|
#############################################################################
##
#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,
-1,-1,-1,-1,2,2,0,0,0,0,0,0,5,5,0,0,0,0,0,1,0,0,0,0,0,0,0,-1,-1,0,0,0,0,0],[
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--> --------------------
--> maximum size reached
--> --------------------
[ Dauer der Verarbeitung: 0.18 Sekunden
(vorverarbeitet)
]
|
