#############################################################################
##
#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,
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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,
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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,
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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,
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[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
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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,
0,-1,3,-1,0,1,15,-1,0,-1,3,-1,0,1,15,-1,0,-1,3,-1,0,0,1,1,-3,-3,1,1,0,0,1,1,
-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],
--> --------------------
--> maximum size reached
--> --------------------
