Spracherkennung für: .tbl vermutete Sprache: Unknown {[0] [0] [0]} [Methode: Schwerpunktbildung, einfache Gewichte, sechs Dimensionen]
#############################################################################
##
#W ctomaxi3.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 Co3, Co2 and Co1.
##
#H ctbllib history
#H ---------------
#H $Log: ctomaxi3.tbl,v $
#H Revision 4.28 2012/06/20 14:45:31 gap
#H added tables and fusions, as documented in ctbldiff.dat
#H TB
#H
#H Revision 4.27 2012/01/30 08:31:56 gap
#H removed #H entries from the headers
#H TB
#H
#H Revision 4.26 2011/09/28 14:32:21 gap
#H removed revision entry and SET_TABLEFILENAME call
#H TB
#H
#H Revision 4.25 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 4.24 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 4.23 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 4.22 2007/07/03 08:50:15 gap
#H added fusions,
#H encoded several tables as index two subdirect products
#H TB
#H
#H Revision 4.21 2004/08/31 12:33:33 gap
#H added tables of 4.L2(25).2_3,
#H L2(49).2^2,
#H L2(81).2^2,
#H L2(81).(2x4),
#H 3.L3(4).3.2_2,
#H L3(9).2^2,
#H L4(4).2^2,
#H 2x2^3:L3(2)x2,
#H (2xA6).2^2,
#H 2xL2(11).2,
#H S3xTh,
#H 41:40,
#H 7^(1+4):(3x2.S7),
#H 7xL2(8),
#H (7xL2(8)).3,
#H O7(3)N3A,
#H O8+(3).2_1',
#H O8+(3).2_1'',
#H O8+(3).2_2',
#H O8+(3).(2^2)_{122},
#H S4(9),
#H S4(9).2_i,
#H 2.U4(3).2_2',
#H 2.U4(3).(2^2)_{133},
#H 2.U4(3).D8,
#H 3.U6(2).S3,
#H added fusions 3.A6.2_i -> 3.A6.2^2,
#H L2(49).2_i -> L2(49).2^2,
#H L3(9).2_i -> L3(9).2^2,
#H L4(4).2_i -> L4(4).2^2,
#H G2(3) -> O7(3),
#H L2(17) -> S8(2),
#H 2.L3(4).2_2 -> 2.M22.2
#H 3.L3(4).2_2 -> 3.L3(4).3.2_2
#H 3.L3(4).3 -> 3.L3(4).3.2_2
#H 2^5:S6 -> 2.M22.2
#H O8+(3) -> O8+(3).2_1',
#H O8+(3) -> O8+(3).2_1'',
#H O8+(3) -> O8+(3).2_2',
#H O8+(3) -> O8+(3).(2^2)_{122},
#H O8+(3).2_1 -> O8+(3).(2^2)_{122},
#H O8+(3).2_2 -> O8+(3).(2^2)_{122},
#H 2.U4(3) -> 2.U4(3).2_2',
#H 2.U4(3).2_1 -> 2.U4(3).(2^2)_{133},
#H 2.U4(3).2_2 -> O7(3),
#H 2.U4(3).2_2' -> U4(3).2_2,
#H 2.U4(3).2_3 -> 2.U4(3).(2^2)_{133},
#H 2.U4(3).2_3' -> 2.U4(3).(2^2)_{133},
#H 2.U4(3).4 -> 2.U4(3).D8,
#H 3.U6(2).2 -> 3.U6(2).S3,
#H 3.U6(2).3 -> 3.U6(2).S3,
#H replaced table of psl(3,4):d12 by L3(4).D12,
#H changed table of O8+(3).S4 to a construction table,
#H changed encoding of the table of 12.A6.2_3,
#H added maxes of Sz(8), Sz(8).3,
#H TB
#H
#H Revision 4.20 2004/03/30 08:05:55 gap
#H unified tables `u4q3:2^2' and `U4(3).(2^2)_{133}'
#H TB
#H
#H Revision 4.19 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 4.18 2003/06/20 15:02:59 gap
#H added several fusions
#H TB
#H
#H Revision 4.17 2003/05/15 17:38:08 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 4.16 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 4.15 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 4.14 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 4.13 2002/10/22 12:44:08 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 4.12 2002/09/23 14:54:24 gap
#H replaced 2xM12 and A4xS5 by ``construction'' tables
#H TB
#H
#H Revision 4.11 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 4.10 2002/08/21 13:53:50 gap
#H removed names of the form `c1m<n>', `c2m<n>', `c3m<n>'
#H TB
#H
#H Revision 4.9 2002/07/12 06:45:55 gap
#H further tidying up: removed `irredinfo' stuff, rearranged constructions
#H TB
#H
#H Revision 4.8 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 4.7 2002/03/04 17:08:48 gap
#H added some fusions and admissible names
#H TB
#H
#H Revision 4.6 2001/05/04 16:48:13 gap
#H first revision for ctbllib
#H
#H
#H tbl history (GAP 4)
#H -------------------
#H (Rev. 4.6 of ctbllib coincides with Rev. 4.5 of tbl in GAP 4)
#H
#H RCS file: /gap/CVS/GAP/4.0/tbl/ctomaxi3.tbl,v
#H Working file: ctomaxi3.tbl
#H head: 4.5
#H branch:
#H locks: strict
#H access list:
#H symbolic names:
#H GAP4R2: 4.5.0.8
#H GAP4R2PRE2: 4.5.0.6
#H GAP4R2PRE1: 4.5.0.4
#H GAP4R1: 4.5.0.2
#H keyword substitution: kv
#H total revisions: 6; selected revisions: 6
#H description:
#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 14:53:29; 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 08:05:38; author: gap; state: Exp; lines: +5 -2
#H mainly new fusions to tables of marks added
#H
#H TB
#H ----------------------------
#H revision 4.2
#H date: 1997/11/25 15:45:07; author: gap; state: Exp; lines: +4 -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 15:42:06; author: fceller; state: Exp; lines: +2 -2
#H for version 4
#H ----------------------------
#H revision 1.1
#H date: 1996/10/21 15:59:57; author: sam; state: Exp;
#H first proposal of the table library
#H ==========================================================================
##
MOT("(A4xG2(4)):2",
[
"origin: computed using GAP from tables of A4, S4, G2(4), G2(4).2, Co1,\n",
"7th maximal subgroup of Co1"
],
[6038323200,1474560,92160,1451520,4320,36864,18432,12288,3600,3600,4608,288,
504,768,768,240,240,1152,1152,1152,156,180,180,252,48384,768,192,864,72,384,
192,128,96,24,28,32,32,48,48,48,2012774400,491520,30720,483840,1440,12288,
6144,4096,1200,1200,1536,96,168,256,256,80,80,384,384,384,52,60,60,84,
754790400,184320,11520,181440,540,4608,2304,1536,900,900,900,900,576,36,63,96,
96,60,60,60,60,144,144,144,39,39,45,45,45,45,63,63,48384,768,192,864,72,384,
192,128,96,24,28,32,32,48,48,48],
[,[1,1,1,4,5,2,2,2,9,10,4,5,13,6,8,10,9,11,11,11,21,22,23,24,1,2,3,4,5,6,7,6,
11,12,13,15,15,18,19,20,1,1,1,4,5,2,2,2,9,10,4,5,13,6,8,10,9,11,11,11,21,22,
23,24,65,65,65,68,69,66,66,66,73,74,75,76,68,69,79,70,72,75,76,73,74,77,77,77,
89,90,91,92,93,94,95,96,41,42,43,44,45,46,47,46,51,52,53,55,55,58,59,60],[1,2,
3,1,1,6,7,8,9,10,2,3,13,14,15,16,17,6,7,7,21,9,10,13,25,26,27,25,25,30,31,32,
26,27,35,37,36,30,31,31,41,42,43,41,41,46,47,48,49,50,42,43,53,54,55,56,57,46,
47,47,61,49,50,53,1,2,3,1,1,6,7,8,9,9,10,10,2,3,13,14,15,16,16,17,17,6,7,7,21,
21,9,9,10,10,13,13,97,98,99,97,97,102,103,104,98,99,107,109,108,102,103,
103],,[1,2,3,4,5,6,7,8,1,1,11,12,13,14,15,2,3,18,20,19,21,4,5,24,25,26,27,28,
29,30,31,32,33,34,35,36,37,38,40,39,41,42,43,44,45,46,47,48,41,41,51,52,53,54,
55,42,43,58,60,59,61,44,45,64,65,66,67,68,69,70,71,72,65,65,65,65,77,78,79,80,
81,66,66,67,67,86,88,87,89,90,68,68,69,69,96,95,97,98,99,100,101,102,103,104,
105,106,107,108,109,110,112,111],,[1,2,3,4,5,6,7,8,9,10,11,12,1,14,15,16,17,
18,19,20,21,22,23,4,25,26,27,28,29,30,31,32,33,34,25,37,36,38,39,40,41,42,43,
44,45,46,47,48,49,50,51,52,41,54,55,56,57,58,59,60,61,62,63,44,65,66,67,68,69,
70,71,72,74,73,76,75,77,78,65,80,81,83,82,85,84,86,87,88,90,89,92,91,94,93,68,
68,97,98,99,100,101,102,103,104,105,106,97,109,108,110,111,112],,,,,,[1,2,3,4,
5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,1,22,23,24,25,26,27,28,29,30,31,32,
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,
59,60,41,62,63,64,65,66,67,68,69,70,71,72,74,73,76,75,77,78,79,80,81,83,82,85,
84,86,87,88,65,65,92,91,94,93,96,95,97,98,99,100,101,102,103,104,105,106,107,
108,109,110,111,112]],
0,
[(95,96),(89,90),(73,74)(75,76)(82,83)(84,85)(91,92)(93,94),( 36, 37)
(108,109),( 19, 20)( 39, 40)( 59, 60)( 73, 74)( 75, 76)( 82, 83)( 84, 85)
( 87, 88)( 89, 90)( 91, 92)( 93, 94)(111,112)],
["ConstructIndexTwoSubdirectProduct","a4","Symm(4)","G2(4)","G2(4).2",[145,
146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,185,186,187,188,
189,190,191,192,193,194,195,196,197,198,199,200],(25,41,57,73,89,33,49,65,81)
(26,42,58,74,90,34,50,66,82)(27,43,59,75,91,35,51,67,83)(28,44,60,76,92,36,52,
68,84)(29,45,61,77,93,37,53,69,85)(30,46,62,78,94,38,54,70,86)(31,47,63,79,95,
39,55,71,87)(32,48,64,80,96,40,56,72,88),(3,6,9,18,27,77,14,23,48,34,69,94,74,
5,8,17,26,52,55,61,84,41)(4,7,16,25,51,56,62,86,43,11,20,31,82,39,75,12,21,53,
57,79,36,71,98,68,93,73)(10,19,30,81,38,97,67,92,60,83,40,76,13,22,54,58,80,
37,72,100,95,65,90,47,33,88,45,29,64,89,46,32,87,44,28,63,85,42)(15,24,49,35,
70,99,107,102,108,103,109,104,110,112,106,101,96,66,91,59,78)(105,111)]);
ALF("(A4xG2(4)):2","Co1",[1,2,3,5,8,9,12,10,16,15,18,25,27,29,31,38,40,45,
47,47,58,62,63,74,3,12,13,19,25,29,34,30,47,56,59,66,66,80,83,83,3,3,4,19,
25,12,10,12,40,39,19,26,59,30,32,39,43,47,46,46,86,90,91,100,5,18,19,6,8,
45,47,46,62,62,61,61,22,25,74,80,81,89,89,90,90,49,54,54,97,98,64,64,63,
63,75,75,13,13,14,50,56,34,31,34,50,57,88,67,67,83,81,81],[
"fusion map is unique up to table automorphisms"
]);
ALF("(A4xG2(4)):2","(3xG2(4)).2",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,
17,18,19,20,21,22,23,24,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,1,
2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,
29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,
53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72]);
ALF("(A4xG2(4)):2","Symm(4)",[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,
2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,
5,5,5,5,5,5,5,5,5,5,5,5,5,5,5]);
ALF("(A4xG2(4)):2","G2(4).2",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,
18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,1,2,
3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,1,2,3,4,5,6,7,
8,9,9,10,10,11,12,13,14,15,16,16,17,17,18,19,20,21,21,22,22,23,23,24,24,
25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40]);
MOT("(A5xJ2):2",
[
"origin: computed using GAP from tables of A5, S5, J2, J2.2, Co1,\n",
"12th maximal subgroup of Co1"
],
[72576000,230400,28800,129600,4320,11520,18000,3000,2880,1440,840,960,1200,
600,1440,900,4838400,15360,1920,8640,288,768,1200,200,192,96,56,64,80,40,96,
60,3628800,11520,1440,6480,216,576,900,150,144,72,42,48,60,30,72,45,3024000,
9600,1200,5400,180,480,1500,1500,250,250,120,60,35,40,100,100,50,50,60,75,75,
4032,576,144,72,576,192,72,72,84,144,144,1344,192,48,24,192,64,24,24,28,48,48,
2016,288,72,36,288,96,36,36,42,72,72],
[,[1,1,1,4,5,2,7,8,4,5,11,6,7,8,9,16,1,1,1,4,5,2,7,8,4,5,11,6,7,8,9,16,33,33,
33,36,37,34,39,40,36,37,43,38,39,40,41,48,49,49,49,52,53,50,55,56,57,58,52,53,
61,54,55,56,57,58,59,68,69,1,2,3,5,6,6,9,10,11,15,15,17,18,19,21,22,22,25,26,
27,31,31,33,34,35,37,38,38,41,42,43,47,47],[1,2,3,1,1,6,7,8,2,3,11,12,13,14,6,
7,17,18,19,17,17,22,23,24,18,19,27,28,29,30,22,23,1,2,3,1,1,6,7,8,2,3,11,12,
13,14,6,7,49,50,51,49,49,54,55,56,57,58,50,51,61,62,63,64,65,66,54,55,56,70,
71,72,70,74,75,71,72,78,74,74,81,82,83,81,85,86,82,83,89,85,85,70,71,72,70,74,
75,71,72,78,74,74],,[1,2,3,4,5,6,1,1,9,10,11,12,3,2,15,4,17,18,19,20,21,22,17,
17,25,26,27,28,19,18,31,20,33,34,35,36,37,38,33,33,41,42,43,44,35,34,47,36,1,
2,3,4,5,6,1,1,1,1,9,10,11,12,3,3,2,2,15,4,4,70,71,72,73,74,75,76,77,78,79,80,
81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102],,[1,2,3,
4,5,6,7,8,9,10,1,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,17,28,29,30,31,
32,33,34,35,36,37,38,39,40,41,42,33,44,45,46,47,48,49,50,51,52,53,54,55,56,57,
58,59,60,49,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,70,80,79,81,82,83,
84,85,86,87,88,81,91,90,92,93,94,95,96,97,98,99,92,102,101]],
0,
[( 79, 80)( 90, 91)(101,102),(55,56)(57,58)(63,64)(65,66)(68,69)],
["ConstructIndexTwoSubdirectProduct","A5","A5.2","J2","J2.2",[125,126,127,128,
129,130,131,132,133,134,135,152,153,154,155,156,157,158,159,160,161,162,179,
180,181,182,183,184,185,186,187,188,189],(),(29,94,84,74,64,54,44,102,92,82,
72,62,52,42,99,89,79,69,59,49,39,33)(30,93,83,73,63,53,43,101,91,81,71,61,51,
41,100,90,80,70,60,50,40,34)(31,95,85,75,65,55,45,35,98,88,78,68,58,48,38,32,
96,86,76,66,56,46,36,97,87,77,67,57,47,37)]);
ALF("(A5xJ2):2","A5.2",[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,
2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,
4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,
7,7,7]);
ALF("(A5xJ2):2","J2.2",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,1,2,3,4,5,
6,7,8,9,10,11,12,13,14,15,16,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,1,2,3,
4,5,6,7,7,8,8,9,10,11,12,13,13,14,14,15,16,16,17,18,19,20,21,22,23,24,25,
26,27,17,18,19,20,21,22,23,24,25,26,27,17,18,19,20,21,22,23,24,25,26,27]);
ALF("(A5xJ2):2","Co1",[1,2,3,5,8,9,16,15,18,25,27,29,40,38,45,62,3,3,4,19,
25,12,40,39,19,26,59,30,43,39,47,90,5,18,19,6,8,45,62,61,22,25,74,80,90,
89,49,64,15,38,39,61,63,71,15,16,17,16,89,91,95,99,39,40,42,41,101,61,62,
3,12,13,25,29,29,47,56,59,80,80,13,13,14,56,34,34,50,57,88,83,83,19,47,50,
25,80,80,54,56,100,82,82],[
"fusion map is unique up to table automorphisms"
]);
MOT("(A6xU3(3)):2",
[
"origin: computed using GAP from tables of A6, S6, U3(3), U3(3).2, Co1,\n",
"14th maximal subgroup of Co1,\n",
"tests: 1.o.r., pow[2,3,5,7]"
],
[4354560,69120,77760,6480,34560,11520,8640,2520,2880,4320,96768,1536,1728,144,
768,256,192,56,64,96,108864,1728,1944,162,864,288,216,63,72,108,108864,1728,
1944,162,864,288,216,63,72,108,48384,768,864,72,384,128,96,28,32,48,30240,480,
540,45,480,480,80,60,35,35,40,40,60,60,1152,1152,144,192,288,288,1152,1152,
144,192,288,288,192,192,24,32,48,48,144,144,18,24,36,36,144,144,18,24,36,36],
[,[1,1,3,4,2,2,3,8,5,7,1,1,3,4,2,2,3,8,5,7,21,21,23,24,22,22,23,28,25,27,31,
31,33,34,32,32,33,38,35,37,11,11,13,14,12,12,13,18,15,17,51,51,53,54,52,52,52,
53,60,59,56,55,58,58,1,2,4,6,7,7,1,2,4,6,7,7,11,12,14,16,17,17,21,22,24,26,27,
27,31,32,34,36,37,37],[1,2,1,1,5,6,2,8,9,5,11,12,11,11,15,16,12,18,19,15,1,2,
1,1,5,6,2,8,9,5,1,2,1,1,5,6,2,8,9,5,41,42,41,41,45,46,42,48,49,45,51,52,51,51,
55,56,57,52,59,60,61,62,55,56,65,66,65,68,66,66,71,72,71,74,72,72,77,78,77,80,
78,78,65,66,65,68,66,66,71,72,71,74,72,72],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,
15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,
41,42,43,44,45,46,47,48,49,50,1,2,3,4,5,5,6,7,8,8,9,9,10,10,65,66,67,68,70,69,
71,72,73,74,76,75,77,78,79,80,82,81,83,84,85,86,88,87,89,90,91,92,94,93],,[1,
2,3,4,5,6,7,1,9,10,11,12,13,14,15,16,17,11,19,20,21,22,23,24,25,26,27,21,29,
30,31,32,33,34,35,36,37,31,39,40,41,42,43,44,45,46,47,41,49,50,51,52,53,54,55,
56,57,58,51,51,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,
82,83,84,85,86,87,88,89,90,91,92,93,94]],
0,
[(69,70)(75,76)(81,82)(87,88)(93,94),(59,60),(55,56)(61,62)(63,64),(55,56)
(59,60)(61,62)(63,64),(21,31)(22,32)(23,33)(24,34)(25,35)(26,36)(27,37)(28,38)
(29,39)(30,40)(65,71)(66,72)(67,73)(68,74)(69,75)(70,76)(83,89)(84,90)(85,91)
(86,92)(87,93)(88,94)],
["ConstructIndexTwoSubdirectProduct","A6","A6.2_1","U3(3)","U3(3).2",[107,108,
109,110,111,112,123,124,125,126,127,128,139,140,141,142,143,144,155,156,157,
158,159,160,171,172,173,174,175,176],(),(52,88,80,72,64,56,89,81,73,65,57,90,
82,74,66,58,54)(53,87,79,71,63,55)(59,91,83,75,67)(60,92,84,76,68)(61,94,86,
78,70,62,93,85,77,69)]);
ALF("(A6xU3(3)):2","A6.2_1",[1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,3,3,
3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,
6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,9,9,9,9,9,10,10,10,10,10,10,11,11,11,
11,11,11]);
ALF("(A6xU3(3)):2","U3(3).2",[1,2,3,4,5,6,7,8,9,10,1,2,3,4,5,6,7,8,9,10,1,
2,3,4,5,6,7,8,9,10,1,2,3,4,5,6,7,8,9,10,1,2,3,4,5,6,7,8,9,10,1,2,3,4,5,5,
6,7,8,8,9,9,10,10,11,12,13,14,15,16,11,12,13,14,15,16,11,12,13,14,15,16,
11,12,13,14,15,16,11,12,13,14,15,16]);
ALF("(A6xU3(3)):2","Co1",[1,2,5,8,9,9,18,27,29,45,3,3,19,25,12,12,19,59,
30,47,5,18,6,8,45,45,22,74,80,49,6,22,7,8,49,49,23,75,82,48,13,13,50,56,
13,13,50,88,34,50,15,38,61,63,71,71,71,89,95,95,99,99,101,101,3,12,25,29,
47,47,4,10,26,30,46,46,13,13,56,34,50,50,19,47,25,80,54,54,24,51,26,84,55,
55],[
"fusion map is unique up to table automorphisms"
]);
MOT("(A7xL2(7)):2",
[
"origin: computed using GAP from tables of A7, S7, L2(7), L2(7).2, Co1,\n",
"17th maximal subgroup of Co1"
],
[846720,40320,15120,20160,17640,8064,384,144,192,168,12096,576,216,288,252,
3024,144,54,72,63,1344,64,24,32,28,1680,80,30,40,35,4032,192,72,96,84,1176,56,
21,28,49,49,1440,720,960,960,288,144,192,192,144,72,96,96,72,36,48,48,36,18,
24,24,60,30,40,40,72,36,48,48],
