Quelle  ctomisc1.tbl   Sprache: unbekannt

#############################################################################
##
#W  ctomisc1.tbl                GAP table library               Thomas Breuer
##
##  This file contains the ordinary character tables of miscellaneous
##  CAS tables (alphabetical order, up to 'e')
##
#H  ctbllib history
#H  ---------------
#H  $Log: ctomisc1.tbl,v $
#H  Revision 4.39  2012/06/20 14:45:32  gap
#H  added tables and fusions, as documented in ctbldiff.dat
#H      TB
#H
#H  Revision 4.38  2012/04/23 16:16:14  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 4.37  2012/01/30 08:31:57  gap
#H  removed #H entries from the headers
#H      TB
#H
#H  Revision 4.36  2011/09/28 13:23:58  gap
#H  - removed revision entry and SET_TABLEFILENAME call,
#H  - added fusions 2.2^8.f20 -> 2.[2^9]:5:4, 2^2.2^8:s3 -> 2^2.[2^9]:S3,
#H    c3d2 -> Co3
#H      TB
#H
#H  Revision 4.35  2010/12/01 17:47:57  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 4.34  2010/05/05 13:20:07  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 4.33  2010/01/19 17:05:34  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 4.32  2009/07/29 14:00:41  gap
#H  added two tables of maxes of 2F4(2)
#H      TB
#H
#H  Revision 4.31  2009/03/02 16:44:38  gap
#H  moved the tables of A15, A16 from ctomisc1.tbl to ctoalter.tbl
#H      TB
#H
#H  Revision 4.30  2007/07/03 08:27:32  gap
#H  renamed table `"d60"' to `"D120"'
#H  (the name goes back to CAS times; it does not fit to the programmatic use
#H  of names such as `"C<n>"', `"D<n>"', `"S<n>"' etc.)
#H      TB
#H
#H  Revision 4.29  2004/02/17 17:33:14  gap
#H  added certain tables of isoclinic groups of ATLAS groups
#H  (which are available in atlasrep),
#H  added missing maxes of U5(2)
#H      TB
#H
#H  Revision 4.28  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 4.27  2003/06/20 15:03:09  gap
#H  added several fusions
#H      TB
#H
#H  Revision 4.26  2003/06/10 16:19:09  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 4.25  2003/05/15 17:38:17  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 4.24  2003/03/07 15:53:40  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 4.23  2003/01/24 15:57:34  gap
#H  replaced several fusions by ones that are compatible with Brauer tables
#H      TB
#H
#H  Revision 4.22  2003/01/21 16:25:32  gap
#H  further standardizations of `InfoText' strings,
#H  added and corrected `Maxes' infos,
#H  added some fusions
#H      TB
#H
#H  Revision 4.21  2003/01/14 17:28:50  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 4.20  2002/10/22 12:44:11  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 4.19  2002/09/23 15:00:11  gap
#H  changed 2x3.A7.2 into a ``construction'' table,
#H  corrected fusion A11Syl2 -> A11,
#H  changed the name `c2m24' to `M24C2B'
#H      TB
#H
#H  Revision 4.18  2002/09/18 15:22:01  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 4.17  2002/08/21 13:53:50  gap
#H  removed names of the form `c1m<n>', `c2m<n>', `c3m<n>'
#H      TB
#H
#H  Revision 4.16  2002/07/26 16:58:05  gap
#H  added more missing table automorphisms,
#H  removed a few inconvenient names such as `c2' for `Co2'
#H  (note that `c2' is used for the cyclic group of order 2,
#H  which occurs in direct product constructions ...)
#H      TB
#H
#H  Revision 4.15  2002/07/12 06:45:55  gap
#H  further tidying up: removed `irredinfo' stuff, rearranged constructions
#H      TB
#H
#H  Revision 4.14  2001/05/04 16:48:49  gap
#H  first revision for ctbllib
#H
#H
#H  tbl history (GAP 4)
#H  -------------------
#H  (Rev. 4.14 of ctbllib coincides with Rev. 4.13 of tbl in GAP 4)
#H  
#H  RCS file: /gap/CVS/GAP/4.0/tbl/ctomisc1.tbl,v
#H  Working file: ctomisc1.tbl
#H  head: 4.13
#H  branch:
#H  locks: strict
#H  access list:
#H  symbolic names:
#H   GAP4R2: 4.13.0.6
#H   GAP4R2PRE2: 4.13.0.4
#H   GAP4R2PRE1: 4.13.0.2
#H   GAP4R1: 4.10.0.2
#H  keyword substitution: kv
#H  total revisions: 15; selected revisions: 15
#H  description:
#H  ----------------------------
#H  revision 4.13
#H  date: 2000/01/06 14:47:53;  author: gap;  state: Exp;  lines: +2 -2174
#H  removed tables with name `2.cenc1'
#H  (a relic from old CAS times that is inconsistent;
#H  time to get rid of it, before someone finds it interesting ...)
#H  
#H      TB
#H  ----------------------------
#H  revision 4.12
#H  date: 1999/10/04 15:57:15;  author: gap;  state: Exp;  lines: +6 -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 4.11
#H  date: 1999/09/14 13:28:19;  author: gap;  state: Exp;  lines: +2 -484
#H  really removed corrupted tables (had only been commented out before)
#H  
#H      TB
#H  ----------------------------
#H  revision 4.10
#H  date: 1999/07/21 11:11:30;  author: gap;  state: Exp;  lines: +12 -20
#H  renamed `a15' and `a16' to `A15' and `A16', respectively
#H  (just for unified treatment of tables via names)
#H  
#H      TB
#H  ----------------------------
#H  revision 4.9
#H  date: 1999/07/19 16:00:31;  author: gap;  state: Exp;  lines: +20 -12
#H  added fusion A16 -> S16
#H  
#H      TB
#H  ----------------------------
#H  revision 4.8
#H  date: 1999/07/16 10:53:37;  author: gap;  state: Exp;  lines: +58 -45
#H  changed `classtext' components of tables of alternating and symmetric
#H  groups to `ClassParameters' values (same format as computed from
#H  generic tables)
#H  
#H      TB
#H  ----------------------------
#H  revision 4.7
#H  date: 1999/07/14 15:18:38;  author: gap;  state: Exp;  lines: +483 -483
#H  removed incomplete CAS table of `D2MJ4'
#H  
#H      TB
#H  ----------------------------
#H  revision 4.6
#H  date: 1999/07/14 11:39:40;  author: gap;  state: Exp;  lines: +4 -3
#H  cosmetic changes for the release ...
#H  
#H      TB
#H  ----------------------------
#H  revision 4.5
#H  date: 1999/06/11 14:35:34;  author: gap;  state: Exp;  lines: +17 -2
#H  added fusions A15 -> S15, A16 -> S16
#H  
#H      TB
#H  ----------------------------
#H  revision 4.4
#H  date: 1997/11/25 15:45:25;  author: gap;  state: Exp;  lines: +7 -5
#H  first attempt to link the library of character tables and the
#H      library of tables of marks
#H          TB
#H  ----------------------------
#H  revision 4.3
#H  date: 1997/08/05 15:03:47;  author: gap;  state: Exp;  lines: +5 -5
#H  removed unnecessary (and ugly) `return' statements in the calls of
#H      `ConstructPermuted' and `ConstructSubdirect'
#H  ----------------------------
#H  revision 4.2
#H  date: 1997/08/01 15:43:06;  author: gap;  state: Exp;  lines: +2 -40
#H  added table of 2^7:S6(2)
#H      (subgroup of Fi22.2; stored using Clifford matrices);
#H  added tables of A14 mod p for p = 2, 11, 13
#H      (moved ordinary table from `ctomisc1.tbl' to `ctoalter.tbl' for that);
#H  added maxes of 2.M12;
#H  updated the ``table of contents''.
#H  ----------------------------
#H  revision 4.1
#H  date: 1997/07/17 15:43:37;  author: fceller;  state: Exp;  lines: +2 -2
#H  for version 4
#H  ----------------------------
#H  revision 1.2
#H  date: 1997/04/04 12:20:17;  author: sam;  state: Exp;  lines: +59 -96
#H  added 'ConstructPermuted', 'ConstructSubdirect',
#H  changed table constructions involving 'CharTable', 'RecFields'
#H      'Sort...' up to now
#H  ----------------------------
#H  revision 1.1
#H  date: 1996/10/21 16:00:19;  author: sam;  state: Exp;
#H  first proposal of the table library
#H  ==========================================================================
##

MOT("2..11.m23",
[
"origin: CAS library,\n",
"names:= 2..11.m23\n",
"   order: 2^18.3^2.5.7.11.23 = 20,891,566,080\n",
"   number of classes: 56\n",
"   source:gabrysch, thomas\n",
"         ein computerprogramm zur berechnung\n",
"         von charakterentafeln und einige anwendungen,\n",
"         diplomarbeit, univ. of bielefeld [1977]\n",
"   comments:non-split extension of m23 with an\n",
"           elementar-abelian group of order 2..11.m23 \n",
"   test: 1. o.r., sym 2 decompose correctly  \n",
"2nd power map determined by subgroup fusion into Fi23\n",
"tests: 1.o.r., pow[2,3,5,7,11,23]"
],
[20891566080,908328960,82575360,11796480,344064,49152,43008,6144,12288,12288,
512,512,256,128,128,128,32,32,32,32,5760,1152,576,576,1152,5760,96,96,96,96,
48,48,120,40,40,120,30,30,30,30,56,28,56,56,28,56,28,28,28,28,22,22,22,22,23,
23],
[,[1,1,1,1,1,1,3,3,4,4,6,6,5,9,9,10,12,11,16,16,21,21,21,21,21,21,21,21,25,25,
23,23,33,33,33,33,37,37,39,39,41,41,41,44,44,44,41,43,44,46,53,53,51,51,55,
56],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,1,2,3,4,4,4,5,6,9,10,
7,8,33,34,35,36,33,36,33,36,44,45,46,41,42,43,49,50,47,48,51,52,53,54,55,
56],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,20,19,21,22,23,24,25,26,27,
28,29,30,31,32,1,2,3,4,21,26,21,26,44,45,46,41,42,43,49,50,47,48,51,52,53,54,
56,55],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,20,19,21,22,23,24,25,26,
27,28,29,30,31,32,33,34,35,36,39,40,37,38,1,2,3,1,2,3,5,7,5,7,53,54,51,52,56,
55],,,,[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,
27,28,29,30,31,32,33,34,35,36,39,40,37,38,41,42,43,44,45,46,47,48,49,50,1,2,1,
2,56,55],,,,,,,,,,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,20,19,21,22,
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,
49,50,51,52,53,54,1,1]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[22,22,22,22,6,6,6,6,6,6,2,2,2,2,2,2,0,0,
0,0,4,4,4,4,4,4,0,0,0,0,0,0,2,2,2,2,-1,-1,-1,-1,1,1,1,1,1,1,-1,-1,-1,-1,0,0,0,
0,-1,-1],[230,230,230,230,22,22,22,22,22,22,2,2,2,2,2,2,0,0,0,0,5,5,5,5,5,5,1,
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,-1,0,0],[231,231,
231,231,7,7,7,7,7,7,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,6,6,6,6,6,6,-2,-2,-2,-2,-2,
-2,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1],[45,45,45,45,-3,-3,-3,-3,
-3,-3,1,1,1,1,1,1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
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)+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)-E(7)^2-E(7)^4,-E(7)-E(7)^2-E(7)^4,1,1,1,1,-1,
-1],
[GALOIS,[5,3]],[231,231,231,231,7,7,7,7,7,7,-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,-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)^8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1],
[GALOIS,[7,7]],[253,253,253,253,13,13,13,13,13,13,1,1,1,1,1,1,-1,-1,-1,-1,1,1,
1,1,1,1,1,1,1,1,1,1,-2,-2,-2,-2,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,0,0,0,0,0,0],[
770,770,770,770,-14,-14,-14,-14,-14,-14,-2,-2,-2,-2,-2,-2,0,0,0,0,5,5,5,5,5,5,
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,E(23)+E(23)^2+E(23)^3
 +E(23)^4+E(23)^6+E(23)^8+E(23)^9+E(23)^12+E(23)^13+E(23)^16+E(23)^18,
E(23)^5+E(23)^7+E(23)^10+E(23)^11+E(23)^14+E(23)^15+E(23)^17+E(23)^19+E(23)^20
 +E(23)^21+E(23)^22],
[GALOIS,[10,5]],[896,896,896,896,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-4,-4,-4,-4,
-4,-4,0,0,0,0,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,E(11)+E(11)^3+E(11)^4
 +E(11)^5+E(11)^9,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,E(11)^2+E(11)^6+E(11)^7+E(11)^8
 +E(11)^10,-1,-1],
[GALOIS,[12,2]],[990,990,990,990,-18,-18,-18,-18,-18,-18,2,2,2,2,2,2,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,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,
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[GALOIS,[45,2]],[12880,-560,-560,80,-112,16,0,0,16,-16,0,0,0,0,0,0,0,0,
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[GALOIS,[55,7]]],
[(55,56),(51,53)(52,54),(41,44)(42,45)(43,46)(47,49)(48,50),(37,39)(38,40),
(19,20)]);
ALF("2..11.m23","Fi23",[1,2,3,4,3,4,9,11,10,12,12,10,11,31,30,32,31,32,63,
64,7,18,24,26,25,20,24,26,49,53,51,55,13,38,39,40,62,91,62,91,29,59,60,29,
59,60,60,88,60,88,41,78,41,79,80,81],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("2..11.m23","M23",[1,1,1,1,2,2,2,2,2,2,4,4,4,4,4,4,9,9,9,9,3,3,3,3,3,
3,6,6,6,6,6,6,5,5,5,5,14,14,15,15,7,7,7,8,8,8,12,12,13,13,10,10,11,11,16,
17]);
ALN("2..11.m23",["f23m6"]);

