,0,2,-2,0,0,0,0,0,0,0,0,0,0,0,0],[180,-12,0,-4,4,0,0,0,0,12,8,
-12,0,0,-4,0,0,0,0,0,0,0,0,0,0,3,-3,-3,3,-1,1,0,0,-2,2,0,0,0,0,0,0,0,0,0,0,0,
0],[360,-24,0,-8,8,0,0,0,0,0,8,0,8,0,-8,0,0,0,0,0,0,0,0,0,0,-3,3,3,-3,1,-1,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[540,-36,0,-12,12,0,0,0,0,-12,-8,12,0,0,4,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,2,0,0,0,0,0,0,0,0,0,0,0,0],[540,-36,0,-12,
12,0,0,0,0,12,0,-12,-8,0,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,-2,0,0,0,0,0,
0,0,0,0,0,0,0]],
[(40,44)(41,45)(42,46)(43,47),( 6, 8)( 7, 9)(18,21)(19,22)(20,23)(27,28)
(36,38)(37,39)(42,43)(46,47)]);
ARC("2^4+6:3a6","projectives",["2.SuzM7",[[12,-4,0,4,0,-6,2,-6,2,4,0,-4,0,0,0,
0,-2,-2,-2,0,-2,-2,0,0,0,0,-2,-2,-4,-2,0,0,0,0,0,0,0,0,0,2,0,-1,-1,2,0,-1,-1],
[12,-4,0,4,0,-6*E(3)^2,2*E(3)^2,-6*E(3),2*E(3),4,0,-4,0,0,0,0,-2,-2*E(3)^2,
-2*E(3)^2,0,-2*E(3),-2*E(3),0,0,0,3,E(3)+3*E(3)^2,3*E(3)+E(3)^2,-1,1,
-E(3)+E(3)^2,0,0,0,0,0,0,0,0,2,0,-E(3)^2,-E(3),2,0,-E(3)^2,-E(3)],
[GALOIS,[2,2]],[36,-12,0,12,0,-18,6,-18,6,-4,0,4,0,0,0,0,2,2,2,0,2,2,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,-2*E(5)^2-2*E(5)^3,0,E(5)^2+E(5)^3,E(5)^2+E(5)^3,
-2*E(5)-2*E(5)^4,0,E(5)+E(5)^4,E(5)+E(5)^4],[36,-12,0,12,0,-18*E(3),6*E(3),
-18*E(3)^2,6*E(3)^2,-4,0,4,0,0,0,0,2,2*E(3),2*E(3),0,2*E(3)^2,2*E(3)^2,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,-2*E(5)^2-2*E(5)^3,0,E(15)^11+E(15)^14,
E(15)+E(15)^4,-2*E(5)-2*E(5)^4,0,E(15)^2+E(15)^8,E(15)^7+E(15)^13],
[GALOIS,[5,11]],
[GALOIS,[4,2]],
[GALOIS,[5,2]],
[GALOIS,[5,7]],[48,-16,0,16,0,-24,8,-24,8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
-2,-2,-4,-2,0,0,0,0,0,0,0,0,0,-2,0,1,1,-2,0,1,1],[48,-16,0,16,0,-24*E(3)^2,
8*E(3)^2,-24*E(3),8*E(3),0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,3,E(3)+3*E(3)^2,
3*E(3)+E(3)^2,-1,1,-E(3)+E(3)^2,0,0,0,0,0,0,0,0,-2,0,E(3)^2,E(3),-2,0,E(3)^2,
E(3)],
[GALOIS,[11,2]],[60,-20,0,20,0,-30,10,-30,10,4,0,-4,0,0,0,0,-2,-2,-2,0,-2,-2,
0,0,0,0,2,2,4,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[60,-20,0,20,0,-30*E(3)^2,
10*E(3)^2,-30*E(3),10*E(3),4,0,-4,0,0,0,0,-2,-2*E(3)^2,-2*E(3)^2,0,-2*E(3),
-2*E(3),0,0,0,-3,-E(3)-3*E(3)^2,-3*E(3)-E(3)^2,1,-1,E(3)-E(3)^2,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0],
[GALOIS,[14,2]],[80,16,0,0,0,-10,-2,-10,-2,-8,0,-8,0,0,0,0,0,-2,2,0,-2,2,0,2,
0,2,2,2,-2,0,0,4,0,0,0,-2,0,-2,0,0,0,0,0,0,0,0,0],[80,16,0,0,0,-10,-2,-10,-2,
-8,0,-8,0,0,0,0,0,-2,2,0,-2,2,0,2,0,2,2,2,-2,0,0,-4,0,0,0,2,0,2,0,0,0,0,0,0,0,
0,0],[80,16,0,0,0,-10,-2,-10,-2,8,0,8,0,0,0,0,0,2,-2,0,2,-2,0,2,0,2,2,2,-2,0,0
,0,4*E(4),0,0,0,-2*E(4),0,-2*E(4),0,0,0,0,0,0,0,0],
[GALOIS,[18,3]],[180,-60,0,-4,0,0,0,0,0,12,0,-12,0,0,0,0,2,0,0,0,0,0,0,0,0,-6
,0,0,-6,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[180,-60,0,-4,0,0,0,0,0,12,0,-12,
0,0,0,0,2,0,0,0,0,0,0,0,0,3,3*E(3)-3*E(3)^2,-3*E(3)+3*E(3)^2,3,-1,-E(3)+E(3)^2
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[21,2]],[240,48,0,0,0,-30*E(3)^2,-6*E(3)^2,-30*E(3),-6*E(3),8,0,8,0,0
,0,0,0,2*E(3)^2,-2*E(3)^2,0,2*E(3),-2*E(3),0,0,0,0,0,0,0,0,0,4,0,0,0,-2*E(3)^2
,0,-2*E(3),0,0,0,0,0,0,0,0,0],[240,48,0,0,0,-30*E(3)^2,-6*E(3)^2,-30*E(3),
-6*E(3),8,0,8,0,0,0,0,0,2*E(3)^2,-2*E(3)^2,0,2*E(3),-2*E(3),0,0,0,0,0,0,0,0,0,
-4,0,0,0,2*E(3)^2,0,2*E(3),0,0,0,0,0,0,0,0,0],[240,48,0,0,0,-30*E(3)^2,
-6*E(3)^2,-30*E(3),-6*E(3),-8,0,-8,0,0,0,0,0,-2*E(3)^2,2*E(3)^2,0,-2*E(3),
2*E(3),0,0,0,0,0,0,0,0,0,0,4*E(4),0,0,0,-2*E(12)^11,0,-2*E(12)^7,0,0,0,0,0,0,0
,0],
[GALOIS,[25,7]],
[GALOIS,[23,2]],
[GALOIS,[24,2]],
[GALOIS,[25,5]],
[GALOIS,[25,11]],[320,64,0,0,0,-40,-8,-40,-8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,0,
-4,-4,-4,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[320,64,0,0,0,-40,-8,-40,-8,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,-4,0,2,2,2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[
540,-180,0,-12,0,0,0,0,0,-12,0,12,0,0,0,0,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0]],]);
ALF("2^4+6:3a6","Suz",[1,2,3,7,8,4,13,4,13,2,3,7,9,9,8,19,20,13,27,29,13,
27,29,6,17,5,14,15,16,28,31,9,19,10,21,29,43,29,43,12,25,37,37,12,25,37,
37],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("2^4+6:3a6","3.A6",[1,1,1,1,1,2,2,3,3,4,4,4,4,4,4,4,4,5,5,5,6,6,6,7,7,
8,8,8,8,8,8,9,9,9,9,10,10,11,11,12,12,13,14,15,15,16,17]);
ALF("2^4+6:3a6","2^(4+6):3S6",[1,2,3,4,5,6,7,6,7,8,9,10,12,11,13,15,14,16,
17,18,16,17,18,19,20,21,23,23,22,25,24,26,28,27,29,30,31,30,31,32,33,34,
35,32,33,35,34],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);

MOT("2.SuzM7",
[
"7th maximal subgroup of 2.Suz,\n",
"structure (2.2^4.2^6):3A6,\n",
"origin: Dixon's Algorithm"
],
[2211840,2211840,147456,147456,3840,6144,6144,3072,34560,34560,2304,2304,34560
,34560,2304,2304,3072,3072,512,3072,3072,512,768,256,64,128,128,192,192,192,
192,48,192,192,192,192,48,72,72,12,288,288,288,288,288,288,288,288,48,48,48,48
,192,192,192,192,32,32,48,48,48,48,48,48,48,48,120,120,20,30,30,30,30,120,120,
20,30,30,30,30],
[,[1,1,1,1,2,3,3,3,13,13,13,13,9,9,9,9,1,1,2,3,3,4,4,3,7,8,8,13,13,15,15,16,9,
9,11,11,12,38,38,39,41,41,41,41,41,41,41,41,47,47,47,47,17,17,20,20,19,22,33,
33,36,36,28,28,31,31,74,74,75,79,79,77,77,67,67,68,72,72,70,70],[1,2,3,4,5,6,7
,8,1,2,3,4,1,2,3,4,17,18,19,20,21,22,23,24,25,26,27,17,18,21,20,23,17,18,21,20
,23,1,2,5,1,2,4,3,4,3,3,4,6,7,8,8,53,54,56,55,57,58,53,54,56,55,53,54,56,55,74
,75,76,74,75,74,75,67,68,69,67,68,67,68],,[1,2,3,4,5,6,7,8,13,14,15,16,9,10,11
,12,17,18,19,20,21,22,23,24,25,26,27,33,34,35,36,37,28,29,30,31,32,38,39,40,41
,42,45,46,43,44,47,48,49,50,52,51,53,54,55,56,57,58,63,64,65,66,59,60,61,62,1,
2,5,13,14,9,10,1,2,5,13,14,9,10]],
0,
[(55,56)(61,62)(65,66),(53,54)(59,60)(63,64),
(67,74)(68,75)(69,76)(70,77)(71,78)(72,79)(73,80),
( 9,13)(10,14)(11,15)(12,16)(28,33)(29,34)(30,35)(31,36)(32,37)(43,45)(44,46)
(51,52)(59,63)(60,64)(61,65)(62,66)(70,72)(71,73)(77,79)(78,80)],
["ConstructProj",[["2^4+6:3a6",[]],["2.SuzM7",[]]]]);
ALF("2.SuzM7","2.Suz",[1,2,3,4,5,13,12,14,6,7,21,22,6,7,21,22,4,3,5,12,13,
15,15,14,32,34,33,22,21,46,45,49,22,21,46,45,49,10,11,29,8,9,24,23,26,25,
27,28,48,47,53,52,15,15,32,32,16,35,49,49,75,76,49,49,76,75,19,20,42,63,
64,63,64,19,20,42,63,64,63,64],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("2.SuzM7","2^4+6:3a6",[1,1,2,2,3,4,4,5,6,6,7,7,8,8,9,9,10,10,11,12,12,13,
14,15,16,17,17,18,18,19,19,20,21,21,22,22,23,24,24,25,26,26,27,27,28,28,29,29,
30,30,31,31,32,32,33,33,34,35,36,36,37,37,38,38,39,39,40,40,41,42,42,43,43,44,
44,45,46,46,47,47]);
ALF("2.SuzM7","3.A6",[1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4,4,4,4,4,4,4,
4,5,5,5,5,5,6,6,6,6,6,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,10,10,10,
10,11,11,11,11,12,12,12,13,13,14,14,15,15,15,16,16,17,17]);

MOT("2^4.s6",
[
"origin: CAS library,\n",
"6th maximal subgroup of HS,\n",
"tests: 1.o.r., pow[2,3,5]"
],
[11520,768,64,64,32,18,72,24,16,16,5,192,64,96,384,128,16,16,12,12,6],
[,[1,1,1,2,2,6,7,7,3,4,11,1,2,1,2,2,3,4,7,8,6],[1,2,3,4,5,1,1,2,9,10,11,12,13,
14,15,16,17,18,14,15,12],,[1,2,3,4,5,6,7,8,9,10,1,12,13,14,15,16,17,18,19,20,
21]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1],[5,5,1,1,1,-1,2,2,-1,-1,0,1,1,-3,-3,-3,-1,-1,0,0,1],
[TENSOR,[3,2]],[5,5,1,1,1,2,-1,-1,-1,-1,0,3,3,-1,-1,-1,1,1,-1,-1,0],
[TENSOR,[5,2]],[9,9,1,1,1,0,0,0,1,1,-1,3,3,3,3,3,-1,-1,0,0,0],
[TENSOR,[7,2]],[10,10,-2,-2,-2,1,1,1,0,0,0,2,2,-2,-2,-2,0,0,1,1,-1],
[TENSOR,[9,2]],[16,16,0,0,0,-2,-2,-2,0,0,1,0,0,0,0,0,0,0,0,0,0],[15,-1,3,-1,
-1,0,3,-1,1,-1,0,3,-1,-1,-5,3,1,-1,-1,1,0],
[TENSOR,[12,2]],[15,-1,-1,3,-1,0,3,-1,-1,1,0,3,-1,-1,7,-1,-1,1,-1,1,0],
[TENSOR,[14,2]],[30,-2,2,2,-2,0,-3,1,0,0,0,6,-2,-2,2,2,0,0,1,-1,0],
[TENSOR,[16,2]],[45,-3,1,-3,1,0,0,0,-1,1,0,3,-1,3,3,-5,1,-1,0,0,0],
[TENSOR,[18,2]],[45,-3,-3,1,1,0,0,0,1,-1,0,3,-1,3,-9,-1,-1,1,0,0,0],
[TENSOR,[20,2]]],
[]);
ARC("2^4.s6","projectives",["2.2^4.S6",[[6,2,-2,-2,0,0,3,1,0,0,1,0,0,2*E(4),
4*E(4),0,0,2*E(4),E(4),-E(4),0],[10,-2,2,-2,0,1,1,-1,0,2*E(4),0,-4,0,-2*E(4),
4*E(4),0,0,0,-E(4),-E(4),1],
[GALOIS,[2,3]],[20,-4,-4,4,0,2,2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0],[24,8,0,0,0,0,
3,1,0,0,-1,0,0,4*E(4),8*E(4),0,0,0,-E(4),E(4),0],[30,10,-2,-2,0,0,-3,-1,0,0,0,
0,0,2*E(4),4*E(4),0,0,-2*E(4),E(4),-E(4),0],[36,12,4,4,0,0,0,0,0,0,1,0,0,0,0,0
,0,0,0,0,0],[40,-8,0,0,0,1,-2,2,0,0,0,-8,0,0,0,0,0,0,0,0,-1],[40,-8,0,0,0,-2,1
,-1,0,0,0,0,0,4*E(4),-8*E(4),0,0,0,-E(4),-E(4),0]],]);
ARC("2^4.s6","tomfusion",rec(name:="2^4.S6",map:=[1,2,5,16,20,7,6,31,25,64,29,
3,14,4,8,11,26,62,34,100,36],text:=[
"fusion map is unique"
]));
ALF("2^4.s6","HS",[1,2,2,6,7,4,4,12,6,14,10,2,6,3,5,6,7,14,11,21,12],[
"fusion map is unique, equal to that on the CAS table"
]);
ALF("2^4.s6","A6.2_1",[1,1,2,2,2,3,4,4,5,5,6,7,7,8,8,8,9,9,11,11,10]);
ALF("2^4.s6","U4(3).2_1",[1,2,2,7,8,6,4,11,8,15,9,19,22,20,21,22,22,27,24,
31,26],[
"fusion map is unique up to table autom."
],"tom:966");
ALF("2^4.s6","2^5.S6",[1,2,3,6,7,5,4,10,8,11,9,12,16,13,14,15,17,20,18,21,
19],[
"fusion map is unique"
]);

MOT("U4(3).2_1M10",
[
"10th maximal subgroup of U4(3).2_1,\n",
"differs from U4(3).2_1M9 only by fusion map"
],
0,
0,
0,
0,
["ConstructPermuted",["2^4.s6"]]);
ALF("U4(3).2_1M10","U4(3).2_1",[1,2,2,7,8,6,5,12,8,15,9,19,22,20,21,22,22,
27,25,32,26],[
"fusion 2^4.s6 -> U4(3).2_1 mapped under U4(3).4"
]);

MOT("2^5.S6",
[
"5th maximal subgroup of HS.2,\n",
"origin: Dixon's Algorithm"
],
[23040,1536,128,144,36,128,64,32,10,48,32,384,192,768,256,128,32,24,12,32,24,
3840,2304,768,384,256,128,192,128,128,64,32,32,144,48,36,24,12,32,32,10,24],
[,[1,1,1,4,5,2,2,3,9,4,6,1,1,2,2,2,3,4,5,6,10,1,1,1,1,1,1,2,2,2,2,3,3,4,4,5,4,
5,6,6,9,10],[1,2,3,1,1,6,7,8,9,2,11,12,13,14,15,16,17,13,12,20,14,22,23,24,25,
26,27,28,29,30,31,32,33,23,22,23,24,25,39,40,41,28],,[1,2,3,4,5,6,7,8,1,10,11,
12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,
38,39,40,22,42]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1
,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1
,-1,-1,-1,-1,-1,-1,1,1,1,-1,1,-1,1,-1,1,-1,-1,-1,-1,1,1,1,-1,-1,1],
[TENSOR,[2,3]],[5,5,1,2,-1,1,1,-1,0,2,-1,-1,3,3,3,-1,1,0,-1,1,0,5,5,3,-1,3,1,
3,1,-1,1,1,-1,2,2,-1,0,-1,1,-1,0,0],
[TENSOR,[5,4]],
[TENSOR,[5,3]],
[TENSOR,[5,2]],[5,5,1,-1,2,1,1,-1,0,-1,-1,-3,1,1,1,-3,-1,1,0,-1,1,-5,-5,-1,3,
-1,-1,-1,-1,3,-1,1,1,1,1,-2,-1,0,1,1,0,-1],
[TENSOR,[9,4]],
[TENSOR,[9,3]],
[TENSOR,[9,2]],[9,9,1,0,0,1,1,1,-1,0,1,-3,-3,-3,-3,-3,1,0,0,1,0,9,9,-3,-3,-3,
1,-3,1,-3,1,1,1,0,0,0,0,0,1,1,-1,0],
[TENSOR,[13,4]],
[TENSOR,[13,3]],
[TENSOR,[13,2]],[10,10,-2,1,1,-2,-2,0,0,1,0,-2,2,2,2,-2,0,-1,1,0,-1,-10,-10,
-2,2,-2,2,-2,2,2,2,0,0,-1,-1,-1,1,-1,0,0,0,1],
[TENSOR,[17,4]],
[TENSOR,[17,3]],
[TENSOR,[17,2]],[16,16,0,-2,-2,0,0,0,1,-2,0,0,0,0,0,0,0,0,0,0,0,16,16,0,0,0,0
,0,0,0,0,0,0,-2,-2,-2,0,0,0,0,1,0],
[TENSOR,[21,2]],[15,-1,-1,3,0,3,-1,-1,0,-1,1,3,-1,7,-1,-1,-1,-1,0,1,1,-5,3,-5
,3,3,3,-1,-1,-1,-1,-1,-1,-3,1,0,1,0,1,1,0,-1],[15,-1,3,3,0,-1,-1,1,0,-1,-1,-3,
1,5,-3,1,-1,1,0,1,-1,-5,3,-7,-3,1,-1,1,3,1,-1,-1,1,-3,1,0,-1,0,1,-1,0,1],
[TENSOR,[23,4]],
[TENSOR,[24,4]],
[TENSOR,[23,3]],
[TENSOR,[24,3]],
[TENSOR,[23,2]],
[TENSOR,[24,2]],[30,-2,2,-3,0,2,-2,0,0,1,0,6,-2,2,2,-2,0,1,0,0,-1,10,-6,-2,-6
,-2,-2,2,-2,2,2,0,0,-3,1,0,1,0,0,0,0,-1],
[TENSOR,[31,4]],
[TENSOR,[31,3]],
[TENSOR,[31,2]],[45,-3,1,0,0,-3,1,-1,0,0,1,-3,-3,-3,5,1,-1,0,0,1,0,-15,9,9,-3
,1,-3,-3,1,1,1,-1,-1,0,0,0,0,0,1,1,0,0],
[TENSOR,[35,4]],
[TENSOR,[35,3]],
[TENSOR,[35,2]],[45,-3,-3,0,0,1,1,1,0,0,-1,3,3,-9,-1,-1,-1,0,0,1,0,15,-9,-3,
-3,5,-1,-3,3,1,-1,1,-1,0,0,0,0,0,-1,1,0,0],
[TENSOR,[39,4]],
[TENSOR,[39,3]],
[TENSOR,[39,2]]],
[]);
ALF("2^5.S6","HS.2",[1,2,2,4,4,6,7,6,10,12,14,2,3,5,6,6,7,11,12,14,19,23,
22,22,22,23,23,25,24,24,25,24,25,27,29,28,28,28,30,31,33,34],[
"fusion map is unique"
]);

MOT("2.2^4.S6",
[
"6th maximal subgroup of 2.HS,\n",
"origin: Dixon's Algorithm"
],
[23040,23040,1536,1536,128,128,128,128,32,36,36,144,144,48,48,16,32,32,10,10,
384,384,64,192,192,768,768,128,16,32,32,24,24,24,24,12,12],
[,[1,1,1,1,1,1,4,4,3,10,10,12,12,12,12,6,7,7,19,19,1,1,4,2,2,4,4,4,5,7,7,13,13
,14,14,10,10],[1,2,3,4,5,6,7,8,9,1,2,1,2,4,3,16,18,17,19,20,21,22,23,25,24,27,
26,28,29,31,30,24,25,26,27,22,21],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,
18,1,2,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37]],
0,
[(17,18)(21,22)(36,37),(17,18)(24,25)(26,27)(30,31)(32,33)(34,35)],
["ConstructProj",[["2^4.s6",[]],["2.2^4.S6",[]]]]);
ALF("2.2^4.S6","2^4.s6",[1,1,2,2,3,3,4,4,5,6,6,7,7,8,8,9,10,10,11,11,12,
12,13,14,14,15,15,16,17,18,18,19,19,20,20,21,21]);
ALF("2.2^4.S6","2.HS",[1,2,3,4,3,4,10,10,11,6,7,6,7,21,20,10,24,25,16,17,
3,4,10,5,5,8,9,10,11,24,25,19,18,35,36,21,20],[
"map is unique up to table automorphisms, compatible with 2^4.s6 -> HS"
]);
ALF("2.2^4.S6","A6.2_1",[1,1,1,1,2,2,2,2,2,3,3,4,4,4,4,5,5,5,6,6,7,7,7,8,
8,8,8,8,9,9,9,11,11,11,11,10,10]);

MOT("2^4.(S4x2)",
[
"stabilizer of chain (2A^4 < 2A^4.[2^3]) in HS,\n",
"origin: Dixon's Algorithm"
],
[768,256,64,192,64,64,64,32,32,128,128,64,6,6,32,32,16,32,32,16,16,16,16,16],
[,[1,1,1,1,2,1,2,2,1,2,2,2,13,13,1,2,3,1,2,3,6,7,6,7],[1,2,3,4,5,6,7,8,9,10,
11,12,1,4,15,16,17,18,19,20,21,22,23,24],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,
15,16,17,18,19,20,21,22,23,24],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,
19,20,21,22,23,24]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,-1,-1,1,1,1,-1,-1,
-1,-1,1,-1,1,1,1,-1,-1,-1,1,1,-1,-1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,
-1,-1,-1,-1,-1,-1],
[TENSOR,[2,3]],[2,2,2,2,2,2,2,2,2,2,2,2,-1,-1,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[5,2]],[3,3,3,3,3,-1,-1,-1,-1,-1,-1,-1,0,0,1,1,1,1,1,1,-1,-1,-1,-1],
[TENSOR,[7,2]],
[TENSOR,[7,3]],
[TENSOR,[7,4]],[3,3,-1,3,-1,-1,3,-1,-1,3,3,-1,0,0,-1,-1,1,-1,-1,1,1,-1,1,-1],
[TENSOR,[11,3]],
[TENSOR,[11,4]],
[TENSOR,[11,2]],[3,3,-1,3,-1,3,-1,-1,-1,-1,-1,3,0,0,-1,-1,1,-1,-1,1,-1,1,-1,
1],
[TENSOR,[15,4]],
[TENSOR,[15,2]],
[TENSOR,[15,3]],[6,6,-2,6,-2,-2,-2,2,2,-2,-2,-2,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[19,2]],[12,-4,0,0,0,0,0,0,0,-4,4,0,0,0,-2,2,0,2,-2,0,0,0,0,0],
[TENSOR,[21,3]],
[TENSOR,[21,2]],
[TENSOR,[21,4]]],
[(15,18)(16,19)(17,20)(21,23)(22,24),( 3, 6)( 5,12)(17,21)(20,23)]);
ALF("2^4.(S4x2)","2^4.s6",[1,2,2,12,13,3,4,5,14,16,15,16,6,21,3,4,5,12,13,
13,9,10,17,18]);
ALF("2^4.(S4x2)","HS",[1,2,2,2,6,2,6,7,3,6,5,6,4,12,2,6,7,2,6,6,6,14,7,14]);

MOT("2^5.psl(5,2)",
[
"origin: CAS library,\n",
"maximal subgroup of Th,\n",
"Received from Bielefeld 18.1.1989\n",
"Test: 1.OR, JAMES, JAMES,n=3,\n",
"and restricted characters decompose properly.\n",
"tests: 1.o.r., pow[2,3,5,7,31]"
],
[319979520,10321920,43008,43008,1536,128,384,32,16,360,360,12,4032,576,96,96,
48,24,24,30,30,30,30,30,30,168,56,28,28,21,168,56,28,28,21,31,31,31,31,31,31],
[,[1,1,1,2,2,3,4,5,6,10,10,11,13,13,14,14,13,16,15,20,20,22,22,24,24,26,26,26,
27,30,31,31,31,32,35,36,37,38,39,40,41],[1,2,3,4,5,6,7,8,9,1,2,5,1,2,4,4,3,7,
7,20,21,20,21,20,21,31,32,33,34,31,26,27,28,29,26,37,38,41,40,36,39],,[1,2,3,
4,5,6,7,8,9,10,11,12,13,14,16,15,17,19,18,1,2,10,11,10,11,31,32,33,34,35,26,
27,28,29,30,38,41,39,36,37,40],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,
19,20,21,24,25,22,23,1,2,3,4,13,1,2,3,4,13,39,40,36,38,41,37],,,,[1,2,3,4,5,6,
7,8,9,10,11,12,13,14,16,15,17,19,18,20,21,24,25,22,23,26,27,28,29,30,31,32,33,
34,35,40,36,37,41,39,38],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,
21,24,25,22,23,31,32,33,34,35,26,27,28,29,30,40,36,37,41,39,38],,,,[1,2,3,4,5,
6,7,8,9,10,11,12,13,14,16,15,17,19,18,20,21,22,23,24,25,31,32,33,34,35,26,27,
28,29,30,37,38,41,40,36,39],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,
20,21,22,23,24,25,31,32,33,34,35,26,27,28,29,30,39,40,36,38,41,37],,,,[1,2,3,
4,5,6,7,8,9,10,11,12,13,14,16,15,17,19,18,20,21,22,23,24,25,26,27,28,29,30,31,
32,33,34,35,41,39,40,37,38,36],,,,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,16,15,
17,19,18,20,21,24,25,22,23,26,27,28,29,30,31,32,33,34,35,41,39,40,37,38,36],,[
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,31,32,33,34,
35,26,27,28,29,30,1,1,1,1,1,1]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1],[30,30,14,14,6,2,6,2,0,0,0,0,6,6,2,2,2,0,0,0,0,0,0,0,0,2,2,0,0,-1,2,2,
0,0,-1,-1,-1,-1,-1,-1,-1],[124,124,28,28,12,4,4,0,0,4,4,0,1,1,1,1,1,1,1,-1,-1,
-1,-1,-1,-1,-2,-2,0,0,1,-2,-2,0,0,1,0,0,0,0,0,0],[155,155,27,27,-5,-5,3,-1,-1,
5,5,1,8,8,0,0,0,0,0,0,0,0,0,0,0,1,1,-1,-1,1,1,1,-1,-1,1,0,0,0,0,0,0],[217,217,
-7,-7,9,1,-7,1,1,4,4,0,7,7,-1,-1,-1,-1,-1,2,2,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0],[280,280,56,56,8,0,8,0,0,-5,-5,-1,7,7,-1,-1,-1,-1,-1,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1],[315,315,-21,-21,3,-1,3,-1,1,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,E(31)^3+E(31)^6+E(31)^12+E(31)^17+E(31)^24
 ,E(31)^5+E(31)^9+E(31)^10+E(31)^18+E(31)^20,E(31)^15+E(31)^23+E(31)^27
 +E(31)^29+E(31)^30,E(31)^11+E(31)^13+E(31)^21+E(31)^22+E(31)^26,
E(31)+E(31)^2+E(31)^4+E(31)^8+E(31)^16,E(31)^7+E(31)^14+E(31)^19+E(31)^25
 +E(31)^28],
[GALOIS,[7,3]],
[GALOIS,[7,5]],
[GALOIS,[7,15]],
[GALOIS,[7,7]],
[GALOIS,[7,11]],[465,465,17,17,-15,1,1,1,1,0,0,0,3,3,-1,-1,-1,1,1,0,0,0,0,0,0,
E(7)+E(7)^2+E(7)^4,E(7)+E(7)^2+E(7)^4,E(7)+E(7)^2+E(7)^4,E(7)+E(7)^2+E(7)^4,
E(7)+E(7)^2+E(7)^4,E(7)^3+E(7)^5+E(7)^6,E(7)^3+E(7)^5+E(7)^6,
E(7)^3+E(7)^5+E(7)^6,E(7)^3+E(7)^5+E(7)^6,E(7)^3+E(7)^5+E(7)^6,0,0,0,0,0,0],
[GALOIS,[13,3]],[465,465,-31,-31,9,-3,1,1,-1,0,0,0,3,3,-1,-1,-1,1,1,0,0,0,0,0,
0,E(7)+E(7)^2+E(7)^4,E(7)+E(7)^2+E(7)^4,-E(7)-E(7)^2-E(7)^4,
-E(7)-E(7)^2-E(7)^4,E(7)+E(7)^2+E(7)^4,E(7)^3+E(7)^5+E(7)^6,
E(7)^3+E(7)^5+E(7)^6,-E(7)^3-E(7)^5-E(7)^6,-E(7)^3-E(7)^5-E(7)^6,
E(7)^3+E(7)^5+E(7)^6,0,0,0,0,0,0],
[GALOIS,[15,3]],[496,496,48,48,16,0,0,0,0,1,1,1,-8,-8,0,0,0,0,0,1,1,1,1,1,1,
-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0],[651,651,-21,-21,-5,3,3,-1,-1,6,6,
-2,0,0,0,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[651,651,-21,
-21,-5,3,3,-1,-1,-3,-3,1,0,0,0,0,0,0,0,1,1,-E(15)^7-E(15)^11-E(15)^13-E(15)^14
 ,-E(15)^7-E(15)^11-E(15)^13-E(15)^14,-E(15)-E(15)^2-E(15)^4-E(15)^8,
-E(15)-E(15)^2-E(15)^4-E(15)^8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[19,7]],[868,868,-28,-28,4,4,-4,0,0,1,1,1,7,7,-1,-1,-1,-1,-1,-2,-2,1,
1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[930,930,50,50,-6,-2,-6,-2,0,0,0,0,6,6,
2,2,2,0,0,0,0,0,0,0,0,-1,-1,1,1,-1,-1,-1,1,1,-1,0,0,0,0,0,0],[930,930,-14,-14,
-6,-2,2,2,0,0,0,0,-3,-3,1,1,1,-1,-1,0,0,0,0,0,0,2*E(7)+2*E(7)^2+2*E(7)^4,
2*E(7)+2*E(7)^2+2*E(7)^4,0,0,-E(7)-E(7)^2-E(7)^4,2*E(7)^3+2*E(7)^5+2*E(7)^6,
2*E(7)^3+2*E(7)^5+2*E(7)^6,0,0,-E(7)^3-E(7)^5-E(7)^6,0,0,0,0,0,0],
[GALOIS,[23,3]],[960,960,64,64,0,0,0,0,0,0,0,0,-6,-6,-2,-2,-2,0,0,0,0,0,0,0,0,
1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1],[1024,1024,0,0,0,0,0,0,0,4,4,0,-8,-8,0,
0,0,0,0,-1,-1,-1,-1,-1,-1,2,2,0,0,-1,2,2,0,0,-1,1,1,1,1,1,1],[1240,1240,-8,-8,
8,0,-8,0,0,-5,-5,-1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,-1,-1,1,1,1,-1,-1,1,0,0,0,0,
0,0],[248,-8,-8,8,0,0,0,0,0,-4,4,0,14,-2,2,2,-2,0,0,-2,2,1,-1,1,-1,3,-1,-1,1,
0,3,-1,-1,1,0,0,0,0,0,0,0],[1488,-48,-48,48,0,0,0,0,0,6,-6,0,0,0,0,0,0,0,0,-2,
2,1,-1,1,-1,-3,1,1,-1,0,-3,1,1,-1,0,0,0,0,0,0,0],[3720,-120,8,-8,0,0,0,0,0,0,
0,0,42,-6,-2,-2,2,0,0,0,0,0,0,0,0,3,-1,1,-1,0,3,-1,1,-1,0,0,0,0,0,0,0],[3720,
-120,8,-8,0,0,0,0,0,0,0,0,-21,3,E(3)-3*E(3)^2,-3*E(3)+E(3)^2,-1,E(3)-E(3)^2,
-E(3)+E(3)^2,0,0,0,0,0,0,3,-1,1,-1,0,3,-1,1,-1,0,0,0,0,0,0,0],
[GALOIS,[31,2]],[11160,-360,24,-24,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
3*E(7)+3*E(7)^2+3*E(7)^4,-E(7)-E(7)^2-E(7)^4,E(7)+E(7)^2+E(7)^4,
-E(7)-E(7)^2-E(7)^4,0,3*E(7)^3+3*E(7)^5+3*E(7)^6,-E(7)^3-E(7)^5-E(7)^6,
E(7)^3+E(7)^5+E(7)^6,-E(7)^3-E(7)^5-E(7)^6,0,0,0,0,0,0,0],
[GALOIS,[33,3]],[1984,-64,-64,64,0,0,0,0,0,4,-4,0,-14,2,-2,-2,2,0,0,-1,1,-1,1,
-1,1,3,-1,-1,1,0,3,-1,-1,1,0,0,0,0,0,0,0],[1736,-56,-56,56,0,0,0,0,0,2,-2,0,
14,-2,2,2,-2,0,0,1,-1,-E(15)-E(15)^2-E(15)^4-E(15)^8,E(15)+E(15)^2+E(15)^4
 +E(15)^8,-E(15)^7-E(15)^11-E(15)^13-E(15)^14,E(15)^7+E(15)^11+E(15)^13
 +E(15)^14,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[36,7]],[1736,-56,-56,56,0,0,0,0,0,-4,4,0,-7,1,3*E(3)-E(3)^2,
-E(3)+3*E(3)^2,1,-E(3)+E(3)^2,E(3)-E(3)^2,1,-1,1,-1,1,-1,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0],
[GALOIS,[38,2]],[744,-24,-24,24,0,0,0,0,0,-6,6,0,0,0,0,0,0,0,0,-1,1,-1,1,-1,1,
3*E(7)+3*E(7)^2+3*E(7)^4,-E(7)-E(7)^2-E(7)^4,-E(7)-E(7)^2-E(7)^4,
E(7)+E(7)^2+E(7)^4,0,3*E(7)^3+3*E(7)^5+3*E(7)^6,-E(7)^3-E(7)^5-E(7)^6,
-E(7)^3-E(7)^5-E(7)^6,E(7)^3+E(7)^5+E(7)^6,0,0,0,0,0,0,0],
[GALOIS,[40,3]]],
[(36,37,38,41,39,40),(26,31)(27,32)(28,33)(29,34)(30,35),(22,24)(23,25),
(15,16)(18,19),(15,16)(18,19)(22,24)(23,25),(36,40,39,41,38,37)]);
ALF("2^5.psl(5,2)","Th",[1,2,2,6,7,7,13,14,14,5,9,22,3,10,19,20,10,33,32,
8,18,25,40,26,41,12,24,24,39,31,12,24,24,39,31,42,43,42,42,43,43],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("2^5.psl(5,2)","L5(2)",[1,1,2,2,3,7,6,8,14,5,5,11,4,4,10,10,10,15,15,
9,9,18,18,19,19,12,12,16,16,20,13,13,17,17,21,22,27,24,26,25,23]);
ALN("2^5.psl(5,2)",["2^5.L5(2)"]);

MOT("2^6.U4(2)",
[
"origin: Dixon's Algorithm,\n",
"7th maximal subgroup of HN,\n",
"equal to Aut(2^{1+6}_-)',\n",
"non-split extension (table is very similar to that of split extension),\n",
"table is sorted w.r. to normal subgroup 2^6,\n",
"tests: 1.o.r., pow[2,3,5]"
],
[1658880,61440,46080,9216,3072,768,1536,512,1536,512,192,648,648,1728,288,192,
216,72,192,64,32,32,32,32,20,20,20,20,72,72,144,48,144,48,72,24,48,48,24,9,9,
12,12],
[,[1,1,1,1,1,2,1,1,2,2,3,13,12,14,14,14,17,17,4,5,8,7,10,9,25,25,25,25,13,12,
14,16,14,16,17,17,14,16,15,41,40,30,29],[1,2,3,4,5,6,7,8,9,10,11,1,1,1,3,2,1,
3,19,20,21,22,23,24,25,27,26,28,4,4,4,6,4,6,4,5,7,9,11,12,13,19,19],,[1,2,3,4,
5,6,7,8,9,10,11,13,12,14,15,16,17,18,19,20,21,22,23,24,1,2,2,3,30,29,33,34,31,
32,35,36,37,38,39,41,40,43,42]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1],[5,5,5,-3,-3,-3,1,1,1,1,1,E(3)-2*E(3)^2,-2*E(3)+E(3)^2,-1,-1,-1,2,
2,1,1,-1,-1,-1,-1,0,0,0,0,E(3)+2*E(3)^2,2*E(3)+E(3)^2,E(3)-E(3)^2,E(3)-E(3)^2,
-E(3)+E(3)^2,-E(3)+E(3)^2,0,0,1,1,1,-E(3),-E(3)^2,E(3),E(3)^2],
[GALOIS,[2,2]],[6,6,6,-2,-2,-2,2,2,2,2,2,-3,-3,3,3,3,0,0,2,2,0,0,0,0,1,1,1,1,
1,1,1,1,1,1,-2,-2,-1,-1,-1,0,0,-1,-1],[10,10,10,2,2,2,-2,-2,-2,-2,-2,
5*E(3)+2*E(3)^2,2*E(3)+5*E(3)^2,1,1,1,1,1,2,2,0,0,0,0,0,0,0,0,E(3)-2*E(3)^2,
-2*E(3)+E(3)^2,-1,-1,-1,-1,-1,-1,1,1,1,E(3)^2,E(3),-E(3),-E(3)^2],
[GALOIS,[5,2]],[15,15,15,-1,-1,-1,-1,-1,-1,-1,-1,6,6,3,3,3,0,0,3,3,-1,-1,-1,
-1,0,0,0,0,2,2,-1,-1,-1,-1,2,2,-1,-1,-1,0,0,0,0],[15,15,15,7,7,7,3,3,3,3,3,-3,
-3,0,0,0,3,3,-1,-1,1,1,1,1,0,0,0,0,1,1,-2,-2,-2,-2,1,1,0,0,0,0,0,-1,-1],[20,
20,20,4,4,4,4,4,4,4,4,2,2,5,5,5,-1,-1,0,0,0,0,0,0,0,0,0,0,-2,-2,1,1,1,1,1,1,1,
1,1,-1,-1,0,0],[24,24,24,8,8,8,0,0,0,0,0,6,6,0,0,0,3,3,0,0,0,0,0,0,-1,-1,-1,
-1,2,2,2,2,2,2,-1,-1,0,0,0,0,0,0,0],[30,30,30,-10,-10,-10,2,2,2,2,2,3,3,3,3,3,
3,3,-2,-2,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,0,0,1,1],[30,30,30,
6,6,6,2,2,2,2,2,6*E(3)-3*E(3)^2,-3*E(3)+6*E(3)^2,-3,-3,-3,0,0,2,2,0,0,0,0,0,0,
0,0,2*E(3)+E(3)^2,E(3)+2*E(3)^2,-E(3)+E(3)^2,-E(3)+E(3)^2,E(3)-E(3)^2,
E(3)-E(3)^2,0,0,-1,-1,-1,0,0,-E(3)^2,-E(3)],
[GALOIS,[12,2]],[40,40,40,-8,-8,-8,0,0,0,0,0,2*E(3)+8*E(3)^2,8*E(3)+2*E(3)^2,
-2,-2,-2,1,1,0,0,0,0,0,0,0,0,0,0,-2*E(3),-2*E(3)^2,-2*E(3),-2*E(3),-2*E(3)^2,
-2*E(3)^2,1,1,0,0,0,E(3)^2,E(3),0,0],
[GALOIS,[14,2]],[45,45,45,-3,-3,-3,-3,-3,-3,-3,-3,-9*E(3),-9*E(3)^2,0,0,0,0,0,
1,1,1,1,1,1,0,0,0,0,3*E(3),3*E(3)^2,0,0,0,0,0,0,0,0,0,0,0,E(3),E(3)^2],
[GALOIS,[16,2]],[60,60,60,-4,-4,-4,4,4,4,4,4,6,6,-3,-3,-3,-3,-3,0,0,0,0,0,0,0,
0,0,0,2,2,-1,-1,-1,-1,-1,-1,1,1,1,0,0,0,0],[64,64,64,0,0,0,0,0,0,0,0,-8,-8,4,
4,4,-2,-2,0,0,0,0,0,0,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0],[81,81,81,9,
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-1,0,0,0,0,2,-2,1,-1,-1,1,0,0,0,0,0,0,3,-1,-2,2,0,0,0,0,0],[36,4,-4,-12,4,0,8,
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0],[81,-15,9,9,9,-3,9,1,-3,5,-3,0,0,0,0,0,0,0,-3,1,1,1,-1,-1,1,
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0,0,0,0],
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0,0,1,1,-1,0,0,0,0],
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0,0,0,0,0,0],[180,20,-20,12,-4,0,12,4,0,-8,0,0,0,12,4,-4,-3,1,0,0,0,0,-2,2,0,
0,0,0,0,0,0,0,0,0,3,-1,0,0,0,0,0,0,0],[270,-50,30,6,6,-2,10,-6,-14,2,2,0,0,9,
-3,1,0,0,6,-2,0,0,0,0,0,0,0,0,0,0,-3,1,-3,1,0,0,1,1,-1,0,0,0,0],[270,-50,30,6,
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0,0,0],[360,40,-40,24,-8,0,-8,8,-16,0,0,0,0,6,2,-2,3,-1,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,-3,1,-2,2,0,0,0,0,0],[405,-75,45,-27,-27,9,9,1,-3,5,-3,0,0,0,0,0,0,
0,-3,1,-1,-1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[540,-100,60,12,12,-4,
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0,0,0],[576,64,-64,0,0,0,0,0,0,0,0,0,0,-12,-4,4,-6,2,0,0,0,0,0,0,1,-1,-1,1,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0]],
[(12,13)(29,30)(31,33)(32,34)(40,41)(42,43),(26,27)]);
ALF("2^6.U4(2)","HN",[1,3,2,3,2,6,2,3,6,6,7,5,5,4,14,15,4,14,8,7,6,7,19,
19,13,27,28,26,16,16,15,31,15,31,15,14,14,31,30,20,20,32,32],[
"fusion map is unique up to table automorphisms"
]);
ALF("2^6.U4(2)","U4(2)",[1,1,1,2,2,2,3,3,3,3,3,4,5,6,6,6,7,7,8,8,9,9,9,9,
10,10,10,10,11,12,13,13,14,14,15,15,16,16,16,17,18,19,20]);
ALF("2^6.U4(2)","S8(3)",[1,3,4,2,4,20,3,4,17,20,21,14,15,12,60,56,13,63,
19,21,21,20,68,67,23,92,92,93,62,61,49,138,50,139,57,63,59,129,143,88,89,
141,142],[
"fusion map is unique up to table automorphisms"
]);
ALF("2^6.U4(2)","2^6.U4(2).2",[1,2,3,4,5,6,7,8,9,10,11,12,12,13,14,15,16,
17,18,19,21,20,23,22,24,26,26,25,27,27,28,29,28,29,30,31,32,33,34,35,35,
36,36],[
"fusion map is unique"
]);

MOT("2^6.U4(2).2",
[
"origin: Dixon's Algorithm,\n",
"7th maximal subgroup of HN.2,\n",
"equal to Aut(2^{1+6}_-),\n",
"tests: 1.o.r., pow[2,3,5]"
],
[3317760,122880,92160,18432,6144,1536,3072,1024,3072,1024,384,648,3456,576,
384,432,144,384,128,64,64,64,64,40,40,20,72,144,48,144,48,96,96,48,9,12,7680,
4608,46080,3072,768,768,256,256,192,768,256,64,256,256,128,288,96,288,96,72,
72,24,24,16,16,20,20,24,24],
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24,25,32,33],[1,2,3,4,5,6,7,8,9,10,11,1,1,3,2,1,3,18,19,20,21,22,23,24,25,26,
4,4,6,4,5,7,9,11,12,18,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,38,37,39,
40,38,39,41,42,60,61,62,63,45,46],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,
18,19,20,21,22,23,1,3,2,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,
45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,37,39,64,65]],
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1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,
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0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[6,6,6,-2,-2,-2,2,2,2,2,
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0,0,0],[15,15,15,-1,-1,-1,-1,-1,-1,-1,-1,6,3,3,3,0,0,3,3,-1,-1,-1,-1,0,0,0,2,
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-1,1,0,0,0,0,0,0],
[TENSOR,[56,2]],[360,40,-40,-24,8,0,-16,0,-8,8,0,0,6,2,-2,3,-1,0,0,0,0,0,0,0,
0,0,0,0,0,3,-1,2,-2,0,0,0,0,-16,40,8,8,-8,0,0,0,0,0,0,0,0,0,-4,0,-2,2,-1,1,-1,
1,0,0,0,0,0,0],
[TENSOR,[58,2]],[405,-75,45,-27,-27,9,9,1,-3,5,-3,0,0,0,0,0,0,-3,1,-1,-1,1,1,
0,0,0,0,0,0,0,0,0,0,0,0,0,-15,9,45,-3,-3,-3,1,1,3,-3,-3,-1,-3,5,1,0,0,0,0,0,0,
0,0,-1,1,0,0,0,0],
[TENSOR,[60,2]],[540,-100,60,12,12,-4,-4,-4,-4,-4,4,0,-9,3,-1,0,0,0,0,0,0,0,0,
0,0,0,0,3,-1,0,0,-1,-1,1,0,0,-10,6,30,-2,6,6,-2,-2,2,-2,-2,2,-2,-2,-2,3,-1,-3,
1,0,0,0,0,0,0,0,0,-1,1],
[TENSOR,[62,2]],[576,64,-64,0,0,0,0,0,0,0,0,0,-12,-4,4,-6,2,0,0,0,0,0,0,1,1,
-1,0,0,0,0,0,0,0,0,0,0,-16,-16,16,16,0,0,0,0,0,0,0,0,0,0,0,2,2,-2,-2,2,-2,0,0,
0,0,-1,1,0,0],
[TENSOR,[64,2]]],
[]);
ALF("2^6.U4(2).2","HN.2",[1,3,2,3,2,6,2,3,6,6,7,5,4,13,14,4,13,8,7,7,6,18,
18,12,24,25,15,14,28,14,13,13,28,27,19,29,45,45,46,47,45,47,48,47,47,53,
52,48,53,52,53,49,50,58,59,50,58,50,59,54,55,57,64,59,67],[
"fusion map is unique"
]);
ALF("2^6.U4(2).2","U4(2).2",[1,1,1,2,2,2,3,3,3,3,3,4,5,5,5,6,6,7,7,8,8,8,
8,9,9,9,10,11,11,12,12,13,13,13,14,15,16,16,16,16,17,17,17,17,18,18,18,19,
19,19,19,20,20,20,20,21,21,22,22,23,23,24,24,25,25]);

MOT("2^6:u3(3):2",
[
"origin: CAS library,\n",
"maximal subgroup of Ru,\n",
"  structure:= 2^6:U(3,3):2\n",
"  1st & 2nd orthogonality relations are satisfied\n",
"  symmetric squares decompose properly\n",
"  created september 1984,\n",
"tests: 1.o.r., pow[2,3,7]"
],
[774144,12288,3072,1024,256,216,72,24,384,128,128,128,64,24,7,16,16,12,384,
384,192,128,64,128,12,16,16,12,12,12],
[,[1,1,1,1,2,6,7,7,3,4,3,4,4,6,15,9,10,14,1,2,3,2,4,2,7,12,11,8,14,14],[1,2,3,
4,5,1,1,2,9,10,11,12,13,3,15,16,17,9,19,20,21,22,23,24,19,26,27,20,21,21],,,,[
1,2,3,4,5,6,7,8,9,10,11,12,13,14,1,16,17,18,19,20,21,22,23,24,25,26,27,28,29,
30]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[6,6,-2,-2,-2,-3,0,
0,-2,-2,2,2,2,1,-1,0,0,1,0,0,0,0,0,0,0,0,0,0,E(3)-E(3)^2,-E(3)+E(3)^2],
[TENSOR,[3,2]],[7,7,-1,-1,-1,-2,1,1,3,3,-1,-1,-1,2,0,-1,-1,0,1,1,-3,1,-3,1,1,
-1,-1,1,0,0],
[TENSOR,[5,2]],[14,14,6,6,6,-4,2,2,-2,-2,2,2,2,0,0,0,0,-2,0,0,0,0,0,0,0,0,0,0,
0,0],[14,14,-2,-2,-2,5,-1,-1,2,2,2,2,2,1,0,0,0,-1,2,2,-2,2,-2,2,-1,0,0,-1,1,
1],
[TENSOR,[8,2]],[21,21,5,5,5,3,0,0,1,1,1,1,1,-1,0,-1,-1,1,3,3,-1,3,-1,3,0,1,1,
0,-1,-1],
[TENSOR,[10,2]],[27,27,3,3,3,0,0,0,3,3,-1,-1,-1,0,-1,1,1,0,3,3,3,3,3,3,0,-1,
-1,0,0,0],
[TENSOR,[12,2]],[42,42,2,2,2,6,0,0,-6,-6,-2,-2,-2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0],[56,56,-8,-8,-8,2,2,2,0,0,0,0,0,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[
63,-1,15,-1,-1,0,3,-1,3,-1,3,-1,-1,0,0,1,-1,0,-1,7,3,-1,-1,-1,-1,-1,1,1,0,0],[
63,-1,-9,7,-1,0,3,-1,3,-1,-1,3,-1,0,0,-1,1,0,5,1,-3,-3,1,1,-1,1,-1,1,0,0],
[TENSOR,[16,2]],
[TENSOR,[17,2]],[64,64,0,0,0,-8,-2,-2,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0],[126,-2,6,6,-2,0,-3,1,6,-2,2,2,-2,0,0,0,0,0,4,8,0,-4,0,0,1,0,0,-1,0,0],
[TENSOR,[21,2]],[189,-3,21,5,-3,0,0,0,-3,1,1,-3,1,0,0,-1,1,0,9,-3,-3,1,1,-3,0,
-1,1,0,0,0],[189,-3,-3,13,-3,0,0,0,-3,1,-3,1,1,0,0,1,-1,0,3,3,3,3,-1,-5,0,1,
-1,0,0,0],
[TENSOR,[24,2]],
[TENSOR,[23,2]],[378,-6,18,-14,2,0,0,0,-6,2,-2,6,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0],[378,-6,-30,2,2,0,0,0,-6,2,6,-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0],[378,-6,-6,-6,2,0,0,0,6,-2,-2,-2,2,0,0,0,0,0,-6,6,-6,2,2,-2,0,0,0,0,0,0],
[TENSOR,[29,2]]],
[(29,30)]);
ARC("2^6:u3(3):2","projectives",["2.2^6:u3(3):2",[[28,4,4,-4,0,-1,-1,1,4,0,0,
0,0,1,0,2*E(4),0,1,-4,4,-4*E(4),0,0,0,1,0,0,-1,-E(4),-E(4)],
[GALOIS,[1,3]],[36,-4,12,4,0,0,-3,-1,0,0,-4,0,0,0,-1,0,0,0,4,4,0,0,0,0,-1,0,2,
-1,0,0],[56,8,8,-8,0,-2,-2,2,-8,0,0,0,0,2,0,0,0,-2,0,0,0,0,0,0,0,0,0,0,0,0],[
56,8,-8,8,0,-2,-2,2,0,0,0,0,0,-2,0,0,-2*E(8)+2*E(8)^3,0,0,0,0,0,0,0,0,0,0,0,0,
0],
[GALOIS,[5,3]],[168,24,-8,8,0,3,0,0,8,0,0,0,0,1,0,0,0,-1,0,0,8*E(4),0,0,0,0,0,
0,0,-E(4),-E(4)],[168,24,-8,8,0,3,0,0,-8,0,0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,
0,-E(12)^7+E(12)^11,E(12)^7-E(12)^11],[216,-24,-24,-8,0,0,0,0,0,0,-8,0,0,0,1,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[216,-24,24,8,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,
0,0,0,0,0,-2*E(8)+2*E(8)^3,0,0,0,0],[224,32,0,0,0,-8,1,-1,0,0,0,0,0,0,0,0,0,0,
8,-8,0,0,0,0,1,0,0,-1,0,0],[252,-28,-12,-4,0,0,-3,-1,0,0,4,0,0,0,0,0,0,0,-4,
-4,0,0,0,0,1,0,2,1,0,0],[288,-32,0,0,0,0,3,1,0,0,0,0,0,0,-1,0,0,0,-8,-8,0,0,0,
0,-1,0,0,-1,0,0],[336,48,16,-16,0,6,0,0,0,0,0,0,0,-2,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0]],]);
ALF("2^6:u3(3):2","Ru",[1,2,2,2,7,4,4,11,5,8,8,8,7,11,12,13,15,18,2,5,6,7,
7,8,11,15,15,18,19,19],[
"fusion map is unique, equal to that on the CAS table"
]);
ALF("2^6:u3(3):2","U3(3).2",[1,1,2,2,2,3,4,4,5,5,6,6,6,7,8,9,9,10,11,11,
12,11,12,11,13,14,14,13,15,16]);

MOT("2xa6.2^2",
[
"origin: CAS library,\n",
"11th maximal subgroup of HS,\n",
"tests: 1.o.r., pow[2,3,5]"
],
[2880,64,36,32,20,16,16,96,80,32,12,16,20,2880,64,36,32,20,16,16,96,80,32,12,
16,20],
[,[1,1,3,2,5,2,4,1,1,2,3,4,5,1,1,3,2,5,2,4,1,1,2,3,4,5],[1,2,1,4,5,6,7,8,9,10,
8,12,13,14,15,14,17,18,19,20,21,22,23,21,25,26],,[1,2,3,4,1,6,7,8,9,10,11,12,
9,14,15,16,17,14,19,20,21,22,23,24,25,22]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,-1,-1,
-1,-1,-1,-1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1],[1,1,1,1,1,-1,-1,1,-1,1,1,-1,-1,
1,1,1,1,1,-1,-1,1,-1,1,1,-1,-1],
[TENSOR,[2,3]],[9,1,0,1,-1,1,-1,3,-1,-1,0,1,-1,9,1,0,1,-1,1,-1,3,-1,-1,0,1,
-1],
[TENSOR,[5,2]],
[TENSOR,[5,3]],
[TENSOR,[5,4]],[10,2,1,-2,0,0,0,2,0,2,-1,0,0,10,2,1,-2,0,0,0,2,0,2,-1,0,0],
[TENSOR,[9,2]],[16,0,-2,0,1,0,0,0,4,0,0,0,-1,16,0,-2,0,1,0,0,0,4,0,0,0,-1],
[TENSOR,[11,2]],[20,-4,2,0,0,0,0,0,0,0,0,0,0,20,-4,2,0,0,0,0,0,0,0,0,0,0],[1,
1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],
[TENSOR,[2,14]],
[TENSOR,[3,14]],
[TENSOR,[2,16]],
[TENSOR,[5,14]],
[TENSOR,[5,15]],
[TENSOR,[5,16]],
[TENSOR,[5,17]],
[TENSOR,[9,14]],
[TENSOR,[9,15]],
[TENSOR,[11,14]],
[TENSOR,[11,15]],
[TENSOR,[13,14]]],
[( 6,19)( 7,20)( 8,21)(10,23)(11,24),( 6,19)( 7,20)( 9,22)(12,25)(13,26)]);
ARC("2xa6.2^2","projectives",["2.HSM11",[[2,-2,2,-2,2,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,-2*E(4),0,-2*E(4),-2*E(4),0,0],[10,-2,1,2,0,0,0,-4,0,0,-1,0,0,0,0,3*E(4)
,0,0,0,0,2*E(4),0,2*E(4),-E(4),0,0],[18,-2,0,-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,6*E(4),0,-2*E(4),0,0,0],[20,4,2,0,0,0,0,4,0,0,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0],[32,0,-4,0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]],]);
ARC("2xa6.2^2","tomfusion",rec(name:="2xA6.2^2",map:=[1,2,9,15,30,10,72,3,5,
20,33,67,83,8,6,34,12,88,11,76,7,4,23,36,75,82],text:=[
"fusion map is unique up to table automorphisms"
]));
ALF("2xa6.2^2","HS",[1,2,4,7,9,7,15,2,3,7,12,15,18,3,3,11,6,18,7,16,3,3,5,11,
16,18],[
"fusion is unique up to table automorphisms,\n",
"chosen compatibly with the fusion 2.HSM11 -> 2.HS"
]);
ALF("2xa6.2^2","A6.2^2",[1,2,3,4,5,12,13,6,9,7,8,10,11,1,2,3,4,5,12,13,6,
9,7,8,10,11]);
ALF("2xa6.2^2","(2xA6.2^2).2",[1,9,12,15,22,20,32,6,10,16,29,30,35,2,8,23,
14,34,20,32,7,10,17,28,30,35],[
"fusion map is unique up to table automorphisms"
]);
ALF("2xa6.2^2","U4(3).(2^2)_{133}",[1,2,5,6,8,7,12,15,16,18,21,22,23,27,
27,29,28,33,28,31,36,36,37,38,39,42],[
"determined as extension from A6.2^2 < U4(3).2_1"
]);
ALN("2xa6.2^2",["HSC2B","HSN2B"]);

MOT("U4(3).(2^2)_{133}M11",
0,
0,
0,
0,
0,
["ConstructPermuted",["2xa6.2^2"]]);
ALF("U4(3).(2^2)_{133}M11","U4(3).(2^2)_{133}",[1,2,5,6,8,7,12,15,16,18,
21,22,23,36,36,38,37,42,37,40,27,27,28,29,30,33],[
"fusion 2xa6.2^2 -> U4(3).(2^2)_{133} mapped under U4(3).D8"
]);

MOT("U4(3).(2^2)_{133}M12",
0,
0,
0,
0,
0,
["ConstructPermuted",["2xa6.2^2"]]);
ALF("U4(3).(2^2)_{133}M12","U4(3).(2^2)_{133}",[1,2,4,7,8,28,32,2,27,7,10,
32,33,16,16,20,17,23,37,41,16,36,18,20,41,42],[
"determined as novelty extending S6x2 < U4(2):2 < U4(3).2_1"
]);

MOT("(2xA6.2^2).2",
[
"8th maximal subgroup of HS.2,\n",
"origin: Dixon's Algorithm"
],
[5760,5760,2880,192,192,192,192,128,128,80,64,72,80,64,64,64,64,32,32,16,16,40
,72,72,72,24,24,24,24,16,16,16,16,40,20,20,20],
[,[1,1,1,1,1,1,1,1,1,1,1,12,2,9,9,9,9,9,9,9,8,22,12,12,12,12,12,12,12,15,14,15
,14,22,22,22,34],[1,2,3,4,5,6,7,8,9,10,11,1,13,14,15,16,17,18,19,20,21,22,2,3,
3,5,4,7,6,30,31,32,33,34,35,36,37],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17
,18,19,20,21,1,23,24,25,26,27,28,29,30,31,32,33,2,10,3,13]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[
1,1,-1,-1,-1,1,1,1,1,-1,-1,1,1,1,1,1,1,-1,-1,-1,1,1,1,-1,-1,-1,-1,1,1,-1,1,-1,
1,1,-1,-1,1],[1,1,-1,1,1,-1,-1,1,1,-1,-1,1,1,1,1,-1,-1,-1,1,1,-1,1,1,-1,-1,1,1
,-1,-1,-1,1,1,-1,1,-1,-1,1],[1,1,-1,-1,-1,1,1,1,1,1,-1,1,-1,1,1,1,1,-1,-1,1,-1
,1,1,-1,-1,-1,-1,1,1,1,-1,1,-1,1,1,-1,-1],[1,1,-1,1,1,-1,-1,1,1,1,-1,1,-1,1,1,
-1,-1,-1,1,-1,1,1,1,-1,-1,1,1,-1,-1,1,-1,-1,1,1,1,-1,-1],
[TENSOR,[2,5]],
[TENSOR,[2,4]],
[TENSOR,[2,3]],[2,-2,0,0,0,2,-2,-2,2,0,0,2,0,-2,2,2,-2,0,0,0,0,2,-2,0,0,0,0,
-2,2,0,0,0,0,-2,0,0,0],
[TENSOR,[9,3]],[9,9,-9,-3,-3,3,3,1,1,1,-1,0,-1,1,1,-1,-1,-1,1,-1,1,-1,0,0,0,0
,0,0,0,-1,1,1,-1,-1,1,1,-1],
[TENSOR,[11,8]],
[TENSOR,[11,7]],
[TENSOR,[11,6]],
[TENSOR,[11,5]],
[TENSOR,[11,4]],
[TENSOR,[11,3]],
[TENSOR,[11,2]],[10,10,-10,2,2,-2,-2,2,2,0,-2,1,0,-2,-2,-2,-2,2,2,0,0,0,1,-1,
-1,-1,-1,1,1,0,0,0,0,0,0,0,0],
[TENSOR,[19,6]],
[TENSOR,[19,3]],
[TENSOR,[19,2]],[10,-10,0,4,-4,2,-2,-2,2,0,0,1,0,2,-2,2,-2,0,0,0,0,0,-1,-3,3,
-1,1,1,-1,0,0,0,0,0,0,0,0],
[TENSOR,[23,6]],
[TENSOR,[23,3]],
[TENSOR,[23,2]],[16,16,-16,0,0,0,0,0,0,-4,0,-2,4,0,0,0,0,0,0,0,0,1,-2,2,2,0,0
,0,0,0,0,0,0,1,1,-1,-1],
[TENSOR,[27,6]],
[TENSOR,[27,2]],
[TENSOR,[27,4]],[18,-18,0,0,0,-6,6,-2,2,0,0,0,0,-2,2,2,-2,0,0,0,0,-2,0,0,0,0,
0,0,0,0,0,0,0,2,0,0,0],
[TENSOR,[31,3]],[20,-20,0,4,-4,0,0,4,-4,0,0,2,0,0,0,0,0,0,0,0,0,0,-2,0,0,2,-2
,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[33,2]],[20,20,-20,0,0,0,0,-4,-4,0,4,2,0,0,0,0,0,0,0,0,0,0,2,-2,-2,0,
0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[35,2]],[32,-32,0,0,0,0,0,0,0,0,0,-4,0,0,0,0,0,0,0,0,0,2,4,0,0,0,0,0,
0,0,0,0,0,-2,0,0,0]],
[( 4, 5)( 6, 7)(16,17)(26,27)(28,29),( 6, 7)(16,17)(24,25)(28,29)]);
ALF("(2xA6.2^2).2","HS.2",[1,3,22,22,23,2,3,3,2,3,23,4,26,6,7,7,5,25,25,7,
26,9,11,27,28,29,28,11,12,15,30,15,31,17,17,32,36],[
"fusion map is unique up to table automorphisms"
]);

MOT("2.HSM11",
[
"origin: Dixon's Algorithm"
],
[5760,5760,128,128,72,72,64,64,40,40,16,16,192,192,80,32,24,24,16,20,2880,64,
72,72,32,20,16,16,192,192,80,64,64,24,24,16,20],
[,[1,1,1,1,5,5,4,4,9,9,4,8,1,1,2,4,5,5,7,10,2,2,6,6,3,10,4,8,2,2,2,3,3,6,6,7,
10],[1,2,3,4,1,2,7,8,9,10,11,12,13,14,15,16,13,14,19,20,21,22,21,21,25,26,27,
28,30,29,31,33,32,30,29,36,37],,[1,2,3,4,5,6,7,8,1,2,11,12,13,14,15,16,17,18,
19,15,21,22,23,24,25,21,27,28,29,30,31,32,33,34,35,36,31]],
0,
[(11,27)(12,28)(15,31)(19,36)(20,37),(13,14)(17,18)(29,30)(32,33)(34,35),(23,
24)(29,30)(32,33)(34,35)],
["ConstructProj",[["2xa6.2^2",[]],["2.HSM11",[]]]]);
ALF("2.HSM11","2xa6.2^2",[1,1,2,2,3,3,4,4,5,5,6,7,8,8,9,10,11,11,12,13,14,
15,16,16,17,18,19,20,21,21,22,23,23,24,24,25,26]);
ALF("2.HSM11","2.HS",[1,2,4,3,6,7,11,11,14,15,11,26,3,4,5,11,20,21,26,30,
5,5,18,19,10,30,11,27,5,5,5,9,8,19,18,27,30],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("2.HSM11","2F4(2)'M7",[1,1,2,2,3,3,4,4,5,5,12,13,6,6,9,7,8,8,10,11,1,
2,3,3,4,5,12,13,6,6,9,7,7,8,8,10,11]);