[,[1,1,3,2,5,1,1,3,2,5,11,11,13,12,15,16,16,18,17,20,6,6,8,7,10,26,26,28,27,
30,11,11,13,12,15,36,36,38,37,40,41,1,3,4,4,1,3,4,4,6,8,9,9,11,13,14,14,16,18,
19,19,26,28,29,29,31,33,34,34],[1,2,1,4,5,6,7,6,9,10,1,2,1,4,5,1,2,1,4,5,21,
22,21,24,25,26,27,26,29,30,6,7,6,9,10,36,37,36,39,40,41,42,42,45,44,46,46,49,
48,50,50,53,52,42,42,45,44,46,46,49,48,62,62,65,64,50,50,53,52],,[1,2,3,4,5,6,
7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,1,2,3,4,5,31,32,33,34,
35,36,37,38,39,40,41,42,43,45,44,46,47,49,48,50,51,53,52,54,55,57,56,58,59,61,
60,42,43,45,44,66,67,69,68],,[1,2,3,4,1,6,7,8,9,6,11,12,13,14,11,16,17,18,19,
16,21,22,23,24,21,26,27,28,29,26,31,32,33,34,31,1,2,3,4,1,1,42,43,44,45,46,47,
48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69]],
0,
[(44,45)(48,49)(52,53)(56,57)(60,61)(64,65)(68,69),(40,41)],
["ConstructIndexTwoSubdirectProduct","L3(2)","L3(2).2","A7","A7.2",[84,85,86,
87,88,89,90,99,100,101,102,103,104,105,114,115,116,117,118,119,120,129,130,
131,132,133,134,135],(2,6,26,9)(3,11,12,17)(4,16,37,25)(5,21,23,33)(7,31,34,
10)(8,36,20,18)(13,22,28,19)(14,27)(15,32,39,35)(24,38,30,29)(43,46,58,52,55,
67,61,64,49)(44,50,47,62,68,65,53,59,56)(45,54,63)(48,66,57),(3,10,41,7,24,61,
31,27,13,51,55,8,32,35,45,28,14,59,22,43,16)(4,11,42,15,60,30,26,5,19,69,67,
58,18,68,66,57,17,12,50,47,37,54,65,49,46,29,20,25)(6,23,52,56,9,33,36,53,64,
48,38,62,39,63,40)(21,34,44)]);
ALF("(A7xL2(7)):2","L3(2).2",[1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,
3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,5,6,7,8,9,6,7,8,9,6,7,8,9,6,7,8,9,6,7,
8,9,6,7,8,9,6,7,8,9]);
ALF("(A7xL2(7)):2","A7.2",[1,1,1,1,1,2,2,2,2,2,3,3,3,3,3,4,4,4,4,4,5,5,5,
5,5,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,8,9,9,9,9,10,10,10,10,11,11,11,11,12,12,
12,12,13,13,13,13,14,14,14,14,15,15,15,15]);
ALF("(A7xL2(7)):2","Co1",[1,2,8,9,27,3,3,25,12,59,5,18,8,45,74,6,22,8,49,
75,13,13,56,13,88,15,38,63,71,95,19,19,25,47,100,28,60,76,87,27,28,3,25,
29,29,4,26,30,30,13,56,34,34,19,25,80,80,24,26,84,84,39,91,99,99,50,56,83,
83],[
"fusion map is unique up to table automorphisms"
]);
ALN("(A7xL2(7)):2",["(A7xL3(2)):2"]);
MOT("(D10x(A5xA5).2).2",
[
"origin: Dixon's Algorithm,\n",
"18th maximal subgroup of Co1"
],
[144000,36000,28800,500,640,250,960,72,360,100,500,128,600,3000,40,30,150,
3600,720,90,160,240,4800,250,48,75,1500,75,1500,100,100,200,60,900,1200,125,
100,20,480,160,50,2400,24,30,600,120,40,32,50,100,48,48,24,24,480,480,20,20,
32,32,32,32,72,72,288,288,24,24,72,72],
[,[1,2,1,4,1,6,1,9,9,11,11,1,14,14,14,17,17,18,18,20,2,18,1,24,18,26,27,28,29,
29,4,14,34,34,2,36,27,4,1,5,6,1,9,20,2,9,21,5,24,4,7,7,8,8,3,3,10,10,12,12,12,
12,19,19,3,3,25,25,8,8],[1,2,3,4,5,6,7,3,1,10,11,12,13,14,15,13,14,1,3,2,21,
23,23,24,7,27,27,29,29,30,31,32,35,2,35,36,37,38,39,40,41,42,39,45,45,42,47,
48,49,50,52,51,55,56,56,55,58,57,60,59,62,61,65,66,66,65,51,52,65,66],,[1,1,3,
1,5,1,7,8,9,3,1,12,3,1,7,19,18,18,19,9,5,22,23,1,25,18,1,18,1,23,3,23,22,18,
23,1,23,39,39,40,42,42,43,46,42,46,40,48,42,42,51,52,53,54,55,56,56,55,59,60,
61,62,63,64,65,66,67,68,69,70]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-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]],[8,8,8,-2,0,-2,4,2,2,-2,-2,0,3,3,-1,0,0,5,5,2,0,1,4,-2,1,0,3,0,
3,-1,-2,-1,1,5,4,-2,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,-2,0,0,0,0,0,0,0,0,0,0,-1,
-1,-4,-4,1,1,2,2],
[TENSOR,[5,2]],[10,10,10,0,2,0,6,-2,-2,0,0,2,5,5,1,-1,-1,4,4,-2,2,0,6,0,0,-1,
5,-1,5,1,0,1,0,4,6,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,2,0,0,-2,
-2,-2,-2,0,0,-2,-2],
[TENSOR,[7,2]],[12,12,12,2,-4,2,4,0,0,2,2,-4,7,7,-1,1,1,6,6,0,-4,-2,4,2,-2,1,
7,1,7,-1,2,-1,-2,6,4,2,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0],[16,16,16,1,0,1,0,1,1,1,1,0,-4,-4,0,-1,-1,4,4,1,0,0,0,1,0,-1,
-4,-1,-4,0,1,0,0,4,0,1,0,1,-4,0,1,-4,-1,-1,-4,-1,0,0,1,1,0,0,-1,-1,-4,-4,1,1,
0,0,0,0,-2,-2,4,4,0,0,1,1],
[TENSOR,[10,2]],
[TENSOR,[10,4]],
[TENSOR,[10,3]],[18,18,18,3,2,3,-6,0,0,-2,-2,2,3,3,-1,0,0,0,0,0,2,0,-6,3,0,0,
3,0,3,-1,3,-1,0,0,-6,-2,-1,1,6,-2,1,6,0,0,6,0,-2,-2,1,1,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0],
[TENSOR,[14,3]],[18,18,18,-2,2,-2,-6,0,0,3,3,2,3,3,-1,0,0,0,0,0,2,0,-6,-2,0,0,
3,0,3,-1,-2,-1,0,0,-6,3,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-6,-6,-1,-1,0,0,
2,2,0,0,0,0,0,0,0,0],
[TENSOR,[16,2]],[25,25,25,0,1,0,5,1,1,0,0,1,0,0,0,0,0,-5,-5,1,1,-1,5,0,-1,0,0,
0,0,0,0,0,-1,-5,5,0,0,0,-5,-1,0,-5,1,1,-5,1,-1,-1,0,0,-1,-1,1,1,-5,-5,0,0,1,1,
-1,-1,1,1,1,1,-1,-1,1,1],
[TENSOR,[18,2]],
[TENSOR,[18,4]],
[TENSOR,[18,3]],[40,40,40,0,0,0,4,-2,-2,0,0,0,-5,-5,-1,1,1,1,1,-2,0,1,4,0,1,1,
-5,1,-5,-1,0,-1,1,1,4,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,2,2,0,0,0,0,0,0,0,0,0,0,
-1,-1,-4,-4,-1,-1,2,2],
[TENSOR,[22,2]],[48,48,48,-2,0,-2,-8,0,0,-2,-2,0,-2,-2,2,1,1,6,6,0,0,-2,-8,-2,
-2,1,-2,1,-2,2,-2,2,-2,6,-8,-2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0],[60,60,60,0,-4,0,-4,0,0,0,0,-4,5,5,1,-1,-1,-6,-6,0,-4,
2,-4,0,2,-1,5,-1,5,1,0,1,2,-6,-4,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0],[1,1,-1,1,1,1,-1,-1,1,-1,1,-1,-1,1,-1,-1,1,1,-1,1,
1,1,1,1,-1,1,1,1,1,1,-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),-E(4),E(4),E(4),-E(4)],
[TENSOR,[2,26]],
[TENSOR,[3,27]],
[TENSOR,[2,28]],
[TENSOR,[5,26]],
[TENSOR,[5,27]],
[TENSOR,[7,26]],
[TENSOR,[7,27]],
[TENSOR,[9,26]],
[TENSOR,[10,29]],
[TENSOR,[10,28]],
[TENSOR,[10,27]],
[TENSOR,[10,26]],
[TENSOR,[14,28]],
[TENSOR,[14,26]],
[TENSOR,[16,27]],
[TENSOR,[16,26]],
[TENSOR,[18,29]],
[TENSOR,[18,28]],
[TENSOR,[18,27]],
[TENSOR,[18,26]],
[TENSOR,[22,27]],
[TENSOR,[22,26]],
[TENSOR,[24,26]],
[TENSOR,[25,26]],[4,-1,0,4,4,-1,0,0,4,0,4,0,0,4,0,0,4,4,0,-1,-1,4,4,-1,0,-1,
-1,-1,-1,-1,0,4,-1,-1,-1,-1,-1,0,0,-4,1,-4,0,1,1,-4,1,0,1,-4,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[51,3]],[24,-6,0,4,-8,4,0,0,0,0,4,0,0,14,0,0,2,12,0,0,2,-4,8,-6,0,2,
-1,-3,-6,-2,0,-2,1,-3,-2,-1,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0],[24,-6,0,4,-8,-6,0,0,0,0,4,0,0,14,0,0,2,12,0,0,2,-4,8,4,0,
-3,-6,2,-1,3,0,-2,1,-3,-2,-1,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0],[32,-8,0,-8,0,2,0,0,8,0,-8,0,0,12,0,0,0,20,0,-2,0,4,16,2,
0,0,-3,0,-3,1,0,-4,-1,-5,-4,2,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0],[36,-9,0,6,4,1,0,0,0,0,-4,0,0,6,0,0,0,0,0,0,-1,0,-12,-4,
0,0,6,0,-9,3,0,-2,0,0,3,1,-2,0,0,-4,-3,12,0,0,-3,0,1,0,2,2,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0],[36,-9,0,6,4,-4,0,0,0,0,-4,0,0,6,0,0,0,0,0,0,-1,0,-12,
1,0,0,-9,0,6,-2,0,-2,0,0,3,1,3,0,0,-4,2,12,0,0,-3,0,1,0,-3,2,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[57,3]],
[TENSOR,[56,3]],[40,-10,0,0,8,0,0,0,-8,0,0,0,0,20,0,0,-4,16,0,2,-2,0,24,0,0,1,
-5,1,-5,-1,0,4,0,-4,-6,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0],[64,-16,0,4,0,-1,0,0,4,0,4,0,0,-16,0,0,-4,16,0,-1,0,0,0,-1,0,
1,4,1,4,0,0,0,0,-4,0,-1,0,0,0,0,-1,-16,0,1,4,-4,0,0,-1,4,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0],
[TENSOR,[61,3]],[72,-18,0,-8,8,2,0,0,0,0,12,0,0,12,0,0,0,0,0,0,-2,0,-24,2,0,0,
-3,0,-3,1,0,-4,0,0,6,-3,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0],[96,-24,0,-4,0,-4,0,0,0,0,-4,0,0,-4,0,0,2,12,0,0,0,-4,-16,6,0,
2,11,-3,-9,-1,0,4,1,-3,4,1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0],[96,-24,0,-4,0,6,0,0,0,0,-4,0,0,-4,0,0,2,12,0,0,0,-4,-16,
-4,0,-3,-9,2,11,-1,0,4,1,-3,4,1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0],[100,-25,0,0,4,0,0,0,4,0,0,0,0,0,0,0,0,-20,0,-1,-1,
-4,20,0,0,0,0,0,0,0,0,0,1,5,-5,0,0,0,0,-4,0,-20,0,-1,5,4,1,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[66,3]],[120,-30,0,0,-8,0,0,0,0,0,0,0,0,10,0,0,-2,-12,0,0,2,4,-8,0,0,
-2,10,3,-15,-3,0,2,-1,3,2,0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0],[120,-30,0,0,-8,0,0,0,0,0,0,0,0,10,0,0,-2,-12,0,0,2,4,-8,0,
0,3,-15,-2,10,2,0,2,-1,3,2,0,-3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0],[160,-40,0,0,0,0,0,0,-8,0,0,0,0,-20,0,0,4,4,0,2,0,4,16,0,
0,-1,5,-1,5,1,0,-4,-1,-1,-4,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0]],
[(51,52)(53,54)(55,56)(57,58)(59,60)(61,62)(63,64)(65,66)(67,68)(69,70),
( 6,24)(26,28)(27,29)(30,37)(41,49)]);
ALF("(D10x(A5xA5).2).2","5:4",[1,2,4,1,1,2,4,4,1,4,1,4,4,1,4,4,1,1,4,2,2,
1,1,2,4,2,2,2,2,2,4,1,2,2,2,2,2,4,4,1,2,1,4,2,2,1,2,4,2,1,3,5,5,3,3,5,5,3,
5,3,3,5,3,5,5,3,5,3,3,5]);
ALF("(D10x(A5xA5).2).2","Co1",[1,16,2,16,4,15,3,22,6,42,17,4,38,15,39,89,
61,5,18,64,43,19,3,17,19,62,16,61,15,39,41,39,90,62,40,16,40,43,4,14,38,2,
24,92,41,20,72,14,42,41,13,13,53,53,11,11,73,73,14,14,14,14,47,47,12,12,
50,50,54,54],[
"fusion map is unique up to table automorphisms"
]);
MOT("2.2^11:M24",
[
"origin: computed by Thomas Breuer using tables of 2.Co1 and 2^11:M24,\n",
"3rd maximal subgroup of 2.Co1,\n",
"tests: 1.o.r., pow[2,3]"
],
[1002795171840,1002795171840,1321205760,1321205760,389283840,5505024,5505024,
393216,5505024,5505024,393216,49152,98304,98304,491520,491520,32768,32768,
15360,69120,69120,4608,4608,11520,11520,3456,8064,8064,576,6144,6144,6144,
6144,1024,1024,4096,4096,2048,4096,4096,2048,1024,1024,512,512,768,256,768,
256,960,960,240,240,160,384,384,192,384,384,192,96,192,192,96,96,48,336,336,
112,112,336,336,112,112,128,128,64,128,128,64,80,80,40,44,44,44,44,48,48,48,
48,24,24,56,56,56,56,56,56,56,56,60,60,60,60,60,60,60,60,42,42,42,42,46,46,46,
46],
[,[1,1,1,1,1,1,1,1,4,4,4,3,3,3,1,2,4,3,5,20,20,20,20,20,20,20,27,27,27,6,7,9,
10,8,11,6,6,6,11,11,11,8,9,13,13,15,17,16,18,50,50,50,50,50,20,20,20,23,23,23,
22,22,22,27,28,29,67,67,67,67,71,71,71,71,36,36,38,41,41,39,50,51,54,84,84,84,
84,55,59,56,58,64,65,67,67,70,70,71,71,74,74,102,102,102,102,106,106,106,106,
110,110,112,112,114,114,116,116],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,
18,19,1,2,3,4,3,4,5,1,2,5,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,
47,48,49,50,51,52,53,54,6,7,8,9,10,11,12,13,14,15,16,19,71,72,73,74,67,68,69,
70,75,76,77,78,79,80,81,82,83,84,85,86,87,30,33,31,32,46,48,98,99,100,101,94,
95,96,97,50,51,52,53,50,51,52,53,71,72,67,68,114,115,116,117],,[1,2,3,4,5,6,7,
8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,
34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,1,2,3,4,5,55,56,57,58,59,60,
61,62,63,64,65,66,71,72,73,74,67,68,69,70,75,76,77,78,79,80,15,16,19,84,85,86,
87,88,89,90,91,92,93,98,99,100,101,94,95,96,97,20,21,24,25,20,21,24,25,112,
113,110,111,116,117,114,115],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,
19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,
45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,1,2,3,4,1,2,
3,4,75,76,77,78,79,80,81,82,83,84,85,87,86,88,89,90,91,92,93,6,7,9,10,6,7,9,
10,106,107,108,109,102,103,104,105,27,28,27,28,116,117,114,115],,,,[1,2,3,4,5,
6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,
33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,
59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,1,
2,5,5,88,89,90,91,92,93,94,95,96,97,98,99,100,101,106,107,108,109,102,103,104,
105,110,111,112,113,116,117,114,115],,,,,,,,,,,,[1,2,3,4,5,6,7,8,9,10,11,12,
13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,
39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,
65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,
91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,
112,113,1,2,1,2]],
0,
[(114,116)(115,117),(102,106)(103,107)(104,108)(105,109),(86,87),( 67, 71)
( 68, 72)( 69, 73)( 70, 74)( 94, 98)( 95, 99)( 96,100)( 97,101)(110,112)
(111,113)],
["ConstructProj",[["2^11:M24",[]],["2.2^11:M24",[]]]]);
ALF("2.2^11:M24","2^11:M24",[1,1,2,2,3,4,4,5,6,6,7,8,9,9,10,11,12,13,14,
15,15,16,16,17,17,18,19,19,20,21,22,23,24,25,26,27,27,28,29,29,30,31,32,
33,33,34,35,36,37,38,38,39,39,40,41,41,42,43,43,44,45,46,46,47,48,49,50,
50,51,51,52,52,53,53,54,54,55,56,56,57,58,59,60,61,61,62,62,63,64,65,66,
67,68,69,69,70,70,71,71,72,72,73,73,74,74,75,75,76,76,77,77,78,78,79,79,
80,80]);
ALF("2.2^11:M24","2.Co1",[1,2,3,4,6,3,4,6,15,16,17,20,18,19,6,5,17,20,22,
9,10,36,37,32,33,40,13,14,42,20,17,48,47,22,51,18,19,20,49,50,51,22,48,52,
53,22,51,21,54,25,26,65,66,69,36,37,40,78,79,81,86,84,85,42,41,90,45,46,
94,95,45,46,94,95,52,53,54,107,108,106,69,64,117,70,71,126,127,86,135,81,
137,90,89,94,95,141,142,94,95,141,142,102,103,149,150,102,103,149,150,124,
125,124,125,128,129,130,131],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("2.2^11:M24","M24",[1,1,1,1,1,2,2,2,2,2,2,2,2,2,3,3,3,3,3,4,4,4,4,4,4,
4,5,5,5,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,8,8,8,8,9,9,9,9,9,10,10,10,10,10,
10,10,10,10,11,11,11,12,12,12,12,13,13,13,13,14,14,14,14,14,14,15,15,15,
16,16,16,16,17,17,17,17,18,18,19,19,19,19,20,20,20,20,21,21,21,21,22,22,
22,22,23,23,24,24,25,25,26,26]);
MOT("2^(1+8)+.O8+(2)",
[
"origin: CAS library,\n",
"maximal subgroup (involution centralizer) in Co1,\n",
"tests: 1.o.r., pow[2,3,5,7]"
],
[89181388800,89181388800,330301440,371589120,294912,196608,2949120,491520,
92160,1474560,1474560,49152,737280,49152,49152,49152,8192,6144,147456,786432,
1179648,7077888,1024,768,1024,3072,768,3072,1536,1536,256,768,256,6144,24576,
147456,147456,256,128,256,1024,4096,2048,8192,8192,64,128,128,256,256,128,64,
1152,20736,20736,1728,15552,15552,2592,184320,138240,9953280,9953280,155520,
155520,155520,155520,576,4608,4608,1536,1536,576,576,288,2304,27648,9216,3456,
3456,1728,288,288,144,96,576,576,96,288,576,384,3456,864,288,864,288,48,96,96,
1728,1728,288,96,96,96,96,48,48,24,192,1152,1152,288,288,288,288,288,288,48,
216,216,36,54,54,54,54,960,480,9600,9600,600,600,600,600,40,80,80,40,40,20,
120,120,60,60,60,30,30,30,30,56,56,28,28,28],
[,[1,1,1,2,2,3,3,1,4,1,1,3,2,3,1,3,3,4,3,1,2,1,7,8,6,6,5,7,10,10,12,13,14,21,
22,22,22,16,17,15,20,22,21,22,22,34,35,37,45,45,44,43,54,54,54,55,58,58,57,62,
63,62,62,64,64,66,66,61,60,63,60,62,64,64,67,60,62,63,64,64,66,53,55,56,53,54,
54,53,55,55,54,54,54,53,54,53,56,54,53,58,58,57,69,71,70,72,74,74,75,78,77,77,
80,80,81,81,100,100,101,121,121,120,124,124,126,126,129,130,129,129,131,131,
134,134,128,129,127,131,131,133,141,141,141,142,141,146,146,149,149,150,150,
150,150,151],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,
25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,
51,52,3,1,2,4,2,1,4,3,4,1,2,1,2,1,2,9,7,5,6,8,11,10,13,19,22,21,22,22,22,7,5,
9,12,11,10,14,13,21,20,22,22,19,22,19,18,15,16,22,22,21,28,26,27,24,29,30,32,
34,36,37,37,36,36,37,37,36,35,57,58,59,57,58,57,58,127,128,129,130,131,132,
133,134,135,136,137,138,139,140,129,130,127,128,127,131,132,133,134,150,151,
153,152,154],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,
25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,
51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,
77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,
102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,
121,122,123,124,125,126,3,4,1,2,1,2,2,1,9,8,7,10,11,13,62,63,60,61,60,64,65,
67,66,150,151,153,152,154],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,
20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,
46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,
72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,
98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,
118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,
137,138,139,140,141,142,145,144,143,146,147,148,149,1,2,3,3,4]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[
28,28,28,28,4,4,4,4,4,4,4,4,4,4,-4,-4,-4,-4,-4,-4,-4,-4,0,0,0,0,0,0,0,0,0,0,0,
8,8,8,8,0,0,0,0,0,0,0,0,-2,-2,-2,2,2,2,2,1,1,1,1,1,1,1,10,10,10,10,10,10,10,
10,-2,-2,-2,-2,-2,-2,-2,-2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,
-1,-1,-1,5,5,5,0,0,0,0,0,0,0,2,2,2,2,2,2,2,-1,-1,-1,1,1,1,1,1,1,1,3,3,3,3,3,3,
3,3,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[35,35,35,35,-5,-5,-5,-5,
-5,11,11,11,-5,-5,3,3,3,3,3,3,3,3,-1,-1,-1,-1,-1,-1,3,3,3,-1,-1,7,7,7,7,-1,-1,
-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,2,2,2,2,-1,-1,-1,5,5,5,5,14,14,5,5,1,1,1,1,1,
2,2,1,-3,-3,-3,6,6,-3,-2,-2,-2,2,2,2,-2,-2,0,0,0,0,0,0,0,0,0,0,3,3,3,-1,-1,-1,