MOT("2.2^8.f20",
[
"origin: CAS library,\n",
"maximal subgroup of 2F4(2)',\n",
"  centralizer of 2a-element\n",
"  structure:= 2*[2^8]:f20 [f20: frobenius group of order 20]\n",
"  1st & 2nd orthogonality relations are satisfied\n",
"  symmetric squares decompose properly\n",
"  created August 1984,\n",
"  test: 1. o.r., sym 2 decompose correctly,\n",
"tests: 1.o.r., pow[2,5]"
],
[10240,10240,1024,128,512,128,128,64,32,32,128,64,64,32,32,32,10,32,16,32,16,
16,16,10,16,16,16,16],
[,[1,1,1,1,1,1,1,5,7,7,2,3,5,5,7,7,17,11,12,11,12,13,13,17,18,20,20,18],,,[1,
2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,1,18,19,20,21,22,23,2,28,27,26,25]],
[[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,-E(4),
E(4),1,-1,1,-1,-E(4),E(4),1,-1,-E(4),-1,E(4),-1,-1,1,E(4),-E(4),-E(4),E(4)],
[TENSOR,[2,3]],[4,4,4,0,4,4,0,4,0,0,4,0,4,0,0,0,-1,0,0,0,0,0,0,-1,0,0,0,0],[5,
5,5,1,5,-3,1,1,1,1,-3,1,1,1,1,1,0,1,1,1,1,-1,-1,0,-1,-1,-1,-1],
[TENSOR,[6,2]],
[TENSOR,[6,3]],
[TENSOR,[6,4]],[10,10,10,2,10,2,2,-2,0,0,2,2,-2,2,0,0,0,-2,0,-2,0,0,0,0,0,0,0,
0],
[TENSOR,[10,3]],[10,10,-6,-2,2,2,-2,-2,0,0,-2,-2,2,2,0,0,0,0,0,0,0,0,0,0,
E(8)+E(8)^3,-E(8)-E(8)^3,E(8)+E(8)^3,-E(8)-E(8)^3],
[TENSOR,[12,2]],[10,10,-6,0,2,2,0,2,1-E(4),1+E(4),-2,0,-2,0,1-E(4),1+E(4),0,
2*E(4),-1+E(4),-2*E(4),-1-E(4),0,0,0,0,0,0,0],
[TENSOR,[14,4]],
[TENSOR,[12,3]],
[TENSOR,[12,4]],
[TENSOR,[14,2]],
[TENSOR,[14,3]],[16,-16,0,-4,0,0,4,0,-2,-2,0,0,0,0,2,2,1,0,0,0,0,0,0,-1,0,0,0,
0],
[TENSOR,[20,2]],
[TENSOR,[20,3]],
[TENSOR,[20,4]],[20,20,-12,0,4,-4,0,0,0,0,4,0,0,0,0,0,0,0,0,0,0,2,-2,0,0,0,0,
0],
[TENSOR,[24,3]],[40,40,8,4,-8,0,4,0,0,0,0,-4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[26,3]],[64,-64,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,1,0,0,0,
0]],
[(25,28)(26,27),(22,23),( 9,10)(15,16)(18,20)(19,21)(25,26)(27,28),( 9,10)
(15,16)(18,20)(19,21)(25,27)(26,28),( 9,15)(10,16)]);
ARC("2.2^8.f20","tomfusion",rec(name:="2.[2^8]:5:4",map:=[1,2,3,6,4,5,7,
26,36,36,18,23,24,35,37,37,38,108,115,108,115,89,90,119,243,243,243,243],
text:=[
"fusion map is unique up to table autom."
]));
ALF("2.2^8.f20","2F4(2)'",[1,2,2,2,3,3,3,5,5,5,6,6,7,7,7,7,8,10,10,11,11,
12,13,14,19,20,22,21],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("2.2^8.f20","2.[2^9]:5:4",[1,2,3,19,4,7,20,11,36,37,8,24,12,26,38,39,
15,28,42,27,43,31,31,16,47,46,46,47]);
ALN("2.2^8.f20",["2F4(2)'C2a","2F4(2)'N2a"]);

MOT("2^10:(2^5:s5)",
[
"origin: CAS library,\n",
"One intersection between a Co2M8 and a Co2M2, has index 3 in Co2M8.\n",
"Computed using Clifford matrices and lots of information from Co2M2.\n",
"Test: 1.OR, JAMES, JAMES,n=3,\n",
"and restricted characters from Co2M2 (and Co2) decompose properly.\n",
"tests: 1.o.r., pow[2,3,5]"
],
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2048,2048,2048,2048,2048,1024,1024,1024,512,512,512,512,128,128,128,128,64,64,
48,48,48,48,192,192,192,192,96,96,96,96,48,6144,6144,6144,6144,2048,2048,2048,
2048,512,512,512,512,64,64,32,1024,1024,512,512,512,128,16384,16384,16384,
16384,8192,8192,8192,8192,4096,2048,2048,1024,1024,512,512,512,512,256,256,
128,128,20,20,40,40,20,20480,4096,2048,1280,49152,49152,24576,4096,4096,4096,
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1024,1024,1024,1024,1024,1024,512,96,96,96,96,48,48,256,256,256,256,64,64,64,
32,96,96,96,96,48,48,512,512,512,512,256,256,256,256,128,1024,1024,512,256,
256,256,2048,2048,1024,512,512,512,256,256,256,256,256,256,128,128],
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[( 13, 14)( 15, 16)( 19, 20)( 21, 22)( 73, 74)( 76, 77)( 95, 98)( 96, 97)
(112,113)(116,117)(118,119)(122,123)(124,125)(126,128)(127,129)(132,137)
(133,136)(134,135)(139,142)(140,141)(150,151)(153,156)(154,155)(159,161)
(160,162)(163,166)(164,165)(168,169)(171,173)]);
ALF("2^10:(2^5:s5)","2^10:m22:2",[1,2,3,2,3,4,3,4,2,4,3,4,57,58,60,60,59,
60,62,61,61,62,5,9,11,10,8,12,6,6,11,7,9,7,7,8,6,7,6,7,6,24,25,27,26,28,
28,32,34,34,33,13,17,14,17,16,16,15,15,17,5,12,12,10,11,8,9,8,6,6,7,7,69,
70,71,18,19,20,21,22,23,5,10,11,9,12,8,11,9,8,7,6,7,6,18,21,21,19,22,20,
23,23,72,73,29,30,31,49,50,51,52,43,48,47,47,45,46,46,45,44,44,43,48,46,
45,47,46,47,45,44,47,44,46,46,45,45,44,44,63,65,66,64,67,68,24,25,26,27,
28,39,40,41,63,65,66,64,67,68,57,59,58,59,62,62,61,61,60,57,58,59,62,60,
61,49,50,51,50,51,51,52,52,53,54,56,55,56,55],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("2^10:(2^5:s5)","Co2",[1,2,3,2,3,4,3,4,2,4,3,4,8,11,23,23,12,23,27,24,
24,27,3,4,10,7,9,8,12,12,10,11,4,11,11,9,12,11,12,11,12,11,25,13,23,28,28,
20,39,39,36,6,20,19,20,21,21,18,18,20,3,8,8,7,10,9,4,9,12,12,11,11,24,28,
49,9,11,25,12,26,27,3,7,10,4,8,9,10,4,9,11,12,11,12,9,12,12,11,26,25,27,
27,32,52,15,32,31,4,10,12,13,2,3,4,4,9,8,8,9,12,12,2,3,8,9,4,8,4,9,12,4,
12,8,8,9,9,12,12,19,37,39,20,21,41,11,25,23,13,28,27,28,48,19,37,39,20,21,
41,8,12,11,12,27,27,24,24,23,8,11,12,27,23,24,4,10,12,10,12,12,13,13,12,
23,26,13,26,13],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("2^10:(2^5:s5)","A5.2",[1,1,1,1,1,1,1,1,1,1,1,1,6,6,6,6,6,6,6,6,6,6,2,
2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,6,6,6,6,6,6,7,7,7,7,3,3,3,3,3,3,3,3,3,
5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,5,5,5,
5,5,5,5,5,4,4,4,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,5,5,5,5,5,5,5,5,5,5,5,5,5,
5,5,5,5,7,7,7,7,7,7,2,2,2,2,2,6,6,6,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,2,2,2,2,
2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2]);

MOT("2^2.2^8:s3",
[
"origin: CAS library,\n",
"maximal subgroup of 2F4(2)',\n",
"  normalizer of klein four group contained in class 2b\n",
"  structure:= 2^2.[2^8]:s3 [s3: symmetric group on 3 elements]\n",
"  1st & 2nd orthogonality relations are satisfied\n",
"  symmetric squares decompose properly\n",
"  created august 1984\n",
"tests: 1.o.r., pow[2,3]"
],
[6144,2048,256,1536,256,256,32,12,32,192,32,128,32,64,32,32,12,32,32,16,16,12,
12,16,16,16,16],
[,[1,1,1,1,1,1,1,8,5,4,6,2,2,4,5,6,8,12,12,14,14,17,17,18,19,19,18],[1,2,3,4,
5,6,7,1,9,10,11,12,13,14,15,16,4,19,18,20,21,10,10,26,27,24,25]],
[[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],[2,2,2,2,2,2,0,-1,2,2,0,2,0,2,2,
0,-1,2,2,0,0,-1,-1,0,0,0,0],[2,2,-2,2,-2,2,0,-1,0,-2,0,-2,0,2,0,0,-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],
[TENSOR,[4,2]],[3,3,3,3,3,3,-1,0,-1,3,-1,3,-1,3,-1,-1,0,-1,-1,-1,-1,0,0,1,1,1,
1],
[TENSOR,[6,2]],[3,3,-1,3,-1,3,1,0,1,3,1,-1,1,-1,1,1,0,-1+2*E(4),-1-2*E(4),-1,
-1,0,0,-E(4),E(4),E(4),-E(4)],
[TENSOR,[8,2]],
[GALOIS,[8,3]],
[TENSOR,[10,2]],[4,4,-4,4,-4,4,0,1,0,-4,0,-4,0,4,0,0,1,0,0,0,0,-1,-1,0,0,0,
0],[6,6,-2,6,-2,6,0,0,-2,6,0,-2,0,-2,-2,0,0,2,2,0,0,0,0,0,0,0,0],[6,6,2,6,2,6,
0,0,0,-6,0,2,0,-2,0,0,0,0,0,0,0,0,0,E(8)-E(8)^3,E(8)-E(8)^3,-E(8)+E(8)^3,
-E(8)+E(8)^3],
[TENSOR,[14,2]],[12,12,-4,12,-4,-4,0,0,0,0,0,4,0,0,0,0,0,0,0,2,-2,0,0,0,0,0,
0],[12,12,4,12,4,-4,-2,0,0,0,2,-4,-2,0,0,2,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[16,2]],
[TENSOR,[17,2]],[16,16,0,-16,0,0,0,-2,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0],[
16,16,0,-16,0,0,0,1,0,0,0,0,0,0,0,0,-1,0,0,0,0,-E(12)^7+E(12)^11,
E(12)^7-E(12)^11,0,0,0,0],
[GALOIS,[21,5]],[24,-8,-4,0,4,0,2,0,-2,0,-2,0,-2,0,2,2,0,0,0,0,0,0,0,0,0,0,
0],[24,-8,-4,0,4,0,2,0,2,0,2,0,-2,0,-2,-2,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[23,2]],
[TENSOR,[24,2]],[48,-16,8,0,-8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]],
[(24,27)(25,26),(22,23),(20,21),(18,19)(24,25)(26,27),(18,19)(24,26)(25,27),
(18,19)(22,23)(24,25)(26,27),(18,19)(22,23)(24,26)(25,27),( 9,15)(11,16)]);
ARC("2^2.2^8:s3","tomfusion",rec(name:="2^2.[2^8]:S3",map:=[1,2,5,3,4,6,7,
8,29,14,43,18,44,27,35,42,47,131,131,111,128,152,152,321,321,321,321],text:=[
"fusion map is unique up to table autom."
]));
ALF("2^2.2^8:s3","2F4(2)'",[1,2,2,3,3,3,3,4,5,5,5,6,6,7,7,7,9,10,11,12,13,
15,16,19,20,22,21],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("2^2.2^8:s3","2^2.[2^9]:S3",[1,2,7,3,8,4,28,23,18,5,35,9,33,12,19,34,
24,20,21,37,37,25,25,42,41,41,42]);