MOT("3.3^(1+4):2S5",
[
"origin: computed from factor group 3^(1+4):2S5 and 3.McL,\n",
"maximal subgroup of 3.Mcl,\n",
"characters are sorted w.r. to normal series given by 3.3.3^4.2.A5.2,\n",
"3rd power map determined only up to matrix automorphism (41,42),\n",
"tests: 1.o.r., pow[2,3,5]"
],
[174960,174960,174960,87480,87480,87480,243,2160,2160,2160,1080,1080,1080,72,
72,72,36,36,36,972,972,972,486,486,486,27,27,54,54,54,108,108,108,90,90,90,90,
90,90,90,90,90,90,90,90,90,90,90,90,90,90,36,36,36,24,24,24,24,24,24,36,36,36,
36,36,36],
[,[1,3,2,4,6,5,7,1,3,2,4,6,5,8,10,9,11,13,12,20,22,21,23,25,24,27,26,23,25,24,
20,22,21,34,36,35,37,39,38,40,42,41,34,36,35,37,39,38,40,42,41,8,10,9,14,16,
15,14,16,15,31,33,32,31,33,32],[1,1,1,1,1,1,1,8,8,8,8,8,8,14,14,14,14,14,14,1,
1,1,1,1,1,5,6,8,8,8,8,8,8,34,34,34,34,34,34,34,34,34,43,43,43,43,43,43,43,43,
43,52,52,52,58,58,58,55,55,55,52,52,52,52,52,52],,[1,3,2,4,6,5,7,8,10,9,11,13,
12,14,16,15,17,19,18,20,22,21,23,25,24,27,26,28,30,29,31,33,32,1,3,2,4,6,5,4,
6,5,8,10,9,11,13,12,11,13,12,52,54,53,58,60,59,55,57,56,64,66,65,61,63,62]],
0,
[(37,40)(38,41)(39,42)(46,49)(47,50)(48,51),(55,58)(56,59)(57,60),(61,64)
(62,65)(63,66),( 2, 3)( 5, 6)( 9,10)(12,13)(15,16)(18,19)(21,22)(24,25)(26,27)
(29,30)(32,33)(35,36)(38,39)(41,42)(44,45)(47,48)(50,51)(53,54)(56,57)(59,60)
(62,63)(65,66)],
["ConstructProj",[["3^(1+4):2S5",[]],,["3.3^(1+4):2S5",[-1,-1,-1,-1,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1]]]]);
ALF("3.3^(1+4):2S5","3^(1+4):2S5",[1,1,1,2,2,2,3,4,4,4,5,5,5,6,6,6,7,7,7,
8,8,8,9,9,9,10,11,12,12,12,13,13,13,14,14,14,15,15,15,16,16,16,17,17,17,
18,18,18,19,19,19,20,20,20,21,21,21,22,22,22,23,23,23,24,24,24]);
ALF("3.3^(1+4):2S5","3.McL",[1,3,2,7,9,8,10,4,6,5,20,22,21,11,13,12,46,48,
47,7,9,8,10,10,10,36,35,23,25,24,20,22,21,14,16,15,55,57,56,58,60,59,37,
39,38,61,63,62,64,66,65,11,13,12,32,34,33,32,34,33,46,48,47,46,48,47],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("3.3^(1+4):2S5","3.3^(1+4):4S5",[1,2,2,3,4,4,5,6,7,7,8,9,9,10,11,11,
12,13,13,14,15,15,16,17,17,18,18,19,20,20,21,22,22,23,24,24,25,26,27,25,
27,26,28,29,29,30,31,32,30,32,31,33,34,34,35,36,37,35,37,36,38,39,40,38,
40,39]);
ALF("3.3^(1+4):2S5","Isoclinic(2.A5.2)",[1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,
3,3,3,4,4,4,4,4,4,4,4,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,8,8,
8,9,9,9,10,10,10,11,11,11,12,12,12]);

MOT("3.3^(1+4):4S5",
[
"maximal subgroup of 3.McL.2,\n",
"tests: 1.o.r., pow[2,3,5]"
],
[349920,174960,174960,87480,486,4320,2160,2160,1080,144,72,72,36,1944,972,972,
486,27,108,54,216,108,180,90,90,90,90,180,90,90,90,90,72,36,24,24,24,36,36,36,
240,18,144,12,20,20,72,36,24,24,24,36,36,36],
[,[1,2,3,4,5,1,2,3,4,6,7,8,9,14,15,16,17,18,16,17,14,15,23,24,25,27,26,23,24,
25,27,26,6,7,10,11,11,21,22,22,6,5,1,21,28,28,6,8,10,12,12,21,19,19],[1,1,1,1,
1,6,6,6,6,10,10,10,10,1,1,1,1,4,6,6,6,6,23,23,23,23,23,28,28,28,28,28,33,33,
35,35,35,33,33,33,41,43,43,41,45,46,47,47,49,49,49,47,47,47],,[1,2,3,4,5,6,7,
8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,1,2,3,4,4,6,7,8,9,9,33,34,35,36,37,
38,39,40,41,42,43,44,41,41,47,48,49,50,51,52,53,54]],
0,
[(50,51),(45,46),(36,37),(26,27)(31,32),(53,54),(39,40),( 2, 3)( 7, 8)(11,12)
(15,16)(19,22)(24,25)(29,30)(33,47)(34,48)(35,49)(36,50)(37,51)(38,52)(39,53)
(40,54)],
["ConstructMGA","3.3^(1+4):2S5","3^(1+4):4S5",[[25,27],[26,28],[29,30],[31,
33],[32,34],[35,38],[36,37],[39,40],[41,42],[43,44],[45,47],[46,48],[49,50],
[51,52],[53,54],[55,58],[56,57],[59,60],[61,62],[63,64],[65,66]],()]);
ALF("3.3^(1+4):4S5","3^(1+4):4S5",[1,1,2,2,3,4,4,5,5,6,6,7,7,8,8,9,9,10,
11,11,12,12,13,13,14,14,14,15,15,16,16,16,17,17,18,18,18,19,19,19,20,21,
22,23,24,25,26,27,28,29,30,31,32,33]);
ALF("3.3^(1+4):4S5","3.McL.2",[1,2,5,6,7,3,4,14,15,8,9,30,31,5,6,7,7,23,
16,17,14,15,10,11,35,36,37,24,25,38,39,40,8,9,21,22,22,30,31,31,42,43,41,
47,49,50,42,47,44,53,54,47,48,48],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("3.3^(1+4):4S5","3^(2+4):2A5.D8",[1,2,2,3,4,5,6,6,7,8,9,9,10,11,12,12,
13,14,15,16,17,15,18,19,19,20,20,21,22,22,23,23,24,25,26,27,28,29,30,31,
32,33,34,35,36,37,24,25,26,27,28,29,30,31],[
"fusion is unique up to table automorphisms"
]);

MOT("2^(1+3):L3(2)",
[
"origin: Dixon's Algorithm,\n",
"table of the intersection of maximal subgroups 2.A8 and 2^4:A7 in McL"
],
[2688,2688,192,32,16,32,12,12,12,12,8,8,14,14,14,14],
[,[1,1,1,2,3,1,7,7,7,7,4,6,13,13,15,15],[1,2,3,4,5,6,1,2,3,3,11,12,15,16,13,
14],,,,[1,2,3,4,5,6,7,8,9,10,11,12,1,2,1,2]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[3,3,3,-1,-1,-1,0,0,0,0,1,1,
E(7)+E(7)^2+E(7)^4,E(7)+E(7)^2+E(7)^4,E(7)^3+E(7)^5+E(7)^6,
E(7)^3+E(7)^5+E(7)^6],
[GALOIS,[2,3]],[6,6,6,2,2,2,0,0,0,0,0,0,-1,-1,-1,-1],[7,7,7,-1,-1,-1,1,1,1,1,
-1,-1,0,0,0,0],[8,8,8,0,0,0,-1,-1,-1,-1,0,0,1,1,1,1],[7,7,-1,3,-1,-1,1,1,-1,
-1,1,-1,0,0,0,0],[7,7,-1,-1,-1,3,1,1,-1,-1,-1,1,0,0,0,0],[14,14,-2,2,-2,2,-1,
-1,1,1,0,0,0,0,0,0],[21,21,-3,1,1,-3,0,0,0,0,-1,1,0,0,0,0],[21,21,-3,-3,1,1,0,
0,0,0,1,-1,0,0,0,0],[8,-8,0,0,0,0,2,-2,0,0,0,0,1,-1,1,-1],[8,-8,0,0,0,0,-1,1,
E(3)-E(3)^2,-E(3)+E(3)^2,0,0,1,-1,1,-1],
[GALOIS,[13,2]],[24,-24,0,0,0,0,0,0,0,0,0,0,E(7)^3+E(7)^5+E(7)^6,
-E(7)^3-E(7)^5-E(7)^6,E(7)+E(7)^2+E(7)^4,-E(7)-E(7)^2-E(7)^4],
[GALOIS,[15,3]]],
[( 9,10),(13,15)(14,16)]);
ALF("2^(1+3):L3(2)","2^3:sl(3,2)",[1,1,2,4,5,3,8,8,9,9,7,6,10,10,11,11]);
ALF("2^(1+3):L3(2)","L3(2)",[1,1,1,2,2,2,3,3,3,3,4,4,5,5,6,6]);
ALF("2^(1+3):L3(2)","2.A8",[1,2,3,4,9,3,7,8,14,15,10,9,16,17,18,19],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("2^(1+3):L3(2)","2^4:a7",[1,2,2,4,4,3,6,7,7,7,9,8,12,13,14,15],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("2^(1+3):L3(2)","McL",[1,2,2,5,5,2,4,9,9,9,12,5,10,19,11,20],[
"fusion map is unique up to table automorphisms"
]);

MOT("2^(2+4):(3x3):2",
[
"origin: Dixon's Algorithm,\n",
"table of the intersection of (nonconjugate) maximal subgroups\n",
"2^4:A7 and 2^4:A7 in McL"
],
[1152,384,96,96,32,36,36,36,9,12,12,12,16,16,8,8,8],
[,[1,1,1,1,2,6,7,8,9,6,7,8,1,2,3,4,5],[1,2,3,4,5,1,1,1,1,2,4,3,13,14,15,16,
17]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,
-1],[2,2,2,2,2,-1,-1,-1,2,-1,-1,-1,0,0,0,0,0],[2,2,2,2,2,2,-1,-1,-1,2,-1,-1,0,
0,0,0,0],[2,2,2,2,2,-1,2,-1,-1,-1,2,-1,0,0,0,0,0],[2,2,2,2,2,-1,-1,2,-1,-1,-1,
2,0,0,0,0,0],[3,3,-1,3,-1,0,0,3,0,0,0,-1,-1,-1,1,-1,1],[3,3,3,-1,-1,0,3,0,0,0,
-1,0,-1,-1,-1,1,1],
[TENSOR,[7,2]],
[TENSOR,[8,2]],[6,6,-2,6,-2,0,0,-3,0,0,0,1,0,0,0,0,0],[6,6,6,-2,-2,0,-3,0,0,0,
1,0,0,0,0,0,0],[9,9,-3,-3,1,0,0,0,0,0,0,0,-1,-1,1,1,-1],
[TENSOR,[13,2]],[12,-4,0,0,0,3,0,0,0,-1,0,0,2,-2,0,0,0],
[TENSOR,[15,2]],[24,-8,0,0,0,-3,0,0,0,1,0,0,0,0,0,0,0]],
[( 3, 4)( 7, 8)(11,12)(15,16)]);
ARC("2^(2+4):(3x3):2","projectives",["3.2^(2+4):(3x3):2",[[3,3,3,3,3,0,0,0,0,
0,0,0,1,1,1,1,1],[3,3,-1,3,-1,0,0,0,0,0,0,2,-1,-1,1,-1,1],[3,3,3,-1,-1,0,0,0,
0,0,2,0,-1,-1,-1,1,1],[6,6,-2,6,-2,0,0,0,0,0,0,-2,0,0,0,0,0],[6,6,6,-2,-2,0,0,
0,0,0,-2,0,0,0,0,0,0],[9,9,-3,-3,1,0,0,0,0,0,0,0,1,1,-1,-1,1],[12,-4,0,0,0,0,
0,0,0,2,0,0,-2,2,0,0,0],[24,-8,0,0,0,0,0,0,0,-2,0,0,0,0,0,0,0]],]);
ALF("2^(2+4):(3x3):2","2^4:a7",[1,2,2,3,4,6,5,6,5,7,11,7,3,4,4,8,9],[
"fusion map is unique up to table automorphisms"
]);
ALF("2^(2+4):(3x3):2","McLM10",[1,2,2,3,4,6,5,6,5,7,11,7,3,4,4,8,9],[
"fusion map is unique up to table automorphisms"
]);
ALF("2^(2+4):(3x3):2","McL",[1,2,2,2,5,4,4,4,4,9,9,9,2,5,5,5,12],[
"fusion map is unique"
]);
ALF("2^(2+4):(3x3):2","2^(2+4):(S3xS3)",[1,2,3,3,4,9,10,10,5,11,12,12,16,17,
18,18,22],[
"fusion map is unique"
]);
ALF("2^(2+4):(3x3):2","M23",[1,2,2,2,4,3,3,3,3,6,6,6,2,4,4,4,9],[
"fusion map is unique"
]);

MOT("3.2^(2+4):(3x3):2",
[
"origin: constructed by Thomas Breuer 1996/09/17 using the tables of\n",
"2^(2+4):(3x3):2, 2^4:a7, and 3.2^4:a7,\n",
"table of the intersection of (nonconjugate) maximal subgroups\n",
"3.2^4:A7 and 3.2^4:A7 in 3.McL"
],
[3456,3456,3456,1152,1152,1152,288,288,288,288,288,288,96,96,96,36,36,36,9,36,
36,36,36,36,36,36,36,36,48,48,48,48,48,48,24,24,24,24,24,24,24,24,24],
[,[1,3,2,1,3,2,1,3,2,1,3,2,4,6,5,16,17,18,19,16,16,16,17,17,17,18,18,18,1,3,2,
4,6,5,7,9,8,10,12,11,13,15,14],[1,1,1,4,4,4,7,7,7,10,10,10,13,13,13,1,1,1,1,4,
4,4,10,10,10,7,7,7,29,29,29,32,32,32,35,35,35,38,38,38,41,41,41]],
0,
[(2,3)(5,6)(8,9)(11,12)(14,15)(21,22)(24,25)(27,28)(30,31)(33,34)(36,37)(39,
40)(42,43),(7,10)(8,11)(9,12)(17,18)(23,26)(24,27)(25,28)(35,38)(36,39)(37,
40)],
["ConstructProj",[["2^(2+4):(3x3):2",[]],,["3.2^(2+4):(3x3):2",[-1,-1,-1,-1,
-1,-1,-1,-1]]]]);
ALF("3.2^(2+4):(3x3):2","2^(2+4):(3x3):2",[1,1,1,2,2,2,3,3,3,4,4,4,5,5,5,
6,7,8,9,10,10,10,11,11,11,12,12,12,13,13,13,14,14,14,15,15,15,16,16,16,17,
17,17]);
ALF("3.2^(2+4):(3x3):2","3.2^4:a7",[1,2,3,4,5,6,4,5,6,7,8,9,10,11,12,14,
13,14,13,15,16,17,27,28,29,15,16,17,7,8,9,10,11,12,10,11,12,18,19,20,21,
22,23],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("3.2^(2+4):(3x3):2","3.McLM10",[1,2,3,4,5,6,4,5,6,7,8,9,10,11,12,14,
13,14,13,15,16,17,27,28,29,15,16,17,7,8,9,10,11,12,10,11,12,18,19,20,21,
22,23],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("3.2^(2+4):(3x3):2","3.McL",[1,2,3,4,5,6,4,5,6,4,5,6,11,12,13,10,10,
10,10,23,24,25,23,24,25,23,24,25,4,5,6,11,12,13,11,12,13,11,12,13,32,33,
34],[
"fusion map is unique up to table automorphisms"
]);
ALF("3.2^(2+4):(3x3):2","3.2^(2+4):(S3xS3)",[1,2,2,3,4,4,5,6,7,5,7,6,8,9,
9,10,11,11,12,13,14,14,15,16,17,15,17,16,18,19,19,20,21,21,22,23,24,22,24,
23,25,26,26]);

MOT("2^(1+1+2+2):S3",
[
"origin: Dixon's Algorithm,\n",
"table of the intersection of maximal subgroups 2^4:A7, 2^4:A7, and 2.A8\n",
"in McL"
],
[384,384,192,32,32,16,32,12,12,12,12,16,8,8,16,8],
[,[1,1,1,1,1,3,2,8,8,8,8,1,4,5,2,7],[1,2,3,4,5,6,7,1,2,3,3,12,13,14,15,16],,[
1,2,3,4,5,6,7,8,9,11,10,12,13,14,15,16],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,
16]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1],[2,
2,2,2,2,2,2,-1,-1,-1,-1,0,0,0,0,0],[3,3,3,3,-1,-1,-1,0,0,0,0,-1,-1,1,-1,1],
[TENSOR,[4,2]],[3,3,3,-1,-1,-1,3,0,0,0,0,-1,1,1,-1,-1],
[TENSOR,[6,2]],[3,3,3,-1,3,-1,-1,0,0,0,0,-1,1,-1,-1,1],
[TENSOR,[8,2]],[6,6,6,-2,-2,2,-2,0,0,0,0,0,0,0,0,0],[4,4,-4,0,0,0,0,1,1,-1,-1,
-2,0,0,2,0],
[TENSOR,[11,2]],[8,8,-8,0,0,0,0,-1,-1,1,1,0,0,0,0,0],[8,-8,0,0,0,0,0,2,-2,0,0,
0,0,0,0,0],[8,-8,0,0,0,0,0,-1,1,E(3)-E(3)^2,-E(3)+E(3)^2,0,0,0,0,0],
[GALOIS,[15,2]]],
[(10,11),( 4, 5)(13,14)]);
ALF("2^(1+1+2+2):S3","2^(1+3):L3(2)",[1,2,3,3,6,5,4,7,8,9,10,6,5,12,4,11],[
"fusion map is unique up to table automorphisms"
]);
ALF("2^(1+1+2+2):S3","2^(2+4):(3x3):2",[1,2,2,3,4,5,5,6,10,10,10,13,15,16,14,
17],[
"fusion map is unique up to table automorphisms"
]);
ALF("2^(1+1+2+2):S3","McL",[1,2,2,2,2,5,5,4,9,9,9,2,5,5,5,12],[
"fusion map is unique"
]);

MOT("2^(2+4).S3",
[
"origin: Dixon's Algorithm"
],
0,
0,
0,
0,
["ConstructPermuted",["2^(1+1+2+2):S3"],(4,5,6,7)(13,15),(4,7,5,9,8,6)]);
ALF("2^(2+4).S3","McL",[1,2,2,5,2,2,5,4,9,9,9,2,5,5,5,12],[
"fusion map is unique"
]);

MOT("2^(2+4).(S3x2)",
[
"origin: Dixon's Algorithm"
],
[768,768,384,64,32,32,24,24,12,32,32,8,16,96,16,96,12,32,32,16,16,16,12],
[,[1,1,1,2,1,3,7,7,7,1,2,5,4,1,1,2,7,4,4,6,6,4,8],[1,2,3,4,5,6,1,2,3,10,11,12,
13,14,15,16,14,18,19,20,21,22,16]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,
-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,1,-1,1,1,-1,-1,
-1,-1,1,1],
[TENSOR,[2,3]],[2,2,2,2,2,2,-1,-1,-1,0,0,0,0,2,0,2,-1,0,0,0,0,2,-1],
[TENSOR,[5,2]],[3,3,3,3,-1,-1,0,0,0,-1,-1,1,-1,3,-1,3,0,-1,-1,1,1,-1,0],
[TENSOR,[7,2]],
[TENSOR,[7,3]],
[TENSOR,[7,4]],[6,6,6,-2,2,-2,0,0,0,-2,-2,0,2,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[11,3]],[6,6,6,-2,-2,2,0,0,0,0,0,0,0,0,2,0,0,-2,-2,0,0,0,0],
[TENSOR,[13,2]],[4,4,-4,0,0,0,1,1,-1,-2,2,0,0,2,0,-2,-1,-2,2,0,0,0,1],
[TENSOR,[15,2]],
[TENSOR,[15,3]],
[TENSOR,[15,4]],[8,8,-8,0,0,0,-1,-1,1,0,0,0,0,4,0,-4,1,0,0,0,0,0,-1],
[TENSOR,[19,2]],[8,-8,0,0,0,0,2,-2,0,0,0,0,0,0,0,0,0,0,0,2,-2,0,0],
[TENSOR,[21,2]],[16,-16,0,0,0,0,-2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]],
[(20,21)]);
ALF("2^(2+4).(S3x2)","J2.2",[1,2,2,6,3,6,4,9,9,17,18,19,22,2,17,6,9,22,21,
21,22,12,15],[
"fusion map is unique up to table aut."
]);
ALF("2^(2+4).(S3x2)","J3.2",[1,2,2,5,2,5,3,7,7,18,19,19,22,2,18,5,7,22,21,
21,22,8,13],[
"fusion map is unique up to table aut."
]);
ALF("2^(2+4).(S3x2)","McL.2",[1,2,2,5,2,5,4,9,9,2,5,5,11,20,20,21,22,23,24,23,
24,24,27],[
"fusion map is unique up to table automorphisms"
]);
ALF("2^(2+4).(S3x2)","Ly",[1,2,2,5,2,5,4,9,10,2,5,5,12,2,2,5,10,12,13,12,
13,13,20],[
"determined uniquely by factorization through 3.McL.2"
]);

MOT("3.ONM5",
[
"constructed by T. Breuer (1995/08/15) using the tables of ON, 3.ON, ONM5,\n",
"structure is 3.(3^2:4xA6).2,\n",
"5th maximal subgroup of 3.ON,\n",
"table is sorted w.r. to normal series given by 3.3^2.2.2.A6.2,\n",
"tests: 1.o.r., pow[2,3,5]"
],
[77760,77760,77760,3240,8640,8640,8640,4320,4320,4320,1728,1728,1728,324,864,
864,864,540,540,540,72,81,81,36,45,45,192,192,192,36,96,96,96,60,60,60,96,96,
96,36,36,48,48,48,60,60,60,60,60,60,24,24,24,48,48,48,48,48,48,24,24,24,48,48,
48,48,48,48],
[,[1,3,2,4,1,3,2,5,7,6,1,3,2,14,11,13,12,18,20,19,4,22,23,21,26,25,1,3,2,14,
11,13,12,18,20,19,5,7,6,30,30,27,29,28,34,36,35,34,36,35,27,29,28,31,33,32,31,
33,32,27,29,28,31,33,32,31,33,32],[1,1,1,1,5,5,5,8,8,8,11,11,11,1,15,15,15,18,
18,18,11,1,1,15,18,18,27,27,27,5,31,31,31,34,34,34,37,37,37,8,8,42,42,42,45,
45,45,48,48,48,51,51,51,54,54,54,57,57,57,60,60,60,63,63,63,66,66,66],,[1,3,2,
4,5,7,6,8,10,9,11,13,12,14,15,17,16,1,3,2,21,22,23,24,4,4,27,29,28,30,31,33,
32,5,7,6,37,39,38,40,41,42,44,43,8,10,9,8,10,9,51,53,52,57,59,58,54,56,55,60,
62,61,66,68,67,63,65,64]],
0,
[(54,57)(55,58)(56,59)(63,66)(64,67)(65,68),(51,60)(52,61)(53,62)(54,63)
(55,64)(56,65)(57,66)(58,67)(59,68),(40,41),(25,26),(22,23),(45,48)(46,49)
(47,50),( 2, 3)( 6, 7)( 9,10)(12,13)(16,17)(19,20)(28,29)(32,33)(35,36)(38,39)
(43,44)(46,47)(49,50)(52,53)(55,56)(58,59)(61,62)(64,65)(67,68)],
["ConstructProj",[["ONM5",[]],,["3.ONM5",[-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1]]]]);
ALF("3.ONM5","ONM5",[1,1,1,2,3,3,3,4,4,4,5,5,5,6,7,7,7,8,8,8,9,10,11,12,
13,14,15,15,15,16,17,17,17,18,18,18,19,19,19,20,21,22,22,22,23,23,23,24,
24,24,25,25,25,26,26,26,27,27,27,28,28,28,29,29,29,30,30,30]);
ALF("3.ONM5","3.ON",[1,2,3,7,4,5,6,8,9,10,4,5,6,7,8,9,10,14,15,16,17,7,7,
36,40,41,4,5,6,17,11,12,13,30,31,32,11,12,13,36,36,11,12,13,63,64,65,66,
67,68,11,12,13,24,25,26,24,25,26,11,12,13,27,28,29,27,28,29],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("3.ONM5","3.ON.2M4",[1,2,2,3,4,5,5,6,7,7,8,9,9,10,11,12,12,13,14,14,
15,16,16,17,18,19,20,21,21,22,23,24,24,25,26,26,27,28,28,29,30,31,32,32,
33,34,35,33,35,34,36,37,38,39,40,41,42,43,44,36,38,37,42,44,43,39,41,40]);

MOT("31:15",
[
"15th maximal subgroup of Th"
],
0,
0,
0,
[( 4,10, 7,16)( 5,17,11,14)( 6, 9,15,12),( 4,14)( 5,10)( 7,17)( 8,13)(11,16),
(2,3)],
["ConstructPermuted",["P:Q",[31,15]]]);
ALF("31:15","L2(31)",[1,17,18,10,11,5,12,3,6,9,9,6,3,12,5,11,10]);
ALF("31:15","ON",[1,29,30,16,17,6,16,3,6,17,17,6,3,16,6,17,16],[
"fusion map is unique up to table automorphisms"
]);
ALF("31:15","Th",[1,42,43,25,25,8,25,5,8,26,25,8,5,26,8,26,26],[
"fusion map is unique up to table automorphisms"
]);
ALF("31:15","B",[1,145,146,82,82,19,82,7,19,82,82,19,7,82,19,82,82],[
"determined up to table automorphisms by factorization through Th"
]);
ALF("31:15","31:30",[1,2,2,16,30,14,28,12,26,10,24,8,22,6,20,4,18],[
"fusion map is unique up to table aut."
]);
ALN("31:15",["ONN31","ThN31","BN31"]);

MOT("31:30",
[
"8th maximal subgroup of ON.2,\n",
"constructions: AGL(1,31)",
],
0,
0,
0,
[(3,9,21,15)(4,16,10,28)(5,23,29,11)(6,30,18,24)(8,14,26,20)(13,19,31,25),(3,
13)(4,24)(6,16)(7,27)(9,19)(10,30)(12,22)(15,25)(18,28)(21,31)],
["ConstructPermuted",["P:Q",[31,30]]]);
ALF("31:30","ON.2",[1,25,37,16,32,15,27,6,38,16,31,3,37,6,38,15,26,15,38,
6,37,3,31,16,38,6,27,15,32,16,37],[
"fusion is unique up to table automorphisms"
]);
ALN("31:30",["AGL(1,31)"]);

MOT("37:18",
[
"9th maximal subgroup of Ly"
],
0,
0,
0,
[( 4,14,16,20,10, 8)( 5, 7,11,19,17,13)( 6,18)( 9,15),(2,3)],
["ConstructPermuted",["P:Q",[37,18]]]);
ALF("37:18","Ly",[1,45,46,25,14,10,14,25,4,25,14,2,14,25,4,25,14,10,14,25],[
"fusion map is unique up to table automorphisms"
]);
ALF("37:18","R(27).3",[1,18,19,30,27,6,26,31,5,30,27,2,26,31,4,30,27,7,26,
31],[
"fusion map determined using the groups"
]);
ALN("37:18",["LyN37","R(27).3M5","R(27).3N37"]);

MOT("47:23",
[
"30th maximal subgroup of B"
],
0,
0,
0,
[(2,3),(4,5,7,11,19,12,21,16,6,9,15)(8,13,23,20,14,25,24,22,18,10,17),(4,8,5,
13,7,23,11,20,19,14,12,25,21,24,16,22,6,18,9,10,15,17)],
["ConstructPermuted",["P:Q",[47,23]]]);
ALF("47:23","B",[1,172,173,112,112,112,112,113,112,113,112,112,113,113,
112,112,113,113,112,113,112,113,113,113,113],[
"fusion map is unique up to table automorphisms"
]);

MOT("3^(1+4):2S5",
[
"origin: CAS library,\n",
"maximal subgroup (normalizer of 3A element) in McL,\n",
"table sorted w.r. to normal series 3.3^4.2.A5.2,\n",
"tests: 1.o.r., pow[2,3,5]"
],
[58320,29160,243,720,360,24,12,324,162,27,27,18,36,30,30,30,30,30,30,12,8,8,
12,12],
[,[1,2,3,1,2,4,5,8,9,11,10,9,8,14,15,16,14,15,16,4,6,6,13,13],[1,1,1,4,4,6,6,
1,1,2,2,4,4,14,14,14,17,17,17,20,22,21,20,20],,[1,2,3,4,5,6,7,8,9,11,10,12,13,
1,2,2,4,5,5,20,22,21,24,23]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,-1,-1,-1,-1,-1],[6,6,6,6,6,-2,-2,0,0,0,0,0,0,1,1,1,1,1,1,0,0,0,0,
0],[4,4,4,4,4,0,0,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,2,0,0,-1,-1],
[TENSOR,[4,2]],[5,5,5,5,5,1,1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0,1,-1,-1,1,1],
[TENSOR,[6,2]],[4,4,4,-4,-4,0,0,-2,-2,-2,-2,2,2,-1,-1,-1,1,1,1,0,0,0,0,0],[4,
4,4,-4,-4,0,0,1,1,1,1,-1,-1,-1,-1,-1,1,1,1,0,0,0,-E(12)^7+E(12)^11,
E(12)^7-E(12)^11],
[TENSOR,[9,2]],[6,6,6,-6,-6,0,0,0,0,0,0,0,0,1,1,1,-1,-1,-1,0,E(8)-E(8)^3,
-E(8)+E(8)^3,0,0],
[TENSOR,[11,2]],[80,80,-1,0,0,0,0,8,8,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0],[80,80,
-1,0,0,0,0,-4,-4,-2*E(3)+E(3)^2,E(3)-2*E(3)^2,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[14,2]],[18,-9,0,2,-1,2,-1,-6,3,0,0,-1,2,-2,1,1,2,-1,-1,0,0,0,0,0],[
36,-18,0,-4,2,0,0,6,-3,0,0,-1,2,1,-E(15)^7-E(15)^11-E(15)^13-E(15)^14,
-E(15)-E(15)^2-E(15)^4-E(15)^8,1,-E(15)^7-E(15)^11-E(15)^13-E(15)^14,
-E(15)-E(15)^2-E(15)^4-E(15)^8,0,0,0,0,0],
[GALOIS,[17,7]],[54,-27,0,6,-3,-2,1,0,0,0,0,0,0,-1,E(15)^7+E(15)^11+E(15)^13
 +E(15)^14,E(15)+E(15)^2+E(15)^4+E(15)^8,1,-E(15)^7-E(15)^11-E(15)^13-E(15)^14
 ,-E(15)-E(15)^2-E(15)^4-E(15)^8,0,0,0,0,0],
[GALOIS,[19,7]],[72,-36,0,8,-4,0,0,-6,3,0,0,-1,2,2,-1,-1,-2,1,1,0,0,0,0,0],[
72,-36,0,-8,4,0,0,-6,3,0,0,1,-2,2,-1,-1,2,-1,-1,0,0,0,0,0],[90,-45,0,10,-5,2,
-1,6,-3,0,0,1,-2,0,0,0,0,0,0,0,0,0,0,0],[108,-54,0,-12,6,0,0,0,0,0,0,0,0,-2,1,
1,-2,1,1,0,0,0,0,0]],
[(15,16)(18,19),(23,24),(10,11)(15,16)(18,19)(23,24),(21,22),(21,22)(23,24),
(10,11)]);
ARC("3^(1+4):2S5","projectives",["3.3^(1+4):2S5",[[9,9,0,1,1,1,1,-3,-3,0,0,1,
1,-1,-1,-1,1,1,1,1,-1,-1,1,1],[18,-9,0,2,-1,2,-1,6,-3,0,0,-1,2,-2,1,1,2,-1,-1,
0,0,0,0,0],[36,36,0,4,4,0,0,-3,-3,0,0,1,1,1,1,1,-1,-1,-1,-2,0,0,1,1],[36,36,0,
-4,-4,0,0,-3,-3,0,0,-1,-1,1,1,1,1,1,1,0,0,0,-E(12)^7+E(12)^11,E(12)^7-E(12)^11
 ],[36,36,0,-4,-4,0,0,6,6,0,0,2,2,1,1,1,1,1,1,0,0,0,0,0],[36,-18,0,-4,2,0,0,
-6,3,0,0,-1,2,1,-E(15)^7-E(15)^11-E(15)^13-E(15)^14,-E(15)-E(15)^2-E(15)^4
 -E(15)^8,1,-E(15)^7-E(15)^11-E(15)^13-E(15)^14,-E(15)-E(15)^2-E(15)^4-E(15)^8
 ,0,0,0,0,0],
[GALOIS,[6,7]],[45,45,0,5,5,1,1,3,3,0,0,-1,-1,0,0,0,0,0,0,-1,-1,-1,-1,-1],[54,
-27,0,6,-3,-2,1,0,0,0,0,0,0,-1,E(15)^7+E(15)^11+E(15)^13+E(15)^14,
E(15)+E(15)^2+E(15)^4+E(15)^8,1,-E(15)^7-E(15)^11-E(15)^13-E(15)^14,
-E(15)-E(15)^2-E(15)^4-E(15)^8,0,0,0,0,0],
[GALOIS,[9,7]],[54,54,0,6,6,-2,-2,0,0,0,0,0,0,-1,-1,-1,1,1,1,0,0,0,0,0],[54,
54,0,-6,-6,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,0,E(8)-E(8)^3,-E(8)+E(8)^3,0,0],[
72,-36,0,8,-4,0,0,6,-3,0,0,-1,2,2,-1,-1,-2,1,1,0,0,0,0,0],[72,-36,0,-8,4,0,0,
6,-3,0,0,1,-2,2,-1,-1,2,-1,-1,0,0,0,0,0],[90,-45,0,10,-5,2,-1,-6,3,0,0,1,-2,0,
0,0,0,0,0,0,0,0,0,0],[108,-54,0,-12,6,0,0,0,0,0,0,0,0,-2,1,1,-2,1,1,0,0,0,0,
0]],]);
ARC("3^(1+4):2S5","CAS",[rec(name:="3^1+4:2.s5",
permchars:=( 3,10, 6, 8)( 7, 9)(11,12)(13,18,19,22,15,23,16)(14,24,17,20,21),
permclasses:=( 2, 3, 4)( 5,10,15,22,14, 9)( 6, 7,18,24,20, 8)(11,16,21,13)
(19,23),
text:=[
"normalizer of 3a-element in mcl. structure: extension of\n",
"extraspecial group of order 3^(1+4) by a double cover of symmetric\n",
"group s5 (transposition of s5 corresponds to element of order 4\n",
"test: 1. o.r., sym 2 decompose correctly\n",
""])]);
ARC("3^(1+4):2S5","tomfusion",rec(name:="3^(1+4)+:2S5",map:=[1,3,5,2,10,7,
28,4,6,24,24,13,11,9,32,32,25,62,62,8,15,15,30,30],text:=[
"fusion map is unique"
]));
ALF("3^(1+4):2S5","3^(1+4):4S5",[1,2,3,4,5,6,7,8,9,10,10,11,12,13,14,14,
15,16,16,17,18,18,19,19]);
ALF("3^(1+4):2S5","McL",[1,3,4,2,8,5,18,3,4,14,13,9,8,6,21,22,15,23,24,5,
12,12,18,18],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("3^(1+4):2S5","Isoclinic(2.A5.2)",[1,1,1,2,2,3,3,4,4,4,4,5,5,6,6,6,7,
7,7,8,9,10,11,12]);
ALN("3^(1+4):2S5",["3^1+4:2.s5","McLN3A"]);

MOT("3^(1+4):4A5",
[
"origin: constructed from tables HNC3B, 4A5, and permutation character,\n",
"14th maximal subgroup of HN,\n",
"3B normalizer,\n",
"tests: 1.o.r., pow[2,3,5]"
],
[58320,29160,486,486,720,360,324,162,27,24,60,60,36,18,27,60,60,12,30,30,30,
30,72,240,240,18,18,12,12,20,20,20,20],
[,[1,2,3,4,1,2,7,8,9,5,12,11,7,8,15,12,11,6,20,19,20,19,1,5,5,3,4,13,13,17,17,
16,16],[1,1,1,1,5,5,1,1,1,10,12,11,5,5,2,17,16,10,12,11,17,16,23,25,24,23,23,
25,24,33,32,31,30],,[1,2,3,4,5,6,7,8,9,10,1,1,13,14,15,5,5,18,2,2,6,6,23,24,
25,26,27,28,29,24,25,24,25]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[3,3,3,
3,3,3,0,0,0,-1,-E(5)-E(5)^4,-E(5)^2-E(5)^3,0,0,0,-E(5)-E(5)^4,-E(5)^2-E(5)^3,
-1,-E(5)-E(5)^4,-E(5)^2-E(5)^3,-E(5)-E(5)^4,-E(5)^2-E(5)^3,-1,3,3,-1,-1,0,0,
-E(5)-E(5)^4,-E(5)-E(5)^4,-E(5)^2-E(5)^3,-E(5)^2-E(5)^3],
[TENSOR,[3,2]],
[GALOIS,[4,2]],
[TENSOR,[5,2]],[4,4,4,4,4,4,1,1,1,0,-1,-1,1,1,1,-1,-1,0,-1,-1,-1,-1,0,-4,-4,0,
0,-1,-1,1,1,1,1],
[TENSOR,[7,2]],[5,5,5,5,5,5,-1,-1,-1,1,0,0,-1,-1,-1,0,0,1,0,0,0,0,-1,-5,-5,-1,
-1,1,1,0,0,0,0],
[TENSOR,[9,2]],[2,2,2,2,-2,-2,-1,-1,-1,0,E(5)^2+E(5)^3,E(5)+E(5)^4,1,1,-1,
-E(5)^2-E(5)^3,-E(5)-E(5)^4,0,E(5)^2+E(5)^3,E(5)+E(5)^4,-E(5)^2-E(5)^3,
-E(5)-E(5)^4,0,-2*E(4),2*E(4),0,0,E(4),-E(4),-E(20)^13-E(20)^17,
E(20)^13+E(20)^17,-E(20)-E(20)^9,E(20)+E(20)^9],
[TENSOR,[11,2]],
[GALOIS,[11,13]],
[TENSOR,[13,2]],[4,4,4,4,-4,-4,1,1,1,0,-1,-1,-1,-1,1,1,1,0,-1,-1,1,1,0,
-4*E(4),4*E(4),0,0,-E(4),E(4),E(4),-E(4),E(4),-E(4)],
[TENSOR,[15,2]],[6,6,6,6,-6,-6,0,0,0,0,1,1,0,0,0,-1,-1,0,1,1,-1,-1,0,-6*E(4),
6*E(4),0,0,0,0,-E(4),E(4),-E(4),E(4)],
[TENSOR,[17,2]],[40,40,4,-5,0,0,4,4,-2,0,0,0,0,0,1,0,0,0,0,0,0,0,4,0,0,-2,1,0,
0,0,0,0,0],[40,40,-5,4,0,0,4,4,1,0,0,0,0,0,-2,0,0,0,0,0,0,0,4,0,0,1,-2,0,0,0,
0,0,0],
[TENSOR,[20,2]],
[TENSOR,[19,2]],[80,80,-10,8,0,0,-4,-4,-1,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0],[80,80,8,-10,0,0,-4,-4,2,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0],[18,-9,0,0,2,-1,6,-3,0,2,-2,-2,2,-1,0,2,2,-1,1,1,-1,-1,0,0,0,0,0,0,
0,0,0,0,0],[36,-18,0,0,-4,2,-6,3,0,0,-2*E(5)-2*E(5)^4,-2*E(5)^2-2*E(5)^3,2,-1,
0,-2*E(5)-2*E(5)^4,-2*E(5)^2-2*E(5)^3,0,E(5)+E(5)^4,E(5)^2+E(5)^3,E(5)+E(5)^4,
E(5)^2+E(5)^3,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[26,2]],[54,-27,0,0,6,-3,0,0,0,-2,2*E(5)^2+2*E(5)^3,2*E(5)+2*E(5)^4,0,
0,0,-2*E(5)^2-2*E(5)^3,-2*E(5)-2*E(5)^4,1,-E(5)^2-E(5)^3,-E(5)-E(5)^4,
E(5)^2+E(5)^3,E(5)+E(5)^4,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[28,2]],[72,-36,0,0,-8,4,6,-3,0,0,2,2,-2,1,0,2,2,0,-1,-1,-1,-1,0,0,0,
0,0,0,0,0,0,0,0],[72,-36,0,0,8,-4,6,-3,0,0,2,2,2,-1,0,-2,-2,0,-1,-1,1,1,0,0,0,
0,0,0,0,0,0,0,0],[90,-45,0,0,10,-5,-6,3,0,2,0,0,-2,1,0,0,0,-1,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0],[108,-54,0,0,-12,6,0,0,0,0,-2,-2,0,0,0,-2,-2,0,1,1,1,1,0,0,0,0,
0,0,0,0,0,0,0]],
[(24,25)(28,29)(30,31)(32,33),(11,12)(16,17)(19,20)(21,22)(30,32)(31,33)]);
ALF("3^(1+4):4A5","HN",[1,5,4,5,3,16,5,4,5,8,11,12,16,15,20,24,25,32,35,
36,49,50,3,8,8,15,16,32,32,42,42,43,43],[
"fusion map is unique up to table automorphisms"
]);
ALF("3^(1+4):4A5","HN.2M13",[1,2,3,4,5,6,13,14,15,9,20,20,16,17,18,21,21,
12,22,22,25,25,8,7,7,11,10,19,19,23,24,24,23],[
"fusion map is unique up to table aut."
]);
ALN("3^(1+4):4A5",["HNN3B"]);

MOT("3^(1+4):4S5",
[
"origin: Dixon's algorithm,\n",
"maximal subgroup of McL.2, normalizer of 3A element,\n",
"the table is sorted w.r. to normal series 3.3^4.2.(S5x2),\n",
"tests: 1.o.r., pow[2,3,5]"
],
[116640,58320,486,1440,720,48,24,648,324,27,36,72,60,30,60,30,24,8,12,240,18,
144,12,20,20,72,36,24,24,24,36,36,36],
[,[1,2,3,1,2,4,5,8,9,10,9,8,13,14,13,14,4,6,12,4,3,1,12,15,15,4,5,6,7,7,12,11,
11],[1,1,1,4,4,6,6,1,1,2,4,4,13,13,15,15,17,18,17,20,22,22,20,24,25,26,26,28,
28,28,26,26,26],,[1,2,3,4,5,6,7,8,9,10,11,12,1,2,4,5,17,18,19,20,21,22,23,20,
20,26,27,28,29,30,31,32,33]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1],
[TENSOR,[2,3]],[6,6,6,6,6,-2,-2,0,0,0,0,0,1,1,1,1,0,0,0,6,-2,-2,0,1,1,0,0,0,0,
0,0,0,0],
[TENSOR,[5,2]],[4,4,4,4,4,0,0,1,1,1,1,1,-1,-1,-1,-1,2,0,-1,4,0,0,1,-1,-1,2,2,
0,0,0,-1,-1,-1],
[TENSOR,[7,2]],
[TENSOR,[7,3]],
[TENSOR,[7,4]],[5,5,5,5,5,1,1,-1,-1,-1,-1,-1,0,0,0,0,1,-1,1,5,1,1,-1,0,0,1,1,
-1,-1,-1,1,1,1],
[TENSOR,[11,2]],
[TENSOR,[11,3]],
[TENSOR,[11,4]],[4,4,4,-4,-4,0,0,-2,-2,-2,2,2,-1,-1,1,1,0,0,0,0,0,0,0,
E(20)+E(20)^9-E(20)^13-E(20)^17,-E(20)-E(20)^9+E(20)^13+E(20)^17,0,0,0,0,0,0,
0,0],
[TENSOR,[15,2]],[8,8,8,-8,-8,0,0,2,2,2,-2,-2,-2,-2,2,2,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0],[12,12,12,-12,-12,0,0,0,0,0,0,0,2,2,-2,-2,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0],[80,80,-1,0,0,0,0,8,8,-1,0,0,0,0,0,0,0,0,0,0,-1,8,0,0,0,0,0,0,0,
0,0,0,0],
[TENSOR,[19,2]],[160,160,-2,0,0,0,0,-8,-8,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0],[18,-9,0,2,-1,2,-1,-6,3,0,-1,2,-2,1,2,-1,0,0,0,0,0,0,0,0,0,2,-1,
-2,1,1,2,-1,-1],
[TENSOR,[22,2]],[72,-36,0,-8,4,0,0,12,-6,0,-2,4,2,-1,2,-1,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0],[72,-36,0,8,-4,0,0,-6,3,0,-1,2,2,-1,-2,1,0,0,0,0,0,0,0,0,0,-4,
2,0,0,0,2,-1,-1],
[TENSOR,[25,2]],[72,-36,0,-8,4,0,0,-6,3,0,1,-2,2,-1,2,-1,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,3*E(4),-3*E(4)],
[TENSOR,[27,2]],[90,-45,0,10,-5,2,-1,6,-3,0,1,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,
1,-2,1,1,-2,1,1],
[TENSOR,[29,2]],[108,-54,0,12,-6,-4,2,0,0,0,0,0,-2,1,2,-1,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0],[108,-54,0,-12,6,0,0,0,0,0,0,0,-2,1,-2,1,0,0,0,0,0,0,0,0,0,0,0,
0,E(24)+E(24)^11-E(24)^17-E(24)^19,-E(24)-E(24)^11+E(24)^17+E(24)^19,0,0,0],
[TENSOR,[32,2]]],
[(29,30),(24,25),(24,25)(32,33)]);
ARC("3^(1+4):4S5","tomfusion",rec(name:="3^(1+4)+:4S5",map:=[1,4,6,2,14,
10,51,5,7,41,20,18,13,60,42,123,11,30,54,8,23,3,55,91,91,9,47,27,101,101,
49,52,52],text:=[
"fusion map is unique"
]));
ALF("3^(1+4):4S5","McL.2",[1,3,4,2,8,5,16,3,4,12,9,8,6,18,13,19,5,11,16,
21,22,20,26,28,29,21,26,23,32,33,26,27,27],[
"fusion is unique up to table automorphisms"
]);
ALN("3^(1+4):4S5",["McL.2N3A"]);

MOT("3^(1+6):2^(3+4):3^2:2",
[
"origin: Dixon's Algorithm,\n",
"maximal subgroup of Fi22,\n",
"table sorted w.r. to normal series 3.3^6.2^3.2^4.3^2.2,\n",
"tests: 1.o.r., pow[2,3]"
],
[5038848,2519424,69984,13122,8748,4374,186624,20736,6912,93312,10368,3888,
3456,972,864,1728,288,288,192,864,144,144,144,144,96,5832,5832,5832,1944,1944,
1944,1944,1944,1944,486,486,486,243,648,648,648,216,216,216,216,216,216,216,
216,216,216,216,216,54,54,54,324,162,81,81,81,27,36,36,36,36,36,36,108,108,54,
36,432,48,216,108,108,54,54,48,48,16,16,16,16,24,24,24],
[,[1,2,3,4,5,6,1,1,1,2,2,3,2,5,3,8,9,9,8,11,15,13,13,15,11,26,27,28,29,30,31,
32,33,34,35,36,37,38,27,28,26,27,26,26,28,28,29,27,30,34,33,31,32,35,37,36,57,
58,59,60,61,62,51,50,47,52,49,53,57,57,58,57,1,8,3,5,5,6,4,16,16,17,17,18,18,
15,21,21],[1,1,1,1,1,1,7,8,9,7,8,7,9,7,8,16,17,18,19,16,16,17,18,16,19,1,1,1,
1,1,1,1,1,1,1,1,1,1,7,7,7,9,9,8,8,9,9,8,9,9,9,9,9,9,9,9,2,2,4,4,4,6,18,18,17,
17,18,17,10,10,10,11,73,74,73,73,73,73,73,80,81,82,83,84,85,74,81,80]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[2,2,2,2,2,2,2,2,
2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,-1,-1,-1,-1,-1,-1,-1,-1,-1,2,2,2,2,2,
2,2,2,2,-1,2,-1,-1,-1,-1,-1,-1,-1,-1,2,2,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,2,2,2,
2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,
2,2,2,2,-1,-1,-1,2,-1,2,2,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,2,-1,-1,
-1,-1,2,2,-1,-1,-1,-1,-1,-1,2,-1,-1,-1,-1,2,2,-1,2,-1,-1,-1,-1,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0],[2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,-1,-1,
-1,-1,2,-1,-1,2,2,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,2,2,2,-1,-1,-1,-1,
-1,-1,-1,-1,-1,2,-1,2,2,-1,-1,2,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0],[2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,-1,-1,-1,-1,-1,-1,-1,-1,
-1,2,2,2,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,2,2,2,-1,-1,2,-1,-1,
2,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[3,3,3,3,3,3,
3,3,3,3,3,3,3,3,3,-1,-1,3,-1,-1,-1,-1,3,-1,-1,0,0,0,3,0,3,3,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,3,0,0,0,0,3,3,0,0,0,0,0,0,3,0,0,0,0,-1,-1,0,-1,0,0,0,0,1,1,1,1,1,1,
1,-1,-1,-1,-1,1,1,1,-1,-1],
[TENSOR,[7,2]],[3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,-1,3,-1,-1,-1,-1,3,-1,-1,-1,0,0,
0,0,3,0,0,3,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,3,3,3,0,0,0,0,0,0,0,0,0,3,0,-1,-1,0,
0,-1,0,0,0,0,0,1,1,1,1,1,1,1,-1,-1,1,1,-1,-1,1,-1,-1],
[TENSOR,[9,2]],[6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,-2,-2,6,-2,-2,-2,-2,6,-2,-2,0,0,
0,-3,0,-3,-3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-3,0,0,0,0,-3,-3,0,0,0,0,0,0,-3,0,0,
0,0,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[6,6,6,6,6,6,6,6,6,6,6,6,
6,6,6,-2,6,-2,-2,-2,-2,6,-2,-2,-2,0,0,0,0,-3,0,0,-3,-3,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,-3,-3,-3,0,0,0,0,0,0,0,0,0,-3,0,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0],[9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,1,-3,-3,1,1,1,-3,-3,1,1,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,1,1,1],
[TENSOR,[13,2]],[4,4,4,4,4,4,-4,4,-4,-4,4,-4,-4,-4,4,0,0,0,0,0,0,0,0,0,0,1,1,
1,-2,-2,-2,-2,-2,-2,1,1,1,1,-1,-1,-1,-1,-1,1,1,-1,2,1,2,2,2,2,2,-1,-1,-1,1,1,
1,-2,-2,1,0,0,0,0,0,0,-1,-1,-1,1,0,0,0,0,0,0,0,2,-2,0,0,0,0,0,-2,2],
[TENSOR,[15,2]],[6,6,6,6,6,6,2,-2,-6,2,-2,2,-6,2,-2,2,0,0,-2,2,2,0,0,2,-2,-3,
-3,-3,0,0,0,0,0,0,0,0,0,-3,-1,-1,-1,3,3,1,1,3,0,1,0,0,0,0,0,0,0,0,-3,-3,0,0,0,
0,0,0,0,0,0,0,-1,-1,-1,1,0,0,0,0,0,0,0,0,0,E(8)+E(8)^3,-E(8)-E(8)^3,
E(8)+E(8)^3,-E(8)-E(8)^3,0,0,0],
[TENSOR,[17,2]],[8,8,8,8,8,8,-8,8,-8,-8,8,-8,-8,-8,8,0,0,0,0,0,0,0,0,0,0,2,2,
2,2,2,2,2,2,2,-1,-1,-1,2,-2,-2,-2,-2,-2,2,2,-2,-2,2,-2,-2,-2,-2,-2,1,1,1,2,2,
-1,2,2,-1,0,0,0,0,0,0,-2,-2,-2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[8,8,8,8,8,
8,-8,8,-8,-8,8,-8,-8,-8,8,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,-4,2,-4,-4,2,2,-1,-1,
-1,-1,1,1,1,1,1,-1,-1,1,4,-1,-2,-2,-2,4,4,1,1,1,-1,-1,-1,-4,2,-1,0,0,0,0,0,0,
1,1,1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[8,8,8,8,8,8,-8,8,-8,-8,8,-8,-8,-8,
8,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,2,2,2,2,2,2,2,2,2,-1,1,1,1,1,1,-1,-1,1,-2,-1,
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[(82,83)(84,85),(69,70),(29,31,32)(30,34,33)(35,37,36)(47,52,53)(49,50,51)(54,
55,56)(63,67,64)(65,66,68),(26,27,28)(30,33,34)(35,37,36)(39,40,41)(42,46,43)
(44,48,45)(49,51,50)(54,55,56)(63,64,67),(17,18)(22,23)(29,30)(31,33)(32,34)
(36,37)(47,49)(50,53)(51,52)(55,56)(60,61)(63,66)(64,68)(65,67)(82,84)(83,
85)]);
ALF("3^(1+6):2^(3+4):3^2:2","Fi22",[1,6,5,6,7,8,2,3,4,16,17,15,21,19,18,9,
12,12,11,38,39,42,43,40,45,5,6,7,6,7,7,8,8,6,8,7,8,8,16,19,15,21,20,18,23,
24,21,17,22,21,25,22,25,25,25,24,31,32,32,32,32,33,48,42,43,44,44,48,55,
56,57,58,4,13,20,24,22,25,21,28,27,30,30,30,30,46,64,63],[
"fusion is unique up to table automorphisms"
]);
ALF("3^(1+6):2^(3+4):3^2:2","3^(1+6)_+:2^(3+4):(S3xS3)",[1,2,3,6,4,5,10,7,
14,11,8,12,15,13,9,16,22,22,20,17,18,23,23,19,21,42,44,43,54,55,55,56,56,
54,25,24,25,47,32,31,30,37,35,38,39,36,51,40,52,51,53,52,53,29,29,28,45,
46,27,57,57,26,50,48,48,49,49,50,33,33,34,41,66,64,69,68,67,70,71,60,62,
58,59,58,59,65,63,61],[
"fusion map is unique up to table aut."
]);
ALN("3^(1+6):2^(3+4):3^2:2",["Fi22N3B"]);

MOT("3^(1+6)_+:2^(3+4):(S3xS3)",
[
"origin: Dixon's Algorithm,\n",
"maximal subgroup of Fi22.2,\n",
"table sorted w.r. to normal series 3.3^6.2^3.2^4.3^2.2.2,\n",
"tests: 1.o.r., pow[2,3]"
],
[10077696,5038848,139968,17496,8748,26244,41472,20736,1728,373248,186624,7776,
1944,13824,6912,3456,1728,288,288,384,192,288,144,972,486,54,162,108,54,1296,
1296,1296,108,108,432,432,432,432,432,432,72,11664,11664,11664,648,324,486,36,
36,36,216,216,216,1944,1944,1944,81,16,16,96,48,96,48,96,48,864,216,216,432,
108,108,36,18,36,18,2592,432,216,324,2592,432,216,324,192,96,96,48,192,96,
46656,23328,2592,1944,324,7776,972,576,288,5184,2592,288,864,5184,2592,216,48,
48,48,648,648,648,108,108,54,72,72,72,216,216,216,36,216,216,216,36],
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[(107,108),(58,59)(84,88)(85,89),
( 30, 31, 32)( 35, 36, 37)( 38, 39, 40)( 42, 43, 44)( 48, 49, 50)( 51, 52, 53)
( 54, 55, 56)(109,110,111)(115,116,117)(118,119,120)
(122,123,124)
]);
ALF("3^(1+6)_+:2^(3+4):(S3xS3)","Fi22.2",[1,6,5,7,8,6,3,17,18,2,16,15,19,
4,21,9,37,38,39,11,43,12,41,7,8,33,32,24,25,15,19,16,51,52,20,24,21,18,23,
17,53,5,7,6,31,32,8,41,42,46,21,22,25,6,7,8,32,30,30,28,57,27,58,13,44,4,
22,24,20,25,21,77,102,78,101,61,73,77,76,62,71,78,74,79,104,80,105,79,104,
60,70,69,72,75,68,70,65,92,63,87,88,86,62,74,78,81,106,107,68,72,70,99,
100,75,91,93,92,86,89,87,111,71,78,74,101],[
"fusion map is unique up to table automorphisms"
]);
ALN("3^(1+6)_+:2^(3+4):(S3xS3)",["Fi22.2N3B"]);

MOT("3^(2+4):2A5.D8",
[
"7th maximal subgroup of Ly,\n",
"origin: computed from tables of subgroup 3.3^(1+4):4S5, Sylow 2 subgroup,\n",
"        and supergroup Ly\n",
"table is sorted w.r. to normal series given by 3^2.3^4.2.A5.D8,\n",
"tests: 1.o.r., pow[2,3,5]"
],
[699840,174960,174960,972,8640,2160,2160,288,72,72,3888,972,972,54,108,108,
432,360,90,90,360,90,90,72,36,24,24,24,36,36,36,480,36,288,24,40,40,648,108,
108,108,324,108,36,24,18,24,24,480,480,16,24,24,40,40,40,40],
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1,1,1,5,5,5,8,8,8,1,1,1,3,5,5,5,18,18,18,21,21,21,24,24,26,26,26,24,24,24,32,
34,34,32,36,37,38,38,38,38,38,38,38,45,42,45,45,49,50,51,49,50,54,55,56,57],,[
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,1,2,3,5,6,7,24,25,26,27,28,29,30,31,
32,33,34,35,32,32,38,39,40,41,42,43,44,45,46,47,48,50,49,51,53,52,49,50,50,
49]],
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[TENSOR,[39,3]],[144,-72,36,0,-16,8,-4,0,0,0,-24,12,-6,0,-4,2,8,4,-2,1,4,-2,1,
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[TENSOR,[42,2]],[144,-72,36,0,-16,8,-4,0,0,0,12,-6,3,0,2,-1,-4,4,-2,1,4,-2,1,
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0],
[TENSOR,[46,3]],[180,45,-90,0,20,5,-10,4,1,-2,12,3,-6,0,-1,2,-4,0,0,0,0,0,0,
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[TENSOR,[48,3]],[180,-90,45,0,20,-10,5,4,-2,1,-12,6,-3,0,2,-1,-4,0,0,0,0,0,0,
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[TENSOR,[50,2]],[216,54,-108,0,24,6,-12,-8,-2,4,0,0,0,0,0,0,0,-4,-1,2,4,1,-2,
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0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[216,54,-108,0,-24,-6,12,0,0,0,
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[TENSOR,[54,3]],[216,-108,54,0,-24,12,-6,0,0,0,0,0,0,0,0,0,0,-4,2,-1,-4,2,-1,
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 -E(24)^19,E(24)-E(24)^11-E(24)^17+E(24)^19,0,0,0,0,0,0,0,0,0],
[TENSOR,[56,2]]],
[(47,48),(36,37)(54,57)(55,56),(30,31)(36,37)(47,48)(49,50)(52,53)(54,55)
(56,57),(27,28)(47,48),(27,28)(47,48)(49,50)(52,53)(54,56)(55,57),(49,50)
(52,53)(54,56)(55,57)]);
ALF("3^(2+4):2A5.D8","Ly",[1,3,4,4,2,8,9,5,19,20,3,4,4,14,9,10,8,6,22,23,
15,36,37,5,19,12,31,31,19,20,20,5,10,2,19,26,26,2,8,9,9,10,10,10,13,25,32,
33,12,12,13,31,31,47,47,48,48],[
"fusion is unique up to table automorphisms"
]);

MOT("3^2+4:2(2^2xa4)2",
[
"origin: Dixon algorithm,\n",
"11th maximal subgroup of Suz,\n",
"tests: 1.o.r., pow[2,3]"
],
[139968,34992,34992,486,324,1728,432,432,1296,1296,1296,54,288,36,1944,972,
972,486,54,54,96,288,72,72,144,36,36,16,48,24,24,12,216,108,108,54,108,108,
108,18,108,108,108,18,8,24,24,24,12],
[,[1,2,3,4,5,1,2,3,1,3,3,4,1,5,15,17,16,18,20,19,6,6,7,8,13,14,14,13,6,8,6,7,
15,17,16,18,17,15,17,20,16,15,16,19,21,22,23,23,33],[1,1,1,1,1,6,6,6,9,9,9,9,
13,13,1,1,1,1,3,3,21,22,22,22,25,25,25,28,29,29,31,31,6,6,6,6,9,9,9,10,9,9,9,
11,45,46,46,46,21]],
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1,1,1,-1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,1,-1,-1,-1,1],[1,1,1,1,1,1,
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[TENSOR,[2,3]],[2,2,2,2,2,2,2,2,-2,-2,-2,-2,2,2,-1,-1,-1,-1,-1,-1,2,2,2,2,0,0,
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[TENSOR,[5,2]],[2,2,2,2,2,2,2,2,0,0,0,0,-2,-2,-1,-1,-1,-1,-1,-1,-2,2,2,2,0,0,
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E(3)-E(3)^2,E(3)-E(3)^2,E(3)-E(3)^2,E(3)-E(3)^2,0,0,0,0,1],[2,2,2,2,2,2,2,2,0,
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[TENSOR,[7,2]],[3,3,3,3,3,3,3,3,3,3,3,3,-1,-1,0,0,0,0,0,0,3,-1,-1,-1,1,1,1,1,
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[TENSOR,[10,4]],
[TENSOR,[10,3]],
[TENSOR,[10,2]],[4,4,4,4,4,-4,-4,-4,0,0,0,0,0,0,-2,-2,-2,-2,-2,-2,0,0,0,0,2,2,
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[TENSOR,[14,3]],[6,6,6,6,6,6,6,6,0,0,0,0,2,2,0,0,0,0,0,0,-6,-2,-2,-2,0,0,0,0,
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[TENSOR,[18,2]],
[TENSOR,[19,2]],
[TENSOR,[20,2]],[48,48,48,-6,3,0,0,0,0,0,0,0,8,-1,0,0,0,0,0,0,0,0,0,0,8,-1,-1,
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[TENSOR,[24,3]],
[TENSOR,[25,3]],[36,9,-18,0,0,4,1,-2,0,0,0,0,0,0,-12,6,6,-3,0,0,0,4,1,-2,0,0,
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[TENSOR,[28,2]],[72,18,-36,0,0,8,2,-4,0,0,0,0,0,0,12,-6,-6,3,0,0,0,8,2,-4,0,0,
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[TENSOR,[33,2]],[144,36,-72,0,0,-16,-4,8,0,0,0,0,0,0,-12,6,6,-3,0,0,0,0,0,0,0,
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6*E(3)-3*E(3)^2,3,0,0,0,4,-2,1,0,0,0,0,-2,1,0,0,-2,-E(3)+2*E(3)^2,
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[TENSOR,[36,2]],
[GALOIS,[37,2]],
[TENSOR,[37,2]],
[TENSOR,[39,2]],[108,-54,27,0,0,12,-6,3,-18,9,9,0,0,0,0,0,0,0,0,0,0,-4,2,-1,0,
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[TENSOR,[42,2]],[72,-36,18,0,0,-8,4,-2,0,6*E(3)-6*E(3)^2,-6*E(3)+6*E(3)^2,0,0,
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E(3)+2*E(3)^2,-2*E(3)-4*E(3)^2,E(3)+2*E(3)^2,0,0,0,0,0,0],[72,-36,18,0,0,-8,4,
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[TENSOR,[45,2]],
[TENSOR,[44,2]],
[TENSOR,[46,2]]],
[(47,48),(26,27),(26,27)(47,48),(10,11)(16,17)(19,20)(34,35)(37,41)(38,42)
(39,43)(40,44),(10,11)(16,17)(19,20)(34,35)(37,41)(38,42)(39,43)(40,44)
(47,48)]);
ARC("3^2+4:2(2^2xa4)2","CAS",[rec(name:="3^2+4:2(2^2xa4)2",
permchars:=(),
permclasses:=(),
text:=[
"maximal subgroup of sporadic simple Suzuki group Suz,\n",
"test:1.OR,JAMES,JAMES,n=3,\n",
"and restricted characters decompose properly.\n",
"Fusion into suz may be not correct: probably the images of 6h and 6i\n",
"(of this group) in suz should be swapped (while keeping the images of\n",
"the other pairs of algebraic conjugate classes).\n",
""])]);
ARC("3^2+4:2(2^2xa4)2","projectives",["3.3^(2+4):2(A4x2^2).2",[[36,-18,9,9,0,
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0,0,2,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[12,-6,3,3,0,-4,2,-1,2,-E(3)
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0,0,2,-1,0,0,2,-E(3)-3*E(3)^2,-3*E(3)-E(3)^2,-1,-E(3)-3*E(3)^2,2*E(3),-1,-1,
-3*E(3)-E(3)^2,2*E(3)^2,-1,-1,0,0,0,0,0],[24,-12,6,6,0,8,-4,2,8,2*E(3)
+6*E(3)^2,6*E(3)+2*E(3)^2,2,0,0,6,-3,-3,-3,E(3)-E(3)^2,-E(3)+E(3)^2,0,0,0,0,0,
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-E(3)-3*E(3)^2,-1,0,0,0,0,0],[36,9,-18,0,0,4,1,-2,0,0,0,0,0,0,12,-6*E(3),
-6*E(3)^2,3,0,0,0,4,1,-2,0,0,0,0,0,0,-2,1,4,-2*E(3),-2*E(3)^2,1,0,0,0,0,0,0,0,
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+E(3)^2,2*E(3)+E(3)^2,0,0,0,0,0,-1],[12,-6,3,3,0,-4,2,-1,-2,E(3)-3*E(3)^2,
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-2*E(3)^2,E(3),0,0,0,0,0],[18,18,18,0,0,2,2,2,0,0,0,0,6,0,-6,-6*E(3),
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3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,4,-2*E(3),-2*E(3)^2,1,0,0,0,0,0,0,0,0,0,0,0,0,0]
],]);
ALF("3^2+4:2(2^2xa4)2","Suz",[1,4,5,5,6,2,13,16,2,14,15,16,3,17,4,5,5,5,
22,23,9,7,27,28,10,30,30,10,8,31,9,29,13,14,15,16,16,13,15,38,16,13,14,39,
21,19,43,43,29],[
"fusion determined by construction of the table,\n",
"the map on the CAS table is wrong"
]);
ALF("3^2+4:2(2^2xa4)2","3^(2+4):2(S4xD8)",[1,2,3,5,4,6,7,8,27,28,28,29,19,
20,12,14,14,13,15,15,21,9,10,11,33,32,32,34,30,31,38,39,16,18,18,17,25,23,
24,26,25,23,24,26,35,37,36,36,22],[
"fusion map is unique"
]);