-1,0,0,-1,1,1,1,-2,-2,1,1,1,1,1,-1,-1,-1,2,2,-1,-1,0,0,0,0,5,5,0,0,0,0,0,1,1,
0,0,0,0,0,0,-1,-1,0,0,0,0,0,0,0],[35,35,35,35,11,11,11,11,11,-5,-5,-5,-5,-5,3,
3,3,3,3,3,3,3,3,3,3,3,3,3,-1,-1,-1,-1,-1,7,7,7,7,-1,-1,-1,-1,-1,-1,-1,-1,1,1,
1,1,1,1,1,2,2,2,2,-1,-1,-1,14,14,14,14,5,5,5,5,2,2,2,2,2,1,1,1,6,6,6,-3,-3,-3,
2,2,2,-2,-2,-2,-2,-2,0,0,0,0,0,0,0,0,0,0,3,3,3,0,0,0,0,-1,-1,-1,-2,-2,-2,1,1,
1,1,1,1,1,2,2,2,-1,-1,-1,-1,5,5,5,5,0,0,0,0,1,1,1,0,0,0,-1,-1,-1,-1,-1,0,0,0,
0,0,0,0,0,0],[35,35,35,35,-5,-5,-5,-5,-5,-5,-5,-5,11,11,3,3,3,3,3,3,3,3,-1,-1,
-1,-1,-1,-1,-1,-1,-1,3,3,7,7,7,7,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,2,2,2,
2,-1,-1,-1,5,5,5,5,5,5,14,14,1,1,1,1,1,1,1,2,-3,-3,-3,-3,-3,6,-2,-2,-2,-2,-2,
-2,2,2,0,0,0,0,0,0,0,0,0,0,3,3,3,-1,-1,-1,-1,-1,-1,0,1,1,1,1,1,-2,-2,1,1,1,-1,
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[(152,153),(143,145)]);
ARC("2^(1+8)+.O8+(2)","CAS",[rec(permchars:=(),
permclasses:=(),
text:="Zentralisator einer Involution in Co1")]);
ALF("2^(1+8)+.O8+(2)","Co1",[1,2,2,9,12,10,9,3,29,2,4,11,11,10,4,11,12,30,
12,4,10,2,30,13,32,31,34,29,11,12,33,33,32,31,11,10,9,33,34,14,14,12,32,
11,10,66,33,30,32,31,33,67,22,6,22,49,23,7,48,18,45,5,18,6,20,7,21,80,45,
47,46,19,24,22,52,47,18,46,20,22,23,49,54,82,53,24,20,51,53,51,24,20,22,
54,22,54,84,24,53,23,21,55,80,81,83,50,53,54,85,81,46,45,49,51,55,48,48,
55,52,68,35,96,70,37,69,36,38,71,15,38,16,41,42,17,99,39,71,41,43,73,61,
89,89,101,89,64,92,93,65,28,60,60,60,87],[
"fusion map is unique, equal to that on the CAS table"
]);
ALF("2^(1+8)+.O8+(2)","O8+(2)",[1,1,1,1,3,3,3,3,3,4,4,4,5,5,6,6,6,6,2,2,2,
2,14,14,14,14,14,14,15,15,15,16,16,12,12,12,12,17,17,17,13,13,13,13,13,36,
36,36,37,37,37,37,11,11,11,11,10,10,10,7,7,7,7,8,8,9,9,24,24,24,24,24,25,
25,26,21,21,21,22,22,23,31,31,31,32,32,32,33,33,28,28,28,29,29,30,30,34,
34,34,27,27,27,48,48,48,48,49,49,50,44,44,44,45,45,46,46,47,47,47,38,38,
38,39,39,40,40,18,18,18,18,19,19,20,20,41,41,41,42,42,43,51,51,51,51,51,
52,52,53,53,35,35,35,35,35]);
ALN("2^(1+8)+.O8+(2)",["cenc1","Co1C2A","Co1N2A"]);
MOT("2^(2+12):(A8xS3)",
[
"origin: Dixon's Algorithm,\n",
"8th maximal subgroup of Co1,\n",
"table is sorted w.r. to normal series 2^2.2^12.3.2.A8,\n",
"tests: 1.o.r., pow[2,3,5,7]"
],
[1981808640,660602880,4718592,1474560,786432,5898240,393216,294912,60480,
5160960,5160960,73728,92160,294912,196608,196608,98304,98304,49152,8192,8192,
8192,8192,3072,576,49152,49152,8192,6144,6144,1024,6144,1024,147456,24576,
98304,98304,16384,16384,8192,8192,6144,6144,2048,2048,288,24576,24576,12288,
2048,1024,768,6144,3072,2048,768,1105920,368640,18432,4608,9216,4608,3072,
2160,720,11520,11520,1152,576,6912,2304,576,576,576,288,864,144,96,288,288,
144,144,144,1536,1024,1024,512,512,256,48,1024,1024,512,512,512,128,128,128,
768,512,512,256,256,128,24,256,128,512,512,256,256,128,64,64,5760,1920,240,
160,45,240,240,40,1152,768,768,192,192,144,48,768,768,384,96,192,192,192,96,
576,384,384,192,192,96,72,24,96,96,48,48,48,168,56,21,28,28,168,56,21,28,28,
360,120,180,60,60,60,360,120,180,60,60,60],
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2,3,3,3,6,7,7,6,9,1,2,3,3,5,4,6,7,6,8,57,57,57,57,58,58,58,64,64,57,58,59,61,
70,70,70,70,71,71,76,76,76,70,71,72,73,74,14,16,16,17,18,19,25,16,16,14,17,18,
23,22,20,34,39,39,37,38,40,46,34,35,37,37,39,38,41,43,44,115,115,115,116,119,
115,116,118,57,59,59,63,61,64,64,57,58,59,60,63,63,61,62,70,70,70,70,71,71,76,
78,70,71,72,73,74,151,151,153,151,152,156,156,158,156,157,161,161,163,163,161,
162,167,167,169,169,167,168],[1,2,3,4,5,6,7,8,1,10,11,12,13,14,15,16,17,18,19,
20,21,22,23,24,14,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,
34,47,48,49,50,51,52,53,54,55,56,1,2,3,4,6,8,7,1,4,10,11,12,13,1,2,3,3,6,8,1,
4,5,10,11,12,12,13,84,85,86,87,88,89,84,91,92,93,94,95,96,97,98,99,100,101,
102,103,104,99,106,107,108,109,110,111,112,113,114,115,116,117,118,115,120,
121,122,34,37,36,43,42,34,35,47,48,49,52,54,54,53,56,14,15,16,17,18,19,14,24,
26,27,30,29,32,156,157,156,159,160,151,152,151,154,155,115,116,115,117,120,
121,115,116,115,117,120,121],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,
19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,
45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,
71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,
97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,1,2,4,6,
9,10,11,13,123,124,125,126,127,128,129,130,131,132,133,135,134,136,137,138,
139,140,141,142,143,144,145,146,147,148,149,150,156,157,158,159,160,151,152,
153,154,155,57,58,64,65,66,67,57,58,64,65,66,67],,[1,2,3,4,5,6,7,8,9,10,11,12,
13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,
39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,
65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,
91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,
112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,
131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,
150,1,2,9,10,11,1,2,9,10,11,167,168,169,170,171,172,161,162,163,164,165,166]],
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1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,1,1,1,1,1,1,
1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,
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-1,-1,-1,-1,-1,1,1,1,-1,-1,1,1,1,-1,-1,1,1,1,1,-1,-1,1,1,1,1,-1,-1],[2,2,2,2,
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-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,
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[TENSOR,[4,2]],[14,14,14,14,14,14,14,14,-7,0,0,0,0,-2,-2,-2,-2,-2,-2,-2,-2,-2,
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0,-2,-2,1,1,0,0],[14,14,14,14,14,14,14,14,14,14,14,14,14,6,6,6,6,6,6,6,6,6,6,
6,6,6,6,6,6,6,6,6,6,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,-1,-1,-1,-1,
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2,2,2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
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[TENSOR,[7,2]],[28,28,28,28,28,28,28,28,-14,0,0,0,0,12,12,12,12,12,12,12,12,
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1,0,0,-2,-2,1,1,0,0],[20,20,20,20,20,20,20,20,20,20,20,20,20,4,4,4,4,4,4,4,4,
4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,
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0,0,0,0,0,0,0],
[TENSOR,[10,2]],[40,40,40,40,40,40,40,40,-20,0,0,0,0,8,8,8,8,8,8,8,8,8,8,8,-4,
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0,0,0],[21,21,21,21,21,21,21,21,21,21,21,21,21,-3,-3,-3,-3,-3,-3,-3,-3,-3,-3,
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[TENSOR,[13,2]],[42,42,42,42,42,42,42,42,-21,0,0,0,0,-6,-6,-6,-6,-6,-6,-6,-6,
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-E(15)^8,-E(15)-E(15)^2-E(15)^4-E(15)^8,-E(15)-E(15)^2-E(15)^4-E(15)^8,
-E(15)-E(15)^2-E(15)^4-E(15)^8,-E(15)-E(15)^2-E(15)^4-E(15)^8],
[TENSOR,[16,2]],[42,42,42,42,42,42,42,42,-21,0,0,0,0,-6,-6,-6,-6,-6,-6,-6,-6,
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-2*E(15)^4-2*E(15)^8,E(15)+E(15)^2+E(15)^4+E(15)^8,E(15)+E(15)^2+E(15)^4
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[GALOIS,[16,7]],
[TENSOR,[19,2]],
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[(134,135),(161,167)(162,168)(163,169)(164,170)(165,171)(166,172),(134,135)
(161,167)(162,168)(163,169)(164,170)(165,171)(166,172),(151,156)(152,157)
(153,158)(154,159)(155,160)]);
ALF("2^(2+12):(A8xS3)","A8xS3",[1,1,1,1,1,1,1,1,2,3,3,3,3,4,4,4,4,4,4,4,4,
4,4,4,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,8,9,9,9,9,9,9,9,9,9,9,10,
10,10,10,10,10,10,11,11,12,12,12,12,13,13,13,13,13,13,14,14,14,15,15,15,
15,15,16,16,16,16,16,16,17,18,18,18,18,18,18,18,18,19,19,19,19,19,19,20,
21,21,21,21,21,21,21,21,21,22,22,22,22,23,24,24,24,25,25,25,25,25,26,26,
27,27,27,27,27,27,27,27,28,28,28,28,28,28,29,29,30,30,30,30,30,31,31,32,
33,33,34,34,35,36,36,37,37,38,38,39,39,40,40,41,41,42,42]);
ALF("2^(2+12):(A8xS3)","Co1",[1,2,2,3,4,9,10,12,8,2,9,12,29,4,4,2,4,10,11,
10,12,11,12,14,26,4,10,12,11,10,14,30,32,3,4,10,9,12,10,11,12,29,31,32,30,
25,3,12,10,12,14,13,29,31,30,34,5,18,18,19,45,47,46,8,25,18,45,47,80,6,22,
22,22,49,54,8,25,26,22,49,54,54,82,14,11,12,14,32,33,57,10,12,14,14,32,34,
33,32,13,32,31,30,34,33,56,13,14,29,30,32,34,34,66,67,15,38,39,71,63,38,
71,99,19,45,46,81,80,25,26,19,47,46,50,81,81,80,83,24,24,20,24,51,53,26,
57,24,51,51,53,84,28,60,76,60,87,28,60,76,60,87,61,89,63,91,89,101,61,89,
63,91,89,101],[
"fusion map is unique"
]);
MOT("2^(4+10)(S5xS3)",
[
"origin: Dixon's Algorithm,\n",
"8th maximal subgroup of Co2,\n",
"table is sorted w.r. to normal series 2^4.2^10.(S5xS3),\n",
"tests: 1.o.r., pow[2,3,5]"
],
[11796480,2359296,1179648,98304,98304,49152,40960,32768,32768,8192,49152,
49152,12288,8192,8192,8192,6144,2048,5760,1152,576,122880,24576,12288,3072,
3072,1536,1280,1024,1024,12288,4096,12288,6144,4096,2048,2048,2048,2048,2048,
512,512,512,256,512,512,256,96,96,48,2048,2048,1024,1024,1024,512,512,512,512,
256,128,256,256,128,128,64,576,576,288,192,192,96,1152,1152,576,96,96,96,48,
96,96,48,96,96,48,120,40,15,20,20,36864,12288,12288,4096,36864,12288,12288,
4096,1024,1024,1024,1024,512,512,768,256,288,96,288,96,1536,6144,6144,2048,
2048,1536,1024,1024,512,512,512,256,256,256,256,128,128,768,256,768,256,128,
128,64,24,24,128,128,128,128,128,128,64,32,32,288,96,288,96,144,144,24,48,48,
48,48],
[,[1,1,1,1,1,1,1,1,1,1,2,2,3,3,2,3,3,3,19,19,19,1,1,1,5,5,5,7,8,8,1,1,2,3,2,8,
8,8,3,8,8,8,8,9,11,11,12,19,20,21,1,2,3,8,8,8,5,8,4,7,10,14,14,13,15,17,67,67,
67,67,67,67,73,73,73,74,75,75,74,67,67,67,71,71,71,86,86,88,86,87,1,1,1,1,3,3,
3,3,8,8,8,8,8,8,13,13,19,19,21,21,1,4,5,5,4,3,8,8,5,5,8,13,13,15,15,14,12,31,
31,33,33,36,36,37,48,49,31,32,35,36,33,36,38,45,46,67,67,68,68,73,74,76,67,70,
68,71],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,1,2,3,22,23,24,25,26,27,
28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,31,33,34,51,52,53,
54,55,56,57,58,59,60,61,62,63,64,65,66,1,3,2,4,5,6,1,3,2,13,11,12,17,24,22,23,
25,26,27,86,87,86,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,
106,91,92,95,96,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,
126,127,128,129,130,131,132,133,134,128,130,137,138,139,140,141,142,143,144,
145,91,93,95,97,91,95,105,111,112,116,113],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,
15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,
41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,
67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,1,7,19,22,28,91,92,
93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,
114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,
133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,
152,153,154,155,156]],
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[TENSOR,[131,4]],[360,-216,72,-48,48,0,0,8,-8,0,24,-24,0,-8,0,8,0,0,0,0,0,60,
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0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[960,192,-192,-32,-32,32,0,0,0,
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0,1,1,-1,-1],
[TENSOR,[152,2]],
[TENSOR,[152,5]],
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[]);
ALF("2^(4+10)(S5xS3)","Co2",[1,2,3,2,3,4,4,3,4,4,10,7,9,9,10,8,11,12,6,19,
20,2,3,4,8,9,12,13,12,11,3,4,7,12,10,9,11,11,12,8,12,12,11,13,25,26,23,20,
36,41,4,10,11,12,9,12,12,11,10,13,13,24,27,27,26,28,6,20,18,19,20,21,5,16,
17,35,38,34,40,21,18,20,39,37,41,15,32,45,31,52,2,4,3,4,9,8,8,9,12,9,12,8,
11,12,24,27,18,21,37,39,4,7,8,9,10,12,8,9,11,12,12,24,27,26,25,27,23,8,11,
23,23,24,27,28,39,55,12,13,25,27,23,24,28,49,48,19,20,37,39,17,35,56,21,
36,41,39],[
"fusion map is unique"
]);
ALF("2^(4+10)(S5xS3)","S5xS3",[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,
3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,
6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,8,9,9,9,9,9,9,10,10,11,12,12,13,
13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,14,14,14,14,15,15,15,15,15,
15,15,15,15,15,15,15,15,15,15,15,15,16,16,16,16,16,16,16,17,17,18,18,18,
18,18,18,18,18,18,19,19,19,19,20,20,20,21,21,21,21]);
MOT("2^(4+12).(S3x3S6)",
[
"origin: computed by Alexander Hulpke using Dixon's algorithm,\n",
"9th maximal subgroup of Co1,\n",
"table is sorted w.r. to normal series 2^4.2^12.S3.3S6,\n",
"tests: 1.o.r., pow[2,3,5]"
],
[849346560,56623104,786432,786432,49152,32768,1179648,1179648,65536,196608,
983040,1474560,6912,103680,12288,12288,15360,737280,442368,6912,103680,221184,
3317760,9216,9216,11520,3456,5760,2048,2048,4096,4096,1024,4096,4096,24576,
49152,49152,6144,6144,32768,16384,32768,294912,147456,294912,512,256,24576,
24576,12288,2048,2048,512,1024,4096,4096,576,288,576,288,576,576,192,768,1536,
1536,2304,4608,4608,192,192,192,96,576,576,384,384,3456,6912,6912,288,288,96,
1728,3456,3456,96,96,576,288,576,288,192,1728,144,96,864,48,144,128,1536,1536,
128,512,512,768,768,512,512,4608,4608,144,144,48,48,96,96,288,288,144,144,45,
240,160,1440,120,40,180,60,30,90,60,180,30,90,36864,147456,49152,2048,2048,
768,1024,12288,12288,256,1024,1024,512,6144,6144,12288,16384,49152,12288,
12288,1024,2048,2048,1152,384,288,512,1536,4096,4096,3072,24576,73728,512,
2048,2048,768,256,1024,4096,4096,1536,8192,24576,192,576,512,512,512,512,64,
64,256,256,128,128,128,1536,1536,512,512,128,48,48,288,288,96,96,96,96,96,96,
48,48,24,144,144,48,144,24,72,48,48,24],
[,[1,1,1,1,2,2,2,2,2,1,1,1,14,14,3,3,11,1,1,21,21,23,23,22,22,23,21,21,8,7,3,
3,4,3,3,2,1,2,8,7,1,2,2,2,2,1,9,5,1,2,2,3,3,10,11,3,3,13,13,14,20,20,21,25,22,
22,23,22,23,22,24,20,21,20,81,81,80,80,80,80,80,85,85,87,86,86,86,77,77,80,80,
80,95,95,95,98,98,98,94,95,31,46,44,32,43,41,37,38,43,41,44,46,60,58,62,63,66,
67,70,69,63,62,123,126,126,126,126,125,129,129,132,132,134,134,136,136,2,1,1,
3,3,5,10,3,3,5,9,9,7,7,7,3,3,3,2,1,9,3,3,14,14,13,9,11,3,3,10,2,1,10,7,7,12,6,
9,3,3,11,2,1,13,14,43,41,46,44,39,29,37,38,35,32,35,46,44,41,43,31,60,58,80,
81,77,77,81,80,77,77,75,75,84,87,86,94,95,97,98,95,94,93],[1,2,3,4,5,6,7,8,9,
10,11,12,2,1,15,16,17,18,19,2,1,2,1,7,8,12,19,18,29,30,31,32,33,34,35,36,37,
38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,44,45,46,45,44,46,
39,36,38,37,45,46,44,40,50,49,51,7,8,3,4,2,1,2,7,8,5,2,1,2,16,15,18,18,19,12,
11,1,12,10,1,17,19,101,102,103,104,105,106,107,108,109,110,111,112,112,111,
103,102,108,107,111,112,112,111,126,124,125,126,127,128,126,124,127,126,124,
126,127,126,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,
153,154,155,156,157,158,159,138,139,137,163,164,165,166,167,168,169,170,171,
172,173,174,175,176,177,178,179,180,168,169,183,184,185,186,187,188,189,190,
191,192,193,194,195,196,197,198,194,195,138,137,144,145,155,156,152,154,150,
151,142,137,138,164,169,167,169,180,178,173],,[1,2,3,4,5,6,7,8,9,10,11,12,13,
14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,
40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,
66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,
92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,
113,114,115,116,117,118,119,120,121,122,14,12,11,1,18,17,23,26,28,21,26,23,28,
21,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,
155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,
174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,
193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,
212,213,214,215,216,217,218,219,220]],
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1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
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-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,
5,5,5,5,5,5,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
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,-1,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,
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540,-12,12,0,0,0,0,0,0,0,0,0,0,16,0,-32,0,0,16,0,-16,48,0,-48,0,0,0,0,0,0,0,0,