MOT("2.[2^9]:5:4",
[
"origin: Dixon's Algorithm"
],
[20480,20480,2048,1024,1280,1280,256,256,256,256,128,128,128,128,20,20,20,20,
256,256,256,256,128,128,64,64,64,64,32,16,16,64,64,64,64,64,64,64,64,32,32,32,
32,16,16,16,16],
[,[1,1,1,1,2,2,1,2,3,3,4,4,3,3,15,15,16,16,1,1,3,3,2,3,4,4,8,8,8,11,12,19,19,
19,19,20,20,20,20,24,24,24,24,27,28,27,28],,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14
,1,2,6,5,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,
42,43,44,45,46,47]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[1,1,1,1,1,1,1,1,1,1,1,1,
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,[2,3]],[4,4,4,4,4,4,4,4,4,4,4,4,4,4,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[5,5,5,5,5,5,-3,-3,1,1,1,1,-3,1,0,0,0,0,
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],
[TENSOR,[6,2]],
[TENSOR,[6,4]],
[TENSOR,[6,3]],[10,10,10,10,10,10,2,2,-2,-2,-2,-2,2,-2,0,0,0,0,-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],
[TENSOR,[10,3]],[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],
[TENSOR,[2,12]],
[TENSOR,[3,13]],
[TENSOR,[2,14]],
[TENSOR,[5,12]],
[TENSOR,[6,13]],
[TENSOR,[6,12]],
[TENSOR,[6,15]],
[TENSOR,[6,14]],
[TENSOR,[10,12]],
[TENSOR,[10,14]],[10,10,-6,2,0,0,2,-2,-4*E(4),4*E(4),2,-2,0,0,0,0,0,0,0,0,2,2
,2,0,-2,0,-2*E(4),2*E(4),0,0,0,-1+E(4),-1-E(4),-1+E(4),-1-E(4),-1+E(4),-1-E(4)
,-1+E(4),-1-E(4),1-E(4),1+E(4),1-E(4),1+E(4),0,0,0,0],
[TENSOR,[23,15]],
[TENSOR,[23,2]],
[TENSOR,[23,14]],
[TENSOR,[23,13]],
[TENSOR,[23,4]],
[TENSOR,[23,12]],
[TENSOR,[23,3]],[20,20,-12,4,0,0,4,-4,0,0,-4,4,0,0,0,0,0,0,-4,-4,0,0,0,-4,0,4
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[31,3]],[40,40,8,-8,0,0,0,0,4,4,0,0,0,-4,0,0,0,0,-4,-4,-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],
[TENSOR,[33,14]],
[TENSOR,[33,12]],
[TENSOR,[33,3]],[40,40,-24,8,0,0,-8,8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[16,-16,0,0,-4*E(4),4*E(4),0,0,0,0,0,0
,0,0,1,-1,-E(4),E(4),-4,4,-4*E(4),4*E(4),0,0,0,0,0,0,0,0,0,-2*E(4),2*E(4),
2*E(4),-2*E(4),-2,-2,2,2,0,0,0,0,0,0,0,0],
[TENSOR,[38,12]],
[TENSOR,[38,2]],
[TENSOR,[38,13]],
[TENSOR,[38,14]],
[TENSOR,[38,3]],
[TENSOR,[38,15]],
[TENSOR,[38,4]],[64,-64,0,0,-16*E(4),16*E(4),0,0,0,0,0,0,0,0,-1,1,E(4),-E(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],
[TENSOR,[46,12]]],
[(32,34)(33,35)(36,38)(37,39),
(19,20)(21,22)(32,36)(33,37)(34,38)(35,39)(40,42)(41,43)(44,46)(45,47),
( 9,10)(27,28)(32,33)(34,35)(36,39)(37,38)(40,41)(42,43)(44,45)(46,47),
( 5, 6)(17,18)(21,22)(36,38)(37,39)]);
ALF("2.[2^9]:5:4","2F4(2)'.2",[1,2,2,3,18,19,3,6,19,18,5,7,21,21,8,13,29,
28,2,3,18,19,21,6,20,7,11,10,22,23,12,19,18,21,21,5,5,7,7,22,22,10,11,27,
26,17,16],[
"compatible with 2.2^8.f20 -> 2F4(2)'"
]);

MOT("2^2.[2^9]:S3",
[
"origin: Dixon's Algorithm"
],
[12288,4096,3072,512,384,192,512,512,256,256,256,128,128,128,128,128,128,64,64
,64,64,32,24,24,12,12,12,64,128,128,128,128,64,64,64,32,16,16,16,16,16,16],
[,[1,1,1,1,3,3,1,1,2,2,2,3,2,7,7,7,7,8,8,9,9,9,23,23,24,24,24,1,7,7,7,7,2,4,4,
7,12,5,20,21,21,20],[1,2,3,4,5,6,7,8,9,11,10,12,13,15,14,17,16,18,19,21,20,22,
1,3,5,6,6,28,30,29,32,31,33,34,35,36,37,38,40,39,42,41]],
[[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],[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,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[3,3,3,3,3,3,3,3,3,3,3,3,3,-1,-1
,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1],
[TENSOR,[4,2]],[3,3,3,3,3,3,-1,-1,-1,-1,-1,-1,-1,-1-2*E(4),-1+2*E(4),
-1-2*E(4),-1+2*E(4),1,1,-1+2*E(4),-1-2*E(4),1,0,0,0,0,0,-1,1,1,1,1,-1,-1,-1,1,
1,-1,E(4),-E(4),-E(4),E(4)],
[GALOIS,[6,3]],
[TENSOR,[6,2]],
[TENSOR,[7,2]],[6,6,6,6,6,6,-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],[1,1,1,1,1,-1,1,1,1,-1,-1,1,-1,-1,-1,-1,-1,1
,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,[2,11]],
[TENSOR,[3,11]],
[TENSOR,[4,12]],
[TENSOR,[4,11]],
[TENSOR,[7,12]],
[TENSOR,[6,12]],
[TENSOR,[7,11]],
[TENSOR,[6,11]],
[TENSOR,[10,11]],[4,4,4,4,-4,0,-4,-4,-4,0,0,4,0,0,0,0,0,0,0,0,0,0,-2,-2,2,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[4,4,4,4,-4,0,-4,-4,-4,0,0,4,0,0,0,0,0,0,0,0,0
,0,1,1,-1,-E(3)+E(3)^2,E(3)-E(3)^2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[22,11]],[12,12,12,12,-12,0,4,4,4,0,0,-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],[12,12,12,-4,0,0,4,4,-4,4,4,0,-4,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,-2,2,2,2,2,-2,2,2,-2,0,0,0,0,0,0],
[TENSOR,[25,2]],
[TENSOR,[25,12]],
[TENSOR,[25,11]],[24,24,24,-8,0,0,-8,-8,8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[16,16,-16,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,-2,2,0,0,0,0,-4,-4,4,4,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[30,2]],[32,32,-32,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,-2,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[24,-8,0,0,0,0,-4,4,0,4*E(4),-4*E(4),0,0,-2*E(4)
,2*E(4),2*E(4),-2*E(4),-2,2,0,0,0,0,0,0,0,0,-2,4*E(4),-4*E(4),0,0,2,-2,2,0,0,0
,0,0,0,0],
[TENSOR,[33,12]],
[TENSOR,[33,2]],
[TENSOR,[33,11]],[24,-8,0,0,0,0,-4,4,0,-4*E(4),4*E(4),0,0,-2*E(4),2*E(4),
2*E(4),-2*E(4),2,-2,0,0,0,0,0,0,0,0,-2,0,0,-4*E(4),4*E(4),2,2,-2,0,0,0,0,0,0,0
],
[TENSOR,[37,12]],
[TENSOR,[37,2]],
[TENSOR,[37,11]],[48,-16,0,0,0,0,8,-8,0,0,0,0,0,-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],
[TENSOR,[41,11]]],
[(26,27),(14,17)(15,16)(20,21)(39,40)(41,42),
(10,11)(14,16)(15,17)(29,30)(31,32),(14,16)(15,17)(18,19)(29,31)(30,32)(34,35)
]);
ALF("2^2.[2^9]:S3","2F4(2)'.2",[1,2,3,3,5,20,2,3,6,18,19,7,21,18,19,21,21,
5,7,10,11,22,4,9,14,24,25,3,21,21,19,18,6,7,5,21,12,23,26,27,17,16],[
"fusion map is unique up to table automorphisms"
]);