MOT("3^4:2(A4xA4).4",
[
"origin: computed by Klaus Lux using Dixon's Algorithm,\n",
"13th maximal subgroup of HN,\n",
"table is sorted w.r. to normal series 3^4.2.2^4.3^2.2.2,\n",
"tests: 1.o.r., pow[2,3],"
],
[93312,2916,1944,1152,576,96,72,648,162,81,81,72,18,27,12,144,288,32,36,36,8,
36,24,24,16,16,16,16,12,12],
[,[1,2,3,1,1,4,3,8,9,10,11,8,9,14,12,1,5,5,2,3,6,7,16,16,18,18,18,18,19,19],[
1,1,1,4,5,6,5,1,1,1,1,4,4,2,6,16,17,18,16,16,21,17,24,23,28,27,26,25,24,23]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1],[1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-E(4),E(4),-E(4),-E(4),E(4),E(4),-E(4),E(4)],
[TENSOR,[2,3]],[4,4,4,4,4,4,4,1,-2,1,-2,1,-2,-2,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0],[4,4,4,4,4,4,4,-2,1,-2,1,-2,1,1,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[6,6,6,6,
-2,2,-2,3,0,3,0,3,0,0,-1,-2,2,2,-2,-2,0,2,0,0,0,0,0,0,0,0],
[TENSOR,[7,3]],[9,9,9,9,1,-3,1,0,0,0,0,0,0,0,0,1,1,1,1,1,-1,1,1,1,-1,-1,-1,-1,
1,1],
[TENSOR,[9,2]],
[TENSOR,[9,3]],
[TENSOR,[9,4]],[12,12,12,12,-4,4,-4,-3,0,-3,0,-3,0,0,1,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0],[4,4,4,-4,0,0,0,-2,1,-2,1,2,-1,1,0,0,2,-2,0,0,0,2,0,0,-E(8)-E(8)^3,
E(8)+E(8)^3,E(8)+E(8)^3,-E(8)-E(8)^3,0,0],
[TENSOR,[14,2]],
[TENSOR,[14,3]],
[TENSOR,[14,4]],[16,16,16,-16,0,0,0,-2,-2,-2,-2,2,2,-2,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0],[16,16,16,-16,0,0,0,4,1,4,1,-4,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0],[32,5,-4,0,0,0,0,8,2,-1,2,0,0,-1,0,4,0,0,1,-2,0,0,-2,-2,0,0,0,0,1,1],
[TENSOR,[20,2]],
[TENSOR,[20,3]],
[TENSOR,[20,4]],[48,-6,3,0,8,0,-1,0,6,0,-3,0,0,0,0,4,8,0,-2,1,0,-1,0,0,0,0,0,
0,0,0],
[TENSOR,[24,3]],[96,-12,6,0,16,0,-2,0,-6,0,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0],[128,20,-16,0,0,0,0,-16,2,2,2,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[
128,20,-16,0,0,0,0,8,-4,-1,-4,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[144,-18,
9,0,-8,0,1,0,0,0,0,0,0,0,0,-4,8,0,2,-1,0,-1,0,0,0,0,0,0,0,0],
[TENSOR,[29,3]]],
[(25,26)(27,28),(23,24)(25,27)(26,28)(29,30)]);
ALF("3^4:2(A4xA4).4","HN",[1,5,4,3,2,6,14,4,5,5,4,15,16,20,31,3,7,7,16,15,
19,30,8,8,18,18,18,18,32,32],[
"fusion map is unique"
]);
ALF("3^4:2(A4xA4).4","3^4:2(S4xS4).2",[1,2,3,4,5,6,7,8,9,11,10,12,13,14,
15,16,17,18,20,19,21,22,23,23,24,25,25,24,26,26],[
"fusion map is unique up to table aut."
]);

MOT("3^4:m10",
[
"origin: CAS library,\n",
" maximal subgroup of mcl\n",
"  structure:= 3^4:m10\n",
"  1st & 2nd orthogonality relations are satisfied\n",
"  symmetric squares decompose properly\n",
"  created 30/01/1985\n",
"tests: 1.o.r., pow[2,3,5]"
],
[58320,2916,972,144,36,36,81,81,81,27,27,8,5,12,12,12,8,8],
[,[1,2,3,1,3,2,7,8,9,11,10,4,13,4,6,6,12,12],[1,1,1,4,4,4,1,1,1,2,2,12,13,14,
14,14,17,18],,[1,2,3,4,5,6,7,8,9,11,10,12,1,14,16,15,18,17]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,
-1],[9,9,9,1,1,1,0,0,0,0,0,1,-1,1,1,1,-1,-1],
[TENSOR,[3,2]],[10,10,10,2,2,2,1,1,1,1,1,-2,0,0,0,0,0,0],[10,10,10,-2,-2,-2,1,
1,1,1,1,0,0,0,0,0,E(8)+E(8)^3,-E(8)-E(8)^3],
[TENSOR,[6,2]],[16,16,16,0,0,0,-2,-2,-2,-2,-2,0,1,0,0,0,0,0],[20,-7,2,4,-2,1,
2,2,2,-1,-1,0,0,2,-1,-1,0,0],
[TENSOR,[9,2]],[20,-7,2,-4,2,-1,2,2,2,-1,-1,0,0,0,-E(12)^7+E(12)^11,
E(12)^7-E(12)^11,0,0],
[TENSOR,[11,2]],[60,6,-3,4,1,-2,6,-3,-3,0,0,0,0,0,0,0,0,0],[60,6,-3,4,1,-2,-3,
6,-3,0,0,0,0,0,0,0,0,0],[60,6,-3,4,1,-2,-3,-3,6,0,0,0,0,0,0,0,0,0],[80,-28,8,
0,0,0,-1,-1,-1,E(3)-2*E(3)^2,-2*E(3)+E(3)^2,0,0,0,0,0,0,0],
[GALOIS,[16,2]],[180,18,-9,-4,-1,2,0,0,0,0,0,0,0,0,0,0,0,0]],
[(17,18),(15,16),(15,16)(17,18),(10,11),(10,11)(15,16),(8,9),(7,8)]);
ARC("3^4:m10","projectives",["3^5:M10",[[36,9,0,4,-2,1,0,0,0,0,0,0,1,2,-1,
-1,0,0],[36,9,0,-4,2,-1,0,0,0,0,0,0,1,0,-E(12)^7+E(12)^11,E(12)^7-E(12)^11,0,
0],[45,-9,0,-3,0,3,0,0,0,0,0,1,0,1,1,1,-1,-1],[45,-9,0,5,2,-1,0,0,0,0,0,1,0,1,
1,1,1,1],[90,-18,0,2,2,2,0,0,0,0,0,-2,0,0,0,0,0,0],[90,-18,0,-2,-2,-2,0,0,0,0,
0,0,0,0,0,0,-E(8)-E(8)^3,E(8)+E(8)^3],[144,36,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,
0]],]);
ARC("3^4:m10","tomfusion",rec(name:="3^4:M10",map:=[1,3,4,2,17,16,5,6,7,34,34,
10,11,9,44,44,19,19],text:=[
"fusion map is unique up to table automorphisms"
]));
ALF("3^4:m10","McL",[1,3,4,2,9,8,4,4,4,13,14,5,7,5,18,18,12,12],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("3^4:m10","A6.2_3",[1,1,1,2,2,2,3,3,3,3,3,4,5,6,6,6,7,8]);
ALF("3^4:m10","U4(3).2_3",[1,3,4,2,10,9,4,5,5,13,14,7,8,17,23,23,21,21],[
"fusion map is unique up to table autom."
]);
ALF("3^4:m10","3^4:(M10x2)",[1,2,3,4,6,5,7,8,8,9,9,10,11,12,13,13,14,15],[
"fusion map is unique up to table aut."
]);

MOT("3^5:M10",
[
"6th maximal subgroup of 3.McL,\n",
"constructed 1996/09/09 by Thomas Breuer using the tables of 3^4.m10, McL,\n",
"and 3.McL"
],
[174960,174960,174960,8748,8748,8748,972,432,432,432,108,108,108,108,108,108,
81,81,81,27,27,24,24,24,15,15,15,36,36,36,36,36,36,36,36,36,24,24,24,24,24,
24],
[,[1,3,2,4,6,5,7,1,3,2,7,7,7,4,6,5,17,18,19,21,20,8,10,9,25,27,26,8,10,9,14,
16,15,14,16,15,22,24,23,22,24,23],[1,1,1,1,1,1,1,8,8,8,8,8,8,8,8,8,1,1,1,5,6,
22,22,22,25,25,25,28,28,28,28,28,28,28,28,28,37,37,37,40,40,40],,[1,3,2,4,6,5,
7,8,10,9,11,13,12,14,16,15,17,18,19,21,20,22,24,23,1,3,2,28,30,29,34,36,35,31,
33,32,40,42,41,37,39,38]],
0,
[(37,40)(38,41)(39,42),(18,19),(17,18),(31,34)(32,35)(33,36),( 2, 3)( 5, 6)
( 9,10)(12,13)(15,16)(20,21)(23,24)(26,27)(29,30)(32,33)(35,36)(37,40)(38,42)
(39,41)],
["ConstructProj",[["3^4:m10",[]],,["3^5:M10",[-1,-1,-1,-1,-1,-1,-1]]]]);
ALF("3^5:M10","3^4:m10",[1,1,1,2,2,2,3,4,4,4,5,5,5,6,6,6,7,8,9,10,11,12,
12,12,13,13,13,14,14,14,15,15,15,16,16,16,17,17,17,18,18,18]);
ALF("3^5:M10","A6.2_3",[1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,3,3,3,3,3,4,4,4,
5,5,5,6,6,6,6,6,6,6,6,6,7,7,7,8,8,8]);
ALF("3^5:M10","3.McL",[1,2,3,7,8,9,10,4,5,6,23,24,25,20,21,22,10,10,10,
35,36,11,12,13,17,18,19,11,12,13,46,47,48,46,47,48,32,33,34,32,33,34],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("3^5:M10","3^5:(M10x2)",[1,2,2,3,4,4,5,6,7,7,8,9,9,10,11,11,12,
13,13,14,14,15,16,16,17,18,18,19,20,20,21,22,23,21,23,22,24,25,25,26,27,
27]);
ALN("3^5:M10",["3.3^4:m10"]);

MOT("3^4.3^2.Q8",
[
"origin: Dixon's Algorithm,\n",
"table of an intersection of maximal subgroups 3^{1+4}:4S_5 and 3^4:M_{10}\n",
"of the sporadic simple McLaughlin group McL"
],
[5832,2916,243,324,162,81,81,81,27,27,36,72,36,18,4,12,12,12,12,12,12],
[,[1,2,3,4,5,6,7,8,10,9,2,1,4,5,12,12,13,13,11,11,12],[1,1,1,1,1,1,1,1,2,2,12,
12,12,12,15,16,16,16,21,21,21],,[1,2,3,4,5,6,7,8,10,9,11,12,13,14,15,16,18,17,
20,19,21],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,17,20,19,21],,,,[1,2,3,
4,5,6,7,8,10,9,11,12,13,14,15,16,17,18,19,20,21]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
-1,-1,-1,-1,-1,-1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,1,1,1,-1,-1,-1],
[TENSOR,[2,3]],[2,2,2,2,2,2,2,2,2,2,-2,-2,-2,-2,0,0,0,0,0,0,0],[8,8,8,8,8,-1,
-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0],[2,2,2,-1,-1,2,2,2,-1,-1,2,2,-1,-1,0,2,-1,
-1,0,0,0],
[TENSOR,[7,2]],[2,2,2,-1,-1,2,2,2,-1,-1,-2,-2,1,1,0,0,E(12)^7-E(12)^11,
-E(12)^7+E(12)^11,0,0,0],
[TENSOR,[9,2]],[8,8,8,-4,-4,-1,-1,-1,-2*E(3)+E(3)^2,E(3)-2*E(3)^2,0,0,0,0,0,0,
0,0,0,0,0],
[GALOIS,[11,2]],[24,24,-3,0,0,6,-3,-3,0,0,0,0,0,0,0,0,0,0,0,0,0],[24,24,-3,0,
0,-3,6,-3,0,0,0,0,0,0,0,0,0,0,0,0,0],[24,24,-3,0,0,-3,-3,6,0,0,0,0,0,0,0,0,0,
0,0,0,0],[18,-9,0,-6,3,0,0,0,0,0,-1,2,2,-1,0,0,0,0,-1,-1,2],
[TENSOR,[16,2]],[18,-9,0,-6,3,0,0,0,0,0,1,-2,-2,1,0,0,0,0,-E(12)^7+E(12)^11,
E(12)^7-E(12)^11,0],
[TENSOR,[18,2]],[36,-18,0,6,-3,0,0,0,0,0,-2,4,-2,1,0,0,0,0,0,0,0],[36,-18,0,6,
-3,0,0,0,0,0,2,-4,2,-1,0,0,0,0,0,0,0]],
[(19,20),(17,18),( 9,10),( 7, 8),( 6, 7)]);
ARC("3^4.3^2.Q8","projectives",["3.3^4.3^2.Q8",[[9,9,0,-3,-3,0,0,0,0,0,1,1,1,
1,1,1,1,1,1,1,1],[18,-9,0,6,-3,0,0,0,0,0,-1,2,2,-1,0,0,0,0,1,1,-2],[18,-9,0,6,
-3,0,0,0,0,0,1,-2,-2,1,0,0,0,0,E(12)^7-E(12)^11,-E(12)^7+E(12)^11,0],[18,18,0,
-6,-6,0,0,0,0,0,-2,-2,-2,-2,0,0,0,0,0,0,0],[18,18,0,3,3,0,0,0,0,0,-2,-2,1,1,0,
0,E(12)^7-E(12)^11,-E(12)^7+E(12)^11,0,0,0],[18,18,0,3,3,0,0,0,0,0,2,2,-1,-1,
0,2,-1,-1,0,0,0],[36,-18,0,-6,3,0,0,0,0,0,-2,4,-2,1,0,0,0,0,0,0,0],[36,-18,0,
-6,3,0,0,0,0,0,2,-4,2,-1,0,0,0,0,0,0,0]],]);
ALF("3^4.3^2.Q8","3^(1+4):2S5",[1,2,3,8,9,3,3,3,10,11,5,4,13,12,20,20,23,
24,7,7,6],[
"fusion map is unique up to table automorphisms"
]);
ALF("3^4.3^2.Q8","3^4:m10",[1,2,3,2,3,7,8,9,11,10,6,4,6,5,12,14,15,16,15,
16,14],[
"fusion map is unique up to table automorphisms"
]);
ALF("3^4.3^2.Q8","McL",[1,3,4,3,4,4,4,4,14,13,8,2,8,9,5,5,18,18,18,18,5]);
ALF("3^4.3^2.Q8","McL.2N3",[1,2,3,6,7,4,5,5,8,8,13,11,14,15,12,16,18,18,
19,19,17],[
"fusion map is unique up to table aut."
]);

MOT("3.3^4.3^2.Q8",
[
"origin: constructed 1996/09/09 by T. Breuer using the tables of\n",
"3^4.3^2.Q8, 3^(2+4):2S5, McL, and 3.McL"
],
[17496,17496,17496,8748,8748,8748,243,972,972,972,486,486,486,81,81,81,27,27,
108,108,108,216,216,216,108,108,108,54,54,54,12,12,12,36,36,36,36,36,36,36,36,
36,36,36,36,36,36,36,36,36,36],
[,[1,3,2,4,6,5,7,8,10,9,11,13,12,14,15,16,18,17,4,6,5,1,3,2,8,10,9,11,13,12,
22,24,23,22,24,23,25,27,26,25,27,26,19,21,20,19,21,20,22,24,23],[1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,6,5,22,22,22,22,22,22,22,22,22,22,22,22,31,31,31,34,34,34,
34,34,34,34,34,34,49,49,49,49,49,49,49,49,49]],
0,
[(43,46)(44,47)(45,48),(15,16),(14,15),(37,40)(38,41)(39,42),( 2, 3)( 5, 6)
( 9,10)(12,13)(17,18)(20,21)(23,24)(26,27)(29,30)(32,33)(35,36)(38,39)(41,42)
(43,46)(44,48)(45,47)(50,51)],
["ConstructProj",[["3^4.3^2.Q8",[]],,["3.3^4.3^2.Q8",[-1,-1,-1,-1,-1,-1,-1,
-1]]]]);
ALF("3.3^4.3^2.Q8","3^4.3^2.Q8",[1,1,1,2,2,2,3,4,4,4,5,5,5,6,7,8,9,10,11,
11,11,12,12,12,13,13,13,14,14,14,15,15,15,16,16,16,17,17,17,18,18,18,19,
19,19,20,20,20,21,21,21]);
ALF("3.3^4.3^2.Q8","3^4:(3^2:Q8)",[1,1,1,3,3,3,5,4,4,4,6,6,6,7,8,9,16,17,
14,14,14,2,2,2,13,13,13,15,15,15,12,12,12,10,10,10,18,18,18,19,19,19,20,
20,20,21,21,21,11,11,11]);
ALF("3.3^4.3^2.Q8","3.3^(1+4):2S5",[1,3,2,4,6,5,7,20,22,21,23,25,24,7,7,7,
26,27,11,13,12,8,10,9,31,33,32,28,30,29,52,54,53,52,54,53,61,63,62,64,66,
65,17,19,18,17,19,18,14,16,15],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("3.3^4.3^2.Q8","3^5:M10",[1,2,3,4,5,6,7,4,5,6,7,7,7,17,18,19,21,20,
14,15,16,8,9,10,14,15,16,11,12,13,22,23,24,28,29,30,31,32,33,34,35,36,31,
32,33,34,35,36,28,29,30],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("3.3^4.3^2.Q8","3.McL",[1,3,2,7,9,8,10,7,9,8,10,10,10,10,10,10,35,36,
20,22,21,4,6,5,20,22,21,23,25,24,11,13,12,11,13,12,46,48,47,46,48,47,46,
48,47,46,48,47,11,13,12],[
"fusion map is unique up to table autom.,\n",
"compatible with 3^4:(3^2:Q8) -> McL"
]);
ALF("3.3^4.3^2.Q8","3.McL.2N3",[1,2,2,3,4,4,5,6,7,7,8,9,9,10,11,11,12,12,
13,14,14,15,16,16,17,18,18,19,20,20,21,22,22,23,24,24,25,26,27,25,27,26,
28,29,30,28,30,29,31,32,32]);
ALN("3.3^4.3^2.Q8",["3.McLN3"]);

MOT("3xL3(4).2_2",
[
"7th maximal subgroup of 3.McL"
],
0,
0,
0,
[(2,3)(5,6)(8,9)(11,12)(14,15)(17,18)(20,21)(23,24)(26,27)(29,30)(32,33)(35,
36)(38,39)(41,42),(19,22)(20,23)(21,24)(37,40)(38,41)(39,42)],
["ConstructDirectProduct",[["L3(4).2_2"],["Cyclic",3]]]);
ALF("3xL3(4).2_2","3.McL",[1,2,3,4,5,6,10,10,10,11,12,13,11,12,13,17,18,
19,26,27,28,29,30,31,4,5,6,11,12,13,23,24,25,32,33,34,49,50,51,52,53,54],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);

MOT("3x2.A8",
[
"8th maximal subgroup of 3.McL"
],
0,
0,
0,
[(58,64)(59,65)(60,66)(61,67)(62,68)(63,69),(40,43)(41,44)(42,45),(2,3)(5,6)
(8,9)(11,12)(14,15)(17,18)(20,21)(23,24)(26,27)(29,30)(32,33)(35,36)(38,39)
(41,42)(44,45)(47,48)(50,51)(53,54)(56,57)(59,60)(62,63)(65,66)(68,69),(46,52)
(47,53)(48,54)(49,55)(50,56)(51,57)],
["ConstructDirectProduct",[["2.A8"],["Cyclic",3]]]);
ALF("3x2.A8","3.McL",[1,2,3,4,5,6,4,5,6,11,12,13,7,8,9,20,21,22,10,10,10,
23,24,25,11,12,13,32,33,34,14,15,16,37,38,39,46,47,48,25,23,24,24,25,23,
26,27,28,49,50,51,29,30,31,52,53,54,55,56,57,61,62,63,58,59,60,64,65,66],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);
ALF("3x2.A8","(2.A8x3).2",[1,2,2,3,4,4,5,6,6,7,8,8,9,10,10,11,12,12,13,14,
14,15,16,16,17,18,18,19,20,20,21,22,22,23,24,24,25,26,26,27,28,29,27,29,
28,30,31,32,33,34,35,30,32,31,33,35,34,36,37,38,39,40,41,36,38,37,39,41,
40],[ 
"fusion map is unique up to table automorphisms"
]);

MOT("3xM11",
[
"11th maximal subgroup of 3.McL"
],
0,
0,
0,
[(19,22)(20,23)(21,24),(2,3)(5,6)(8,9)(11,12)(14,15)(17,18)(20,21)(23,24)(26,
27)(29,30),(25,28)(26,29)(27,30)],
["ConstructDirectProduct",[["M11"],["Cyclic",3]]]);
ALF("3xM11","3.McL",[1,2,3,4,5,6,10,10,10,11,12,13,17,18,19,23,24,25,32,
33,34,32,33,34,40,41,42,43,44,45],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("3xM11","3.ON",[1,2,3,4,5,6,7,7,7,11,12,13,14,15,16,17,17,17,24,25,26,
24,25,26,33,34,35,33,34,35],[
"fusion map is unique up to table aut."
]);

MOT("3xONM11",
[
"11th maximal subgroup of 3.ON,\n",
"differs from 3.ONM10 only by fusion map"
],
0,
0,
0,
0,
["ConstructPermuted",["3xM11"]]);
ALF("3xONM11","3.ON",[1,2,3,4,5,6,7,7,7,11,12,13,14,15,16,17,17,17,27,28,
29,27,28,29,33,34,35,33,34,35],[
"fusion map is unique up to table automorphisms,\n",
"equals the map from 3.ONM10, mapped under the outer autom."
]);

MOT("3x5^(1+2):3:8",
[
"12th maximal subgroup of 3.McL"
],
0,
0,
0,
[(46,49)(47,50)(48,51)(52,55)(53,56)(54,57),(25,31)(26,32)(27,33)(28,34)(29,
35)(30,36),(10,13)(11,14)(12,15)(25,28)(26,29)(27,30)(31,34)(32,35)(33,36)(40,
43)(41,44)(42,45),(2,3)(5,6)(8,9)(11,12)(14,15)(17,18)(20,21)(23,24)(26,27)
(29,30)(32,33)(35,36)(38,39)(41,42)(44,45)(47,48)(50,51)(53,54)(56,57)],
["ConstructDirectProduct",[["5^(1+2):3:8"],["Cyclic",3]]]);
ALF("3x5^(1+2):3:8","5^(1+2):3:8",[1,1,1,2,2,2,3,3,3,4,4,4,5,5,5,6,6,6,7,
7,7,8,8,8,9,9,9,10,10,10,11,11,11,12,12,12,13,13,13,14,14,14,15,15,15,16,
16,16,17,17,17,18,18,18,19,19,19]);
ALF("3x5^(1+2):3:8","3.McL.2N5",[1,2,2,3,4,4,5,6,6,7,8,8,9,10,10,11,12,12,
13,14,14,15,16,16,17,18,19,20,21,22,17,19,18,20,22,21,23,24,24,25,26,26,
27,28,28,29,30,31,29,31,30,32,33,34,32,34,33],[
"fusion map is unique up to table automorphisms"
]);
ALF("3x5^(1+2):3:8","3.McL",[1,2,3,4,5,6,7,8,9,11,12,13,11,12,13,14,15,16,
17,18,19,20,21,22,32,33,34,32,33,34,32,33,34,32,33,34,37,38,39,46,47,48,
46,47,48,55,56,57,58,59,60,61,62,63,64,65,66],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALN("3x5^(1+2):3:8",["3.McLN5","3xMcLN5"]);

MOT("3^5:2S6",
[
"origin: contructed in GAP using table of 3^4:2A6, and perm. char.,\n",
"8th maximal subgroup of Th,\n",
"3C normalizer,\n",
"table is sorted w.r. to normal series given by 3.3^4.2.A6.2,\n",
"tests: 1.o.r., pow[2,3,5]"
],
[349920,174960,4374,2187,4320,2160,48,24,972,486,486,486,243,243,243,243,243,
108,54,972,486,243,243,243,243,243,243,108,54,24,24,24,30,30,30,30,30,30,432,
54,48,8,36,18,36,18,12,12],
[,[1,2,3,4,1,2,5,6,9,11,10,12,13,15,14,16,17,9,12,20,21,23,22,27,26,25,24,20,
21,7,8,8,33,34,35,33,35,34,1,3,5,7,9,10,9,11,28,28],[1,1,1,1,5,5,7,7,1,1,1,1,
1,1,1,1,1,5,5,1,1,1,1,1,1,1,1,5,5,30,30,30,33,33,33,36,36,36,39,39,41,42,39,
39,39,39,41,41],,[1,2,3,4,5,6,7,8,9,11,10,12,13,15,14,16,17,18,19,20,21,23,22,
27,26,25,24,28,29,30,31,32,1,2,2,5,6,6,39,40,41,42,45,46,43,44,48,47]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[5,5,5,5,5,5,1,1,2,2,2,2,2,
2,2,2,2,2,2,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0,3,3,-1,1,0,0,0,
0,-1,-1],
[TENSOR,[3,2]],[5,5,5,5,5,5,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,2,2,2,2,2,2,
2,2,2,2,-1,-1,-1,0,0,0,0,0,0,-1,-1,3,1,-1,-1,-1,-1,0,0],
[TENSOR,[5,2]],[16,16,16,16,16,16,0,0,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,
-2,-2,-2,-2,-2,-2,-2,-2,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0],[9,9,9,9,9,9,1,
1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,-1,-1,-1,-1,-1,-1,3,3,3,-1,
0,0,0,0,0,0],
[TENSOR,[8,2]],[10,10,10,10,10,10,-2,-2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,0,0,0,0,0,0,0,0,0,2,2,-2,0,-1,-1,-1,-1,1,1],
[TENSOR,[10,2]],[4,4,4,4,-4,-4,0,0,-2,-2,-2,-2,-2,-2,-2,-2,-2,2,2,1,1,1,1,1,1,
1,1,-1,-1,0,0,0,-1,-1,-1,1,1,1,0,0,0,0,0,0,0,0,-E(12)^7+E(12)^11,
E(12)^7-E(12)^11],
[TENSOR,[12,2]],[4,4,4,4,-4,-4,0,0,1,1,1,1,1,1,1,1,1,-1,-1,-2,-2,-2,-2,-2,-2,
-2,-2,2,2,0,0,0,-1,-1,-1,1,1,1,0,0,0,0,E(3)-E(3)^2,E(3)-E(3)^2,-E(3)+E(3)^2,
-E(3)+E(3)^2,0,0],
[TENSOR,[14,2]],[16,16,16,16,-16,-16,0,0,-2,-2,-2,-2,-2,-2,-2,-2,-2,2,2,-2,-2,
-2,-2,-2,-2,-2,-2,2,2,0,0,0,1,1,1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0],[20,20,20,20,
-20,-20,0,0,2,2,2,2,2,2,2,2,2,-2,-2,2,2,2,2,2,2,2,2,-2,-2,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0],[80,80,-1,-1,0,0,0,0,8,-1,-1,8,-1,-1,-1,-1,-1,0,0,8,8,-1,
-1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,-8,1,0,0,-2,1,-2,1,0,0],
[TENSOR,[18,2]],[80,80,-1,-1,0,0,0,0,2,E(3)+4*E(3)^2,4*E(3)+E(3)^2,2,2,
E(3)+4*E(3)^2,4*E(3)+E(3)^2,2,2,0,0,-4,-4,-2*E(3)+E(3)^2,E(3)-2*E(3)^2,
-2*E(3)+E(3)^2,E(3)-2*E(3)^2,-2*E(3)+E(3)^2,E(3)-2*E(3)^2,0,0,0,0,0,0,0,0,0,0,
0,8,-1,0,0,2*E(3)^2,-E(3)^2,2*E(3),-E(3),0,0],
[GALOIS,[20,2]],
[TENSOR,[20,2]],
[TENSOR,[21,2]],[160,160,-2,-2,0,0,0,0,4,4,4,4,-5,4,4,-5,-5,0,0,-8,-8,1,1,1,1,
1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[160,160,-2,-2,0,0,0,0,-8,
2*E(3)-4*E(3)^2,-4*E(3)+2*E(3)^2,-8,1,2*E(3)-4*E(3)^2,-4*E(3)+2*E(3)^2,1,1,0,
0,4,4,-E(3)+2*E(3)^2,2*E(3)-E(3)^2,-E(3)+2*E(3)^2,2*E(3)-E(3)^2,
-E(3)+2*E(3)^2,2*E(3)-E(3)^2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[25,2]],[2,-1,2,-1,2,-1,2,-1,2,2,2,-1,2,-1,-1,-1,-1,2,-1,2,-1,2,2,-1,
-1,-1,-1,2,-1,2,-1,-1,2,-1,-1,2,-1,-1,0,0,0,0,0,0,0,0,0,0],[8,-4,8,-4,-8,4,0,
0,-4,-4,-4,2,-4,2,2,2,2,4,-2,2,-1,2,2,-1,-1,-1,-1,-2,1,0,0,0,-2,1,1,2,-1,-1,0,
0,0,0,0,0,0,0,0,0],[8,-4,8,-4,-8,4,0,0,2,2,2,-1,2,-1,-1,-1,-1,-2,1,-4,2,-4,-4,
2,2,2,2,4,-2,0,0,0,-2,1,1,2,-1,-1,0,0,0,0,0,0,0,0,0,0],[10,-5,10,-5,10,-5,2,
-1,-2,-2,-2,1,-2,1,1,1,1,-2,1,4,-2,4,4,-2,-2,-2,-2,4,-2,-2,1,1,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0],[10,-5,10,-5,10,-5,2,-1,4,4,4,-2,4,-2,-2,-2,-2,4,-2,-2,1,
-2,-2,1,1,1,1,-2,1,-2,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[16,-8,16,-8,-16,8,
0,0,-2,-2,-2,1,-2,1,1,1,1,2,-1,-2,1,-2,-2,1,1,1,1,2,-1,0,0,0,1,
-E(15)-E(15)^2-E(15)^4-E(15)^8,-E(15)^7-E(15)^11-E(15)^13-E(15)^14,-1,
E(15)^7+E(15)^11+E(15)^13+E(15)^14,E(15)+E(15)^2+E(15)^4+E(15)^8,0,0,0,0,0,0,
0,0,0,0],
[GALOIS,[32,7]],[16,-8,16,-8,16,-8,0,0,-2,-2,-2,1,-2,1,1,1,1,-2,1,-2,1,-2,-2,
1,1,1,1,-2,1,0,0,0,1,-E(15)-E(15)^2-E(15)^4-E(15)^8,-E(15)^7-E(15)^11-E(15)^13
 -E(15)^14,1,-E(15)^7-E(15)^11-E(15)^13-E(15)^14,-E(15)-E(15)^2-E(15)^4
 -E(15)^8,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[34,7]],[18,-9,18,-9,18,-9,2,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,2,-1,-1,-2,1,1,-2,1,1,0,0,0,0,0,0,0,0,0,0],[20,-10,20,-10,20,-10,-4,2,2,2,
2,-1,2,-1,-1,-1,-1,2,-1,2,-1,2,2,-1,-1,-1,-1,2,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0],[20,-10,20,-10,-20,10,0,0,2,2,2,-1,2,-1,-1,-1,-1,-2,1,2,-1,2,2,-1,
-1,-1,-1,-2,1,0,-E(24)-E(24)^11+E(24)^17+E(24)^19,E(24)+E(24)^11-E(24)^17
 -E(24)^19,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[38,13]],[160,-80,-2,1,0,0,0,0,4,4,4,-2,-5,-2,-2,7,-2,0,0,-8,4,1,1,-5,
4,4,-5,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[160,-80,-2,1,0,0,0,0,4,4,4,
-2,-5,-2,-2,-2,7,0,0,-8,4,1,1,4,-5,-5,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0],[160,-80,-2,1,0,0,0,0,16,-2,-2,-8,-2,1,1,1,1,0,0,16,-8,-2,-2,1,1,1,1,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[160,-80,-2,1,0,0,0,0,-8,
2*E(3)-4*E(3)^2,-4*E(3)+2*E(3)^2,4,1,-E(3)+2*E(3)^2,2*E(3)-E(3)^2,4,-5,0,0,4,
-2,-E(3)+2*E(3)^2,2*E(3)-E(3)^2,-4*E(3)-E(3)^2,-E(3)+5*E(3)^2,5*E(3)-E(3)^2,
-E(3)-4*E(3)^2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[160,-80,-2,1,0,0,0,
0,-8,2*E(3)-4*E(3)^2,-4*E(3)+2*E(3)^2,4,1,-E(3)+2*E(3)^2,2*E(3)-E(3)^2,-5,4,0,
0,4,-2,-E(3)+2*E(3)^2,2*E(3)-E(3)^2,5*E(3)-E(3)^2,-E(3)-4*E(3)^2,
-4*E(3)-E(3)^2,-E(3)+5*E(3)^2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[43,2]],
[GALOIS,[44,2]],[160,-80,-2,1,0,0,0,0,4,2*E(3)+8*E(3)^2,8*E(3)+2*E(3)^2,-2,4,
-E(3)-4*E(3)^2,-4*E(3)-E(3)^2,-2,-2,0,0,-8,4,-4*E(3)+2*E(3)^2,2*E(3)-4*E(3)^2,
2*E(3)-E(3)^2,-E(3)+2*E(3)^2,2*E(3)-E(3)^2,-E(3)+2*E(3)^2,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[47,2]]],
[(47,48),(34,35)(37,38),(31,32),(16,17)(24,26)(25,27),(10,11)(14,15)(22,23)
(24,27)(25,26)(43,45)(44,46)]);
ALF("3^5:2S6","Th",[1,5,4,5,2,9,7,22,3,4,4,4,5,5,5,4,5,10,11,5,3,5,5,5,4,
4,5,9,10,14,34,35,8,25,26,18,41,40,2,11,7,14,10,11,10,11,22,22],[
"fusion map is unique up to table automorphisms"
]);
ALF("3^5:2S6","2.A6.2_1",[1,1,1,1,2,2,3,3,4,4,4,4,4,4,4,4,4,5,5,6,6,6,6,6,
6,6,6,7,7,8,8,8,9,9,9,10,10,10,11,11,12,13,14,14,15,15,16,17]);
ALF("3^5:2S6","S3",[1,2,1,2,1,2,1,2,1,1,1,2,1,2,2,2,2,1,2,1,2,1,1,2,2,2,2,
1,2,1,2,2,1,2,2,1,2,2,3,3,3,3,3,3,3,3,3,3]);
ALN("3^5:2S6",["ThN3C"]);

MOT("3^5:M11",
[
"maximal subgroup of Suz,\n",
"tests: 1.o.r., pow[2,3,5,11]"
],
[1924560,87480,8748,1296,324,324,216,108,162,81,54,54,24,12,15,15,15,18,18,18,
8,8,11,11],
[,[1,2,3,1,3,3,2,3,9,10,12,11,4,7,15,16,17,9,12,11,13,13,24,23],[1,1,1,4,4,4,
4,4,1,1,3,3,13,13,15,15,15,4,6,5,21,22,23,24],,[1,2,3,4,6,5,7,8,9,10,12,11,13,
14,1,2,2,18,20,19,22,21,23,24],,,,,,[1,2,3,4,6,5,7,8,9,10,12,11,13,14,15,17,
16,18,20,19,21,22,1,1]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[10,10,10,2,2,2,2,2,1,1,1,
1,2,2,0,0,0,-1,-1,-1,0,0,-1,-1],[10,10,10,-2,-2,-2,-2,-2,1,1,1,1,0,0,0,0,0,1,
1,1,E(8)+E(8)^3,-E(8)-E(8)^3,-1,-1],
[GALOIS,[3,5]],[11,11,11,3,3,3,3,3,2,2,2,2,-1,-1,1,1,1,0,0,0,-1,-1,0,0],[16,
16,16,0,0,0,0,0,-2,-2,-2,-2,0,0,1,1,1,0,0,0,0,0,E(11)+E(11)^3+E(11)^4+E(11)^5
 +E(11)^9,E(11)^2+E(11)^6+E(11)^7+E(11)^8+E(11)^10],
[GALOIS,[6,2]],[44,44,44,4,4,4,4,4,-1,-1,-1,-1,0,0,-1,-1,-1,1,1,1,0,0,0,0],[
45,45,45,-3,-3,-3,-3,-3,0,0,0,0,1,1,0,0,0,0,0,0,-1,-1,1,1],[55,55,55,-1,-1,-1,
-1,-1,1,1,1,1,-1,-1,0,0,0,-1,-1,-1,1,1,0,0],[110,-25,2,14,-4,-4,-1,2,2,2,-1,
-1,2,-1,0,0,0,2,-1,-1,0,0,0,0],[110,-25,2,-2,-2,-2,7,-2,2,2,-1,-1,2,-1,0,0,0,
-2,1,1,0,0,0,0],[110,-25,2,6,6*E(3),6*E(3)^2,3,0,2,2,-1,-1,-2,1,0,0,0,0,
E(3)-E(3)^2,-E(3)+E(3)^2,0,0,0,0],
[GALOIS,[13,2]],[132,24,-3,12,3,3,0,-3,6,-3,0,0,0,0,2,-1,-1,0,0,0,0,0,0,0],[
220,-50,4,-12,6,6,-6,0,4,4,-2,-2,0,0,0,0,0,0,0,0,0,0,0,0],[396,72,-9,-12,-3,
-3,0,3,0,0,0,0,0,0,1,-E(15)^7-E(15)^11-E(15)^13-E(15)^14,
-E(15)-E(15)^2-E(15)^4-E(15)^8,0,0,0,0,0,0,0],
[GALOIS,[17,7]],[440,-100,8,8,-2*E(3)+4*E(3)^2,4*E(3)-2*E(3)^2,-4,2,-1,-1,
-2*E(3)+E(3)^2,E(3)-2*E(3)^2,0,0,0,0,0,-1,-E(3)^2,-E(3),0,0,0,0],[440,-100,8,
-8,2*E(3)-4*E(3)^2,-4*E(3)+2*E(3)^2,4,-2,-1,-1,-2*E(3)+E(3)^2,E(3)-2*E(3)^2,0,
0,0,0,0,1,E(3)^2,E(3),0,0,0,0],
[GALOIS,[20,2]],
[GALOIS,[19,2]],[528,96,-12,0,0,0,0,0,6,-3,0,0,0,0,-2,1,1,0,0,0,0,0,0,0],[660,
120,-15,12,3,3,0,-3,-6,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0]],
[(23,24),(16,17),(21,22),( 5, 6)(11,12)(19,20)]);
ARC("3^5:M11","projectives",["3^6.M11",[[12,-6,3,4,E(3)+3*E(3)^2,
3*E(3)+E(3)^2,-2,1,3,0,E(3)-E(3)^2,-E(3)+E(3)^2,0,0,2,-1,-1,1,1,1,0,0,1,1],[
60,-30,15,4,E(3)+3*E(3)^2,3*E(3)+E(3)^2,-2,1,-3,0,-E(3)+E(3)^2,E(3)-E(3)^2,0,
0,0,0,0,1,1,1,0,0,E(11)^2+E(11)^6+E(11)^7+E(11)^8+E(11)^10,
E(11)+E(11)^3+E(11)^4+E(11)^5+E(11)^9],
[GALOIS,[2,7]],[66,21,3,2,-E(3)+3*E(3)^2,3*E(3)-E(3)^2,5,-1,3,0,E(3)+2*E(3)^2,
2*E(3)+E(3)^2,-2,1,1,1,1,-1,-E(3),-E(3)^2,0,0,0,0],[66,21,3,10,
-5*E(3)-3*E(3)^2,-3*E(3)-5*E(3)^2,1,1,3,0,E(3)+2*E(3)^2,2*E(3)+E(3)^2,2,-1,1,
1,1,1,E(3),E(3)^2,0,0,0,0],[120,-60,30,-8,-2*E(3)-6*E(3)^2,-6*E(3)-2*E(3)^2,4,
-2,3,0,E(3)-E(3)^2,-E(3)+E(3)^2,0,0,0,0,0,1,1,1,0,0,-1,-1],[120,-60,30,8,
2*E(3)+6*E(3)^2,6*E(3)+2*E(3)^2,-4,2,3,0,E(3)-E(3)^2,-E(3)+E(3)^2,0,0,0,0,0,
-1,-1,-1,0,0,-1,-1],[132,-66,33,-4,-E(3)-3*E(3)^2,-3*E(3)-E(3)^2,2,-1,-3,0,
-E(3)+E(3)^2,E(3)-E(3)^2,0,0,2,-1,-1,-1,-1,-1,0,0,0,0],[144,-72,36,0,0,0,0,0,
0,0,0,0,0,0,-1,E(15)^7+E(15)^11+E(15)^13+E(15)^14,E(15)+E(15)^2+E(15)^4
 +E(15)^8,0,0,0,0,0,1,1],
[GALOIS,[9,7]],[165,-15,-6,13,4*E(3),4*E(3)^2,1,-2,3,0,-2*E(3)-E(3)^2,
-E(3)-2*E(3)^2,1,1,0,0,0,1,E(3)^2,E(3),1,1,0,0],[165,-15,-6,-11,-2*E(3),
-2*E(3)^2,1,4,3,0,-2*E(3)-E(3)^2,-E(3)-2*E(3)^2,1,1,0,0,0,1,E(3)^2,E(3),-1,-1,
0,0],[264,84,12,-8,4*E(3)+6*E(3)^2,6*E(3)+4*E(3)^2,4,-2,3,0,E(3)+2*E(3)^2,
2*E(3)+E(3)^2,0,0,-1,-1,-1,1,E(3),E(3)^2,0,0,0,0],[264,84,12,8,
-4*E(3)-6*E(3)^2,-6*E(3)-4*E(3)^2,-4,2,3,0,E(3)+2*E(3)^2,2*E(3)+E(3)^2,0,0,-1,
-1,-1,-1,-E(3),-E(3)^2,0,0,0,0],[330,105,15,2,-E(3)+3*E(3)^2,3*E(3)-E(3)^2,5,
-1,-3,0,-E(3)-2*E(3)^2,-2*E(3)-E(3)^2,2,-1,0,0,0,-1,-E(3),-E(3)^2,0,0,0,0],[
330,-30,-12,-2,-2*E(3),-2*E(3)^2,-2,-2,-3,0,2*E(3)+E(3)^2,E(3)+2*E(3)^2,0,0,0,
0,0,1,E(3)^2,E(3),-E(8)-E(8)^3,E(8)+E(8)^3,0,0],
[GALOIS,[16,7]],[330,-30,-12,2,2*E(3),2*E(3)^2,2,2,-3,0,2*E(3)+E(3)^2,
E(3)+2*E(3)^2,2,2,0,0,0,-1,-E(3)^2,-E(3),0,0,0,0],[330,105,15,10,
-5*E(3)-3*E(3)^2,-3*E(3)-5*E(3)^2,1,1,-3,0,-E(3)-2*E(3)^2,-2*E(3)-E(3)^2,-2,1,
0,0,0,1,E(3),E(3)^2,0,0,0,0],[396,126,18,-12,6*E(3),6*E(3)^2,-6,0,0,0,0,0,0,0,
1,1,1,0,0,0,0,0,0,0],[495,-45,-18,-9,0,0,3,6,0,0,0,0,-1,-1,0,0,0,0,0,0,1,1,0,
0],[495,-45,-18,15,6*E(3),6*E(3)^2,3,0,0,0,0,0,-1,-1,0,0,0,0,0,0,-1,-1,0,0],[
660,-60,-24,-4,-4*E(3),-4*E(3)^2,-4,-4,3,0,-2*E(3)-E(3)^2,-E(3)-2*E(3)^2,0,0,
0,0,0,-1,-E(3)^2,-E(3),0,0,0,0]],]);
ARC("3^5:M11","CAS",[rec(name:="3^5:m11",
permchars:=( 3,13,15, 9, 5)( 4,19,17,16,10, 6,14,21,23,11, 7,20,18,22,24,12, 8
 ),
permclasses:=( 5, 6, 7)( 9,13)(10,14)(11,15,20,19,18,17,22,12,16,21),
text:=[
"origin: CAS library,\n",
" maximal subgroup of suz\n",
" subgroup of index 2 in maximal subgroup of ly \n",
" test:= 1. o.r.,sym 2 decompose correctly \n",
""])]);
ALF("3^5:M11","Suz",[1,4,5,2,14,15,13,16,5,6,23,22,9,29,12,37,37,16,39,38,
21,21,26,26],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("3^5:M11","Ly",[1,3,4,2,10,10,8,9,4,4,14,14,5,19,7,24,24,10,25,25,13,
13,17,18],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("3^5:M11","LyM6",[1,2,3,4,5,5,6,7,8,9,10,10,11,12,13,14,14,15,16,16,
17,18,19,20],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables"
]);
ALF("3^5:M11","3^5:(M11x2)",[1,2,3,4,6,6,5,7,8,9,10,10,11,12,13,14,14,15,
16,16,17,18,19,20],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables"
]);
ALF("3^5:M11","M11",[1,1,1,2,2,2,2,2,3,3,3,3,4,4,5,5,5,6,6,6,7,8,9,10]);
ALN("3^5:M11",["lyu1"]);

MOT("3^6.M11",
[
"5th maximal subgroup of 3.Suz,\n",
"table constructed in GAP using tables of SuzM5 and 3.Suz,\n",
"tests: 1.o.r., pow[2,3,5,11]"
],
[5773680,5773680,5773680,262440,262440,262440,26244,26244,26244,3888,3888,
3888,972,972,972,972,972,972,648,648,648,324,324,324,486,486,486,81,162,162,
162,162,162,162,72,72,72,36,36,36,45,45,45,45,45,45,45,45,45,54,54,54,54,54,
54,54,54,54,24,24,24,24,24,24,33,33,33,33,33,33],
[,[1,3,2,4,6,5,7,9,8,1,3,2,7,9,8,7,9,8,4,6,5,7,9,8,25,27,26,28,32,34,33,29,31,
30,10,12,11,19,21,20,41,43,42,44,46,45,47,49,48,25,27,26,32,34,33,29,31,30,35,
37,36,35,37,36,68,70,69,65,67,66],[1,1,1,1,1,1,1,1,1,10,10,10,10,10,10,10,10,
10,10,10,10,10,10,10,1,1,1,1,8,8,8,9,9,9,35,35,35,35,35,35,41,41,41,41,41,41,
41,41,41,10,10,10,17,17,17,15,15,15,59,59,59,62,62,62,65,65,65,68,68,68],,[1,
3,2,4,6,5,7,9,8,10,12,11,16,18,17,13,15,14,19,21,20,22,24,23,25,27,26,28,32,
34,33,29,31,30,35,37,36,38,40,39,1,3,2,4,6,5,4,6,5,50,52,51,56,58,57,53,55,54,
62,64,63,59,61,60,65,67,66,68,70,69],,,,,,[1,3,2,4,6,5,7,9,8,10,12,11,16,18,
17,13,15,14,19,21,20,22,24,23,25,27,26,28,32,34,33,29,31,30,35,37,36,38,40,39,
41,43,42,47,49,48,44,46,45,50,52,51,56,58,57,53,55,54,59,61,60,62,64,63,1,3,2,
1,3,2]],
0,
[(59,62)(60,63)(61,64),(44,47)(45,48)(46,49),(65,68)(66,69)(67,70),( 2, 3)
( 5, 6)( 8, 9)(11,12)(13,16)(14,18)(15,17)(20,21)(23,24)(26,27)(29,32)(30,34)
(31,33)(36,37)(39,40)(42,43)(45,46)(48,49)(51,52)(53,56)(54,58)(55,57)(60,61)
(63,64)(66,67)(69,70)],
["ConstructProj",[["3^5:M11",[]],,["3^6.M11",[-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1]]]]);
ALF("3^6.M11","3^5:M11",[1,1,1,2,2,2,3,3,3,4,4,4,5,5,5,6,6,6,7,7,7,8,8,8,
9,9,9,10,11,11,11,12,12,12,13,13,13,14,14,14,15,15,15,16,16,16,17,17,17,
18,18,18,19,19,19,20,20,20,21,21,21,22,22,22,23,23,23,24,24,24]);
ALF("3^6.M11","3.Suz",[1,2,3,10,11,12,13,14,15,4,5,6,38,39,40,41,42,43,35,
36,37,44,45,46,13,14,15,16,63,64,65,60,61,62,23,24,25,81,82,83,32,33,34,
99,100,101,99,100,101,44,45,46,105,106,107,102,103,104,57,58,59,57,58,59,
72,73,74,72,73,74],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("3^6.M11","3^6:(M11x2)",[1,2,2,3,4,4,5,6,6,7,8,8,9,10,11,9,11,10,12,
13,13,14,15,15,16,17,17,18,19,20,21,19,21,20,22,23,23,24,25,25,26,27,27,
28,29,30,28,30,29,31,32,32,33,34,35,33,35,34,36,37,37,38,39,39,40,41,41,
42,43,43],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);
ALF("3^6.M11","M11",[1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,
3,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,7,7,7,8,8,
8,9,9,9,10,10,10]);
ALN("3^6.M11",["3^6:M11"]);

MOT("3x2.SuzM4",
[
"4th maximal subgroup of 6.Suz"
],
0,
0,
0,
[(58,60)(59,61)(160,162)(161,163)(262,264)(263,265),(85,86)(187,188)(289,290),
(103,205)(104,206)(105,207)(106,208)(107,209)(108,210)(109,211)(110,212)(111,
213)(112,214)(113,215)(114,216)(115,217)(116,218)(117,219)(118,220)(119,221)
(120,222)(121,223)(122,224)(123,225)(124,226)(125,227)(126,228)(127,229)(128,
230)(129,231)(130,232)(131,233)(132,234)(133,235)(134,236)(135,237)(136,238)
(137,239)(138,240)(139,241)(140,242)(141,243)(142,244)(143,245)(144,246)(145,
247)(146,248)(147,249)(148,250)(149,251)(150,252)(151,253)(152,254)(153,255)
(154,256)(155,257)(156,258)(157,259)(158,260)(159,261)(160,262)(161,263)(162,
264)(163,265)(164,266)(165,267)(166,268)(167,269)(168,270)(169,271)(170,272)
(171,273)(172,274)(173,275)(174,276)(175,277)(176,278)(177,279)(178,280)(179,
281)(180,282)(181,283)(182,284)(183,285)(184,286)(185,287)(186,288)(187,289)
(188,290)(189,291)(190,292)(191,293)(192,294)(193,295)(194,296)(195,297)(196,
298)(197,299)(198,300)(199,301)(200,302)(201,303)(202,304)(203,305)(204,306),
(19,23)(20,24)(21,25)(22,26)(62,66)(63,67)(64,68)(65,69)(70,73)(71,74)(72,75)
(76,78)(77,79)(80,81)(87,91)(88,92)(89,93)(90,94)(95,100)(96,99)(97,101)(98,
102)(121,125)(122,126)(123,127)(124,128)(164,168)(165,169)(166,170)(167,171)
(172,175)(173,176)(174,177)(178,180)(179,181)(182,183)(189,193)(190,194)(191,
195)(192,196)(197,202)(198,201)(199,203)(200,204)(223,227)(224,228)(225,229)
(226,230)(266,270)(267,271)(268,272)(269,273)(274,277)(275,278)(276,279)(280,
282)(281,283)(284,285)(291,295)(292,296)(293,297)(294,298)(299,304)(300,303)
(301,305)(302,306)],
["ConstructDirectProduct",[["Cyclic",3],["2.SuzM4"]]]);
ALF("3x2.SuzM4","3x2^(1+6)_-.U4(2)",[1,1,2,2,3,3,4,4,5,5,6,7,8,8,9,10,11,
12,13,13,14,14,15,15,16,16,17,17,18,18,19,19,20,20,21,21,22,22,23,23,24,
24,25,25,26,26,27,27,28,29,30,31,31,32,32,33,33,34,34,35,35,36,36,37,37,
38,38,39,39,40,40,41,42,42,43,44,44,45,45,46,46,47,47,48,49,49,50,50,51,
51,52,52,53,53,54,54,55,55,56,56,57,57,58,58,59,59,60,60,61,61,62,62,63,
64,65,65,66,67,68,69,70,70,71,71,72,72,73,73,74,74,75,75,76,76,77,77,78,
78,79,79,80,80,81,81,82,82,83,83,84,84,85,86,87,88,88,89,89,90,90,91,91,
92,92,93,93,94,94,95,95,96,96,97,97,98,99,99,100,101,101,102,102,103,103,
104,104,105,106,106,107,107,108,108,109,109,110,110,111,111,112,112,113,
113,114,114,115,115,116,116,117,117,118,118,119,119,120,121,122,122,123,
124,125,126,127,127,128,128,129,129,130,130,131,131,132,132,133,133,134,
134,135,135,136,136,137,137,138,138,139,139,140,140,141,141,142,143,144,
145,145,146,146,147,147,148,148,149,149,150,150,151,151,152,152,153,153,
154,154,155,156,156,157,158,158,159,159,160,160,161,161,162,163,163,164,
164,165,165,166,166,167,167,168,168,169,169,170,170,171,171]);
ALF("3x2.SuzM4","2^1+6.u4q2",[1,1,2,2,3,3,4,4,5,5,6,7,8,8,9,10,11,12,13,
13,14,14,15,15,16,16,17,17,18,18,19,19,20,20,21,21,22,22,23,23,24,24,25,
25,26,26,27,27,28,29,30,31,31,32,32,33,33,34,34,35,35,36,36,37,37,38,38,
39,39,40,40,41,42,42,43,44,44,45,45,46,46,47,47,48,49,49,50,50,51,51,52,
52,53,53,54,54,55,55,56,56,57,57,1,1,2,2,3,3,4,4,5,5,6,7,8,8,9,10,11,12,
13,13,14,14,15,15,16,16,17,17,18,18,19,19,20,20,21,21,22,22,23,23,24,24,
25,25,26,26,27,27,28,29,30,31,31,32,32,33,33,34,34,35,35,36,36,37,37,38,
38,39,39,40,40,41,42,42,43,44,44,45,45,46,46,47,47,48,49,49,50,50,51,51,
52,52,53,53,54,54,55,55,56,56,57,57,1,1,2,2,3,3,4,4,5,5,6,7,8,8,9,10,11,
12,13,13,14,14,15,15,16,16,17,17,18,18,19,19,20,20,21,21,22,22,23,23,24,
24,25,25,26,26,27,27,28,29,30,31,31,32,32,33,33,34,34,35,35,36,36,37,37,
38,38,39,39,40,40,41,42,42,43,44,44,45,45,46,46,47,47,48,49,49,50,50,51,
51,52,52,53,53,54,54,55,55,56,56,57,57]);
ALF("3x2.SuzM4","3xU4(2)",[1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,5,5,5,5,4,
4,4,4,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,9,9,9,9,10,10,10,10,10,10,
10,10,10,10,12,12,12,12,11,11,11,11,13,13,13,14,14,14,15,15,15,15,15,15,
16,16,16,16,16,17,17,17,17,18,18,18,18,20,20,20,20,19,19,19,19,21,21,21,
21,21,21,21,21,22,22,22,22,23,23,23,23,23,23,25,25,25,25,24,24,24,24,26,
26,26,26,26,26,26,26,27,27,27,27,27,27,28,28,28,28,28,28,29,29,29,29,29,
30,30,30,30,30,30,30,30,30,30,32,32,32,32,31,31,31,31,33,33,33,34,34,34,
35,35,35,35,35,35,36,36,36,36,36,37,37,37,37,38,38,38,38,40,40,40,40,39,
39,39,39,41,41,41,41,41,41,41,41,42,42,42,42,43,43,43,43,43,43,45,45,45,
45,44,44,44,44,46,46,46,46,46,46,46,46,47,47,47,47,47,47,48,48,48,48,48,
48,49,49,49,49,49,50,50,50,50,50,50,50,50,50,50,52,52,52,52,51,51,51,51,
53,53,53,54,54,54,55,55,55,55,55,55,56,56,56,56,56,57,57,57,57,58,58,58,
58,60,60,60,60,59,59,59,59]);
ALF("3x2.SuzM4","6.Suz",[1,4,7,10,30,33,7,10,7,10,36,39,30,33,39,36,13,88,
24,27,65,68,26,23,73,70,16,19,57,60,57,60,127,130,22,25,75,78,133,136,30,
33,36,36,91,94,91,94,42,97,88,45,48,112,115,187,190,112,115,112,115,71,74,
77,80,67,64,79,76,57,60,139,57,60,139,69,72,63,66,144,147,127,130,139,205,
208,110,107,185,182,102,105,177,180,146,149,135,138,148,145,137,134,3,6,9,
12,32,35,9,12,9,12,38,41,32,35,41,38,15,90,26,23,67,64,22,25,69,72,18,21,
59,62,59,62,129,132,24,27,77,80,135,138,32,35,38,38,93,96,93,96,44,99,90,
47,50,114,117,189,192,114,117,114,117,73,70,79,76,63,66,75,78,59,62,141,
59,62,141,71,74,65,68,146,149,129,132,141,207,210,106,109,181,184,104,101,
179,176,148,145,137,134,144,147,133,136,5,2,11,8,34,31,11,8,11,8,37,40,34,
31,40,37,14,89,22,25,63,66,24,27,71,74,20,17,61,58,61,58,131,128,26,23,79,
76,137,134,34,31,37,37,95,92,95,92,43,98,89,49,46,116,113,191,188,116,113,
116,113,69,72,75,78,65,68,77,80,61,58,140,61,58,140,73,70,67,64,148,145,
131,128,140,209,206,108,111,183,186,100,103,175,178,144,147,133,136,146,
149,135,138],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);

MOT("2x3^6.M11",
[
"5th maximal subgroup of 6.Suz"
],
0,
0,
0,
[(44,47)(45,48)(46,49)(114,117)(115,118)(116,119),(59,62)(60,63)(61,64)(129,
132)(130,133)(131,134),(65,68)(66,69)(67,70)(135,138)(136,139)(137,140),(2,3)
(5,6)(8,9)(11,12)(13,16)(14,18)(15,17)(20,21)(23,24)(26,27)(29,32)(30,34)(31,
33)(36,37)(39,40)(42,43)(45,46)(48,49)(51,52)(53,56)(54,58)(55,57)(60,61)(63,
64)(66,67)(69,70)(72,73)(75,76)(78,79)(81,82)(83,86)(84,88)(85,87)(90,91)(93,
94)(96,97)(99,102)(100,104)(101,103)(106,107)(109,110)(112,113)(115,116)(118,
119)(121,122)(123,126)(124,128)(125,127)(130,131)(133,134)(136,137)(139,140)],
["ConstructDirectProduct",[["Cyclic",2],["3^6.M11"]]]);
ALF("2x3^6.M11","2x3^5:M11",[1,1,1,2,2,2,3,3,3,4,4,4,5,5,5,6,6,6,7,7,7,8,
8,8,9,9,9,10,11,11,11,12,12,12,13,13,13,14,14,14,15,15,15,16,16,16,17,17,
17,18,18,18,19,19,19,20,20,20,21,21,21,22,22,22,23,23,23,24,24,24,25,25,
25,26,26,26,27,27,27,28,28,28,29,29,29,30,30,30,31,31,31,32,32,32,33,33,
33,34,35,35,35,36,36,36,37,37,37,38,38,38,39,39,39,40,40,40,41,41,41,42,
42,42,43,43,43,44,44,44,45,45,45,46,46,46,47,47,47,48,48,48]);
ALF("2x3^6.M11","6.Suz",[1,5,3,16,20,18,22,26,24,10,8,12,66,64,68,72,70,
74,60,58,62,78,76,80,22,26,24,28,106,110,108,100,104,102,39,40,41,139,140,
141,51,55,53,169,173,171,169,173,171,78,76,80,184,182,186,178,176,180,97,
98,99,97,98,99,121,125,123,121,125,123,4,2,6,19,17,21,25,23,27,7,11,9,63,
67,65,69,73,71,57,61,59,75,79,77,25,23,27,29,109,107,111,103,101,105,39,
40,41,139,140,141,54,52,56,172,170,174,172,170,174,75,79,77,181,185,183,
175,179,177,97,98,99,97,98,99,124,122,126,124,122,126],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("2x3^6.M11","2xM11",[1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,
3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,7,7,7,
8,8,8,9,9,9,10,10,10,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,
12,12,12,12,12,12,12,13,13,13,13,13,13,13,13,13,13,14,14,14,14,14,14,15,
15,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,17,17,17,18,18,18,19,
19,19,20,20,20]);

MOT("3x2.J2.2",
[
"6th maximal subgroup of 6.Suz"
],
0,
0,
0,
[(41,42)(87,88)(133,134),(47,93)(48,94)(49,95)(50,96)(51,97)(52,98)(53,99)(54,
100)(55,101)(56,102)(57,103)(58,104)(59,105)(60,106)(61,107)(62,108)(63,109)
(64,110)(65,111)(66,112)(67,113)(68,114)(69,115)(70,116)(71,117)(72,118)(73,
119)(74,120)(75,121)(76,122)(77,123)(78,124)(79,125)(80,126)(81,127)(82,128)
(83,129)(84,130)(85,131)(86,132)(87,133)(88,134)(89,135)(90,136)(91,137)(92,
138),(37,38)(43,45)(44,46)(83,84)(89,91)(90,92)(129,130)(135,137)(136,138),
(31,32)(34,35)(39,40)(43,46)(44,45)(77,78)(80,81)(85,86)(89,92)(90,91)(123,
124)(126,127)(131,132)(135,138)(136,137)],
["ConstructDirectProduct",[["Cyclic",3],["2.J2.2"]]]);
ALF("3x2.J2.2","3xJ2.2",[1,1,2,2,3,4,4,5,5,6,6,7,7,8,8,9,9,10,11,11,12,13,
14,14,15,15,16,16,17,18,19,19,20,21,21,22,23,23,24,24,25,25,26,26,27,27,
28,28,29,29,30,31,31,32,32,33,33,34,34,35,35,36,36,37,38,38,39,40,41,41,
42,42,43,43,44,45,46,46,47,48,48,49,50,50,51,51,52,52,53,53,54,54,55,55,
56,56,57,58,58,59,59,60,60,61,61,62,62,63,63,64,65,65,66,67,68,68,69,69,
70,70,71,72,73,73,74,75,75,76,77,77,78,78,79,79,80,80,81,81]);
ALF("3x2.J2.2","6.Suz",[1,4,7,10,13,16,19,28,29,33,30,51,54,45,48,57,60,
81,82,85,88,118,112,115,130,127,169,172,13,39,42,42,81,88,88,88,139,139,
142,143,162,162,208,205,205,208,5,2,11,8,14,20,17,28,29,31,34,55,52,49,46,
61,58,81,86,83,89,119,116,113,128,131,173,170,14,40,43,43,81,89,89,89,140,
140,142,143,163,163,206,209,209,206,3,6,9,12,15,18,21,28,29,35,32,53,56,
47,50,59,62,81,84,87,90,120,114,117,132,129,171,174,15,41,44,44,81,90,90,
90,141,141,142,143,164,164,210,207,207,210],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);