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[TENSOR,[204,2]],[4320,-288,-96,96,0,0,96,-96,0,0,0,0,0,0,0,0,0,0,0,0,0,-36,
540,-12,12,0,0,0,0,0,0,0,0,0,0,16,-32,0,0,0,-16,0,16,-48,0,48,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,4,0,-8,0,-12,12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,4,-4,0,0,0,0,0,0,0,0,2,-2,0,0,0,0,0,0,0,0,0,0,0,
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0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[206,2]],
[TENSOR,[202,18]],
[TENSOR,[202,17]],[5760,-384,-128,128,0,0,128,-128,0,0,0,0,0,0,0,0,0,0,0,0,0,
24,-360,8,-8,0,0,0,0,0,0,0,0,0,0,-64,64,64,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,8,-8,-8,0,0,0,0,0,0,0,-4,4,4,-4,12,-12,-12,2,-2,0,0,-12,12,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
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0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[6480,-432,48,-48,0,0,-144,144,0,0,0,0,0,0,
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0,0],
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[TENSOR,[213,2]],
[TENSOR,[211,18]],
[TENSOR,[211,17]],
[TENSOR,[213,18]],
[TENSOR,[213,17]],[8640,-576,-192,192,0,0,192,-192,0,0,0,0,0,0,0,0,0,0,0,0,0,
36,-540,12,-12,0,0,0,0,0,0,0,0,0,0,32,0,-64,0,0,32,0,-32,96,0,-96,0,0,0,0,0,0,
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0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[8640,-576,-192,192,0,0,192,-192,0,0,0,0,0,0,0,
0,0,0,0,0,0,36,-540,12,-12,0,0,0,0,0,0,0,0,0,0,32,-64,0,0,0,-32,0,32,-96,0,96,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-4,0,8,0,12,-12,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,8,-8,0,0,0,0,0,0,0,0,-2,2,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
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0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]],
[(129,134)(130,133)(131,135)(132,136)]);
ALF("2^(4+12).(S3x3S6)","S3x3.S6",[1,1,1,1,1,1,1,1,1,1,1,1,2,2,3,3,3,3,3,
4,4,5,5,5,5,5,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,9,9,9,9,9,9,9,9,9,9,
9,8,8,8,10,10,10,11,11,11,11,11,11,11,11,12,12,12,13,13,13,13,13,13,13,14,
14,14,14,14,14,15,15,15,15,15,16,16,16,17,17,17,18,18,21,21,21,21,21,21,
19,19,19,19,19,19,20,20,24,24,23,23,23,23,22,22,26,25,25,25,27,27,29,29,
30,28,32,32,33,31,34,34,34,34,34,34,34,34,34,36,36,36,36,36,36,36,36,36,
36,36,36,36,36,35,35,35,37,37,37,37,37,37,37,39,39,39,39,39,39,39,39,39,
39,39,38,38,42,42,42,42,42,42,42,42,42,42,40,40,40,40,40,40,41,41,43,43,
43,43,45,45,45,45,45,45,44,44,44,46,46,47,47,48,48,48]);
ALF("2^(4+12).(S3x3S6)","2^12.(S3x3S6)",[1,1,2,2,3,4,5,5,6,7,8,9,10,10,11,
11,12,13,13,14,14,15,15,16,16,17,18,18,19,20,21,22,23,24,25,26,26,26,27,
28,29,29,29,30,30,30,31,32,33,33,33,34,34,35,36,37,37,38,38,38,39,39,39,
40,41,41,41,42,42,42,43,44,44,44,45,45,46,46,47,47,47,48,48,49,50,50,50,
51,51,52,52,52,53,54,55,56,57,58,59,60,61,62,62,63,64,64,65,65,66,66,67,
67,68,68,69,69,70,70,71,71,72,72,73,74,75,76,77,78,79,80,81,82,83,84,85,
86,87,87,87,88,88,89,90,91,91,92,93,93,94,95,95,96,96,96,97,97,98,99,99,
100,100,100,101,102,103,103,104,105,105,106,107,107,108,109,110,111,111,
112,113,113,114,114,115,115,116,116,117,118,119,119,120,121,122,123,123,
124,124,125,126,126,127,127,128,128,129,129,130,130,131,131,132,133,133,
134,135,136,137,138,139,140]);
ALF("2^(4+12).(S3x3S6)","Co1",[1,2,2,4,11,12,9,10,10,4,4,3,22,6,11,12,14,
2,4,22,6,18,5,45,46,19,24,20,32,30,12,10,14,12,11,10,3,12,31,29,4,12,10,9,
12,2,32,33,4,10,11,10,12,14,14,11,12,49,54,22,54,49,22,81,46,47,19,47,18,
45,80,51,24,53,49,51,22,24,20,6,22,48,55,52,23,7,21,54,53,20,22,24,25,26,
8,25,26,8,57,26,34,10,30,32,32,14,13,34,32,14,29,12,54,82,84,51,83,50,80,
47,54,82,64,40,43,16,41,72,62,90,92,64,90,62,92,64,11,2,4,11,12,33,14,10,
12,33,31,32,30,29,30,11,10,9,12,4,32,11,12,20,24,53,32,14,12,10,14,10,4,
14,30,29,13,34,32,10,12,14,12,3,51,24,31,14,12,30,66,67,13,34,33,32,33,11,
30,14,32,34,53,84,22,53,51,54,54,24,53,49,82,84,85,52,23,57,26,57,26,25,
57,56],[
"fusion map is unique"
]);
MOT("2^1+4+6.a8",
[
"origin: CAS library,\n",
"maximal subgroup of Co2,\n",
"Received from Bielefeld 18.01.89\n",
"Test: JAMES, JAMES,n=3,\n",
"and restricted characters decompose properly.\n",
"tests: 1.o.r., pow[2,3,5,7]"
],
[41287680,41287680,2752512,2752512,589824,196608,49152,122880,73728,24576,
8192,6144,24576,8192,6144,49152,49152,16384,16384,12288,12288,24576,8192,6144,
2048,2048,1024,1024,1024,6144,2048,2048,2048,1024,12288,12288,4096,4096,2048,
2048,1024,768,256,256,256,128,512,512,512,512,256,256,256,256,128,256,256,128,
64,64,64,64,128,128,128,128,64,64,5760,5760,576,288,48,96,96,24,30,30,30,30,
576,576,192,192,288,288,96,96,96,288,48,48,96,96,96,96,48,48,48,48,120,120,20,
28,28,28,28,28,28,28,28],
[,[1,1,1,1,1,1,1,2,2,1,1,3,3,3,1,1,1,1,1,3,3,4,4,2,6,6,6,6,6,2,4,3,1,3,5,5,6,
6,6,5,6,9,9,10,10,11,18,18,18,18,18,18,23,23,22,14,14,14,30,31,32,33,40,40,39,
39,37,35,69,69,69,70,70,71,71,72,77,77,79,79,81,81,81,81,81,81,81,81,82,82,81,
83,81,81,83,83,84,82,83,81,101,101,102,104,104,104,104,108,108,108,108],[1,2,
3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,
31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,
57,58,59,60,61,62,63,64,65,66,67,68,1,2,5,9,30,36,35,42,101,102,101,102,1,2,3,
4,5,5,6,7,8,9,10,12,17,16,21,20,22,24,13,15,101,102,103,108,109,110,111,104,
105,106,107],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,
25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,
51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,
69,70,69,70,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,1,2,
8,108,109,110,111,104,105,106,107],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,
17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,
43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,
69,70,71,72,73,74,75,76,79,80,77,78,81,82,83,84,85,86,87,88,89,90,91,92,93,94,
95,96,97,98,99,100,101,102,103,1,2,3,4,1,2,3,4],,,,[1,2,3,4,5,6,7,8,9,10,11,
12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,
38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,
64,65,66,67,68,69,70,71,72,73,74,75,76,79,80,77,78,81,82,83,84,85,86,87,88,89,
90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,
111],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,
27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,
53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,79,80,
77,78,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,
103,108,109,110,111,104,105,106,107],,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,
16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,
42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,
68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,
94,95,96,97,98,99,100,101,102,103,108,109,110,111,104,105,106,107],,[1,2,3,4,
5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,
32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,
58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,
84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,108,109,110,
111,104,105,106,107],,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,
21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,
47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,
73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,
99,100,101,102,103,104,105,106,107,108,109,110,111],,,,,,[1,2,3,4,5,6,7,8,9,
10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,
36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,
62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,79,80,77,78,81,82,83,84,85,86,87,
88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,
110,111]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[7,7,7,7,
7,7,7,7,7,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,3,3,3,3,
3,3,3,3,3,3,3,3,3,3,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,
1,1,1,1,4,4,4,4,0,0,0,0,-1,-1,-1,-1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,
-1,-1,-1,2,2,2,0,0,0,0,0,0,0,0],[14,14,14,14,14,14,14,14,14,6,6,6,6,6,6,6,6,6,
6,6,6,6,6,6,6,6,6,6,6,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,
2,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,2,2,2,2,2,2,2,2,2,2,
0,0,0,0,0,0,0,0,0,0,-1,-1,-1,0,0,0,0,0,0,0,0],[20,20,20,20,20,20,20,20,20,4,4,
4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,5,5,5,5,1,1,1,1,0,0,0,0,-1,-1,-1,-1,-1,-1,
-1,-1,-1,-1,1,1,1,1,1,1,1,1,1,1,0,0,0,-1,-1,-1,-1,-1,-1,-1,-1],[21,21,21,21,
21,21,21,21,21,-3,-3,-3,-3,-3,-3,-3,-3,-3,-3,-3,-3,-3,-3,-3,-3,-3,-3,-3,-3,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,
-1,-1,-1,6,6,6,6,-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,
1,1,1,0,0,0,0,0,0,0,0],[28,28,28,28,28,28,28,28,28,-4,-4,-4,-4,-4,-4,-4,-4,-4,
-4,-4,-4,-4,-4,-4,-4,-4,-4,-4,-4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,0,0,0,0,0,0,0,0,
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-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-2,-2,-2,0,0,0,0,0,0,0,0],[35,35,35,35,35,35,35,
35,35,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,-5,-5,-5,-5,-5,-5,-5,-5,-5,-5,
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-1,-1,-1,5,5,5,5,1,1,1,1,0,0,0,0,2,2,2,2,2,2,2,2,2,2,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0],[56,56,56,56,56,56,56,56,56,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,
8,8,8,8,8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,-4,-4,-4,-4,0,0,0,0,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,1,1,1,0,0,0,0,0,0,0,0],[64,64,64,64,64,64,64,64,64,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
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-2,-2,-2,-2,-2,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,1,1,1,1,1,1,1,1],[70,70,70,70,70,
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2,2,2,2,2,2,2,2,2,2,2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,0,0,0,0,0,
0,0,0,0,0,-5,-5,-5,-5,-1,-1,-1,-1,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,0,0,0,0,0,0,0,0,0,0,0],[35,35,35,35,3,3,3,-5,-5,11,11,11,-5,-5,-5,3,3,3,3,
3,3,3,3,3,-1,-1,-1,-1,-1,7,7,-1,-1,-1,-5,-5,-5,-5,3,3,3,-1,-1,3,3,3,-1,-1,-1,
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0,2,2,2,2,0,0,0,0,-2,-2,2,2,0,0,0,0,0,0,-2,-2,0,0,0,0,0,0,0,0,0,0,0],[35,35,
35,35,3,3,3,-5,-5,-5,-5,-5,11,11,11,3,3,3,3,3,3,3,3,3,-1,-1,-1,-1,-1,7,7,-1,
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1,-1,-1,-1,-1,-1,-1,5,5,-3,1,1,1,1,-1,0,0,0,0,2,2,2,2,0,0,0,0,-2,-2,-2,-2,0,0,
0,0,0,0,2,2,0,0,0,0,0,0,0,0,0,0,0],[35,35,35,35,3,3,3,-5,-5,3,3,3,3,3,3,11,11,
11,11,11,11,-5,-5,-5,-1,-1,-1,-1,-1,-5,-5,3,3,3,7,7,7,7,-1,-1,-1,-1,-1,-1,-1,
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35,35,35,3,3,3,-5,-5,3,3,3,3,3,3,-5,-5,-5,-5,-5,-5,11,11,11,-1,-1,-1,-1,-1,-5,
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-2,-2,-2,2,2,0,0,0,0,0,0,0,0,0,0,0,0,0],[70,70,70,70,6,6,6,-10,-10,14,14,14,
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0,0,0,0],[70,70,70,70,6,6,6,-10,-10,-2,-2,-2,14,14,14,-2,-2,-2,-2,-2,-2,14,14,
14,-2,-2,-2,-2,-2,2,2,2,2,2,2,2,2,2,2,2,2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,2,
2,2,2,2,2,0,0,0,0,0,0,0,0,0,0,-5,-5,3,-1,-1,-1,-1,1,0,0,0,0,1,1,1,1,-3,3,3,-3,
-1,-1,1,1,1,1,1,1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0],[70,70,70,70,6,6,6,-10,
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2,2,2,2,2,-2,-2,2,2,2,-2,-2,-2,-2,-2,-2,2,2,2,-2,-2,-2,0,0,0,0,0,0,0,0,0,0,-5,
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0,0,0,0,0,0,0,0,0,0],[70,70,70,70,6,6,6,-10,-10,-2,-2,-2,14,14,14,14,14,14,14,
14,14,-2,-2,-2,-2,-2,-2,-2,-2,2,2,2,2,2,2,2,2,2,2,2,2,-2,-2,-2,-2,-2,2,2,2,2,
2,2,-2,-2,-2,2,2,2,0,0,0,0,0,0,0,0,0,0,-5,-5,3,-1,-1,-1,-1,1,0,0,0,0,1,1,1,1,
3,-3,-3,3,-1,-1,1,1,-1,-1,-1,-1,1,1,-1,-1,0,0,0,0,0,0,0,0,0,0,0],[140,140,140,
140,12,12,12,-20,-20,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,-4,-4,-4,-4,
-4,4,4,4,4,4,4,4,4,4,4,4,4,-4,-4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,5,5,-3,1,1,1,1,-1,0,0,0,0,-4,-4,-4,-4,0,0,0,0,4,4,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0],[315,315,315,315,27,27,27,-45,-45,27,27,27,-21,-21,-21,3,
3,3,3,3,3,3,3,3,-1,-1,-1,-1,-1,3,3,-5,-5,-5,-9,-9,-9,-9,-1,-1,-1,3,3,-1,-1,-1,
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0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[315,315,
315,315,27,27,27,-45,-45,-21,-21,-21,27,27,27,3,3,3,3,3,3,3,3,3,-1,-1,-1,-1,
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0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[315,315,315,315,27,27,27,-45,-45,3,3,
3,3,3,3,27,27,27,27,27,27,-21,-21,-21,-1,-1,-1,-1,-1,-9,-9,-1,-1,-1,3,3,3,3,
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-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0],[315,315,315,315,27,27,27,-45,-45,3,3,3,3,3,3,-21,-21,-21,-21,
-21,-21,27,27,27,-1,-1,-1,-1,-1,-9,-9,-1,-1,-1,3,3,3,3,-5,-5,-5,3,3,-1,-1,-1,
3,3,3,3,3,3,-1,-1,-1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[210,210,210,
210,18,18,18,-30,-30,-6,-6,-6,-6,-6,-6,-6,-6,-6,-6,-6,-6,-6,-6,-6,2,2,2,2,2,
14,14,-2,-2,-2,-10,-10,-10,-10,6,6,6,-2,-2,-2,-2,-2,2,2,2,2,2,2,2,2,2,-2,-2,
-2,0,0,0,0,0,0,0,0,0,0,15,15,-9,3,-1,-1,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[210,210,210,210,18,18,18,-30,-30,-6,
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15,-9,3,-1,-1,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0],[420,420,420,420,36,36,36,-60,-60,-12,-12,-12,-12,-12,-12,-12,
-12,-12,-12,-12,-12,-12,-12,-12,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,-4,-4,0,0,0,
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0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[28,28,28,28,-4,-4,
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0,0,0,0],[28,28,28,28,-4,-4,-4,4,4,-4,-4,-4,-4,-4,-4,4,4,4,4,4,4,4,4,4,0,0,0,
0,0,4,4,-4,-4,-4,8,8,8,8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,2,
2,2,-2,-2,10,10,2,-2,-2,2,2,0,0,0,0,0,1,1,1,1,-1,-1,-1,-1,1,1,-1,-1,1,1,1,1,1,
1,-1,-1,3,3,-1,0,0,0,0,0,0,0,0],[140,140,140,140,-20,-20,-20,20,20,-4,-4,-4,
-4,-4,-4,4,4,4,4,4,4,4,4,4,0,0,0,0,0,12,12,4,4,4,0,0,0,0,-8,-8,-8,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,-2,-2,-2,2,2,20,20,4,-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,-1,0,0,0,0,0,0,0,0,0,0,0],[140,
140,140,140,-20,-20,-20,20,20,4,4,4,4,4,4,-4,-4,-4,-4,-4,-4,-4,-4,-4,0,0,0,0,
0,0,0,-8,-8,-8,12,12,12,12,4,4,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,-2,2,2,
0,0,0,0,0,0,20,20,4,-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,-1,1,1,0,0,0,0,0,0,0,0,0,0,0],[140,140,140,140,-20,-20,-20,20,20,12,12,
12,12,12,12,-12,-12,-12,-12,-12,-12,-12,-12,-12,0,0,0,0,0,4,4,-4,-4,-4,8,8,8,
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,-2,-2,-2,-2,2,2,-10,-10,-2,
2,-2,2,2,0,0,0,0,0,2,2,2,2,-2,-2,-2,-2,2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0],[140,140,140,140,-20,-20,-20,20,20,-12,-12,-12,-12,-12,-12,12,12,12,
12,12,12,12,12,12,0,0,0,0,0,8,8,0,0,0,4,4,4,4,-4,-4,-4,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,-2,-2,2,2,0,0,0,0,0,0,-10,-10,-2,2,2,-2,-2,0,0,0,0,0,2,2,2,2,-2,
-2,-2,-2,2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[252,252,252,252,-36,
-36,-36,36,36,12,12,12,12,12,12,-12,-12,-12,-12,-12,-12,-12,-12,-12,0,0,0,0,0,
12,12,4,4,4,0,0,0,0,-8,-8,-8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,2,2,
2,-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-3,-3,
1,0,0,0,0,0,0,0,0],[252,252,252,252,-36,-36,-36,36,36,-12,-12,-12,-12,-12,-12,
12,12,12,12,12,12,12,12,12,0,0,0,0,0,0,0,-8,-8,-8,12,12,12,12,4,4,4,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,2,2,-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-3,-3,1,0,0,0,0,0,0,0,0],[280,280,280,280,-40,
-40,-40,40,40,-8,-8,-8,-8,-8,-8,8,8,8,8,8,8,8,8,8,0,0,0,0,0,-8,-8,8,8,8,-16,
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2,-2,-2,2,2,0,0,0,0,0,1,1,1,1,-1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1,-1,-1,1,1,0,0,0,
0,0,0,0,0,0,0,0],[280,280,280,280,-40,-40,-40,40,40,8,8,8,8,8,8,-8,-8,-8,-8,