MOT("2^6:u3(3)",
[
"origin: CAS library,\n",
"subgroup of index 2 in maximal subgroup of ru\n",
"  structure:= 2^6:u[3,3]\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]"
],
[387072,6144,1536,512,128,108,36,12,384,128,384,128,64,64,32,12,7,7,16,16,16,
16,12,12],
[,[1,1,1,1,2,6,7,7,3,4,3,4,3,4,4,6,17,18,9,10,11,12,16,16],[1,2,3,4,5,1,1,2,
11,12,9,10,13,14,15,3,18,17,21,22,19,20,11,9],,,,[1,2,3,4,5,6,7,8,11,12,9,10,
13,14,15,16,1,1,21,22,19,20,24,23]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[6,6,-2,-2,-2,-3,0,0,-2,-2,
-2,-2,2,2,2,1,-1,-1,0,0,0,0,1,1],[7,7,-1,-1,-1,-2,1,1,3,3,3,3,-1,-1,-1,2,0,0,
-1,-1,-1,-1,0,0],[7,7,3,3,3,-2,1,1,-1-2*E(4),-1-2*E(4),-1+2*E(4),-1+2*E(4),1,
1,1,0,0,0,E(4),E(4),-E(4),-E(4),-1+E(4),-1-E(4)],
[GALOIS,[4,3]],[14,14,-2,-2,-2,5,-1,-1,2,2,2,2,2,2,2,1,0,0,0,0,0,0,-1,-1],[21,
21,5,5,5,3,0,0,1,1,1,1,1,1,1,-1,0,0,-1,-1,-1,-1,1,1],[21,21,1,1,1,3,0,0,
-3+2*E(4),-3+2*E(4),-3-2*E(4),-3-2*E(4),-1,-1,-1,1,0,0,E(4),E(4),-E(4),-E(4),
-E(4),E(4)],
[GALOIS,[8,3]],[27,27,3,3,3,0,0,0,3,3,3,3,-1,-1,-1,0,-1,-1,1,1,1,1,0,0],[28,
28,-4,-4,-4,1,1,1,4*E(4),4*E(4),-4*E(4),-4*E(4),0,0,0,-1,0,0,0,0,0,0,E(4),
-E(4)],
[GALOIS,[11,3]],[32,32,0,0,0,-4,-1,-1,0,0,0,0,0,0,0,0,-E(7)-E(7)^2-E(7)^4,
-E(7)^3-E(7)^5-E(7)^6,0,0,0,0,0,0],
[GALOIS,[13,3]],[63,-1,15,-1,-1,0,3,-1,3,-1,3,-1,3,-1,-1,0,0,0,1,-1,1,-1,0,
0],[63,-1,-9,7,-1,0,3,-1,3,-1,3,-1,-1,3,-1,0,0,0,-1,1,-1,1,0,0],[126,-2,6,6,
-2,0,-3,1,6,-2,6,-2,2,2,-2,0,0,0,0,0,0,0,0,0],[189,-3,-3,13,-3,0,0,0,-3,1,-3,
1,-3,1,1,0,0,0,1,-1,1,-1,0,0],[189,-3,21,5,-3,0,0,0,-3,1,-3,1,1,-3,1,0,0,0,-1,
1,-1,1,0,0],[189,-3,9,-7,1,0,0,0,-3-6*E(4),1+2*E(4),-3+6*E(4),1-2*E(4),-1,3,
-1,0,0,0,E(4),-E(4),-E(4),E(4),0,0],
[GALOIS,[20,3]],[189,-3,-15,1,1,0,0,0,-3+6*E(4),1-2*E(4),-3-6*E(4),1+2*E(4),3,
-1,-1,0,0,0,E(4),-E(4),-E(4),E(4),0,0],
[GALOIS,[22,3]],[378,-6,-6,-6,2,0,0,0,6,-2,6,-2,-2,-2,2,0,0,0,0,0,0,0,0,0]],
[(17,18),( 9,11)(10,12)(19,21)(20,22)(23,24)]);
ALF("2^6:u3(3)","Ru",[1,2,2,2,7,4,4,11,5,8,5,8,8,8,7,11,12,12,13,15,13,15,
18,18],[
"fusion map is unique, equal to that on the CAS table"
]);
ALF("2^6:u3(3)","U3(3)",[1,1,2,2,2,3,4,4,5,5,6,6,7,7,7,8,9,10,11,11,12,12,
13,14]);

MOT("2^{1+6}:3^{1+2}:2A4",
[
"1st maximal subgroup of U5(2), origin: CAYLEY"
],
[82944,82944,1536,1152,1296,1296,1296,1296,216,216,36,2304,2304,384,96,144,
144,144,144,96,96,16,24,24,24,24,1728,1728,432,432,108,108,1728,1728,432,432,
144,144,144,144,144,144,144,144,108,108,96,96,36,36,36,36,18,18,144,144,72,72,
24,24,24,24,18,18],
[,[1,1,1,2,6,5,6,5,9,9,10,1,1,2,3,5,6,5,6,12,12,14,16,17,17,16,28,27,30,29,32,
31,27,28,30,29,29,30,27,28,28,27,29,30,32,31,28,27,31,32,32,31,54,53,34,33,36,
35,35,36,47,48,53,54],[1,2,3,4,1,1,2,2,1,2,4,12,13,14,15,12,12,13,13,20,21,22,
21,21,20,20,1,1,1,1,1,1,2,2,2,2,12,12,12,12,13,13,13,13,2,2,3,3,13,13,12,12,6,
5,4,4,4,4,14,14,15,15,7,8]],
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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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E(3)^2,E(3)^2,E(3),E(3),E(3)^2,E(3),E(3)^2,E(3)^2,E(3),E(3)^2,E(3),E(3),
E(3)^2,E(3)^2,E(3),E(3)^2,E(3)],
[TENSOR,[2,2]],[3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,-1,-1,-1,-1,-1,-1,-1,0,
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-1],
[TENSOR,[5,2]],
[TENSOR,[5,3]],[8,8,8,8,8,8,8,8,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,2,2,
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[TENSOR,[8,2]],
[TENSOR,[8,3]],[3,3,3,3,3*E(3),3*E(3)^2,3*E(3),3*E(3)^2,0,0,0,-1,-1,-1,-1,
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[TENSOR,[11,3]],
[TENSOR,[11,2]],
[GALOIS,[12,2]],
[TENSOR,[14,3]],
[TENSOR,[14,2]],[6,6,6,6,6*E(3),6*E(3)^2,6*E(3),6*E(3)^2,0,0,0,2,2,2,2,
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[TENSOR,[17,3]],
[TENSOR,[17,2]],
[GALOIS,[18,2]],
[TENSOR,[20,2]],
[TENSOR,[20,3]],[9,9,9,9,9*E(3),9*E(3)^2,9*E(3),9*E(3)^2,0,0,0,-3,-3,-3,-3,
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[TENSOR,[25,2]],
[TENSOR,[25,3]],[36,36,4,-4,0,0,0,0,3,3,-1,12,12,-4,0,0,0,0,0,0,0,0,0,0,0,0,6,
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[TENSOR,[28,2]],
[TENSOR,[29,2]],
[TENSOR,[28,3]],
[TENSOR,[29,3]],[54,54,-10,6,0,0,0,0,0,0,0,-6,-6,-6,2,0,0,0,0,0,0,0,0,0,0,0,
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[TENSOR,[34,2]],
[TENSOR,[34,3]],[72,72,8,-8,0,0,0,0,-3,-3,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-6,
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0,0],
[TENSOR,[37,2]],
[TENSOR,[37,3]],[81,81,-15,9,0,0,0,0,0,0,0,9,9,9,-3,0,0,0,0,-3,-3,1,0,0,0,0,0,
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[TENSOR,[41,2]],
[TENSOR,[41,3]],[16,-16,0,0,-2,-2,2,2,4,-4,0,8,-8,0,0,2,2,-2,-2,0,0,0,0,0,0,0,
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0,0,0,-1,-1],
[TENSOR,[44,2]],
[TENSOR,[44,3]],[24,-24,0,0,-3,-3,3,3,6,-6,0,-12,12,0,0,-3,-3,3,3,-2,2,0,-1,
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0,0,0],[24,-24,0,0,-3*E(3),-3*E(3)^2,3*E(3),3*E(3)^2,0,0,0,4,-4,0,0,E(3)^2,
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-E(3)^2,E(3)^2,E(3),0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[48,3]],
[TENSOR,[48,2]],
[GALOIS,[50,2]],
[TENSOR,[51,2]],
[TENSOR,[51,3]],[48,-48,0,0,-6*E(3),-6*E(3)^2,6*E(3),6*E(3)^2,0,0,0,-8,8,0,0,
-2*E(3)^2,-2*E(3),2*E(3)^2,2*E(3),0,0,0,0,0,0,0,4*E(3)+8*E(3)^2,
8*E(3)+4*E(3)^2,2*E(3)+4*E(3)^2,4*E(3)+2*E(3)^2,E(3)-E(3)^2,-E(3)+E(3)^2,
-8*E(3)-4*E(3)^2,-4*E(3)-8*E(3)^2,-2*E(3)-4*E(3)^2,-4*E(3)-2*E(3)^2,-2*E(3)^2,
-2*E(3),-2*E(3)^2,-2*E(3),2*E(3),2*E(3)^2,2*E(3)^2,2*E(3),-E(3)+E(3)^2,
E(3)-E(3)^2,0,0,-1,-1,1,1,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[54,2]],
[TENSOR,[54,3]],
[GALOIS,[55,2]],
[TENSOR,[57,2]],
[TENSOR,[57,3]],[64,-64,0,0,-8,-8,8,8,-2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-8,
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-1],
[TENSOR,[60,2]],
[TENSOR,[60,3]],[72,-72,0,0,-9*E(3),-9*E(3)^2,9*E(3),9*E(3)^2,0,0,0,12,-12,0,
0,3*E(3)^2,3*E(3),-3*E(3)^2,-3*E(3),-2,2,0,-E(3),-E(3)^2,E(3)^2,E(3),0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[63,2]]],
[( 5, 6)( 7, 8)(16,17)(18,19)(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)(61,62)(63,64)]);
ARC("2^{1+6}:3^{1+2}:2A4","tomfusion",rec(name:="2^(1+6)-:3^(1+2)+:2A4",map:=[
1,2,5,14,7,7,24,24,9,28,80,4,3,17,21,30,30,34,34,20,22,61,91,91,92,92,6,6,8,8,
10,10,23,23,27,27,31,31,33,33,29,29,32,32,35,35,36,36,37,37,38,38,69,69,74,74,
78,78,89,89,90,90,141,141],text:=[
"fusion map is unique"
]));
ALF("2^{1+6}:3^{1+2}:2A4","U5(2)",[1,2,3,10,6,7,16,17,8,22,39,2,3,11,12,
19,18,24,23,10,11,28,42,43,38,37,5,4,6,7,9,9,14,15,18,19,17,16,14,15,21,
20,24,23,26,25,21,20,27,27,25,26,30,29,35,36,37,38,43,42,40,41,46,47],[
"fusion is unique up to table automorphisms"
]);
ALN("2^{1+6}:3^{1+2}:2A4",["U5(2)C2A","U5(2)N2A"]);

MOT("2^(4+4):(3xA5)",
[
"origin: Dixon's Algorithm,\n",
"3rd maximal subgroup of U5(2)"
],
[46080,9216,4608,384,384,2880,576,288,2880,576,288,192,192,96,16,48,48,24,48,
48,24,144,144,144,144,144,144,144,144,36,36,36,36,24,24,24,24,15,15,15,15,15,
15],
[,[1,1,1,2,2,9,9,9,6,6,6,1,2,3,5,9,10,11,6,7,8,26,26,26,26,22,22,22,22,30,30,
30,30,29,29,25,25,41,43,42,38,40,39],[1,2,3,4,5,1,2,3,1,2,3,12,13,14,15,12,13,
14,12,13,14,1,3,2,2,1,3,2,2,1,3,2,2,4,5,4,5,41,41,41,38,38,38],,[1,2,3,4,5,9,
10,11,6,7,8,12,13,14,15,19,20,21,16,17,18,26,27,28,29,22,23,24,25,30,31,33,32,
36,37,34,35,1,9,6,1,9,6]],
[[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],[3,3,3,3,3,3,3,3,3,3,3,-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,-E(5)-E(5)^4,-E(5)-E(5)^4,-E(5)-E(5)^4,-E(5)^2-E(5)^3,
-E(5)^2-E(5)^3,-E(5)^2-E(5)^3],
[GALOIS,[2,2]],[4,4,4,4,4,4,4,4,4,4,4,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1
,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1],[5,5,5,5,5,5,5,5,5,5,5,1,1,1,1,1,1,1,1,1,1,-1,
-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0],[1,1,1,1,1,E(3),E(3)
,E(3),E(3)^2,E(3)^2,E(3)^2,1,1,1,1,E(3),E(3),E(3),E(3)^2,E(3)^2,E(3)^2,E(3),
E(3),E(3),E(3),E(3)^2,E(3)^2,E(3)^2,E(3)^2,1,1,1,1,E(3),E(3),E(3)^2,E(3)^2,1,
E(3),E(3)^2,1,E(3),E(3)^2],
[TENSOR,[6,6]],
[TENSOR,[3,6]],
[TENSOR,[3,7]],
[TENSOR,[2,6]],
[TENSOR,[2,7]],
[TENSOR,[4,6]],
[TENSOR,[4,7]],
[TENSOR,[5,6]],
[TENSOR,[5,7]],[15,15,15,-1,-1,0,0,0,0,0,0,3,3,3,-1,0,0,0,0,0,0,3,3,3,3,3,3,3
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[TENSOR,[16,6]],
[TENSOR,[16,7]],[45,45,45,-3,-3,0,0,0,0,0,0,-3,-3,-3,1,0,0,0,0,0,0,0,0,0,0,0,
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[TENSOR,[20,7]],[10,-6,2,2,-2,-5*E(3),3*E(3),-E(3),-5*E(3)^2,3*E(3)^2,-E(3)^2
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[GALOIS,[23,2]],
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[TENSOR,[24,6]],
[TENSOR,[23,6]],
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[TENSOR,[29,6]],
[TENSOR,[29,7]],[40,8,-8,0,0,10,2,-2,10,2,-2,-4,4,0,0,2,-2,0,2,-2,0,-2,-2,2,2
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[TENSOR,[33,6]],[60,-36,12,-4,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,3,-3,-3,3,3,
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[TENSOR,[38,7]],
[TENSOR,[38,6]],[80,16,-16,0,0,20,4,-4,20,4,-4,0,0,0,0,0,0,0,0,0,0,2,2,-2,-2,
2,2,-2,-2,-1,-1,1,1,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[41,6]],
[TENSOR,[41,7]]],
[(38,41)(39,42)(40,43),
( 6, 9)( 7,10)( 8,11)(16,19)(17,20)(18,21)(22,26)(23,27)(24,28)(25,29)(32,33)
(34,36)(35,37)(39,40)(42,43)
]);
ARC("2^(4+4):(3xA5)","tomfusion",rec(name:="2^(4+4):(3xA5)",map:=[1,2,3,
11,12,5,20,21,5,20,21,4,13,16,56,26,67,76,26,67,76,6,23,24,22,6,23,24,22,
7,25,28,28,74,77,74,77,19,79,79,19,79,79],text:=["fusion map is unique"
]));
ALF("2^(4+4):(3xA5)","U5(2)",[1,2,3,10,11,4,14,20,5,15,21,3,10,12,28,20,
35,40,21,36,41,7,24,17,19,6,23,16,18,9,27,26,25,38,43,37,42,13,45,44,13,
45,44],[
"fusion map is unique up to table automorphisms"
]);
ALF("2^(4+4):(3xA5)","j3m4",[1,1,1,2,2,3,3,3,4,4,4,5,5,5,6,7,7,7,8,8,8,9,
9,9,9,10,10,10,10,11,11,11,11,12,12,13,13,14,15,16,17,18,19]);