MOT("3x2.SuzM7",
[
"7th maximal subgroup of 6.Suz,\n",
"structure 3x(2.2^4.2^6):3A6"
],
0,
0,
0,
[(53,54)(59,60)(63,64)(133,134)(139,140)(143,144)(213,214)(219,220)(223,224),
(55,56)(61,62)(65,66)(135,136)(141,142)(145,146)(215,216)(221,222)(225,226),
(67,74)(68,75)(69,76)(70,77)(71,78)(72,79)(73,80)(147,154)(148,155)(149,156)
(150,157)(151,158)(152,159)(153,160)(227,234)(228,235)(229,236)(230,237)(231,
238)(232,239)(233,240),(81,161)(82,162)(83,163)(84,164)(85,165)(86,166)(87,
167)(88,168)(89,169)(90,170)(91,171)(92,172)(93,173)(94,174)(95,175)(96,176)
(97,177)(98,178)(99,179)(100,180)(101,181)(102,182)(103,183)(104,184)(105,185)
(106,186)(107,187)(108,188)(109,189)(110,190)(111,191)(112,192)(113,193)(114,
194)(115,195)(116,196)(117,197)(118,198)(119,199)(120,200)(121,201)(122,202)
(123,203)(124,204)(125,205)(126,206)(127,207)(128,208)(129,209)(130,210)(131,
211)(132,212)(133,213)(134,214)(135,215)(136,216)(137,217)(138,218)(139,219)
(140,220)(141,221)(142,222)(143,223)(144,224)(145,225)(146,226)(147,227)(148,
228)(149,229)(150,230)(151,231)(152,232)(153,233)(154,234)(155,235)(156,236)
(157,237)(158,238)(159,239)(160,240),(9,13)(10,14)(11,15)(12,16)(28,33)(29,34)
(30,35)(31,36)(32,37)(43,45)(44,46)(51,52)(59,63)(60,64)(61,65)(62,66)(70,72)
(71,73)(77,79)(78,80)(89,93)(90,94)(91,95)(92,96)(108,113)(109,114)(110,115)
(111,116)(112,117)(123,125)(124,126)(131,132)(139,143)(140,144)(141,145)(142,
146)(150,152)(151,153)(157,159)(158,160)(169,173)(170,174)(171,175)(172,176)
(188,193)(189,194)(190,195)(191,196)(192,197)(203,205)(204,206)(211,212)(219,
223)(220,224)(221,225)(222,226)(230,232)(231,233)(237,239)(238,240)],
["ConstructDirectProduct",[["Cyclic",3],["2.SuzM7"]]]);
ALF("3x2.SuzM7","3x2^(4+6).3A6",[1,1,2,2,3,4,4,5,6,6,7,7,8,8,9,9,10,10,11,
12,12,13,14,15,16,17,17,18,18,19,19,20,21,21,22,22,23,24,24,25,26,26,27,
27,28,28,29,29,30,30,31,31,32,32,33,33,34,35,36,36,37,37,38,38,39,39,40,
40,41,42,42,43,43,44,44,45,46,46,47,47,48,48,49,49,50,51,51,52,53,53,54,
54,55,55,56,56,57,57,58,59,59,60,61,62,63,64,64,65,65,66,66,67,68,68,69,
69,70,71,71,72,73,73,74,74,75,75,76,76,77,77,78,78,79,79,80,80,81,82,83,
83,84,84,85,85,86,86,87,87,88,89,89,90,90,91,91,92,93,93,94,94,95,95,96,
96,97,98,98,99,100,100,101,101,102,102,103,103,104,104,105,106,106,107,
108,109,110,111,111,112,112,113,113,114,115,115,116,116,117,118,118,119,
120,120,121,121,122,122,123,123,124,124,125,125,126,126,127,127,128,129,
130,130,131,131,132,132,133,133,134,134,135,136,136,137,137,138,138,139,
140,140,141,141]);
ALF("3x2.SuzM7","6.Suz",[1,4,7,10,13,33,30,36,18,21,59,62,20,17,61,58,10,
7,13,30,33,39,39,36,88,94,91,62,59,132,129,141,58,61,128,131,140,28,29,81,
22,25,66,63,72,69,75,78,136,133,147,144,39,39,88,88,42,97,141,141,207,210,
140,140,206,209,51,54,118,171,174,173,170,51,54,118,171,174,173,170,5,2,
11,8,14,31,34,37,16,19,57,60,18,21,59,62,8,11,14,34,31,40,40,37,89,92,95,
60,57,130,127,139,62,59,132,129,141,28,29,81,26,23,64,67,70,73,79,76,134,
137,145,148,40,40,89,89,43,98,139,139,205,208,141,141,210,207,55,52,119,
169,172,171,174,55,52,119,169,172,171,174,3,6,9,12,15,35,32,38,20,17,61,
58,16,19,57,60,12,9,15,32,35,41,41,38,90,96,93,58,61,128,131,140,60,57,
130,127,139,28,29,81,24,27,68,65,74,71,77,80,138,135,149,146,41,41,90,90,
44,99,140,140,209,206,139,139,208,205,53,56,120,173,170,169,172,53,56,120,
173,170,169,172],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);

MOT("3x2.SuzM9",
[
"9th maximal subgroup of 6.Suz",
],
0,
0,
0,
[(23,25)(24,26)(69,71)(70,72)(105,107)(106,108)(151,153)(152,154)(187,189)
(188,190)(233,235)(234,236),(52,53)(59,62)(60,61)(69,70)(71,72)(134,135)(141,
144)(142,143)(151,152)(153,154)(216,217)(223,226)(224,225)(233,234)(235,236),
(73,74)(155,156)(237,238),(83,165)(84,166)(85,167)(86,168)(87,169)(88,170)(89,
171)(90,172)(91,173)(92,174)(93,175)(94,176)(95,177)(96,178)(97,179)(98,180)
(99,181)(100,182)(101,183)(102,184)(103,185)(104,186)(105,187)(106,188)(107,
189)(108,190)(109,191)(110,192)(111,193)(112,194)(113,195)(114,196)(115,197)
(116,198)(117,199)(118,200)(119,201)(120,202)(121,203)(122,204)(123,205)(124,
206)(125,207)(126,208)(127,209)(128,210)(129,211)(130,212)(131,213)(132,214)
(133,215)(134,216)(135,217)(136,218)(137,219)(138,220)(139,221)(140,222)(141,
223)(142,224)(143,225)(144,226)(145,227)(146,228)(147,229)(148,230)(149,231)
(150,232)(151,233)(152,234)(153,235)(154,236)(155,237)(156,238)(157,239)(158,
240)(159,241)(160,242)(161,243)(162,244)(163,245)(164,246),(48,49)(50,51)(59,
61)(60,62)(65,66)(67,68)(75,76)(77,78)(79,80)(81,82)(130,131)(132,133)(141,
143)(142,144)(147,148)(149,150)(157,158)(159,160)(161,162)(163,164)(212,213)
(214,215)(223,225)(224,226)(229,230)(231,232)(239,240)(241,242)(243,244)(245,
246),(30,34)(31,35)(32,36)(33,37)(44,46)(45,47)(75,79)(76,80)(77,81)(78,82)
(112,116)(113,117)(114,118)(115,119)(126,128)(127,129)(157,161)(158,162)(159,
163)(160,164)(194,198)(195,199)(196,200)(197,201)(208,210)(209,211)(239,243)
(240,244)(241,245)(242,246)],
["ConstructDirectProduct",[["Cyclic",3],["2.SuzM9"]]]);
ALF("3x2.SuzM9","3x2^(2+8):(A5xS3)",[1,1,2,2,3,3,4,5,5,6,7,8,9,9,10,11,12,
12,13,13,14,14,15,15,16,16,17,17,18,19,19,20,20,21,21,22,22,23,23,24,25,
25,26,27,27,28,28,29,29,30,30,31,31,32,33,34,35,36,37,37,38,38,39,40,41,
41,42,42,43,43,44,44,45,45,46,46,47,47,48,48,49,49,50,50,51,51,52,52,53,
54,54,55,56,57,58,58,59,60,61,61,62,62,63,63,64,64,65,65,66,66,67,68,68,
69,69,70,70,71,71,72,72,73,74,74,75,76,76,77,77,78,78,79,79,80,80,81,82,
83,84,85,86,86,87,87,88,89,90,90,91,91,92,92,93,93,94,94,95,95,96,96,97,
97,98,98,99,99,100,100,101,101,102,103,103,104,105,106,107,107,108,109,
110,110,111,111,112,112,113,113,114,114,115,115,116,117,117,118,118,119,
119,120,120,121,121,122,123,123,124,125,125,126,126,127,127,128,128,129,
129,130,131,132,133,134,135,135,136,136,137,138,139,139,140,140,141,141,
142,142,143,143,144,144,145,145,146,146,147,147]);
ALF("3x2.SuzM9","6.Suz",[1,4,7,10,10,7,13,33,30,39,36,13,30,33,36,88,94,
91,16,19,57,60,57,60,57,60,127,130,139,45,48,112,115,45,48,112,115,28,29,
81,28,29,81,165,166,167,168,7,10,30,33,39,39,88,13,39,36,88,94,91,91,94,
97,42,60,57,127,130,139,139,139,139,205,208,112,115,187,190,112,115,187,
190,5,2,11,8,8,11,14,31,34,40,37,14,34,31,37,89,92,95,20,17,61,58,61,58,
61,58,131,128,140,49,46,116,113,49,46,116,113,28,29,81,28,29,81,165,166,
167,168,11,8,34,31,40,40,89,14,40,37,89,92,95,95,92,98,43,58,61,131,128,
140,140,140,140,209,206,116,113,191,188,116,113,191,188,3,6,9,12,12,9,15,
35,32,41,38,15,32,35,38,90,96,93,18,21,59,62,59,62,59,62,129,132,141,47,
50,114,117,47,50,114,117,28,29,81,28,29,81,165,166,167,168,9,12,32,35,41,
41,90,15,41,38,90,96,93,93,96,99,44,62,59,129,132,141,141,141,141,207,210,
114,117,189,192,114,117,189,192],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);

MOT("3xIsoclinic(2.M12.2)",
[
"10th maximal subgroup of 6.Suz"
],
0,
0,
0,
[(27,28)(61,62)(95,96),(31,33)(32,34)(65,67)(66,68)(99,101)(100,102),(35,69)
(36,70)(37,71)(38,72)(39,73)(40,74)(41,75)(42,76)(43,77)(44,78)(45,79)(46,80)
(47,81)(48,82)(49,83)(50,84)(51,85)(52,86)(53,87)(54,88)(55,89)(56,90)(57,91)
(58,92)(59,93)(60,94)(61,95)(62,96)(63,97)(64,98)(65,99)(66,100)(67,101)(68,
102),(22,23)(24,25)(29,30)(31,32)(33,34)(56,57)(58,59)(63,64)(65,66)(67,68)
(90,91)(92,93)(97,98)(99,100)(101,102),(16,17)(24,25)(29,30)(50,51)(58,59)(63,
64)(84,85)(92,93)(97,98)],
["ConstructDirectProduct",[["Cyclic",3],["Isoclinic(2.M12.2)"]]]);
ALF("3xIsoclinic(2.M12.2)","3xM12.2",[1,1,2,3,3,4,4,5,5,6,7,7,8,9,9,10,10,
11,12,12,13,14,14,15,15,16,17,18,19,19,20,20,21,21,22,22,23,24,24,25,25,
26,26,27,28,28,29,30,30,31,31,32,33,33,34,35,35,36,36,37,38,39,40,40,41,
41,42,42,43,43,44,45,45,46,46,47,47,48,49,49,50,51,51,52,52,53,54,54,55,
56,56,57,57,58,59,60,61,61,62,62,63,63]);
ALF("3xIsoclinic(2.M12.2)","6.Suz",[1,4,13,10,7,22,25,28,29,39,51,54,81,
78,75,97,97,118,121,124,13,36,36,42,42,81,118,118,142,143,144,147,147,144,
5,2,14,8,11,26,23,28,29,40,55,52,81,76,79,98,98,119,125,122,14,37,37,43,
43,81,119,119,142,143,148,145,145,148,3,6,15,12,9,24,27,28,29,41,53,56,81,
80,77,99,99,120,123,126,15,38,38,44,44,81,120,120,142,143,146,149,149,146],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);

MOT("4.2^4.S5",
[
"origin: CAS library, tests: 1.o.r., pow[2,3,5]"
],
[7680,7680,3840,256,256,64,64,16,128,128,64,24,24,12,20,20,20,20,96,96,32,32,
16,16,16,16,12,12],
[,[1,1,2,2,1,2,1,4,5,5,5,12,12,13,15,15,16,16,1,1,5,5,6,6,9,9,12,12],[1,2,3,4,
5,6,7,8,9,10,11,1,2,3,15,16,17,18,19,20,21,22,23,24,26,25,20,19],,[1,2,3,4,5,
6,7,8,9,10,11,12,13,14,1,2,3,3,19,20,21,22,23,24,25,26,27,28]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[4,4,4,4,4,0,0,0,0,0,0,1,1,1,
-1,-1,-1,-1,2,2,2,2,0,0,0,0,-1,-1],
[TENSOR,[3,2]],[5,5,5,5,5,1,1,1,1,1,1,-1,-1,-1,0,0,0,0,1,1,1,1,-1,-1,-1,-1,1,
1],
[TENSOR,[5,2]],[6,6,6,6,6,-2,-2,-2,-2,-2,-2,0,0,0,1,1,1,1,0,0,0,0,0,0,0,0,0,
0],[15,15,15,-1,-1,3,3,-1,-1,-1,-1,0,0,0,0,0,0,0,3,3,-1,-1,1,1,-1,-1,0,0],
[TENSOR,[8,2]],[15,15,15,-1,-1,-1,-1,-1,3,3,3,0,0,0,0,0,0,0,3,3,-1,-1,-1,-1,1,
1,0,0],
[TENSOR,[10,2]],[30,30,30,-2,-2,-2,-2,2,-2,-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0],[6,6,-6,2,-2,2,-2,0,2,2,-2,0,0,0,1,1,-1,-1,0,0,0,0,2,-2,0,0,0,0],
[TENSOR,[13,2]],[6,6,-6,2,-2,-2,2,0,-2,-2,2,0,0,0,1,1,-1,-1,0,0,0,0,0,0,
2*E(4),-2*E(4),0,0],
[TENSOR,[15,2]],[10,10,-10,-2,2,2,-2,0,-2,-2,2,1,1,-1,0,0,0,0,4,-4,0,0,0,0,0,
0,-1,1],
[TENSOR,[17,2]],[10,10,-10,-2,2,-2,2,0,2,2,-2,1,1,-1,0,0,0,0,2,-2,2,-2,0,0,0,
0,1,-1],
[TENSOR,[19,2]],[20,20,-20,-4,4,0,0,0,0,0,0,-1,-1,1,0,0,0,0,2,-2,-2,2,0,0,0,0,
1,-1],
[TENSOR,[21,2]],[24,24,-24,8,-8,0,0,0,0,0,0,0,0,0,-1,-1,1,1,0,0,0,0,0,0,0,0,0,
0],[8,-8,0,0,0,0,0,0,4,-4,0,2,-2,0,-2,2,0,0,0,0,0,0,0,0,0,0,0,0],[24,-24,0,0,
0,0,0,0,-4,4,0,0,0,0,-1,1,E(20)+E(20)^9-E(20)^13-E(20)^17,
-E(20)-E(20)^9+E(20)^13+E(20)^17,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[25,11]],[32,-32,0,0,0,0,0,0,0,0,0,2,-2,0,2,-2,0,0,0,0,0,0,0,0,0,0,0,
0],[40,-40,0,0,0,0,0,0,4,-4,0,-2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]],
[(23,24),(19,20)(21,22)(27,28),(17,18),(17,18)(25,26),(25,26)]);
ARC("4.2^4.S5","CAS",[rec(name:="g",
permchars:=( 9,10,12)(13,22,20,21,19,18,15,26,28,17)(14,23,24)(16,25,27),
permclasses:=( 4, 5)( 6,12,20, 7,10,14,22, 8,15,25,17,27,23,16,26,18,28,24,19)
( 9,13,21),
text:=""),rec(name:="hsm10",
permchars:=(),
permclasses:=(),
text:=[
" maximal subgroup of hs \n",
" test:= 1. o.r. sym 2 decompose correctly \n",
""])]);
ARC("4.2^4.S5","projectives",["2.HSM10",[[4,-4,-4*E(4),0,0,0,0,0,-2*E(4),
2*E(4),-2,1,1,-E(4),-1,-1,E(4),-E(4),-2,2*E(4),0,0,0,0,1-E(4),-1-E(4),-E(4),1]
,
[GALOIS,[1,3]],[12,12,0,0,4,0,0,2*E(4),4*E(4),4*E(4),0,0,0,0,2,-2,0,0,0,0,0,0
,0,0,0,0,0,0],
[GALOIS,[3,3]],[16,-16,-16*E(4),0,0,0,0,0,0,0,0,1,1,-E(4),1,1,-E(4),E(4),-4,
4*E(4),0,0,0,0,0,0,E(4),-1],
[GALOIS,[5,3]],[20,20,0,0,-4,0,0,2*E(4),-4*E(4),-4*E(4),0,2,-2,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0],
[GALOIS,[7,3]],[20,-20,-20*E(4),0,0,0,0,0,-2*E(4),2*E(4),-2,-1,-1,E(4),0,0,0,
0,-2,2*E(4),0,0,0,0,-1+E(4),1+E(4),-E(4),1],
[GALOIS,[9,3]],[24,-24,24*E(4),0,0,0,0,0,-4*E(4),4*E(4),4,0,0,0,-1,-1,-E(4),
E(4),0,0,0,0,0,0,0,0,0,0],
[GALOIS,[11,3]],[24,24,0,0,8,0,0,0,0,0,0,0,0,0,-1,1,
-E(5)+E(5)^2+E(5)^3-E(5)^4,-E(5)+E(5)^2+E(5)^3-E(5)^4,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[13,2]],[40,40,0,0,-8,0,0,0,0,0,0,-2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
],]);
ARC("4.2^4.S5","tomfusion",rec(name:="4.2^4:S5",map:=[1,2,8,10,3,18,6,77,12,
13,17,7,33,101,30,97,215,215,4,5,26,22,74,84,91,91,34,35],text:=[
"fusion map is unique up to table automorphisms"
]));
ALF("4.2^4.S5","HS",[1,2,5,6,2,7,3,14,6,5,6,4,12,21,8,17,23,24,2,3,6,7,15,
16,14,14,11,12],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("4.2^4.S5","Co3",[1,2,7,8,2,8,3,19,8,7,8,5,13,28,9,22,33,34,2,3,8,8,
19,17,19,19,14,13],[
"fusion is unique up to table automorphisms,\n",
"the map on the CAS table is wrong"
]);
ALF("4.2^4.S5","A5.2",[1,1,1,1,1,2,2,2,2,2,2,3,3,3,4,4,4,4,5,5,5,5,6,6,6,
6,7,7]);
ALF("4.2^4.S5","2^(1+6)_+:S5",[1,2,3,5,4,14,9,23,13,12,15,11,18,25,17,24,
26,26,31,32,37,34,46,46,45,45,41,42],[
"fusion map is unique up to table automorphisms"
]);
ALN("4.2^4.S5",["HSC2A","g"]);

MOT("2^(1+6)_+:S5",
[
"7th maximal subgroup of HS.2,\n",
"origin: Dixon's Algorithm"
],
[15360,15360,7680,512,512,768,768,640,128,64,48,256,256,128,128,64,40,48,24,24
,64,64,32,40,24,20,20,20,384,384,192,192,192,64,64,64,64,16,48,48,24,24,32,32,
16,16,24],
[,[1,1,2,1,2,1,1,2,1,1,11,4,4,2,4,4,17,11,11,11,5,5,5,17,18,24,24,24,1,1,1,1,2
,4,4,4,4,9,11,11,11,11,15,15,13,14,18],[1,2,3,4,5,6,7,8,9,10,1,12,13,14,15,16,
17,2,7,6,21,22,23,24,3,26,28,27,29,30,31,32,33,34,35,36,37,38,29,30,32,31,43,
44,45,46,33],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,1,18,19,20,21,22,23,2,25
,3,8,8,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1
,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[4,4,4,4,4,4,4,4,0,0,1
,0,0,0,0,0,-1,1,1,1,0,0,0,-1,1,-1,-1,-1,2,2,2,2,2,2,2,2,2,0,-1,-1,-1,-1,0,0,0,
0,-1],
[TENSOR,[3,2]],[5,5,5,5,5,5,5,5,1,1,-1,1,1,1,1,1,0,-1,-1,-1,1,1,1,0,-1,0,0,0,
-1,-1,-1,-1,-1,-1,-1,-1,-1,1,-1,-1,-1,-1,1,1,1,1,-1],
[TENSOR,[5,2]],[6,6,6,6,6,6,6,6,-2,-2,0,-2,-2,-2,-2,-2,1,0,0,0,-2,-2,-2,1,0,1
,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[1,1,1,1,1,-1,-1,-1,1,-1,1,1,1,1,1
,-1,1,1,-1,-1,-1,-1,1,1,1,1,-1,-1,1,1,-1,-1,1,-1,1,1,-1,1,1,1,-1,-1,1,1,-1,-1,
1],
[TENSOR,[2,8]],
[TENSOR,[3,8]],
[TENSOR,[3,9]],
[TENSOR,[5,8]],
[TENSOR,[5,9]],
[TENSOR,[7,8]],[15,15,15,-1,-1,3,3,-5,-1,3,0,3,3,-1,3,-1,0,0,0,0,-1,-1,-1,0,0
,0,0,0,3,3,3,3,3,-1,-1,-1,-1,-1,0,0,0,0,1,1,1,-1,0],[15,15,15,-1,-1,3,3,-5,3,
-1,0,-1,-1,3,-1,3,0,0,0,0,-1,-1,-1,0,0,0,0,0,3,3,3,3,3,-1,-1,-1,-1,1,0,0,0,0,
-1,-1,-1,1,0],
[TENSOR,[15,2]],
[TENSOR,[16,2]],
[TENSOR,[15,9]],
[TENSOR,[16,9]],
[TENSOR,[15,8]],
[TENSOR,[16,8]],[30,30,30,-2,-2,-6,-6,10,-2,2,0,-2,-2,-2,-2,2,0,0,0,0,-2,-2,2
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[23,8]],[10,10,-10,2,-2,4,-4,0,2,0,1,2,2,-2,-2,0,0,1,-1,1,2,-2,0,0,-1
,0,0,0,-4,-4,2,-2,4,-2,0,0,2,0,-1,-1,1,-1,0,0,0,0,1],[10,10,-10,2,-2,4,-4,0,-2
,0,1,-2,-2,2,2,0,0,1,-1,1,-2,2,0,0,-1,0,0,0,-2,-2,4,-4,2,0,2,-2,0,0,1,1,-1,1,0
,0,0,0,-1],
[TENSOR,[25,2]],
[TENSOR,[26,2]],
[TENSOR,[25,8]],
[TENSOR,[26,8]],
[TENSOR,[25,9]],
[TENSOR,[26,9]],[12,12,-12,-4,4,0,0,0,-4,0,0,4,4,4,-4,0,2,0,0,0,0,0,0,2,0,-2,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[12,12,-12,-4,4,0,0,0,4,0,0,-4,-4,
-4,4,0,2,0,0,0,0,0,0,2,0,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[20,20,
-20,4,-4,8,-8,0,0,0,-1,0,0,0,0,0,0,-1,1,-1,0,0,0,0,1,0,0,0,-2,-2,-2,2,2,-2,-2,
2,2,0,1,1,-1,1,0,0,0,0,-1],
[TENSOR,[35,2]],
[TENSOR,[35,8]],
[TENSOR,[35,9]],[24,24,-24,-8,8,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,-1,0,1,
-E(5)+E(5)^2+E(5)^3-E(5)^4,E(5)-E(5)^2-E(5)^3+E(5)^4,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0],
[TENSOR,[39,8]],[8,-8,0,0,0,0,0,0,0,0,2,-4,4,0,0,0,-2,-2,0,0,0,0,0,2,0,0,0,0,
-4,4,0,0,0,0,0,0,0,0,2,-2,0,0,2,-2,0,0,0],
[TENSOR,[41,2]],[32,-32,0,0,0,0,0,0,0,0,2,0,0,0,0,0,2,-2,0,0,0,0,0,-2,0,0,0,0
,8,-8,0,0,0,0,0,0,0,0,2,-2,0,0,0,0,0,0,0],
[TENSOR,[43,2]],[40,-40,0,0,0,0,0,0,0,0,-2,-4,4,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0
,4,-4,0,0,0,0,0,0,0,0,-2,2,0,0,2,-2,0,0,0],
[TENSOR,[45,2]],[48,-48,0,0,0,0,0,0,0,0,0,8,-8,0,0,0,-2,0,0,0,0,0,0,2,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]],
[(29,30)(39,40)(43,44),(27,28),( 6, 7)(19,20)(21,22)(31,32)(34,37)(41,42)]);
ALF("2^(1+6)_+:S5","A5.2",[1,1,1,1,1,1,1,1,2,2,3,2,2,2,2,2,4,3,3,3,2,2,2,
4,3,4,4,4,5,5,5,5,5,5,5,5,5,6,7,7,7,7,6,6,6,6,7]);
ALF("2^(1+6)_+:S5","HS.2",[1,2,5,2,6,23,22,24,3,23,4,5,6,7,6,25,8,12,28,
29,30,31,14,16,19,21,37,38,22,23,2,3,25,7,25,24,6,26,27,29,11,12,31,30,14,
15,34],[
"compatible with 4.2^4.S5 -> HS"
]);

MOT("2.HSM10",
[
"preimage in 2.HS of the 2A centralizer in HS,\n",
"origin: Dixon's Algorithm"
],
[15360,15360,15360,15360,7680,7680,256,512,512,64,64,32,32,256,256,256,256,128
,128,48,48,48,48,24,24,40,40,40,40,40,40,40,40,192,192,192,192,32,32,16,16,32,
32,32,32,24,24,24,24],
[,[1,1,1,1,3,3,3,1,1,4,2,7,7,9,9,9,9,9,9,20,20,20,20,23,23,26,26,26,26,29,29,
29,29,1,1,2,2,9,8,10,10,15,15,14,14,21,21,20,20],[1,2,3,4,6,5,7,8,9,10,11,13,
12,15,14,17,16,18,19,1,2,4,3,6,5,26,27,28,29,31,30,33,32,34,35,37,36,38,39,40,
41,45,44,43,42,37,36,34,35],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,
20,21,22,23,24,25,1,2,4,3,5,6,6,5,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48
,49]],
0,
[(30,33)(31,32),(40,41),(34,35)(36,37)(42,43)(44,45)(46,47)(48,49),(5,6)(12,
13)(14,15)(16,17)(24,25)(30,31)(32,33)(36,37)(42,45)(43,44)(46,47)],
["ConstructProj",[["4.2^4.S5",[]],["2.HSM10",[]]]]);
ALF("2.HSM10","4.2^4.S5",[1,1,2,2,3,3,4,5,5,6,7,8,8,9,9,10,10,11,
11,12,12,13,13,14,14,15,15,16,16,17,17,18,18,19,19,20,20,21,22,23,24,25,
25,26,26,27,27,28,28]);
ALF("2.HSM10","2.HS",[1,2,4,3,8,9,10,3,4,11,5,25,24,10,10,8,9,10,10,6,7,
20,21,36,35,12,13,28,29,39,40,42,41,3,4,5,5,10,11,26,27,25,24,25,24,18,19,
20,21],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("2.HSM10","A5.2",[1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,4,
4,4,4,4,4,4,4,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7]);

MOT("4.2^4:(2xS3)",
[
"origin: Dixon's Algorithm,\n",
"normalizer of 4.2^4:2 in HS,\n",
"table is sorted w.r.t. normal series 2.2.2^2.2^2.3.2.2"
],
[768,768,384,128,128,64,64,64,64,24,24,12,32,32,32,32,16,16,96,96,32,32,32,32,
64,32,64,12,12,16,16],
[,[1,1,2,1,2,1,1,2,2,10,10,11,1,1,4,4,7,7,1,1,1,2,4,4,4,4,4,10,10,8,8],[1,2,3,
4,5,6,7,8,9,1,2,3,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,20,19,30,31]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[1,1,1,1,1,1,
1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,1,1,-1,-1,1,1,-1,-1,-1,1,1,-1,-1],
[TENSOR,[2,3]],[2,2,2,2,2,2,2,2,2,-1,-1,-1,0,0,0,0,0,0,2,2,0,0,2,2,0,0,0,-1,
-1,0,0],
[TENSOR,[5,2]],[3,3,3,3,3,-1,-1,-1,-1,0,0,0,-1,-1,-1,-1,1,1,3,3,-1,-1,-1,-1,
-1,-1,-1,0,0,1,1],
[TENSOR,[7,3]],
[TENSOR,[7,4]],
[TENSOR,[7,2]],[6,6,6,-2,-2,2,-2,2,-2,0,0,0,0,0,0,0,0,0,0,0,-2,-2,0,0,2,2,2,0,
0,0,0],
[TENSOR,[11,2]],[6,6,6,-2,-2,-2,2,-2,2,0,0,0,-2,-2,2,2,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0],
[TENSOR,[13,3]],[1,1,-1,1,-1,-1,1,1,-1,1,1,-1,-1,1,1,-1,-1,1,-1,1,-1,1,1,-1,
-1,1,-1,1,-1,1,-1],
[TENSOR,[3,15]],
[TENSOR,[2,16]],
[TENSOR,[2,15]],
[TENSOR,[5,15]],
[TENSOR,[5,17]],
[TENSOR,[7,16]],
[TENSOR,[7,15]],
[TENSOR,[7,18]],
[TENSOR,[7,17]],
[TENSOR,[11,16]],
[TENSOR,[11,15]],
[TENSOR,[13,15]],
[TENSOR,[13,16]],[8,-8,0,0,0,0,0,0,0,2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,-4,0,4,0,
0,0,0],
[TENSOR,[29,2]],[16,-16,0,0,0,0,0,0,0,-2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0]],
[(25,27),(13,14)(15,16)(17,18)(19,20)(23,24)(28,29)]);
ALF("4.2^4:(2xS3)","4.2^4.S5",[1,2,3,5,4,5,5,4,4,12,13,14,19,20,21,22,21,
22,19,20,7,6,21,22,9,11,10,27,28,8,8],[
"fusion map is unique up to table automorphisms"
]);
ALF("4.2^4:(2xS3)","HS",[1,2,5,2,6,2,2,6,6,4,12,21,2,3,6,7,6,7,2,3,3,7,6,
7,6,6,5,11,12,14,14],[
"fusion map is unique up to table automorphisms"
]);

MOT("4.2^4",
[
"stabilizer of chain (2A < [2^8]) in HS,\n",
"stabilizer of chain (2A < Sylow2) in HS,\n",
"origin: Dixon's Algorithm"
],
[64,64,32,16,32,16,32,16,32,16,64,32,16,16,16,16,64,16,16,16,16,32],
[,[1,1,2,1,1,1,2,1,2,1,1,1,2,3,1,3,1,1,3,2,3,2],[1,2,3,4,5,6,7,8,9,10,11,12,
13,14,15,16,17,18,19,20,21,22],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,
19,20,21,22],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,-1,1,-1,-1,1,-1,1,-1,-1,
-1,1,-1,1,-1,1,-1,1,-1,1],[1,1,1,-1,1,-1,-1,1,-1,1,-1,-1,1,-1,1,-1,-1,-1,1,-1,
1,1],[1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1],[1,1,1,1,1,1,-1,
-1,-1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1,-1,1],[1,1,1,1,-1,-1,1,1,-1,-1,-1,1,1,1,-1,
-1,-1,1,1,-1,-1,-1],[1,1,1,1,-1,-1,1,1,-1,-1,-1,1,-1,-1,1,1,-1,-1,-1,1,1,-1],[
1,1,1,-1,-1,1,1,-1,-1,1,-1,1,1,-1,-1,1,-1,1,-1,-1,1,-1],[1,1,1,-1,-1,1,1,-1,
-1,1,-1,1,-1,1,1,-1,-1,-1,1,1,-1,-1],
[TENSOR,[2,9]],
[TENSOR,[2,8]],
[TENSOR,[2,7]],
[TENSOR,[2,6]],
[TENSOR,[2,5]],
[TENSOR,[2,4]],
[TENSOR,[2,3]],[2,2,-2,0,-2,0,2,0,-2,0,2,-2,0,0,0,0,2,0,0,0,0,2],
[TENSOR,[17,2]],
[TENSOR,[17,6]],
[TENSOR,[17,10]],[4,-4,0,0,0,0,0,0,0,0,-4,0,0,0,0,0,4,0,0,0,0,0],
[TENSOR,[21,2]]],
[(11,17),(13,20)(14,21)(15,18)(16,19),( 5,12)( 6, 8)( 7,22)(15,18)(16,19),
( 4, 6)( 8,10)(14,16)(19,21)]);
ALF("4.2^4","4.2^4.S5",[1,2,6,19,5,19,3,20,4,20,7,7,6,23,7,23,7,7,24,6,24,
6]);
ALF("4.2^4","HS",[1,2,7,2,2,2,5,3,6,3,3,3,7,15,3,15,3,3,16,7,16,7]);

MOT("S4x2^2",
[
"normalizer of chain (2A < 4.2^4.2) in HS",
],
0,
0,
0,
[(13,14)(15,16)(17,18)(19,20),(13,15)(14,16)(17,19)(18,20),( 3, 4)( 7, 8)
(11,12)(15,16)(19,20),( 2, 3)( 6, 7)(10,11)(14,15)(18,19)],
["ConstructDirectProduct",[["s4"],["V4"]]]);
ALF("S4x2^2","4.2^4:(2xS3)",[1,2,19,19,4,4,19,19,10,11,29,29,14,14,21,21,
15,15,25,27]);
ALF("S4x2^2","HS",[1,2,2,2,2,2,2,2,4,12,12,12,3,3,3,3,6,6,6,5],[
"fusion map of chain normalizer determined using the groups"
]);

MOT("4.2^4:S4",
[
"origin: Dixon's Algorithm,\n",
"normalizer of 4.2^4:2^2 in HS, of structure 4.2^4:S4,\n",
"table is sorted w.r.t. normal series 2.2.2^2.2^2.2^2.3.2"
],
[1536,1536,768,256,256,128,128,64,64,64,64,64,16,12,12,12,12,32,32,32,32,16,
16,16,16,16,16],
[,[1,1,2,1,2,4,4,4,1,1,2,2,5,14,14,15,15,1,1,4,4,6,6,10,10,12,12],[1,2,3,4,5,
6,7,8,9,10,11,12,13,1,2,3,3,18,19,20,21,23,22,24,25,26,27]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[2,2,2,2,2,2,2,2,2,2,2,2,2,-1,-1,
-1,-1,0,0,0,0,0,0,0,0,0,0],[3,3,3,3,3,3,3,3,-1,-1,-1,-1,-1,0,0,0,0,1,1,1,1,1,
1,-1,-1,-1,-1],
[TENSOR,[4,2]],[3,3,3,3,3,-1,-1,-1,3,-1,-1,3,-1,0,0,0,0,-1,-1,-1,-1,1,1,1,1,
-1,-1],[3,3,3,3,3,-1,-1,-1,-1,3,3,-1,-1,0,0,0,0,-1,-1,-1,-1,1,1,-1,-1,1,1],
[TENSOR,[6,2]],
[TENSOR,[7,2]],[6,6,6,6,6,-2,-2,-2,-2,-2,-2,-2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,
0],[12,12,12,-4,-4,0,0,0,0,0,0,0,0,0,0,0,0,2,2,-2,-2,0,0,0,0,0,0],
[TENSOR,[11,2]],[4,4,-4,4,-4,0,0,0,0,0,0,0,0,1,1,-1,-1,-2,2,-2,2,0,0,0,0,0,0],
[TENSOR,[13,2]],[6,6,-6,-2,2,-2,-2,2,-2,2,-2,2,0,0,0,0,0,2,-2,-2,2,0,0,0,0,0,
0],
[TENSOR,[15,2]],[6,6,-6,-2,2,2,2,-2,2,2,-2,-2,0,0,0,0,0,0,0,0,0,0,0,2,-2,0,0],
[TENSOR,[17,2]],[6,6,-6,-2,2,2,2,-2,-2,-2,2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,2],
[TENSOR,[19,2]],[6,6,-6,-2,2,-2,-2,2,2,-2,2,-2,0,0,0,0,0,0,0,0,0,-2*E(4),
2*E(4),0,0,0,0],
[TENSOR,[21,2]],[8,8,-8,8,-8,0,0,0,0,0,0,0,0,-1,-1,1,1,0,0,0,0,0,0,0,0,0,0],[
8,-8,0,0,0,4,-4,0,0,0,0,0,0,2,-2,0,0,0,0,0,0,0,0,0,0,0,0],[8,-8,0,0,0,4,-4,0,
0,0,0,0,0,-1,1,E(12)^7-E(12)^11,-E(12)^7+E(12)^11,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[25,5]],[24,-24,0,0,0,-4,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]],
[(22,23),(18,19)(20,21),(16,17),(26,27),(24,25)]);
ALF("4.2^4:S4","4.2^4.S5",[1,2,3,5,4,9,10,11,7,5,4,6,8,12,13,14,14,19,20,
21,22,25,26,21,22,23,24]);
ALF("4.2^4:S4","HS",[1,2,5,2,6,6,5,6,3,2,6,7,14,4,12,21,21,2,3,6,7,14,14,
6,7,15,16]);

MOT("J1x2",
[
"2nd maximal subgroup of ON.2",
],
0,
0,
0,
[(7,9)(8,10)(15,17)(16,18)(21,23)(22,24),(25,27,29)(26,28,30)],
["ConstructDirectProduct",[["J1"],["Cyclic",2]]]);
ALF("J1x2","ON.2",[1,26,2,26,3,27,6,31,6,32,7,27,9,33,11,31,11,32,12,34,
15,37,16,38,19,39,20,40,21,41],[
"fusion map determined up to table aut. by compatibility with Brauer tables"
]);

MOT("7^(1+2)_+:(3xD16)",
[
"7th maximal subgroup of ON.2,\n",
"origin: Dixon's Algorithm"
],
[16464,2744,98,98,48,48,336,48,48,56,168,24,24,56,56,84,12,12,14,84,12,12,168,
168,14,24,24,24,24,56,56,56,56],
[,[1,2,3,4,6,5,1,6,5,2,7,9,8,10,10,1,6,5,3,1,5,6,11,11,4,12,13,12,13,14,15,15,
14],[1,2,3,4,1,1,7,7,7,10,11,11,11,14,15,16,16,16,19,20,20,20,24,23,25,24,24,
23,23,33,32,31,30],,,,[1,1,1,1,5,6,7,8,9,7,11,12,13,11,11,16,17,18,16,20,21,22
,23,24,20,26,27,28,29,23,23,24,24]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,1,1,-1,1,1,1,1,1,1,1,1],
[TENSOR,[2,3]],[2,2,2,2,2,2,2,2,2,2,-2,-2,-2,-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0],[2,2,2,2,2,2,-2,-2,-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,-E(8)+E(8)^3,
E(8)-E(8)^3,0,-E(8)+E(8)^3,-E(8)+E(8)^3,E(8)-E(8)^3,E(8)-E(8)^3,-E(8)+E(8)^3,
-E(8)+E(8)^3,E(8)-E(8)^3,E(8)-E(8)^3],
[TENSOR,[6,2]],[1,1,1,1,E(3)^2,E(3),1,E(3)^2,E(3),1,1,E(3)^2,E(3),1,1,-1,
-E(3)^2,-E(3),-1,-1,-E(3),-E(3)^2,1,1,-1,E(3),E(3)^2,E(3),E(3)^2,1,1,1,1],
[GALOIS,[8,2]],
[TENSOR,[8,4]],
[TENSOR,[9,4]],
[TENSOR,[2,8]],
[TENSOR,[2,9]],
[TENSOR,[2,10]],
[TENSOR,[2,11]],
[TENSOR,[6,8]],
[TENSOR,[6,9]],
[TENSOR,[6,10]],
[TENSOR,[6,11]],
[TENSOR,[5,8]],
[TENSOR,[5,9]],[24,24,-4,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,6,0,0,0,0,-1,0,0,0,0
,0,0,0,0],
[TENSOR,[22,2]],[24,24,3,-4,0,0,0,0,0,0,0,0,0,0,0,-6,0,0,1,0,0,0,0,0,0,0,0,0,
0,0,0,0,0],
[TENSOR,[24,3]],[42,-7,0,0,0,0,-6,0,0,1,-6,0,0,1,1,0,0,0,0,0,0,0,6,6,0,0,0,0,
0,-1,-1,-1,-1],
[TENSOR,[26,2]],[42,-7,0,0,0,0,-6,0,0,1,6,0,0,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,-E(28)^3+E(28)^11+E(28)^15-E(28)^19+E(28)^23-E(28)^27,
E(28)^3-E(28)^11-E(28)^15+E(28)^19-E(28)^23+E(28)^27,
E(28)^3-E(28)^11-E(28)^15+E(28)^19-E(28)^23+E(28)^27,
-E(28)^3+E(28)^11+E(28)^15-E(28)^19+E(28)^23-E(28)^27],
[TENSOR,[28,2]],[42,-7,0,0,0,0,6,0,0,-1,0,0,0,
-E(28)^3+E(28)^11+E(28)^15-E(28)^19+E(28)^23-E(28)^27,
E(28)^3-E(28)^11-E(28)^15+E(28)^19-E(28)^23+E(28)^27,0,0,0,0,0,0,0,
3*E(8)-3*E(8)^3,-3*E(8)+3*E(8)^3,0,0,0,0,0,
-E(56)^29+E(56)^31-E(56)^37+E(56)^47-E(56)^53+E(56)^55,
-E(56)^5-E(56)^13+E(56)^15+E(56)^23+E(56)^39-E(56)^45,
E(56)^5+E(56)^13-E(56)^15-E(56)^23-E(56)^39+E(56)^45,
E(56)^29-E(56)^31+E(56)^37-E(56)^47+E(56)^53-E(56)^55],
[TENSOR,[30,2]],
[GALOIS,[30,15]],
[TENSOR,[32,2]]],
[(14,15)(30,31)(32,33),(14,15)(23,24)(26,28)(27,29)(30,32)(31,33),
( 3, 4)(16,20)(17,22)(18,21)(19,25),
( 5, 6)( 8, 9)(12,13)(17,18)(21,22)(26,27)(28,29)]);
ALF("7^(1+2)_+:(3xD16)","ON.2",[1,8,8,9,3,3,2,7,7,14,4,13,13,23,24,2,7,7,
14,26,27,27,28,29,33,35,35,36,36,42,44,45,43],[
"fusion map is unique up to table automorphisms"
]);
ALN("7^(1+2)_+:(3xD16)",["ON.2N7"]);

MOT("4^3.L3(2)",
[
"origin: Dixon's Algorithm,\n",
"9th maximal subgroup of ON,\n",
"table is sorted w.r. to normal series given by 2^3.2^3.L3(2),\n",
"tests: 1.o.r., pow[2,3,7]"
],
[10752,1536,768,256,32,32,32,32,12,12,12,12,16,16,16,16,7,7],
[,[1,1,2,2,1,2,4,4,9,9,10,10,7,7,8,8,17,18],[1,2,3,4,5,6,7,8,1,2,3,3,14,13,16,
15,18,17],,,,[1,2,3,4,5,6,7,8,9,10,12,11,13,14,15,16,1,1]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[3,3,3,3,-1,-1,-1,-1,0,0,0,0,1,1,1,1,
E(7)+E(7)^2+E(7)^4,E(7)^3+E(7)^5+E(7)^6],
[GALOIS,[2,3]],[6,6,6,6,2,2,2,2,0,0,0,0,0,0,0,0,-1,-1],[7,7,7,7,-1,-1,-1,-1,1,
1,1,1,-1,-1,-1,-1,0,0],[8,8,8,8,0,0,0,0,-1,-1,-1,-1,0,0,0,0,1,1],[7,7,-1,-1,
-1,-1,3,-1,1,1,-1,-1,-1,-1,1,1,0,0],[7,7,-1,-1,-1,-1,-1,3,1,1,-1,-1,1,1,-1,-1,
0,0],[14,14,-2,-2,-2,-2,2,2,-1,-1,1,1,0,0,0,0,0,0],[21,21,-3,-3,1,1,1,-3,0,0,
0,0,1,1,-1,-1,0,0],[21,21,-3,-3,1,1,-3,1,0,0,0,0,-1,-1,1,1,0,0],[28,-4,-12,4,
0,0,0,0,-2,2,0,0,0,0,0,0,0,0],[28,-4,-12,4,0,0,0,0,1,-1,E(12)^7-E(12)^11,
-E(12)^7+E(12)^11,0,0,0,0,0,0],
[GALOIS,[13,5]],[42,-6,6,-2,2,-2,0,0,0,0,0,0,E(8)-E(8)^3,-E(8)+E(8)^3,
E(8)-E(8)^3,-E(8)+E(8)^3,0,0],
[GALOIS,[15,3]],[42,-6,6,-2,-2,2,0,0,0,0,0,0,E(8)-E(8)^3,-E(8)+E(8)^3,
-E(8)+E(8)^3,E(8)-E(8)^3,0,0],
[GALOIS,[17,3]]],
[(13,14)(15,16),(17,18),(11,12),( 7, 8)(13,15)(14,16)]);
ALF("4^3.L3(2)","ON",[1,2,4,5,2,5,10,11,3,7,14,14,18,19,21,20,9,9],[
"fusion map is unique up to table automorphisms"
]);
ALF("4^3.L3(2)","L3(2)",[1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4,5,6]);
ALF("4^3.L3(2)","2^3.L3(2)",[1,1,2,2,3,3,4,5,6,6,7,7,8,8,9,9,10,11]);
ALF("4^3.L3(2)","4^3.(L3(2)x2)",[1,2,3,4,6,8,17,17,7,9,20,20,23,24,24,23,
12,13],[
"fusion map is unique up to table aut."
]);

MOT("(3^2:4xA6).2^2",
[
"origin: Dixon's Algorithm,\n",
"4th maximal subgroup of ON.2"
],
[51840,6480,5760,2880,1152,128,648,81,576,64,64,32,360,144,72,40,72,72,72,90,
90,20,8,16,16,120,60,192,192,192,192,48,48,32,32,60,60,24,24,24,24,24,24,30,30
],
[,[1,2,1,3,1,1,7,8,5,5,3,6,13,2,7,13,14,15,15,21,20,16,6,10,10,1,2,4,4,4,4,9,9
,11,11,13,13,17,17,19,19,18,18,20,21],[1,1,3,4,5,6,1,1,9,10,11,12,13,5,3,16,9,
4,4,13,13,22,23,24,25,26,26,30,31,28,29,33,32,34,35,37,36,33,32,30,31,28,29,37
,36],,[1,2,3,4,5,6,7,8,9,10,11,12,1,14,15,3,17,18,19,2,2,4,23,25,24,26,27,29,
28,31,30,33,32,35,34,26,26,39,38,41,40,43,42,27,27]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,1,1,1,1,-1,-1,1,1,-1,-1,-1,-1,1,1,1,1,-1,-1],
[TENSOR,[2,3]],[9,9,9,9,1,1,0,0,1,1,1,1,-1,1,0,-1,1,0,0,-1,-1,-1,1,-1,-1,1,1,
-3,-3,-3,-3,-1,-1,1,1,1,1,-1,-1,0,0,0,0,1,1],
[TENSOR,[5,4]],
[TENSOR,[5,2]],
[TENSOR,[5,3]],[10,10,10,10,2,2,1,1,-2,-2,2,-2,0,2,1,0,-2,1,1,0,0,0,0,0,0,0,0
,-2,-2,-2,-2,0,0,-2,-2,0,0,0,0,1,1,1,1,0,0],
[TENSOR,[9,2]],[16,16,16,16,0,0,-2,-2,0,0,0,0,1,0,-2,1,0,-2,-2,1,1,1,0,0,0,4,
4,0,0,0,0,0,0,0,0,-1,-1,0,0,0,0,0,0,-1,-1],
[TENSOR,[11,2]],[20,20,20,20,-4,-4,2,2,0,0,-4,0,0,-4,2,0,0,2,2,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[2,2,2,-2,2,2,2,2,2,2,-2,-2,2,2,2,2,2,
-2,-2,2,2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[10,10,10,-10,2,2,
1,1,-2,-2,-2,2,0,2,1,0,-2,-1,-1,0,0,0,0,0,0,0,0,-4*E(4),-4*E(4),4*E(4),4*E(4),
0,0,0,0,0,0,0,0,-E(4),-E(4),E(4),E(4),0,0],
[TENSOR,[15,2]],[10,10,10,-10,-2,-2,1,1,0,0,2,0,0,-2,1,0,0,-1,-1,0,0,0,0,
-E(8)-E(8)^3,E(8)+E(8)^3,0,0,-2*E(4),-2*E(4),2*E(4),2*E(4),-E(8)+E(8)^3,
E(8)-E(8)^3,0,0,0,0,-E(8)+E(8)^3,E(8)-E(8)^3,E(4),E(4),-E(4),-E(4),0,0],
[TENSOR,[17,4]],
[TENSOR,[17,2]],
[TENSOR,[17,3]],[16,16,16,-16,0,0,-2,-2,0,0,0,0,1,0,-2,1,0,2,2,1,1,-1,0,0,0,0
,0,0,0,0,0,0,0,0,0,-E(5)+E(5)^2+E(5)^3-E(5)^4,E(5)-E(5)^2-E(5)^3+E(5)^4,0,0,0,
0,0,0,-E(5)+E(5)^2+E(5)^3-E(5)^4,E(5)-E(5)^2-E(5)^3+E(5)^4],
[TENSOR,[21,2]],[18,18,18,-18,2,2,0,0,2,2,-2,-2,-2,2,0,-2,2,0,0,-2,-2,2,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[2,2,-2,0,2,-2,2,2,2,-2,0,0,2,2,-2,
-2,2,0,0,2,2,0,0,0,0,0,0,E(8)+E(8)^3,-E(8)-E(8)^3,E(8)+E(8)^3,-E(8)-E(8)^3,0,0
,-E(8)-E(8)^3,E(8)+E(8)^3,0,0,0,0,E(8)+E(8)^3,-E(8)-E(8)^3,E(8)+E(8)^3,
-E(8)-E(8)^3,0,0],
[TENSOR,[24,2]],[10,10,-10,0,2,-2,1,1,-2,2,0,0,0,2,-1,0,-2,3*E(4),-3*E(4),0,0
,0,0,0,0,0,0,-E(8)+3*E(8)^3,E(8)-3*E(8)^3,3*E(8)-E(8)^3,-3*E(8)+E(8)^3,0,0,
-E(8)-E(8)^3,E(8)+E(8)^3,0,0,0,0,-E(8),E(8),-E(8)^3,E(8)^3,0,0],
[GALOIS,[26,7]],
[TENSOR,[26,2]],
[TENSOR,[27,2]],[18,18,-18,0,2,-2,0,0,2,-2,0,0,-2,2,0,2,2,0,0,-2,-2,0,0,0,0,0
,0,-3*E(8)-3*E(8)^3,3*E(8)+3*E(8)^3,-3*E(8)-3*E(8)^3,3*E(8)+3*E(8)^3,0,0,
-E(8)-E(8)^3,E(8)+E(8)^3,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[30,2]],[20,20,-20,0,-4,4,2,2,0,0,0,0,0,-4,-2,0,0,0,0,0,0,0,0,0,0,0,0
,-2*E(8)+2*E(8)^3,2*E(8)-2*E(8)^3,2*E(8)-2*E(8)^3,-2*E(8)+2*E(8)^3,0,0,0,0,0,0
,0,0,E(8)-E(8)^3,-E(8)+E(8)^3,-E(8)+E(8)^3,E(8)-E(8)^3,0,0],
[TENSOR,[32,2]],[32,32,-32,0,0,0,-4,-4,0,0,0,0,2,0,4,-2,0,0,0,2,2,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[8,-1,0,0,8,0,8,-1,8,0,0,0,8,-1,0,0,-1,0
,0,-1,-1,0,0,0,0,2,-1,0,0,0,0,2,2,0,0,2,2,-1,-1,0,0,0,0,-1,-1],
[TENSOR,[35,2]],[64,-8,0,0,0,0,-8,1,0,0,0,0,4,0,0,0,0,0,0,
2*E(5)-E(5)^2-E(5)^3+2*E(5)^4,-E(5)+2*E(5)^2+2*E(5)^3-E(5)^4,0,0,0,0,4,-2,0,0,
0,0,0,0,0,0,2*E(5)+2*E(5)^4,2*E(5)^2+2*E(5)^3,0,0,0,0,0,0,-E(5)-E(5)^4,
-E(5)^2-E(5)^3],
[GALOIS,[37,2]],
[TENSOR,[38,2]],
[TENSOR,[37,2]],[72,-9,0,0,8,0,0,0,8,0,0,0,-8,-1,0,0,-1,0,0,1,1,0,0,0,0,-2,1,
0,0,0,0,2,2,0,0,-2,-2,-1,-1,0,0,0,0,1,1],
[TENSOR,[41,2]],[80,-10,0,0,16,0,8,-1,-16,0,0,0,0,-2,0,0,2,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[80,-10,0,0,-16,0,8,-1,0,0,0,0,0,2,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2*E(8)-2*E(8)^3,-2*E(8)+2*E(8)^3,0,0,0,0,
-E(8)+E(8)^3,E(8)-E(8)^3,0,0,0,0,0,0],
[TENSOR,[44,2]]],
[(24,25)(32,33)(38,39),(20,21)(36,37)(44,45),
(28,29)(30,31)(34,35)(40,41)(42,43),(18,19)(24,25)(28,30)(29,31)(40,42)(41,43)
]);
ALF("(3^2:4xA6).2^2","ON.2",[1,3,2,4,2,2,3,3,4,5,5,5,6,7,7,11,13,13,13,15,
16,22,5,10,10,26,27,28,29,29,28,28,29,30,30,32,31,35,36,35,36,36,35,38,37],[
"fusion map is unique up to table automorphisms"
]);

MOT("4^3.(L3(2)x2)",
[
"origin: Dixon's Algorithm,\n",
"6th maximal subgroup of ON.2"
],
[21504,3072,1536,512,336,64,24,64,24,12,12,14,14,64,64,32,32,16,16,12,14,14,16
,16],
[,[1,1,2,2,1,1,7,2,7,7,7,12,13,3,3,4,4,8,8,9,12,13,17,17],[1,2,3,4,5,6,1,8,2,5
,5,13,12,15,14,16,17,19,18,3,22,21,24,23],,,,[1,2,3,4,5,6,7,8,9,10,11,1,1,14,
15,16,17,19,18,20,5,5,23,24]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[3,3,3,3,3,-1,0,-1,0,0,0,
E(7)^3+E(7)^5+E(7)^6,E(7)+E(7)^2+E(7)^4,-1,-1,-1,-1,1,1,0,E(7)^3+E(7)^5+E(7)^6
,E(7)+E(7)^2+E(7)^4,1,1],
[GALOIS,[2,3]],[6,6,6,6,6,2,0,2,0,0,0,-1,-1,2,2,2,2,0,0,0,-1,-1,0,0],[7,7,7,7
,7,-1,1,-1,1,1,1,0,0,-1,-1,-1,-1,-1,-1,1,0,0,-1,-1],[8,8,8,8,8,0,-1,0,-1,-1,-1
,1,1,0,0,0,0,0,0,-1,1,1,0,0],[1,1,1,1,-1,1,1,1,1,-1,-1,1,1,-1,-1,-1,1,-1,-1,1,
-1,-1,1,1],
[TENSOR,[2,7]],
[TENSOR,[3,7]],
[TENSOR,[4,7]],
[TENSOR,[5,7]],
[TENSOR,[6,7]],[14,14,-2,-2,0,-2,2,-2,2,0,0,0,0,0,0,0,2,0,0,-2,0,0,0,0],[14,
14,-2,-2,0,-2,-1,-2,-1,-E(3)+E(3)^2,E(3)-E(3)^2,0,0,0,0,0,2,0,0,1,0,0,0,0],
[TENSOR,[14,7]],[42,42,-6,-6,0,2,0,2,0,0,0,0,0,0,0,0,-2,0,0,0,0,0,0,0],[28,-4
,-12,4,0,0,-2,0,2,0,0,0,0,0,0,0,0,-2*E(4),2*E(4),0,0,0,0,0],
[TENSOR,[17,7]],[42,-6,6,-2,0,-2,0,2,0,0,0,0,0,-2+2*E(8)-2*E(8)^3,
-2-2*E(8)+2*E(8)^3,2,0,0,0,0,0,0,-E(8)+E(8)^3,E(8)-E(8)^3],
[GALOIS,[19,3]],
[TENSOR,[20,7]],
[TENSOR,[19,7]],[56,-8,-24,8,0,0,2,0,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[84,
-12,12,-4,0,4,0,-4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]],
[(18,19),(14,15)(23,24),(10,11),(12,13)(21,22)]);
ALF("4^3.(L3(2)x2)","ON.2",[1,2,4,5,26,2,3,5,7,27,27,9,9,28,29,30,10,30,
30,13,33,33,17,18],[
"fusion map is unique up to table automorphisms"
]);

MOT("4^3:psl(3,2)",
[
"origin: CAS library,\n",
"7th maximal subgroup of HS,\n",
"tests: 1.o.r., pow[2,3,7]"
],
[10752,1536,768,256,64,64,64,64,16,12,12,12,12,16,16,16,16,7,7],
[,[1,1,2,2,1,2,1,2,4,10,10,11,11,5,5,8,8,18,19],[1,2,3,4,5,6,7,8,9,1,2,3,3,14,
15,16,17,19,18],,,,[1,2,3,4,5,6,7,8,9,10,11,13,12,14,15,16,17,1,1]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[3,3,3,3,-1,-1,-1,-1,-1,0,0,0,0,1,1,
1,1,E(7)+E(7)^2+E(7)^4,E(7)^3+E(7)^5+E(7)^6],
[GALOIS,[2,3]],[6,6,6,6,2,2,2,2,2,0,0,0,0,0,0,0,0,-1,-1],[7,7,7,7,-1,-1,-1,-1,
-1,1,1,1,1,-1,-1,-1,-1,0,0],[8,8,8,8,0,0,0,0,0,-1,-1,-1,-1,0,0,0,0,1,1],[7,7,
-1,-1,3,3,-1,-1,-1,1,1,-1,-1,1,1,-1,-1,0,0],[7,7,-1,-1,-1,-1,3,3,-1,1,1,-1,-1,
-1,-1,1,1,0,0],[14,14,-2,-2,2,2,2,2,-2,-1,-1,1,1,0,0,0,0,0,0],[21,21,-3,-3,1,
1,-3,-3,1,0,0,0,0,-1,-1,1,1,0,0],[21,21,-3,-3,-3,-3,1,1,1,0,0,0,0,1,1,-1,-1,0,
0],[14,-2,-6,2,2,-2,-2,2,0,2,-2,0,0,0,0,0,0,0,0],[14,-2,-6,2,2,-2,-2,2,0,-1,1,
-E(12)^7+E(12)^11,E(12)^7-E(12)^11,0,0,0,0,0,0],
[GALOIS,[13,5]],[42,-6,-18,6,-2,2,2,-2,0,0,0,0,0,0,0,0,0,0,0],[42,-6,6,-2,2,
-2,2,-2,0,0,0,0,0,2,-2,0,0,0,0],[42,-6,6,-2,2,-2,2,-2,0,0,0,0,0,-2,2,0,0,0,
0],[42,-6,6,-2,-2,2,-2,2,0,0,0,0,0,0,0,2,-2,0,0],[42,-6,6,-2,-2,2,-2,2,0,0,0,
0,0,0,0,-2,2,0,0]],
[(18,19),(12,13),(16,17),(14,15)]);
ARC("4^3:psl(3,2)","projectives",["2.4^3.L3(2)",[[8,-8,0,0,0,0,0,0,0,-1,1,
-E(3)+E(3)^2,E(3)-E(3)^2,0,0,0,0,1,1],
[GALOIS,[1,2]],[8,-8,0,0,0,0,0,0,0,2,-2,0,0,0,0,0,0,1,1],[24,-24,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,E(7)^3+E(7)^5+E(7)^6,E(7)+E(7)^2+E(7)^4],
[GALOIS,[4,3]],[28,4,-8*E(4),0,-4,0,0,0,-2*E(4),1,1,-E(4),-E(4),0,0,0,0,0,0],
[28,4,-8*E(4),0,4,0,0,0,2*E(4),1,1,-E(4),-E(4),0,0,0,0,0,0],
[GALOIS,[6,3]],
[GALOIS,[7,3]],[56,8,-16*E(4),0,0,0,0,0,0,-1,-1,E(4),E(4),0,0,0,0,0,0],
[GALOIS,[10,3]]],]);
ARC("4^3:psl(3,2)","tomfusion",rec(name:="4^3:L3(2)",map:=[1,2,7,8,3,10,4,11,
53,5,24,81,81,22,23,57,67,27,27],text:=[
"fusion map is unique up to table automorphisms"
]));
ALF("4^3:psl(3,2)","HS",[1,2,5,6,2,6,3,7,14,4,12,21,21,6,7,15,16,13,13],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("4^3:psl(3,2)","L3(2)",[1,1,1,1,2,2,2,2,2,3,3,3,3,4,4,4,4,5,6]);
ALN("4^3:psl(3,2)",["2^3+3:psl(3,2)"]);
ALF("4^3:psl(3,2)","4^3:(L3(2)x2)",[1,2,3,4,5,8,6,9,15,7,12,17,17,10,11,
16,16,13,14],[
"fusion map is unique up to table automorphisms"
]);

MOT("4^3:(L3(2)x2)",
[
"6th maximal subgroup of 2.HS,\n",
"origin: Dixon's Algorithm"
],
[21504,3072,1536,512,128,128,24,128,128,32,32,24,14,14,32,16,12,2688,384,256,
256,128,64,32,32,16,12,12,64,64,14,14],
[,[1,1,2,2,1,1,7,2,2,5,5,7,13,14,4,9,12,1,1,1,1,2,2,5,5,6,7,7,4,4,13,14],[1,2,
3,4,5,6,1,8,9,10,11,2,14,13,15,16,3,18,19,20,21,22,23,24,25,26,18,19,29,30,32,
31],,,,[1,2,3,4,5,6,7,8,9,10,11,12,1,1,15,16,17,18,19,20,21,22,23,24,25,26,27,
28,29,30,18,18]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[3,3,3,3
,-1,-1,0,-1,-1,1,1,0,E(7)+E(7)^2+E(7)^4,E(7)^3+E(7)^5+E(7)^6,-1,1,0,-3,-3,1,1,
1,1,-1,-1,-1,0,0,1,1,-E(7)-E(7)^2-E(7)^4,-E(7)^3-E(7)^5-E(7)^6],
[GALOIS,[3,3]],
[TENSOR,[4,2]],
[TENSOR,[3,2]],[6,6,6,6,2,2,0,2,2,0,0,0,-1,-1,2,0,0,6,6,2,2,2,2,0,0,0,0,0,2,2
,-1,-1],
[TENSOR,[7,2]],[7,7,7,7,-1,-1,1,-1,-1,-1,-1,1,0,0,-1,-1,1,7,7,-1,-1,-1,-1,-1,
-1,-1,1,1,-1,-1,0,0],
[TENSOR,[9,2]],[8,8,8,8,0,0,-1,0,0,0,0,-1,1,1,0,0,-1,8,8,0,0,0,0,0,0,0,-1,-1,
0,0,1,1],
[TENSOR,[11,2]],[7,7,-1,-1,3,-1,1,3,-1,1,1,1,0,0,-1,-1,-1,7,-1,3,3,3,-1,1,1,
-1,1,-1,-1,-1,0,0],
[TENSOR,[13,2]],[7,7,-1,-1,-1,3,1,-1,3,-1,-1,1,0,0,-1,1,-1,-7,1,1,1,1,-3,1,1,
-1,-1,1,1,1,0,0],
[TENSOR,[15,2]],[14,14,-2,-2,2,2,-1,2,2,0,0,-1,0,0,-2,0,1,14,-2,2,2,2,2,0,0,0
,-1,1,-2,-2,0,0],
[TENSOR,[17,2]],[21,21,-3,-3,1,-3,0,1,-3,-1,-1,0,0,0,1,1,0,21,-3,1,1,1,-3,-1,
-1,1,0,0,1,1,0,0],
[TENSOR,[19,2]],[21,21,-3,-3,-3,1,0,-3,1,1,1,0,0,0,1,-1,0,-21,3,3,3,3,-1,-1,
-1,1,0,0,-1,-1,0,0],
[TENSOR,[21,2]],[14,-2,-6,2,2,-2,2,-2,2,0,0,-2,0,0,0,0,0,0,0,-4,4,0,0,-2,2,0,
0,0,-2,2,0,0],
[TENSOR,[23,2]],[28,-4,-12,4,4,-4,-2,-4,4,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0],[42,-6,6,-2,2,2,0,-2,-2,-2,2,0,0,0,0,0,0,0,0,8,0,-4,0,0,0,0,0,0,-2
,2,0,0],
[TENSOR,[26,2]],[42,-6,-18,6,-2,2,0,2,-2,0,0,0,0,0,0,0,0,0,0,4,-4,0,0,-2,2,0,
0,0,2,-2,0,0],
[TENSOR,[28,2]],[42,-6,6,-2,2,2,0,-2,-2,2,-2,0,0,0,0,0,0,0,0,0,8,-4,0,0,0,0,0
,0,2,-2,0,0],
[TENSOR,[30,2]],[84,-12,12,-4,-4,-4,0,4,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0]],
[(10,11)(20,21)(24,25)(29,30),(13,14)(31,32)]);
ALF("4^3:(L3(2)x2)","HS.2",[1,2,5,6,2,3,4,6,7,6,7,12,13,13,14,15,19,22,23,
23,22,24,25,25,24,26,28,29,31,30,35,35],[
"fusion map is unique up to table automorphisms"
]);
ALF("4^3:(L3(2)x2)","L3(2)",[1,1,1,1,2,2,3,2,2,4,4,3,5,6,2,4,3,1,1,2,2,2,2,
4,4,4,3,3,2,2,5,6]);