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[GALOIS,[102,3]],
[GALOIS,[105,3]],[21,21,21,21,21,21,21,21,21,-3,-3,-3,-3,-3,-3,-3,-3,-3,-3,-3,
-3,-3,-3,-3,-3,-3,-3,-3,-3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-3,-3,-3,-3,1,1,1,1,
-E(15)-E(15)^2-E(15)^4-E(15)^8,-E(15)-E(15)^2-E(15)^4-E(15)^8,
-E(15)^7-E(15)^11-E(15)^13-E(15)^14,-E(15)^7-E(15)^11-E(15)^13-E(15)^14,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,0,0,0,0,0,0,0],
[GALOIS,[108,7]],[168,-168,168,-168,0,0,0,0,0,0,0,0,0,0,0,-12,12,-12,12,-12,
12,0,0,0,0,0,0,0,0,0,0,0,0,0,4,-4,4,-4,0,0,0,0,0,0,0,0,2,-2,2,-2,2,-2,0,0,0,0,
0,0,0,0,0,0,-2,2,-2,2,0,0,12,-12,0,0,0,2,-2,0,-E(15)-E(15)^2-E(15)^4-E(15)^8,
E(15)+E(15)^2+E(15)^4+E(15)^8,-E(15)^7-E(15)^11-E(15)^13-E(15)^14,
E(15)^7+E(15)^11+E(15)^13+E(15)^14,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,
2,0,0,0,0,0,0,0,0,0],
[GALOIS,[110,7]]],
[(104,108)(105,109)(106,110)(107,111),(77,79)(78,80)]);
ALF("2^1+4+6.a8","Co2",[1,3,3,2,2,3,4,8,9,3,4,12,8,9,4,4,2,3,4,9,8,7,10,
12,9,8,11,12,12,11,10,11,4,12,7,10,9,8,9,10,12,24,27,11,12,13,9,12,12,8,
11,12,25,26,23,27,24,27,28,26,28,13,25,26,27,24,27,23,5,16,17,35,40,38,34,
56,46,59,47,60,6,20,20,19,18,19,20,21,39,37,20,41,18,21,39,37,36,41,39,21,
14,30,51,22,43,43,42,22,44,44,42],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("2^1+4+6.a8","A8",[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,
2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,
7,7,7,7,7,7,4,4,4,4,9,9,9,9,13,13,14,14,5,5,5,5,5,5,5,5,5,5,10,10,10,10,
10,10,10,10,10,10,8,8,8,11,11,11,11,12,12,12,12]);
ALN("2^1+4+6.a8",["Co2C2B","Co2N2B"]);
MOT("2^1+8:s6f2",
[
"origin: CAS library,\n",
"maximal subgroup of Co2,\n",
"Source: Table from Birmingham.\n",
"Test: 1.OR, JAMES, JAMES,n=3,\n",
"and restricted characters decompose properly.\n",
"tests: 1.o.r., pow[2,3,5,7]"
],
[743178240,743178240,2752512,3096576,288,288,48,48,48,96,48,96,576,96,576,
6144,512,3072,12288,12288,5184,864,5184,18,18,3456,3456,288,192,4320,4320,
32768,6144,49152,589824,589824,49152,49152,8192,2048,56,28,56,28,28,64,32,128,
128,256,1024,512,4096,4096,2048,737280,737280,24576,6144,1024,768,12288,12288,
1536,1536,256,1536,1536,256,256,256,128,64,60,60,20,20,30,30,48,48,48,48,96,
96,128,64,32,128,288,288,288,288,48,24,96,96,288,288,48],
[,[1,1,1,2,26,26,29,15,15,13,15,13,21,23,21,35,34,35,36,36,21,23,21,24,24,26,
26,27,26,30,30,1,3,2,1,1,1,1,3,3,41,41,41,43,41,54,52,55,55,32,35,34,35,35,36,
1,1,3,1,3,4,3,3,37,37,39,37,37,39,37,37,39,40,74,74,74,74,78,78,85,85,85,85,
30,30,16,19,17,16,30,30,30,30,26,28,29,29,26,26,29],[1,2,3,4,35,36,33,16,18,
20,18,19,36,34,35,16,17,18,19,20,1,4,2,21,23,1,2,4,3,1,2,32,33,34,35,36,37,38,
39,40,41,45,43,44,42,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,
65,66,67,68,69,70,71,72,73,74,75,76,77,74,75,67,68,65,64,38,37,86,87,88,89,36,
35,57,56,59,61,62,63,56,57,58],,[1,2,3,4,5,6,7,8,11,10,9,12,13,14,15,16,17,18,
19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,45,43,44,
42,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,
71,72,73,1,2,57,56,30,31,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,
97,98,99,100],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,
24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,1,3,2,4,3,46,47,48,49,50,
51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,
77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100],,,,[
1,2,3,4,5,6,7,8,11,10,9,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,
30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,
56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,
82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100],,[1,2,3,4,5,6,7,8,
9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,
35,36,37,38,39,40,41,45,43,44,42,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,
61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,
87,88,89,90,91,92,93,94,95,96,97,98,99,100],,,,[1,2,3,4,5,6,7,8,11,10,9,12,13,
14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,
40,41,45,43,44,42,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,
66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,
92,93,94,95,96,97,98,99,100],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,
19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,45,43,44,
42,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,
71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,
97,98,99,100],,,,[1,2,3,4,5,6,7,8,11,10,9,12,13,14,15,16,17,18,19,20,21,22,23,
24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,
50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,
76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,
100],,,,,,[1,2,3,4,5,6,7,8,11,10,9,12,13,14,15,16,17,18,19,20,21,22,23,24,25,
26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,
52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,
78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[7,7,7,7,-1,-1,-1,0,0,0,0,0,2,
2,2,3,3,3,3,3,-2,-2,-2,1,1,1,1,1,1,4,4,-1,-1,-1,-1,-1,3,3,3,3,0,0,0,0,0,1,1,1,
1,-1,-1,-1,-1,-1,-1,-5,-5,-5,-1,-1,-1,-1,-1,1,1,1,-3,-3,-3,1,1,1,1,2,2,0,0,-1,
-1,0,0,-2,-2,0,0,-1,-1,-1,-1,2,2,-2,-2,-1,-1,-1,-1,1,1,1],[15,15,15,15,1,1,1,
-1,-1,-1,-1,-1,1,1,1,-1,-1,-1,-1,-1,-3,-3,-3,0,0,3,3,3,3,0,0,7,7,7,7,7,3,3,3,
3,1,1,1,1,1,-1,-1,-1,-1,3,3,3,3,3,3,-5,-5,-5,-1,-1,-1,-1,-1,-3,-3,-3,1,1,1,1,
1,1,1,0,0,0,0,0,0,-2,-2,0,0,0,0,1,1,1,1,-2,-2,-2,-2,-1,-1,-1,-1,1,1,1],[21,21,
21,21,0,0,0,-1,-1,-1,-1,-1,3,3,3,5,5,5,5,5,3,3,3,0,0,0,0,0,0,6,6,-3,-3,-3,-3,
-3,1,1,1,1,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,9,9,9,-3,-3,-3,-3,-3,-1,-1,-1,3,3,3,
-1,-1,-1,-1,1,1,-1,-1,1,1,0,0,2,2,-2,-2,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0],[
21,21,21,21,2,2,2,1,1,1,1,1,-1,-1,-1,1,1,1,1,1,3,3,3,0,0,0,0,0,0,6,6,5,5,5,5,
5,5,5,5,5,0,0,0,0,0,-1,-1,-1,-1,1,1,1,1,1,1,-11,-11,-11,-3,-3,-3,-3,-3,-3,-3,
-3,-3,-3,-3,1,1,1,1,1,1,-1,-1,1,1,0,0,0,0,2,2,-1,-1,-1,-1,2,2,-2,-2,0,0,0,0,
-2,-2,-2],[27,27,27,27,0,0,0,0,0,0,0,0,0,0,0,3,3,3,3,3,0,0,0,0,0,0,0,0,0,9,9,
3,3,3,3,3,7,7,7,7,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,15,15,15,3,3,3,
3,3,1,1,1,5,5,5,1,1,1,1,2,2,0,0,-1,-1,-1,-1,1,1,1,1,1,1,1,1,3,3,3,3,0,0,0,0,0,
0,0],[35,35,35,35,0,0,0,1,1,1,1,1,3,3,3,7,7,7,7,7,-1,-1,-1,-1,-1,2,2,2,2,5,5,
3,3,3,3,3,-5,-5,-5,-5,0,0,0,0,0,1,1,1,1,-1,-1,-1,-1,-1,-1,-5,-5,-5,3,3,3,3,3,
-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0,-1,-1,-1,-1,1,1,1,1,1,1,-3,-3,1,1,0,
0,0,0,-2,-2,-2],[35,35,35,35,2,2,2,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
-1,-1,-1,-1,2,2,2,2,5,5,11,11,11,11,11,7,7,7,7,0,0,0,0,0,1,1,1,1,3,3,3,3,3,3,
15,15,15,3,3,3,3,3,5,5,5,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,-1,-1,1,1,-1,-1,-1,-1,
-1,-1,3,3,0,0,0,0,0,0,0],[56,56,56,56,-2,-2,-2,0,0,0,0,0,-2,-2,-2,0,0,0,0,0,2,
2,2,-1,-1,2,2,2,2,11,11,-8,-8,-8,-8,-8,8,8,8,8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
-24,-24,-24,0,0,0,0,0,4,4,4,-4,-4,-4,0,0,0,0,1,1,1,1,1,1,-1,-1,1,1,-1,-1,0,0,
0,0,1,1,-3,-3,0,0,0,0,0,0,0],[70,70,70,70,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,2,
2,2,2,2,7,7,7,1,1,1,1,1,1,-5,-5,-10,-10,-10,-10,-10,6,6,6,6,0,0,0,0,0,0,0,0,0,
2,2,2,2,2,2,-10,-10,-10,-2,-2,-2,-2,-2,2,2,2,2,2,2,-2,-2,-2,-2,0,0,0,0,0,0,-1,
-1,-1,-1,3,3,0,0,0,0,-1,-1,-1,-1,1,1,1,1,-1,-1,-1],[84,84,84,84,-1,-1,-1,1,1,
1,1,1,-1,-1,-1,4,4,4,4,4,3,3,3,0,0,3,3,3,3,-6,-6,20,20,20,20,20,4,4,4,4,0,0,0,
0,0,0,0,0,0,4,4,4,4,4,4,4,4,4,4,4,4,4,4,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,
0,0,0,0,-2,-2,0,0,0,0,2,2,-2,-2,1,1,1,1,1,1,1],[105,105,105,105,1,1,1,-1,-1,
-1,-1,-1,1,1,1,5,5,5,5,5,-3,-3,-3,0,0,-3,-3,-3,-3,15,15,1,1,1,1,1,5,5,5,5,0,0,
0,0,0,-1,-1,-1,-1,1,1,1,1,1,1,-35,-35,-35,1,1,1,1,1,-1,-1,-1,-5,-5,-5,-1,-1,
-1,-1,0,0,0,0,0,0,1,1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[105,105,105,
105,-1,-1,-1,0,0,0,0,0,2,2,2,-3,-3,-3,-3,-3,6,6,6,0,0,3,3,3,3,0,0,17,17,17,17,
17,-3,-3,-3,-3,0,0,0,0,0,-1,-1,-1,-1,1,1,1,1,1,1,5,5,5,-7,-7,-7,-7,-7,3,3,3,
-1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0,2,2,0,0,0,0,1,1,1,1,2,2,2,2,-1,-1,-1,-1,-1,
-1,-1],[105,105,105,105,-1,-1,-1,0,0,0,0,0,2,2,2,-3,-3,-3,-3,-3,6,6,6,0,0,3,3,
3,3,0,0,-7,-7,-7,-7,-7,9,9,9,9,0,0,0,0,0,-1,-1,-1,-1,-3,-3,-3,-3,-3,-3,25,25,
25,1,1,1,1,1,-3,-3,-3,-3,-3,-3,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-4,
-4,4,4,1,1,1,1,1,1,1],[120,120,120,120,-2,-2,-2,0,0,0,0,0,-2,-2,-2,0,0,0,0,0,
-6,-6,-6,0,0,0,0,0,0,15,15,-8,-8,-8,-8,-8,8,8,8,8,1,1,1,1,1,0,0,0,0,0,0,0,0,0,
0,40,40,40,0,0,0,0,0,-4,-4,-4,4,4,4,0,0,0,0,0,0,0,0,0,0,1,1,-1,-1,-1,-1,0,0,0,
0,1,1,1,1,0,0,0,0,-2,-2,-2],[168,168,168,168,-1,-1,-1,0,0,0,0,0,2,2,2,0,0,0,0,
0,6,6,6,0,0,-3,-3,-3,-3,6,6,8,8,8,8,8,8,8,8,8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
40,40,40,8,8,8,8,8,0,0,0,0,0,0,0,0,0,0,-2,-2,0,0,1,1,0,0,0,0,2,2,0,0,0,0,2,2,
-2,-2,-1,-1,-1,-1,1,1,1],[189,189,189,189,0,0,0,0,0,0,0,0,0,0,0,9,9,9,9,9,0,0,
0,0,0,0,0,0,0,9,9,-3,-3,-3,-3,-3,-11,-11,-11,-11,0,0,0,0,0,-1,-1,-1,-1,1,1,1,
1,1,1,21,21,21,-3,-3,-3,-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,-3,-3,-3,-3,0,0,0,0,0,0,0],[189,189,189,189,0,0,0,0,0,0,0,0,0,0,0,
-3,-3,-3,-3,-3,0,0,0,0,0,0,0,0,0,9,9,21,21,21,21,21,1,1,1,1,0,0,0,0,0,1,1,1,1,
1,1,1,1,1,1,-39,-39,-39,-3,-3,-3,-3,-3,-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,-1,3,3,3,3,0,0,0,0,0,0,0],[189,189,189,189,0,0,
0,0,0,0,0,0,0,0,0,-3,-3,-3,-3,-3,0,0,0,0,0,0,0,0,0,9,9,-3,-3,-3,-3,-3,13,13,
13,13,0,0,0,0,0,1,1,1,1,-3,-3,-3,-3,-3,-3,-51,-51,-51,-3,-3,-3,-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,-3,-3,-3,-3,0,0,0,0,0,0,0],[
210,210,210,210,2,2,2,1,1,1,1,1,-1,-1,-1,-2,-2,-2,-2,-2,3,3,3,0,0,0,0,0,0,15,
15,2,2,2,2,2,2,2,2,2,0,0,0,0,0,0,0,0,0,-2,-2,-2,-2,-2,-2,50,50,50,-6,-6,-6,-6,
-6,2,2,2,2,2,2,-2,-2,-2,-2,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,0,0,0,0,-1,-1,-1,-1,
0,0,0,0,2,2,2],[210,210,210,210,1,1,1,0,0,0,0,0,-2,-2,-2,6,6,6,6,6,-6,-6,-6,0,
0,3,3,3,3,-15,-15,-14,-14,-14,-14,-14,10,10,10,10,0,0,0,0,0,0,0,0,0,-2,-2,-2,
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0,0,0,0,0,0,0],
[GALOIS,[99,3]]],
[(42,45),( 9,11)]);
ALF("2^1+8:s6f2","Co2",[1,2,3,7,20,19,41,35,40,38,40,34,17,38,16,9,25,11,
7,10,5,34,17,29,50,6,19,36,20,6,18,4,12,10,3,2,3,4,9,11,22,43,42,57,44,27,
48,26,25,13,12,26,8,9,10,2,4,8,4,12,23,9,8,9,12,27,12,8,24,11,12,27,28,15,
31,32,31,45,58,41,39,41,37,21,20,24,23,49,27,18,20,21,19,21,55,37,39,18,
21,39],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("2^1+8:s6f2","2^8:S6(2)",[1,1,3,2,45,45,46,66,68,67,69,67,42,43,42,23,
26,25,24,24,18,19,18,62,62,20,20,21,22,17,17,8,9,7,6,6,10,10,11,12,52,54,
52,53,55,59,61,60,60,35,33,34,31,31,32,4,4,5,13,15,16,14,14,29,29,30,27,
27,28,36,36,37,38,39,39,63,63,70,70,64,64,65,65,44,44,56,57,58,56,41,41,
40,40,49,51,50,50,47,47,48]);
ALF("2^1+8:s6f2","S6(2)",[1,1,1,1,20,20,20,29,29,29,29,29,17,17,17,9,9,9,
9,9,7,7,7,25,25,8,8,8,8,6,6,3,3,3,3,3,4,4,4,4,22,22,22,22,22,24,24,24,24,
12,12,12,12,12,12,2,2,2,5,5,5,5,5,10,10,10,11,11,11,13,13,13,13,14,14,26,
26,30,30,28,28,27,27,18,18,23,23,23,23,16,16,15,15,21,21,21,21,19,19,19]);
ALN("2^1+8:s6f2",["c2c2","Co2C2A","Co2N2A"]);
MOT("2^10:m22:2",
[
"origin: CAS library,\n",
"tests: 1.o.r., pow[2,3,5,7,11]"
],
[908328960,11796480,2752512,1474560,49152,2048,2048,8192,16384,49152,16384,
24576,1152,1152,288,288,192,1024,1024,512,512,512,128,256,256,256,256,64,40,
40,20,96,96,48,28,28,28,28,64,64,32,11,344064,6144,12288,12288,24576,344064,
20480,4096,2048,1280,768,768,256,256,1024,1024,512,256,256,256,96,96,96,96,48,
48,64,64,32,20,20,24,24,28,28,28,28],
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13,13,17,17,13,17,18,19,20,29,30,32,33,35,35,37,37],[1,2,3,4,5,6,7,8,9,10,11,
12,1,2,2,4,3,18,19,20,21,22,23,24,25,26,27,28,29,30,31,5,10,12,37,38,35,36,39,
40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,43,48,45,
46,47,44,69,70,71,72,73,53,54,78,79,76,77],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,
15,16,17,18,19,20,21,22,23,24,25,26,27,28,1,4,2,32,33,34,37,38,35,36,39,40,41,
42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,
68,69,70,71,49,52,74,75,78,79,76,77],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,
17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,1,3,1,3,39,40,41,42,43,
44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,
70,71,72,73,74,75,43,48,43,48],,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,
18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,1,43,
44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,
70,71,72,73,74,75,76,77,78,79],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,
19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,37,38,35,36,39,40,41,42,43,44,
45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,
71,72,73,74,75,78,79,76,77],,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,
19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,37,38,35,36,39,40,41,42,43,44,
45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,
71,72,73,74,75,78,79,76,77],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,
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46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,
72,73,74,75,78,79,76,77],,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,
20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,
46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,
72,73,74,75,76,77,78,79]],
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[TENSOR,[58,2]],[770,-30,-14,10,34,2,-2,-2,-6,-14,10,-10,5,-3,-3,1,1,10,-6,-2,
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-4,0,0,4,-4,0,0,-2,2,3,-1,-3,1,-1,1,0,0,0,0,0,1,-1,0,0,0,0],[770,-30,-14,10,
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1,-1,0,0,0,0,0,-1,1,0,0,0,0],
[TENSOR,[61,2]],
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[TENSOR,[66,2]],
[TENSOR,[65,2]],[4620,-180,-84,60,44,-4,4,-12,-4,-52,28,4,3,3,-3,-3,3,-4,-4,4,
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[TENSOR,[69,2]],
[TENSOR,[70,2]],[6930,-270,-126,90,18,2,-2,14,-22,-30,-6,6,0,0,0,0,0,-6,10,-2,
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[TENSOR,[75,2]],[9240,-360,-168,120,-8,-8,8,-24,24,-8,24,8,-3,-3,3,3,-3,0,0,0,
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[TENSOR,[77,2]],[13860,-540,-252,180,-60,4,-4,28,-12,36,-44,12,0,0,0,0,0,-4,
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0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]],
[(35,37)(36,38)(76,78)(77,79),(18,19)(39,40)(43,48)(45,46)(57,58)(61,62)
(63,64)(65,66)(69,70)(76,77)(78,79)]);
ALF("2^10:m22:2","Co2",[1,2,3,4,3,12,11,9,4,7,10,8,6,19,18,21,20,9,11,25,
12,26,27,11,25,23,13,28,15,32,31,20,36,39,22,43,22,44,27,28,48,33,2,12,9,
8,4,3,4,10,12,13,12,23,13,26,8,11,12,23,24,27,19,20,37,39,21,41,24,28,49,
32,52,41,55,42,43,42,44],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("2^10:m22:2","M22.2",[1,1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,3,4,4,4,4,4,4,5,
5,5,5,5,6,6,6,7,7,7,8,8,9,9,10,10,10,11,12,12,12,12,12,12,13,13,13,13,14,
14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,17,17,17,18,18,19,19,20,20,
21,21]);
MOT("2^11:M24",
[
"origin: computed by C. Jansen using B. Fischer's Clifford matrices,\n",
"maximal subgroup of Co1,\n",
"the 2nd power map is determined only up to matrix automorphisms,\n",
"tests: 1.o.r., pow[2,3,5,7,11,23]"
],
[501397585920,660602880,389283840,2752512,393216,2752512,393216,49152,49152,
491520,491520,32768,32768,15360,34560,2304,5760,3456,4032,576,6144,6144,6144,
6144,1024,1024,2048,2048,2048,2048,1024,1024,256,768,256,768,256,480,120,160,
192,192,192,192,96,96,96,96,48,168,56,168,56,64,64,64,64,80,80,40,22,22,48,48,
48,48,24,24,28,28,28,28,30,30,30,30,21,21,23,23],
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12,11,13,38,38,38,15,15,16,16,16,16,19,19,20,50,50,52,52,27,28,30,29,38,38,40,
61,61,41,43,41,43,47,48,50,51,52,53,73,73,75,75,77,78,79,80],[1,2,3,4,5,6,7,8,