MOT("3^4:S5",
[
"origin: Dixon's Algorithm,\n",
"4th maximal subgroup of U5(2)"
],
[9720,1944,1944,972,972,486,324,72,72,72,36,36,36,54,27,54,54,27,27,5,324,324,
324,108,108,108,108,108,108,54,12,12,12,18,18,18],
[,[1,3,2,5,4,6,7,1,3,2,7,5,4,14,15,17,16,19,18,20,1,5,4,7,7,2,3,4,5,6,8,10,9,
14,16,17],[1,1,1,1,1,1,1,8,8,8,8,8,8,1,1,5,4,5,4,20,21,21,21,21,21,21,21,21,21
,21,31,31,31,21,22,23],,[1,3,2,5,4,6,7,8,10,9,11,13,12,14,15,17,16,19,18,1,21,
23,22,25,24,27,26,29,28,30,31,33,32,34,36,35]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
-1,-1,-1],[6,6,6,6,6,6,6,-2,-2,-2,-2,-2,-2,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0],[4,4,4,4,4,4,4,0,0,0,0,0,0,1,1,1,1,1,1,-1,2,2,2,2,2,2,2,2,2,2,0,0,
0,-1,-1,-1],
[TENSOR,[4,2]],[5,5,5,5,5,5,5,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,0,1,1,1,1,1,1,1,1
,1,1,-1,-1,-1,1,1,1],
[TENSOR,[6,2]],[5,E(3)+4*E(3)^2,4*E(3)+E(3)^2,-2*E(3)+E(3)^2,E(3)-2*E(3)^2,2,
-1,1,E(3),E(3)^2,1,E(3)^2,E(3),2,-1,2*E(3),2*E(3)^2,-E(3),-E(3)^2,0,-3,
-3*E(3)^2,-3*E(3),E(3)-E(3)^2,-E(3)+E(3)^2,-2*E(3)-E(3)^2,-E(3)-2*E(3)^2,
E(3)+2*E(3)^2,2*E(3)+E(3)^2,0,-1,-E(3),-E(3)^2,0,0,0],
[GALOIS,[8,2]],
[TENSOR,[8,2]],
[TENSOR,[9,2]],[10,2*E(3)+8*E(3)^2,8*E(3)+2*E(3)^2,-4*E(3)+2*E(3)^2,
2*E(3)-4*E(3)^2,4,-2,2,2*E(3),2*E(3)^2,2,2*E(3)^2,2*E(3),-2,1,-2*E(3),
-2*E(3)^2,E(3),E(3)^2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[12,2]],[10,-4*E(3)+2*E(3)^2,2*E(3)-4*E(3)^2,5*E(3)+2*E(3)^2,
2*E(3)+5*E(3)^2,1,1,-2,-2*E(3)^2,-2*E(3),1,E(3),E(3)^2,1,1,E(3),E(3)^2,E(3),
E(3)^2,0,-2,-E(3)-4*E(3)^2,-4*E(3)-E(3)^2,1,1,-2,-2,2*E(3)-E(3)^2,
-E(3)+2*E(3)^2,1,0,0,0,1,E(3)^2,E(3)],
[GALOIS,[14,2]],
[TENSOR,[14,2]],
[TENSOR,[15,2]],[10,-4*E(3)+2*E(3)^2,2*E(3)-4*E(3)^2,5*E(3)+2*E(3)^2,
2*E(3)+5*E(3)^2,1,1,2,2*E(3)^2,2*E(3),-1,-E(3),-E(3)^2,1,1,E(3),E(3)^2,E(3),
E(3)^2,0,4,-E(3)+2*E(3)^2,2*E(3)-E(3)^2,3*E(3)+E(3)^2,E(3)+3*E(3)^2,-2*E(3)^2,
-2*E(3),E(3)^2,E(3),1,0,0,0,1,E(3)^2,E(3)],
[GALOIS,[18,2]],
[TENSOR,[18,2]],
[TENSOR,[19,2]],[15,3*E(3)+12*E(3)^2,12*E(3)+3*E(3)^2,-6*E(3)+3*E(3)^2,
3*E(3)-6*E(3)^2,6,-3,-1,-E(3),-E(3)^2,-1,-E(3)^2,-E(3),0,0,0,0,0,0,0,-3,
-3*E(3)^2,-3*E(3),E(3)-E(3)^2,-E(3)+E(3)^2,-2*E(3)-E(3)^2,-E(3)-2*E(3)^2,
E(3)+2*E(3)^2,2*E(3)+E(3)^2,0,1,E(3),E(3)^2,0,0,0],
[GALOIS,[22,2]],
[TENSOR,[22,2]],
[TENSOR,[23,2]],[20,8,8,2,2,-1,-4,0,0,0,0,0,0,2,-1,2,2,-1,-1,0,-6,-6,-6,0,0,0
,0,0,0,3,0,0,0,0,0,0],
[TENSOR,[26,2]],[20,-8*E(3)+4*E(3)^2,4*E(3)-8*E(3)^2,10*E(3)+4*E(3)^2,
4*E(3)+10*E(3)^2,2,2,0,0,0,0,0,0,-1,-1,-E(3),-E(3)^2,-E(3),-E(3)^2,0,2,2,2,
2*E(3),2*E(3)^2,2*E(3),2*E(3)^2,2*E(3),2*E(3)^2,2,0,0,0,-1,-E(3)^2,-E(3)],
[GALOIS,[28,2]],
[TENSOR,[28,2]],
[TENSOR,[29,2]],[30,-6,-6,3,3,-6,3,2,2,2,-1,-1,-1,0,0,0,0,0,0,0,-6,3,3,-3,-3,
0,0,3,3,0,0,0,0,0,0,0],
[TENSOR,[32,2]],[30,-6,-6,3,3,-6,3,-2,-2,-2,1,1,1,0,0,0,0,0,0,0,0,
-3*E(3)+3*E(3)^2,3*E(3)-3*E(3)^2,E(3)-E(3)^2,-E(3)+E(3)^2,-2*E(3)+2*E(3)^2,
2*E(3)-2*E(3)^2,E(3)-E(3)^2,-E(3)+E(3)^2,0,0,0,0,0,0,0],
[TENSOR,[34,2]],[40,16,16,4,4,-2,-8,0,0,0,0,0,0,-2,1,-2,-2,1,1,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0]],
[( 2, 3)( 4, 5)( 9,10)(12,13)(16,17)(18,19)(22,23)(24,25)(26,27)(28,29)(32,33)
(35,36)]);
ARC("3^4:S5","tomfusion",rec(name:="3^4:S5",map:=[1,4,4,5,5,6,7,3,23,23,
24,26,26,8,9,38,38,41,41,13,2,15,15,20,20,19,19,16,16,17,12,54,54,25,80,
80],text:=[
"fusion map is unique"
]));
ALF("3^4:S5","U5(2)",[1,4,5,6,7,8,9,3,20,21,27,23,24,8,9,30,29,32,31,13,2,
16,17,26,25,15,14,19,18,22,12,40,41,22,46,47],[
"fusion map is unique up to table automorphisms"
]);
ALF("3^4:S5","A5.2",[1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,4,5,5,5,5,5,5,
5,5,5,5,6,6,6,7,7,7]);

MOT("3.s7x2",
[
"origin: CAS library,\n",
"tests: 1.o.r., pow[2,3,5,7]"
],
0,
0,
0,
[(14,15)(36,37),(16,38)(17,39)(18,40)(19,41)(20,42)(21,43)(22,44)],
["ConstructDirectProduct",[["Cyclic",2],["3.A7.2"]],(),(5,11,10,9,8,7,6)(17,
18)(21,22)(27,33,32,31,30,29,28)(39,40)(43,44)]);
ALF("3.s7x2","He.2",[1,4,2,10,4,5,6,17,9,21,10,10,13,23,24,2,3,6,10,11,16,
17,27,29,27,30,30,31,28,36,35,43,29,30,37,44,45,27,27,28,30,31,35,36],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("3.s7x2","S7x2",[1,1,3,3,5,7,9,9,11,11,13,13,15,15,15,17,19,21,23,25,
27,29,2,2,4,4,6,8,10,10,12,12,14,14,16,16,16,18,20,22,24,26,28,30]);

MOT("4.s4",
[
"origin: CAS library,\n",
" test:= 1. o.r., sym 2 decompose correctly \n",
"tests: 1.o.r., pow[2,3]"
],
[96,96,96,96,16,16,12,12,12,12,16,16,16,16,8,8],
[,[1,1,2,2,1,2,7,7,8,8,5,5,5,5,3,4],[1,2,4,3,5,6,1,2,4,3,12,11,14,13,16,15]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1],[2,
2,2,2,2,2,-1,-1,-1,-1,0,0,0,0,0,0],[3,3,3,3,-1,-1,0,0,0,0,1,1,1,1,-1,-1],
[TENSOR,[4,2]],[1,1,-1,-1,-1,1,1,1,-1,-1,-E(4),E(4),-E(4),E(4),-E(4),E(4)],
[TENSOR,[2,6]],
[TENSOR,[3,6]],
[TENSOR,[4,7]],
[TENSOR,[4,6]],[2,-2,2*E(4),-2*E(4),0,0,-1,1,-E(4),E(4),-1+E(4),-1-E(4),
1-E(4),1+E(4),0,0],
[TENSOR,[11,2]],
[TENSOR,[11,6]],
[TENSOR,[11,7]],[4,-4,4*E(4),-4*E(4),0,0,1,-1,E(4),-E(4),0,0,0,0,0,0],
[TENSOR,[15,6]]],
[( 3, 4)( 9,10)(11,12)(13,14)(15,16),(11,13)(12,14)]);
ALF("4.s4","U3(3)",[1,2,5,6,2,7,3,8,13,14,5,6,7,7,11,12],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("4.s4","2^(1+4).S3",[1,2,3,3,4,5,6,7,8,8,14,14,15,15,16,16],[
"fusion map is unique up to table aut."
]);