MOT("2.4^3.L3(2)",
[
"7th maximal subgroup of 2.HS"
],
[21504,21504,3072,3072,1536,1536,256,128,128,64,64,64,32,32,24,24,24,24,24,24,
24,24,16,16,16,16,14,14,14,14],
[,[1,1,1,1,4,4,4,1,1,4,2,3,7,7,15,15,15,15,18,18,18,18,9,8,12,12,27,27,29,
29],[1,2,3,4,6,5,7,8,9,10,11,12,14,13,1,2,3,4,5,6,5,6,23,24,25,26,29,30,27,
28],,,,[1,2,3,4,6,5,7,8,9,10,11,12,14,13,15,16,17,18,22,21,20,19,23,24,25,26,
1,2,1,2]],
0,
[(27,29)(28,30),(25,26),(19,21)(20,22),(5,6)(13,14)(19,20)(21,22),(8,9)(13,14)
(23,24)],
["ConstructProj",[["4^3:psl(3,2)",[]],["2.4^3.L3(2)",[]]]]);
ALF("2.4^3.L3(2)","4^3:psl(3,2)",[1,1,2,2,3,3,4,5,5,6,7,8,9,9,10,10,11,11,
12,12,13,13,14,15,16,17,18,18,19,19]);
ALF("2.4^3.L3(2)","2.HS",[1,2,3,4,8,9,10,3,4,10,5,11,24,25,6,7,20,21,35,
36,35,36,10,11,26,27,22,23,22,23],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("2.4^3.L3(2)","L3(2)",[1,1,1,1,1,1,1,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,4,
4,4,4,5,5,6,6]);

MOT("4^3:S4",
[
"origin: Dixon's Algorithm,\n",
"normalizer of 4^3:2^2 in HS,\n",
"table is sorted w.r.t. normal series 2^2.2.2^3.2^2.3.2"
],
[1536,512,384,256,256,192,128,64,64,64,64,64,16,12,12,12,12,32,32,32,32,16,16,
16,16,16,16],
[,[1,1,1,2,2,3,2,3,1,1,2,2,5,14,14,15,15,1,1,2,2,7,7,9,9,12,12],[1,2,3,4,5,6,
7,8,9,10,11,12,13,1,3,6,6,18,19,20,21,22,23,24,25,26,27]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[2,2,2,2,2,2,2,2,2,2,2,2,2,-1,-1,
-1,-1,0,0,0,0,0,0,0,0,0,0],[3,3,3,3,3,3,3,3,-1,-1,-1,-1,-1,0,0,0,0,1,1,1,1,1,
1,-1,-1,-1,-1],
[TENSOR,[4,2]],[1,1,1,1,1,-1,1,-1,1,1,1,1,-1,1,1,-1,-1,1,-1,1,-1,-1,1,1,1,-1,
-1],
[TENSOR,[2,6]],
[TENSOR,[3,6]],
[TENSOR,[4,6]],
[TENSOR,[4,7]],[6,6,6,-2,-2,0,-2,0,-2,2,-2,2,0,0,0,0,0,0,-2,0,-2,2,0,0,0,0,0],
[TENSOR,[11,2]],[6,6,6,-2,-2,0,-2,0,2,-2,2,-2,0,0,0,0,0,-2,0,-2,0,0,2,0,0,0,
0],
[TENSOR,[13,2]],[2,2,-2,-2,-2,0,2,0,2,-2,-2,2,0,2,-2,0,0,0,0,0,0,0,0,0,0,0,
0],[2,2,-2,-2,-2,0,2,0,2,-2,-2,2,0,-1,1,-E(12)^7+E(12)^11,E(12)^7-E(12)^11,0,
0,0,0,0,0,0,0,0,0],
[TENSOR,[16,6]],[6,6,-6,-6,-6,0,6,0,-2,2,2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[
6,6,-6,2,2,0,-2,0,2,2,-2,-2,0,0,0,0,0,0,0,0,0,0,0,2,-2,0,0],
[TENSOR,[19,2]],[6,6,-6,2,2,0,-2,0,-2,-2,2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,2,-2],
[TENSOR,[21,2]],[12,-4,0,-4,4,6,0,-2,0,0,0,0,0,0,0,0,0,2,2,-2,-2,0,0,0,0,0,0],
[TENSOR,[23,2]],
[TENSOR,[23,6]],
[TENSOR,[23,7]],[24,-8,0,8,-8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]],
[(16,17),(26,27),(24,25)]);
ALF("4^3:S4","4^3:psl(3,2)",[1,2,2,3,4,3,4,4,5,7,6,8,9,10,11,12,13,5,7,6,
8,9,9,14,15,16,17],[
"fusion map is unique up to table automorphisms"
]);
ALF("4^3:S4","HS",[1,2,2,5,6,5,6,6,2,3,6,7,14,4,12,21,21,2,3,6,7,14,14,6,
7,15,16],[
"fusion map is unique up to table automorphisms"
]);

MOT("5:4xa5",
[
"origin: CAS library,\n",
"maximal subgroup of Ru,\n",
"source: received from S.Mattarei\n",
"test: 1.OR, JAMES, JAMES,n=5,\n",
"and restricted characters decompose properly.\n",
"tests: 1.o.r., pow[2,3,5]"
],
[1200,240,80,16,60,240,240,16,16,300,100,100,25,25,12,20,20,20,12,12,15,20,20,
20,20],
[,[1,1,1,1,5,2,2,2,2,10,12,11,14,13,5,10,12,11,15,15,21,18,17,18,17],[1,2,3,4,
1,7,6,9,8,10,12,11,14,13,2,16,18,17,7,6,10,25,24,23,22],,[1,2,3,4,5,6,7,8,9,1,
1,1,1,1,15,3,2,2,19,20,5,6,6,7,7]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,-1,1,-1,1,E(4),-E(4),
E(4),-E(4),1,1,1,1,1,-1,1,-1,-1,E(4),-E(4),1,E(4),E(4),-E(4),-E(4)],
[TENSOR,[2,2]],
[TENSOR,[2,3]],[3,3,-1,-1,0,3,3,-1,-1,3,-E(5)^2-E(5)^3,-E(5)-E(5)^4,
-E(5)^2-E(5)^3,-E(5)-E(5)^4,0,-1,-E(5)^2-E(5)^3,-E(5)-E(5)^4,0,0,0,
-E(5)^2-E(5)^3,-E(5)-E(5)^4,-E(5)^2-E(5)^3,-E(5)-E(5)^4],
[GALOIS,[5,2]],
[TENSOR,[5,2]],
[TENSOR,[6,2]],
[TENSOR,[5,3]],
[TENSOR,[6,3]],
[TENSOR,[5,4]],
[TENSOR,[6,4]],[4,4,0,0,1,4,4,0,0,4,-1,-1,-1,-1,1,0,-1,-1,1,1,1,-1,-1,-1,-1],
[TENSOR,[13,2]],
[TENSOR,[13,3]],
[TENSOR,[13,4]],[4,0,4,0,4,0,0,0,0,-1,4,4,-1,-1,0,-1,0,0,0,0,-1,0,0,0,0],[5,5,
1,1,-1,5,5,1,1,5,0,0,0,0,-1,1,0,0,-1,-1,-1,0,0,0,0],
[TENSOR,[18,2]],
[TENSOR,[18,3]],
[TENSOR,[18,4]],[12,0,-4,0,0,0,0,0,0,-3,-4*E(5)^2-4*E(5)^3,-4*E(5)-4*E(5)^4,
E(5)^2+E(5)^3,E(5)+E(5)^4,0,1,0,0,0,0,0,0,0,0,0],
[GALOIS,[22,2]],[16,0,0,0,4,0,0,0,0,-4,-4,-4,1,1,0,0,0,0,0,0,-1,0,0,0,0],[20,
0,4,0,-4,0,0,0,0,-5,0,0,0,0,0,-1,0,0,0,0,1,0,0,0,0]],
[(11,12)(13,14)(17,18)(22,23)(24,25),( 6, 7)( 8, 9)(19,20)(22,24)(23,25)]);
ARC("5:4xa5","tomfusion",rec(name:="5:4xA5",map:=[1,2,3,4,5,7,7,8,8,11,12,
12,13,13,15,23,24,24,30,30,31,40,40,40,40],text:=[
"fusion map is unique"
]));
ALF("5:4xa5","Ru",[1,2,3,3,4,6,6,8,8,10,9,9,10,10,11,17,16,16,19,19,24,28,
29,28,29],[
"together with the fact that N(5B) must contain 20BC elements,\n",
"the fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("5:4xa5","HS",[1,2,3,3,4,5,5,7,7,9,8,8,9,9,12,18,17,17,21,21,22,24,23,
23,24],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("5:4xa5","5:4xS5",[1,22,2,23,3,15,29,16,30,8,4,4,11,11,24,9,25,25,17,
31,10,18,18,32,32],[
"fusion map is unique up to table aut."
]);
ALF("5:4xa5","Co3",[1,2,3,3,5,7,7,8,8,10,9,9,10,10,13,23,22,22,28,28,31,
33,34,34,33],[
"fusion map is unique up to table aut."
]);

MOT("5:4xS5",
[
"10th maximal subgroup of HS.2,\n",
"structure 5:4xS5"
],
0,
0,
0,
[(15,29)(16,30)(17,31)(18,32)(19,33)(20,34)(21,35)],
["ConstructDirectProduct",[["P:Q",[5,4]],["A5.2"]]]);
ALF("5:4xS5","HS.2",[1,3,4,8,22,26,27,9,17,20,9,32,36,39,5,7,19,21,25,
26,34,2,3,12,16,23,26,29,5,7,19,21,25,26,34],[
"fusion map is unique"
]);
ALF("5:4xS5","He.2",[1,2,4,9,27,28,29,9,16,21,9,35,40,43,28,28,36,40,6,7,
17,2,3,10,16,27,28,30,28,28,36,40,6,7,17],[
"fusion map is unique"
]);
ALF("5:4xS5","Co2",[1,4,6,14,2,13,18,15,32,45,15,31,52,58,8,11,39,51,12,
13,41,3,4,20,30,4,13,21,8,11,39,51,12,13,41],[
"fusion map is unique"
]);
ALF("5:4xS5","Fi22",[1,3,5,14,2,10,15,14,35,52,14,34,59,65,10,13,41,59,13,
12,46,3,4,18,35,4,13,20,10,13,41,59,13,12,46],[
"fusion map is unique"
]);
ALF("5:4xS5","5:4xS5x2",[1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,
35,37,39,41,43,45,47,49,51,53,55,57,59,61,63,65,67,69],[
"fusion map is unique up to table aut."
]);

MOT("5:4x2.A5",
[
"12th maximal subgroup of 2.HS,\n",
"15th maximal subgroup of 2.Ru,\n",
"structure 5:4x2.A5"
],
0,
0,
0,
[(19,20)(22,23)(24,25)(26,27)(37,38)(40,41)(42,43)(44,45),(19,37)(20,38)(21,
39)(22,40)(23,41)(24,42)(25,43)(26,44)(27,45),(6,8)(7,9)(15,17)(16,18)(24,26)
(25,27)(33,35)(34,36)(42,44)(43,45)],
["ConstructDirectProduct",[["P:Q",[5,4]],["2.A5"]]]);
ALF("5:4x2.A5","2.HS",[1,2,5,6,7,12,13,12,13,14,15,30,37,38,14,15,14,15,8,
9,11,36,35,41,42,39,40,4,3,5,21,20,29,28,29,28,9,8,11,35,36,40,39,42,41],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("5:4x2.A5","5:4xa5",[1,1,3,5,5,11,11,12,12,10,10,16,21,21,13,13,14,14,
6,6,8,19,19,22,22,23,23,2,2,4,15,15,17,17,18,18,7,7,9,20,20,24,24,25,25]);
ALF("5:4x2.A5","2.Ru",[1,2,5,6,7,14,15,14,15,16,17,29,39,40,16,17,16,17,
10,11,13,32,33,47,48,49,50,4,3,5,19,18,28,27,28,27,11,10,13,33,32,48,47,
50,49],[
"determined up to table automorphisms by the fusion 5:4xA5 -> Ru"
]);

MOT("5:4xA4",
[
"normalizer of 2B^2 in HS, contained in HSM12\n",
],
0,
0,
0,
[( 9,17)(10,18)(11,19)(12,20),( 3, 4)( 7, 8)(11,12)(15,16)(19,20)],
["ConstructDirectProduct",[["P:Q",[5,4]],["Alternating",4]]]);
ALF("5:4xA4","HS",[1,3,4,4,9,18,22,22,5,7,21,21,2,3,12,12,5,7,21,21],[
"fusion map is unique"
]);
ALF("5:4xA4","5:4xa5",[1,3,5,5,10,16,21,21,6,8,19,19,2,4,15,15,7,9,20,20],[
"fusion map is unique up to table automorphisms"
]);

MOT("5:4x2^2",
[
"normalizer of chain (2B < 2B^2) in HS, contained in HSM12\n",
],
0,
0,
0,
[( 9,10)(11,12)(17,18)(19,20),( 9,11)(10,12)(17,19)(18,20),( 9,17)(10,18)
(11,19)(12,20),( 3, 4)( 7, 8)(11,12)(15,16)(19,20),( 2, 3)( 6, 7)(10,11)
(14,15)(18,19)],
["ConstructDirectProduct",[["P:Q",[5,4]],["V4"]]]);
ALF("5:4x2^2","2x5:4",[1,1,6,6,2,2,7,7,3,3,8,8,4,4,9,9,5,5,10,10]);
ALF("5:4x2^2","5:4xA4",[1,2,2,2,5,6,6,6,9,10,10,10,13,14,14,14,17,18,18,18]);
ALF("5:4x2^2","HS",[1,3,3,3,9,18,18,18,5,7,7,7,2,3,3,3,5,7,7,7]);
ALF("5:4x2^2","2^2.Sz(8)",[1,2,3,4,8,9,10,11,6,6,6,6,5,5,5,5,7,7,7,7],[
"fusion map is unique up to table automorphisms"
]);

MOT("A4xC4",
[
"stabilizer of chain ([4] < [256]) in HS",
],
0,
0,
0,
[( 9,13)(10,14)(11,15)(12,16),( 2, 4)( 6, 8)(10,12)(14,16)],
["ConstructDirectProduct",[["Alternating",4],["Cyclic",4]]]);
ALF("A4xC4","HS",[1,5,2,5,3,7,3,7,4,21,12,21,4,21,12,21],[
"fusion map of chain normalizer determined using the groups"
]);

MOT("D8xV4",
[
"normalizer of a chain (2B < Syl2) in HS"
],
0,
0,
0,
[(3,11)(4,12),(13,14)(15,16)(17,18)(19,20),(13,15)(14,16)(17,19)(18,20),(13,
17)(14,18)(15,19)(16,20),(5,6)(7,8)(17,18)(19,20),(5,7)(6,8)(17,19)(18,20),(3,
4)(7,8)(11,12)(15,16)(19,20),(2,3)(6,7)(10,11)(14,15)(18,19)],
["ConstructDirectProduct",[["Dihedral",8],["V4"]]]);
ALF("D8xV4","HS",[1,2,3,3,6,5,7,7,2,2,3,3,3,3,2,2,2,2,3,3],[
"fusion map determined by considering the groups\n",
"(the fixed points in the degree 100 representation suffice),\n",
"compatible with Brauer tables"
]);

MOT("5^(1+4):2^(1+4).5.4",
[
"origin: CAS library,\n",
"names:=group4; 5**[1+4].2**(1+4).5.4\n",
" order: 2,000,000 = 2^7.5^6\n",
" number of classes: 53\n",
" source: koichiro harada\n",
"         on the simple group f of order\n",
"         2^14.3^6.5^6.7.11.19\n",
"         proceedings of the conference\n",
"         on finite groups\n",
"         park city, utah (1975)\n",
" test: 1. o.r. satisfied\n",
" comments: - \n",
"tests: 1.o.r., pow[2,5]"
],
[2000000,500000,5000,2500,2500,2500,6250,3200,800,8000,160,2000,200,100,80,80,
250,250,250,250,250,25,25,50,50,50,50,50,400,160,160,8,100,100,100,100,50,40,
40,40,40,80,80,16,16,20,20,20,20,40,40,40,40],
[,[1,2,3,4,6,5,7,1,2,1,8,2,3,4,9,9,17,19,18,21,20,23,22,17,19,18,21,20,1,10,
10,11,4,4,6,5,7,13,13,29,29,30,31,30,31,36,35,36,35,38,39,38,39],,,[1,1,1,1,1,
1,1,8,8,10,11,10,10,10,11,11,1,1,1,1,1,2,2,8,8,8,8,8,29,30,31,32,29,29,29,29,
29,30,31,40,41,42,43,44,45,40,40,41,41,42,43,42,43]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,
-1,-1,-1,E(4),-E(4),E(4),-E(4),E(4),-E(4),E(4),E(4),-E(4),-E(4),E(4),-E(4),
E(4),-E(4)],
[TENSOR,[2,3]],[4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[5,5,5,5,5,5,5,5,5,
-3,1,-3,-3,-3,1,1,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,-1,1,1,1,1,1,1,1,1,1,-1,-1,-1,
-1,1,1,1,1,-1,-1,-1,-1],
[TENSOR,[6,2]],
[TENSOR,[6,3]],
[TENSOR,[6,4]],[10,10,10,10,10,10,10,10,10,2,-2,2,2,2,-2,-2,0,0,0,0,0,0,0,0,0,
0,0,0,2,-2,-2,0,2,2,2,2,2,-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[10,3]],[4,4,4,4,4,4,4,-4,-4,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,1,1,1,
1,1,0,2*E(4),-2*E(4),0,0,0,0,0,0,2*E(4),-2*E(4),0,0,1-E(4),1+E(4),-1+E(4),
-1-E(4),0,0,0,0,1-E(4),1+E(4),1-E(4),1+E(4)],
[TENSOR,[12,2]],
[TENSOR,[12,3]],
[TENSOR,[12,4]],[16,16,16,16,16,16,16,-16,-16,0,0,0,0,0,0,0,1,1,1,1,1,1,1,-1,
-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[80,80,-5,10,0,
0,-20,0,0,8,0,8,3,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,4,4,0,0,0,0,0,0,-1,-1,0,0,
4,4,0,0,0,0,0,0,-1,-1,-1,-1],
[TENSOR,[17,2]],
[TENSOR,[17,3]],
[TENSOR,[17,4]],[80,80,-5,10,0,0,-20,0,0,-8,0,-8,-3,2,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,4*E(4),-4*E(4),0,0,0,0,0,0,-E(4),E(4),0,0,0,0,0,0,0,0,0,0,
E(40)^13-E(40)^21-E(40)^29+E(40)^37,E(40)^7+E(40)^23-E(40)^31-E(40)^39,
-E(40)^13+E(40)^21+E(40)^29-E(40)^37,-E(40)^7-E(40)^23+E(40)^31+E(40)^39],
[TENSOR,[21,2]],
[TENSOR,[21,3]],
[TENSOR,[21,4]],[160,160,20,5,-10,-10,10,0,0,16,0,16,-4,1,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,8,0,0,0,3,3,-2,-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[25,3]],[160,160,20,5,-10,-10,10,0,0,-16,0,-16,4,-1,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,E(5)-E(5)^2-E(5)^3+E(5)^4,-E(5)+E(5)^2+E(5)^3-E(5)^4,
-2*E(5)+2*E(5)^2+2*E(5)^3-2*E(5)^4,2*E(5)-2*E(5)^2-2*E(5)^3+2*E(5)^4,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[27,3]],[320,320,0,-20,10,10,-5,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,8,0,0,0,-2,-2,-2,-2,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[29,3]],[100,-25,0,0,0,0,0,4,-1,20,4,-5,0,0,-1,-1,0,5,5,-5,-5,0,0,4,
-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[100,-25,0,0,0,
0,0,4,-1,20,4,-5,0,0,-1,-1,-5,0,0,-5*E(5)-5*E(5)^4,-5*E(5)^2-5*E(5)^3,0,0,-1,
2*E(5)^2+2*E(5)^3,2*E(5)+2*E(5)^4,-E(5)-2*E(5)^2-2*E(5)^3-E(5)^4,
-2*E(5)-E(5)^2-E(5)^3-2*E(5)^4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0],
[GALOIS,[32,2]],[100,-25,0,0,0,0,0,4,-1,20,4,-5,0,0,-1,-1,5,5*E(5)^2+5*E(5)^3,
5*E(5)+5*E(5)^4,0,0,0,0,-1,-2*E(5)-E(5)^2-E(5)^3-2*E(5)^4,
-E(5)-2*E(5)^2-2*E(5)^3-E(5)^4,2*E(5)^2+2*E(5)^3,2*E(5)+2*E(5)^4,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[34,2]],[500,-125,0,0,0,0,0,20,-5,-60,4,15,0,0,-1,-1,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[500,-125,0,0,0,0,
0,20,-5,20,-4,-5,0,0,-3*E(5)+E(5)^2+E(5)^3-3*E(5)^4,E(5)-3*E(5)^2-3*E(5)^3
 +E(5)^4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0],
[GALOIS,[37,2]],[400,-100,0,0,0,0,0,-16,4,0,0,0,0,0,0,0,0,-5,-5,5,5,0,0,4,-1,
-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[400,-100,0,0,0,0,
0,-16,4,0,0,0,0,0,0,0,-5,-5*E(5)^2-5*E(5)^3,-5*E(5)-5*E(5)^4,0,0,0,0,-1,
-2*E(5)-E(5)^2-E(5)^3-2*E(5)^4,-E(5)-2*E(5)^2-2*E(5)^3-E(5)^4,
2*E(5)^2+2*E(5)^3,2*E(5)+2*E(5)^4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0],
[GALOIS,[40,2]],[400,-100,0,0,0,0,0,-16,4,0,0,0,0,0,0,0,5,0,0,5*E(5)+5*E(5)^4,
5*E(5)^2+5*E(5)^3,0,0,-1,2*E(5)^2+2*E(5)^3,2*E(5)+2*E(5)^4,
-E(5)-2*E(5)^2-2*E(5)^3-E(5)^4,-2*E(5)-E(5)^2-E(5)^3-2*E(5)^4,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[42,2]],[128,128,-32,8,12*E(5)-8*E(5)^2-8*E(5)^3+12*E(5)^4,
-8*E(5)+12*E(5)^2+12*E(5)^3-8*E(5)^4,28,0,0,0,0,0,0,0,0,0,-2,-2,-2,-2,-2,
-E(5)-E(5)^4,-E(5)^2-E(5)^3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0],
[GALOIS,[44,2]],[32,32,-8,2,3*E(5)-2*E(5)^2-2*E(5)^3+3*E(5)^4,-2*E(5)+3*E(5)^2
 +3*E(5)^3-2*E(5)^4,7,0,0,0,0,0,0,0,0,0,2,2,2,2,2,E(5)+E(5)^4,E(5)^2+E(5)^3,0,
0,0,0,0,-4,0,0,0,-2*E(5)-2*E(5)^4,-2*E(5)^2-2*E(5)^3,E(5)+2*E(5)^2+2*E(5)^3
 +E(5)^4,2*E(5)+E(5)^2+E(5)^3+2*E(5)^4,1,0,0,2*E(4),-2*E(4),0,0,0,0,
E(20)+E(20)^9,E(20)^13+E(20)^17,-E(20)-E(20)^9,-E(20)^13-E(20)^17,0,0,0,0],
[TENSOR,[46,2]],
[TENSOR,[46,4]],
[TENSOR,[46,3]],
[GALOIS,[46,13]],
[TENSOR,[50,2]],
[TENSOR,[50,4]],
[TENSOR,[50,3]]],
[(50,52)(51,53),(30,31)(38,39)(40,41)(42,43)(44,45)(46,48)(47,49)(50,51)
(52,53),(30,31)(38,39)(40,41)(42,43)(44,45)(46,48)(47,49)(50,53)(51,52),
(18,19)(20,21)(25,26)(27,28),(15,16),( 5, 6)(15,16)(18,19)(20,21)(22,23)
(25,26)(27,28)(33,34)(35,36)(46,47)(48,49)(50,52)(51,53),( 5, 6)(22,23)(33,34)
(35,36)(46,47)(48,49)]);
ARC("5^(1+4):2^(1+4).5.4","CAS",[rec(name:="group4",
permchars:=(),
permclasses:=())]);
ALF("5^(1+4):2^(1+4).5.4","HN",[1,10,9,13,11,12,10,3,23,2,6,21,22,26,39,
40,10,11,12,13,13,47,46,23,24,25,27,28,3,7,7,19,27,28,24,25,23,41,41,8,8,
18,18,18,18,42,43,42,43,53,53,54,54],[
"fusion map is unique up to table automorphisms"
]);
ALF("5^(1+4):2^(1+4).5.4","5^(1+4)_+:(4Y2^(1+4)_-.5.4)",[1,2,4,5,6,6,3,7,
8,11,13,15,16,17,20,21,22,23,23,24,24,30,30,25,26,26,27,27,31,34,35,38,41,
41,40,40,39,46,47,51,52,55,56,59,60,63,63,64,64,67,68,67,68],[
"fusion map is unique up to table automorphisms"
]);
ALN("5^(1+4):2^(1+4).5.4",["HNN5B","group4","hamax2"]);

MOT("5^(1+4):4S6",
[
"5th maximal subgroup of Ly,\n",
"origin: computed using permutation characters, tables of LyN2, LyN5,\n",
"G2(5)M1, and 2.(2xA6),\n",
"characters are sorted w.r. to normal series given by 5.5^4.2.2.A6.2,\n",
"tests: 1.o.r., pow[2,3,5]"
],
[9000000,2250000,12500,3750,14400,3600,2880,2880,800,160,100,50,40,9000,360,
72,72,2250,75,90,360,360,72,72,90,90,80,16,40,40,500,250,250,100,50,50,20,20,
25,96,96,96,96,80,80,20,20,24,24,24,24,24,24,24,24],
[,[1,2,3,4,1,2,5,5,1,5,3,4,6,14,14,15,15,18,19,18,21,21,22,22,25,25,10,10,13,
13,31,32,33,31,32,33,34,34,39,7,8,8,7,9,9,11,11,16,17,16,17,24,23,23,24],[1,2,
3,4,5,6,8,7,9,10,11,12,13,1,5,7,8,2,4,6,1,5,7,8,2,6,27,28,29,30,31,32,33,34,
35,36,38,37,39,41,40,43,42,45,44,47,46,40,41,40,41,42,43,43,42],,[1,1,1,1,5,5,
7,8,9,10,9,9,10,14,15,16,17,14,14,15,21,22,23,24,21,22,27,28,27,27,1,1,1,5,5,
5,8,7,2,40,41,42,43,44,45,44,45,48,49,50,51,52,53,54,55]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
-1,-1],[5,5,5,5,5,5,5,5,1,1,1,1,1,2,2,2,2,2,2,2,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
0,0,0,0,0,0,0,0,0,3,3,-1,-1,1,1,1,1,0,0,0,0,-1,-1,-1,-1],
[TENSOR,[3,2]],[5,5,5,5,5,5,5,5,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,2,2,2,2,2,2,-1,
-1,-1,-1,0,0,0,0,0,0,0,0,0,-1,-1,3,3,1,1,1,1,-1,-1,-1,-1,0,0,0,0],
[TENSOR,[5,2]],[16,16,16,16,16,16,16,16,0,0,0,0,0,-2,-2,-2,-2,-2,-2,-2,-2,-2,
-2,-2,-2,-2,0,0,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[9,9,9,
9,9,9,9,9,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,
-1,3,3,3,3,-1,-1,-1,-1,0,0,0,0,0,0,0,0],
[TENSOR,[8,2]],[10,10,10,10,10,10,10,10,-2,-2,-2,-2,-2,1,1,1,1,1,1,1,1,1,1,1,
1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,2,2,-2,-2,0,0,0,0,-1,-1,-1,-1,1,1,1,1],
[TENSOR,[10,2]],[1,1,1,1,1,1,-1,-1,-1,1,-1,-1,1,1,1,-1,-1,1,1,1,1,1,-1,-1,1,1,
1,-1,1,1,1,1,1,1,1,1,-1,-1,1,E(4),-E(4),E(4),-E(4),-E(4),E(4),-E(4),E(4),
-E(4),E(4),-E(4),E(4),-E(4),E(4),E(4),-E(4)],
[TENSOR,[2,12]],
[TENSOR,[3,12]],
[TENSOR,[3,13]],
[TENSOR,[5,12]],
[TENSOR,[5,13]],
[TENSOR,[7,12]],
[TENSOR,[8,12]],
[TENSOR,[8,13]],
[TENSOR,[10,12]],
[TENSOR,[10,13]],[4,4,4,4,-4,-4,-4*E(4),4*E(4),0,0,0,0,0,-2,2,-2*E(4),2*E(4),
-2,-2,2,1,-1,E(4),-E(4),1,-1,0,0,0,0,-1,-1,-1,1,1,1,-E(4),E(4),-1,0,0,0,0,0,0,
0,0,0,0,0,0,-E(24)+E(24)^17,E(24)^11-E(24)^19,-E(24)^11+E(24)^19,
E(24)-E(24)^17],
[TENSOR,[23,2]],[4,4,4,4,-4,-4,-4*E(4),4*E(4),0,0,0,0,0,1,-1,E(4),-E(4),1,1,
-1,-2,2,-2*E(4),2*E(4),-2,2,0,0,0,0,-1,-1,-1,1,1,1,-E(4),E(4),-1,0,0,0,0,0,0,
0,0,-E(24)^11+E(24)^19,-E(24)+E(24)^17,E(24)^11-E(24)^19,E(24)-E(24)^17,0,0,0,
0],
[TENSOR,[25,2]],
[TENSOR,[23,13]],
[TENSOR,[23,12]],
[TENSOR,[25,12]],
[TENSOR,[25,13]],[16,16,16,16,-16,-16,-16*E(4),16*E(4),0,0,0,0,0,-2,2,-2*E(4),
2*E(4),-2,-2,2,-2,2,-2*E(4),2*E(4),-2,2,0,0,0,0,1,1,1,-1,-1,-1,E(4),-E(4),1,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[31,12]],[20,20,20,20,-20,-20,-20*E(4),20*E(4),0,0,0,0,0,2,-2,2*E(4),
-2*E(4),2,2,-2,2,-2,2*E(4),-2*E(4),2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0],
[TENSOR,[33,12]],[144,144,19,-6,0,0,0,0,-8,0,-3,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,4,4,4,0,0,0,0,0,-1,0,0,0,0,-4*E(4),4*E(4),E(4),-E(4),0,0,0,0,0,0,0,0],
[TENSOR,[35,2]],
[TENSOR,[35,12]],
[TENSOR,[35,13]],[480,480,-20,5,0,0,0,0,-16,0,4,-1,0,24,0,0,0,24,-1,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[39,12]],[576,576,76,-24,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,-4,-4,-4,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[960,960,-40,10,
0,0,0,0,0,0,0,0,0,-24,0,0,0,-24,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0],[100,-25,0,0,4,-1,0,0,0,4,0,0,-1,-20,4,0,0,5,0,
-1,4,4,0,0,-1,-1,-4,0,1,1,0,5,-5,4,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0],[400,-100,0,0,-16,4,0,0,0,0,0,0,0,-20,-4,0,0,5,0,1,-8,8,0,0,2,-2,0,0,0,0,0,
-5,5,4,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[400,-100,0,0,-16,4,0,0,0,
0,0,0,0,40,8,0,0,-10,0,-2,4,-4,0,0,-1,1,0,0,0,0,0,-5,5,4,-1,-1,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0],[500,-125,0,0,20,-5,0,0,0,4,0,0,-1,-40,8,0,0,10,0,-2,
-4,-4,0,0,1,1,4,0,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[
500,-125,0,0,20,-5,0,0,0,4,0,0,-1,20,-4,0,0,-5,0,1,8,8,0,0,-2,-2,4,0,-1,-1,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[800,-200,0,0,-32,8,0,0,0,0,
0,0,0,20,4,0,0,-5,0,-1,-4,4,0,0,1,-1,0,0,0,0,-10,5,0,-2,3,-2,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0],[800,-200,0,0,-32,8,0,0,0,0,0,0,0,20,4,0,0,-5,0,-1,-4,
4,0,0,1,-1,0,0,0,0,10,0,-5,-2,-2,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[
800,-200,0,0,32,-8,0,0,0,0,0,0,0,20,-4,0,0,-5,0,1,-4,-4,0,0,1,1,0,0,0,0,-10,5,
0,2,-3,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[800,-200,0,0,32,-8,0,0,0,0,0,
0,0,20,-4,0,0,-5,0,1,-4,-4,0,0,1,1,0,0,0,0,10,0,-5,2,2,-3,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0],[900,-225,0,0,36,-9,0,0,0,4,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,
0,-4,0,1,1,0,-5,5,-4,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[1000,-250,0,
0,-40,10,0,0,0,0,0,0,0,-20,-4,0,0,5,0,1,4,-4,0,0,-1,1,0,0,-E(40)^7+E(40)^13
 -E(40)^21-E(40)^23-E(40)^29+E(40)^31+E(40)^37+E(40)^39,E(40)^7-E(40)^13
 +E(40)^21+E(40)^23+E(40)^29-E(40)^31-E(40)^37-E(40)^39,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[53,7]],[1000,-250,0,0,40,-10,0,0,0,-8,0,0,2,-20,4,0,0,5,0,-1,4,4,0,0,
-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]],
[(52,55)(53,54),(48,50)(49,51)(52,55)(53,54),(29,30),(29,30)(48,50)(49,51)
(52,55)(53,54),( 7, 8)(16,17)(23,24)(37,38)(40,41)(42,43)(44,45)(46,47)(48,49)
(50,51)(52,54)(53,55)]);
ALF("5^(1+4):4S6","Ly",[1,6,6,7,2,15,5,5,2,5,15,16,26,3,8,19,19,22,24,36,
4,9,20,20,23,37,12,13,47,48,6,7,7,15,16,16,26,26,34,12,12,13,13,5,5,26,26,
31,31,31,31,32,32,33,33],[
"fusion is unique up to table automorphisms"
]);
ALN("5^(1+4):4S6",["5^(1+4).4S6"]);

MOT("5^2.5.5^2.4A5",
[
"origin: constructed by Alexander Hulpke,\n",
"10th maximal subgroup of HN,\n",
"table is sorted w.r. to normal series 5^2.5.5^2.2.2.A5,\n",
"tests: 1.o.r., pow[2,3,5]"
],
[750000,31250,15000,15000,1250,1250,1250,1250,1250,1200,600,600,240,240,200,
60,40,2500,2500,1250,1250,1250,1250,625,625,625,625,625,625,625,625,625,625,
60,100,100,50,50,50,50,50,50,50,50,50,50,12,12,30,30,20,20,20,20,20,20,25,25,
30,30],
[,[1,2,4,3,5,9,8,7,6,1,3,4,10,10,1,16,10,19,18,21,20,23,22,25,24,28,29,26,27,
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 +3*E(5)^4,2*E(5)+3*E(5)^2+3*E(5)^3+2*E(5)^4,2*E(5)-2*E(5)^2-2*E(5)^3+2*E(5)^4
 ,-2*E(5)+2*E(5)^2+2*E(5)^3-2*E(5)^4,-3*E(5)-2*E(5)^2-2*E(5)^3-3*E(5)^4,
-3*E(5)-2*E(5)^2-2*E(5)^3-3*E(5)^4,-2*E(5)-3*E(5)^2-3*E(5)^3-2*E(5)^4,
-2*E(5)-3*E(5)^2-3*E(5)^3-2*E(5)^4,3*E(5)+2*E(5)^2+2*E(5)^3+3*E(5)^4,
3*E(5)+2*E(5)^2+2*E(5)^3+3*E(5)^4,2*E(5)+3*E(5)^2+3*E(5)^3+2*E(5)^4,
2*E(5)+3*E(5)^2+3*E(5)^3+2*E(5)^4,0,-2,-2,-E(5)^2-E(5)^3,-E(5)-E(5)^4,0,0,0,0,
0,0,-E(5)^2-E(5)^3,-E(5)-E(5)^4,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[39,2]],[120,-5,0,0,0,-5,5,5,-5,0,0,0,0,0,-4,0,0,0,0,0,0,10,10,0,0,5,
-5,5,-5,-5,0,-5,0,0,0,0,0,0,-4,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[41,6]],[120,-5,0,0,5,0,5*E(5)+5*E(5)^4,5*E(5)^2+5*E(5)^3,0,0,0,0,0,0,
4,0,0,-4*E(5)+4*E(5)^2+4*E(5)^3-4*E(5)^4,4*E(5)-4*E(5)^2-4*E(5)^3+4*E(5)^4,
-4*E(5)-6*E(5)^2-6*E(5)^3-4*E(5)^4,-6*E(5)-4*E(5)^2-4*E(5)^3-6*E(5)^4,
-6*E(5)-4*E(5)^2-4*E(5)^3-6*E(5)^4,-4*E(5)-6*E(5)^2-6*E(5)^3-4*E(5)^4,
E(5)-E(5)^2-E(5)^3+E(5)^4,-E(5)+E(5)^2+E(5)^3-E(5)^4,E(5)+4*E(5)^2+4*E(5)^3
 +E(5)^4,E(5)-E(5)^2-E(5)^3+E(5)^4,4*E(5)+E(5)^2+E(5)^3+4*E(5)^4,
-E(5)+E(5)^2+E(5)^3-E(5)^4,-E(5)-4*E(5)^2-4*E(5)^3-E(5)^4,
4*E(5)+6*E(5)^2+6*E(5)^3+4*E(5)^4,-4*E(5)-E(5)^2-E(5)^3-4*E(5)^4,
6*E(5)+4*E(5)^2+4*E(5)^3+6*E(5)^4,0,0,0,0,0,-1,-2*E(5)-E(5)^2-E(5)^3-2*E(5)^4,
2*E(5)^2+2*E(5)^3,2*E(5)+2*E(5)^4,-E(5)-2*E(5)^2-2*E(5)^3-E(5)^4,-1,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[43,6]],[120,-5,0,0,-5,-5*E(5)-5*E(5)^4,0,0,-5*E(5)^2-5*E(5)^3,0,0,0,
0,0,4,0,0,-8*E(5)-12*E(5)^2-12*E(5)^3-8*E(5)^4,-12*E(5)-8*E(5)^2-8*E(5)^3
 -12*E(5)^4,-8*E(5)-2*E(5)^2-2*E(5)^3-8*E(5)^4,-2*E(5)-8*E(5)^2-8*E(5)^3
 -2*E(5)^4,-2*E(5)+2*E(5)^2+2*E(5)^3-2*E(5)^4,2*E(5)-2*E(5)^2-2*E(5)^3
 +2*E(5)^4,2*E(5)+3*E(5)^2+3*E(5)^3+2*E(5)^4,3*E(5)+2*E(5)^2+2*E(5)^3+3*E(5)^4
 ,2*E(5)+3*E(5)^2+3*E(5)^3+2*E(5)^4,2*E(5)-2*E(5)^2-2*E(5)^3+2*E(5)^4,
3*E(5)+2*E(5)^2+2*E(5)^3+3*E(5)^4,-2*E(5)+2*E(5)^2+2*E(5)^3-2*E(5)^4,
3*E(5)+2*E(5)^2+2*E(5)^3+3*E(5)^4,-2*E(5)-3*E(5)^2-3*E(5)^3-2*E(5)^4,
2*E(5)+3*E(5)^2+3*E(5)^3+2*E(5)^4,-3*E(5)-2*E(5)^2-2*E(5)^3-3*E(5)^4,0,0,0,0,
0,-1,2*E(5)^2+2*E(5)^3,-E(5)-2*E(5)^2-2*E(5)^3-E(5)^4,-2*E(5)-E(5)^2-E(5)^3
 -2*E(5)^4,2*E(5)+2*E(5)^4,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[45,6]],
[GALOIS,[46,2]],
[TENSOR,[47,6]],
[GALOIS,[44,2]],
[TENSOR,[49,6]],[240,-10,0,0,10,0,10*E(5)^2+10*E(5)^3,10*E(5)+10*E(5)^4,0,0,0,
0,0,0,0,0,0,-12*E(5)-8*E(5)^2-8*E(5)^3-12*E(5)^4,-8*E(5)-12*E(5)^2-12*E(5)^3
 -8*E(5)^4,8*E(5)+2*E(5)^2+2*E(5)^3+8*E(5)^4,2*E(5)+8*E(5)^2+8*E(5)^3+2*E(5)^4
 ,2*E(5)+8*E(5)^2+8*E(5)^3+2*E(5)^4,8*E(5)+2*E(5)^2+2*E(5)^3+8*E(5)^4,
3*E(5)+2*E(5)^2+2*E(5)^3+3*E(5)^4,2*E(5)+3*E(5)^2+3*E(5)^3+2*E(5)^4,
-7*E(5)-3*E(5)^2-3*E(5)^3-7*E(5)^4,3*E(5)+2*E(5)^2+2*E(5)^3+3*E(5)^4,
-3*E(5)-7*E(5)^2-7*E(5)^3-3*E(5)^4,2*E(5)+3*E(5)^2+3*E(5)^3+2*E(5)^4,
-3*E(5)-2*E(5)^2-2*E(5)^3-3*E(5)^4,2*E(5)-2*E(5)^2-2*E(5)^3+2*E(5)^4,
-2*E(5)-3*E(5)^2-3*E(5)^3-2*E(5)^4,-2*E(5)+2*E(5)^2+2*E(5)^3-2*E(5)^4,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[51,2]],[240,-10,0,0,-10,-10*E(5)^2-10*E(5)^3,0,0,-10*E(5)-10*E(5)^4,
0,0,0,0,0,0,0,0,16*E(5)+4*E(5)^2+4*E(5)^3+16*E(5)^4,4*E(5)+16*E(5)^2+16*E(5)^3
 +4*E(5)^4,-4*E(5)-6*E(5)^2-6*E(5)^3-4*E(5)^4,-6*E(5)-4*E(5)^2-4*E(5)^3
 -6*E(5)^4,4*E(5)+6*E(5)^2+6*E(5)^3+4*E(5)^4,6*E(5)+4*E(5)^2+4*E(5)^3+6*E(5)^4
 ,-4*E(5)-E(5)^2-E(5)^3-4*E(5)^4,-E(5)-4*E(5)^2-4*E(5)^3-E(5)^4,
-4*E(5)-E(5)^2-E(5)^3-4*E(5)^4,6*E(5)+4*E(5)^2+4*E(5)^3+6*E(5)^4,
-E(5)-4*E(5)^2-4*E(5)^3-E(5)^4,4*E(5)+6*E(5)^2+6*E(5)^3+4*E(5)^4,
-E(5)-4*E(5)^2-4*E(5)^3-E(5)^4,-E(5)+E(5)^2+E(5)^3-E(5)^4,
-4*E(5)-E(5)^2-E(5)^3-4*E(5)^4,E(5)-E(5)^2-E(5)^3+E(5)^4,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[53,2]],[240,-10,0,0,10,0,10*E(5)^2+10*E(5)^3,10*E(5)+10*E(5)^4,0,0,0,
0,0,0,0,0,0,8*E(5)+12*E(5)^2+12*E(5)^3+8*E(5)^4,12*E(5)+8*E(5)^2+8*E(5)^3
 +12*E(5)^4,-2*E(5)+2*E(5)^2+2*E(5)^3-2*E(5)^4,2*E(5)-2*E(5)^2-2*E(5)^3
 +2*E(5)^4,2*E(5)-2*E(5)^2-2*E(5)^3+2*E(5)^4,-2*E(5)+2*E(5)^2+2*E(5)^3
 -2*E(5)^4,-2*E(5)-3*E(5)^2-3*E(5)^3-2*E(5)^4,-3*E(5)-2*E(5)^2-2*E(5)^3
 -3*E(5)^4,3*E(5)+2*E(5)^2+2*E(5)^3+3*E(5)^4,-2*E(5)-3*E(5)^2-3*E(5)^3
 -2*E(5)^4,2*E(5)+3*E(5)^2+3*E(5)^3+2*E(5)^4,-3*E(5)-2*E(5)^2-2*E(5)^3
 -3*E(5)^4,7*E(5)+3*E(5)^2+3*E(5)^3+7*E(5)^4,-8*E(5)-2*E(5)^2-2*E(5)^3
 -8*E(5)^4,3*E(5)+7*E(5)^2+7*E(5)^3+3*E(5)^4,-2*E(5)-8*E(5)^2-8*E(5)^3
 -2*E(5)^4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[55,2]],[240,-10,0,0,-10,-10*E(5)^2-10*E(5)^3,0,0,-10*E(5)-10*E(5)^4,
0,0,0,0,0,0,0,0,-4*E(5)+4*E(5)^2+4*E(5)^3-4*E(5)^4,4*E(5)-4*E(5)^2-4*E(5)^3
 +4*E(5)^4,6*E(5)+14*E(5)^2+14*E(5)^3+6*E(5)^4,14*E(5)+6*E(5)^2+6*E(5)^3
 +14*E(5)^4,-6*E(5)-4*E(5)^2-4*E(5)^3-6*E(5)^4,-4*E(5)-6*E(5)^2-6*E(5)^3
 -4*E(5)^4,E(5)-E(5)^2-E(5)^3+E(5)^4,-E(5)+E(5)^2+E(5)^3-E(5)^4,
E(5)-E(5)^2-E(5)^3+E(5)^4,-4*E(5)-6*E(5)^2-6*E(5)^3-4*E(5)^4,
-E(5)+E(5)^2+E(5)^3-E(5)^4,-6*E(5)-4*E(5)^2-4*E(5)^3-6*E(5)^4,
-E(5)+E(5)^2+E(5)^3-E(5)^4,4*E(5)+E(5)^2+E(5)^3+4*E(5)^4,E(5)-E(5)^2-E(5)^3
 +E(5)^4,E(5)+4*E(5)^2+4*E(5)^3+E(5)^4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0],
[GALOIS,[57,2]],[240,-10,0,0,0,-10,10,10,-10,0,0,0,0,0,0,0,0,0,0,0,0,
10*E(5)^2+10*E(5)^3,10*E(5)+10*E(5)^4,0,0,5*E(5)+5*E(5)^4,-5*E(5)-5*E(5)^4,
5*E(5)^2+5*E(5)^3,-5*E(5)^2-5*E(5)^3,-5*E(5)^2-5*E(5)^3,0,-5*E(5)-5*E(5)^4,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[59,2]]],
[(13,14)(47,48)(51,53)(52,54),( 3, 4)( 6, 9)( 7, 8)(11,12)(18,19)(20,21)
(22,23)(24,25)(26,28)(27,29)(30,32)(31,33)(35,36)(37,38)(40,43)(41,42)(45,46)
(49,50)(51,54)(52,53)(55,56)(57,58)(59,60)]);
ALF("5^2.5.5^2.4A5","HN",[1,10,11,12,10,13,12,11,13,3,25,24,8,8,3,5,8,11,
12,10,10,13,13,12,11,11,13,12,13,12,9,11,9,16,25,24,23,23,23,24,27,28,25,
23,27,28,32,32,36,35,42,43,42,43,43,42,47,46,49,50],[
"fusion map is unique up to table automorphisms"
]);
ALF("5^2.5.5^2.4A5","5^2.5.5^2.4S5",[1,2,3,3,4,6,5,5,6,7,8,8,9,10,13,18,
11,24,24,26,26,25,25,27,27,28,31,28,31,30,29,30,29,19,32,32,33,33,15,16,
17,17,16,14,34,34,23,22,20,20,37,36,36,37,12,12,35,35,21,21],[
"fusion map is unique up to table automorphisms"
]);

MOT("5^2:4s5",
[
"origin: CAS library,\n",
"maximal subgroup of Ru,\n",
"source: received from S.Mattarei\n",
"test: 1.OR, JAMES, JAMES,n=3, JAMES,n=5,\n",
"and restricted characters decompose properly.\n",
"constructions: AGL(2,5),\n",
"tests: 1.o.r., pow[2,3,5]"
],
[12000,500,480,480,480,100,25,20,20,20,80,20,80,20,80,20,16,16,16,24,24,24,24,
24,24,24,24,24,24],
[,[1,2,4,1,4,6,7,9,6,9,13,14,1,2,13,14,13,4,13,21,23,3,25,28,25,5,21,23,28],[
1,2,5,4,3,6,7,10,9,8,15,16,13,14,11,12,19,18,17,22,3,26,4,26,1,22,22,5,26],,[
1,1,3,4,5,1,1,3,4,5,11,11,13,13,15,15,17,18,19,20,21,22,23,24,25,26,27,28,
29]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,-1,1,-1,1,1,
-1,1,-1,E(4),E(4),-1,-1,-E(4),-E(4),-E(4),1,E(4),E(4),-1,-E(4),1,-E(4),1,E(4),
E(4),-1,-E(4)],
[TENSOR,[2,2]],
[TENSOR,[2,3]],[5,5,5,5,5,0,0,0,0,0,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,
-1,-1],
[TENSOR,[5,2]],
[TENSOR,[5,3]],
[TENSOR,[5,4]],[6,6,6*E(4),-6,-6*E(4),1,1,E(4),-1,-E(4),1+E(4),1+E(4),0,0,
1-E(4),1-E(4),-1+E(4),0,-1-E(4),0,0,0,0,0,0,0,0,0,0],[6,6,-6,6,-6,1,1,-1,1,-1,
0,0,2,2,0,0,0,-2,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[9,4]],
[TENSOR,[9,2]],
[TENSOR,[10,2]],
[TENSOR,[9,3]],[4,4,4*E(4),-4,-4*E(4),-1,-1,-E(4),1,E(4),0,0,0,0,0,0,0,0,0,
-E(24)+E(24)^17,-E(4),0,-1,-E(24)^11+E(24)^19,1,0,E(24)-E(24)^17,E(4),
E(24)^11-E(24)^19],[4,4,-4,4,-4,-1,-1,1,-1,1,0,0,0,0,0,0,0,0,0,-E(4),-1,
-2*E(4),1,E(4),1,2*E(4),-E(4),-1,E(4)],[4,4,-4*E(4),-4,4*E(4),-1,-1,E(4),1,
-E(4),0,0,0,0,0,0,0,0,0,0,-2*E(4),0,2,0,-2,0,0,2*E(4),0],
[TENSOR,[16,4]],
[TENSOR,[15,2]],
[TENSOR,[16,2]],
[TENSOR,[17,2]],
[TENSOR,[15,3]],
[TENSOR,[16,3]],
[TENSOR,[15,4]],[24,-1,0,0,0,4,-1,0,0,0,4,-1,4,-1,4,-1,0,0,0,0,0,0,0,0,0,0,0,
0,0],
[TENSOR,[25,2]],
[TENSOR,[25,3]],
[TENSOR,[25,4]],[96,-4,0,0,0,-4,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0]],
[(20,27)(24,29),( 3, 5)( 8,10)(11,15)(12,16)(17,19)(20,24)(21,28)(22,26)
(27,29),( 3, 5)( 8,10)(11,15)(12,16)(17,19)(20,29)(21,28)(22,26)(24,27)]);
ARC("5^2:4s5","tomfusion",rec(name:="5^2:GL2(5)",map:=[1,10,5,2,5,11,12,
40,25,40,6,41,3,24,6,41,9,8,9,49,28,16,13,49,4,16,49,28,49],text:=[
"fusion map is unique"
]));
ALF("5^2:4s5","L3(5)",[1,7,4,2,5,7,8,15,12,16,5,16,2,12,4,15,6,6,6,18,14,
10,9,19,3,11,20,13,17],[
"fusion map is unique up to table autom."
]);
ALF("5^2:4s5","Ru",[1,9,5,2,5,9,10,27,16,27,5,27,2,16,5,27,8,8,8,30,18,13,
11,31,4,13,31,18,30],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("5^2:4s5","Th",[1,8,7,2,7,8,8,30,18,30,7,30,2,18,7,30,7,7,7,34,22,14,
9,34,5,14,35,22,35],[
"fusion map is unique up to table automorphisms"
]);
ALF("5^2:4s5","gl25",[1,1,2,3,4,5,5,6,7,8,9,9,10,10,11,11,12,13,14,15,16,
17,18,19,20,21,22,23,24]);
ALN("5^2:4s5",["AGL(2,5)"]);

MOT("2xU3(5).2",
[
"5th maximal subgroup of 2.Ru"
],
0,
0,
0,
[(35,37)(36,38),(23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36)(37,38)],
["ConstructDirectProduct",[["U3(5).2"],["Cyclic",2]]]);
ALF("2xU3(5).2","2.Ru",[1,2,3,4,6,7,13,13,14,15,14,15,16,17,18,19,20,21,
26,26,27,28,3,4,8,9,18,19,26,26,27,28,30,31,45,46,45,46],[
"fusion map is unique up to table automorphisms"
]);

MOT("L2(25).(2x4)",
[
"7th maximal subgroup of 2.Ru"
],
0,
0,
0,
[(35,36)(37,38)(39,40)(41,42)(43,44)(45,46)(47,48),(25,27)(26,28),(21,22)(23,
24)(25,26)(27,28)(29,30)(31,32)(33,34)(43,44)(45,46)(47,48),(15,17,19)(16,18,
20)(29,31,33)(30,32,34)],
["ConstructIsoclinic",[["L2(25).2^2"],["Cyclic",2]],[1,2,3,4,5,6,7,8,9,10,11,
12,13,14,15,16,17,18,19,20,35,36,37,38,39,40,41,42]]);
ALF("L2(25).(2x4)","L2(25).2^2",[1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,9,10,
10,11,11,12,12,13,13,14,14,15,15,16,16,17,17,18,18,19,19,20,20,21,21,22,
22,23,23,24,24]);
ALF("L2(25).(2x4)","2.Ru",[1,2,3,4,6,7,8,9,14,15,18,19,30,31,34,35,34,35,
34,35,5,5,22,23,51,52,53,54,55,55,57,57,56,56,3,4,13,13,18,19,27,28,11,10,
23,22,33,32],[
"fusion map is unique up to table automorphisms"
]);

MOT("2x5^2:4S5",
[
"10th maximal subgroup of 2.Ru"
],
0,
0,
0,
[(21,22)(23,24)(29,30)(31,32)(33,34)(37,38)(39,40)(43,44)(47,48)(51,52)(53,
54)(57,58),(39,53)(40,54)(47,57)(48,58),(5,9)(6,10)(15,19)(16,20)(21,29)(22,
30)(23,31)(24,32)(33,37)(34,38)(39,47)(40,48)(41,55)(42,56)(43,51)(44,52)(53,
57)(54,58)],
["ConstructDirectProduct",[["5^2:4s5"],["Cyclic",2]]]);
ALF("2x5^2:4S5","2.Ru",[1,2,14,15,9,8,3,4,9,8,14,15,16,17,46,45,27,28,46,
45,8,9,45,46,3,4,27,28,8,9,45,46,13,13,13,13,13,13,51,52,31,30,23,22,18,
19,54,53,6,7,22,23,53,54,31,30,52,51],[
"fusion map is unique up to table automorphisms"
]);

MOT("3.A6.(2x4)",
[
"11th maximal subgroup of 2.Ru"
],
0,
0,
0,
[(37,39)(38,40),(19,20)(21,22)(23,24)(25,26)(27,28)(29,30),(19,20)(21,22)(23,
24)(31,32)(33,34)(35,36)(37,38)(39,40)],
["ConstructIsoclinic",[["3.A6.2^2"],["Cyclic",2]],[1..24]]);
ALF("3.A6.(2x4)","3.A6.2^2",[1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,9,10,10,11,
11,12,12,13,13,14,14,15,15,16,16,17,17,18,18,19,19,20,20]);
ALF("3.A6.(2x4)","2.Ru",[1,2,6,7,3,4,18,19,6,7,8,9,30,31,16,17,39,40,3,4,
13,13,18,19,5,5,22,23,29,29,10,11,32,33,23,22,52,51,54,53],[
"fusion map is unique up to table automorphisms"
]);

MOT("Isoclinic(L2(13).2x2)",
[
"subdirect product of L2(13).2 and C4,\n",
"13th maximal subgroup of 2.Ru"
],
0,
0,
0,
[(21,23)(22,24),(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30),(9,11,13)
(10,12,14)(25,27,29)(26,28,30)],
["ConstructIsoclinic",[["L2(13).2"],["Cyclic",2]]]);
ALF("Isoclinic(L2(13).2x2)","L2(13).2",[1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,
9,10,10,11,11,12,12,13,13,14,14,15,15]);
ALF("Isoclinic(L2(13).2x2)","2.Ru",[1,2,3,4,6,7,18,19,20,21,20,21,20,21,
34,35,5,5,10,11,32,33,32,33,36,36,38,38,37,37],[
"fusion map is unique up to table automorphisms"
]);

MOT("5^3.psl(3,5)",
[
"origin: CAS library,\n",
"maximal subgroup of Ly,\n",
"test : 1.OR satisfied, JAMES, JAMES,n=5,\n",
"and restricted characters decompose correctly\n",
"tests: 1.o.r., pow[2,3,5,31]"
],
[46500000,375000,2400,600,120,30,480,480,80,20,2500,1250,1250,25,120,30,24,24,
100,50,50,24,24,20,20,24,24,24,24,31,31,31,31,31,31,31,31,31,31],
[,[1,2,1,2,5,6,3,3,3,4,11,12,13,14,5,6,7,8,11,13,12,15,15,19,19,22,22,23,23,
34,35,36,37,38,39,30,31,32,33],[1,2,3,4,1,2,8,7,9,10,11,12,13,14,3,4,18,17,19,
20,21,8,7,25,24,18,18,17,17,31,32,33,34,35,36,37,38,39,30],,[1,1,3,3,5,5,7,8,
9,9,1,1,1,2,15,15,17,18,3,3,3,22,23,7,8,26,27,28,29,30,31,32,33,34,35,36,37,
38,39],,,,,,,,,,,,,,,,,,,,,,,,,,[1,2,3,4,5,6,8,7,9,10,11,12,13,14,15,16,18,17,
19,20,21,23,22,25,24,28,29,26,27,1,1,1,1,1,1,1,1,1,1]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1],[30,30,6,6,0,0,6,6,2,2,5,5,5,0,0,0,0,0,1,1,1,0,0,1,1,0,0,0,0,-1,-1,-1,-1,
-1,-1,-1,-1,-1,-1],[31,31,7,7,1,1,-5,-5,-1,-1,6,6,6,1,1,1,-1,-1,2,2,2,1,1,0,0,
-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0],[31,31,-5,-5,1,1,-1+6*E(4),-1-6*E(4),1,1,6,6,
6,1,1,1,E(4),-E(4),0,0,0,-1,-1,-1+E(4),-1-E(4),E(4),E(4),-E(4),-E(4),0,0,0,0,
0,0,0,0,0,0],
[GALOIS,[4,3]],[96,96,0,0,0,0,0,0,0,0,-4,-4,-4,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,E(31)+E(31)^5+E(31)^25,E(31)^3+E(31)^13+E(31)^15,E(31)^8+E(31)^9+E(31)^14,
E(31)^11+E(31)^24+E(31)^27,E(31)^2+E(31)^10+E(31)^19,E(31)^6+E(31)^26+E(31)^30
 ,E(31)^16+E(31)^18+E(31)^28,E(31)^17+E(31)^22+E(31)^23,
E(31)^4+E(31)^7+E(31)^20,E(31)^12+E(31)^21+E(31)^29],
[GALOIS,[6,3]],
[GALOIS,[6,8]],
[GALOIS,[6,11]],
[GALOIS,[6,2]],
[GALOIS,[6,6]],
[GALOIS,[6,16]],
[GALOIS,[6,17]],
[GALOIS,[6,4]],
[GALOIS,[6,12]],[124,124,4,4,1,1,4,4,0,0,-1,-1,-1,-1,1,1,2,2,-1,-1,-1,1,1,-1,
-1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0],[124,124,4,4,1,1,4,4,0,0,-1,-1,-1,-1,1,1,
-2,-2,-1,-1,-1,1,1,-1,-1,1,1,1,1,0,0,0,0,0,0,0,0,0,0],[124,124,4,4,1,1,-4,-4,
0,0,-1,-1,-1,-1,1,1,2*E(4),-2*E(4),-1,-1,-1,-1,-1,1,1,-E(4),-E(4),E(4),E(4),0,
0,0,0,0,0,0,0,0,0],
[GALOIS,[18,3]],[124,124,-4,-4,1,1,4*E(4),-4*E(4),0,0,-1,-1,-1,-1,-1,-1,0,0,1,
1,1,E(4),-E(4),-E(4),E(4),-E(24)^11+E(24)^19,E(24)^11-E(24)^19,
-E(24)+E(24)^17,E(24)-E(24)^17,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[20,13]],
[GALOIS,[20,7]],
[GALOIS,[20,19]],[124,124,-4,-4,-2,-2,4*E(4),-4*E(4),0,0,-1,-1,-1,-1,2,2,0,0,
1,1,1,-2*E(4),2*E(4),-E(4),E(4),0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[24,3]],[125,125,5,5,-1,-1,5,5,1,1,0,0,0,0,-1,-1,-1,-1,0,0,0,-1,-1,0,
0,-1,-1,-1,-1,1,1,1,1,1,1,1,1,1,1],[155,155,11,11,-1,-1,-1,-1,-1,-1,5,5,5,0,
-1,-1,1,1,1,1,1,-1,-1,-1,-1,1,1,1,1,0,0,0,0,0,0,0,0,0,0],[155,155,-1,-1,-1,-1,
-5+6*E(4),-5-6*E(4),1,1,5,5,5,0,-1,-1,-E(4),E(4),-1,-1,-1,1,1,E(4),-E(4),
-E(4),-E(4),E(4),E(4),0,0,0,0,0,0,0,0,0,0],
[GALOIS,[28,3]],[186,186,-6,-6,0,0,6,6,-2,-2,11,11,11,1,0,0,0,0,-1,-1,-1,0,0,
1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[620,-5,4,-1,-4,1,0,0,-4,1,20,-5,-5,0,4,-1,0,
0,4,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[1860,-15,12,-3,0,0,0,0,4,-1,
10,10,-15,0,0,0,0,0,2,-3,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[1860,-15,12,
-3,0,0,0,0,4,-1,10,-15,10,0,0,0,0,0,2,2,-3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0],[2480,-20,16,-4,-4,1,0,0,0,0,-20,5,5,0,4,-1,0,0,-4,1,1,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0],[3100,-25,20,-5,4,-1,0,0,-4,1,0,0,0,0,-4,1,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0],[1240,-10,-8,2,4,-1,0,0,0,0,-10,15,-10,0,4,-1,0,
0,2,2,-3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[1240,-10,-8,2,4,-1,0,0,0,0,-10,
-10,15,0,4,-1,0,0,2,-3,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[2480,-20,-16,4,
-4,1,0,0,0,0,-20,5,5,0,-4,1,0,0,4,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[
3720,-30,-24,6,0,0,0,0,0,0,20,-5,-5,0,0,0,0,0,-4,1,1,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0]],
[(30,31,32,33,34,35,36,37,38,39),(26,27)(28,29),(12,13)(20,21),( 7, 8)(17,18)
(22,23)(24,25)(26,28)(27,29),( 7, 8)(17,18)(22,23)(24,25)(26,29)(27,28),
(30,39,38,37,36,35,34,33,32,31)]);
ALF("5^3.psl(3,5)","L3(5)",[1,1,2,2,3,3,4,5,6,6,7,7,7,8,9,9,10,11,12,12,
12,13,14,15,16,17,19,20,18,23,22,29,28,25,24,21,30,27,26]);
ALF("5^3.psl(3,5)","Ly",[1,6,2,15,4,23,5,5,5,26,6,7,7,34,9,37,13,13,15,16,
16,20,20,26,26,33,32,32,33,39,38,42,41,40,39,38,42,41,40],[
"fusion is unique up to table automorphisms,\n",
"the representative is compatible with the 5-modular tables of Ly, L3(5),\n",
"the representative differs from the fusion map on the CAS table"
]);
ALF("5^3.psl(3,5)","B",[1,19,5,53,7,82,17,17,17,108,19,18,19,128,28,142,
45,45,53,53,52,72,72,108,108,127,127,127,127,145,146,145,146,145,146,145,
146,145,146],[
"fusion map is unique up to table automorphisms"
]);
ALN("5^3.psl(3,5)",["5^3.L3(5)"]);

MOT("67:22",
[
"8th maximal subgroup of Ly"
],
0,
0,
0,
[( 5,17,19,23, 9,25,13,11, 7,21)( 6, 8,12,20,14,24,22,18,10,16),(2,3,4)],
["ConstructPermuted",["P:Q",[67,22]]]);
ALF("67:22","Ly",[1,51,52,53,29,18,29,17,29,18,30,18,29,18,2,17,30,17,29,17,
30,18,30,17,30],[
"fusion map is unique up to table automorphisms"
]);
ALN("67:22",["LyN67"]);