9,10,11,12,13,14,1,2,2,3,1,3,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,
37,38,39,40,4,5,6,7,8,9,10,11,14,52,53,50,51,54,55,56,57,58,59,60,61,62,21,24,
22,23,34,36,71,72,69,70,38,39,38,39,52,50,79,80],,[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,
2,3,41,42,43,44,45,46,47,48,49,52,53,50,51,54,55,56,57,10,11,14,61,62,63,64,
65,66,67,68,71,72,69,70,15,17,15,17,78,77,80,79],,[1,2,3,4,5,6,7,8,9,10,11,12,
13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,
39,40,41,42,43,44,45,46,47,48,49,1,2,1,2,54,55,56,57,58,59,60,61,62,63,64,65,
66,67,68,4,6,4,6,75,76,73,74,19,19,80,79],,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,
14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,
40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,1,3,63,64,65,
66,67,68,69,70,71,72,75,76,73,74,77,78,80,79],,,,,,,,,,,,[1,2,3,4,5,6,7,8,9,
10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,
36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,
62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,1,1]],
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ALF("2^11:M24","M24",[1,1,1,2,2,2,2,2,2,3,3,3,3,3,4,4,4,4,5,5,6,6,6,6,6,6,
7,7,7,7,7,7,7,8,8,8,8,9,9,9,10,10,10,10,10,10,11,11,11,12,12,13,13,14,14,
14,14,15,15,15,16,16,17,17,17,17,18,18,19,19,20,20,21,21,22,22,23,24,25,
26]);
ALF("2^11:M24","Co1",[1,2,4,2,4,9,10,12,11,4,3,10,12,14,6,22,20,24,8,26,
12,10,30,29,14,32,11,12,31,32,14,30,33,14,32,13,34,16,41,43,22,24,49,51,
54,53,26,25,57,28,60,28,60,33,34,67,66,43,40,72,44,77,54,82,51,84,57,56,
60,87,60,87,64,92,64,92,76,76,78,79],[
"fusion is unique up to table automorphisms"
]);
ALN("2^11:M24",["2^11.M24"]);
MOT("2^2.[2^7*3^2].S3",
[
"origin: CAS library,\n",
"maximal subgroup of Co3,\n",
"Computed using CAYLEY.\n",
"Test: 1.OR, JAMES, JAMES,n=3,\n",
"and restricted characters decompose properly.\n",
"tests: 1.o.r., pow[2,3]"
],
[27648,9216,768,384,384,192,128,96,288,216,72,36,1536,1536,384,384,256,192,
128,128,32,288,144,72,24,24,12,12,12,192,192,64,64,64,64,32,32,32,48,48,24,12,
12,24,24],
[,[1,1,1,1,1,1,1,1,9,10,11,12,2,2,2,3,2,2,3,2,3,9,9,10,11,9,11,10,12,13,13,17,
17,17,17,13,17,17,22,22,22,24,25,39,39],[1,2,3,4,5,6,7,8,1,1,1,1,13,14,15,16,
17,18,19,20,21,2,2,2,3,6,8,4,5,30,31,32,33,34,35,36,37,38,13,14,18,15,16,30,
31]],
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1],
[TENSOR,[2,3]],[2,2,2,0,2,2,0,0,-1,2,2,-1,2,2,0,0,2,2,0,0,2,-1,-1,2,2,-1,0,0,
-1,2,2,0,0,0,0,0,0,2,-1,-1,-1,0,0,-1,-1],[2,2,2,0,2,0,0,2,2,2,-1,-1,2,2,0,2,2,
0,2,0,0,2,2,2,-1,0,-1,0,-1,0,0,2,2,0,0,2,0,0,2,2,0,0,-1,0,0],
[TENSOR,[6,3]],
[TENSOR,[5,2]],[4,4,4,0,4,0,0,0,-2,4,-2,1,4,4,0,0,4,0,0,0,0,-2,-2,4,-2,0,0,0,
1,0,0,0,0,0,0,0,0,0,-2,-2,0,0,0,0,0],[6,6,6,-2,6,0,-2,0,0,-3,0,0,6,6,-2,0,6,0,
0,-2,0,0,0,-3,0,0,0,1,0,0,0,0,0,-2,-2,0,-2,0,0,0,0,1,0,0,0],
[TENSOR,[10,2]],[9,9,5,3,-3,-3,-1,-1,0,0,3,0,-3,-3,3,1,1,-3,1,-1,-1,0,0,0,-1,
0,-1,0,0,3,3,-1,-1,3,-1,1,-1,1,0,0,0,0,1,0,0],
[TENSOR,[12,3]],
[TENSOR,[12,2]],
[TENSOR,[12,4]],[18,18,10,0,-6,0,0,-2,0,0,-3,0,-6,-6,0,2,2,0,2,0,0,0,0,0,1,0,
1,0,0,0,0,-2,-2,0,0,2,0,0,0,0,0,0,-1,0,0],
[TENSOR,[16,3]],[27,27,3,-3,3,3,-3,-3,0,0,0,0,3,3,-3,-3,-5,3,-3,-3,-1,0,0,0,0,
0,0,0,0,3,3,1,1,1,1,1,1,-1,0,0,0,0,0,0,0],
[TENSOR,[18,2]],
[TENSOR,[18,4]],
[TENSOR,[18,3]],[9,9,-3,3,-3,-1,-1,-3,3,0,0,0,5,5,3,3,1,-1,3,-1,1,3,3,0,0,-1,
0,0,0,1,1,1,1,-1,3,-1,-1,-1,-1,-1,-1,0,0,1,1],
[TENSOR,[22,4]],
[TENSOR,[22,2]],
[TENSOR,[22,3]],[18,18,-6,0,-6,2,0,0,-3,0,0,0,10,10,0,0,2,2,0,0,-2,-3,-3,0,0,
-1,0,0,0,-2,-2,0,0,0,0,0,0,2,1,1,-1,0,0,1,1],
[TENSOR,[26,2]],[18,18,-6,-6,2,0,2,0,0,0,0,3,-6,-6,-6,0,2,0,0,2,0,0,0,0,0,0,0,
0,-1,0,0,0,0,2,2,0,-2,0,0,0,0,0,0,0,0],
[TENSOR,[28,2]],[36,36,-12,0,4,0,0,0,0,0,0,-3,-12,-12,0,0,4,0,0,0,0,0,0,0,0,0,
0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[12,-4,0,2,0,-2,-2,0,-3,3,0,0,4,-4,-2,
6,0,2,-2,2,0,5,-1,-1,0,1,0,-1,0,2,-2,2,-2,0,0,0,0,0,1,-1,-1,1,0,-1,1],
[TENSOR,[31,3]],
[TENSOR,[31,2]],
[TENSOR,[31,4]],[24,-8,0,-4,0,0,4,0,6,-3,0,0,8,-8,4,0,0,0,0,-4,0,-2,-2,1,0,0,
0,-1,0,0,0,0,0,0,0,0,0,0,2,-2,0,1,0,0,0],
[TENSOR,[35,2]],[24,-8,0,0,0,4,0,0,3,6,0,0,8,-8,0,0,0,-4,0,0,0,-5,1,-2,0,1,0,
0,0,-4,4,0,0,0,0,0,0,0,-1,1,-1,0,0,-1,1],
[TENSOR,[37,2]],[36,-12,0,-6,0,-2,-2,0,3,0,0,0,-4,4,6,6,0,2,-2,2,0,3,-3,0,0,1,
0,0,0,-2,2,-2,2,0,0,0,0,0,-1,1,-1,0,0,1,-1],
[TENSOR,[39,2]],
[TENSOR,[39,3]],
[TENSOR,[39,4]],[48,-16,0,0,0,0,0,0,-6,-6,0,0,16,-16,0,0,0,0,0,0,0,2,2,2,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,-2,2,0,0,0,0,0],[72,-24,0,0,0,4,0,0,-3,0,0,0,-8,8,0,0,
0,-4,0,0,0,-3,3,0,0,1,0,0,0,4,-4,0,0,0,0,0,0,0,1,-1,-1,0,0,1,-1],
[TENSOR,[44,2]]],
[]);
ALF("2^2.[2^7*3^2].S3","Co3",[1,2,2,3,3,2,3,3,4,5,5,6,8,7,7,7,8,8,8,8,8,
11,12,13,13,12,14,14,15,18,17,18,17,18,17,19,19,19,27,26,27,28,28,41,40],[
"fusion map is unique, equal to that on the CAS table"
]);
ALN("2^2.[2^7*3^2].S3",["2^2.2^6.3.(S3xS3)"]);
MOT("2^4.a8",
[
"origin: CAS library,\n",
"maximal subgroup of Co3,\n",
"non-split extension\n",
"computed using ordinary characters of the inertia group 2^3:gl(3,2)\n",
"(there must be a degree-15-character extended from 2^4 to restrict\n",
"the degree-23-character of c3 properly), the irreducible character\n",
"of degree 23 of c3 and Clifford matrices which differ from those\n",
"in split-case by representative orders and, for the 3x3-Matrices,\n",
"some signs.\n",
"tests: 1.o.r., pow[2,3,5,7]"
],
[322560,21504,512,384,1536,384,128,180,72,24,64,64,32,16,16,15,12,12,12,14,14,
14,14,15,15],
[,[1,1,2,1,2,1,2,8,9,9,3,3,3,6,7,16,8,10,9,20,20,22,22,24,25],[1,2,3,4,5,6,7,
1,1,2,11,12,13,14,15,16,6,5,4,22,23,20,21,16,16],,[1,2,3,4,5,6,7,8,9,10,11,12,
13,14,15,1,17,18,19,22,23,20,21,8,8],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,
17,18,19,1,2,1,2,25,24]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[7,7,-1,-1,-1,3,3,4,1,1,
-1,-1,-1,1,1,2,0,-1,-1,0,0,0,0,-1,-1],[14,14,6,6,6,2,2,-1,2,2,2,2,2,0,0,-1,-1,
0,0,0,0,0,0,-1,-1],[20,20,4,4,4,4,4,5,-1,-1,0,0,0,0,0,0,1,1,1,-1,-1,-1,-1,0,
0],[21,21,-3,-3,-3,1,1,6,0,0,1,1,1,-1,-1,1,-2,0,0,0,0,0,0,1,1],[21,21,-3,-3,
-3,1,1,-3,0,0,1,1,1,-1,-1,1,1,0,0,0,0,0,0,-E(15)^7-E(15)^11-E(15)^13-E(15)^14,
-E(15)-E(15)^2-E(15)^4-E(15)^8],
[GALOIS,[6,7]],[28,28,-4,-4,-4,4,4,1,1,1,0,0,0,0,0,-2,1,-1,-1,0,0,0,0,1,1],[
35,35,3,3,3,-5,-5,5,2,2,-1,-1,-1,-1,-1,0,1,0,0,0,0,0,0,0,0],[45,45,-3,-3,-3,
-3,-3,0,0,0,1,1,1,1,1,0,0,0,0,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)^6,0,0],
[GALOIS,[10,3]],[56,56,8,8,8,0,0,-4,-1,-1,0,0,0,0,0,1,0,-1,-1,0,0,0,0,1,1],[
64,64,0,0,0,0,0,4,-2,-2,0,0,0,0,0,-1,0,0,0,1,1,1,1,-1,-1],[70,70,-2,-2,-2,2,2,
-5,1,1,-2,-2,-2,0,0,0,-1,1,1,0,0,0,0,0,0],[15,-1,3,-1,-5,3,-1,0,3,-1,-3,1,1,1,
-1,0,0,1,-1,1,-1,1,-1,0,0],[45,-3,1,-3,9,-3,1,0,0,0,-1,3,-1,1,-1,0,0,0,0,
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)^6,0,0],
[GALOIS,[16,3]],[90,-6,10,-6,-6,6,-2,0,0,0,-2,-2,2,0,0,0,0,0,0,-1,1,-1,1,0,
0],[105,-7,5,-7,13,-3,1,0,3,-1,3,-1,-1,-1,1,0,0,1,-1,0,0,0,0,0,0],[120,-8,8,
-8,8,0,0,0,-3,1,0,0,0,0,0,0,0,-1,1,1,-1,1,-1,0,0],[105,-7,-3,1,5,9,-3,0,3,-1,
3,-1,-1,1,-1,0,0,-1,1,0,0,0,0,0,0],[105,-7,5,1,-19,-3,1,0,3,-1,-1,3,-1,-1,1,0,
0,-1,1,0,0,0,0,0,0],[210,-14,2,2,-14,6,-2,0,-3,1,2,2,-2,0,0,0,0,1,-1,0,0,0,0,
0,0],[315,-21,-9,3,15,3,-1,0,0,0,-3,1,1,-1,1,0,0,0,0,0,0,0,0,0,0],[315,-21,-1,
3,-9,-9,3,0,0,0,1,-3,1,1,-1,0,0,0,0,0,0,0,0,0,0]],
[(24,25),(20,22)(21,23)]);
ARC("2^4.a8","tomfusion",rec(name:="2^4`A8",map:=[1,2,9,3,8,4,12,5,6,22,
49,53,63,17,72,19,26,94,25,27,99,27,99,100,100],text:=[
"fusion map is unique"
]));
ALF("2^4.a8","A8",[1,1,2,2,2,3,3,4,5,5,6,6,6,7,7,8,9,10,10,11,11,12,12,13,
14],[
"factor fusion equal to that on the CAS table"
]);
ALF("2^4.a8","Co3",[1,2,8,3,7,2,8,5,5,13,18,17,19,8,19,10,13,28,14,16,29,
16,29,31,31],[
"fusion map is unique, equal to that on the CAS table"
]);
MOT("2xm12",
[
"origin: CAS library,\n",
"maximal subgroup of Co3,\n",
"Restricted characters decompose properly.\n",
"tests: 1.o.r., pow[2,3,5,11]"
],
0,
0,
0,
[(14,15)(29,30),( 6, 7)(11,12)(21,22)(26,27)],
["ConstructDirectProduct",[["Cyclic",2],["M12"]],(),(2,3)(17,18)]);
ARC("2xm12","tomfusion",rec(name:="2xM12",map:=[1,4,5,7,8,14,16,24,34,37,
76,72,99,100,100,2,3,6,25,26,13,17,96,33,38,63,82,98,219,219],text:=[
"fusion map is unique up to table autom."
]));
ALF("2xm12","Co3",[1,3,2,5,6,8,8,10,15,13,19,17,23,24,25,3,3,3,14,15,7,8,
23,15,14,18,19,23,36,37],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("2xm12","2.Fi22",[1,5,7,14,12,20,20,23,40,44,51,52,61,63,65,2,6,7,15,
13,21,21,24,41,45,52,51,62,64,66],[
"fusion map is unique up to table aut."
]);
ALN("2xm12",["Co3C2B","Co3N2B"]);
MOT("3^(3+4):2(S4xS4)",
[
"origin: Dixon's Algorithm,\n",
"15th maximal subgroup of Co1,\n",
"table is sorted w.r. to normal series 3^3.3^4.2.2^2.3.2.2^2.3.2"
],
[2519424,314928,209952,419904,8748,4374,1944,31104,3888,2592,5184,288,576,
3888,1944,486,243,432,216,7776,3888,3888,3888,3888,162,324,192,192,5184,648,
432,864,72,864,1728,72,36,288,72,144,144,32,8748,5832,2916,8748,34992,486,486,
486,972,648,324,972,3888,36,72,486,486,486,27,243,243,243,54,54,54,324,324,
324,324,324,324,324,324,324,54,54,54,24,24,864,108,72,288,72,36,18,432,216,36,
36,48,24,192,192,72,72,288,24,24,48,24,48,96,36,432,864],
[,[1,2,3,4,5,6,7,1,2,3,4,11,8,14,15,16,17,14,15,1,2,2,4,3,6,5,13,13,8,9,10,11,
7,4,1,18,19,8,9,11,10,13,43,44,45,46,47,48,49,50,43,44,45,46,47,52,55,58,59,
60,61,62,63,64,58,59,60,44,45,43,45,44,46,43,46,47,48,49,50,57,57,1,5,10,8,11,
14,16,1,3,7,5,13,12,29,29,31,32,29,36,36,29,31,34,35,33,34,35],[1,1,1,1,1,1,1,
8,8,8,8,13,13,1,2,1,2,8,9,20,20,20,20,20,20,20,27,28,29,29,29,29,35,35,35,29,
30,38,38,38,38,42,1,1,1,1,1,2,2,2,8,8,8,8,8,13,13,2,2,1,6,2,1,2,9,9,8,20,20,
20,20,20,20,20,20,20,22,22,22,27,28,82,82,85,85,85,82,82,89,89,89,89,93,93,95,
96,99,99,99,95,96,102,102,105,105,108,108,108]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,1,-1,-1,-1,
-1,-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,1,
1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,
-1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,-1,-1,-1,-1,
-1,-1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1],
[TENSOR,[2,3]],[2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,-2,-2,-2,-2,-2,-2,-2,-2,
-2,2,2,2,2,2,2,2,2,2,-2,-2,-2,-2,-2,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[5,2]],[2,2,2,2,2,2,2,2,2,2,2,2,2,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,
2,2,2,2,2,2,2,-1,-1,0,0,0,0,0,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,-1,-1,-1,-1,-1,-1,
-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,2,2,2,2,-1,-1,0,0,0,0,0,0,2,2,2,2,2,
-1,-1,0,0,0,0,0,0,0],
[TENSOR,[7,2]],[3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,-3,-3,-3,-3,-3,-3,-3,-3,
-3,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,
-1,-1,-1,-1,-1,1,1,1,1,1,1,1],
[TENSOR,[9,4]],[3,3,3,3,3,3,3,3,3,3,3,-1,-1,0,0,0,0,0,0,1,1,1,1,1,1,1,-1,-1,3,
3,3,3,-1,-1,-1,0,0,1,1,1,1,-1,3,3,3,3,3,3,3,3,3,3,3,3,3,-1,-1,0,0,0,0,0,0,0,0,
0,0,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,3,3,-1,-1,-1,0,0,1,1,1,1,-1,-1,3,3,-1,-1,-1,
0,0,1,1,-1,-1,-1,-1,-1],
[TENSOR,[11,4]],
[TENSOR,[9,2]],
[TENSOR,[9,3]],
[TENSOR,[11,2]],
[TENSOR,[11,3]],[4,4,4,4,4,4,4,4,4,4,4,4,4,-2,-2,-2,-2,-2,-2,0,0,0,0,0,0,0,0,
0,4,4,4,4,4,4,4,-2,-2,0,0,0,0,0,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,
1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0],[4,4,4,4,4,4,4,-4,-4,-4,-4,0,0,-2,-2,-2,-2,2,2,0,0,0,
0,0,0,0,2*E(8)+2*E(8)^3,-2*E(8)-2*E(8)^3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,-2,-2,
-2,-2,-2,-2,-2,2,2,2,2,2,0,0,1,1,1,1,1,1,1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,
-E(8)-E(8)^3,E(8)+E(8)^3,0,0,0,0,0,0,0,0,0,0,0,0,0,2*E(8)+2*E(8)^3,
-2*E(8)-2*E(8)^3,0,0,0,-E(8)-E(8)^3,E(8)+E(8)^3,0,0,-2,-2,2,2,2],
[TENSOR,[18,2]],
[TENSOR,[18,4]],
[TENSOR,[18,3]],[6,6,6,6,6,6,6,6,6,6,6,-2,-2,0,0,0,0,0,0,2,2,2,2,2,2,2,-2,-2,
6,6,6,6,-2,-2,-2,0,0,2,2,2,2,-2,-3,-3,-3,-3,-3,-3,-3,-3,-3,-3,-3,-3,-3,1,1,0,
0,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[22,2]],[6,6,6,6,6,6,6,6,6,6,6,6,6,-3,-3,-3,-3,-3,-3,0,0,0,0,0,0,0,0,
0,-2,-2,-2,-2,-2,-2,-2,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,2,2,2,2,-1,-1,0,0,0,0,0,0,-2,-2,-2,-2,
-2,1,1,0,0,0,0,0,0,0],
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[TENSOR,[93,2]],[216,-108,0,108,0,0,0,-24,12,0,-12,0,0,0,0,0,0,0,0,0,0,0,0,0,
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-1,2,-4,0,0,-2,1,0,0,0,0,0],
[TENSOR,[98,4]],
[TENSOR,[98,3]],
[TENSOR,[98,2]],[384,-48,96,-192,-12,6,0,0,0,0,0,0,0,0,0,-6,3,0,0,0,0,0,0,0,0,
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0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[432,-216,0,216,0,0,0,-48,24,0,-24,0,0,0,0,0,0,
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0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[432,108,-108,0,0,0,0,-48,-12,12,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,9,0,-9,9,36,0,0,0,-3,
0,3,-3,-12,0,0,0,0,0,0,0,0,0,0,0,0,6,-3,-3,-3,6,-3,-3,-3,6,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[106,2]],[432,108,-108,0,0,0,0,-48,-12,12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-18,0,18,-18,-72,0,0,0,6,0,-6,6,24,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0]],
[( 27, 28)( 80, 81)( 95, 96)(100,101)]);
ALF("3^(3+4):2(S4xS4)","2(S4xS4)",[1,1,1,1,1,1,1,2,2,2,2,3,3,4,4,4,4,5,5,
6,6,6,6,6,6,6,7,8,9,9,9,9,10,10,10,11,11,12,12,12,12,13,14,14,14,14,14,14,
14,14,15,15,15,15,15,16,16,17,17,17,17,17,17,17,18,18,18,19,19,19,19,19,
19,19,19,19,19,19,19,20,21,22,22,23,23,23,24,24,25,25,25,25,26,26,27,28,
29,29,29,30,31,32,32,33,33,34,34,34]);
ALF("3^(3+4):2(S4xS4)","Co1",[1,7,6,5,6,7,8,2,23,22,18,47,12,6,35,8,36,22,
68,2,21,23,18,20,23,22,34,34,9,48,49,45,25,19,3,49,96,10,55,46,51,34,6,6,
7,7,5,37,36,35,20,22,23,21,18,54,47,37,36,7,36,37,8,35,70,69,23,22,21,22,
23,22,23,20,23,18,70,69,68,83,83,4,24,54,12,47,24,26,4,24,26,24,34,83,30,
30,82,80,29,84,84,30,84,50,13,56,50,13],[
"fusion map is unique"
]);
MOT("3^1+4:2^1+4.s5",
[
"origin: CAS library,\n",
"maximal subgroup of Co2,\n",
"Source: Table named 'gg' from Birmingham.\n",
"Test: 1.OR, JAMES, JAMES,n=3,\n",
"and restricted characters decompose properly.\n",
"tests: 1.o.r., pow[2,3,5]"
],
[933120,466560,3888,11520,5760,10368,5184,432,576,288,96,48,1728,864,72,192,
96,48,24,1296,648,54,144,72,72,36,108,108,108,18,30,30,30,30,30,30,96,288,36,
192,192,32,8,48,24,48,24,12,24,24],
[,[1,2,3,1,2,1,2,3,4,5,4,5,6,7,8,6,7,9,10,20,21,22,20,21,23,24,20,21,21,22,31,
32,33,31,32,33,4,1,3,9,9,9,11,13,15,13,15,23,25,25],[1,1,1,4,4,6,6,6,9,9,11,
11,13,13,13,16,16,18,18,1,1,2,4,4,9,9,6,6,6,7,31,31,31,34,34,34,37,38,38,40,
41,42,43,44,44,46,46,37,41,40],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,
19,20,21,22,23,24,25,26,27,28,29,30,1,2,2,4,5,5,37,38,39,41,40,42,43,46,47,44,
45,48,50,49]],
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1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[4,4,4,4,4,4,4,
4,4,4,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,2,2,2,2,2,2,0,
0,0,0,0,-1,-1,-1],
[TENSOR,[3,2]],[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,
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[TENSOR,[5,2]],[6,6,6,6,6,6,6,6,6,6,-2,-2,-2,-2,-2,-2,-2,-2,-2,0,0,0,0,0,0,0,
0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[5,5,5,5,5,-3,-3,-3,1,1,1,1,
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[TENSOR,[8,2]],[10,10,10,10,10,-6,-6,-6,2,2,2,2,2,2,2,2,2,-2,-2,-2,-2,-2,-2,
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[TENSOR,[11,2]],[10,10,10,10,10,2,2,2,-2,-2,2,2,-2,-2,-2,-2,-2,0,0,1,1,1,1,1,
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[TENSOR,[13,2]],[10,10,10,10,10,2,2,2,-2,-2,-2,-2,2,2,2,2,2,0,0,1,1,1,1,1,1,1,
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[TENSOR,[15,2]],[20,20,20,20,20,4,4,4,-4,-4,0,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,