MOT("4^2:s3",
[
"origin: CAS library,\n",
"maximal subgroup of U3(3),\n",
" test:= 1. o.r., sym 2 decompose correctly \n",
"tests: 1.o.r., pow[2,3]"
],
[96,32,32,32,16,8,3,8,8,8],
[,[1,1,2,2,2,2,7,1,4,3],[1,2,4,3,5,6,1,8,10,9]],
[[1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,-1,1,-1,-1,-1],[2,2,2,2,2,0,-1,0,0,0],[3,-1,
-1-2*E(4),-1+2*E(4),1,-1,0,1,-E(4),E(4)],
[GALOIS,[4,3]],[3,3,-1,-1,-1,-1,0,-1,1,1],
[TENSOR,[6,2]],
[TENSOR,[4,2]],
[TENSOR,[5,2]],[6,-2,2,2,-2,0,0,0,0,0]],
[( 3, 4)( 9,10)]);
ARC("4^2:s3","tomfusion",rec(name:="4^2:S3",map:=[1,2,6,6,7,8,4,3,16,16],
text:=[
"fusion map is unique"
]));
ALF("4^2:s3","L3(5)",[1,2,4,5,6,6,3,2,11,10],[
"fusion map is unique up to table autom."
]);
ALF("4^2:s3","U3(3)",[1,2,5,6,7,7,4,2,12,11],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("4^2:s3","4^2:D12",[1,2,3,3,4,12,5,10,14,14],[
"fusion map is unique up to table aut."
]);

MOT("A11Syl2",
[
"origin: cayley, tests: 1.o.r.\n",
"table of sylow 2 subgroup of the alternating group A11,"
],
[128,128,64,32,32,32,32,32,32,16,16,32,32,32,16,16,16,8,8,8],
[,[1,1,1,1,1,1,1,1,1,1,1,2,3,3,2,3,3,4,5,12]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,-1,1,1,1,1,-1,1,
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],
[TENSOR,[3,5]],
[TENSOR,[2,6]],
[TENSOR,[2,5]],[2,2,2,2,-2,-2,-2,0,0,0,0,-2,0,0,0,2,0,0,0,0],
[TENSOR,[9,5]],[2,2,2,-2,2,0,0,-2,-2,0,0,-2,0,0,0,0,2,0,0,0],
[TENSOR,[11,3]],[2,2,2,-2,-2,0,0,0,0,0,2,2,-2,-2,0,0,0,0,0,0],
[TENSOR,[13,3]],[4,4,-4,0,0,0,0,0,0,2,0,0,0,0,-2,0,0,0,0,0],
[TENSOR,[15,2]],[4,-4,0,0,0,-2,2,2,-2,0,0,0,-2,2,0,0,0,0,0,0],
[TENSOR,[17,3]],
[TENSOR,[17,6]],
[TENSOR,[17,5]]],
[( 8, 9)(13,14),( 6, 7)(13,14),( 4, 5)( 6, 8)( 7, 9)(16,17)(18,19)]);
ALF("A11Syl2","A11",[1,3,2,3,2,3,2,3,2,3,3,8,7,9,8,7,9,8,9,18],[
"fusion map is unique up to table autom.,\n",
"unique map that is compatible with LyN2 -> 2.A11"
]);

MOT("a4",
[
"origin: CAS library,\n",
"    names:=     a4; psl[2,3]\n",
"                    a1(3)     (lie-not.)\n",
"    order:     2^2.3 = 12\n",
"    number of classes: 4\n",
"    source:    generated by dixon-algorithm aachen (1982)\n",
"    comments:  alternating group, catalogue nr.12.5\n",
"    test:      orth, min, sym(3)\n",
"constructions: AGL(1,4),\n",
"tests: 1.o.r., pow[2,3]"
],
[12,4,3,3],
[,[1,1,4,3],[1,2,1,1]],
[[1,1,1,1],[1,1,E(3),E(3)^2],
[TENSOR,[2,2]],[3,-1,0,0]],
[(3,4)]);
ARC("a4","CharacterParameters",[[1,[1,1,1,1]],[1,[[2,2],'+']],[1,[[2,2],'-']],
[1,[2,1,1]]]);
ARC("a4","ClassParameters",[[1,[1,1,1,1]],[1,[2,2]],[1,[[3,1],'+']],[1,[[3,1],
'-']]]);
ARC("a4","projectives",["2.L2(3)",[[2,0,-1,-1]],]);
ALF("a4","A5",[1,2,3,3],[
"fusion map is unique"
]);
ALF("a4","Symm(4)",[1,2,3,3],[
"fusion map is unique"
]);
ALF("a4","L2(13)",[1,2,3,3]);
ALF("a4","L2(27)",[1,2,3,4]);
ALF("a4","s4",[1,2,3,3],[
"fusion map is unique"
]);
ALN("a4",["A5N2","AGL(1,4)","L2(3)"]);

MOT("2.L2(3)",
[
"origin: Dixon's Algorithm"
],
[24,24,4,6,6,6,6],
[,[1,1,2,6,6,4,4],[1,2,3,1,2,1,2],,[1,2,3,6,7,4,5]],
0,
[(4,6)(5,7)],
["ConstructProj",[["a4",[]],["2.L2(3)",[]]]]);
ALF("2.L2(3)","a4",[1,1,2,3,3,4,4]);
ALF("2.L2(3)","2.A5",[1,2,3,4,5,4,5]);
ALF("2.L2(3)","2A4xA5",[1,6,11,16,21,26,31],[
"fusion map determined by the direct product construction"
]);
ALF("2.L2(3)","2.L2(13)",[1,2,3,4,5,4,5]);
ALF("2.L2(3)","2.L2(27)",[1,2,3,4,5,6,7],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("2.L2(3)","2.S4",[1,2,3,7,8,7,8],[
"fusion map is unique"
]);
ALF("2.L2(3)","2.Symm(4)",[1,2,3,4,5,4,5],[
"fusion map is unique"
]);
ALN("2.L2(3)",["2.A5N2","sl(2,3)"]);

MOT("a5wc2",
[
"origin: CAS library,\n",
"tests: 1.o.r., pow[2,3,5]"
],
[7200,240,120,32,180,18,8,300,300,50,50,25,12,6,20,20,10,10,15,15],
[,[1,1,1,1,5,6,4,9,8,11,10,12,5,6,8,9,10,11,20,19],[1,2,3,4,1,1,7,9,8,11,10,
12,2,3,16,15,18,17,9,8],,[1,2,3,4,5,6,7,1,1,1,1,1,13,14,2,2,3,3,5,5]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,-1,1,1,1,-1,1,1,1,1,1,1,-1,1,
1,-1,-1,1,1],[6,2,0,-2,3,0,0,-3*E(5)-4*E(5)^2-4*E(5)^3-3*E(5)^4,
-4*E(5)-3*E(5)^2-3*E(5)^3-4*E(5)^4,-2*E(5)^2-2*E(5)^3,-2*E(5)-2*E(5)^4,1,-1,0,
E(5)^2+E(5)^3,E(5)+E(5)^4,0,0,-E(5)^2-E(5)^3,-E(5)-E(5)^4],
[GALOIS,[3,2]],[8,4,0,0,5,2,0,3,3,-2,-2,-2,1,0,-1,-1,0,0,0,0],[9,-3,-3,1,0,0,
1,-3*E(5)^2-3*E(5)^3,-3*E(5)-3*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,-1,0,0,E(5)+E(5)^4,E(5)^2+E(5)^3,E(5)^2+E(5)^3,
E(5)+E(5)^4,0,0],
[TENSOR,[6,2]],
[GALOIS,[6,2]],
[TENSOR,[8,2]],[10,6,0,2,4,-2,0,5,5,0,0,0,0,0,1,1,0,0,-1,-1],[16,0,4,0,4,1,0,
-4,-4,1,1,1,0,1,0,0,-1,-1,-1,-1],
[TENSOR,[11,2]],[18,-6,0,2,0,0,0,3,3,-2,-2,3,0,0,-1,-1,0,0,0,0],[24,-4,0,0,3,
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,
2*E(5)^2+2*E(5)^3,2*E(5)+2*E(5)^4,-1,-1,0,1,1,0,0,-E(5)^2-E(5)^3,
-E(5)-E(5)^4],
[GALOIS,[14,2]],[25,5,-5,1,-5,1,-1,0,0,0,0,0,-1,1,0,0,0,0,0,0],
[TENSOR,[16,2]],[30,-2,0,-2,-3,0,0,-5*E(5)^2-5*E(5)^3,-5*E(5)-5*E(5)^4,0,0,0,
1,0,-E(5)-E(5)^4,-E(5)^2-E(5)^3,0,0,E(5)^2+E(5)^3,E(5)+E(5)^4],
[GALOIS,[18,2]],[40,4,0,0,1,-2,0,-5,-5,0,0,0,1,0,-1,-1,0,0,1,1]],
[( 8, 9)(10,11)(15,16)(17,18)(19,20)]);
ARC("a5wc2","tomfusion",rec(name:="(A5xA5):2",map:=[1,2,3,4,5,6,11,14,14,
16,16,15,19,21,32,32,34,34,45,45],text:=[
"fusion map is unique"
]));
ALF("a5wc2","S4(4)",[1,3,2,4,6,5,8,11,12,10,9,13,15,14,19,18,16,17,22,23],[
"fusion map is unique up to table autom."
]);

MOT("S4(4)M6",
[
"6th maximal subgroup of S4(4),\n",
"differs from S4(4)M5 only by fusion map"
],
0,
0,
0,
0,
["ConstructPermuted",["a5wc2"]]);
ALF("S4(4)M6","S4(4)",[1,2,3,4,5,6,8,9,10,11,12,13,14,15,17,16,19,18,20,
21],[
"fusion map is unique up to table autom.,\n",
"equals the map from S4(4)M5, mapped under the outer autom."
],"tom:490");

MOT("affine",
[
"origin: CAS library,\n",
"tests: 1.o.r., pow[2,3,5]"
],
[311040,3888,3840,3456,432,192,32,576,72,64,16,432,54,48,24,36,18,10,10,96,
288,36,192,192,32,8,48,24,48,24,12,24,24],
[,[1,2,1,1,2,3,3,4,5,4,6,12,13,12,14,12,13,18,18,3,1,2,6,6,6,7,8,9,8,9,14,15,
15],[1,1,3,4,4,6,7,8,8,10,11,1,1,3,6,4,4,18,19,20,21,21,23,24,25,26,27,27,29,
29,20,24,23],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,1,3,20,21,22,24,23,
25,26,29,30,27,28,31,33,32]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[4,4,
4,4,4,4,0,0,0,0,0,1,1,1,1,1,1,-1,-1,2,2,2,2,2,2,0,0,0,0,0,-1,-1,-1],
[TENSOR,[3,2]],[5,5,5,5,5,5,1,1,1,1,1,-1,-1,-1,-1,-1,-1,0,0,-1,-1,-1,-1,-1,-1,
1,1,1,1,1,-1,-1,-1],
[TENSOR,[5,2]],[6,6,6,6,6,6,-2,-2,-2,-2,-2,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,
0,0,0,0,0],[5,5,5,-3,-3,1,1,1,1,1,-1,2,2,2,-2,0,0,0,0,3,-1,-1,-3,-3,1,1,-1,-1,
-1,-1,0,0,0],
[TENSOR,[8,2]],[10,10,10,-6,-6,2,2,2,2,2,-2,-2,-2,-2,2,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0],[15,15,15,-9,-9,3,-1,-1,-1,-1,1,0,0,0,0,0,0,0,0,3,-1,-1,-3,-3,
1,-1,1,1,1,1,0,0,0],
[TENSOR,[11,2]],[10,10,10,2,2,-2,2,-2,-2,-2,0,1,1,1,1,-1,-1,0,0,4,0,0,2,2,-2,
0,0,0,0,0,1,-1,-1],
[TENSOR,[13,2]],[10,10,10,2,2,-2,-2,2,2,2,0,1,1,1,1,-1,-1,0,0,2,-2,-2,4,4,0,0,
0,0,0,0,-1,1,1],
[TENSOR,[15,2]],[20,20,20,4,4,-4,0,0,0,0,0,-1,-1,-1,-1,1,1,0,0,-2,-2,-2,2,2,2,
0,0,0,0,0,1,-1,-1],
[TENSOR,[17,2]],[4,4,-4,0,0,0,0,2,2,-2,0,-2,-2,2,0,0,0,-1,1,0,0,0,
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],
[TENSOR,[19,2]],[16,16,-16,0,0,0,0,0,0,0,0,-2,-2,2,0,0,0,1,-1,0,0,0,
4*E(8)+4*E(8)^3,-4*E(8)-4*E(8)^3,0,0,0,0,0,0,0,-E(8)-E(8)^3,E(8)+E(8)^3],
[TENSOR,[21,2]],[20,20,-20,0,0,0,0,2,2,-2,0,2,2,-2,0,0,0,0,0,0,0,0,
-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,-E(8)-E(8)^3,E(8)+E(8)^3],
[TENSOR,[23,2]],[24,24,-24,0,0,0,0,-4,-4,4,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,0,0,0,
0,0,0,0,0,0],[80,-1,0,8,-1,0,0,8,-1,0,0,8,-1,0,0,2,-1,0,0,0,8,-1,0,0,0,0,2,-1,
2,-1,0,0,0],
[TENSOR,[26,2]],[160,-2,0,16,-2,0,0,16,-2,0,0,-8,1,0,0,-2,1,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0],[240,-3,0,24,-3,0,0,-8,1,0,0,0,0,0,0,0,0,0,0,0,8,-1,0,0,0,0,-2,
1,-2,1,0,0,0],
[TENSOR,[29,2]],[160,-2,0,-16,2,0,0,0,0,0,0,-8,1,0,0,2,-1,0,0,0,0,0,0,0,0,0,
2*E(8)+2*E(8)^3,-E(8)-E(8)^3,-2*E(8)-2*E(8)^3,E(8)+E(8)^3,0,0,0],
[TENSOR,[31,2]],[320,-4,0,-32,4,0,0,0,0,0,0,8,-1,0,0,-2,1,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0]],
[(23,24)(27,29)(28,30)(32,33)]);
ALF("affine","twd5a",[1,1,2,3,3,4,5,6,6,7,8,9,9,10,11,12,12,13,14,15,16,
16,17,18,19,20,21,21,22,22,23,24,25]);