MOT("7:3xpsl(3,2)",
[
"origin: CAS library,\n",
"maximal subgroup of He,\n",
"test: 1.OR, JAMES, JAMES,n=3,\n",
"and restricted characters decompose properly.\n",
"tests: 1.o.r., pow[2,3,7]"
],
0,
0,
0,
[(19,25)(20,26)(21,27)(22,28)(23,29)(24,30),( 5, 6)( 7,13)( 8,14)( 9,15)
(10,16)(11,18)(12,17)(23,24)(29,30),( 5, 6)(11,12)(17,18)(23,24)(29,30)],
["ConstructDirectProduct",[["P:Q",[7,3]],["L3(2)"]]]);
ARC("7:3xpsl(3,2)","tomfusion",rec(name:="7:3xL3(2)",map:=[1,2,4,8,12,12,11,
24,28,40,13,14,11,24,28,40,14,13,3,10,5,23,29,29,3,10,5,23,29,29],text:=[
"fusion map is unique up to table automorphisms"
]));
ALF("7:3xpsl(3,2)","He",[1,2,5,6,14,14,12,21,30,32,12,12,13,22,31,33,13,
13,4,10,5,19,28,29,4,10,5,19,29,28],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("7:3xpsl(3,2)","7:6xL3(2)",[1,2,3,4,5,6,7,8,9,10,11,12,7,8,9,10,11,12,
19,20,21,22,23,24,31,32,33,34,35,36],[
"fusion map is unique up to table aut."
]);

MOT("7^2:(3x2S4)",
[
"origin: Dixon's Algorithm,\n",
"11th maximal subgroup of Th,\n",
"table is sorted w.r. to normal series 7^2.3.2.2^2.3.2,\n",
"tests: 1.o.r., pow[2,3,5,7]"
],
[7056,147,144,144,144,144,144,24,24,24,126,126,18,18,18,18,21,21,12,24,24,12,
12,24,24,24,24],
[,[1,2,4,3,1,4,3,5,7,6,12,11,13,13,12,11,18,17,5,8,8,7,6,10,10,9,9],[1,2,1,1,
5,5,5,8,8,8,1,1,1,5,5,5,2,2,19,21,20,19,19,21,20,21,20],,[1,2,4,3,5,7,6,8,10,
9,12,11,13,14,16,15,18,17,19,21,20,23,22,27,26,25,24],,[1,1,3,4,5,6,7,8,9,10,
11,12,13,14,15,16,11,12,19,20,21,22,23,24,25,26,27]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[2,2,2,2,2,2,2,2,2,2,-1,-1,-1,-1,
-1,-1,-1,-1,0,0,0,0,0,0,0,0,0],[3,3,3,3,3,3,3,-1,-1,-1,0,0,0,0,0,0,0,0,-1,1,1,
-1,-1,1,1,1,1],
[TENSOR,[4,2]],[2,2,2,2,-2,-2,-2,0,0,0,-1,-1,-1,1,1,1,-1,-1,0,E(8)-E(8)^3,
-E(8)+E(8)^3,0,0,E(8)-E(8)^3,-E(8)+E(8)^3,E(8)-E(8)^3,-E(8)+E(8)^3],
[TENSOR,[6,2]],[4,4,4,4,-4,-4,-4,0,0,0,1,1,1,-1,-1,-1,1,1,0,0,0,0,0,0,0,0,0],[
1,1,E(3)^2,E(3),1,E(3)^2,E(3),1,E(3)^2,E(3),E(3)^2,E(3),1,1,E(3)^2,E(3),
E(3)^2,E(3),-1,-1,-1,-E(3)^2,-E(3),-E(3)^2,-E(3)^2,-E(3),-E(3)],
[TENSOR,[2,9]],
[TENSOR,[9,10]],
[TENSOR,[2,11]],
[TENSOR,[3,9]],
[TENSOR,[3,11]],
[TENSOR,[6,10]],
[TENSOR,[6,9]],
[TENSOR,[6,12]],
[TENSOR,[6,11]],
[TENSOR,[4,12]],
[TENSOR,[4,11]],
[TENSOR,[4,10]],
[TENSOR,[4,9]],
[TENSOR,[8,9]],
[TENSOR,[8,11]],[48,-1,0,0,0,0,0,0,0,0,6,6,0,0,0,0,-1,-1,0,0,0,0,0,0,0,0,0],
[TENSOR,[25,9]],
[TENSOR,[25,11]]],
[(20,21)(24,25)(26,27),( 3, 4)( 6, 7)( 9,10)(11,12)(15,16)(17,18)(22,23)
(24,26)(25,27)]);
ALF("7^2:(3x2S4)","F4(2).2",[1,25,6,6,4,24,24,16,45,46,5,5,6,24,23,23,58,
58,65,71,71,75,75,83,83,84,84],[
"fusion map determined using the known map 7^2:(3x2A4) -> F4(2)"
]);
ALF("7^2:(3x2S4)","Th",[1,12,5,5,2,9,9,7,22,22,3,3,5,9,10,10,31,31,7,14,
14,22,22,34,35,35,34],[
"fusion map is unique up to table automorphisms"
]);
ALN("7^2:(3x2S4)",["F4(2).2N7","ThN7"]);

MOT("7^2:2psl(2,7)",
[
"origin: CAS library,\n",
"maximal subgroup of He and M,\n",
"test: 1.OR, JAMES, JAMES,n=3,\n",
"and restricted characters decompose properly.\n",
"tests: 1.o.r., pow[2,3,7]"
],
[16464,343,336,8,6,6,8,8,98,49,49,49,14,98,49,49,49,14],
[,[1,2,1,3,5,5,4,4,9,10,11,12,9,14,15,16,17,14],[1,2,3,4,1,3,8,7,14,17,15,16,
18,9,11,12,10,13],,,,[1,1,3,4,5,6,7,8,1,1,1,1,3,1,1,1,1,3]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[3,3,3,-1,0,0,1,1,E(7)+E(7)^2+E(7)^4,
E(7)+E(7)^2+E(7)^4,E(7)+E(7)^2+E(7)^4,E(7)+E(7)^2+E(7)^4,E(7)+E(7)^2+E(7)^4,
E(7)^3+E(7)^5+E(7)^6,E(7)^3+E(7)^5+E(7)^6,E(7)^3+E(7)^5+E(7)^6,
E(7)^3+E(7)^5+E(7)^6,E(7)^3+E(7)^5+E(7)^6],
[GALOIS,[2,3]],[6,6,6,2,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[7,7,7,-1,1,1,
-1,-1,0,0,0,0,0,0,0,0,0,0],[8,8,8,0,-1,-1,0,0,1,1,1,1,1,1,1,1,1,1],[4,4,-4,0,
1,-1,0,0,-E(7)-E(7)^2-E(7)^4,-E(7)-E(7)^2-E(7)^4,-E(7)-E(7)^2-E(7)^4,
-E(7)-E(7)^2-E(7)^4,E(7)+E(7)^2+E(7)^4,-E(7)^3-E(7)^5-E(7)^6,
-E(7)^3-E(7)^5-E(7)^6,-E(7)^3-E(7)^5-E(7)^6,-E(7)^3-E(7)^5-E(7)^6,
E(7)^3+E(7)^5+E(7)^6],
[GALOIS,[7,3]],[6,6,-6,0,0,0,E(8)-E(8)^3,-E(8)+E(8)^3,-1,-1,-1,-1,1,-1,-1,-1,
-1,1],
[GALOIS,[9,3]],[8,8,-8,0,-1,1,0,0,1,1,1,1,-1,1,1,1,1,-1],[48,-1,0,0,0,0,0,0,6,
-1,-1,-1,0,6,-1,-1,-1,0],[48,-1,0,0,0,0,0,0,2*E(7)+2*E(7)^2+2*E(7)^4,-1,
2*E(7)^3+2*E(7)^5+2*E(7)^6,-2*E(7)-2*E(7)^2-3*E(7)^3-2*E(7)^4-3*E(7)^5
 -3*E(7)^6,0,2*E(7)^3+2*E(7)^5+2*E(7)^6,2*E(7)+2*E(7)^2+2*E(7)^4,
-3*E(7)-3*E(7)^2-2*E(7)^3-3*E(7)^4-2*E(7)^5-2*E(7)^6,-1,0],[48,-1,0,0,0,0,0,0,
2*E(7)+2*E(7)^2+2*E(7)^4,2*E(7)^3+2*E(7)^5+2*E(7)^6,-2*E(7)-2*E(7)^2-3*E(7)^3
 -2*E(7)^4-3*E(7)^5-3*E(7)^6,-1,0,2*E(7)^3+2*E(7)^5+2*E(7)^6,-3*E(7)-3*E(7)^2
 -2*E(7)^3-3*E(7)^4-2*E(7)^5-2*E(7)^6,-1,2*E(7)+2*E(7)^2+2*E(7)^4,0],[48,-1,0,
0,0,0,0,0,2*E(7)^3+2*E(7)^5+2*E(7)^6,-3*E(7)-3*E(7)^2-2*E(7)^3-3*E(7)^4
 -2*E(7)^5-2*E(7)^6,-1,2*E(7)+2*E(7)^2+2*E(7)^4,0,2*E(7)+2*E(7)^2+2*E(7)^4,-1,
2*E(7)^3+2*E(7)^5+2*E(7)^6,-2*E(7)-2*E(7)^2-3*E(7)^3-2*E(7)^4-3*E(7)^5
 -3*E(7)^6,0],
[GALOIS,[15,3]],
[GALOIS,[14,3]],
[GALOIS,[13,3]]],
[( 9,14)(10,17)(11,15)(12,16)(13,18),(7,8),(10,11,12)(15,16,17)]);
ARC("7^2:2psl(2,7)","tomfusion",rec(name:="7^2:2L2(7)",map:=[1,6,2,4,3,5,13,
13,7,8,10,9,16,7,10,9,8,16],text:=[
"ambiguous fusion, determined using explicit embedding of the group"
]));
ALF("7^2:2psl(2,7)","He",[1,14,3,8,5,11,17,17,15,14,16,12,23,16,15,13,14,
24],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("7^2:2psl(2,7)","2.L3(2)",[1,1,2,3,4,5,6,7,8,8,8,8,9,10,10,10,10,11]);
ALF("7^2:2psl(2,7)","7^2:2.L2(7).2",[1,2,3,4,5,6,7,8,9,10,11,12,13,9,11,
12,10,13],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables"
]);
ALF("7^2:2psl(2,7)","M",[1,20,3,10,6,18,26,26,20,20,20,20,49,20,20,20,20,
49],[
"fusion determined uniquely by the fact that the group contains 4D and\n",
"6F elements, and no 7A elements"
]);
ALN("7^2:2psl(2,7)",["7^2:2.L2(7)"]);

MOT("LyM6",
[
"maximal subgroup of Ly,\n",
"of structure 3^5:(2xM11),\n",
"origin: table constructed from tables of subgroup 3^5:M11,\n",
"        factor group 2xM11, and supergroup Ly;\n",
"tests: 1.o.r., pow[2,3,5,11]"
],
0,
0,
0,
0,
["ConstructPermuted",["3^5:(M11x2)"],(5,6)(26,27)(29,30),(6,7)(12,13)(21,22)
(25,26)(30,31)(35,36)]);
ALF("LyM6","Ly",[1,3,4,2,10,8,9,4,4,14,5,19,7,24,10,25,13,13,17,18,2,2,10,
10,5,19,20,16,10,9,12,31,12,31,29,30],[
"fusion is unique up to table automorphisms"
]);
ALF("LyM6","2xM11",[1,1,1,2,2,2,2,3,3,3,4,4,5,5,6,6,7,8,9,10,11,12,12,13,
14,14,14,15,16,16,17,17,18,18,19,20]);

MOT("ONM5",
[
"origin: constructed as subdirect product of 3^2:Q8 and M10,\n",
"structure is (3^2:4xA6).2,\n",
"5th maximal subgroup of ON,\n",
"table is sorted w.r. to normal series given by 3^2.2.2.A6.2,\n",
"tests: 1.o.r., pow[2,3,5]"
],
[25920,3240,2880,1440,576,324,288,180,72,81,81,36,45,45,64,36,32,20,32,36,36,
16,20,20,8,16,16,8,16,16],
[,[1,2,1,3,1,6,5,8,2,10,11,9,14,13,1,6,5,8,3,16,16,15,18,18,15,17,17,15,17,
17],[1,1,3,4,5,1,7,8,5,1,1,7,8,8,15,3,17,18,19,4,4,22,23,24,25,26,27,28,29,
30],,[1,2,3,4,5,6,7,1,9,10,11,12,2,2,15,16,17,3,19,20,21,22,4,4,25,27,26,28,
30,29]],
0,
[(26,27)(29,30),(23,24),(20,21)(23,24)(26,27)(29,30),(13,14)(23,24),(10,11),
(25,28)(26,29)(27,30)],
["ConstructIndexTwoSubdirectProduct","3^2:4","3^2:Q8","A6","A6.2_3",[38,39,40,
46,47,48],(2,5,8,16,13,10,18,4,7,15,12,9,17,14,11)(3,6),(1,2)(5,6)(7,8)(9,10)
(13,14)(15,16)(18,23,19,22)(25,30,26,29)]);
ARC("ONM5","projectives",["3.ONM5",[[18,0,-6,-6,-6,0,6,3,0,0,0,0,0,0,2,0,-2,
-1,2,0,0,-2,-1,-1,0,0,0,0,0,0],[18,0,-6,6,6,0,0,3,0,0,0,0,0,0,-2,0,0,-1,2,0,0,
0,1,1,0,E(8)+E(8)^3,-E(8)-E(8)^3,0,E(8)+E(8)^3,-E(8)-E(8)^3],[18,0,6,0,-6,0,6,
3,0,0,0,0,0,0,-2,0,2,1,0,0,0,0,E(20)+E(20)^9-E(20)^13-E(20)^17,
-E(20)-E(20)^9+E(20)^13+E(20)^17,0,0,0,0,0,0],[27,0,-9,-9,3,0,3,-3,0,0,0,0,0,
0,-1,0,-1,1,-1,0,0,-1,1,1,1,-1,-1,-1,1,1],[36,0,12,0,12,0,0,6,0,0,0,0,0,0,4,0,
0,2,0,0,0,0,0,0,0,0,0,0,0,0],[45,0,-15,-15,-3,0,-3,0,0,0,0,0,0,0,1,0,1,0,1,0,
0,1,0,0,1,1,1,-1,-1,-1],[54,0,18,0,6,0,6,-6,0,0,0,0,0,0,2,0,2,-2,0,0,0,0,0,0,
0,0,0,0,0,0],[90,0,30,0,-6,0,-6,0,0,0,0,0,0,0,-2,0,-2,0,0,0,0,0,0,0,0,0,0,0,0,
0]],]);
ALF("ONM5","3^2:Q8",[1,3,2,4,1,1,1,1,3,3,3,3,3,3,2,2,2,2,4,4,4,4,4,4,5,5,
5,6,6,6]);
ALF("ONM5","A6.2_3",[1,1,1,1,2,3,4,5,2,3,3,4,5,5,2,3,4,5,2,3,3,4,5,5,6,7,
8,6,7,8]);
ALF("ONM5","ON",[1,3,2,4,2,3,4,6,7,3,3,14,16,17,2,7,5,12,5,14,14,5,25,26,
5,10,10,5,11,11],[
"fusion map is unique up to table automorphisms"
]);
ALF("ONM5","(3^2:4xA6).2^2",[1,2,3,4,5,7,9,13,14,8,8,17,20,21,6,15,10,16,
11,18,19,12,22,22,23,24,25,23,25,24]);


MOT("ThM7",
[
"origin: constructed by Alexander Hulpke,\n",
"7th maximal subgroup of Th,\n",
"3B^2 normalizer in Th,\n",
"table is sorted w.r. to normal series 3^2.3^3.3^2.3^2.2.2^2.3.2,\n",
"tests: 1.o.r., pow[2,3]"
],
[944784,118098,17496,13122,8748,1458,729,1458,1458,1458,486,243,243,162,1296,
216,162,108,24,24,24,162,81,18,486,243,243,243,243,162,81,18,18,27,27,27,324,
162,108,108,54,54,54,18,24,24,18,18,24,24,24,24],
[,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,1,3,4,5,15,16,16,22,23,22,25,26,27,28,29,
30,31,25,30,35,34,36,1,2,5,5,9,10,8,11,19,19,6,14,20,21,20,21],[1,1,1,1,1,2,2,
1,1,1,1,1,2,2,15,15,15,15,19,19,19,1,1,15,4,4,4,4,4,4,4,17,17,7,7,7,37,37,37,
37,37,37,37,37,45,46,38,38,45,45,46,46]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[2,2,
2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,
-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,-1,1,1,-1,-1,1,1,
1,1],
[TENSOR,[4,2]],[2,2,2,2,2,2,2,2,2,2,2,2,2,2,-2,-2,-2,-2,0,0,0,-1,-1,1,-1,-1,
-1,-1,-1,-1,-1,1,1,-1,-1,-1,0,0,0,0,0,0,0,0,-E(8)-E(8)^3,E(8)+E(8)^3,0,0,
-E(8)-E(8)^3,-E(8)-E(8)^3,E(8)+E(8)^3,E(8)+E(8)^3],
[TENSOR,[6,2]],[4,4,4,4,4,4,4,4,4,4,4,4,4,4,-4,-4,-4,-4,0,0,0,1,1,-1,1,1,1,1,
1,1,1,-1,-1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[8,8,8,8,8,8,8,-1,-1,-1,-1,
-1,-1,-1,0,0,0,0,0,0,0,2,2,0,2,2,2,2,2,2,2,0,0,-1,-1,-1,2,2,2,2,-1,-1,-1,-1,0,
0,2,-1,0,0,0,0],
[TENSOR,[9,2]],[16,16,16,16,16,16,16,-2,-2,-2,-2,-2,-2,-2,0,0,0,0,0,0,0,-2,-2,
0,-2,-2,-2,-2,-2,-2,-2,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[8,8,8,8,8,
-1,-1,5,5,5,-1,-1,-4,2,0,0,0,0,0,0,0,2,-1,0,2,-1,-1,-1,2,2,-1,0,0,-1,-1,2,2,2,
2,2,-1,-1,-1,-1,0,0,-1,2,0,0,0,0],
[TENSOR,[12,2]],[16,16,16,16,16,-2,-2,-8,-8,-8,-2,-2,1,4,0,0,0,0,0,0,0,4,-2,0,
4,-2,-2,-2,4,4,-2,0,0,1,1,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[16,16,16,16,16,
-2,-2,10,10,10,-2,-2,-8,4,0,0,0,0,0,0,0,-2,1,0,-2,1,1,1,-2,-2,1,0,0,1,1,-2,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[16,16,16,16,16,-2,-2,-8,-8,-8,-2,-2,1,4,0,0,0,
0,0,0,0,-2,1,0,-2,1,1,1,-2,-2,1,0,0,-E(3)+2*E(3)^2,2*E(3)-E(3)^2,1,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[16,2]],[24,24,24,24,24,-3,-3,6,6,6,-3,-3,6,-3,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,-2,-2,-2,-2,-2,-2,-2,1,0,0,1,1,0,0,0,0],
[TENSOR,[18,2]],[24,24,24,24,24,-3,-3,-3,-3,-3,6,6,-3,-3,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,-2,-2,-2,-2,1,1,1,-2,0,0,1,1,0,0,0,0],
[TENSOR,[20,2]],[24,24,-12,-3,6,6,-3,0,0,0,6,-3,0,0,8,-4,-1,2,0,0,0,-3,0,-1,0,
3,3,3,0,3,-3,2,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[24,24,-12,-3,6,6,-3,
0,0,0,6,-3,0,0,8,-4,-1,2,0,0,0,0,3,2,3,-3,-3,-3,3,-3,0,-1,-1,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0],[24,24,-12,-3,6,6,-3,0,0,0,6,-3,0,0,8,-4,-1,2,0,0,0,3,
-3,-1,-3,0,0,0,-3,0,3,-1,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[24,24,-12,
-3,6,6,-3,0,0,0,6,-3,0,0,-8,4,1,-2,0,0,0,-3,0,1,0,3,3,3,0,3,-3,-2,1,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0],[24,24,-12,-3,6,6,-3,0,0,0,6,-3,0,0,-8,4,1,-2,0,
0,0,0,3,-2,3,-3,-3,-3,3,-3,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[24,
24,-12,-3,6,6,-3,0,0,0,6,-3,0,0,-8,4,1,-2,0,0,0,3,-3,1,-3,0,0,0,-3,0,3,1,-2,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[48,48,-24,-6,12,12,-6,0,0,0,-6,3,0,0,0,
0,0,0,0,0,0,-6,0,0,0,-3,-3,-3,0,6,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0],[48,48,-24,-6,12,12,-6,0,0,0,-6,3,0,0,0,0,0,0,0,0,0,0,-3,0,6,3,3,3,6,-6,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[48,48,-24,-6,12,12,-6,0,0,0,-6,3,
0,0,0,0,0,0,0,0,0,6,3,0,-6,0,0,0,-6,0,-3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0],[54,54,27,-27,0,0,0,0,0,0,0,0,0,0,6,3,-3,0,2,-1,-1,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,-2,-2,0,0,1,1,1,1],
[TENSOR,[31,2]],[54,54,27,-27,0,0,0,0,0,0,0,0,0,0,-6,-3,3,0,0,E(12)^7-E(12)^11
 ,-E(12)^7+E(12)^11,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,E(8)+E(8)^3,
-E(8)-E(8)^3,0,0,E(24)^17+E(24)^19,E(24)+E(24)^11,-E(24)^17-E(24)^19,
-E(24)-E(24)^11],
[TENSOR,[33,2]],
[GALOIS,[33,5]],
[TENSOR,[35,2]],[54,54,27,-27,0,0,0,0,0,0,0,0,0,0,6,3,-3,0,-2,1,1,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-E(12)^7+E(12)^11,E(12)^7-E(12)^11,
-E(12)^7+E(12)^11,E(12)^7-E(12)^11],
[TENSOR,[37,2]],[108,108,0,27,-27,0,0,0,0,0,0,0,0,0,12,0,3,-3,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,6,6,-3,-3,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[39,2]],[108,108,0,27,-27,0,0,0,0,0,0,0,0,0,-12,0,-3,3,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,-3*E(3)+3*E(3)^2,3*E(3)-3*E(3)^2,0,0,0,0,0,0,0,0,0,
0,0,0],
[TENSOR,[41,2]],[144,144,-72,-18,36,-18,9,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[216,-27,0,0,0,0,0,-9,
9,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,6,-3,-3,6,-3,0,0,0,0,0,0,0,-6,3,0,0,-3,0,3,0,
0,0,0,0,0,0,0,0],
[TENSOR,[44,2]],[216,-27,0,0,0,0,0,9,0,-9,0,0,0,0,0,0,0,0,0,0,0,0,0,0,6,-3,6,
-3,-3,0,0,0,0,0,0,0,-6,3,0,0,0,3,-3,0,0,0,0,0,0,0,0,0],
[TENSOR,[46,2]],[216,-27,0,0,0,0,0,0,-9,9,0,0,0,0,0,0,0,0,0,0,0,0,0,0,6,6,-3,
-3,-3,0,0,0,0,0,0,0,-6,3,0,0,3,-3,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[48,2]],[432,-54,0,0,0,0,0,-18,18,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-6,3,
3,-6,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[432,-54,0,0,0,0,0,18,0,
-18,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-6,3,-6,3,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0],[432,-54,0,0,0,0,0,0,-18,18,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-6,-6,3,
3,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]],
[(45,46)(49,51)(50,52),(39,40),(34,35),(20,21)(45,46)(49,52)(50,51),(20,21)
(34,35)(39,40)(49,50)(51,52),( 8, 9,10)(26,27,28)(41,42,43)]);
ALF("ThM7","Th",[1,4,5,4,3,15,16,3,4,5,4,5,16,17,2,9,11,10,7,22,22,4,5,11,
15,16,15,16,16,17,17,27,28,37,38,36,2,11,10,10,11,9,10,11,14,14,27,28,34,
35,35,34],[
"fusion map is unique up to table automorphisms"
]);

MOT("ThN3B",
[
"origin: constructed by Alexander Hulpke,\n",
"6th maximal subgroup of Th,\n",
"3B normalizer in Th,\n",
"table is sorted w.r. to normal series 3.3^2.3.3^2.3.3^2.2.2^2.3.2,\n",
"tests: 1.o.r., pow[2,3]"
],
[944784,472392,39366,34992,34992,4374,4374,4374,5832,729,486,243,486,243,162,
1296,648,432,432,72,216,108,72,72,36,36,36,486,486,486,486,243,243,243,243,54,
54,54,18,162,81,81,18,27,27,27,324,162,108,108,54,54,54,18,24,24,18,18,24,24,
24,24],
[,[1,2,3,5,4,6,7,8,9,10,11,12,13,14,15,1,2,5,4,9,16,17,19,18,20,20,20,28,29,
30,31,32,35,34,33,28,29,30,31,40,41,42,40,44,46,45,1,3,5,4,8,6,7,11,21,21,15,
13,23,24,23,24],[1,1,1,1,1,1,1,1,2,2,1,1,3,3,3,16,16,16,16,17,21,21,21,21,22,
22,22,1,1,1,1,1,1,1,1,16,16,16,16,2,3,3,17,10,10,10,47,47,47,47,47,47,47,47,
55,56,48,48,55,55,56,56]],
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1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,
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[TENSOR,[4,2]],[2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,-2,-2,-2,-2,-2,0,0,0,0,0,0,0,-1,
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[TENSOR,[6,2]],[4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,-4,-4,-4,-4,-4,0,0,0,0,0,0,0,1,
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3,3,3,-3,-3,0,0,0,1,1,1,1,0,3,-3,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[6,
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3,1,1,1,-2,3,-3,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[6,6,6,6,6,6,6,6,
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-3,0,3,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[12,12,12,12,12,12,12,12,-6,
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0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[12,12,12,12,12,12,12,12,-6,-6,0,0,0,0,0,
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0,0,0,0,0],[18,18,18,18,18,18,18,18,-9,-9,0,0,0,0,0,-6,-6,-6,-6,3,-2,-2,-2,-2,
1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[
8,8,8,8,8,-1,-1,-1,8,-1,5,-4,-1,-1,2,0,0,0,0,0,0,0,0,0,0,0,0,2,2,2,2,2,-1,-1,
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[TENSOR,[19,2]],[16,16,16,16,16,-2,-2,-2,16,-2,10,-8,-2,-2,4,0,0,0,0,0,0,0,0,
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0,0,0,0],[16,16,16,16,16,-2,-2,-2,16,-2,-8,1,-2,-2,4,0,0,0,0,0,0,0,0,0,0,0,0,
4,4,4,4,4,-2,-2,-2,0,0,0,0,4,-2,-2,0,-2,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[
16,16,16,16,16,-2,-2,-2,16,-2,-8,1,-2,-2,4,0,0,0,0,0,0,0,0,0,0,0,0,-2,-2,-2,
-2,-2,1,1,1,0,0,0,0,-2,1,1,0,1,2*E(3)-E(3)^2,-E(3)+2*E(3)^2,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0],
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0,0],[24,24,24,24,24,-3,-3,-3,24,-3,-3,-3,6,6,-3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
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[TENSOR,[26,2]],
[TENSOR,[25,2]],[48,48,48,48,48,-6,-6,-6,-24,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,6,6,3,3,3,0,0,0,0,-6,0,-3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[
48,48,48,48,48,-6,-6,-6,-24,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,6,6,6,-6,-6,0,
0,0,0,0,0,0,0,-3,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[48,48,48,48,48,
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0,6,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[27,27,27,27*E(3)^2,27*E(3),
0,0,0,0,0,0,0,0,0,0,3,3,3*E(3)^2,3*E(3),0,-1,-1,-E(3)^2,-E(3),2,2*E(3)^2,
2*E(3),0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-3,-3,-3*E(3)^2,-3*E(3),0,0,0,0,
1,1,0,0,E(3),E(3)^2,E(3),E(3)^2],[27,27,27,27*E(3)^2,27*E(3),0,0,0,0,0,0,0,0,
0,0,3,3,3*E(3)^2,3*E(3),0,3,3,3*E(3)^2,3*E(3),0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,-3,-3,-3*E(3)^2,-3*E(3),0,0,0,0,-1,-1,0,0,-E(3),-E(3)^2,-E(3),
-E(3)^2],
[TENSOR,[32,2]],
[TENSOR,[33,2]],
[GALOIS,[32,2]],
[GALOIS,[33,2]],
[TENSOR,[36,2]],
[TENSOR,[37,2]],[54,54,54,54*E(3)^2,54*E(3),0,0,0,0,0,0,0,0,0,0,-6,-6,
-6*E(3)^2,-6*E(3),0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,E(8)+E(8)^3,-E(8)-E(8)^3,0,0,E(24)^11+E(24)^17,E(24)+E(24)^19,
-E(24)^11-E(24)^17,-E(24)-E(24)^19],
[TENSOR,[40,2]],
[GALOIS,[40,11]],
[TENSOR,[42,2]],[54,54,54,54*E(3)^2,54*E(3),0,0,0,0,0,0,0,0,0,0,6,6,6*E(3)^2,
6*E(3),0,-2,-2,-2*E(3)^2,-2*E(3),-2,-2*E(3)^2,-2*E(3),0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[44,2]],[72,72,-9,0,0,0,-9,9,0,0,0,0,6,-3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,6,-3,-3,6,-3,0,0,0,0,0,0,0,0,0,0,0,6,-3,0,0,3,0,-3,0,0,0,0,0,0,0,0,0],
[TENSOR,[46,2]],[144,144,-18,0,0,0,-18,18,0,0,0,0,-6,3,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,12,-6,3,-6,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0],[144,144,-18,0,0,0,-18,18,0,0,0,0,12,-6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-6,
3,3,-6,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[144,144,-18,
0,0,0,-18,18,0,0,0,0,-6,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-6,3,
-3*E(3)+6*E(3)^2,3,6*E(3)-3*E(3)^2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0],
[GALOIS,[50,2]],[216,216,-27,0,0,27,0,-27,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-6,3,0,0,3,-3,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[52,2]],[216,216,-27,0,0,-27,27,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-6,3,0,0,0,3,-3,0,0,0,0,0,0,0,0,0],
[TENSOR,[54,2]],[162,-81,0,0,0,0,0,0,0,0,0,0,0,0,0,-6,3,0,0,0,6,-3,0,0,0,0,0,
9,-9,0,0,0,0,0,0,-3,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[162,
-81,0,0,0,0,0,0,0,0,0,0,0,0,0,-6,3,0,0,0,6,-3,0,0,0,0,0,0,9,-9,0,0,0,0,0,0,-3,
3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[162,-81,0,0,0,0,0,0,0,0,0,
0,0,0,0,-6,3,0,0,0,6,-3,0,0,0,0,0,-9,0,9,0,0,0,0,0,3,0,-3,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0],[324,-162,0,0,0,0,0,0,0,0,0,0,0,0,0,12,-6,0,0,0,
0,0,0,0,0,0,0,9,0,-9,0,0,0,0,0,3,0,-3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0],[324,-162,0,0,0,0,0,0,0,0,0,0,0,0,0,12,-6,0,0,0,0,0,0,0,0,0,0,-9,9,0,
0,0,0,0,0,-3,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[324,-162,0,
0,0,0,0,0,0,0,0,0,0,0,0,12,-6,0,0,0,0,0,0,0,0,0,0,0,-9,9,0,0,0,0,0,0,-3,3,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[486,-243,0,0,0,0,0,0,0,0,0,0,0,
0,0,-18,9,0,0,0,-6,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0]],
[(55,56)(59,61)(60,62),(45,46),(33,35),(28,29,30)(36,37,38),( 4, 5)(18,19)
(23,24)(26,27)(33,35)(45,46)(49,50)(59,60)(61,62)]);
ALF("ThN3B","Th",[1,4,4,3,3,4,5,3,15,16,4,5,15,16,17,2,11,10,10,27,6,21,
19,20,44,46,45,3,5,4,4,5,5,4,5,10,9,11,11,17,17,16,28,36,37,38,2,11,10,10,
10,11,9,11,13,13,28,27,32,33,32,33],[
"fusion map is unique up to table automorphisms"
]);

MOT("s4xpsl(3,2)",
[
"origin: CAS library,\n",
"maximal subgroup of He,\n",
"test: 1.OR, JAMES, JAMES,n=3,\n",
"and restricted characters decompose properly.\n",
"tests: 1.o.r., pow[2,3,7]"
],
0,
0,
0,
[( 5, 6)(11,12)(17,18)(23,24)(29,30)],
["ConstructDirectProduct",[["s4"],["L3(2)"]]]);
ARC("s4xpsl(3,2)","tomfusion",rec(name:="S4xL3(2)",map:=[1,4,8,15,42,42,2,5,
36,19,108,108,7,38,9,95,153,153,3,6,39,31,109,109,12,24,103,27,188,188],
text:=[
"fusion map is unique"
]));
ALF("s4xpsl(3,2)","He",[1,3,4,7,12,13,2,2,10,7,21,22,5,11,5,20,30,31,2,3,
10,8,21,22,6,6,19,6,32,33],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("s4xpsl(3,2)","S4xL3(2).2",[1,2,3,4,5,5,19,20,21,22,23,23,28,29,30,31,
32,32,10,11,12,13,14,14,37,38,39,40,41,41],[
"fusion map is unique"
]);

MOT("2^(1+6)_+.L3(2).2",
[
"origin: Dixon's Algorithm"
],
[43008,43008,1536,1024,768,512,512,128,256,64,64,64,48,48,12,24,64,64,16,32,14
,14,96,32,192,192,32,12,24,24,32,32,16,32,32,16],
[,[1,1,1,1,2,1,1,1,2,4,3,3,13,13,13,14,6,6,8,9,21,21,1,4,5,5,5,13,16,16,17,17,
20,17,17,20],[1,2,3,4,5,6,7,8,9,10,11,12,1,2,3,5,17,18,19,20,21,22,23,24,26,25
,27,23,25,26,34,35,36,31,32,33],,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,
18,19,20,1,2,23,24,25,26,27,28,29,30,31,32,33,34,35,36]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
-1,-1],[6,6,6,6,6,-2,-2,-2,-2,-2,-2,-2,0,0,0,0,2,2,2,2,-1,-1,0,0,0,0,0,0,0,0,0
,0,0,0,0,0],[6,6,6,6,6,2,2,2,2,2,2,2,0,0,0,0,0,0,0,0,-1,-1,0,0,0,0,0,0,0,0,
E(8)-E(8)^3,E(8)-E(8)^3,E(8)-E(8)^3,-E(8)+E(8)^3,-E(8)+E(8)^3,-E(8)+E(8)^3],
[TENSOR,[4,2]],[7,7,7,7,7,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1,0,0,1,1,1,
1,1,1,1,1,-1,-1,-1,-1,-1,-1],
[TENSOR,[6,2]],[8,8,8,8,8,0,0,0,0,0,0,0,-1,-1,-1,-1,0,0,0,0,1,1,2,2,2,2,2,-1,
-1,-1,0,0,0,0,0,0],
[TENSOR,[8,2]],[14,14,6,-2,-2,6,6,2,-2,-2,-2,2,2,2,0,-2,2,2,0,-2,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0],[14,14,6,-2,-2,-2,-2,2,6,-2,2,-2,2,2,0,-2,-2,-2,0,2,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0],[21,21,-3,5,-3,5,5,1,-3,1,1,-3,0,0,0,0,1,1,-1,1,0,
0,-3,1,-3,-3,1,0,0,0,-1,-1,1,-1,-1,1],
[TENSOR,[12,2]],[21,21,-3,5,-3,-3,-3,1,5,1,-3,1,0,0,0,0,1,1,-1,1,0,0,-3,1,-3,
-3,1,0,0,0,1,1,-1,1,1,-1],
[TENSOR,[14,2]],[28,28,12,-4,-4,4,4,4,4,-4,0,0,-2,-2,0,2,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0],[28,28,-4,-4,4,4,4,-4,4,0,0,0,1,1,-1,1,0,0,0,0,0,0,-4,0,4
,4,0,-1,1,1,0,0,0,0,0,0],
[TENSOR,[17,2]],[28,28,-4,-4,4,-4,-4,4,-4,0,0,0,1,1,-1,1,0,0,0,0,0,0,-2,2,2,2
,-2,1,-1,-1,0,0,0,0,0,0],
[TENSOR,[19,2]],[42,42,18,-6,-6,2,2,-2,-6,2,-2,2,0,0,0,0,-2,-2,0,2,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0],[42,42,-6,10,-6,2,2,2,2,2,-2,-2,0,0,0,0,-2,-2,2,-2,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0],[42,42,18,-6,-6,-6,-6,-2,2,2,2,-2,0,0,0,0,2,2,0,
-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[42,42,-6,10,-6,-2,-2,-2,-2,-2,2,2,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,E(8)-E(8)^3,E(8)-E(8)^3,-E(8)+E(8)^3,-E(8)+E(8)^3
,-E(8)+E(8)^3,E(8)-E(8)^3],
[TENSOR,[24,2]],[56,56,-8,-8,8,0,0,0,0,0,0,0,-1,-1,1,-1,0,0,0,0,0,0,-2,-2,2,2
,2,1,-1,-1,0,0,0,0,0,0],
[TENSOR,[26,2]],[8,-8,0,0,0,4,-4,0,0,0,0,0,2,-2,0,0,2,-2,0,0,1,-1,0,0,
-2*E(8)+2*E(8)^3,2*E(8)-2*E(8)^3,0,0,-E(8)+E(8)^3,E(8)-E(8)^3,E(8)-E(8)^3,
-E(8)+E(8)^3,0,-E(8)+E(8)^3,E(8)-E(8)^3,0],
[TENSOR,[28,2]],[48,-48,0,0,0,-8,8,0,0,0,0,0,0,0,0,0,4,-4,0,0,-1,1,0,0,0,0,0,
0,0,0,0,0,0,0,0,0],[48,-48,0,0,0,8,-8,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,0,0,0,0,0
,0,0,0,-2,2,0,-2,2,0],
[TENSOR,[31,2]],[56,-56,0,0,0,-4,4,0,0,0,0,0,2,-2,0,0,-2,2,0,0,0,0,0,0,
-2*E(8)+2*E(8)^3,2*E(8)-2*E(8)^3,0,0,-E(8)+E(8)^3,E(8)-E(8)^3,-E(8)+E(8)^3,
E(8)-E(8)^3,0,E(8)-E(8)^3,-E(8)+E(8)^3,0],
[TENSOR,[33,2]],[64,-64,0,0,0,0,0,0,0,0,0,0,-2,2,0,0,0,0,0,0,1,-1,0,0,
-4*E(8)+4*E(8)^3,4*E(8)-4*E(8)^3,0,0,E(8)-E(8)^3,-E(8)+E(8)^3,0,0,0,0,0,0],
[TENSOR,[35,2]]],
[(25,26)(29,30)(31,32)(34,35),(31,35)(32,34)(33,36)]);
ALF("2^(1+6)_+.L3(2).2","He.2",[1,3,3,2,7,3,2,3,8,6,7,8,5,11,11,18,7,8,8,
15,14,20,27,28,32,33,34,31,42,41,32,34,39,33,34,38],[
"fusion map is unique up to table automorphisms"
]);

MOT("S4xL3(2).2",
[
"10-th maximal subgroup of He.2"
],
0,
0,
0,
[(8,9)(17,18)(26,27)(35,36)(44,45)],
["ConstructDirectProduct",[["Symmetric",4],["L3(2).2"]]]);
ALF("S4xL3(2).2","He.2",[1,3,4,7,12,27,29,33,32,2,3,10,8,19,27,30,34,34,2,
2,10,7,19,27,30,32,33,5,11,5,18,25,31,31,42,41,6,6,17,6,26,28,36,33,32],[
"fusion map is unique up to table autom.,\n",
"unique map that is compatible with Brauer tables"
]);

MOT("7:6xL3(2)",
[
"11-th maximal subgroup of He.2"
],
0,
0,
0,
[(13,37)(14,38)(15,39)(16,40)(17,41)(18,42)(19,31)(20,32)(21,33)(22,34)(23,35)
(24,36),(5,6)(11,12)(17,18)(23,24)(29,30)(35,36)(41,42)],
["ConstructDirectProduct",[["7:6"],["L3(2)"]]]);
ALF("7:6xL3(2)","He.2",[1,2,5,6,13,13,12,19,25,26,12,12,29,30,31,36,45,44,
4,10,5,17,23,24,27,27,31,28,37,37,4,10,5,17,24,23,29,30,31,36,44,45],[
"compatible with 7:3xpsl(3,2) -> He"
]);

MOT("2^(1+6)_-.U4(2).2",
[
"2A normalizer in Suz.2, 5th maximal subgroup of Suz.2,\n",
"sorted according to chief series 2.2^6.U4(2).2,\n",
"origin: Dixon's Algorithm"
],
[6635520,6635520,122880,92160,18432,6144,1536,1024,3072,3072,1024,384,1296,
1296,6912,6912,384,576,864,864,144,768,768,128,64,64,64,64,80,80,20,40,144,
144,144,48,144,48,96,96,48,18,18,24,24,7680,4608,46080,3072,768,256,768,256,
1536,1536,256,192,64,256,256,128,96,288,288,96,72,72,24,24,32,32,16,20,40,40,
48,48,24],
[,[1,1,1,2,1,2,3,1,2,3,3,4,13,13,15,15,15,16,19,19,20,5,5,6,8,10,9,11,29,29,
29,30,13,13,15,17,19,20,17,16,18,42,42,34,34,1,2,4,4,1,3,4,4,10,10,10,9,8,10,
10,10,15,16,18,18,20,21,19,21,23,23,24,29,32,32,39,39,40],[1,2,3,4,5,6,7,8,9,
10,11,12,1,2,1,2,3,4,1,2,4,22,23,24,25,26,27,28,29,30,31,32,5,5,5,7,5,6,10,9,
12,13,14,23,22,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,46,47,48,49,47,
48,50,52,70,71,72,73,74,75,54,55,57],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,
17,18,19,20,21,22,23,24,25,26,27,28,1,2,3,4,33,34,35,36,37,38,39,40,41,42,43,
44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,
70,71,72,46,48,48,76,77,78]],
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1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
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[TENSOR,[4,2]],[20,20,20,20,4,4,4,-4,-4,-4,-4,-4,-7,-7,2,2,2,2,2,2,2,4,4,4,0,
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[TENSOR,[9,2]],[20,20,20,20,4,4,4,4,4,4,4,4,2,2,5,5,5,5,-1,-1,-1,0,0,0,0,0,0,
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[TENSOR,[13,2]],[30,30,30,30,-10,-10,-10,2,2,2,2,2,3,3,3,3,3,3,3,3,3,-2,-2,-2,
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[TENSOR,[15,2]],[60,60,60,60,12,12,12,4,4,4,4,4,-3,-3,-6,-6,-6,-6,0,0,0,4,4,4,
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[TENSOR,[20,2]],[64,64,64,64,0,0,0,0,0,0,0,0,-8,-8,4,4,4,4,-2,-2,-2,0,0,0,0,0,
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[TENSOR,[22,2]],[81,81,81,81,9,9,9,-3,-3,-3,-3,-3,0,0,0,0,0,0,0,0,0,-3,-3,-3,
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[TENSOR,[24,2]],[27,27,-5,3,3,3,-1,3,-5,7,-1,-1,0,0,9,9,1,-3,0,0,0,3,3,-1,-1,
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0,-2,0,2,-1,-1,1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,-24,0,-36,12,0,4,0,-4,6,6,-2,0,
0,2,2,-2,0,0,0,0,0,0,0,0,0,0,0,1,-1,-1,0,0,0],
[TENSOR,[54,2]],[360,360,40,-40,24,-8,0,8,-8,-16,0,0,0,0,6,6,-2,2,3,3,-1,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,-3,1,2,-2,0,0,0,0,0,20,4,20,-12,-4,4,4,-4,0,0,0,0,0,
0,0,0,2,-2,-4,0,1,-1,-1,1,0,0,0,0,0,0,0,0,0],
[TENSOR,[56,2]],[360,360,40,-40,-24,8,0,0,-16,-8,8,0,0,0,6,6,-2,2,3,3,-1,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,3,-1,-2,2,0,0,0,0,0,0,16,-40,-8,-8,0,8,0,0,0,0,0,0,
0,0,0,0,4,2,-2,1,-1,1,-1,0,0,0,0,0,0,0,0,0],
[TENSOR,[58,2]],[405,405,-75,45,-27,-27,9,1,9,-3,5,-3,0,0,0,0,0,0,0,0,0,-3,-3,
1,-1,1,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,15,-9,-45,3,3,-1,3,-1,3,3,3,-3,
1,3,-5,-1,0,0,0,0,0,0,0,0,-1,-1,1,0,0,0,0,0,0],
[TENSOR,[60,2]],[540,540,-100,60,12,12,-4,-4,-4,-4,-4,4,0,0,-9,-9,-1,3,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,3,-1,0,0,-1,-1,1,0,0,0,0,-10,6,30,-2,6,-2,6,-2,-2,
-2,-2,2,2,-2,-2,-2,-1,3,-3,1,0,0,0,0,0,0,0,0,0,0,1,1,-1],
[TENSOR,[62,2]],[576,576,64,-64,0,0,0,0,0,0,0,0,0,0,-12,-12,4,-4,-6,-6,2,0,0,
0,0,0,0,0,1,1,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,-16,-16,16,16,0,0,0,0,0,0,0,0,0,
0,0,0,2,2,-2,-2,2,-2,0,0,0,0,0,-1,1,1,0,0,0],
[TENSOR,[64,2]],[64,-64,0,0,0,0,0,0,0,0,0,0,1,-1,16,-16,0,0,4,-4,0,-8,8,0,0,0,
0,0,4,-4,0,0,3,-3,0,0,0,0,0,0,0,1,-1,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[160,-160,0,0,0,0,0,0,0,0,0,0,7,-7,-8,8,0,0,4,
-4,0,-4,4,0,0,0,0,0,0,0,0,0,-3,3,0,0,0,0,0,0,0,1,-1,1,-1,0,0,0,0,0,0,0,0,8,-8,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,2,0,0,0,0,2,-2,0],
[TENSOR,[67,2]],[320,-320,0,0,0,0,0,0,0,0,0,0,-13,13,-16,16,0,0,8,-8,0,-8,8,0,
0,0,0,0,0,0,0,0,-3,3,0,0,0,0,0,0,0,-1,1,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[320,-320,0,0,0,0,0,0,0,0,0,0,-4,4,32,-32,
0,0,-4,4,0,-8,8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,2,-2,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[480,-480,0,0,0,0,0,0,0,0,
0,0,3,-3,24,-24,0,0,0,0,0,4,-4,0,0,0,0,0,0,0,0,0,-3,3,0,0,0,0,0,0,0,0,0,-1,1,
0,0,0,0,0,0,0,0,-8,8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,2,0,0,0,0,-2,2,0],
[TENSOR,[71,2]],[512,-512,0,0,0,0,0,0,0,0,0,0,8,-8,-16,16,0,0,-4,4,0,0,0,0,0,
0,0,0,2,-2,0,0,0,0,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,-E(40)^7+E(40)^13-E(40)^21-E(40)^23-E(40)^29+E(40)^31+
E(40)^37+E(40)^39,E(40)^7-E(40)^13+E(40)^21+E(40)^23+E(40)^29-E(40)^31-
E(40)^37-E(40)^39,0,0,0],
[TENSOR,[73,2]],[576,-576,0,0,0,0,0,0,0,0,0,0,9,-9,0,0,0,0,0,0,0,-8,8,0,0,0,0,
0,-4,4,0,0,3,-3,0,0,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0],[640,-640,0,0,0,0,0,0,0,0,0,0,-8,8,-8,8,0,0,-8,8,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1,0,0,0,0,0,0,0,0,0,0,16,-16,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,2,0],
[TENSOR,[76,2]],[960,-960,0,0,0,0,0,0,0,0,0,0,-3,3,0,0,0,0,12,-12,0,8,-8,0,0,
0,0,0,0,0,0,0,3,-3,0,0,0,0,0,0,0,0,0,1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]],
[(74,75),(54,55)(70,71)(76,77)]);
ALF("2^(1+6)_-.U4(2).2","Suz.2",[1,2,2,7,2,8,9,3,9,7,8,18,5,14,4,13,13,25,
5,15,26,8,7,19,10,18,20,19,11,22,22,35,14,15,13,27,14,29,25,27,37,21,34,
26,29,38,40,46,47,39,40,48,49,46,47,48,50,41,48,47,49,42,54,60,61,55,62,
43,63,48,49,58,52,67,68,60,61,64],[
"fusion map is unique up to table automorphisms"
]);
ALF("2^(1+6)_-.U4(2).2","U4(2).2",[1,1,1,1,2,2,2,3,3,3,3,3,4,4,5,5,5,5,6,
6,6,7,7,7,8,8,8,8,9,9,9,9,10,10,11,11,12,12,13,13,13,14,14,15,15,16,16,16,
16,17,17,17,17,18,18,18,18,19,19,19,19,20,20,20,20,21,21,22,22,23,23,23,
24,24,24,25,25,25]);
ALN("2^(1+6)_-.U4(2).2",["Suz.2C2A","Suz.2N2A"]);

MOT("3^5:(M11x2)",
[
"6th maximal subgroup of Suz.2,\n",
"origin: Dixon's Algorithm"
],
[3849120,174960,17496,2592,432,324,216,324,162,54,48,24,30,15,36,18,16,16,22,
22,15840,864,108,36,144,36,36,10,36,18,48,24,48,24,22,22],
[,[1,2,3,1,2,3,3,8,9,10,4,5,13,14,8,10,11,11,20,19,1,1,3,8,4,7,5,13,8,9,11,12,
11,12,20,19],[1,1,1,4,4,4,4,1,1,3,11,11,13,13,4,6,17,18,19,20,21,22,22,21,25,
25,25,28,22,22,31,31,33,33,35,36],,[1,2,3,4,5,6,7,8,9,10,11,12,1,2,15,16,18,
17,19,20,21,22,23,24,25,26,27,21,29,30,33,34,31,32,35,36],,,,,,[1,2,3,4,5,6,7,
8,9,10,11,12,13,14,15,16,17,18,1,1,21,22,23,24,25,26,27,28,29,30,31,32,33,34,
21,21]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
-1,-1,-1],[10,10,10,2,2,2,2,1,1,1,2,2,0,0,-1,-1,0,0,-1,-1,10,2,2,1,2,2,2,0,-1,
-1,0,0,0,0,-1,-1],
[TENSOR,[3,2]],[10,10,10,-2,-2,-2,-2,1,1,1,0,0,0,0,1,1,E(8)+E(8)^3,
-E(8)-E(8)^3,-1,-1,10,-2,-2,1,0,0,0,0,1,1,E(8)+E(8)^3,E(8)+E(8)^3,
-E(8)-E(8)^3,-E(8)-E(8)^3,-1,-1],
[TENSOR,[5,2]],
[GALOIS,[5,5]],
[TENSOR,[7,2]],[11,11,11,3,3,3,3,2,2,2,-1,-1,1,1,0,0,-1,-1,0,0,11,3,3,2,-1,-1,
-1,1,0,0,-1,-1,-1,-1,0,0],
[TENSOR,[9,2]],[16,16,16,0,0,0,0,-2,-2,-2,0,0,1,1,0,0,0,0,
E(11)+E(11)^3+E(11)^4+E(11)^5+E(11)^9,E(11)^2+E(11)^6+E(11)^7+E(11)^8+E(11)^10
 ,16,0,0,-2,0,0,0,1,0,0,0,0,0,0,E(11)+E(11)^3+E(11)^4+E(11)^5+E(11)^9,
E(11)^2+E(11)^6+E(11)^7+E(11)^8+E(11)^10],
[TENSOR,[11,2]],
[GALOIS,[11,2]],
[TENSOR,[13,2]],[44,44,44,4,4,4,4,-1,-1,-1,0,0,-1,-1,1,1,0,0,0,0,44,4,4,-1,0,
0,0,-1,1,1,0,0,0,0,0,0],
[TENSOR,[15,2]],[45,45,45,-3,-3,-3,-3,0,0,0,1,1,0,0,0,0,-1,-1,1,1,45,-3,-3,0,
1,1,1,0,0,0,-1,-1,-1,-1,1,1],
[TENSOR,[17,2]],[55,55,55,-1,-1,-1,-1,1,1,1,-1,-1,0,0,-1,-1,1,1,0,0,55,-1,-1,
1,-1,-1,-1,0,-1,-1,1,1,1,1,0,0],
[TENSOR,[19,2]],[110,-25,2,14,-1,-4,2,2,2,-1,2,-1,0,0,2,-1,0,0,0,0,0,0,0,0,-4,
2,-1,0,0,0,-2,1,-2,1,0,0],
[TENSOR,[21,2]],[110,-25,2,-2,7,-2,-2,2,2,-1,2,-1,0,0,-2,1,0,0,0,0,0,0,0,0,-4,
2,-1,0,0,0,2,-1,2,-1,0,0],
[TENSOR,[23,2]],[132,24,-3,12,0,3,-3,6,-3,0,0,0,2,-1,0,0,0,0,0,0,0,-8,1,0,-4,
-1,2,0,-2,1,0,0,0,0,0,0],
[TENSOR,[25,2]],[220,-50,4,12,6,-6,0,4,4,-2,-4,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0],[220,-50,4,-12,-6,6,0,4,4,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,-2*E(8)-2*E(8)^3,E(8)+E(8)^3,2*E(8)+2*E(8)^3,-E(8)-E(8)^3,0,0],
[TENSOR,[28,2]],[528,96,-12,0,0,0,0,6,-3,0,0,0,-2,1,0,0,0,0,0,0,0,16,-2,0,0,0,
0,0,-2,1,0,0,0,0,0,0],
[TENSOR,[30,2]],[660,120,-15,12,0,3,-3,-6,3,0,0,0,0,0,0,0,0,0,0,0,0,-8,1,0,4,
1,-2,0,-2,1,0,0,0,0,0,0],
[TENSOR,[32,2]],[792,144,-18,-24,0,-6,6,0,0,0,0,0,2,-1,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0],[880,-200,16,16,-8,-2,4,-2,-2,1,0,0,0,0,-2,1,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[880,-200,16,-16,8,2,-4,-2,-2,1,0,0,0,0,2,-1,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]],
[(17,18)(31,33)(32,34),(19,20)(35,36)]);
ALF("3^5:(M11x2)","Suz.2",[1,4,5,2,13,14,15,5,6,21,9,27,12,33,15,34,20,20,
24,24,39,39,43,43,40,55,54,53,43,45,50,64,50,64,59,59],[
"fusion map is unique"
]);
ALF("3^5:(M11x2)","2xM11",[1,1,1,2,2,2,2,3,3,3,4,4,5,5,6,6,7,8,9,10,11,12,
12,13,14,14,14,15,16,16,17,17,18,18,19,20]);

MOT("J2.2x2",
[
"7th maximal subgroup of Suz.2"
],
0,
0,
0,
[(51,53)(52,54),(33,34)(35,36)(37,38)(39,40)(41,42)(43,44)(45,46)(47,48)(49,
50)(51,52)(53,54)],
["ConstructDirectProduct",[["J2.2"],["Cyclic",2]]]);
ALF("J2.2x2","Suz.2",[1,38,2,38,3,39,4,42,6,44,7,40,12,51,11,52,13,42,16,
45,17,57,18,49,23,53,22,52,25,54,33,66,3,38,9,40,10,41,16,44,18,47,18,47,
27,54,28,56,31,57,37,61,37,61],[
"fusion map is unique up to table automorphisms"
]);

MOT("2^(4+6):3S6",
[
"8th maximal subgroup of Suz.2,\n",
"origin: Dixon's Algorithm"
],
[2211840,147456,7680,6144,6144,17280,1152,3072,1024,3072,1536,1024,512,128,
128,96,96,48,72,24,288,288,144,48,48,192,64,192,64,24,24,60,20,15,15,1536,512,
96,256,256,768,768,3072,1024,768,128,128,64,64,64,64,16,12,12,24,24,24,24],
[,[1,1,1,2,2,6,6,1,1,2,2,2,2,5,4,6,7,7,19,19,21,21,21,22,22,8,9,10,12,16,17,
32,32,34,35,1,2,3,4,4,1,2,4,4,4,4,4,9,8,12,10,14,19,20,21,22,25,25],[1,2,3,4,
5,1,2,8,9,10,11,12,13,14,15,8,10,11,1,3,1,2,2,5,4,26,27,28,29,26,28,32,33,32,
32,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,36,38,41,42,45,43],,[1,
2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,
30,31,1,3,6,6,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,
57,58]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,-1,-1],[5,5,5,5,5,5,5,1,1,1,1,1,1,1,1,1,1,1,2,2,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,3,3,3,3,3,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,0,0,
-1,-1,-1,-1],
[TENSOR,[3,2]],[5,5,5,5,5,5,5,1,1,1,1,1,1,1,1,1,1,1,-1,-1,2,2,2,2,2,-1,-1,-1,
-1,-1,-1,0,0,0,0,-1,-1,-1,-1,-1,3,3,3,3,3,3,3,1,1,1,1,1,-1,-1,0,0,0,0],
[TENSOR,[5,2]],[16,16,16,16,16,16,16,0,0,0,0,0,0,0,0,0,0,0,-2,-2,-2,-2,-2,-2,
-2,0,0,0,0,0,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[9,9,9,
9,9,9,9,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,-1,-1,-1,-1,3,3,3,3,3,
3,3,3,3,3,3,3,-1,-1,-1,-1,-1,0,0,0,0,0,0],
[TENSOR,[8,2]],[10,10,10,10,10,10,10,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,1,1,1,1,
1,1,1,0,0,0,0,0,0,0,0,0,0,2,2,2,2,2,-2,-2,-2,-2,-2,-2,-2,0,0,0,0,0,-1,-1,1,1,
1,1],
[TENSOR,[10,2]],[6,6,6,6,6,-3,-3,-2,-2,-2,-2,-2,-2,-2,-2,1,1,1,0,0,0,0,0,0,0,
2,2,2,2,-1,-1,1,1,-E(15)-E(15)^2-E(15)^4-E(15)^8,-E(15)^7-E(15)^11-E(15)^13
-E(15)^14,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[12,7]],[12,12,12,12,12,-6,-6,4,4,4,4,4,4,4,4,-2,-2,-2,0,0,0,0,0,0,0,
0,0,0,0,0,0,2,2,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[18,18,
18,18,18,-9,-9,2,2,2,2,2,2,2,2,-1,-1,-1,0,0,0,0,0,0,0,2,2,2,2,-1,-1,-2,-2,1,1,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[30,30,30,30,30,-15,-15,-2,-2,
-2,-2,-2,-2,-2,-2,1,1,1,0,0,0,0,0,0,0,-2,-2,-2,-2,1,1,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[18,18,-6,2,2,0,0,6,-2,6,6,-2,-2,2,-2,0,0,0,0,
0,3,3,3,-1,-1,0,0,0,0,0,0,3,-1,0,0,0,0,0,0,0,-4,-4,4,4,4,0,0,2,-2,2,-2,0,0,0,
-1,-1,1,1],
[TENSOR,[17,2]],[45,45,5,-3,-3,0,0,-3,5,-3,-3,5,5,1,-3,0,0,0,3,-1,0,0,0,0,0,
-3,1,-3,1,0,0,0,0,0,0,-5,-5,-1,3,3,3,3,3,3,3,-1,-1,-1,-1,-1,-1,1,1,-1,0,0,0,
0],
[TENSOR,[19,2]],[45,45,5,-3,-3,0,0,9,1,9,9,1,1,-3,1,0,0,0,3,-1,0,0,0,0,0,3,-1,
3,-1,0,0,0,0,0,0,7,7,-1,-1,-1,3,3,3,3,3,-1,-1,1,1,1,1,-1,1,-1,0,0,0,0],
[TENSOR,[21,2]],[60,-4,0,4,-4,15,-1,8,-4,0,-4,4,0,0,0,-1,3,-1,0,0,-3,5,-1,-1,
1,2,0,-2,0,-1,1,0,0,0,0,-6,2,0,2,-2,2,-2,-14,2,2,-2,2,2,0,-2,0,0,0,0,-1,1,-1,
1],
[TENSOR,[23,2]],[60,-4,0,4,-4,15,-1,0,4,8,-4,-4,0,0,0,3,-1,-1,0,0,-3,5,-1,-1,
1,-2,0,2,0,1,-1,0,0,0,0,-6,2,0,2,-2,2,-2,10,-6,2,2,-2,-2,0,2,0,0,0,0,-1,1,-1,
1],
[TENSOR,[25,2]],[72,72,-24,8,8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,3,3,3,-1,-1,0,0,
0,0,0,0,-3,1,0,0,0,0,0,0,0,8,8,-8,-8,-8,0,0,0,0,0,0,0,0,0,-1,-1,1,1],
[TENSOR,[27,2]],[90,90,-30,10,10,0,0,6,-2,6,6,-2,-2,2,-2,0,0,0,0,0,-3,-3,-3,1,
1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,4,4,-4,-4,-4,0,0,2,-2,2,-2,0,0,0,1,1,-1,-1],
[TENSOR,[29,2]],[90,90,10,-6,-6,0,0,6,6,6,6,6,6,-2,-2,0,0,0,-3,1,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,2,2,-2,2,2,6,6,6,6,6,-2,-2,0,0,0,0,0,-1,1,0,0,0,0],
[TENSOR,[31,2]],[108,108,-36,12,12,0,0,-12,4,-12,-12,4,4,-4,4,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,3,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[120,
-8,0,8,-8,30,-2,8,0,8,-8,0,0,0,0,2,2,-2,0,0,3,-5,1,1,-1,0,0,0,0,0,0,0,0,0,0,
12,-4,0,-4,4,-4,4,4,4,-4,0,0,0,0,0,0,0,0,0,-1,1,-1,1],
[TENSOR,[34,2]],[120,-8,0,8,-8,-15,1,0,8,16,-8,-8,0,0,0,-3,1,1,0,0,6,-2,-2,-2,
2,-4,0,4,0,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[120,
-8,0,8,-8,-15,1,16,-8,0,-8,8,0,0,0,1,-3,1,0,0,6,-2,-2,-2,2,4,0,-4,0,1,-1,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[135,135,15,-9,-9,0,0,3,-5,
3,3,-5,-5,-1,3,0,0,0,0,0,0,0,0,0,0,-3,1,-3,1,0,0,0,0,0,0,-9,-9,3,-1,-1,3,3,3,
3,3,-1,-1,1,1,1,1,-1,0,0,0,0,0,0],[135,135,15,-9,-9,0,0,-9,-1,-9,-9,-1,-1,3,
-1,0,0,0,0,0,0,0,0,0,0,3,-1,3,-1,0,0,0,0,0,0,-3,-3,-3,5,5,-3,-3,-3,-3,-3,1,1,
1,1,1,1,-1,0,0,0,0,0,0],
[TENSOR,[39,2]],
[TENSOR,[38,2]],[180,-12,0,-4,4,0,0,12,8,-12,0,0,-4,0,0,0,0,0,0,0,3,3,-3,1,-1,
0,-2,0,2,0,0,0,0,0,0,-6,2,0,-2,2,-2,2,-14,2,2,2,-2,0,-2,0,2,0,0,0,1,-1,-1,1],
[TENSOR,[42,2]],[180,-12,0,-4,4,0,0,-12,0,12,0,8,-4,0,0,0,0,0,0,0,3,3,-3,1,-1,
0,2,0,-2,0,0,0,0,0,0,-6,2,0,-2,2,-2,2,10,-6,2,-2,2,0,2,0,-2,0,0,0,1,-1,-1,1],
[TENSOR,[44,2]],[180,-12,0,12,-12,45,-3,0,-4,-8,4,4,0,0,0,-3,1,1,0,0,0,0,0,0,
0,-2,0,2,0,1,-1,0,0,0,0,-6,2,0,2,-2,-6,6,18,2,-6,2,-2,2,0,-2,0,0,0,0,0,0,0,0],
[TENSOR,[46,2]],[180,-12,0,12,-12,45,-3,-8,4,0,4,-4,0,0,0,1,-3,1,0,0,0,0,0,0,
0,2,0,-2,0,-1,1,0,0,0,0,6,-2,0,-2,2,6,-6,6,-10,6,2,-2,2,0,-2,0,0,0,0,0,0,0,0],
[TENSOR,[48,2]],[240,-16,0,16,-16,-30,2,16,0,16,-16,0,0,0,0,-2,-2,2,0,0,-6,2,
2,2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[360,-24,0,-8,8,0,0,0,8,0,0,8,-8,0,0,0,0,0,0,0,-3,-3,3,-1,1,0,0,0,0,0,0,0,0,0,
0,12,-4,0,4,-4,4,-4,4,4,-4,0,0,0,0,0,0,0,0,0,1,-1,-1,1],
[TENSOR,[51,2]],[360,-24,0,24,-24,-45,3,0,-8,-16,8,8,0,0,0,3,-1,-1,0,0,0,0,0,
0,0,-4,0,4,0,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[360,
-24,0,24,-24,-45,3,-16,8,0,8,-8,0,0,0,-1,3,-1,0,0,0,0,0,0,0,4,0,-4,0,1,-1,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[540,-36,0,-12,12,0,0,12,0,
-12,0,-8,4,0,0,0,0,0,0,0,0,0,0,0,0,0,2,0,-2,0,0,0,0,0,0,6,-2,0,2,-2,-6,6,-18,
-2,6,2,-2,0,2,0,-2,0,0,0,0,0,0,0],
[TENSOR,[55,2]],[540,-36,0,-12,12,0,0,-12,-8,12,0,0,4,0,0,0,0,0,0,0,0,0,0,0,0,
0,-2,0,2,0,0,0,0,0,0,6,-2,0,2,-2,-6,6,6,-10,6,-2,2,0,-2,0,2,0,0,0,0,0,0,0],
[TENSOR,[57,2]]],
[(34,35)]);
ALF("2^(4+6):3S6","Suz.2",[1,2,3,7,8,4,13,2,3,7,9,9,8,19,18,13,25,27,6,16,
5,15,14,29,26,9,10,18,20,27,37,12,23,33,33,38,40,41,49,47,39,40,46,47,48,
48,49,41,40,50,49,58,44,56,43,55,63,62],[
"fusion map is unique"
]);
ALF("2^(4+6):3S6","3.A6.2_1",[1,1,1,1,1,2,2,3,3,3,3,3,3,3,3,4,4,4,5,5,6,6,
6,6,6,7,7,7,7,8,8,9,9,10,11,12,12,12,12,12,13,13,13,13,13,13,13,14,14,14,
14,14,15,15,16,16,16,16]);