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[TENSOR,[17,2]],[4,4,4,-4,-4,0,0,0,0,0,0,0,2,2,2,-2,-2,0,0,-2,-2,-2,2,2,0,0,0,
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[TENSOR,[19,2]],[16,16,16,-16,-16,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,-2,-2,2,2,0,
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[TENSOR,[21,2]],[20,20,20,-20,-20,0,0,0,0,0,0,0,2,2,2,-2,-2,0,0,2,2,2,-2,-2,0,
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[TENSOR,[23,2]],[24,24,24,-24,-24,0,0,0,0,0,0,0,-4,-4,-4,4,4,0,0,0,0,0,0,0,0,
0,0,0,0,0,-1,-1,-1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[80,80,-1,0,0,8,8,-1,0,
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2,-1,0,0,0],
[TENSOR,[26,2]],[160,160,-2,0,0,16,16,-2,0,0,0,0,16,16,-2,0,0,0,0,-8,-8,1,0,0,
0,0,-2,-2,-2,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[240,240,-3,0,0,24,24,
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[TENSOR,[29,2]],[160,160,-2,0,0,-16,-16,2,0,0,0,0,0,0,0,0,0,0,0,-8,-8,1,0,0,0,
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[TENSOR,[31,2]],[320,320,-4,0,0,-32,-32,4,0,0,0,0,0,0,0,0,0,0,0,8,8,-1,0,0,0,
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],[18,-9,0,2,-1,-6,3,0,2,
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0,0,0,0,0,0,0,0],[54,-27,0,6,-3,-18,9,0,6,-3,-2,1,-6,3,0,2,-1,2,-1,0,0,0,0,0,
0,0,0,0,0,0,-1,E(15)^7+E(15)^11+E(15)^13+E(15)^14,E(15)+E(15)^2+E(15)^4
+E(15)^8,1,-E(15)^7-E(15)^11-E(15)^13-E(15)^14,-E(15)-E(15)^2-E(15)^4-E(15)^8
,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[35,7]],[72,-36,0,8,-4,-24,12,0,8,-4,0,0,0,0,0,0,0,0,0,-6,3,0,2,-1,2,
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0,0,0,0,0,0,0,0],[90,-45,0,10,-5,-30,15,0,10,-5,2,-1,6,-3,0,-2,1,-2,1,6,-3,0,
-2,1,-2,1,0,3,-3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[90,-45,0,10,-5,
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-3,0,-2,1,2,-1,-6,3,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[90,-45,0,10,
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0,0,0,0,0,0,0,0,0,0,0,0,0,0],[180,-90,0,20,-10,-12,6,0,-4,2,4,-2,-12,6,0,4,-2,
0,0,-6,3,0,2,-1,2,-1,0,3,-3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[180,
-90,0,20,-10,-12,6,0,-4,2,-4,2,12,-6,0,-4,2,0,0,-6,3,0,2,-1,2,-1,0,3,-3,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[216,-108,0,-24,12,0,0,0,0,0,0,0,-12,6,0,
-4,2,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-E(15)^7-E(15)^11-E(15)^13-E(15)^14,
-E(15)-E(15)^2-E(15)^4-E(15)^8,1,-E(15)^7-E(15)^11-E(15)^13-E(15)^14,
-E(15)-E(15)^2-E(15)^4-E(15)^8,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[45,7]],[270,-135,0,30,-15,54,-27,0,6,-3,-2,1,-6,3,0,2,-1,-2,1,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[288,-144,0,-32,16,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,12,-6,0,4,-2,0,0,0,0,0,0,-2,1,1,-2,1,1,0,0,0,0,0,0,
0,0,0,0,0,0,0,0],[360,-180,0,40,-20,-24,12,0,-8,4,0,0,0,0,0,0,0,0,0,6,-3,0,-2,
1,-2,1,0,-3,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[360,-180,0,-40,20,0,
0,0,0,0,0,0,12,-6,0,4,-2,0,0,-12,6,0,-4,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0]],
[(40,41)(44,46)(45,47)(49,50),(32,33)(35,36)]);
ALF("3^1+4:2^1+4.s5","A5.2",[1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,3,3,3,
3,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,6,6,6,6,6,7,7,7],[
"factor fusion equal to that on the CAS table"
]);
ALF("3^1+4:2^1+4.s5","Co2",[1,5,6,3,16,2,17,19,9,35,11,40,7,34,36,10,38,
24,56,5,6,29,16,20,35,37,17,19,18,50,14,46,47,30,59,60,11,4,21,24,24,27,
28,23,55,23,55,40,56,56],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("3^1+4:2^1+4.s5","twd5a",[1,1,1,2,2,3,3,3,4,4,5,5,6,6,6,7,7,8,8,9,9,9,
10,10,11,11,12,12,12,12,13,13,13,14,14,14,15,16,16,17,18,19,20,21,21,22,
22,23,24,25]);
ALN("3^1+4:2^1+4.s5",["Co2N3A","gg"]);
MOT("3^1+4:4s6",
[
"origin: CAS library,\n",
"maximal subgroup of Co3,\n",
"Computed using CAYLEY\n",
"[to get 4s6 and inertia factor groups]. Complement classes are, if not\n",
"unique, the first of the classes that belong to the corresponding\n",
"class of the factor group.\n",
"Test: OR1, JAMES, JAMES,n=3,\n",
"restricted characters from c3 and induced \n",
"characters from the complement decompose properly.\n",
"tests: 1.o.r., pow[2,3,5]"
],
[699840,349920,2916,8640,4320,2592,1296,108,864,108,288,36,1944,972,81,1944,
972,162,162,1440,96,288,144,96,48,60,30,216,108,216,108,108,108,108,18,36,18,
32,32,48,24,16,48,24,60,30,36,36,36,36,36,12,20,20],
[,[1,2,3,1,2,1,2,3,1,3,1,3,13,14,15,16,17,18,19,4,4,4,5,4,5,26,27,13,14,16,17,
16,17,17,19,16,18,24,24,24,25,24,24,25,26,27,28,30,28,29,29,28,45,45],[1,1,1,
4,4,6,6,6,9,9,11,11,1,1,2,1,1,1,2,20,21,22,22,24,24,26,26,4,4,4,4,6,6,6,7,9,9,
38,39,40,40,42,43,43,45,45,20,20,22,22,22,21,53,54],,[1,2,3,4,5,6,7,8,9,10,11,
12,13,14,15,16,17,18,19,20,21,22,23,24,25,1,2,28,29,30,31,32,33,34,35,36,37,
39,38,40,41,42,43,44,4,5,47,48,49,50,51,52,20,20]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,1,
1,-1,-1,-1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,1,1,-1,-1,-1,1,1,1,1,1,1,-1,-1,
-1,-1,1,1],[1,1,1,1,1,-1,-1,-1,1,1,-1,-1,1,1,1,1,1,1,1,-1,1,-1,-1,1,1,1,1,1,1,
1,1,-1,-1,-1,-1,1,1,-1,-1,-1,-1,1,1,1,1,1,-1,-1,-1,-1,-1,1,-1,-1],
[TENSOR,[2,3]],[5,5,5,5,5,1,1,1,1,1,1,1,2,2,2,-1,-1,-1,-1,5,-3,-3,-3,1,1,0,0,
2,2,-1,-1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,0,0,2,-1,0,0,0,0,0,0],
[TENSOR,[5,3]],[5,5,5,5,5,3,3,3,3,3,1,1,-1,-1,-1,2,2,2,2,5,-1,-1,-1,1,1,0,0,
-1,-1,2,2,0,0,0,0,0,0,-1,-1,1,1,1,-1,-1,0,0,-1,2,-1,-1,-1,-1,0,0],
[TENSOR,[5,4]],
[TENSOR,[7,4]],
[TENSOR,[7,2]],
[TENSOR,[7,3]],
[TENSOR,[5,2]],[8,8,8,-8,-8,0,0,0,0,0,0,0,-4,-4,-4,2,2,2,2,0,0,0,0,0,0,-2,-2,
4,4,-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,2,2,0,0,0,0,0,0,0,0],[8,8,8,-8,-8,0,0,0,0,
0,0,0,2,2,2,-4,-4,-4,-4,0,0,0,0,0,0,-2,-2,-2,-2,4,4,0,0,0,0,0,0,0,0,0,0,0,0,0,
2,2,0,0,0,0,0,0,0,0],[9,9,9,9,9,-3,-3,-3,3,3,-1,-1,0,0,0,0,0,0,0,-9,3,-3,-3,1,
1,-1,-1,0,0,0,0,0,0,0,0,0,0,-1,-1,1,1,-1,1,1,-1,-1,0,0,0,0,0,0,1,1],
[TENSOR,[15,4]],
[TENSOR,[15,2]],
[TENSOR,[15,3]],[10,10,10,10,10,2,2,2,-2,-2,2,2,1,1,1,1,1,1,1,-10,2,-2,-2,-2,
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[TENSOR,[19,4]],
[TENSOR,[19,2]],
[TENSOR,[19,3]],[16,16,16,16,16,0,0,0,0,0,0,0,-2,-2,-2,-2,-2,-2,-2,16,0,0,0,0,
0,1,1,-2,-2,-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,-2,-2,0,0,0,0,1,1],[16,16,16,
-16,-16,0,0,0,0,0,0,0,-2,-2,-2,-2,-2,-2,-2,0,0,0,0,0,0,1,1,2,2,2,2,0,0,0,0,0,
0,0,0,0,0,0,0,0,-1,-1,0,0,0,0,0,0,E(20)+E(20)^9-E(20)^13-E(20)^17,
-E(20)-E(20)^9+E(20)^13+E(20)^17],
[TENSOR,[24,3]],
[TENSOR,[23,3]],[20,20,20,-20,-20,0,0,0,0,0,0,0,2,2,2,2,2,2,2,0,0,0,0,0,0,0,0,
-2,-2,-2,-2,0,0,0,0,0,0,2*E(8)+2*E(8)^3,-2*E(8)-2*E(8)^3,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0],
[TENSOR,[27,3]],[80,80,-1,0,0,8,8,-1,8,-1,8,-1,8,8,-1,8,8,-1,-1,0,0,0,0,0,0,0,
0,0,0,0,0,2,2,2,-1,2,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[29,3]],
[TENSOR,[29,2]],
[TENSOR,[29,4]],[160,160,-2,0,0,16,16,-2,0,0,0,0,-8,-8,1,4,4,4,-5,0,0,0,0,0,0,
0,0,0,0,0,0,-2,-2,-2,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[160,160,-2,0,0,
0,0,0,16,-2,0,0,-8,-8,1,4,4,-5,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,1,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[34,2]],
[TENSOR,[33,2]],[320,320,-4,0,0,0,0,0,0,0,0,0,8,8,-1,-16,-16,2,2,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[18,-9,0,2,-1,6,-3,
0,0,0,0,0,-6,3,0,6,-3,0,0,0,0,-2,1,2,-1,-2,1,2,-1,2,-1,0,3,-3,0,0,0,0,0,2,-1,
0,-2,1,2,-1,0,0,-2,1,1,0,0,0],
[TENSOR,[38,2]],[72,-36,0,-8,4,0,0,0,0,0,0,0,12,-6,0,6,-3,0,0,0,0,0,0,0,0,2,
-1,4,-2,-2,1,-6,3,3,0,0,0,0,0,0,0,0,0,0,2,-1,0,0,0,0,0,0,0,0],
[TENSOR,[40,2]],[72,-36,0,-8,4,0,0,0,0,0,0,0,-6,3,0,-12,6,0,0,0,0,0,0,0,0,2,
-1,-2,1,4,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,2,-1,0,0,0,3*E(4),-3*E(4),0,0,0],
[TENSOR,[42,2]],[90,-45,0,10,-5,-18,9,0,0,0,0,0,6,-3,0,12,-6,0,0,0,0,-2,1,2,
-1,0,0,-2,1,4,-2,0,0,0,0,0,0,0,0,-2,1,0,2,-1,0,0,0,0,-2,1,1,0,0,0],[90,-45,0,
10,-5,6,-3,0,0,0,0,0,-12,6,0,-6,3,0,0,0,0,6,-3,2,-1,0,0,4,-2,-2,1,0,3,-3,0,0,
0,0,0,-2,1,0,2,-1,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[45,2]],
[TENSOR,[44,2]],[162,-81,0,18,-9,-18,9,0,0,0,0,0,0,0,0,0,0,0,0,0,0,6,-3,2,-1,
2,-1,0,0,0,0,0,0,0,0,0,0,0,0,2,-1,0,-2,1,-2,1,0,0,0,0,0,0,0,0],
[TENSOR,[48,2]],[180,-90,0,20,-10,-12,6,0,0,0,0,0,-6,3,0,6,-3,0,0,0,0,-4,2,-4,
2,0,0,2,-1,2,-1,0,3,-3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,-1,-1,0,0,0],
[TENSOR,[50,2]],[288,-144,0,-32,16,0,0,0,0,0,0,0,12,-6,0,-12,6,0,0,0,0,0,0,0,
0,-2,1,4,-2,4,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,1,0,0,0,0,0,0,0,0],[288,-144,0,
32,-16,0,0,0,0,0,0,0,12,-6,0,-12,6,0,0,0,0,0,0,0,0,-2,1,-4,2,-4,2,0,0,0,0,0,0,
0,0,0,0,0,0,0,2,-1,0,0,0,0,0,0,0,0],[360,-180,0,-40,20,0,0,0,0,0,0,0,-12,6,0,
12,-6,0,0,0,0,0,0,0,0,0,0,-4,2,-4,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0]],
[(53,54),(50,51),(50,51)(53,54),(38,39),(38,39)(50,51)(53,54)]);
ALF("3^1+4:4s6","Co3",[1,4,5,2,11,2,12,13,3,14,3,14,4,5,21,5,4,6,20,7,8,7,
26,8,27,9,30,11,13,13,12,13,11,12,32,14,15,19,19,17,40,19,18,41,22,42,26,
28,26,28,28,27,33,34],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALN("3^1+4:4s6",["Co3N3A"]);
MOT("3^5:(2xm11)",
[
"origin: CAS library,\n",
"maximal subgroup of Co3,\n",
"Test: 1.OR, JAMES, JAMES,n=3,\n",
"and restricted characters decompose properly.\n",
"tests: 1.o.r., pow[2,3,5,11]"
],
[3849120,34992,29160,2592,432,324,216,324,162,162,81,48,24,30,15,36,18,16,16,
22,22,15840,864,108,36,144,36,36,10,36,18,48,24,48,24,22,22],
[,[1,2,3,1,2,2,3,8,9,10,11,4,5,14,15,8,9,12,12,21,20,1,1,3,8,4,7,5,14,8,10,12,
13,12,13,21,20],[1,1,1,4,4,4,4,1,2,1,2,12,12,14,14,4,6,18,19,20,21,22,23,23,
22,26,26,26,29,23,23,32,32,34,34,36,37],,[1,2,3,4,5,6,7,8,9,10,11,12,13,1,3,
16,17,19,18,20,21,22,23,24,25,26,27,28,22,30,31,34,35,32,33,36,37],,,,,,[1,2,
3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,1,1,22,23,24,25,26,27,28,29,30,31,
32,33,34,35,22,22]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[
10,10,10,2,2,2,2,1,1,1,1,2,2,0,0,-1,-1,0,0,-1,-1,10,2,2,1,2,2,2,0,-1,-1,0,0,0,
0,-1,-1],[10,10,10,-2,-2,-2,-2,1,1,1,1,0,0,0,0,1,1,E(8)+E(8)^3,-E(8)-E(8)^3,
-1,-1,10,-2,-2,1,0,0,0,0,1,1,E(8)+E(8)^3,E(8)+E(8)^3,-E(8)-E(8)^3,
-E(8)-E(8)^3,-1,-1],
[GALOIS,[3,5]],[11,11,11,3,3,3,3,2,2,2,2,-1,-1,1,1,0,0,-1,-1,0,0,11,3,3,2,-1,
-1,-1,1,0,0,-1,-1,-1,-1,0,0],[16,16,16,0,0,0,0,-2,-2,-2,-2,0,0,1,1,0,0,0,0,
E(11)+E(11)^3+E(11)^4+E(11)^5+E(11)^9,E(11)^2+E(11)^6+E(11)^7+E(11)^8+E(11)^10
,16,0,0,-2,0,0,0,1,0,0,0,0,0,0,E(11)+E(11)^3+E(11)^4+E(11)^5+E(11)^9,
E(11)^2+E(11)^6+E(11)^7+E(11)^8+E(11)^10],
[GALOIS,[6,2]],[44,44,44,4,4,4,4,-1,-1,-1,-1,0,0,-1,-1,1,1,0,0,0,0,44,4,4,-1,
0,0,0,-1,1,1,0,0,0,0,0,0],[45,45,45,-3,-3,-3,-3,0,0,0,0,1,1,0,0,0,0,-1,-1,1,1,
45,-3,-3,0,1,1,1,0,0,0,-1,-1,-1,-1,1,1],[55,55,55,-1,-1,-1,-1,1,1,1,1,-1,-1,0,
0,-1,-1,1,1,0,0,55,-1,-1,1,-1,-1,-1,0,-1,-1,1,1,1,1,0,0],[1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],
[TENSOR,[2,11]],
[TENSOR,[3,11]],
[TENSOR,[4,11]],
[TENSOR,[5,11]],
[TENSOR,[6,11]],
[TENSOR,[7,11]],
[TENSOR,[8,11]],
[TENSOR,[9,11]],
[TENSOR,[10,11]],[22,-5,4,6,3,-3,0,4,-2,-2,1,2,-1,2,-1,0,0,0,0,0,0,0,0,0,0,4,
-2,1,0,0,0,2,-1,2,-1,0,0],
[TENSOR,[21,11]],[198,-45,36,6,3,-3,0,0,0,0,0,2,-1,-2,1,0,0,0,0,0,0,0,0,0,0,4,
-2,1,0,0,0,-2,1,-2,1,0,0],
[TENSOR,[23,11]],[220,-50,40,12,6,-6,0,4,-2,-2,1,-4,2,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0],[220,-50,40,-12,-6,6,0,4,-2,-2,1,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,2*E(8)+2*E(8)^3,-E(8)-E(8)^3,-2*E(8)-2*E(8)^3,E(8)+E(8)^3,
0,0],
[TENSOR,[26,11]],[352,-80,64,0,0,0,0,-8,4,4,-2,0,0,2,-1,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0],[220,4,-5,20,-4,2,-1,4,1,1,-2,0,0,0,0,2,-1,0,0,0,0,0,8,
-1,0,4,1,-2,0,2,-1,0,0,0,0,0,0],
[TENSOR,[29,11]],[220,4,-5,4,4,4,-5,4,1,1,-2,0,0,0,0,-2,1,0,0,0,0,0,-8,1,0,4,
1,-2,0,-2,1,0,0,0,0,0,0],
[TENSOR,[31,11]],[440,8,-10,-24,0,-6,6,8,2,2,-4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0],[880,16,-20,16,-8,-2,4,-2,-5,4,1,0,0,0,0,-2,1,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[880,16,-20,-16,8,2,-4,-2,-5,4,1,0,0,0,0,2,
-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[880,16,-20,0,0,0,0,-2,4,-5,1,0,0,
0,0,0,0,0,0,0,0,0,-16,2,0,0,0,0,0,2,-1,0,0,0,0,0,0],
[TENSOR,[36,11]]],
[(20,21)(36,37),(18,19)(32,34)(33,35)]);
ALF("3^5:(2xm11)","Co3",[1,4,5,2,11,12,13,5,20,6,21,8,27,10,31,13,32,19,
19,24,25,3,3,14,14,7,28,26,23,14,15,18,41,18,41,36,37],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("3^5:(2xm11)","2xM11",[1,1,1,2,2,2,2,3,3,3,3,4,4,5,5,6,6,7,8,9,10,11,
12,12,13,14,14,14,15,16,16,17,17,18,18,19,20]);
MOT("3^6:2M12",
[
"origin: Dixon's Algorithm,\n",
"11th maximal subgroup of Co1,\n",
"table is sorted w.r. to normal series 3^6.2.M12,\n",
"tests: 1.o.r., pow[2,3,5,11]"
],
[138568320,5773680,524880,314928,190080,240,31104,3888,3888,3888,1296,972,
3456,432,2916,1458,486,486,486,486,108,648,81,72,288,72,72,288,72,72,180,45,
45,20,12,108,54,54,54,54,36,18,48,24,48,24,48,24,48,24,20,20,66,33,22,66,33,
22],
[,[1,2,3,4,1,5,1,4,3,2,3,4,1,3,15,16,17,18,19,20,15,22,23,22,7,10,11,7,11,8,
31,32,33,31,24,15,16,20,19,18,15,17,25,26,25,26,28,30,28,30,34,34,56,57,56,53,
54,53],[1,1,1,1,5,6,7,7,7,7,7,7,13,13,1,1,1,4,4,4,5,1,4,5,25,25,25,28,28,28,
31,31,31,34,6,7,7,12,12,12,13,13,43,43,45,45,47,47,49,49,51,52,53,53,55,56,56,
58],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,
28,29,30,1,3,2,5,35,36,37,38,39,40,41,42,45,46,43,44,49,50,47,48,6,6,53,54,55,
56,57,58],,,,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,
24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,
50,52,51,1,2,5,1,2,5]],
[[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,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[11,11,11,11,11,-1,3,3,3,3,3,3,3,3,2,
2,2,2,2,2,2,-1,-1,-1,-1,-1,-1,3,3,3,1,1,1,1,-1,0,0,0,0,0,0,0,-1,-1,-1,-1,1,1,
1,1,-1,-1,0,0,0,0,0,0],[11,11,11,11,11,-1,3,3,3,3,3,3,3,3,2,2,2,2,2,2,2,-1,-1,
-1,3,3,3,-1,-1,-1,1,1,1,1,-1,0,0,0,0,0,0,0,1,1,1,1,-1,-1,-1,-1,-1,-1,0,0,0,0,
0,0],[16,16,16,16,16,4,0,0,0,0,0,0,0,0,-2,-2,-2,-2,-2,-2,-2,1,1,1,0,0,0,0,0,0,
1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,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)+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,E(11)^2+E(11)^6+E(11)^7+E(11)^8+E(11)^10],
[GALOIS,[4,2]],[45,45,45,45,45,5,-3,-3,-3,-3,-3,-3,-3,-3,0,0,0,0,0,0,0,3,3,3,
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0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[2376,594,27,-54,0,0,48,-6,21,-6,3,-6,24,
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0,0,0,0,0,0,0,-2,1,1,1,-2,2,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[2640,660,30,
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2,-1,-1,-1,2,-2,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[3520,-440,-80,64,0,0,64,
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0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[3520,-440,-80,64,0,0,-64,8,8,8,8,-10,0,
0,10,-8,-2,-5,1,7,0,-8,1,0,0,0,0,0,0,0,0,0,0,0,0,2,2,-1,-1,-1,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0],[4224,1056,48,-96,0,0,0,0,0,0,0,0,0,0,-24,-6,6,0,-6,6,0,
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7040,-880,-160,128,0,0,0,0,0,0,0,0,0,0,-16,2,-4,8,2,-4,0,8,-1,0,0,0,0,0,0,0,0,
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[(53,56)(54,57)(55,58),(51,52),(43,45)(44,46)(47,49)(48,50),(43,45)(44,46)
(47,49)(48,50)(51,52)]);
ALF("3^6:2M12","Co1",[1,5,6,7,4,14,2,21,20,18,22,23,4,24,6,7,8,37,35,36,
24,8,36,26,12,47,54,11,53,52,16,64,62,43,57,22,23,69,68,70,24,26,34,83,34,
83,33,85,33,85,72,72,44,94,77,44,94,77],[
"fusion map is unique"
]);
ALF("3^6:2M12","2.M12",[1,1,1,1,2,3,4,4,4,4,4,4,5,5,6,6,6,6,6,6,7,8,8,9,
10,10,10,11,11,11,12,12,12,13,14,15,15,15,15,15,16,16,17,17,18,18,19,19,
20,20,21,22,23,23,24,25,25,26]);
ALN("3^6:2M12",["3^6:2.M12"]);
MOT("5^(1+2):GL2(5)",
[
"origin: Dixon's Algorithm,\n",