MOT("b33141",
[
"origin: CAS library,\n",
"names:b33141\n",
"order: 2^6.3^2 = 576\n",
"number of classes: 23\n",
"source:generated by dixon-algorithm\n",
"aachen  [1981],\n",
"brown, h. / buelow, r. / neubueser, j.\n",
"wondratschek, h. / zassenhaus, h.\n",
"crystallographic groups of\n",
"four dimensional space\n",
"comments:isomorphism type 576.1\n",
"q-classes: 33/14\n",
"generators:\n",
"a:  1  0  0  0    b:  -1 -1 -1  2    c:  1  0  0  0\n",
"0 -1  0  0         0  0  1  0        0 -1  0  0\n",
"0  0 -1  0         0 -1  0  0        0  0  1  0\n",
"0 -1 -1  1        -1 -1  0  1        1  0  1 -1\n",
"\n",
"d:  0  0 -1  0    e:   0 -1  0  1    f:  0  1  0 -1\n",
"1  1  1 -2        -1  0  0  1        0  0 -1 -1\n",
"-1  0  0  0         1  1  1 -1        1  0  0 -1\n",
"0  0  0 -1         0  0  1  0        1  1  0 -1 \n",
"\n",
"test: 1. o.r., sym 2, 3 decompose correctly\n",
"tests: 1.o.r., pow[2,3]"
],
[576,32,48,576,18,18,12,12,12,12,36,36,36,36,12,12,72,72,72,72,48,8,48],
[,[1,1,4,1,5,5,11,12,11,12,12,11,12,11,20,19,18,17,18,17,1,2,1],[1,2,3,4,1,4,
21,21,23,23,1,1,4,4,3,3,1,1,4,4,21,22,23],,[1,2,3,4,5,6,8,7,10,9,12,11,14,13,
16,15,18,17,20,19,21,22,23],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,
20,21,22,23]],
[[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,-E(3),-E(3)^2,
-E(3),-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,E(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],
[TENSOR,[2,2]],
[TENSOR,[3,4]],
[TENSOR,[2,3]],[2,2,2,2,-1,-1,0,0,0,0,2,2,2,2,-1,-1,-1,-1,-1,-1,0,0,0],
[TENSOR,[7,4]],
[TENSOR,[7,2]],[4,0,0,-4,1,-1,E(3),E(3)^2,-E(3),-E(3)^2,E(3)^2,E(3),-E(3)^2,
-E(3),0,0,-2*E(3)^2,-2*E(3),2*E(3)^2,2*E(3),-2,0,2],
[TENSOR,[10,2]],
[TENSOR,[10,6]],
[TENSOR,[10,3]],
[TENSOR,[10,4]],
[TENSOR,[10,5]],[6,-2,2,6,0,0,0,0,0,0,0,0,0,0,-E(3)^2,-E(3),3*E(3)^2,3*E(3),
3*E(3)^2,3*E(3),0,0,0],
[TENSOR,[16,2]],
[TENSOR,[16,4]],[8,0,0,-8,-1,1,0,0,0,0,2*E(3),2*E(3)^2,-2*E(3),-2*E(3)^2,0,0,
2*E(3),2*E(3)^2,-2*E(3),-2*E(3)^2,0,0,0],
[TENSOR,[19,4]],
[TENSOR,[19,2]],[9,1,-3,9,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-3,1,-3],
[TENSOR,[22,2]]],
[( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20),( 7, 9)( 8,10)(21,23)]);
ARC("b33141","tomfusion",rec(name:="2.(A4xA4).2",map:=[1,4,16,2,6,19,21,
21,23,23,7,7,22,22,37,37,8,8,20,20,3,13,5],text:=[
"fusion map is unique up to table autom."
]));
ALF("b33141","U4(2)",[1,3,8,2,7,15,13,14,16,16,6,6,13,14,19,20,4,5,11,12,
2,9,3],[
"fusion map is unique up to table autom."
]);
ALF("b33141","w(f4)",[1,3,4,2,9,10,24,24,25,25,7,7,8,8,11,11,5,5,6,6,18,
21,19],[
"fusion map is unique up to table autom."
]);

MOT("bd10",
[
"origin: CAS library,\n",
"names:=bd10\n",
" order: 2^2.5 = 20\n",
" number of classes: 8\n",
" source: generated by dixon-algorithm\n",
"         aachen [1984]\n",
" comments:generators: a,b,c\n",
" relations: a^2=b^2=c^5=a*b*c \n",
" test: 1. o.r., sym 2 decompose correctly \n",
"tests: 1.o.r., pow[2,5]"
],
[20,4,4,20,10,10,10,10],
[,[1,4,4,1,6,5,5,6],,,[1,2,3,4,1,1,4,4]],
[[1,1,1,1,1,1,1,1],[1,-1,-1,1,1,1,1,1],[1,E(4),-E(4),-1,1,1,-1,-1],
[TENSOR,[2,3]],[2,0,0,-2,E(5)+E(5)^4,E(5)^2+E(5)^3,-E(5)^2-E(5)^3,
-E(5)-E(5)^4],
[TENSOR,[5,3]],
[GALOIS,[6,2]],
[TENSOR,[7,3]]],
[(5,6)(7,8),(2,3)]);
ALF("bd10","D10",[1,4,4,1,2,3,3,2]);
ALF("bd10","C4",[1,2,4,3,1,1,3,3]);
ALF("bd10","2.A5",[1,3,3,2,6,8,9,7],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("bd10","2.A6",[1,3,3,2,10,12,13,11],[
"fusion map is unique up to table aut."
]);
ALF("bd10","5:8",[1,5,6,3,2,2,4,4],[
"fusion map is unique up to table aut."
]);
ALF("bd10","2.D20",[1,12,12,3,8,9,7,6],[
"fusion map is unique up to table aut."
]);
ALN("bd10",["2.A5N5","2.A6N5"]);

MOT("bd6",
[
"origin: CAS library,\n",
"names:=bd6\n",
" order: 2^2.3 = 12\n",
" number of classes: 6\n",
" source:generated by dixon-algorithm\n",
"        aachen [1984]\n",
" test: 1. o.r., sym 2, 3 decompose correctly\n",
" comments:generators: a,b,c\n",
"          relations: a^2=b^2=c^3=a*b*c \n",
"tests: 1.o.r., pow[2,3]"
],
0,
0,
0,
0,
["ConstructPermuted",["2.S3"],(2,4,6,3,5),(3,5,4)]);
ALF("bd6","C4",[1,2,4,3,1,3]);
ALF("bd6","S3",[1,3,3,1,2,2]);

MOT("bd8",
[
"origin: CAS library,\n",
"names:=bd8\n",
" order: 2^4 = 16\n",
" number of classes: 7\n",
" source: generated by dixon-algorithm\n",
"         aachen [1984]\n",
" test: 1. o.r., sym 2 decompose correctly\n",
" comments:generators: a,b,c\n",
"          relations: a^2=b^2=c^4=a*b*c \n",
"tests: 1.o.r., pow[2]"
],
0,
0,
0,
0,
["ConstructPermuted",["2.D8"],(2,3,7,4,5,6),(3,4)(5,7)]);

MOT("M22C2A",
[
"origin: CAS library,\n",
"centralizer of an involution in the sporadic simple Mathieu group M22,\n",
"computed using CAYLEY,\n",
"tests: 1.o.r., pow[2,3],\n",
"2nd power map determined only up to matrix automorphisms,"
],
[384,384,16,8,32,48,16,64,8,32,12,12,12,12,16,16,16],
[,[1,1,1,5,1,1,8,1,10,2,11,11,11,11,8,2,8],[1,2,3,4,5,6,7,8,9,10,1,2,6,6,15,
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],[1,1,1,1,1,-1,-1,1,-1,1,1,1,-1,-1,1,-1,-1],
[TENSOR,[2,3]],[2,2,0,0,2,2,0,2,0,2,-1,-1,-1,-1,0,0,2],
[TENSOR,[5,3]],[3,3,-1,1,-1,3,-1,3,1,-1,0,0,0,0,-1,-1,-1],
[TENSOR,[7,2]],
[TENSOR,[7,3]],
[TENSOR,[7,4]],[6,6,0,0,-2,0,2,-2,0,2,0,0,0,0,0,-2,0],[6,6,2,0,2,0,0,-2,0,-2,
0,0,0,0,-2,0,0],
[TENSOR,[11,2]],
[TENSOR,[12,2]],[8,-8,0,0,0,0,0,0,0,0,2,-2,0,0,0,0,0],[8,-8,0,0,0,0,0,0,0,0,
-1,1,E(3)-E(3)^2,-E(3)+E(3)^2,0,0,0],
[TENSOR,[16,3]]],
[(13,14)]);
ALF("M22C2A","M22",[1,2,2,4,2,2,4,2,10,4,3,7,7,7,5,5,5],[
"determined using the fusion M22N2 -> M22"
]);
ALF("M22C2A","M23C2A",[1,2,4,8,4,3,7,3,14,6,5,9,10,11,7,6,7],[
"fusion map is unique up to table automorphisms"
]);
ALF("M22C2A","M23",[1,2,2,4,2,2,4,2,9,4,3,6,6,6,4,4,4],[
"fusion map is unique"
]);
ALF("M22C2A","McL",[1,2,2,5,2,2,5,2,12,5,4,9,9,9,5,5,5],[
"fusion map is unique"
]);
ALN("M22C2A",["M22N2A"]);