MOT("(A4xL3(4):2_3):2",
[
"9th maximal subgroup of Suz.2,\n",
"origin: Dixon's Algorithm"
],
[967680,322560,120960,3072,1024,432,54,768,384,256,128,120,384,144,168,40,96,
48,56,30,30,21,576,576,64,64,72,32,32,16,16,72,2880,1344,960,1344,64,64,360,
144,48,24,18,384,384,128,128,32,32,120,40,24,28,48,48,28,30,30],
[,[1,1,3,1,1,6,7,4,4,4,4,12,3,6,15,12,13,13,15,20,21,22,1,2,4,5,6,8,10,9,11,
14,1,1,1,2,4,5,3,6,6,6,7,8,8,8,8,8,10,12,12,14,15,17,17,19,21,20],[1,2,1,4,5,
1,1,8,9,10,11,12,4,2,15,16,8,9,19,12,12,15,23,24,25,26,23,28,29,30,31,24,33,
34,35,36,37,38,33,33,35,34,33,44,45,46,47,48,49,50,51,36,53,44,45,56,50,50],,
[1,2,3,4,5,6,7,8,9,10,11,1,13,14,15,2,17,18,19,3,3,22,23,24,25,26,27,28,29,30,
31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,33,35,52,53,54,55,56,
39,39],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,1,16,17,18,2,21,20,3,23,24,25,26,27,
28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,34,
54,55,36,58,57]],
0,
[(20,21)(57,58)],
["ConstructIndexTwoSubdirectProduct","a4","Symm(4)","L3(4).2_3","L3(4).2^2",
[74,75,76,77,78,79,80,81,82,83,96,97,98,99,100,101,102,103,104,105],(2,4,8,33,
39,23,47,48,53,31,20,35,54,36,55,38,58,56,52,29,18,16,10,44,34,43,30,21,41,27,
7,15,14,5,9,40,25,3,6,12,50,26,13)(11,45,37,57,49,24,51,32,22,46,42,28,17),(2,
3)(6,7)(9,10,11,12)(13,18,22,14,17,21,15,20)(16,19)(27,28)(29,35,33,30,36,34,
31)(38,40)(41,43,44,42)(45,47)(49,53,57,50,54,58,51,55)(52,56)]);
ALF("(A4xL3(4):2_3):2","Symm(4)",[1,2,3,1,2,1,3,1,1,2,2,1,3,2,1,2,3,3,2,3,3,
3,4,5,4,5,4,4,5,4,5,5,1,4,2,5,4,5,3,1,2,4,3,1,1,2,2,4,5,1,2,5,4,3,3,5,3,3]);
ALF("(A4xL3(4):2_3):2","L3(4).2^2",[1,1,1,2,2,3,3,4,5,4,5,6,2,3,7,6,4,5,7,
6,6,7,8,8,9,9,10,11,11,12,12,10,18,13,18,13,14,14,18,19,19,15,19,20,21,20,
21,16,16,22,22,15,17,20,21,17,22,22]);
ALF("(A4xL3(4):2_3):2","Suz.2",[1,3,4,2,3,6,6,7,9,9,8,12,13,16,17,23,25,
27,31,33,33,36,3,10,9,10,16,18,20,20,19,28,38,38,39,41,40,41,42,44,45,44,
44,46,47,49,49,49,50,51,53,56,57,60,61,65,66,66],[
"fusion map is unique"
]);

MOT("2^(2+8):(S5xS3)",
[
"10th maximal subgroup of Suz.2,\n",
"origin: Dixon's Algorithm"
],
[737280,245760,12288,3072,6144,3072,2048,768,2304,512,512,120,768,96,128,128,
40,192,96,360,72,24,24,15,7680,512,7680,768,512,256,64,96,384,128,64,64,20,96,
24,20,48,4608,768,768,768,512,128,96,64,32,144,96,72,36,24,3072,3072,512,384,
256,256,192,128,64,64,64,64,96,12,16,96,96,48,24],
[,[1,1,1,1,2,2,2,1,9,3,3,12,9,9,5,7,12,13,13,20,21,20,21,24,1,1,2,3,2,3,4,9,5,
5,6,7,12,13,14,17,18,1,1,1,2,2,3,8,4,8,9,9,21,20,21,5,5,5,5,5,5,6,5,11,11,11,
11,13,22,16,18,18,18,19],[1,2,3,4,5,6,7,8,1,10,11,12,2,3,15,16,17,5,6,1,1,8,4,
12,25,26,27,28,29,30,31,25,33,34,35,36,37,27,28,40,33,42,43,44,45,46,47,48,49,
50,42,43,42,42,44,56,57,58,59,60,61,62,63,64,65,66,67,45,48,70,57,56,59,62],,
[1,2,3,4,5,6,7,8,9,10,11,1,13,14,15,16,2,18,19,20,21,22,23,20,25,26,27,28,29,
30,31,32,33,34,35,36,25,38,39,27,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,
56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
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-1,-1,-1,-1,-1,-1,-1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,-1,1,-1,1,-1,1,1,-1,1,-1,-1,
-1,-1,-1,-1,1,-1,-1,1,1,1,1,-1,-1,1,-1,1,-1,-1,1,1],
[TENSOR,[2,3]],[2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,-1,-1,-1,-1,-1,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,2,0,2,0,2,0,2,0,0,2,0,-1,-1,-1,2,2,2,0,2,2,0,0,0,0,
2,2,0,-1,0,2,2,0,0],
[TENSOR,[5,2]],[4,4,4,4,4,4,4,0,1,0,0,-1,1,1,0,0,-1,1,1,4,1,0,1,-1,-4,0,-4,-4,
0,0,0,-1,-4,0,0,0,1,-1,-1,1,-1,-2,2,-2,2,-2,2,0,2,0,1,-1,1,-2,1,-2,-2,-2,2,-2,
-2,2,2,0,0,0,0,-1,0,0,1,1,-1,-1],
[TENSOR,[7,3]],
[TENSOR,[7,4]],
[TENSOR,[7,2]],[5,5,5,5,5,5,5,1,-1,1,1,0,-1,-1,1,1,0,-1,-1,5,-1,1,-1,0,-5,-1,
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1,-1,1,1,-1,-1,1,1,-1,-1,-1,-1,1,1,1,-1,-1],
[TENSOR,[11,3]],
[TENSOR,[11,4]],
[TENSOR,[11,2]],[6,6,6,6,6,6,6,-2,0,-2,-2,1,0,0,-2,-2,1,0,0,6,0,-2,0,1,-6,2,
-6,-6,2,2,2,0,-6,2,2,2,-1,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[15,3]],[8,8,8,8,8,8,8,0,2,0,0,-2,2,2,0,0,-2,2,2,-4,-1,0,-1,1,0,0,0,0,
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0,0,0,0,0,0,0,0,2,2,0,0],
[TENSOR,[17,2]],[10,10,10,10,10,10,10,2,-2,2,2,0,-2,-2,2,2,0,-2,-2,-5,1,-1,1,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,0,2,0,2,0,-2,0,0,2,0,-1,-1,-1,2,2,2,0,2,
2,0,0,0,0,-2,-2,0,1,0,2,2,0,0],
[TENSOR,[19,2]],[12,12,12,12,12,12,12,-4,0,-4,-4,2,0,0,-4,-4,2,0,0,-6,0,2,0,
-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0],[15,15,-1,3,7,-5,-1,3,6,3,3,0,6,2,-1,-1,0,-2,-2,0,
0,0,0,0,5,1,5,-3,1,1,-1,2,1,1,-1,1,0,2,0,0,-2,-9,-3,3,-3,-1,1,-3,-1,-1,0,0,0,
0,0,3,3,-5,-3,-1,3,3,1,-1,-1,1,1,0,0,1,0,0,0,0],
[TENSOR,[22,3]],
[TENSOR,[22,4]],
[TENSOR,[22,2]],[30,30,-2,6,14,-10,-2,6,-6,6,6,0,-6,-2,-2,-2,0,2,2,0,0,0,0,0,
10,2,10,-6,2,2,-2,-2,2,2,-2,2,0,-2,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[26,3]],[30,30,14,-6,6,2,-2,6,3,-2,-2,0,3,-1,2,-2,0,3,-1,0,0,0,0,0,10,
2,10,2,2,2,0,1,-2,2,0,-2,0,1,-1,0,1,-12,-4,0,-4,-4,0,0,2,0,-3,-1,0,0,0,-8,-8,
0,-4,4,0,-2,0,0,0,0,0,-1,0,0,1,1,-1,1],
[TENSOR,[28,3]],
[TENSOR,[28,4]],
[TENSOR,[28,2]],[30,30,14,-6,6,2,-2,-6,3,2,2,0,3,-1,-2,2,0,3,-1,0,0,0,0,0,-10,
2,-10,-2,2,2,0,-1,2,2,0,-2,0,-1,1,0,-1,6,-2,-6,-2,-2,2,0,0,0,-3,1,0,0,0,10,10,
2,-2,-2,2,-4,2,0,0,0,0,1,0,0,1,1,1,-1],
[TENSOR,[32,2]],
[TENSOR,[32,3]],
[TENSOR,[32,4]],[45,45,-3,9,21,-15,-3,-3,0,-3,-3,0,0,0,1,1,0,0,0,0,0,0,0,0,
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-3,5,-3,1,-3,3,1,1,1,1,1,0,0,-1,0,0,0,0],
[TENSOR,[36,2]],
[TENSOR,[36,3]],
[TENSOR,[36,4]],[60,60,28,-12,12,4,-4,0,-3,0,0,0,-3,1,0,0,0,-3,1,0,0,0,0,0,20,
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-2,2,2,2,-2,0,0,0,0,1,0,0,-1,-1,1,-1],
[TENSOR,[40,3]],
[TENSOR,[40,4]],
[TENSOR,[40,2]],[60,60,-20,0,4,8,-4,0,6,0,0,0,6,-2,0,0,0,-2,2,0,0,0,0,0,0,-4,
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2,0,-2,0,0,0,0,-2,0,0,0,0,2,0],
[TENSOR,[44,3]],
[TENSOR,[44,4]],
[TENSOR,[44,2]],[60,60,12,8,-12,0,-4,0,0,0,0,0,0,0,0,0,0,0,0,0,3,0,-1,0,0,4,0,
0,4,-4,-2,0,0,0,2,0,0,0,0,0,0,-6,-6,-2,-6,2,-2,0,0,0,0,0,-3,0,1,-6,-6,2,6,-2,
2,0,2,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[48,3]],
[TENSOR,[48,4]],
[TENSOR,[48,2]],[90,90,-6,-6,-6,-6,10,6,0,-2,-2,0,0,0,-2,2,0,0,0,0,0,0,0,0,0,
-4,0,0,-4,-4,0,0,0,4,0,0,0,0,0,0,0,-18,0,6,0,-2,0,0,0,2,0,0,0,0,0,6,6,6,0,-2,
-2,0,0,-2,-2,0,0,0,0,0,0,0,0,0],
[TENSOR,[52,4]],
[TENSOR,[52,2]],
[TENSOR,[52,3]],[120,120,24,16,-24,0,-8,0,0,0,0,0,0,0,0,0,0,0,0,0,-3,0,1,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-12,0,-4,0,4,0,0,0,0,0,0,3,0,-1,-12,-12,4,0,
-4,4,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[56,2]],[120,120,-40,0,8,16,-8,0,-6,0,0,0,-6,2,0,0,0,2,-2,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-4,0,-4,0,4,0,0,0,0,2,0,0,0,0,0,0,4,0,0,0,
-4,0,0,0,0,2,0,0,0,0,-2,0],
[TENSOR,[58,2]],[180,180,-12,-12,-12,-12,20,-12,0,4,4,0,0,0,4,-4,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0],[48,-16,0,0,0,0,0,0,12,-4,4,3,-4,0,0,0,-1,0,0,0,0,
0,0,0,-4,4,4,0,-4,0,0,2,0,0,0,0,1,-2,0,-1,0,0,4,0,-4,0,0,0,0,0,0,-2,0,0,0,-8,
8,0,0,0,0,0,0,-2,2,-2,2,2,0,0,2,-2,0,0],
[TENSOR,[61,3]],
[TENSOR,[61,4]],
[TENSOR,[61,2]],[192,-64,0,0,0,0,0,0,12,0,0,-3,-4,0,0,0,1,0,0,0,0,0,0,0,-16,0,
16,0,0,0,0,2,0,0,0,0,-1,-2,0,1,0,0,-8,0,8,0,0,0,0,0,0,-2,0,0,0,16,-16,0,0,0,0,
0,0,0,0,0,0,2,0,0,2,-2,0,0],
[TENSOR,[65,3]],
[TENSOR,[65,4]],
[TENSOR,[65,2]],[240,-80,0,0,0,0,0,0,-12,-4,4,0,4,0,0,0,0,0,0,0,0,0,0,0,-20,4,
20,0,-4,0,0,-2,0,0,0,0,0,2,0,0,0,0,4,0,-4,0,0,0,0,0,0,-2,0,0,0,-8,8,0,0,0,0,0,
0,2,-2,2,-2,2,0,0,2,-2,0,0],
[TENSOR,[69,3]],
[TENSOR,[69,4]],
[TENSOR,[69,2]],[288,-96,0,0,0,0,0,0,0,8,-8,3,0,0,0,0,-1,0,0,0,0,0,0,0,-24,-8,
24,0,8,0,0,0,0,0,0,0,1,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0],
[TENSOR,[73,3]]],
[]);
ALF("2^(2+8):(S5xS3)","Suz.2",[1,2,2,3,7,9,8,3,4,8,7,11,13,13,18,19,22,25,
27,6,6,16,16,32,2,3,7,9,9,8,10,13,18,18,20,19,22,25,27,35,37,38,38,39,40,
40,40,41,41,41,42,42,44,44,45,46,47,47,47,49,48,50,49,49,47,48,49,54,56,
58,61,60,61,64],[
"fusion map is unique"
]);
ALF("2^(2+8):(S5xS3)","S5xS3",[1,1,1,1,1,1,1,4,7,4,4,10,7,7,4,4,10,7,7,2,
8,5,8,11,3,6,3,3,6,6,6,9,3,6,6,6,12,9,9,12,9,13,15,13,15,13,15,16,15,18,
19,21,20,14,20,13,13,13,15,13,13,15,15,18,18,16,16,21,17,18,19,19,21,21]);

MOT("M12.2x2",
[
"11th maximal subgroup of Suz.2",
],
0,
0,
0,
[(25,26)(27,28)(29,30)(31,32)(33,34)(35,36)(37,38)(39,40)(41,42),(39,41)(40,
42),(33,35)(34,36)],
["ConstructDirectProduct",[["M12.2"],["Cyclic",2]]]);
ALF("M12.2x2","Suz.2",[1,39,3,38,2,39,5,43,6,45,9,40,12,53,16,44,15,43,
20,50,23,51,24,59,3,39,8,40,10,41,16,45,23,53,23,53,28,56,29,55,29,55],[
"fusion map is unique up to table automorphisms"
]);

MOT("3^(2+4):2(S4xD8)",
[
"12th maximal subgroup of Suz.2,\n",
"origin: Dixon's Algorithm"
],
[279936,69984,69984,648,972,3456,864,864,576,144,144,3888,972,972,54,432,108,
108,576,72,192,24,108,108,108,18,2592,1296,108,96,48,36,288,32,16,24,48,48,24,
864,432,36,288,144,36,36,36,24,24,32,192,192,36,432,216,36,24,48,288,72,72,72,
72,288,36,288,64,64],
[,[1,2,3,4,5,1,2,3,6,7,8,12,13,14,15,12,13,14,1,4,6,16,12,14,14,15,1,3,5,6,8,
20,19,19,21,10,9,6,7,1,2,4,6,7,16,17,17,22,22,21,21,21,5,1,3,4,11,9,9,10,11,8,
7,6,5,1,9,9],[1,1,1,1,1,6,6,6,9,9,9,1,1,1,3,6,6,6,19,19,21,21,27,27,27,28,27,
27,27,30,30,33,33,34,35,37,37,38,38,40,40,40,43,43,43,43,43,51,52,50,51,52,54,
54,54,54,58,58,59,59,59,64,64,64,66,66,67,68]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,-1,
-1,-1,-1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,
-1,-1],
[TENSOR,[2,3]],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1],
[TENSOR,[2,5]],
[TENSOR,[3,5]],
[TENSOR,[2,7]],[2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,-2,-2,-2,-2,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,-2,-2,-2,-2,-2,2,
2,2,2],
[TENSOR,[9,2]],[2,2,2,2,2,2,2,2,2,2,2,-1,-1,-1,-1,-1,-1,-1,2,2,2,-1,-1,-1,-1,
-1,2,2,2,2,2,0,0,0,0,0,0,0,0,-2,-2,-2,-2,-2,1,1,1,1,1,-2,-2,-2,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0],
[TENSOR,[11,3]],
[TENSOR,[11,2]],
[TENSOR,[11,4]],[3,3,3,3,3,3,3,3,-1,-1,-1,0,0,0,0,0,0,0,-1,-1,3,0,0,0,0,0,-3,
-3,-3,1,1,-1,-1,-1,1,1,1,-1,-1,-1,-1,-1,3,3,0,0,0,0,0,1,-3,-3,1,1,1,1,-1,-1,1,
1,1,-1,-1,-1,-1,-1,1,1],
[TENSOR,[15,5]],
[TENSOR,[15,3]],
[TENSOR,[15,7]],
[TENSOR,[15,2]],
[TENSOR,[15,6]],
[TENSOR,[15,4]],
[TENSOR,[15,8]],[4,4,4,4,4,4,4,4,4,4,4,-2,-2,-2,-2,-2,-2,-2,-4,-4,-4,2,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0],[4,4,4,4,4,-4,-4,-4,0,0,0,-2,-2,-2,-2,2,2,2,0,0,0,0,0,0,0,0,0,0,0,0,
0,-2,-2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,-E(8)-E(8)^3,E(8)+E(8)^3,0,2*E(8)
+2*E(8)^3,-2*E(8)-2*E(8)^3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2*E(8)+2*E(8)^3,-2*E(8)
-2*E(8)^3],
[TENSOR,[24,5]],
[TENSOR,[24,2]],
[TENSOR,[24,6]],[6,6,6,6,6,6,6,6,-2,-2,-2,0,0,0,0,0,0,0,2,2,-6,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,-2,-2,2,2,2,-2,
-2,2,2],
[TENSOR,[28,2]],[8,8,8,8,8,-8,-8,-8,0,0,0,2,2,2,2,-2,-2,-2,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-E(8)-E(8)^3,E(8)+E(8)^3,0,-4*E(8)
-4*E(8)^3,4*E(8)+4*E(8)^3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[30,2]],[32,32,32,-4,5,0,0,0,0,0,0,8,8,8,-1,0,0,0,0,0,0,0,-2,-2,-2,1,
-8,-8,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-4,-4,2,0,0,0,0,0,0,
0,0,-1,8,0,0],
[TENSOR,[32,2]],
[TENSOR,[32,3]],
[TENSOR,[32,4]],[36,-18,9,0,0,4,-2,1,4,-2,1,12,-6,3,0,4,-2,1,0,0,0,0,0,-3,3,0,
-6,3,0,2,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-6,3,0,1,-2,-4,2,-1,1,
-2,4,0,0,0,0],
[TENSOR,[36,2]],
[TENSOR,[36,3]],
[TENSOR,[36,4]],[36,9,-18,0,0,4,1,-2,4,1,-2,-12,-3,6,0,4,1,-2,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,-1,2,-2,1,-6,3,0,2,-1,2,-1,-1,0,0,0,0,0,0,0,0,0,0,0,4,1,-2,
2,-1,-4,0,0,0,0],
[TENSOR,[40,3]],
[TENSOR,[40,2]],
[TENSOR,[40,4]],[48,48,48,3,-6,0,0,0,0,0,0,0,0,0,0,0,0,0,8,-1,0,0,0,0,0,0,0,0,
0,0,0,-1,8,0,0,0,0,0,0,-8,-8,1,0,0,0,0,0,0,0,0,0,0,2,-4,-4,-1,0,0,0,0,0,0,0,0,
0,0,0,0],
[TENSOR,[44,5]],
[TENSOR,[44,2]],
[TENSOR,[44,6]],[64,64,64,-8,10,0,0,0,0,0,0,-8,-8,-8,1,0,0,0,0,0,0,0,-2,-2,-2,
1,16,16,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0],
[TENSOR,[48,3]],[72,-36,18,0,0,8,-4,2,8,-4,2,-12,6,-3,0,-4,2,-1,0,0,0,0,0,-3,
3,0,12,-6,0,-4,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0],
[TENSOR,[50,3]],[72,18,-36,0,0,8,2,-4,8,2,-4,12,3,-6,0,-4,-1,2,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,-12,6,0,4,-2,-2,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0],
[TENSOR,[52,2]],[96,96,96,6,-12,0,0,0,0,0,0,0,0,0,0,0,0,0,-16,2,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0],[108,-54,27,0,0,12,-6,3,-4,2,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-18,9,0,-2,
1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-6,3,0,-1,2,4,-2,1,1,-2,4,0,0,0,
0],
[TENSOR,[55,2]],
[TENSOR,[55,3]],
[TENSOR,[55,4]],[108,27,-54,0,0,12,3,-6,-4,-1,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,-1,2,2,-1,-6,3,0,-6,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-4,-1,2,2,
-1,-4,0,0,0,0],
[TENSOR,[59,3]],
[TENSOR,[59,2]],
[TENSOR,[59,4]],[144,-72,36,0,0,-16,8,-4,0,0,0,12,-6,3,0,-4,2,-1,0,0,0,0,-6,3,
3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0],
[TENSOR,[63,3]],[144,-72,36,0,0,-16,8,-4,0,0,0,-24,12,-6,0,8,-4,2,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0],[144,36,-72,0,0,-16,-4,8,0,0,0,24,6,-12,0,8,2,-4,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0],[144,36,-72,0,0,-16,-4,8,0,0,0,-12,-3,6,0,-4,-1,2,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-3*E(4),3*E(4),0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0],
[TENSOR,[67,2]]],
[(46,47),(48,49)(51,52)(67,68)]);
ALF("3^(2+4):2(S4xD8)","Suz.2",[1,4,5,6,5,2,13,15,7,25,26,4,5,5,21,13,15,
14,3,16,9,27,13,14,15,34,2,14,15,8,29,28,10,10,20,37,18,9,27,38,42,44,40,
54,54,55,55,64,64,50,50,50,43,39,43,45,63,48,46,60,62,55,54,40,43,39,49,
49],[
"fusion map is unique"
]);

MOT("(A6:2_2xA5).2",
[
"13th maximal subgroup of Suz.2,\n",
"origin: Dixon's Algorithm"
],
[86400,1920,1080,960,600,5760,128,4320,54,64,3600,50,50,96,72,80,40,48,45,30,
40,48,16,48,16,24,24,2400,288,160,96,96,32,144,120,36,18,480,32,600,100,50,50,
40,48,12,24,30,40,40],
[,[1,1,3,2,5,1,1,8,9,2,11,12,13,8,3,11,5,14,19,20,16,2,7,4,10,14,18,1,1,1,2,6,
7,8,8,3,9,4,4,5,11,13,12,5,14,15,18,20,21,21],[1,2,1,4,5,6,7,1,1,10,11,12,13,
2,6,16,17,4,11,5,21,22,23,24,25,22,24,28,29,30,31,32,33,29,28,29,29,38,39,40,
41,42,43,44,31,32,38,40,49,50],,[1,2,3,4,1,6,7,8,9,10,1,1,1,14,15,2,6,18,3,8,
4,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,28,28,28,28,30,45,46,
47,35,38,38]],
0,
[(49,50),(12,13)(42,43)],
["ConstructIndexTwoSubdirectProduct","A5","A5.2","A6.2_2","A6.2^2",[58,59,60,
64,65,71,72,73,77,78,84,85,86,90,91],(6,28,21,20,18,14,30,13,17,8,40,24,48,37,
31,41,32,49,26,16,44,23,47,45,25,11,15,39,22,35,42,33,50,27,19,9)(7,38,36,29,
12,10)(34,43,46),(2,3,4)(5,19,36,26,7,21,41,10,16,42,38,12,17,37,49,32,46,30,
29,28,6,20,34,25,8,22,40,9,15,14,13,23,44,47,31,45,48,33,24,43,39,11,18,35,
27)]);
ALF("(A6:2_2xA5).2","A5.2",[1,1,1,1,1,2,2,3,3,2,4,4,4,3,2,4,2,3,4,3,4,5,6,
5,6,7,7,1,5,2,5,6,6,7,3,5,7,1,2,1,4,4,4,2,7,6,3,3,4,4]);
ALF("(A6:2_2xA5).2","A6.2^2",[1,2,3,4,5,1,2,1,3,4,1,5,5,2,3,2,5,4,3,5,4,
12,12,13,13,12,13,9,6,9,7,6,7,6,9,8,8,10,10,11,9,11,11,11,7,8,10,11,10,10]);
ALF("(A6:2_2xA5).2","Suz.2",[1,2,6,7,12,3,3,4,6,9,11,11,12,13,16,22,23,25,
32,33,35,9,10,18,20,27,37,38,38,39,40,41,41,42,42,44,44,46,49,51,52,51,52,
53,54,56,60,66,68,67],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables"
]);

MOT("(3^2:8xA6).2",
[
"14th maximal subgroup of Suz.2,\n",
"normalizer of a 3C^2 subgroup,\n",
"sorted according to chief series 3^2.2.2.2.A6.2,\n",
"origin: Dixon's Algorithm"
],
[51840,6480,5760,2880,2880,2880,1152,288,288,128,1296,1296,162,162,576,64,64,
48,32,360,144,144,144,144,144,36,36,18,18,40,72,72,72,24,45,40,40,64,64,32,32,
72,72,72,72,40,40,40,40,96,96,16,12,12],
[,[1,2,1,3,4,4,1,1,1,1,11,12,13,14,7,3,7,7,10,20,2,2,2,11,12,11,12,13,14,20,
24,25,22,22,35,30,30,4,4,16,16,31,31,32,32,36,36,37,37,3,3,10,24,25],[1,1,3,4,
5,6,7,8,9,10,1,1,1,1,15,16,17,18,19,20,8,7,9,3,3,8,9,8,9,30,4,4,15,18,20,36,
37,38,39,40,41,6,5,6,5,46,47,48,49,50,51,52,50,51],,[1,2,3,4,6,5,7,8,9,10,11,
12,13,14,15,16,17,18,19,1,21,22,23,24,25,26,27,28,29,3,31,32,33,34,2,4,4,39,
38,41,40,43,42,45,44,6,5,6,5,50,51,52,53,54]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,-1,-1,1,1,1,1,1,1,1,1,-1,1,1,
-1,1,-1,1,1,-1,-1,-1,-1,1,1,1,1,-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,
-1],[5,5,5,5,5,5,1,-3,1,1,2,-1,2,-1,-1,1,-1,-1,-1,0,-3,1,1,2,-1,0,1,0,1,0,2,
-1,-1,-1,0,0,0,1,1,-1,-1,2,2,-1,-1,0,0,0,0,-3,1,-1,0,1],[5,5,5,5,5,5,1,-1,3,1,
-1,2,-1,2,-1,1,-1,1,-1,0,-1,1,3,-1,2,-1,0,-1,0,0,-1,2,-1,1,0,0,0,1,1,-1,-1,-1,
-1,2,2,0,0,0,0,-1,3,1,-1,0],
[TENSOR,[4,2]],
[TENSOR,[3,2]],[9,9,9,9,9,9,1,-3,-3,1,0,0,0,0,1,1,1,1,1,-1,-3,1,-3,0,0,0,0,0,
0,-1,0,0,1,1,-1,-1,-1,1,1,1,1,0,0,0,0,-1,-1,-1,-1,-3,-3,1,0,0],
[TENSOR,[7,2]],[10,10,10,10,10,10,-2,-2,2,-2,1,1,1,1,0,-2,0,0,0,0,-2,-2,2,1,1,
1,-1,1,-1,0,1,1,0,0,0,0,0,-2,-2,0,0,1,1,1,1,0,0,0,0,-2,2,0,1,-1],
[TENSOR,[9,2]],[16,16,16,16,16,16,0,0,0,0,-2,-2,-2,-2,0,0,0,0,0,1,0,0,0,-2,-2,
0,0,0,0,1,-2,-2,0,0,1,1,1,0,0,0,0,-2,-2,-2,-2,1,1,1,1,0,0,0,0,0],[1,1,1,1,-1,
-1,1,-1,-1,1,1,1,1,1,1,1,1,-1,1,1,-1,1,-1,1,1,-1,-1,-1,-1,1,1,1,1,-1,1,1,1,-1,
-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1],
[TENSOR,[2,12]],
[TENSOR,[3,13]],
[TENSOR,[4,13]],
[TENSOR,[4,12]],
[TENSOR,[3,12]],
[TENSOR,[7,13]],
[TENSOR,[7,12]],
[TENSOR,[9,13]],
[TENSOR,[9,12]],
[TENSOR,[11,12]],[2,2,2,-2,0,0,2,0,0,2,2,2,2,2,2,-2,2,0,-2,2,0,2,0,2,2,0,0,0,
0,2,-2,-2,2,0,2,-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[10,10,10,-10,0,0,2,
0,0,2,4,-2,4,-2,-2,-2,-2,0,2,0,0,2,0,4,-2,0,0,0,0,0,-4,2,-2,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0],[10,10,10,-10,0,0,2,0,0,2,-2,4,-2,4,-2,-2,-2,0,2,0,0,
2,0,-2,4,0,0,0,0,0,2,-4,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[16,16,
16,-16,0,0,0,0,0,0,-2,-2,-2,-2,0,0,0,0,0,1,0,0,0,-2,-2,0,0,0,0,1,2,2,0,0,1,-1,
-1,0,0,0,0,0,0,0,0,-E(20)-E(20)^9+E(20)^13+E(20)^17,-E(20)-E(20)^9+E(20)^13+
E(20)^17,E(20)+E(20)^9-E(20)^13-E(20)^17,E(20)+E(20)^9-E(20)^13-E(20)^17,0,0,
0,0,0],
[TENSOR,[26,12]],[18,18,18,-18,0,0,2,0,0,2,0,0,0,0,2,-2,2,0,-2,-2,0,2,0,0,0,0,
0,0,0,-2,0,0,2,0,-2,2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[20,20,20,-20,0,0,
-4,0,0,-4,2,2,2,2,0,4,0,0,0,0,0,-4,0,2,2,0,0,0,0,0,-2,-2,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0],[2,2,-2,0,-E(8)-E(8)^3,E(8)+E(8)^3,2,0,0,-2,2,2,2,2,
2,0,-2,0,0,2,0,2,0,-2,-2,0,0,0,0,-2,0,0,2,0,2,0,0,E(8)+E(8)^3,-E(8)-E(8)^3,
-E(8)-E(8)^3,E(8)+E(8)^3,E(8)+E(8)^3,-E(8)-E(8)^3,E(8)+E(8)^3,-E(8)-E(8)^3,
-E(8)-E(8)^3,E(8)+E(8)^3,-E(8)-E(8)^3,E(8)+E(8)^3,0,0,0,0,0],
[TENSOR,[30,12]],[10,10,-10,0,-5*E(8)-5*E(8)^3,5*E(8)+5*E(8)^3,2,0,0,-2,4,-2,
4,-2,-2,0,2,0,0,0,0,2,0,-4,2,0,0,0,0,0,0,0,-2,0,0,0,0,E(8)+E(8)^3,-E(8)-
E(8)^3,E(8)+E(8)^3,-E(8)-E(8)^3,2*E(8)+2*E(8)^3,-2*E(8)-2*E(8)^3,-E(8)-E(8)^3,
E(8)+E(8)^3,0,0,0,0,0,0,0,0,0],
[TENSOR,[32,12]],[10,10,-10,0,-5*E(8)-5*E(8)^3,5*E(8)+5*E(8)^3,2,0,0,-2,-2,4,
-2,4,-2,0,2,0,0,0,0,2,0,2,-4,0,0,0,0,0,0,0,-2,0,0,0,0,E(8)+E(8)^3,-E(8)
-E(8)^3,E(8)+E(8)^3,-E(8)-E(8)^3,-E(8)-E(8)^3,E(8)+E(8)^3,2*E(8)+2*E(8)^3,
-2*E(8)-2*E(8)^3,0,0,0,0,0,0,0,0,0],
[TENSOR,[34,12]],[16,16,-16,0,-8*E(8)-8*E(8)^3,8*E(8)+8*E(8)^3,0,0,0,0,-2,-2,
-2,-2,0,0,0,0,0,1,0,0,0,2,2,0,0,0,0,-1,0,0,0,0,1,E(20)+E(20)^9-E(20)^13
-E(20)^17,-E(20)-E(20)^9+E(20)^13+E(20)^17,0,0,0,0,-E(8)-E(8)^3,E(8)+E(8)^3,
-E(8)-E(8)^3,E(8)+E(8)^3,E(40)^13+E(40)^31+E(40)^37+E(40)^39,-E(40)^13
-E(40)^31-E(40)^37-E(40)^39,E(40)^7+E(40)^21+E(40)^23+E(40)^29,-E(40)^7
-E(40)^21-E(40)^23-E(40)^29,0,0,0,0,0],
[GALOIS,[36,11]],
[TENSOR,[37,12]],
[TENSOR,[36,12]],[18,18,-18,0,-9*E(8)-9*E(8)^3,9*E(8)+9*E(8)^3,2,0,0,-2,0,0,0,
0,2,0,-2,0,0,-2,0,2,0,0,0,0,0,0,0,2,0,0,2,0,-2,0,0,E(8)+E(8)^3,-E(8)-E(8)^3,
-E(8)-E(8)^3,E(8)+E(8)^3,0,0,0,0,E(8)+E(8)^3,-E(8)-E(8)^3,E(8)+E(8)^3,-E(8)
-E(8)^3,0,0,0,0,0],
[TENSOR,[40,12]],[20,20,-20,0,-10*E(8)-10*E(8)^3,10*E(8)+10*E(8)^3,-4,0,0,4,2,
2,2,2,0,0,0,0,0,0,0,-4,0,-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,-2*E(8)-2*E(8)^3,2*E(8)
+2*E(8)^3,0,0,E(8)+E(8)^3,-E(8)-E(8)^3,E(8)+E(8)^3,-E(8)-E(8)^3,0,0,0,0,0,0,0,
0,0],
[TENSOR,[42,12]],[8,-1,0,0,0,0,8,-2,-2,0,8,8,-1,-1,8,0,0,-2,0,8,1,-1,1,0,0,-2,
-2,1,1,0,0,0,-1,1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[44,2]],[40,-5,0,0,0,0,8,6,-2,0,16,-8,-2,1,-8,0,0,2,0,0,-3,-1,1,0,0,0,
-2,0,1,0,0,0,1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[40,-5,0,0,0,0,8,2,
-6,0,-8,16,1,-2,-8,0,0,-2,0,0,-1,-1,3,0,0,2,0,-1,0,0,0,0,1,1,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[47,2]],
[TENSOR,[46,2]],[72,-9,0,0,0,0,8,6,6,0,0,0,0,0,8,0,0,-2,0,-8,-3,-1,-3,0,0,0,0,
0,0,0,0,0,-1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[50,2]],[80,-10,0,0,0,0,-16,4,-4,0,8,8,-1,-1,0,0,0,0,0,0,-2,2,2,0,0,
-2,2,1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[52,2]],[128,-16,0,0,0,0,0,0,0,0,-16,-16,2,2,0,0,0,0,0,8,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]],
[(36,37)(46,48)(47,49),( 5, 6)(38,39)(40,41)(42,43)(44,45)(46,47)(48,49),( 8,
 9)(11,12)(13,14)(21,23)(24,25)(26,27)(28,29)(31,32)(42,44)(43,45)(50,51)(53,
54)]);
ALF("(3^2:8xA6).2","3^2:Q8.2",[1,4,2,5,8,9,1,3,3,2,1,1,4,4,1,5,2,3,5,1,7,
4,7,2,2,3,3,7,7,2,5,5,4,7,4,5,5,9,8,8,9,9,8,9,8,8,9,8,9,6,6,6,6,6]);
ALF("(3^2:8xA6).2","A6.2_1",[1,1,1,1,1,1,2,7,8,2,3,4,3,4,5,2,5,9,5,6,7,2,
8,3,4,10,11,10,11,6,3,4,5,9,6,6,6,2,2,5,5,3,3,4,4,6,6,6,6,7,8,9,10,11]);
ALF("(3^2:8xA6).2","Suz.2",[1,6,2,7,46,46,3,39,38,3,5,4,6,6,10,9,10,41,10,
11,45,16,44,15,13,43,42,45,44,22,26,25,28,56,32,35,35,49,49,50,50,62,62,
60,60,67,68,68,67,8,9,10,29,27],[
"compatible with (3^2:4xa6).2 -> Suz"
]);

MOT("3xG2(4)",
[
"1st maximal subgroup of 3.Suz",
],
0,
0,
0,
[(23,24)(55,56)(87,88),(25,26)(57,58)(89,90),(31,32)(63,64)(95,96),
(33,65)(34,66)(35,67)(36,68)(37,69)(38,70)(39,71)(40,72)(41,73)(42,74)
(43,75)(44,76)(45,77)(46,78)(47,79)(48,80)(49,81)(50,82)(51,83)(52,84)
(53,85)(54,86)(55,87)(56,88)(57,89)(58,90)(59,91)(60,92)(61,93)(62,94)
(63,95)(64,96),( 9,10)(11,12)(18,19)(20,21)(27,28)(29,30)(41,42)(43,44)
(50,51)(52,53)(59,60)(61,62)(73,74)(75,76)(82,83)(84,85)(91,92)(93,94)],
["ConstructDirectProduct",[["Cyclic",3],["G2(4)"]]]);
ALF("3xG2(4)","3.Suz",[1,4,7,10,16,17,23,20,32,32,29,29,35,47,48,51,54,66,
66,69,69,75,81,81,88,91,99,99,97,98,111,114,2,5,8,11,16,18,24,21,33,33,30,
30,36,47,49,52,55,67,67,70,70,76,82,82,89,92,100,100,97,98,112,115,3,6,9,
12,16,19,25,22,34,34,31,31,37,47,50,53,56,68,68,71,71,77,83,83,90,93,101,
101,97,98,113,116],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);
ALF("3xG2(4)","(3xG2(4)).2",[1,2,3,4,5,6,7,8,9,9,10,10,11,12,13,14,15,16,
16,17,17,18,19,20,21,21,22,22,23,23,24,24,25,26,27,28,29,30,31,32,33,34,
35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,25,26,
27,28,29,30,31,32,34,33,36,35,37,38,39,40,41,43,42,45,44,46,47,48,50,49,
52,51,54,53,56,55],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);

MOT("3x2.G2(4)",
[
"1st maximal subgroup of 6.Suz",
],
0,
0,
0,
[(38,39)(93,94)(148,149),(40,42)(41,43)(95,97)(96,98)(150,152)(151,153),(52,
54)(53,55)(107,109)(108,110)(162,164)(163,165),(56,111)(57,112)(58,113)(59,
114)(60,115)(61,116)(62,117)(63,118)(64,119)(65,120)(66,121)(67,122)(68,123)
(69,124)(70,125)(71,126)(72,127)(73,128)(74,129)(75,130)(76,131)(77,132)(78,
133)(79,134)(80,135)(81,136)(82,137)(83,138)(84,139)(85,140)(86,141)(87,142)
(88,143)(89,144)(90,145)(91,146)(92,147)(93,148)(94,149)(95,150)(96,151)(97,
152)(98,153)(99,154)(100,155)(101,156)(102,157)(103,158)(104,159)(105,160)
(106,161)(107,162)(108,163)(109,164)(110,165),(14,16)(15,17)(18,20)(19,21)(30,
32)(31,33)(34,35)(44,46)(45,47)(48,50)(49,51)(69,71)(70,72)(73,75)(74,76)(85,
87)(86,88)(89,90)(99,101)(100,102)(103,105)(104,106)(124,126)(125,127)(128,
130)(129,131)(140,142)(141,143)(144,145)(154,156)(155,157)(158,160)(159,161)],
["ConstructDirectProduct",[["Cyclic",3],["2.G2(4)"]]]);
ALF("3x2.G2(4)","3xG2(4)",[1,1,2,2,3,4,4,5,5,6,6,7,8,9,9,10,10,11,11,12,
12,13,13,14,15,15,16,17,17,18,18,19,19,20,21,22,22,23,24,25,25,26,26,27,
27,28,28,29,29,30,30,31,31,32,32,33,33,34,34,35,36,36,37,37,38,38,39,40,
41,41,42,42,43,43,44,44,45,45,46,47,47,48,49,49,50,50,51,51,52,53,54,54,
55,56,57,57,58,58,59,59,60,60,61,61,62,62,63,63,64,64,65,65,66,66,67,68,
68,69,69,70,70,71,72,73,73,74,74,75,75,76,76,77,77,78,79,79,80,81,81,82,
82,83,83,84,85,86,86,87,88,89,89,90,90,91,91,92,92,93,93,94,94,95,95,96,
96]);
ALF("3x2.G2(4)","6.Suz",[1,4,7,10,13,16,19,28,29,30,33,39,36,51,54,51,54,
45,48,45,48,57,60,81,82,85,88,91,94,112,115,112,115,118,118,127,130,139,
139,150,153,156,159,169,172,169,172,165,166,167,168,193,196,199,202,5,2,
11,8,14,20,17,28,29,34,31,40,37,55,52,55,52,49,46,49,46,61,58,81,86,83,89,
95,92,116,113,116,113,119,119,131,128,140,140,154,151,160,157,173,170,173,
170,165,166,167,168,197,194,203,200,3,6,9,12,15,18,21,28,29,32,35,41,38,
53,56,53,56,47,50,47,50,59,62,81,84,87,90,93,96,114,117,114,117,120,120,
129,132,141,141,152,155,158,161,171,174,171,174,165,166,167,168,195,198,
201,204],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);

MOT("2xU5(2)",
[
"3rd maximal subgroup of 2.Suz,\n",
"1st maximal subgroup of 2.U6(2)"
],
0,
0,
0,
[(33,34)(80,81),( 4, 5)( 6, 7)(14,15)(16,17)(18,19)(20,21)(23,24)(25,26)(29,
30)(31,32)(35,36)(37,38)(40,41)(42,43)(44,45)(46,47)(51,52) (53,54)(61,62)(63,
64)(65,66)(67,68)(70,71)(72,73)(76,77)(78,79)(82,83) (84,85)(87,88)(89,90)(91,
92)(93,94)],
["ConstructDirectProduct",[["Cyclic",2],["U5(2)"]]]);
ALF("2xU5(2)","2.Suz",[1,3,4,6,6,8,8,8,8,13,14,15,19,21,21,23,25,27,27,22,
22,27,26,24,25,23,28,33,36,38,36,38,43,43,46,46,48,48,48,49,49,52,53,63,
63,65,67,2,4,3,7,7,9,9,9,9,12,14,15,20,22,22,24,26,28,28,21,21,28,25,23,
26,24,27,34,37,39,37,39,44,44,45,45,47,47,47,49,49,53,52,64,64,66,68],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("2xU5(2)","2.U6(2)",[1,3,5,8,8,10,10,8,12,14,15,20,23,29,29,25,27,27,
25,33,33,29,31,31,35,35,37,43,48,50,48,50,56,58,62,62,61,60,62,70,70,65,
64,72,72,74,76,2,4,6,9,9,11,11,9,13,14,15,21,24,30,30,26,28,28,26,34,34,
30,32,32,36,36,38,43,49,51,49,51,57,59,63,63,61,60,63,71,71,65,64,73,73,
75,77],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);

MOT("3xU5(2)",
[
"3rd maximal subgroup of 3.Suz,\n",
"1st maximal subgroup of 3.U6(2)"
],
0,
0,
0,
[( 33, 34)( 80, 81)(127,128),( 48, 95)( 49, 96)( 50, 97)( 51, 98)( 52, 99)
( 53,100)( 54,101)( 55,102)( 56,103)( 57,104)( 58,105)( 59,106)( 60,107)
( 61,108)( 62,109)( 63,110)( 64,111)( 65,112)( 66,113)( 67,114)( 68,115)
( 69,116)( 70,117)( 71,118)( 72,119)( 73,120)( 74,121)( 75,122)( 76,123)
( 77,124)( 78,125)( 79,126)( 80,127)( 81,128)( 82,129)( 83,130)( 84,131)
( 85,132)( 86,133)( 87,134)( 88,135)( 89,136)( 90,137)( 91,138)( 92,139)
( 93,140)( 94,141),(  4,  5)(  6,  7)( 14, 15)( 16, 17)( 18, 19)( 20, 21)
( 23, 24)( 25, 26)( 29, 30)( 31, 32)( 35, 36)( 37, 38)( 40, 41)( 42, 43)
( 44, 45)( 46, 47)( 51, 52)( 53, 54)( 61, 62)( 63, 64)( 65, 66)( 67, 68)
( 70, 71)( 72, 73)( 76, 77)( 78, 79)( 82, 83)( 84, 85)( 87, 88)( 89, 90)
( 91, 92)( 93, 94)( 98, 99)(100,101)(108,109)(110,111)(112,113)(114,115)
(117,118)(119,120)(123,124)(125,126)(129,130)(131,132)(134,135)(136,137)
(138,139)(140,141)],
["ConstructDirectProduct",[["Cyclic",3],["U5(2)"]]]);
ALF("3xU5(2)","3.Suz",[1,4,4,12,11,15,14,13,13,17,20,23,32,37,36,40,42,46,
45,37,36,44,43,39,41,38,44,54,61,65,61,65,72,72,77,76,80,79,78,83,82,87,
86,100,101,103,107,2,5,5,10,12,13,15,14,14,18,21,24,33,35,37,38,43,44,46,
35,37,45,41,40,42,39,45,55,62,63,62,63,73,73,75,77,78,80,79,81,83,85,87,
101,99,104,105,3,6,6,11,10,14,13,15,15,19,22,25,34,36,35,39,41,45,44,36,
35,46,42,38,43,40,46,56,60,64,60,64,74,74,76,75,79,78,80,82,81,86,85,99,
100,102,106],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("3xU5(2)","(3xU5(2)).2",[1,2,3,4,4,5,5,6,7,8,9,10,11,12,12,13,13,14,
14,15,15,16,17,17,18,18,19,20,21,21,22,22,23,23,24,24,25,25,26,27,27,28,
28,29,29,30,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,
50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,
74,75,76,77,31,32,33,35,34,37,36,38,39,40,41,42,43,45,44,47,46,49,48,51,
50,52,54,53,56,55,57,58,60,59,62,61,64,63,66,65,68,67,69,71,70,73,72,75,
74,77,76],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables"
]);
ALF("3xU5(2)","3.U6(2)",[1,4,7,15,14,17,18,13,19,20,23,35,41,52,51,45,49,
48,46,58,57,50,54,55,61,60,62,69,82,86,83,85,91,94,105,104,101,99,103,123,
122,110,108,125,126,128,132,2,5,8,13,15,18,16,14,19,21,24,36,42,50,52,46,
47,49,44,56,58,51,55,53,59,61,63,70,83,84,81,86,92,95,103,105,102,97,104,
121,123,111,106,126,124,129,130,3,6,9,14,13,16,17,15,19,22,25,37,43,51,50,
44,48,47,45,57,56,52,53,54,60,59,64,71,81,85,82,84,93,96,104,103,100,98,
105,122,121,109,107,124,125,127,131],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);

MOT("3x2^(1+6)_-.U4(2)",
[
"4th maximal subgroup of 3.Suz",
],
0,
0,
0,
[( 34, 35)( 91, 92)(148,149),( 58,115)( 59,116)( 60,117)( 61,118)( 62,119)
( 63,120)( 64,121)( 65,122)( 66,123)( 67,124)( 68,125)( 69,126)( 70,127)
( 71,128)( 72,129)( 73,130)( 74,131)( 75,132)( 76,133)( 77,134)( 78,135)
( 79,136)( 80,137)( 81,138)( 82,139)( 83,140)( 84,141)( 85,142)( 86,143)
( 87,144)( 88,145)( 89,146)( 90,147)( 91,148)( 92,149)( 93,150)( 94,151)
( 95,152)( 96,153)( 97,154)( 98,155)( 99,156)(100,157)(101,158)(102,159)
(103,160)(104,161)(105,162)(106,163)(107,164)(108,165)(109,166)(110,167)
(111,168)(112,169)(113,170)(114,171),( 13, 15)( 14, 16)( 36, 38)( 37, 39)
( 40, 42)( 41, 43)( 44, 45)( 50, 52)( 51, 53)( 54, 56)( 55, 57)( 70, 72)
( 71, 73)( 93, 95)( 94, 96)( 97, 99)( 98,100)(101,102)(107,109)(108,110)
(111,113)(112,114)(127,129)(128,130)(150,152)(151,153)(154,156)(155,157)
(158,159)(164,166)(165,167)(168,170)(169,171)],
["ConstructDirectProduct",[["Cyclic",3],["2^1+6.u4q2"]]]);
ALF("3x2^(1+6)_-.U4(2)","3.Suz",[1,4,17,4,4,20,23,17,23,20,7,51,15,40,14,
42,10,35,35,75,13,44,78,17,20,54,54,26,57,51,29,66,108,66,66,43,46,39,45,
35,81,35,81,41,38,85,75,81,117,64,106,62,104,87,80,86,79,3,6,19,6,6,22,25,
19,25,22,9,53,14,39,13,41,12,37,37,77,15,46,80,19,22,56,56,28,59,53,31,68,
110,68,68,42,45,38,44,37,83,37,83,43,40,87,77,83,119,63,105,61,103,86,79,
85,78,2,5,18,5,5,21,24,18,24,21,8,52,13,38,15,43,11,36,36,76,14,45,79,18,
21,55,55,27,58,52,30,67,109,67,67,41,44,40,46,36,82,36,82,42,39,86,76,82,
118,65,107,60,102,85,78,87,80],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("3x2^(1+6)_-.U4(2)","(3x2^(1+6)_-.U4(2)).2",[1,2,3,4,5,6,7,8,9,10,11,12,
13,14,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,32,33,34,
33,34,35,36,35,36,37,37,38,39,40,41,42,43,42,43,44,45,44,45,46,47,48,49,
50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,
74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,
98,99,100,101,102,46,47,48,49,50,51,52,53,54,55,56,57,60,61,58,59,62,63,
64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,80,79,83,84,81,82,87,88,85,
86,90,89,91,92,93,94,97,98,95,96,101,102,99,100]);
ALF("3x2^(1+6)_-.U4(2)","3xU4(2)",[1,1,1,1,2,2,2,3,3,3,3,3,4,4,5,5,6,6,6,
6,7,7,7,8,8,8,9,9,9,9,10,10,10,10,10,11,11,12,12,14,14,13,13,15,15,15,16,
16,16,18,18,17,17,19,19,20,20,21,21,21,21,22,22,22,23,23,23,23,23,24,24,
25,25,26,26,26,26,27,27,27,28,28,28,29,29,29,29,30,30,30,30,30,31,31,32,
32,34,34,33,33,35,35,35,36,36,36,38,38,37,37,39,39,40,40,41,41,41,41,42,
42,42,43,43,43,43,43,44,44,45,45,46,46,46,46,47,47,47,48,48,48,49,49,49,
49,50,50,50,50,50,51,51,52,52,54,54,53,53,55,55,55,56,56,56,58,58,57,57,
59,59,60,60]);

MOT("3xJ2.2",
[
"6th maximal subgroup of 3.Suz",
],
0,
0,
0,
[(28,55)(29,56)(30,57)(31,58)(32,59)(33,60)(34,61)(35,62)(36,63)(37,64)
(38,65)(39,66)(40,67)(41,68)(42,69)(43,70)(44,71)(45,72)(46,73)(47,74)
(48,75)(49,76)(50,77)(51,78)(52,79)(53,80)(54,81),(26,27)(53,54)(80,81)],
["ConstructDirectProduct",[["Cyclic",3],["J2.2"]]]);
ALF("3xJ2.2","3.Suz",[1,4,7,10,16,17,32,29,35,47,48,51,69,66,75,99,7,23,
26,47,51,51,81,84,94,117,117,2,5,8,11,16,18,33,30,36,47,49,52,70,67,76,
100,8,24,27,47,52,52,82,84,95,118,118,3,6,9,12,16,19,34,31,37,47,50,53,71,
68,77,101,9,25,28,47,53,53,83,84,96,119,119],[
"fusion map is unique up to table automorphisms"
]);

MOT("3x2^(4+6).3A6",
[
"7th maximal subgroup of 3.Suz",
],
0,
0,
0,
[( 40, 44)( 41, 45)( 42, 46)( 43, 47)( 87, 91)( 88, 92)( 89, 93)( 90, 94)
(134,138)(135,139)(136,140)(137,141),( 48, 95)( 49, 96)( 50, 97)( 51, 98)
( 52, 99)( 53,100)( 54,101)( 55,102)( 56,103)( 57,104)( 58,105)( 59,106)
( 60,107)( 61,108)( 62,109)( 63,110)( 64,111)( 65,112)( 66,113)( 67,114)
( 68,115)( 69,116)( 70,117)( 71,118)( 72,119)( 73,120)( 74,121)( 75,122)
( 76,123)( 77,124)( 78,125)( 79,126)( 80,127)( 81,128)( 82,129)( 83,130)
( 84,131)( 85,132)( 86,133)( 87,134)( 88,135)( 89,136)( 90,137)( 91,138)
( 92,139)( 93,140)( 94,141),(  6,  8)(  7,  9)( 18, 21)( 19, 22)( 20, 23)
( 27, 28)( 36, 38)( 37, 39)( 42, 43)( 46, 47)( 53, 55)( 54, 56)( 65, 68)
( 66, 69)( 67, 70)( 74, 75)( 83, 85)( 84, 86)( 89, 90)( 93, 94)(100,102)
(101,103)(112,115)(113,116)(114,117)(121,122)(130,132)(131,133)(136,137)
(140,141)],
["ConstructDirectProduct",[["Cyclic",3],["2^4+6:3a6"]]]);
ALF("3x2^(4+6).3A6","3.Suz",[1,4,7,17,20,12,37,11,36,4,7,17,23,23,20,51,
54,37,77,83,36,76,82,16,47,13,38,41,44,78,85,23,51,26,57,83,119,82,118,32,
69,101,100,32,69,101,100,2,5,8,18,21,10,35,12,37,5,8,18,24,24,21,52,55,35,
75,81,37,77,83,16,47,14,39,42,45,79,86,24,52,27,58,81,117,83,119,33,70,99,
101,33,70,99,101,3,6,9,19,22,11,36,10,35,6,9,19,25,25,22,53,56,36,76,82,
35,75,81,16,47,15,40,43,46,80,87,25,53,28,59,82,118,81,117,34,71,100,99,
34,71,100,99],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("3x2^(4+6).3A6","(3x2^(4+6):3A6).2",[1,2,3,4,5,6,7,6,7,8,9,10,11,12,
13,14,15,16,17,18,16,17,18,19,20,21,22,22,23,24,25,26,27,28,29,30,31,30,
31,32,33,34,35,32,33,35,34,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,
51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,
75,76,77,78,79,80,81,82,36,37,38,39,40,43,44,41,42,45,46,47,48,49,50,51,
52,56,57,58,53,54,55,59,60,61,63,62,64,65,66,67,68,69,70,73,74,71,72,79,
80,82,81,75,76,78,77],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);

MOT("(A4x3.L3(4)).2",
[
"8th maximal subgroup of 3.Suz",
],
[1451520,1451520,1451520,4608,4608,4608,216,1152,1152,1152,1152,1152,1152,
1152,1152,1152,180,180,180,252,252,252,483840,483840,483840,1536,1536,1536,72,
384,384,384,384,384,384,384,384,384,60,60,60,84,84,84,181440,181440,181440,
576,576,576,27,144,144,144,144,144,144,144,144,144,45,45,45,45,45,45,63,63,63,
63,63,63,864,864,864,864,864,864,96,96,96,96,96,96,36,36,48,48,48,48,48,48,48,
48,48,48,48,48,48,48,48,48,48,48],
[,[1,3,2,1,3,2,7,4,6,5,4,6,5,4,6,5,17,19,18,20,22,21,1,3,2,1,3,2,7,4,6,5,4,6,
5,4,6,5,17,19,18,20,22,21,45,47,46,45,47,46,51,48,50,49,48,50,49,48,50,49,61,
63,62,64,66,65,70,72,71,67,69,68,1,3,2,23,25,24,4,6,5,26,28,27,7,29,8,10,9,30,
32,31,11,13,12,33,35,34,14,16,15,36,38,37],[1,1,1,4,4,4,1,8,8,8,11,11,11,14,
14,14,17,17,17,20,20,20,23,23,23,26,26,26,23,30,30,30,33,33,33,36,36,36,39,39,
39,42,42,42,1,1,1,4,4,4,1,8,8,8,11,11,11,14,14,14,17,17,17,17,17,17,20,20,20,
20,20,20,73,73,73,76,76,76,79,79,79,82,82,82,73,76,87,87,87,90,90,90,93,93,93,
96,96,96,99,99,99,102,102,102],,[1,3,2,4,6,5,7,8,10,9,11,13,12,14,16,15,1,3,2,
20,22,21,23,25,24,26,28,27,29,30,32,31,33,35,34,36,38,37,23,25,24,42,44,43,45,
47,46,48,50,49,51,52,54,53,55,57,56,58,60,59,45,47,46,45,47,46,67,69,68,70,72,
71,73,75,74,76,78,77,79,81,80,82,84,83,85,86,87,89,88,90,92,91,93,95,94,96,98,
97,99,101,100,102,104,103],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,
1,2,3,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,23,24,25,45,46,
47,48,49,50,51,52,53,54,55,56,57,58,59,60,64,65,66,61,62,63,45,46,47,45,46,47,
73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,
99,100,101,102,103,104]],
0,
[( 67, 70)( 68, 71)( 69, 72),( 61, 64)( 62, 65)( 63, 66),( 11, 14)( 12, 15)
( 13, 16)( 33, 36)( 34, 37)( 35, 38)( 55, 58)( 56, 59)( 57, 60)( 93, 99)
( 94,100)( 95,101)( 96,102)( 97,103)( 98,104),(  8, 11)(  9, 12)( 10, 13)
( 30, 33)( 31, 34)( 32, 35)( 52, 55)( 53, 56)( 54, 57)( 87, 93)( 88, 94)
( 89, 95)( 90, 96)( 91, 97)( 92, 98),(  2,  3)(  5,  6)(  9, 10)( 12, 13)
( 15, 16)( 18, 19)( 21, 22)( 24, 25)( 27, 28)( 31, 32)( 34, 35)( 37, 38)
( 40, 41)( 43, 44)( 46, 47)( 49, 50)( 53, 54)( 56, 57)( 59, 60)( 62, 63)
( 65, 66)( 68, 69)( 71, 72)( 74, 75)( 77, 78)( 80, 81)( 83, 84)( 88, 89)
( 91, 92)( 94, 95)( 97, 98)(100,101)(103,104)],
["ConstructProj",[["(a4xpsl(3,4)):2",[]],,["(A4x3.L3(4)).2",[2,2,8,8,2,2,2,2,
2,2,2,2,2,2,11,11,2,2,2,2,2,2,2]]]]);
ALF("(A4x3.L3(4)).2","(a4xpsl(3,4)):2",[1,1,1,2,2,2,3,4,4,4,5,5,5,6,6,6,
7,7,7,8,8,8,9,9,9,10,10,10,11,12,12,12,13,
13,13,14,14,14,15,15,15,16,16,16,17,17,17,18,18,18,19,20,20,20,21,21,21,
22,22,22,23,23,23,24,24,24,25,25,25,26,26,26,27,27,27,28,28,28,29,29,29,
30,30,30,31,32,33,33,33,34,34,34,35,35,35,36,36,36,37,37,37,38,38,38]);
ALF("(A4x3.L3(4)).2","Symm(4)",[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,
3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,5,5,5,4,4,4,5,5,5,4,5,4,4,4,5,5,5,4,4,4,5,
5,5,4,4,4,5,5,5]);
ALF("(A4x3.L3(4)).2","3.L3(4).2_1",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,
16,17,18,19,20,21,22,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,
21,22,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,17,18,19,20,21,22,
20,21,22,23,24,25,23,24,25,26,27,28,26,27,28,29,29,30,31,32,30,31,32,33,
34,35,33,34,35,36,37,38,36,37,38]);
ALF("(A4x3.L3(4)).2","3.Suz",[1,2,3,4,5,6,16,17,18,19,23,24,25,23,24,25,
32,33,34,48,49,50,7,8,9,7,8,9,47,23,24,25,20,21,22,20,21,22,69,70,71,94,
95,96,10,11,12,35,36,37,16,75,76,77,81,82,83,81,82,83,99,100,101,99,100,
101,111,112,113,114,115,116,7,8,9,26,27,28,23,24,25,26,27,28,47,84,51,52,
53,57,58,59,57,58,59,54,55,56,57,58,59,54,55,56],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("(A4x3.L3(4)).2","(A4x3.L3(4).2_3).2",[1,2,2,3,4,4,5,6,7,7,8,9,10,8,
10,9,11,12,12,13,14,14,15,16,16,17,18,18,19,20,21,21,22,23,24,22,24,23,25,
26,26,27,28,28,29,30,30,31,32,32,33,34,35,35,36,37,38,36,38,37,39,40,40,
41,42,42,43,44,45,43,45,44,46,47,47,48,49,49,50,51,51,52,53,53,54,55,56,
57,57,58,59,59,60,61,62,63,64,65,60,62,61,63,65,64],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);

MOT("3x2^(2+8):(A5xS3)",
[
"9th maximal subgroup of 3.Suz"
],
0,
0,
0,
[( 15, 16)( 43, 44)( 64, 65)( 92, 93)(113,114)(141,142),( 37, 38)( 86, 87)
(135,136),( 50, 99)( 51,100)( 52,101)( 53,102)( 54,103)( 55,104)( 56,105)( 57,
106)( 58,107)( 59,108)( 60,109)( 61,110)( 62,111)( 63,112)( 64,113)( 65,114)
( 66,115)( 67,116)( 68,117)( 69,118)( 70,119)( 71,120)( 72,121)( 73,122)( 74,
123)( 75,124)( 76,125)( 77,126)( 78,127)( 79,128)( 80,129)( 81,130)( 82,131)
( 83,132)( 84,133)( 85,134)( 86,135)( 87,136)( 88,137)( 89,138)( 90,139)( 91,
140)( 92,141)( 93,142)( 94,143)( 95,144)( 96,145)( 97,146)( 98,147), ( 19, 21)
( 20, 22)( 27, 28)( 46, 48)( 47, 49)( 68, 70)( 69, 71)( 76, 77)( 95, 97)( 96,
 98)(117,119)(118,120)(125,126)(144,146)(145,147)],
["ConstructDirectProduct",[["Cyclic",3],["2^2+8(a5xs3)"]]]);
ALF("3x2^(2+8):(A5xS3)","3.Suz",[1,4,4,7,17,23,20,7,17,20,51,54,10,35,35,
35,75,81,29,66,29,66,16,47,16,47,97,98,4,17,23,51,7,23,20,51,54,54,57,26,
35,75,81,81,117,66,108,66,108,2,5,5,8,18,24,21,8,18,21,52,55,11,36,36,36,
76,82,30,67,30,67,16,47,16,47,97,98,5,18,24,52,8,24,21,52,55,55,58,27,36,
76,82,82,118,67,109,67,109,3,6,6,9,19,25,22,9,19,22,53,56,12,37,37,37,77,
83,31,68,31,68,16,47,16,47,97,98,6,19,25,53,9,25,22,53,56,56,59,28,37,77,
83,83,119,68,110,68,110],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("3x2^(2+8):(A5xS3)","(3x2^(2+8):(A5xS3)).2",[1,2,3,4,5,6,7,8,9,10,11,12,
13,14,15,15,16,17,18,19,18,19,20,21,22,23,24,24,25,26,27,28,29,30,31,32,33,
33,34,35,36,37,38,38,39,40,41,40,41,42,43,44,45,46,47,48,49,50,51,52,53,
54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,
78,79,80,81,82,83,84,85,86,87,88,89,90,42,43,44,45,46,47,48,49,50,51,52,
53,54,55,57,56,58,59,62,63,60,61,64,65,66,67,69,68,70,71,72,73,74,75,76,
77,79,78,80,81,82,83,85,84,86,89,90,87,88]);

MOT("3xM12.2",
[
"10th maximal subgroup of 3.Suz",
],
0,
0,
0,
[(20,21)(41,42)(62,63),(22,43)(23,44)(24,45)(25,46)(26,47)(27,48)(28,49)(29,
50)(30,51)(31,52)(32,53)(33,54)(34,55)(35,56)(36,57)(37,58)(38,59)(39,60)(40,
61)(41,62)(42,63),(17,18)(38,39)(59,60)],
["ConstructDirectProduct",[["Cyclic",3],["M12.2"]]]);
ALF("3xM12.2","3.Suz",[1,7,4,13,16,23,32,47,44,57,69,72,7,20,26,47,69,69,
84,85,85,2,8,5,14,16,24,33,47,45,58,70,73,8,21,27,47,70,70,84,86,86,3,9,6,
15,16,25,34,47,46,59,71,74,9,22,28,47,71,71,84,87,87],[
"fusion map is unique up to table automorphisms"
]);