"19th maximal subgroup of Co1,\n",
"5C normalizer in Co1,\n",
"table is sorted w.r. to normal series 5.5^2.2.2.A5.2,\n",
"tests: 1.o.r., pow[2,3,5]"
],
[60000,15000,500,2400,600,480,480,80,120,80,500,250,250,25,120,100,50,50,20,
24,24,30,20,20,20,30,80,80,16,16,24,24,20,20,24,24,24,24],
[,[1,2,3,1,2,4,4,1,9,4,11,12,13,14,9,11,12,13,3,15,15,22,16,16,5,22,8,8,8,8,6,
7,19,19,20,21,20,21],[1,2,3,4,5,7,6,8,1,10,11,12,13,14,4,16,17,18,19,6,7,2,24,
23,25,5,28,27,30,29,32,31,34,33,31,32,31,32],,[1,1,1,4,4,6,7,8,9,10,1,1,1,1,
15,4,4,4,8,20,21,9,7,6,10,15,27,28,29,30,31,32,27,28,35,36,37,38]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,
-1,-1,-1,-1,-1],[4,4,4,4,4,4,4,0,1,0,-1,-1,-1,-1,1,-1,-1,-1,0,1,1,1,-1,-1,0,1,
0,0,0,0,-2,-2,0,0,1,1,1,1],
[TENSOR,[3,2]],[5,5,5,5,5,5,5,1,-1,1,0,0,0,0,-1,0,0,0,1,-1,-1,-1,0,0,1,-1,-1,
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[TENSOR,[5,2]],[6,6,6,6,6,6,6,-2,0,-2,1,1,1,1,0,1,1,1,-2,0,0,0,1,1,-2,0,0,0,0,
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,-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,[2,8]],
[TENSOR,[3,8]],
[TENSOR,[3,9]],
[TENSOR,[5,8]],
[TENSOR,[5,9]],
[TENSOR,[7,8]],[4,4,4,-4,-4,-4*E(4),4*E(4),0,-2,0,-1,-1,-1,-1,2,1,1,1,0,
-2*E(4),2*E(4),-2,-E(4),E(4),0,2,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[15,8]],[4,4,4,-4,-4,-4*E(4),4*E(4),0,1,0,-1,-1,-1,-1,-1,1,1,1,0,E(4),
-E(4),1,-E(4),E(4),0,-1,0,0,0,0,0,0,0,0,-E(24)^11+E(24)^19,-E(24)+E(24)^17,
E(24)^11-E(24)^19,E(24)-E(24)^17],
[TENSOR,[17,2]],
[TENSOR,[17,9]],
[TENSOR,[17,8]],[6,6,6,-6,-6,-6*E(4),6*E(4),0,0,0,1,1,1,1,0,-1,-1,-1,0,0,0,0,
E(4),-E(4),0,0,-1-E(4),-1+E(4),1+E(4),1-E(4),0,0,-1-E(4),-1+E(4),0,0,0,0],
[TENSOR,[21,2]],
[TENSOR,[21,8]],
[TENSOR,[21,9]],[24,24,-1,0,0,0,0,4,0,0,4,4,4,-1,0,0,0,0,-1,0,0,0,0,0,0,0,-4,
-4,0,0,0,0,1,1,0,0,0,0],
[TENSOR,[25,2]],
[TENSOR,[25,8]],
[TENSOR,[25,9]],[96,96,-4,0,0,0,0,0,0,0,-4,-4,-4,1,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0],[20,-5,0,4,-1,0,0,0,-4,-4,0,-5,5,0,4,4,-1,-1,0,0,0,1,0,
0,1,-1,0,0,0,0,0,0,0,0,0,0,0,0],[40,-10,0,-8,2,0,0,0,4,0,10,0,-5,0,4,2,2,-3,0,
0,0,-1,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0],[40,-10,0,-8,2,0,0,0,4,0,-10,5,0,0,4,
2,-3,2,0,0,0,-1,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0],[60,-15,0,12,-3,0,0,0,0,4,
10,-5,0,0,0,2,-3,2,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0],[60,-15,0,12,-3,
0,0,0,0,4,-10,0,5,0,0,2,2,-3,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0],[80,
-20,0,-16,4,0,0,0,-4,0,0,5,-5,0,-4,4,-1,-1,0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,
0,0,0],[80,-20,0,16,-4,0,0,0,-4,0,0,5,-5,0,4,-4,1,1,0,0,0,1,0,0,0,-1,0,0,0,0,
0,0,0,0,0,0,0,0],[100,-25,0,20,-5,0,0,0,4,-4,0,0,0,0,-4,0,0,0,0,0,0,-1,0,0,1,
1,0,0,0,0,0,0,0,0,0,0,0,0],[120,-30,0,-24,6,0,0,0,0,0,0,-5,5,0,0,-4,1,1,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]],
[(35,37)(36,38),( 6, 7)(20,21)(23,24)(27,28)(29,30)(31,32)(33,34)(35,36)
(37,38)]);
ARC("5^(1+2):GL2(5)","CAS",[rec(name:="a",
permchars:=( 2, 3, 9, 4,11,12,16,13,17, 8)( 5,20)( 6,19, 7,18)(14,15)
(21,22,24)(25,27,28,26)(31,35)(32,36)(33,38,34,37),
permclasses:=( 4,11)( 5,12, 6,15,29,24,26,30,23,25,22,28,19,14, 7,16, 8,13)
( 9,27,17,10,21,33,18)(20,34)(31,32)(36,37))]);
ALF("5^(1+2):GL2(5)","Co1",[1,17,16,2,42,11,11,4,7,11,17,15,16,17,21,42,
38,41,43,52,52,65,73,73,73,93,14,14,14,14,33,33,72,72,85,85,85,85],[
"fusion map is unique"
]);
ALF("5^(1+2):GL2(5)","gl25",[1,1,1,3,3,2,4,10,20,13,5,5,5,5,18,7,7,7,10,
16,23,20,8,6,13,18,11,9,12,14,17,21,11,9,15,19,22,24]);
ALN("5^(1+2):GL2(5)",["Co1N5C","a"]);
MOT("5^2:2A5",
[
"origin: Dixon's Algorithm,\n",
"21st maximal subgroup of Co1,\n",
"table is sorted w.r. to normal series 5^2.2.A5"
],
[3000,125,120,4,6,6,25,25,50,10,25,25,50,10],
[,[1,2,1,3,5,5,11,12,13,13,8,7,9,9],[1,2,3,4,1,3,12,11,13,14,7,8,9,10],,[1,1,
3,4,5,6,1,1,1,3,1,1,1,3],,[1,2,3,4,5,6,11,12,13,14,8,7,9,10]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1],[3,3,3,-1,0,0,-E(5)-E(5)^4,-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,
-E(5)^2-E(5)^3],
[GALOIS,[2,2]],[4,4,4,0,1,1,-1,-1,-1,-1,-1,-1,-1,-1],[5,5,5,1,-1,-1,0,0,0,0,0,
0,0,0],[2,2,-2,0,-1,1,E(5)+E(5)^4,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,-E(5)^2-E(5)^3],
[GALOIS,[6,2]],[4,4,-4,0,1,-1,-1,-1,-1,1,-1,-1,-1,1],[6,6,-6,0,0,0,1,1,1,-1,1,
1,1,-1],[24,-1,0,0,0,0,-1,-1,4,0,-1,-1,4,0],[24,-1,0,0,0,0,E(5)-E(5)^2-E(5)^4,
-E(5)-E(5)^3+E(5)^4,2*E(5)^2+2*E(5)^3,0,E(5)^2-E(5)^3-E(5)^4,
-E(5)-E(5)^2+E(5)^3,2*E(5)+2*E(5)^4,0],
[GALOIS,[11,4]],
[GALOIS,[11,3]],
[GALOIS,[11,2]]],
[( 7,11, 8,12)( 9,13)(10,14)]);
ALF("5^2:2A5","Co1",[1,17,4,14,8,26,17,17,16,43,17,17,16,43],[
"fusion map is unique"
]);
ALF("5^2:2A5","2.A5",[1,1,2,3,4,5,6,6,6,7,8,8,8,9]);
MOT("5^3:(4xS5)",
[
"origin: Dixon's Algorithm,\n",
"20th maximal subgroup of Co1,\n",
"table is sorted w.r. to normal series 5^3.2.2.A5.2,\n",
"tests: 1.o.r., pow[2,3,5]"
],
[60000,2500,1500,1000,480,480,480,800,160,100,100,100,40,32,32,120,24,30,24,
24,100,25,20,20,20,1200,240,100,100,60,48,48,80,16,20,80,80,20,20,120,24,30,
24,24],
[,[1,2,3,4,1,5,5,1,1,2,3,4,4,5,5,16,16,18,17,17,21,22,21,23,23,1,1,3,4,3,5,5,
9,9,13,8,8,10,10,16,16,18,17,17],[1,2,3,4,5,7,6,8,9,10,11,12,13,15,14,1,5,3,7,
6,21,22,23,25,24,26,27,28,29,30,32,31,33,34,35,37,36,39,38,27,26,30,31,32],,[
1,1,1,1,5,6,7,8,9,8,8,8,9,14,15,16,17,16,19,20,1,1,5,6,7,26,27,26,26,27,31,32,
33,34,33,36,37,36,37,40,41,40,43,44]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-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,-2,-2,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[4,4,4,4,
4,4,4,0,0,0,0,0,0,0,0,1,1,1,1,1,-1,-1,-1,-1,-1,2,2,2,2,2,2,2,0,0,0,0,0,0,0,-1,
-1,-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,-1,0,0,0,0,0,1,1,1,
1,1,1,1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1],
[TENSOR,[6,2]],[1,1,1,1,1,-1,-1,1,1,1,1,1,1,-1,-1,1,1,1,-1,-1,1,1,1,-1,-1,-1,
-1,-1,-1,-1,1,1,-1,-1,-1,1,1,1,1,-1,-1,-1,1,1],
[TENSOR,[2,8]],
[TENSOR,[4,8]],
[TENSOR,[4,9]],
[TENSOR,[6,8]],
[TENSOR,[6,9]],
[TENSOR,[3,8]],[1,1,1,1,-1,E(4),-E(4),-1,1,-1,-1,-1,1,-E(4),E(4),1,-1,1,E(4),
-E(4),1,1,-1,E(4),-E(4),-1,1,-1,-1,1,E(4),-E(4),1,-1,1,-E(4),E(4),-E(4),E(4),
1,-1,1,-E(4),E(4)],
[TENSOR,[15,9]],
[TENSOR,[2,15]],
[TENSOR,[2,16]],
[TENSOR,[4,15]],
[TENSOR,[4,18]],
[TENSOR,[4,16]],
[TENSOR,[4,17]],
[TENSOR,[6,15]],
[TENSOR,[6,18]],
[TENSOR,[6,16]],
[TENSOR,[6,17]],
[TENSOR,[3,15]],
[TENSOR,[3,16]],[24,-1,-6,4,0,0,0,8,0,3,-2,-2,0,0,0,0,0,0,0,0,4,-1,0,0,0,0,0,
0,0,0,0,0,0,0,0,-4,-4,1,1,0,0,0,0,0],
[TENSOR,[29,2]],
[TENSOR,[29,15]],
[TENSOR,[29,16]],[40,-10,5,0,0,0,0,8,0,-2,3,-2,0,0,0,4,0,-1,0,0,0,0,0,0,0,12,
4,-3,2,-1,0,0,0,0,0,0,0,0,0,4,0,-1,0,0],
[TENSOR,[33,17]],
[TENSOR,[33,15]],
[TENSOR,[33,2]],[60,10,0,-5,0,0,0,-8,4,2,2,-3,-1,0,0,0,0,0,0,0,0,0,0,0,0,-12,
0,-2,3,0,0,0,4,0,-1,0,0,0,0,0,0,0,0,0],
[TENSOR,[37,17]],
[TENSOR,[37,2]],
[TENSOR,[37,15]],[80,-20,10,0,0,0,0,0,0,0,0,0,0,0,0,-4,0,1,0,0,0,0,0,0,0,0,8,
0,0,-2,0,0,0,0,0,0,0,0,0,-4,0,1,0,0],
[TENSOR,[41,2]],[96,-4,-24,16,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-4,1,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[120,20,0,-10,0,0,0,0,-8,0,0,0,2,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]],
[( 6, 7)(14,15)(19,20)(24,25)(31,32)(36,37)(38,39)(43,44)]);
ALF("5^3:(4xS5)","Co1",[1,17,15,16,4,14,14,2,4,42,38,41,43,14,14,8,26,63,
57,57,16,17,43,72,72,3,3,39,40,39,14,14,14,14,72,11,11,73,73,25,25,91,57,
57],[
"fusion map is unique"
]);
MOT("A9xS3",
[
"16th maximal subgroup of Co1"
],
0,
0,
0,
[(49,52)(50,53)(51,54),(37,40)(38,41)(39,42)],
["ConstructDirectProduct",[["A9"],["Dihedral",6]]]);
ALF("A9xS3","Co1",[1,8,2,3,25,3,4,26,4,5,8,18,7,8,23,6,8,22,13,56,13,14,
57,14,15,63,38,19,25,19,24,26,24,28,76,60,36,37,69,37,35,70,39,91,39,50,
56,50,61,63,89,61,63,89],[
"fusion map is unique up to table automorphisms"
]);
MOT("a4xs5",
[
"origin: CAS library,\n",
"maximal subgroup of Co3,\n",
"test: restricted characters decompose properly,\n",
"tests: 1.o.r., pow[2,3,5]"
],
0,
0,
0,
[(15,22)(16,23)(17,24)(18,25)(19,26)(20,27)(21,28)],
["ConstructDirectProduct",[["A4"],["A5.2"]],(),(3,7,6,5,4)(10,14,13,12,11)(17,
21,20,19,18)(24,28,27,26,25)]);
ARC("a4xs5","tomfusion",rec(name:="A4xS5",map:=[1,4,8,24,3,13,27,2,6,28,
53,5,19,30,7,33,9,75,32,73,34,7,33,9,75,32,73,34],text:=[
"fusion map is unique"
]));
ALF("a4xs5","Co3",[1,2,6,10,3,7,15,3,3,15,23,3,8,15,5,13,6,31,14,28,15,5,
13,6,31,14,28,15],[
"fusion map is unique, equal to that on the CAS table"
]);
MOT("s3xpsl(2,8).3",
[
"origin: CAS library,\n",
"maximal subgroup of Co3,\n",
"Restricted characters decompose properly.\n",
"tests: 1.o.r., pow[2,3,7]"
],
[9072,144,162,42,54,108,108,36,36,54,54,3024,48,54,14,18,36,36,12,12,18,18,
4536,72,81,21,27,54,54,18,18,27,27],
[,[1,1,3,4,5,7,6,7,6,11,10,1,1,3,4,5,7,6,7,6,11,10,23,23,25,26,27,29,28,29,28,
33,32],[1,2,1,4,3,1,1,2,2,3,3,12,13,12,15,14,12,12,13,13,14,14,1,2,1,4,3,1,1,
2,2,3,3],,,,[1,2,3,1,5,6,7,8,9,10,11,12,13,14,12,16,17,18,19,20,21,22,23,24,
25,23,27,28,29,30,31,32,33]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,
1,E(3),E(3)^2,E(3),E(3)^2,E(3),E(3)^2,1,1,1,1,1,E(3),E(3)^2,E(3),E(3)^2,E(3),
E(3)^2,1,1,1,1,1,E(3),E(3)^2,E(3),E(3)^2,E(3),E(3)^2],
[TENSOR,[2,2]],[7,-1,-2,0,1,1,1,-1,-1,1,1,7,-1,-2,0,1,1,1,-1,-1,1,1,7,-1,-2,0,
1,1,1,-1,-1,1,1],
[TENSOR,[4,2]],
[TENSOR,[4,3]],[21,-3,3,0,0,0,0,0,0,0,0,21,-3,3,0,0,0,0,0,0,0,0,21,-3,3,0,0,0,
0,0,0,0,0],[8,0,-1,1,-1,2,2,0,0,-1,-1,8,0,-1,1,-1,2,2,0,0,-1,-1,8,0,-1,1,-1,2,
2,0,0,-1,-1],
[TENSOR,[8,2]],
[TENSOR,[8,3]],[27,3,0,-1,0,0,0,0,0,0,0,27,3,0,-1,0,0,0,0,0,0,0,27,3,0,-1,0,0,
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],
[TENSOR,[2,12]],
[TENSOR,[2,13]],
[TENSOR,[4,12]],
[TENSOR,[4,13]],
[TENSOR,[4,14]],
[TENSOR,[7,12]],
[TENSOR,[8,12]],
[TENSOR,[8,13]],
[TENSOR,[8,14]],
[TENSOR,[11,12]],[2,2,2,2,2,2,2,2,2,2,2,0,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,
-1,-1,-1,-1,-1,-1],
[TENSOR,[23,2]],
[TENSOR,[23,3]],[14,-2,-4,0,2,2,2,-2,-2,2,2,0,0,0,0,0,0,0,0,0,0,0,-7,1,2,0,-1,
-1,-1,1,1,-1,-1],
[TENSOR,[26,2]],
[TENSOR,[26,3]],[42,-6,6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-21,3,-3,0,0,0,
0,0,0,0,0],[16,0,-2,2,-2,4,4,0,0,-2,-2,0,0,0,0,0,0,0,0,0,0,0,-8,0,1,-1,1,-2,
-2,0,0,1,1],
[TENSOR,[30,2]],
[TENSOR,[30,3]],[54,6,0,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-27,-3,0,1,0,0,
0,0,0,0,0]],
[( 6, 7)( 8, 9)(10,11)(17,18)(19,20)(21,22)(28,29)(30,31)(32,33)]);
ARC("s3xpsl(2,8).3","tomfusion",rec(name:="S3xL2(8):3",map:=[1,3,6,24,29,
8,8,20,20,32,32,2,4,16,46,53,19,19,23,23,58,58,5,15,7,64,33,9,9,22,22,35,
35],text:=[
"fusion map is unique"
]));
ALF("s3xpsl(2,8).3","Co3",[1,3,4,16,20,5,5,14,14,20,20,2,3,12,29,32,13,13,
14,14,32,32,6,15,6,35,21,6,6,15,15,21,21],[
"fusion map is unique, equal to that on the CAS table"
]);
ALF("s3xpsl(2,8).3","L2(8):3x2",[1,3,5,7,9,11,13,15,17,19,21,2,4,6,8,10,
12,14,16,18,20,22,1,3,5,7,9,11,13,15,17,19,21]);
ALF("s3xpsl(2,8).3","3D4(2).3",[1,3,5,11,15,22,23,28,29,32,33,2,3,9,18,19,
26,27,28,29,42,43,4,10,4,20,15,24,25,30,31,32,33],[
"fusion map is unique up to table aut."
]);
MOT("2xCo2",
0,
0,
0,
0,
[(105,107)(106,108),( 91, 93)( 92, 94)(117,119)(118,120),( 85, 87)( 86, 88)],
["ConstructDirectProduct",[["Co2"],["Cyclic",2]],(),()]);
ALF("2xCo2","2.Co1",[1,2,4,3,3,4,6,6,11,12,9,10,15,16,19,18,18,19,17,17,
18,19,20,20,22,22,27,28,25,26,34,35,39,38,33,32,37,36,36,37,40,40,45,46,
48,48,53,52,49,50,51,51,52,53,52,53,59,60,67,68,66,65,69,69,70,71,76,77,
82,83,78,79,84,85,87,88,85,84,82,83,86,86,95,94,94,95,94,95,102,103,104,
105,104,105,107,108,106,106,114,113,119,118,117,117,128,129,130,131,137,
137,139,138,141,142,150,149,151,152,151,152],[
"fusion map is unique up to table aut."
]);
MOT("2xCo3",
0,
0,
0,
0,
[(75,77)(76,78),(65,67)(66,68),(47,49)(48,50)(71,73)(72,74)],
["ConstructDirectProduct",[["Co3"],["Cyclic",2]],(),()]);
ALF("2xCo3","2.Co1",[1,2,3,4,6,6,11,12,9,10,13,14,19,18,18,19,27,28,25,
26,34,35,38,39,36,37,40,40,42,42,45,46,52,53,53,52,52,53,57,58,59,60,67,
68,69,69,70,71,70,71,83,82,82,83,85,84,94,95,104,105,102,103,111,112,119,
118,119,118,124,125,126,127,127,126,128,129,130,131,138,139,139,138,151,
152],[
"fusion map is unique up to table aut."
]);
MOT("2xU6(2).3.2",
0,
0,
0,
0,
[(187,189)(188,190),(137,139)(138,140),
(143,144)(145,146)(147,148)(149,150)(151,152)(153,154)(155,156)(157,158)
(159,160)(161,162)(163,164)(165,166)(167,168)(169,170)(171,172)(173,174)
(175,176)(177,178)(179,180)(181,182)(183,184)(185,186)(187,188)(189,190)
(191,192)(193,194)(195,196)(197,198)
],
["ConstructDirectProduct",[["U6(2).3.2"],["Cyclic",2]],(),()]);
ALF("2xU6(2).3.2","2.Co1",[1,2,4,3,3,4,6,6,9,10,11,12,9,10,15,16,17,17,
18,19,20,20,18,19,25,26,39,38,37,36,34,35,36,37,33,32,36,37,40,40,45,46,
49,50,52,53,59,60,59,60,66,65,70,71,76,77,78,79,87,88,82,83,86,86,102,103,
114,113,7,8,9,10,11,12,13,14,30,29,33,32,29,30,37,36,35,34,32,33,36,37,39,
38,40,40,38,39,42,42,55,56,55,56,57,58,72,73,74,74,78,79,75,75,81,81,76,
77,86,86,88,87,84,85,102,103,98,99,110,109,112,111,124,125,133,134,150,
149,153,154,153,154,157,158,3,4,6,6,19,18,18,19,20,20,32,33,38,39,40,40,
36,37,40,40,48,48,52,53,52,53,53,52,65,66,69,69,85,84,83,82,84,85,85,84,
86,86,94,95,106,106,106,106,113,114,137,137,138,139,149,150],[
"fusion map is unique up to table aut."
]);
MOT("2x3^6:2.M12",
0,
0,
0,
0,
[(105,111)(106,112)(107,113)(108,114)(109,115)(110,116),(101,103)(102,104),
( 85, 89)( 86, 90)( 87, 91)( 88, 92)( 93, 97)( 94, 98)( 95, 99)( 96,100),
( 85, 89)( 86, 90)( 87, 91)( 88, 92)( 93, 97)( 94, 98)( 95, 99)( 96,100)
(101,103)(102,104)
],
["ConstructDirectProduct",[["3^6:2M12"],["Cyclic",2]],(),()]);
ALF("2x3^6:2.M12","2x2.M12",[1,2,1,2,1,2,1,2,3,4,5,6,7,8,7,8,7,8,7,8,7,8,7,
8,9,10,9,10,11,12,11,12,11,12,11,12,11,12,11,12,13,14,15,16,15,16,17,18,
19,20,19,20,19,20,21,22,21,22,21,22,23,24,23,24,23,24,25,26,27,28,29,30,
29,30,29,30,29,30,29,30,31,32,31,32,33,34,33,34,35,36,35,36,37,38,37,38,
39,40,39,40,41,42,43,44,45,46,45,46,47,48,49,50,49,50,51,52]);
ALF("2x3^6:2.M12","2.Co1",[1,2,7,8,9,10,11,12,6,6,22,22,3,4,34,35,32,33,29,
30,36,37,38,39,6,6,40,40,9,10,11,12,13,14,59,60,55,56,57,58,40,40,13,14,
57,58,42,42,20,20,75,75,86,86,18,19,84,85,82,83,25,26,102,103,98,99,69,69,
90,90,36,37,38,39,111,112,109,110,113,114,40,40,42,42,54,54,136,136,54,54,
136,136,52,53,138,139,52,53,138,139,117,117,117,117,70,71,153,154,126,127,
70,71,153,154,127,126],[
"fusion map is unique up to table aut."
]);
MOT("2.A9xS3",
0,
0,
0,
0,
[(79,85)(80,86)(81,87)(82,88)(83,89)(84,90),(73,76)(74,77)(75,78),
(46,49)(47,50)(48,51),
(46,49)(47,50)(48,51)(73,76)(74,77)(75,78)(79,85)(80,86)(81,87)(82,88)(83,89)
(84,90)
,
( 3, 6)(15,18)(21,24)(27,30)(39,42)(48,51)(54,57)(60,63)(66,69)(75,78)(81,84)
(87,90)
,(58,64)(59,65)(60,66)(61,67)(62,68)(63,69)],
["ConstructDirectProduct",[["2.A9"],["S3"]],(),()]);
ALF("2.A9xS3","A9xS3",[1,2,3,1,2,3,4,5,6,7,8,9,10,11,12,10,11,12,13,14,15,
13,14,15,16,17,18,16,17,18,19,20,21,22,23,24,25,26,27,25,26,27,28,29,30,
31,32,33,31,32,33,34,35,36,34,35,36,37,38,39,37,38,39,40,41,42,40,41,42,
43,44,45,46,47,48,46,47,48,49,50,51,49,50,51,52,53,54,52,53,54]);
ALF("2.A9xS3","2.Co1",[1,13,3,2,14,4,5,41,5,6,42,6,7,13,29,8,14,30,11,13,
38,12,14,39,9,13,36,10,14,37,21,89,21,22,90,22,23,100,61,24,101,62,31,41,
31,40,42,40,40,42,40,45,124,94,46,125,95,57,59,111,58,60,112,59,55,113,60,
56,114,63,148,63,80,89,80,80,89,80,96,100,145,97,101,146,96,100,145,97,
101,146],[
"fusion map is unique up to table aut."
]);
MOT("2x5^2:2A5",
0,
0,
0,
0,
[(13,21,15,23)(14,22,16,24)(17,25)(18,26)(19,27)(20,28),
(13,15)(14,16)(21,23)(22,24)],
["ConstructDirectProduct",[["5^2:2A5"],["Cyclic",2]],(),()]);
ALF("2x5^2:2A5","2.Co1",[1,2,27,28,6,6,22,22,13,14,42,42,27,28,27,28,25,
26,69,69,27,28,27,28,25,26,69,69],[
"fusion map is unique"
]);
LIBTABLE.LOADSTATUS.ctomaxi3:="userloaded";
#############################################################################
##
#E