MOT("M24C2B",
[
"origin: CAS library,\n",
"tests: 1.o.r., pow[2,3,5],\n",
"2nd power map determined only up to matrix automorphisms,"
],
[7680,7680,3840,512,512,256,96,96,32,32,128,128,64,64,64,32,32,24,24,12,16,16,
16,16,12,12,20,20,20,20],
[,[1,1,1,1,1,1,1,2,4,5,1,1,1,5,5,6,6,18,18,18,11,12,15,15,18,19,27,27,27,27],[
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,1,2,3,21,22,24,23,7,8,27,28,30,
29],,[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,
2,3,3]],
[[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],[4,4,4,4,4,4,2,2,2,
2,0,0,0,0,0,0,0,1,1,1,0,0,0,0,-1,-1,-1,-1,-1,-1],
[TENSOR,[3,2]],[5,5,5,5,5,5,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,1,1,0,
0,0,0],
[TENSOR,[5,2]],[6,6,6,6,6,6,0,0,0,0,-2,-2,-2,-2,-2,-2,-2,0,0,0,0,0,0,0,0,0,1,
1,1,1],[6,6,-6,-2,-2,2,0,0,0,0,2,2,-2,-2,2,0,0,0,0,0,-2,2,0,0,0,0,1,1,-1,-1],
[TENSOR,[8,2]],[12,-12,0,-4,4,0,0,0,0,0,-4,4,0,0,0,-2,2,0,0,0,0,0,0,0,0,0,2,
-2,0,0],[15,15,15,-1,-1,-1,3,3,-1,-1,3,3,3,-1,-1,-1,-1,0,0,0,1,1,-1,-1,0,0,0,
0,0,0],
[TENSOR,[11,2]],[15,15,15,-1,-1,-1,-3,-3,1,1,-1,-1,-1,3,3,-1,-1,0,0,0,1,1,-1,
-1,0,0,0,0,0,0],
[TENSOR,[13,2]],[24,24,-24,-8,-8,8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,
-1,1,1],[30,30,30,-2,-2,-2,0,0,0,0,-2,-2,-2,-2,-2,2,2,0,0,0,0,0,0,0,0,0,0,0,0,
0],[10,10,-10,2,2,-2,4,-4,0,0,2,2,-2,2,-2,0,0,1,1,-1,0,0,0,0,1,-1,0,0,0,0],[
20,-20,0,4,-4,0,0,0,0,0,-4,4,0,0,0,2,-2,2,-2,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[17,2]],[40,-40,0,8,-8,0,0,0,0,0,0,0,0,0,0,0,0,-2,2,0,0,0,0,0,0,0,0,0,
0,0],[20,20,-20,4,4,-4,2,-2,-2,2,0,0,0,0,0,0,0,-1,-1,1,0,0,0,0,-1,1,0,0,0,0],
[TENSOR,[21,2]],[10,10,-10,2,2,-2,2,-2,2,-2,-2,-2,2,-2,2,0,0,1,1,-1,0,0,0,0,
-1,1,0,0,0,0],
[TENSOR,[23,2]],[20,-20,0,4,-4,0,0,0,0,0,4,-4,0,0,0,-2,2,2,-2,0,0,0,0,0,0,0,0,
0,0,0],[12,-12,0,-4,4,0,0,0,0,0,4,-4,0,0,0,2,-2,0,0,0,0,0,0,0,0,0,2,-2,0,0],[
24,-24,0,-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,
E(5)-E(5)^2-E(5)^3+E(5)^4,-E(5)+E(5)^2+E(5)^3-E(5)^4],
[GALOIS,[27,2]],[6,6,-6,-2,-2,2,0,0,0,0,-2,-2,2,2,-2,0,0,0,0,0,0,0,-2*E(4),
2*E(4),0,0,1,1,-1,-1],
[TENSOR,[29,2]]],
[(29,30),(23,24),(11,12)(16,17)(21,22)]);
ARC("M24C2B","tomfusion",rec(name:="2^2.(2^4S5)",map:=[1,2,3,4,5,6,9,30,
76,57,7,8,10,48,36,71,60,11,85,89,79,81,292,292,86,310,82,300,301,301],
text:=[
"fusion map is unique up to table autom."
]));
ALF("M24C2B","M24",[1,3,3,3,2,2,3,8,8,6,2,3,3,6,7,7,6,5,11,11,7,8,14,14,11,
18,9,15,15,15],[
"fusion map is unique up to table automorphisms"
]);
ALF("M24C2B","2^2.L3(4).2_2",[1,2,3,4,5,6,24,25,27,26,4,5,6,10,11,13,12,7,
8,9,27,26,30,31,28,29,14,15,16,17],[
"fusion map is unique up to table autom."
]);
ALF("M24C2B","A5.2",[1,1,1,1,1,1,5,5,5,5,2,2,2,2,2,2,2,3,3,3,6,6,6,6,7,7,
4,4,4,4]);
ALN("M24C2B",["M24N2B"]);

MOT("c3d2",
[
"origin: CAS library,\n",
"tests: 1.o.r., pow[2,3,7]"
],
[1008,336,144,48,504,36,36,18,18,72,36,36,18,18,12,12,12,12,42,42,14,14,21,
21],
[,[1,1,1,1,5,7,6,9,8,5,6,7,8,9,6,7,6,7,19,20,19,20,23,24],[1,2,3,4,1,1,1,1,1,
3,3,3,3,3,2,2,4,4,20,19,22,21,20,19],,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,
16,17,18,1,1,2,2,5,5]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,-1,1,-1,1,1,1,1,1,1,1,1,
1,1,-1,-1,-1,-1,1,1,-1,-1,1,1],[1,1,1,1,1,E(3)^2,E(3),E(3)^2,E(3),1,E(3),
E(3)^2,E(3),E(3)^2,E(3),E(3)^2,E(3),E(3)^2,1,1,1,1,1,1],
[TENSOR,[2,3]],
[TENSOR,[3,3]],
[TENSOR,[2,5]],[2,0,2,0,-1,2*E(3),2*E(3)^2,-E(3),-E(3)^2,-1,2*E(3)^2,2*E(3),
-E(3)^2,-E(3),0,0,0,0,2,2,0,0,-1,-1],
[TENSOR,[7,3]],
[TENSOR,[7,5]],[3,3,3,3,3,0,0,0,0,3,0,0,0,0,0,0,0,0,E(7)^3+E(7)^5+E(7)^6,
E(7)+E(7)^2+E(7)^4,E(7)^3+E(7)^5+E(7)^6,E(7)+E(7)^2+E(7)^4,
E(7)^3+E(7)^5+E(7)^6,E(7)+E(7)^2+E(7)^4],
[TENSOR,[10,2]],
[GALOIS,[11,3]],
[TENSOR,[12,2]],[6,0,6,0,-3,0,0,0,0,-3,0,0,0,0,0,0,0,0,2*E(7)^3+2*E(7)^5
 +2*E(7)^6,2*E(7)+2*E(7)^2+2*E(7)^4,0,0,-E(7)^3-E(7)^5-E(7)^6,
-E(7)-E(7)^2-E(7)^4],
[GALOIS,[14,3]],[7,-7,-1,1,7,E(3),E(3)^2,E(3),E(3)^2,-1,-E(3)^2,-E(3),-E(3)^2,
-E(3),-E(3)^2,-E(3),E(3)^2,E(3),0,0,0,0,0,0],
[TENSOR,[16,2]],
[TENSOR,[16,5]],
[TENSOR,[16,6]],
[TENSOR,[16,3]],
[TENSOR,[16,4]],[14,0,-2,0,-7,2*E(3)^2,2*E(3),-E(3)^2,-E(3),1,-2*E(3),
-2*E(3)^2,E(3),E(3)^2,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[22,3]],
[TENSOR,[22,5]]],
[(19,20)(21,22)(23,24),( 6, 7)( 8, 9)(11,12)(13,14)(15,16)(17,18)]);
ALF("c3d2","Co3",[1,2,3,3,6,5,5,6,6,15,14,14,15,15,13,13,14,14,16,16,29,
29,35,35],[
"fusion map is unique"
]);
ALN("c3d2",["co3d2"]);

MOT("D120",
[
"origin: CAS library,\n",
"names:d60\n",
"order: 2^3.3.5 = 120\n",
"number of classes: 33\n",
"source:generated by dixon-algorithm\n",
"aachen [1980]\n",
"test: 1. o.r., sym 2 decompose correctly\n",
"comments:generators: a,b\n",
"relations: a^60 = b^2 = (ab)^2 = 1 \n",
"tests: 1.o.r., pow[2,3,5]"
],
0,
0,
0,
[(12,13)(18,19)(20,21)(26,29)(27,32)(28,33)(30,31),(12,13)(14,17)(15,16)
(22,24)(23,25)(26,30)(27,33)(28,32)(29,31),( 7, 8)(10,11)(14,16,17,15)
(18,20,19,21)(22,25,24,23)(26,27,31,28)(29,32,30,33),(2,4),(14,17)(15,16)
(18,19)(20,21)(22,24)(23,25)(26,31)(27,28)(29,30)(32,33)],
["ConstructPermuted",["Dihedral",120],(2,26,13,7,10,21,5,14,28,18,33,4,19,11,
9,15,22,20,30,29,16,6,12,31,3,23,25,8,32)(24,27),(2,3,4)(5,30,15,26,16,9,10,
13,18,14,7,21,31,20,25,19,6,17,29,11,32,23,27,33,28,8,24)(12,22)]);
ARC("D120","tomfusion",rec(name:="30.2^2",map:=[1,2,3,4,5,7,9,9,11,15,15,
18,18,20,20,20,20,22,22,22,22,26,26,26,26,30,30,30,30,30,30,30,30],text:=[
"fusion map is unique up to table autom."
]));
ALF("D120","D10",[1,4,1,4,1,1,2,3,1,3,2,1,1,3,2,2,3,2,2,3,3,3,2,3,2,3,2,2,
3,3,3,2,2]);
ALF("D120","D24",[1,8,7,9,5,4,1,1,3,7,7,2,6,5,5,5,5,4,4,4,4,3,3,3,3,6,6,6,
2,2,6,2,2]);
ALF("D120","D8",[1,4,2,5,1,3,1,1,2,2,2,3,3,1,1,1,1,3,3,3,3,2,2,2,2,3,3,3,3,
3,3,3,3]);
ALF("D120","S3",[1,3,1,3,2,1,1,1,2,1,1,2,2,2,2,2,2,1,1,1,1,2,2,2,2,2,2,2,2,
2,2,2,2]);
ALF("D120","L2(121)",[1,33,33,33,23,18,15,27,13,9,21,8,28,7,11,31,19,30,6,
24,12,17,5,29,25,4,26,16,32,22,14,10,20],[
"fusion map is unique up to table autom."
]);

MOT("esp43t",
[
"origin: CAS library,\n",
"tests: 1.o.r., pow[2,3,5]"
],
0,
0,
0,
0,
["ConstructPermuted",["3^(1+4).2U4(2).2"],(11,20,28,35,16,50,38,63,72,59,68,
57,53,41,30)(12,19,27,26,25,24,23,49,37,62,69,58,54,43,32,13,18,52,40,65,70,
61,67,55,42,31)(14,21,29,36,17,51,39,64,71,60,66,56,44,33)(15,22,34)(45,46,47)
(73,75)(76,77,78)(79,85,82,83,80,86,81,84)(87,89)(88,90),(3,6,13,16,19,37,32,
25,36,30,20,23,28,15,18,34,38,33,26,5,4)(14,17,22,27)(21,24,35,29)(39,40)(42,
43)(44,45)(47,48)(53,54)(58,59)(63,64)(67,68,70,69,71,72)(74,76)(79,80)(81,82)
(83,85,86)]);
ALF("esp43t","2.U4(2).2",[1,1,1,2,2,3,3,3,4,4,11,11,11,12,12,13,13,5,5,5,
5,5,9,9,9,9,7,7,7,16,16,16,16,8,10,10,18,18,18,18,19,19,19,19,17,17,17,17,
8,6,6,6,20,20,23,23,23,23,24,24,24,14,14,15,15,21,21,21,21,22,22,22,26,26,
25,29,27,28,33,33,34,34,32,32,30,31,37,38,35,36]);

MOT("j2nd2",
[
"origin: CAS library,\n",
"tests: 1.o.r., pow[2,3,5]"
],
0,
0,
0,
0,
["ConstructPermuted",["a4xa5"],(12,14,13)(15,16)(17,19,20),(4,8,10,7,6,9)(17,
18)]);
ALN("j2nd2",["j2d2"]);

LIBTABLE.LOADSTATUS.ctomisc1:="userloaded";

#############################################################################
##
#E