MOT("3.3^(2+4):2(A4x2^2).2",
[
"11th maximal subgroup of 3.Suz"
],
[419904,419904,419904,104976,104976,104976,104976,104976,104976,1458,1458,
1458,324,5184,5184,5184,1296,1296,1296,1296,1296,1296,3888,3888,3888,3888,
3888,3888,3888,3888,3888,162,162,162,864,864,864,36,5832,5832,5832,2916,2916,
2916,2916,2916,2916,1458,1458,1458,162,162,162,162,162,162,288,288,288,864,
864,864,216,216,216,216,216,216,432,432,432,36,36,48,48,48,144,144,144,72,72,
72,72,72,72,36,36,36,648,648,648,324,324,324,324,324,324,162,162,162,324,324,
324,324,324,324,324,324,324,54,54,54,324,324,324,324,324,324,324,324,324,54,
54,54,24,24,24,72,72,72,72,72,72,72,72,72,36,36,36],
[,[1,3,2,4,6,5,7,9,8,10,12,11,13,1,3,2,4,6,5,7,9,8,1,3,2,7,9,8,7,9,8,10,12,11,
1,3,2,13,39,41,40,45,47,46,42,44,43,48,50,49,54,56,55,51,53,52,14,16,15,14,16,
15,17,19,18,20,22,21,35,37,36,38,38,35,37,36,14,16,15,20,22,21,14,16,15,17,19,
18,39,41,40,45,47,46,42,44,43,48,50,49,45,47,46,39,41,40,45,47,46,54,56,55,42,
44,43,39,41,40,42,44,43,51,53,52,57,59,58,60,62,61,63,65,64,63,65,64,89,91,
90],[1,1,1,1,1,1,1,1,1,1,1,1,1,14,14,14,14,14,14,14,14,14,23,23,23,23,23,23,
23,23,23,23,23,23,35,35,35,35,1,1,1,1,1,1,1,1,1,1,1,1,9,9,9,8,8,8,57,57,57,60,
60,60,60,60,60,60,60,60,69,69,69,69,69,74,74,74,77,77,77,77,77,77,83,83,83,83,
83,83,14,14,14,14,14,14,14,14,14,14,14,14,23,23,23,23,23,23,23,23,23,28,28,28,
23,23,23,23,23,23,23,23,23,30,30,30,125,125,125,128,128,128,128,128,128,128,
128,128,57,57,57]],
0,
[( 72, 73),(131,134)(132,135)(133,136),(  2,  3)(  5,  6)(  8,  9)( 11, 12)
( 15, 16)( 18, 19)( 21, 22)( 24, 25)( 26, 29)( 27, 31)( 28, 30)( 33, 34)
( 36, 37)( 40, 41)( 42, 45)( 43, 47)( 44, 46)( 49, 50)( 51, 54)( 52, 56)
( 53, 55)( 58, 59)( 61, 62)( 64, 65)( 67, 68)( 70, 71)( 75, 76)( 78, 79)
( 81, 82)( 84, 85)( 87, 88)( 90, 91)( 92, 95)( 93, 97)( 94, 96)( 99,100)
(101,113)(102,115)(103,114)(104,116)(105,118)(106,117)(107,119)(108,121)
(109,120)(110,122)(111,124)(112,123)(126,127)(129,130)(132,133)(135,136)
(138,139)],
["ConstructProj",[["3^2+4:2(2^2xa4)2",[]],,["3.3^(2+4):2(A4x2^2).2",[2,2,2,2,
2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,17]]]]);
ALF("3.3^(2+4):2(A4x2^2).2","3^2+4:2(2^2xa4)2",[1,1,1,2,2,2,3,3,3,4,4,4,5,6,6,
6,7,7,7,8,8,8,9,9,9,10,10,10,11,11,11,12,12,12,13,13,13,14,15,15,15,16,16,16,
17,17,17,18,18,18,19,19,19,20,20,20,21,21,21,22,22,22,23,23,23,24,24,24,25,25,
25,26,27,28,28,28,29,29,29,30,30,30,31,31,31,32,32,32,33,33,33,34,34,34,35,35,
35,36,36,36,37,37,37,38,38,38,39,39,39,40,40,40,41,41,41,42,42,42,43,43,43,44,
44,44,45,45,45,46,46,46,47,47,47,48,48,48,49,49,49]);
ALF("3.3^(2+4):2(A4x2^2).2","3.Suz",[1,2,3,10,11,12,13,14,15,13,14,15,16,
4,5,6,35,36,37,44,45,46,4,5,6,38,39,40,41,42,43,44,45,46,7,8,9,47,10,11,
12,13,14,15,13,14,15,13,14,15,60,61,62,63,64,65,23,24,25,17,18,19,75,76,
77,78,79,80,26,27,28,84,84,26,27,28,20,21,22,85,86,87,23,24,25,81,82,83,
35,36,37,38,39,40,41,42,43,44,45,46,44,45,46,35,36,37,41,42,43,102,103,
104,44,45,46,35,36,37,38,39,40,105,106,107,57,58,59,51,52,53,117,118,119,
117,118,119,81,82,83],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("3.3^(2+4):2(A4x2^2).2","3.3^(2+4):2(S4xD8)",[1,2,2,3,4,4,5,6,6,7,8,
8,9,10,11,11,12,13,13,14,15,15,16,17,17,18,19,20,18,20,19,21,22,22,23,24,
24,25,26,27,27,28,29,30,28,30,29,31,32,32,33,34,35,33,35,34,36,37,37,38,
39,39,40,41,41,42,43,43,44,45,45,46,46,47,48,48,49,50,50,51,52,52,53,54,
54,55,56,56,57,58,58,59,60,61,59,61,60,62,63,63,64,65,66,67,68,69,70,71,
72,73,74,75,64,66,65,67,69,68,70,72,71,73,75,74,76,77,77,78,79,79,80,81,
82,80,82,81,83,84,84]);

MOT("(3.A6xA5):2",
[
"12th maximal subgroup of 3.Suz",
],
[129600,129600,129600,2880,2880,2880,540,1440,1440,1440,900,900,900,8640,8640,
8640,192,192,192,36,96,96,96,60,60,60,6480,6480,6480,144,144,144,27,72,72,72,
45,45,45,5400,5400,5400,120,120,120,45,45,60,60,60,75,75,75,75,75,75,72,72,72,
144,144,144,144,144,144,24,24,24,48,48,48,48,48,48,36,36,36,72,72,72,72,72,
72],
[,[1,3,2,1,3,2,7,4,6,5,11,13,12,1,3,2,1,3,2,7,4,6,5,11,13,12,27,29,28,27,29,
28,33,30,32,31,37,39,38,40,42,41,40,42,41,47,46,43,45,44,51,53,52,54,56,55,4,
6,5,8,10,9,8,10,9,17,19,18,21,23,22,21,23,22,30,32,31,34,36,35,34,36,35],[1,1,
1,4,4,4,1,8,8,8,11,11,11,14,14,14,17,17,17,14,21,21,21,24,24,24,1,1,1,4,4,4,1,
8,8,8,11,11,11,40,40,40,43,43,43,40,40,48,48,48,51,51,51,54,54,54,57,57,57,60,
60,60,63,63,63,66,66,66,69,69,69,72,72,72,57,57,57,60,60,60,63,63,63],,[1,3,2,
4,6,5,7,8,10,9,1,3,2,14,16,15,17,19,18,20,21,23,22,14,16,15,27,29,28,30,32,31,
33,34,36,35,27,29,28,1,3,2,4,6,5,7,7,8,10,9,1,3,2,1,3,2,57,59,58,63,65,64,60,
62,61,66,68,67,72,74,73,69,71,70,75,77,76,81,83,82,78,80,79]],
0,
[(51,54)(52,55)(53,56),(46,47),(60,63)(61,64)(62,65)(69,72)(70,73)(71,74)
(78,81)(79,82)(80,83),( 2, 3)( 5, 6)( 9,10)(12,13)(15,16)(18,19)(22,23)(25,26)
(28,29)(31,32)(35,36)(38,39)(41,42)(44,45)(49,50)(52,53)(55,56)(58,59)(61,62)
(64,65)(67,68)(70,71)(73,74)(76,77)(79,80)(82,83)],
["ConstructProj",[["(a6xa5).2",[]],,["(3.A6xA5):2",[2,2,2,2,2,2,2,17,2,2,2,17,
2,2,2,17,2]]]]);
ALF("(3.A6xA5):2","(a6xa5).2",[1,1,1,2,2,2,3,4,4,4,5,5,5,6,6,6,7,7,7,8,9,9,9,
10,10,10,11,11,11,12,12,12,13,14,14,14,15,15,15,16,16,16,17,17,17,18,19,20,20,
20,21,21,21,22,22,22,23,23,23,24,24,24,25,25,25,26,26,26,27,27,27,28,28,28,29,
29,29,30,30,30,31,31,31]);
ALF("(3.A6xA5):2","A5.2",[1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,
2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,
5,5,5,5,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7]);
ALF("(3.A6xA5):2","3.A6.2_3",[1,2,3,4,5,6,7,8,9,10,11,12,13,1,2,3,4,5,6,7,
8,9,10,11,12,13,1,2,3,4,5,6,7,8,9,10,11,12,13,1,2,3,4,5,6,7,7,8,9,10,11,
12,13,11,12,13,14,15,16,17,18,19,20,21,22,14,15,16,17,18,19,20,21,22,14,
15,16,17,18,19,20,21,22]);
ALF("(3.A6xA5):2","3.Suz",[1,2,3,4,5,6,16,17,18,19,32,33,34,7,8,9,7,8,9,
47,23,24,25,69,70,71,10,11,12,35,36,37,16,75,76,77,99,100,101,29,30,31,66,
67,68,97,98,108,109,110,32,33,34,29,30,31,23,24,25,51,52,53,51,52,53,26,
27,28,57,58,59,57,58,59,81,82,83,117,118,119,117,118,119],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("(3.A6xA5):2","(3.A6.2_2xA5):2",[1,2,2,3,4,4,5,6,7,7,8,9,9,10,11,11,
12,13,13,14,15,16,16,17,18,18,19,20,20,21,22,22,23,24,25,25,26,27,27,28,
29,29,30,31,31,32,32,33,34,34,35,36,36,37,38,38,39,40,40,41,42,43,41,43,
42,44,45,45,46,47,48,46,48,47,49,50,50,51,52,53,51,53,52],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);

MOT("(3^(1+2):4xA6).2",
[
"13th maximal subgroup of 3.Suz",
],
[77760,77760,77760,3240,8640,8640,8640,4320,4320,4320,1728,1728,1728,72,192,
192,192,96,96,96,1944,1944,1944,81,216,216,216,108,108,108,1944,1944,1944,81,
216,216,216,108,108,108,864,864,864,36,96,96,96,48,48,48,540,540,540,45,45,60,
60,60,60,60,60,60,60,60,288,288,288,288,288,288,288,288,288,288,288,288,48,48,
48,48,48,48,36,36,36,36,36,36,36,36,36,36,36,36],
[,[1,3,2,4,1,3,2,5,7,6,1,3,2,4,1,3,2,5,7,6,21,23,22,24,21,23,22,25,27,26,31,
33,32,34,31,33,32,35,37,36,11,13,12,14,11,13,12,15,17,16,51,53,52,55,54,51,53,
52,56,58,57,56,58,57,5,7,6,5,7,6,5,7,6,5,7,6,15,17,16,15,17,16,25,27,26,25,27,
26,35,37,36,35,37,36],[1,1,1,1,5,5,5,8,8,8,11,11,11,11,15,15,15,18,18,18,1,1,
1,1,5,5,5,8,8,8,1,1,1,1,5,5,5,8,8,8,41,41,41,41,45,45,45,48,48,48,51,51,51,51,
51,56,56,56,59,59,59,62,62,62,65,65,65,68,68,68,71,71,71,74,74,74,77,77,77,80,
80,80,65,65,65,68,68,68,71,71,71,74,74,74],,[1,3,2,4,5,7,6,8,10,9,11,13,12,14,
15,17,16,18,20,19,21,23,22,24,25,27,26,28,30,29,31,33,32,34,35,37,36,38,40,39,
41,43,42,44,45,47,46,48,50,49,1,3,2,4,4,5,7,6,8,10,9,8,10,9,65,67,66,68,70,69,
71,73,72,74,76,75,77,79,78,80,82,81,83,85,84,86,88,87,89,91,90,92,94,93]],
0,
[(59,62)(60,63)(61,64),(54,55),(65,68)(66,69)(67,70)(71,74)(72,75)(73,76)
(77,80)(78,81)(79,82)(83,86)(84,87)(85,88)(89,92)(90,93)(91,94),(21,31)(22,32)
(23,33)(24,34)(25,35)(26,36)(27,37)(28,38)(29,39)(30,40)(65,71)(66,72)(67,73)
(68,74)(69,75)(70,76)(83,89)(84,90)(85,91)(86,92)(87,93)(88,94),( 2, 3)( 6, 7)
( 9,10)(12,13)(16,17)(19,20)(22,23)(26,27)(29,30)(32,33)(36,37)(39,40)(42,43)
(46,47)(49,50)(52,53)(57,58)(60,61)(63,64)(66,67)(69,70)(72,73)(75,76)(78,79)
(81,82)(84,85)(87,88)(90,91)(93,94)],
["ConstructProj",[["(3^2:4xa6).2",[]],,["(3^(1+2):4xA6).2",[2,41,2,2,2,2,2,2,
2,2,2,2]]]]);
ALF("(3^(1+2):4xA6).2","(3^2:4xa6).2",[1,1,1,2,3,3,3,4,4,4,5,5,5,6,7,7,7,8,8,
8,9,9,9,10,11,11,11,12,12,12,13,13,13,14,15,15,15,16,16,16,17,17,17,18,19,19,
19,20,20,20,21,21,21,22,23,24,24,24,25,25,25,26,26,26,27,27,27,28,28,28,29,29,
29,30,30,30,31,31,31,32,32,32,33,33,33,34,34,34,35,35,35,36,36,36]);
ALF("(3^(1+2):4xA6).2","3.Suz",[1,2,3,16,4,5,6,17,18,19,7,8,9,47,7,8,9,23,
24,25,13,14,15,16,44,45,46,78,79,80,10,11,12,16,35,36,37,75,76,77,26,27,
28,84,26,27,28,26,27,28,29,30,31,97,98,66,67,68,108,109,110,108,109,110,
20,21,22,20,21,22,23,24,25,23,24,25,26,27,28,26,27,28,85,86,87,85,86,87,
81,82,83,81,82,83],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("(3^(1+2):4xA6).2","A6.2_1",[1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,
3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,
6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,9,9,9,9,9,10,10,10,10,10,10,11,11,
11,11,11,11]);
ALF("(3^(1+2):4xA6).2","(3^(1+2):8xA6).2",[1,2,2,3,4,5,5,6,7,7,8,9,9,10,
11,12,12,13,14,14,15,16,16,17,18,19,19,20,21,21,22,23,23,24,25,26,26,27,
28,28,29,30,30,31,32,33,33,34,35,35,36,37,37,38,38,39,40,40,41,42,42,43,
44,44,45,46,47,45,47,46,48,49,50,48,50,49,51,52,53,51,53,52,54,55,56,54,
56,55,57,58,59,57,59,58],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);

MOT("3xL3(3).2",
[
"14th and 15th maximal subgroup of 3.Suz,\n",
"(fusions differ by an autom. of the subgroup,\n",
"so the same fusion is stored for both maxes)"
],
0,
0,
0,
[( 8, 9)(23,24)(38,39),(16,31)(17,32)(18,33)(19,34)(20,35)(21,36)(22,37)(23,
38)(24,39)(25,40)(26,41)(27,42)(28,43)(29,44)(30,45),(14,15)(29,30)(44,45)],
["ConstructDirectProduct",[["Cyclic",3],["L3(3).2"]]]);
ALF("3xL3(3).2","3.Suz",[1,4,13,16,23,44,57,88,91,7,20,47,57,85,85,2,5,14,
16,24,45,58,89,92,8,21,47,58,86,86,3,6,15,16,25,46,59,90,93,9,22,47,59,87,
87],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("3xL3(3).2","3.G2(3)",[1,4,7,10,15,18,28,40,43,4,12,20,28,34,34,2,5,7,
10,16,18,29,41,44,5,13,20,29,35,35,3,6,7,10,17,18,30,42,45,6,14,20,30,36,
36],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);

MOT("3xL2(25)",
[
"16th maximal subgroup of 3.Suz",
],
0,
0,
0,
[( 5, 6)(20,21)(35,36),( 8, 9)(23,24)(38,39),(16,31)(17,32)(18,33)(19,34)(20,
35)(21,36)(22,37)(23,38)(24,39)(25,40)(26,41)(27,42)(28,43)(29,44)(30,45),(10,
11)(12,13)(14,15)(25,26)(27,28)(29,30)(40,41)(42,43)(44,45),(10,12,14)(11,13,
15)(25,27,29)(26,28,30)(40,42,44)(41,43,45)],
["ConstructDirectProduct",[["Cyclic",3],["L2(25)"]]]);
ALF("3xL2(25)","3.Suz",[1,7,16,26,29,32,47,84,84,88,91,88,91,88,91,2,8,16,
27,30,33,47,84,84,89,92,89,92,89,92,3,9,16,28,31,34,47,84,84,90,93,90,93,
90,93],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("3xL2(25)","(3xL2(25)).2_2",[1,2,3,4,5,6,7,8,8,9,9,10,10,11,11,12,13,
14,15,16,17,18,19,20,21,22,23,24,25,26,12,13,14,15,16,17,18,20,19,22,21,
24,23,26,25],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);

MOT("(3xG2(4)).2",
[
"2nd maximal subgroup of 3.Suz.2",
],
[1509580800,368640,23040,362880,1080,9216,4608,3072,900,900,1152,72,126,192,
192,60,60,288,288,288,39,45,45,63,754790400,184320,11520,181440,540,4608,2304,
1536,900,900,900,900,576,36,63,96,96,60,60,60,60,144,144,144,39,39,45,45,45,
45,63,63,24192,384,96,432,36,192,96,64,48,12,14,16,16,24,24,24],
[,[1,1,1,4,5,2,2,2,9,10,4,5,13,6,8,10,9,11,11,11,21,22,23,24,25,25,25,28,29,
26,26,26,33,34,35,36,28,29,39,30,32,35,36,33,34,37,37,37,49,50,51,52,53,54,55,
56,1,2,3,4,5,6,7,6,11,12,13,15,15,18,19,20],[1,2,3,1,1,6,7,8,9,10,2,3,13,14,
15,16,17,6,7,7,21,9,10,13,1,2,3,1,1,6,7,8,9,9,10,10,2,3,13,14,15,16,16,17,17,
6,7,7,21,21,9,9,10,10,13,13,57,58,59,57,57,62,63,64,58,59,67,69,68,62,63,63],,
[1,2,3,4,5,6,7,8,1,1,11,12,13,14,15,2,3,18,20,19,21,4,5,24,25,26,27,28,29,30,
31,32,25,25,25,25,37,38,39,40,41,26,26,27,27,46,48,47,49,50,28,28,29,29,56,55,
57,58,59,60,61,62,63,64,65,66,67,68,69,70,72,71],,[1,2,3,4,5,6,7,8,9,10,11,12,
1,14,15,16,17,18,19,20,21,22,23,4,25,26,27,28,29,30,31,32,34,33,36,35,37,38,
25,40,41,43,42,45,44,46,47,48,50,49,52,51,54,53,28,28,57,58,59,60,61,62,63,64,
65,66,57,69,68,70,71,72],,,,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,
19,20,1,22,23,24,25,26,27,28,29,30,31,32,34,33,36,35,37,38,39,40,41,43,42,45,
44,46,47,48,25,25,52,51,54,53,56,55,57,58,59,60,61,62,63,64,65,66,67,68,69,70,
71,72]],
0,
[(19,20)(47,48)(71,72),(33,34)(35,36)(42,43)(44,45)(51,52)(53,54),(49,50),(55,
56),(68,69)],
["ConstructMGA","3xG2(4)","G2(4).2",[[33,65],[34,66],[35,67],[36,68],[37,
69],[38,70],[39,71],[40,72],[41,73],[42,74],[43,76],[44,75],[45,78],[46,77],
[47,79],[48,80],[49,82],[50,81],[51,83],[52,85],[53,84],[54,87],[55,86],[56,
89],[57,88],[58,91],[59,90],[60,92],[61,93],[62,95],[63,94],[64,96]],()]);
ALF("(3xG2(4)).2","G2(4).2",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,
19,20,21,22,23,24,1,2,3,4,5,6,7,8,9,9,10,10,11,12,13,14,15,16,16,17,17,18,
19,20,21,21,22,22,23,23,24,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,
39,40]);
ALF("(3xG2(4)).2","S3",[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,
2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,
3,3,3,3,3,3,3,3,3,3]);
ALF("(3xG2(4)).2","3.Suz.2",[1,3,5,7,11,12,16,14,22,20,24,31,32,34,36,43,
45,49,53,53,58,64,63,71,2,4,6,8,11,13,17,15,23,23,21,21,25,31,33,35,37,44,
44,46,46,50,54,54,59,60,65,65,63,63,72,73,76,78,79,80,82,85,88,87,92,94,
95,96,96,99,102,102],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables"
]);

MOT("(3xU5(2)).2",
[
"4th maximal subgroup of 3.Suz.2",
],
[82114560,497664,27648,233280,11664,11664,1944,6912,2304,576,90,5184,3888,
1296,864,1296,432,324,216,96,162,81,33,432,216,216,72,72,45,54,41057280,
248832,13824,233280,233280,11664,11664,5832,972,3456,1152,288,45,5184,5184,
3888,3888,1296,1296,864,864,648,432,432,324,324,108,48,162,162,81,81,33,33,
432,432,216,216,108,72,72,72,72,45,45,54,54,1440,96,36,36,192,192,32,10,12,16,
16,24,24],
[,[1,1,1,4,5,6,7,2,2,3,11,4,5,5,4,6,5,7,7,9,21,22,23,12,14,16,15,14,29,21,31,
31,31,34,35,36,37,38,39,32,32,33,43,34,35,36,37,36,37,34,35,38,36,37,39,39,39,
41,59,60,61,62,63,64,44,45,48,49,52,50,51,48,49,74,75,59,60,1,3,6,7,8,8,8,11,
19,20,20,26,26],[1,2,3,1,1,1,1,8,9,10,11,2,2,2,3,2,3,2,3,20,5,5,23,8,8,8,10,9,
11,13,1,2,3,1,1,1,1,1,1,8,9,10,11,2,2,2,2,2,2,3,3,2,3,3,2,2,3,20,5,5,5,5,23,
23,8,8,8,8,8,10,10,9,9,11,11,13,13,78,79,78,78,82,83,84,85,79,87,88,82,83],,
[1,2,3,4,5,6,7,8,9,10,1,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,4,
30,31,32,33,34,35,36,37,38,39,40,41,42,31,44,45,46,47,48,49,50,51,52,53,54,55,
56,57,58,59,60,61,62,64,63,65,66,67,68,69,70,71,72,73,35,34,76,77,78,79,80,81,
83,82,84,78,86,88,87,90,89],,,,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,
18,19,20,21,22,1,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,
44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,31,31,65,66,67,68,69,
70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90]],
0,
[(63,64),(82,83)(87,88)(89,90),(34,35)(36,37)(44,45)(46,47)(48,49)(50,51)(53,
54)(55,56)(59,60)(61,62)(65,66)(67,68)(70,71)(72,73)(74,75)(76,77)],
["ConstructMGA","3xU5(2)","U5(2).2",[[48,95],[49,96],[50,98],[51,97],[52,
99],[53,100],[54,102],[55,101],[56,104],[57,103],[58,105],[59,107],[60,106],
[61,109],[62,108],[63,110],[64,111],[65,112],[66,114],[67,113],[68,116],[69,
115],[70,118],[71,117],[72,119],[73,121],[74,120],[75,122],[76,124],[77,123],
[78,126],[79,125],[80,128],[81,127],[82,129],[83,131],[84,130],[85,133],[86,
132],[87,134],[88,136],[89,135],[90,138],[91,137],[92,139],[93,141],[94,140]],
()]);
ALF("(3xU5(2)).2","U5(2).2",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,
19,20,21,22,23,24,25,26,27,28,29,30,1,2,3,4,4,5,5,6,7,8,9,10,11,12,12,13,
13,14,14,15,15,16,17,17,18,18,19,20,21,21,22,22,23,23,24,24,25,25,26,27,
27,28,28,29,29,30,30,31,32,33,34,35,36,37,38,39,40,41,42,43]);
ALF("(3xU5(2)).2","S3",[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,
2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3]);
ALF("(3xU5(2)).2","3.Suz.2",[1,3,3,8,10,9,9,12,14,16,22,25,28,30,25,29,27,
26,29,36,41,41,47,50,52,51,54,57,65,67,2,4,4,7,8,9,10,10,10,13,15,17,23,
24,25,26,27,29,30,24,25,30,26,28,28,27,30,37,42,40,42,40,48,48,49,50,51,
52,52,53,54,56,57,65,64,68,66,77,78,81,81,86,86,87,91,93,96,96,101,101],[
"fusion map is unique up to table automorphisms"
]);

MOT("(3x2^(1+6)_-.U4(2)).2",
[
"5th maximal subgroup of 3.Suz.2",
],
[19906560,19906560,276480,368640,55296,18432,4608,9216,9216,3072,3072,1152,
3888,3888,20736,20736,1152,1728,2592,2592,432,2304,2304,384,192,192,192,192,
240,240,120,60,432,432,432,144,432,144,288,288,144,54,54,72,72,9953280,
9953280,138240,184320,27648,9216,2304,4608,4608,1536,1536,576,3888,3888,3888,
3888,10368,10368,576,864,1296,1296,216,1152,1152,192,96,96,96,96,120,120,60,
60,60,432,432,432,432,432,144,432,144,432,432,72,144,144,72,54,54,54,54,72,72,
72,72,7680,4608,46080,3072,768,256,768,256,1536,1536,256,192,64,256,256,128,
96,288,288,96,72,72,24,24,32,32,16,20,40,40,48,48,24],
[,[1,1,2,1,1,2,4,4,2,4,1,3,13,13,15,15,15,16,19,19,20,5,5,6,10,11,9,8,29,29,
30,29,13,13,15,17,19,20,17,16,18,42,42,34,34,46,46,47,46,46,47,49,49,47,49,46,
48,58,58,60,60,62,62,62,63,66,66,67,50,50,51,55,56,54,53,76,76,77,76,76,58,58,
60,60,62,64,62,64,66,66,67,64,63,65,95,95,97,97,82,82,84,84,1,2,3,3,1,4,3,3,8,
8,8,9,11,8,8,8,15,16,18,18,20,21,19,21,22,22,24,29,31,31,39,39,40],[1,2,3,4,5,
6,7,8,9,10,11,12,1,2,1,2,4,3,1,2,3,22,23,24,25,26,27,28,29,30,31,32,5,5,5,7,5,
6,8,9,12,13,14,23,22,1,2,3,4,5,6,7,8,9,10,11,12,1,2,1,2,1,2,4,3,1,2,3,22,23,
24,25,26,27,28,29,30,31,32,32,5,5,5,5,5,7,5,7,5,5,6,8,9,12,13,14,13,14,23,22,
23,22,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,103,104,
105,106,104,105,107,109,127,128,129,130,131,132,111,112,114],,[1,2,3,4,5,6,7,
8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,1,2,3,4,33,34,35,
36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,
62,63,64,65,66,67,68,69,70,71,72,73,74,75,46,47,48,49,49,81,82,83,84,85,86,87,
88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,
110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,
129,103,105,105,133,134,135]],
0,
[(79,80),(111,112)(127,128)(133,134),(131,132),( 58, 60)( 59, 61)( 81, 83)
( 82, 84)( 85, 87)( 86, 88)( 89, 90)( 95, 97)( 96, 98)( 99,101)(100,102)],
["ConstructMGA","3x2^(1+6)_-.U4(2)","2^(1+6)_-.U4(2).2",
 [ [ 58, 115 ], [ 59, 117 ], [ 60, 116 ], [ 61, 118 ], [ 62, 120 ],
   [ 63, 119 ], [ 64, 121 ], [ 65, 122 ], [ 66, 123 ], [ 67, 124 ],
   [ 68, 125 ], [ 69, 127 ], [ 70, 126 ], [ 71, 129 ], [ 72, 128 ],
   [ 73, 131 ], [ 74, 130 ], [ 75, 132 ], [ 76, 133 ], [ 77, 134 ],
   [ 78, 135 ], [ 79, 136 ], [ 80, 137 ], [ 81, 138 ], [ 82, 139 ],
   [ 83, 140 ], [ 84, 141 ], [ 85, 142 ], [ 86, 143 ], [ 87, 144 ],
   [ 88, 145 ], [ 89, 146 ], [ 90, 148 ], [ 91, 147 ], [ 92, 149 ],
   [ 93, 150 ], [ 94, 152 ], [ 95, 151 ], [ 96, 153 ], [ 97, 154 ],
   [ 98, 155 ], [ 99, 156 ], [ 100, 157 ], [ 101, 159 ], [ 102, 158 ],
   [ 103, 160 ], [ 104, 162 ], [ 105, 161 ], [ 106, 164 ], [ 107, 163 ],
   [ 108, 166 ], [ 109, 165 ], [ 110, 167 ], [ 111, 169 ], [ 112, 168 ],
   [ 113, 170 ], [ 114, 171 ] ], ()]);
ALF("(3x2^(1+6)_-.U4(2)).2","2^(1+6)_-.U4(2).2",[1,2,4,3,5,6,7,10,9,11,8,12,
13,14,15,16,17,18,19,20,21,23,22,24,28,25,27,26,29,30,32,31,33,34,35,36,37,
38,39,40,41,42,43,45,44,1,2,4,3,5,6,7,10,9,11,8,12,13,14,13,14,15,16,17,
18,19,20,21,23,22,24,28,25,27,26,29,30,32,31,31,33,34,33,34,35,36,35,36,
37,37,38,39,40,41,42,43,42,43,45,44,45,44,46,47,48,49,50,51,52,53,54,55,
56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78]);
ALF("(3x2^(1+6)_-.U4(2)).2","S3",[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,
2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,
2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,
3,3,3,3]);
ALF("(3x2^(1+6)_-.U4(2)).2","3.Suz.2",[1,3,12,3,3,14,16,12,16,14,5,34,10,
28,7,24,24,49,9,29,51,12,14,36,36,18,38,34,20,43,69,43,27,30,24,53,26,56,
49,53,74,42,68,57,52,2,4,13,4,4,15,17,13,17,15,6,35,10,27,9,26,8,25,25,50,
10,30,52,13,15,37,37,19,39,35,21,44,70,44,44,28,30,26,29,25,54,25,54,27,
28,57,50,54,75,40,66,41,67,57,52,56,51,76,78,84,85,77,78,86,87,84,85,86,
88,79,86,85,87,80,92,98,99,93,100,81,101,86,87,96,90,105,106,98,99,102],[
"fusion map is unique up to table autom.,\n",
"unique representative that is compatible with factors\n",
"and with the fusion 3x2^(1+6)_-.U4(2) -> 3.Suz"
]);
ALN("(3x2^(1+6)_-.U4(2)).2",["3.Suz.2C2A"]);

MOT("3^6:(M11x2)",
[
"6th maximal subgroup of 3.Suz.2",
],
[11547360,5773680,524880,262440,52488,26244,7776,3888,972,972,972,1296,648,
648,324,972,486,162,162,162,162,144,72,72,36,90,45,45,45,45,108,54,54,54,54,
48,24,48,24,66,33,66,33,15840,864,108,36,144,36,36,10,36,18,48,24,48,24,22,
22],
[,[1,2,3,4,5,6,1,2,5,6,6,3,4,5,6,16,17,18,19,20,21,7,8,12,13,26,27,28,30,29,
16,17,19,20,21,22,23,22,23,42,43,40,41,1,1,5,16,7,14,12,26,16,18,22,24,22,24,
42,40],[1,1,1,1,1,1,7,7,7,7,7,7,7,7,7,1,1,1,6,6,6,22,22,22,22,26,26,26,26,26,
7,7,11,11,11,36,36,38,38,40,40,42,42,44,45,45,44,48,48,48,51,45,45,54,54,56,
56,58,59],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,
1,2,3,4,4,31,32,33,34,35,38,39,36,37,40,41,42,43,44,45,46,47,48,49,50,44,52,
53,56,57,54,55,58,59],,,,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,
20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,1,2,1,2,44,45,46,
47,48,49,50,51,52,53,54,55,56,57,44,44]],
0,
[(29,30),(36,38)(37,39)(54,56)(55,57),(40,42)(41,43)(58,59)],
["ConstructMGA","3^6.M11","3^5:(M11x2)",
 [ [ 25, 26 ], [ 27, 30 ], [ 28, 29 ], [ 31, 32 ], [ 33, 34 ],
   [ 35, 36 ], [ 37, 38 ], [ 39, 40 ], [ 41, 42 ], [ 43, 44 ], [ 45, 46 ],
   [ 47, 48 ], [ 49, 50 ], [ 51, 52 ], [ 53, 54 ], [ 55, 58 ], [ 56, 57 ],
   [ 59, 60 ], [ 61, 62 ], [ 63, 64 ], [ 65, 66 ], [ 67, 68 ], [ 69, 70 ] ],
 ()]);
ALF("3^6:(M11x2)","3^5:(M11x2)",[1,1,2,2,3,3,4,4,6,6,6,5,5,7,7,8,8,9,10,
10,10,11,11,12,12,13,13,14,14,14,15,15,16,16,16,17,17,18,18,19,19,20,20,
21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36]);
ALF("3^6:(M11x2)","3.Suz.2",[1,2,7,8,9,10,3,4,26,27,28,24,25,29,30,9,10,
11,40,42,41,16,17,53,54,22,23,64,65,65,29,30,66,68,67,38,39,38,39,47,48,
47,48,77,77,81,81,78,93,92,91,81,83,88,102,88,102,97,97],[
"fusion map is unique"
]);
ALF("3^6:(M11x2)","2xM11",[1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,4,4,
4,4,5,5,5,5,5,6,6,6,6,6,7,7,8,8,9,9,10,10,11,12,12,13,14,14,14,15,16,16,
17,17,18,18,19,20]);

MOT("S3xJ2.2",
[
"7th maximal subgroup of 3.Suz.2"
],
0,
0,
0,
[(26,27)(53,54)(80,81)],
["ConstructDirectProduct",[["Dihedral",6],["J2.2"]]]);
ALF("S3xJ2.2","3.Suz.2",[1,3,5,7,11,12,22,20,24,31,32,34,45,43,49,64,5,16,
18,31,34,34,53,55,61,74,74,2,4,6,8,11,13,23,21,25,31,33,35,46,44,50,65,6,
17,19,31,35,35,54,55,62,75,75,76,76,77,80,82,78,89,90,80,83,95,87,91,90,
92,104,76,78,79,82,85,85,92,94,95,99,99],[
"fusion map is unique"
]);
ALF("S3xJ2.2","J2.2x2",[1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,
37,39,41,43,45,47,49,51,53,1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,
35,37,39,41,43,45,47,49,51,53,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,
34,36,38,40,42,44,46,48,50,52,54]);

MOT("(3x2^(4+6):3A6).2",
[
"8th maximal subgroup of 3.Suz.2",
],
[6635520,442368,23040,18432,18432,51840,3456,9216,3072,9216,3072,4608,1536,
384,384,288,288,144,216,72,864,432,864,144,144,576,576,192,192,72,72,180,60,
45,45,3317760,221184,11520,9216,9216,51840,3456,51840,3456,4608,1536,4608,
1536,2304,768,192,192,288,288,144,288,288,144,108,36,432,432,432,432,72,72,
288,288,96,96,72,72,72,72,180,60,45,45,180,60,45,45,1536,512,96,256,256,768,
768,3072,1024,768,128,128,64,64,64,64,16,12,12,24,24,24,24],
[,[1,1,1,2,2,6,6,1,1,2,2,2,2,4,5,6,7,7,19,19,21,21,21,23,23,8,10,9,11,16,17,
32,32,34,35,36,36,36,37,37,41,41,43,43,36,36,37,37,37,37,39,40,41,42,42,43,44,
44,59,59,61,61,61,61,64,64,45,47,46,48,53,54,56,57,75,75,77,78,79,79,81,82,1,
2,3,4,4,1,2,4,4,4,4,4,9,8,11,10,15,19,20,21,23,24,24],[1,2,3,4,5,1,2,8,9,10,
11,12,13,14,15,8,10,12,1,3,1,2,2,4,5,26,27,28,29,26,27,32,33,32,32,1,2,3,4,5,
1,2,1,2,8,9,10,11,12,13,14,15,8,10,12,8,10,12,1,3,1,2,2,2,4,5,26,27,28,29,26,
27,26,27,32,33,32,32,32,33,32,32,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,
98,99,83,85,88,89,92,90],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,
21,22,23,24,25,26,27,28,29,30,31,1,3,6,6,36,37,38,39,40,41,42,43,44,45,46,47,
48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,
74,36,38,41,43,36,38,41,43,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,
100,101,102,103,104,105]],
0,
[(34,35)(75,79)(76,80)(77,81)(78,82),(34,35)(41,43)(42,44)(53,56)(54,57)(55,
58)(62,63)(71,73)(72,74)(77,78)(81,82)],
["ConstructMGA","3x2^(4+6).3A6","2^(4+6):3S6",
 [ [ 48, 95 ], [ 49, 96 ], [ 50, 97 ], [ 51, 99 ], [ 52, 98 ],
   [ 53, 100 ], [ 54, 101 ], [ 55, 108 ], [ 56, 107 ], [ 57, 109 ],
   [ 58, 110 ], [ 59, 111 ], [ 60, 103 ], [ 61, 102 ], [ 62, 104 ],
   [ 63, 105 ], [ 64, 106 ], [ 65, 112 ], [ 66, 114 ], [ 67, 113 ],
   [ 68, 115 ], [ 69, 116 ], [ 70, 117 ], [ 71, 118 ], [ 72, 119 ],
   [ 73, 120 ], [ 74, 121 ], [ 75, 122 ], [ 76, 124 ], [ 77, 123 ],
   [ 78, 125 ], [ 79, 127 ], [ 80, 126 ], [ 81, 128 ], [ 82, 130 ],
   [ 83, 129 ], [ 84, 131 ], [ 85, 133 ], [ 86, 132 ], [ 87, 134 ],
   [ 88, 136 ], [ 89, 135 ], [ 90, 137 ], [ 91, 138 ], [ 92, 139 ],
   [ 93, 140 ], [ 94, 141 ] ], ()]);
ALF("(3x2^(4+6):3A6).2","2^(4+6):3S6",[1,2,3,4,5,6,7,8,9,10,12,11,13,15,14,16,
17,18,19,20,21,23,22,25,24,26,28,27,29,30,31,32,33,34,35,1,2,3,4,5,6,7,6,
7,8,9,10,12,11,13,15,14,16,17,18,16,17,18,19,20,21,23,23,22,25,24,26,28,
27,29,30,31,30,31,32,33,34,35,32,33,35,34,36,37,38,39,40,41,42,43,44,45,
46,47,48,49,50,51,52,53,54,55,56,57,58]);
ALF("(3x2^(4+6):3A6).2","S3",[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,
2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,
3,3,3,3,3,3,3,3,3]);
ALF("(3x2^(4+6):3A6).2","3.Suz.2",[1,3,5,12,14,8,25,3,5,12,16,16,14,34,36,
25,50,54,11,31,9,26,29,51,56,16,34,18,38,54,75,22,45,65,65,2,4,6,13,15,7,
24,8,25,4,6,13,17,17,15,35,37,24,49,53,25,50,54,11,31,10,27,28,30,52,57,
17,35,19,39,53,74,54,75,23,46,64,65,23,46,64,65,76,78,79,87,85,77,78,84,
85,86,86,87,79,78,88,87,96,82,94,81,93,101,100],[
"fusion map is unique up to table automorphisms"
]);

MOT("(A4x3.L3(4).2_3).2",
[
"9th maximal subgroup of 3.Suz.2",
],
[2903040,1451520,9216,4608,432,2304,1152,1152,1152,1152,360,180,504,252,
967680,483840,3072,1536,144,768,384,384,384,384,120,60,168,84,362880,181440,
1152,576,54,288,144,144,144,144,90,45,90,45,63,63,63,1728,864,1728,864,192,96,
192,96,72,72,96,48,96,48,48,48,48,48,48,48,2880,1344,960,1344,64,64,360,144,
48,24,18,384,384,128,128,32,32,120,40,24,28,48,48,28,30,30],
[,[1,2,1,2,5,3,4,3,4,4,11,12,13,14,1,2,1,2,5,3,4,3,4,4,11,12,13,14,29,30,29,
30,33,31,32,31,32,32,39,40,41,42,43,44,45,1,2,15,16,3,4,17,18,5,19,6,7,20,21,
8,10,9,22,24,23,1,1,1,15,3,17,29,5,5,5,33,6,6,6,6,6,20,11,11,19,13,34,34,27,
41,39],[1,1,3,3,1,6,6,8,8,8,11,11,13,13,15,15,17,17,15,20,20,22,22,22,25,25,
27,27,1,1,3,3,1,6,6,8,8,8,11,11,11,11,13,13,13,46,46,48,48,50,50,52,52,46,48,
56,56,58,58,60,60,60,63,63,63,66,67,68,69,70,71,66,66,68,67,66,77,78,79,80,81,
82,83,84,69,86,77,78,89,83,83],,[1,2,3,4,5,6,7,8,10,9,1,2,13,14,15,16,17,18,
19,20,21,22,24,23,15,16,27,28,29,30,31,32,33,34,35,36,38,37,29,30,29,30,43,45,
44,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,62,61,63,65,64,66,67,68,69,70,
71,72,73,74,75,76,77,78,79,80,81,82,66,68,85,86,87,88,89,72,72],,[1,2,3,4,5,6,
7,8,9,10,11,12,1,2,15,16,17,18,19,20,21,22,23,24,25,26,15,16,29,30,31,32,33,
34,35,36,37,38,41,42,39,40,29,30,30,46,47,48,49,50,51,52,53,54,55,56,57,58,59,
60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,
67,87,88,69,91,90]],
0,
[( 9,10)(23,24)(37,38)(61,62)(64,65),(39,41)(40,42)(90,91),(44,45)],
["ConstructMGA","(A4x3.L3(4)).2","(A4xL3(4):2_3):2",
 [ [ 39, 40 ], [ 41, 42 ], [ 43, 44 ], [ 45, 46 ], [ 47, 49 ],
   [ 48, 50 ], [ 51, 53 ], [ 52, 54 ], [ 55, 57 ], [ 56, 58 ], [ 59, 61 ],
   [ 60, 62 ], [ 63, 64 ], [ 65, 67 ], [ 66, 68 ], [ 69, 71 ], [ 70, 72 ],
   [ 73, 74 ], [ 75, 76 ], [ 77, 78 ], [ 79, 82 ], [ 80, 81 ], [ 83, 84 ],
   [ 85, 95 ], [ 86, 96 ], [ 87, 93 ], [ 88, 94 ], [ 89, 99 ],
   [ 90, 100 ], [ 91, 97 ], [ 92, 98 ], [ 101, 104 ], [ 102, 103 ] ], ()]);
ALF("(A4x3.L3(4).2_3).2","(A4xL3(4):2_3):2",[1,1,4,4,6,8,8,9,9,9,12,12,
15,15,2,2,5,5,14,10,10,11,11,11,16,16,19,19,3,3,13,13,7,17,17,18,18,18,20,
20,21,21,22,22,22,23,23,24,24,25,25,26,26,27,32,28,28,29,29,30,30,30,31,
31,31,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,
55,56,57,58]);
ALF("(A4x3.L3(4).2_3).2","Symm(4)",[1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,
2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,5,5,4,4,5,5,4,5,4,4,
5,5,4,4,4,5,5,5,1,4,2,5,4,5,3,1,2,4,3,1,1,2,2,4,5,1,2,5,4,3,3,5,3,3]);
ALF("(A4x3.L3(4).2_3).2","3.L3(4).2^2",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,
1,2,3,4,5,6,7,8,9,10,11,12,13,14,1,2,3,4,5,6,7,8,9,10,11,12,11,12,13,14,
14,15,16,15,16,17,18,17,18,19,19,20,21,20,21,22,23,24,22,23,24,30,25,30,
25,26,26,30,31,31,27,31,32,33,32,33,28,28,34,34,27,29,32,33,29,34,34]);
ALF("(A4x3.L3(4).2_3).2","3.Suz.2",[1,2,3,4,11,12,13,16,17,17,22,23,32,33,
5,6,5,6,31,16,17,14,15,15,45,46,61,62,7,8,24,25,11,49,50,53,54,54,64,65,
64,65,71,72,73,5,6,18,19,16,17,18,19,31,55,34,35,38,39,38,39,39,36,37,37,
76,76,77,79,78,79,80,82,83,82,82,84,85,87,87,87,88,89,91,94,95,98,99,103,
104,104],[
"fusion map is unique up to table automorphisms"
]);

MOT("(3x2^(2+8):(A5xS3)).2",
[
"10th maximal subgroup of 3.Suz.2",
],
[2211840,737280,36864,9216,18432,9216,6144,2304,1536,1536,384,384,6912,2304,
288,576,288,360,120,1080,72,216,72,45,23040,23040,2304,1152,1536,1536,768,384,
192,192,192,288,288,72,144,60,60,1105920,368640,18432,4608,9216,4608,3072,
1152,768,768,192,192,3456,1152,288,288,288,144,360,120,360,120,540,36,108,36,
45,45,11520,11520,1152,576,768,768,384,192,192,192,96,96,144,144,72,72,72,60,
60,60,60,4608,768,768,768,512,128,96,64,32,144,96,72,36,24,3072,3072,512,384,
256,256,192,128,64,64,64,64,96,12,16,96,96,48,24],
[,[1,1,1,1,2,2,2,1,3,3,5,7,13,13,13,14,14,18,18,20,20,22,22,24,1,2,3,5,1,2,3,
5,7,6,4,13,14,15,16,18,19,42,42,42,42,43,43,43,42,44,44,46,48,54,54,54,54,55,
55,60,60,62,62,64,64,66,66,68,69,42,43,44,46,42,43,44,46,48,48,47,45,54,55,56,
57,58,60,61,62,63,1,1,1,2,2,3,8,4,8,13,13,22,20,22,5,5,5,5,5,5,6,5,9,9,9,9,14,
21,12,16,16,16,17],[1,2,3,4,5,6,7,8,9,10,11,12,1,2,3,5,6,18,19,1,8,1,4,18,25,
26,27,28,29,30,31,32,33,34,35,25,26,27,28,40,41,1,2,3,4,5,6,7,8,9,10,11,12,1,
2,3,3,5,6,18,19,18,19,1,8,1,4,18,18,25,26,27,28,29,30,31,32,33,33,34,35,25,26,
27,27,28,40,41,40,41,91,92,93,94,95,96,97,98,99,91,92,91,91,93,105,106,107,
108,109,110,111,112,113,114,115,116,94,97,119,106,105,108,111],,[1,2,3,4,5,6,
7,8,9,10,11,12,13,14,15,16,17,1,2,20,21,22,23,20,25,26,27,28,29,30,31,32,33,
34,35,36,37,38,39,25,26,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,
42,43,42,43,64,65,66,67,64,64,70,71,72,73,74,75,76,77,79,78,80,81,82,83,84,85,
86,70,71,70,71,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,
109,110,111,112,113,114,115,116,117,118,119,120,121,122,123]],
0,
[(56,57)(84,85),(60,62)(61,63)(68,69)(87,89)(88,90),(78,79)],
["ConstructMGA","3x2^(2+8):(A5xS3)","2^(2+8):(S5xS3)",
 [ [ 50, 99 ], [ 51, 101 ], [ 52, 100 ], [ 53, 102 ], [ 54, 103 ],
   [ 55, 104 ], [ 56, 106 ], [ 57, 105 ], [ 58, 107 ], [ 59, 108 ],
   [ 60, 109 ], [ 61, 111 ], [ 62, 110 ], [ 63, 112 ], [ 64, 113 ],
   [ 65, 114 ], [ 66, 116 ], [ 67, 115 ], [ 68, 117 ], [ 69, 118 ],
   [ 70, 120 ], [ 71, 119 ], [ 72, 121 ], [ 73, 122 ], [ 74, 123 ],
   [ 75, 124 ], [ 76, 125 ], [ 77, 126 ], [ 78, 127 ], [ 79, 128 ],
   [ 80, 129 ], [ 81, 130 ], [ 82, 131 ], [ 83, 132 ], [ 84, 133 ],
   [ 85, 134 ], [ 86, 137 ], [ 87, 136 ], [ 88, 135 ], [ 89, 138 ],
   [ 90, 140 ], [ 91, 139 ], [ 92, 141 ], [ 93, 142 ], [ 94, 143 ],
   [ 95, 145 ], [ 96, 144 ], [ 97, 146 ], [ 98, 147 ] ], ()]);
ALF("(3x2^(2+8):(A5xS3)).2","2^(2+8):(S5xS3)",[1,2,3,4,5,6,7,8,11,10,15,16,9,
13,14,18,19,12,17,20,22,21,23,24,25,27,28,33,26,29,30,34,36,35,31,32,38,
39,41,37,40,1,2,3,4,5,6,7,8,11,10,15,16,9,13,14,14,18,19,12,17,12,17,20,
22,21,23,24,24,25,27,28,33,26,29,30,34,36,36,35,31,32,38,39,39,41,37,40,
37,40,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,
64,65,66,67,68,69,70,71,72,73,74]);
ALF("(3x2^(2+8):(A5xS3)).2","S3",[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,
2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,
3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3]);
ALF("(3x2^(2+8):(A5xS3)).2","3.Suz.2",[1,3,3,5,12,16,14,5,12,14,34,36,7,
24,24,49,53,20,43,11,31,11,31,63,3,12,16,34,5,16,14,34,36,38,18,24,49,53,
74,43,69,2,4,4,6,13,17,15,6,13,15,35,37,8,25,25,25,50,54,21,44,21,44,11,
31,11,31,63,63,4,13,17,35,6,17,15,35,37,37,39,19,25,50,54,54,75,44,70,44,
70,76,76,77,78,78,78,79,79,79,80,80,82,82,83,84,85,85,85,87,86,88,87,87,
85,86,87,92,94,96,99,98,99,102],[
"fusion map is unique"
]);

MOT("S3xM12.2",
[
"11th maximal subgroup of 3.Suz.2"
],
0,
0,
0,
[(20,21)(41,42)(62,63),(17,18)(38,39)(59,60)],
["ConstructDirectProduct",[["Dihedral",6],["M12.2"]]]);
ALF("S3xM12.2","3.Suz.2",[1,5,3,9,11,16,22,31,29,38,45,47,5,14,18,31,45,
45,55,56,56,2,6,4,10,11,17,23,31,30,39,46,48,6,15,19,31,46,46,55,57,57,77,
76,77,81,83,78,91,82,81,88,89,97,77,78,79,83,91,91,94,93,93],[
"fusion map is unique"
]);
ALF("S3xM12.2","M12.2x2",[1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,
35,37,39,41,1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,2,4,
6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42]);

MOT("3.3^(2+4):2(S4xD8)",
[
"12th maximal subgroup of 3.Suz.2"
],
[839808,419904,209952,104976,209952,104976,2916,1458,648,10368,5184,2592,1296,
2592,1296,7776,3888,3888,3888,3888,324,162,1728,864,72,11664,5832,2916,2916,
2916,2916,1458,162,162,162,576,288,1728,864,432,216,432,216,864,432,36,96,48,
288,144,144,72,144,72,72,36,1296,648,324,324,324,324,162,324,324,324,324,324,
324,324,324,324,54,54,54,48,24,144,72,72,72,72,72,36,864,432,36,288,144,36,36,
36,24,24,32,192,192,36,432,216,36,24,48,288,72,72,72,72,288,36,288,64,64],
[,[1,2,3,4,5,6,7,8,9,1,2,3,4,5,6,1,2,5,6,6,7,8,1,2,9,26,27,28,29,30,31,32,33,
34,35,10,11,10,11,12,13,14,15,23,24,25,23,24,10,11,14,15,10,11,12,13,26,27,28,
29,30,31,32,28,29,30,26,27,27,28,29,30,33,34,35,36,37,38,39,40,41,41,57,58,1,
3,9,10,12,57,62,62,83,83,36,36,36,7,1,5,9,42,38,38,40,42,14,12,10,7,1,38,38],
[1,1,1,1,1,1,1,1,1,10,10,10,10,10,10,16,16,16,16,16,16,16,23,23,23,1,1,1,1,1,
1,1,6,6,6,36,36,38,38,38,38,38,38,44,44,44,47,47,49,49,49,49,53,53,53,53,10,
10,10,10,10,10,10,16,16,16,16,16,16,16,16,16,20,20,20,76,76,78,78,78,78,78,36,
36,85,85,85,88,88,88,88,88,96,97,95,96,97,99,99,99,99,103,103,104,104,104,109,
109,109,111,111,112,113]],
0,
[(81,82),(91,92),( 93, 94)( 96, 97)(112,113)],
["ConstructMGA","3.3^(2+4):2(A4x2^2).2","3^(2+4):2(S4xD8)",
 [ [ 50, 52 ], [ 51, 53 ], [ 54, 56 ], [ 55, 57 ], [ 58, 60 ],
   [ 59, 61 ], [ 62, 64 ], [ 63, 65 ], [ 66, 68 ], [ 67, 69 ], [ 70, 72 ],
   [ 71, 73 ], [ 74, 76 ], [ 75, 77 ], [ 78, 80 ], [ 79, 81 ], [ 82, 84 ],
   [ 83, 85 ], [ 86, 88 ], [ 87, 89 ], [ 90, 91 ], [ 92, 96 ], [ 93, 97 ],
   [ 94, 98 ], [ 95, 99 ], [ 100, 102 ], [ 101, 103 ], [ 104, 108 ],
   [ 105, 109 ], [ 106, 110 ], [ 107, 111 ], [ 112, 113 ], [ 114, 116 ],
   [ 115, 117 ], [ 118, 120 ], [ 119, 121 ], [ 122, 123 ], [ 124, 125 ],
   [ 126, 128 ], [ 127, 129 ], [ 130, 131 ], [ 132, 134 ], [ 133, 135 ],
   [ 136, 138 ], [ 137, 139 ] ], ()]);
ALF("3.3^(2+4):2(S4xD8)","3^(2+4):2(S4xD8)",[1,1,2,2,3,3,5,5,4,6,6,7,7,
8,8,27,27,28,28,28,29,29,19,19,20,12,12,14,14,14,13,13,15,15,15,21,21,9,9,
10,10,11,11,33,33,32,34,34,30,30,31,31,38,38,39,39,16,16,18,18,18,17,17,
25,25,25,23,23,23,24,24,24,26,26,26,35,35,37,37,36,36,36,22,22,40,41,42,
43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,
67,68]);
ALF("3.3^(2+4):2(S4xD8)","3.Suz.2",[1,2,7,8,9,10,9,10,11,3,4,24,25,29,30,
3,4,26,27,28,29,30,5,6,31,7,8,9,10,10,9,10,40,41,42,16,17,12,13,49,50,51,
52,18,19,55,18,19,14,15,56,57,16,17,53,54,24,25,26,27,28,29,30,29,30,30,
24,25,25,26,28,27,66,67,68,38,39,34,35,74,75,75,53,54,76,80,82,78,92,92,
93,93,102,102,88,88,88,81,77,81,83,101,86,84,98,100,93,92,78,81,77,87,87],[
"fusion map is unique"
]);

MOT("(3.A6.2_2xA5):2",
[
"13th maximal subgroup of 3.Suz.2"
],
[259200,129600,5760,2880,1080,2880,1440,1800,900,17280,8640,384,192,72,192,96,
120,60,12960,6480,288,144,54,144,72,90,45,10800,5400,240,120,45,120,60,150,75,
150,75,144,72,144,144,144,48,24,48,48,48,72,36,72,72,72,2400,288,160,96,96,32,
144,120,36,18,480,32,600,100,50,50,40,48,12,24,30,40,40],
[,[1,2,1,2,5,3,4,8,9,1,2,1,2,5,3,4,8,9,19,20,19,20,23,21,22,26,27,28,29,28,29,
32,30,31,35,36,37,38,3,4,6,7,7,12,13,15,16,16,21,22,24,25,25,1,1,1,3,10,12,19,
19,5,23,6,6,8,28,37,35,8,21,14,24,26,33,33],[1,1,3,3,1,6,6,8,8,10,10,12,12,10,
15,15,17,17,1,1,3,3,1,6,6,8,8,28,28,30,30,28,33,33,35,35,37,37,39,39,41,41,41,
44,44,46,46,46,39,39,41,41,41,54,55,56,57,58,59,55,54,55,55,64,65,66,67,68,69,
70,57,58,64,66,75,76],,[1,2,3,4,5,6,7,1,2,10,11,12,13,14,15,16,10,11,19,20,21,
22,23,24,25,19,20,1,2,3,4,5,6,7,1,2,1,2,39,40,41,42,43,44,45,46,47,48,49,50,
51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,54,54,54,54,56,71,72,73,61,64,
64]],
0,
[(35,37)(36,38)(68,69),(75,76),(42,43)(47,48)(52,53)],
["ConstructMGA","(3.A6xA5):2","(A6:2_2xA5).2",
 [ [ 32, 34 ], [ 33, 35 ], [ 36, 38 ], [ 37, 39 ], [ 40, 41 ],
   [ 42, 43 ], [ 44, 45 ], [ 46, 47 ], [ 48, 49 ], [ 50, 53 ], [ 51, 52 ],
   [ 54, 55 ], [ 56, 57 ], [ 58, 59 ], [ 60, 63 ], [ 61, 62 ], [ 64, 66 ],
   [ 65, 67 ], [ 68, 70 ], [ 69, 71 ], [ 72, 74 ], [ 73, 75 ], [ 76, 79 ],
   [ 77, 78 ], [ 80, 82 ], [ 81, 83 ] ], ()]);
ALF("(3.A6.2_2xA5):2","(A6:2_2xA5).2",[1,1,2,2,3,4,4,5,5,6,6,7,7,15,10,10,
17,17,8,8,14,14,9,18,18,20,20,11,11,16,16,19,21,21,12,12,13,13,22,22,24,
24,24,23,23,25,25,25,26,26,27,27,27,28,29,30,31,32,33,34,35,36,37,38,39,
40,41,42,43,44,45,46,47,48,49,50]);
ALF("(3.A6.2_2xA5):2","A5.2",[1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,3,3,3,3,
3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,6,6,6,6,6,7,7,7,7,7,1,5,2,5,6,6,
7,3,5,7,1,2,1,4,4,4,2,7,6,3,3,4,4]);
ALF("(3.A6.2_2xA5):2","3.A6.2^2",[1,2,3,4,5,6,7,8,9,1,2,3,4,5,6,7,8,9,1,2,
3,4,5,6,7,8,9,1,2,3,4,5,6,7,8,9,8,9,16,17,18,19,20,16,17,18,19,20,16,17,
18,19,20,13,10,13,11,10,11,10,13,12,12,14,14,15,13,15,15,15,11,12,14,15,
14,14]);
ALF("(3.A6.2_2xA5):2","3.Suz.2",[1,2,3,4,11,12,13,22,23,5,6,5,6,31,16,17,
45,46,7,8,24,25,11,49,50,64,65,20,21,43,44,63,69,70,20,21,22,23,16,17,34,
35,35,18,19,38,39,39,53,54,74,75,75,76,76,77,78,79,79,80,80,82,82,84,87,
89,90,89,90,91,92,94,98,104,106,105],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);

MOT("(3^(1+2):8xA6).2",
[
"14th maximal subgroup of 3.Suz.2",
],
[155520,77760,6480,17280,8640,8640,4320,3456,1728,144,384,192,192,96,3888,
1944,162,432,216,216,108,3888,1944,162,432,216,216,108,1728,864,72,192,96,96,
48,1080,540,45,120,60,120,60,120,60,288,288,288,288,288,288,48,48,48,36,36,36,
36,36,36,2880,2880,288,288,48,144,144,36,36,18,18,24,64,64,32,32,72,72,72,72,
40,40,40,40],
[,[1,2,3,1,2,4,5,1,2,3,1,2,4,5,15,16,17,15,16,18,19,22,23,24,22,23,25,26,8,9,
10,8,9,11,12,36,37,38,36,37,39,40,39,40,4,5,5,4,5,5,11,12,12,18,19,19,25,26,
26,6,6,1,1,8,3,3,15,22,17,24,10,6,6,13,13,20,20,27,27,41,41,43,43],[1,1,1,4,4,
6,6,8,8,8,11,11,13,13,1,1,1,4,4,6,6,1,1,1,4,4,6,6,29,29,29,32,32,34,34,36,36,
36,39,39,41,41,43,43,45,45,45,48,48,48,51,51,51,45,45,45,48,48,48,60,61,62,63,
64,62,63,62,63,62,63,64,72,73,74,75,61,60,61,60,80,81,82,83],,[1,2,3,4,5,6,7,
8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,
34,35,1,2,3,4,5,6,7,6,7,45,47,46,48,50,49,51,53,52,54,56,55,57,59,58,61,60,62,
63,64,65,66,67,68,69,70,71,73,72,75,74,77,76,79,78,61,60,61,60]],
0,
[(41,43)(42,44)(80,82)(81,83),(46,47)(49,50)(52,53)(55,56)(58,59),(60,61)(72,
73)(74,75)(76,77)(78,79)(80,81)(82,83),(15,22)(16,23)(17,24)(18,25)(19,26)(20,
27)(21,28)(45,48)(46,49)(47,50)(54,57)(55,58)(56,59)(62,63)(65,66)(67,68)(69,
70)(76,78)(77,79)],
["ConstructMGA","(3^(1+2):4xA6).2","(3^2:8xA6).2",
 [ [ 37, 39 ], [ 38, 40 ], [ 41, 43 ], [ 42, 44 ], [ 45, 50 ],
   [ 46, 49 ], [ 47, 51 ], [ 48, 52 ], [ 53, 54 ], [ 55, 60 ], [ 56, 59 ],
   [ 57, 61 ], [ 58, 62 ], [ 63, 64 ], [ 65, 70 ], [ 66, 69 ], [ 67, 71 ],
   [ 68, 72 ], [ 73, 77 ], [ 74, 78 ], [ 75, 80 ], [ 76, 79 ], [ 81, 86 ],
   [ 82, 85 ], [ 83, 87 ], [ 84, 88 ], [ 89, 90 ], [ 91, 92 ], [ 93, 94 ] ],
 ()]);
ALF("(3^(1+2):8xA6).2","(3^2:8xA6).2",[1,1,2,3,3,4,4,7,7,22,10,10,16,16,
11,11,13,24,24,31,31,12,12,14,25,25,32,32,15,15,33,17,17,19,19,20,20,35,
30,30,36,36,37,37,50,50,50,51,51,51,52,52,52,53,53,53,54,54,54,5,6,8,9,18,
21,23,26,27,28,29,34,38,39,40,41,42,43,44,45,46,47,48,49]);
ALF("(3^(1+2):8xA6).2","A6.2_1",[1,1,1,1,1,1,1,2,2,2,2,2,2,2,3,3,3,3,3,3,
3,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,7,7,7,8,8,8,9,9,9,10,10,
10,11,11,11,1,1,7,8,9,7,8,10,11,10,11,9,2,2,5,5,3,3,4,4,6,6,6,6]);
ALF("(3^(1+2):8xA6).2","3^(1+2):SD16",[1,4,5,2,8,6,14,1,4,5,2,8,6,14,1,4,
5,2,8,6,14,1,4,5,2,8,6,14,1,4,5,2,8,6,14,1,4,5,2,8,6,14,6,14,7,12,13,7,12,
13,7,12,13,7,12,13,7,12,13,10,11,3,3,3,9,9,3,3,9,9,9,11,10,10,11,11,10,11,
10,10,11,10,11]);
ALF("(3^(1+2):8xA6).2","3.Suz.2",[1,2,11,3,4,12,13,5,6,31,5,6,16,17,7,8,
11,24,25,49,50,9,10,11,29,30,51,52,18,19,55,18,19,18,19,20,21,63,43,44,69,
70,69,70,16,17,17,14,15,15,18,19,19,53,54,54,56,57,57,84,84,76,77,79,82,
83,80,81,82,83,94,87,87,88,88,98,98,100,100,105,106,106,105],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);

MOT("(3xL2(25)).2_2",
[
"15th maximal subgroup of 3.Suz.2"
],
[46800,144,72,72,150,150,72,36,39,39,39,23400,72,36,36,75,75,36,36,36,39,39,
39,39,39,39,240,240,8,12,12,10,10],
[,[1,1,3,2,5,6,3,7,11,9,10,12,12,14,13,16,17,14,18,18,25,26,21,22,23,24,1,1,2,
3,3,5,6],[1,2,1,4,5,6,2,4,11,9,10,1,2,1,4,5,6,2,4,4,11,11,9,9,10,10,27,28,29,
27,28,32,33],,[1,2,3,4,1,1,7,8,9,10,11,12,13,14,15,12,12,18,19,20,21,22,23,24,
25,26,27,28,29,30,31,27,28],,,,,,,,[1,2,3,4,5,6,7,8,1,1,1,12,13,14,15,16,17,
18,19,20,12,12,12,12,12,12,27,28,29,30,31,32,33]],
0,
--> --------------------

--> maximum size reached

--> --------------------