#############################################################################
##
#W ctounit1.tbl GAP table library Thomas Breuer
##
## This file contains the ordinary character tables of groups related to
## the unitary group $U_4(3)$ of the ATLAS.
##
#H ctbllib history
#H ---------------
#H $Log: ctounit1.tbl,v $
#H Revision 4.47 2012/04/23 16:16:16 gap
#H next step of consolidation:
#H
#H - removed a few unnecessary duplicate tables,
#H and changed some related fusions, names of maxes, table constructions
#H - make sure that duplicate tables arise only via `ConstructPermuted'
#H constructions
#H - added some relative names
#H - added fusions A11.2 -> A12.2, L2(11).2 -> A12.2, D8x2F4(2)'.2 -> B,
#H L2(41) -> M, (A5xA12):2 -> A17,
#H - added maxes of A12.2, L6(2), 2.M22.2
#H - added table of QD16.2,
#H - fixed the syntax of two `ALN' calls
#H TB
#H
#H Revision 4.46 2012/03/28 13:14:00 gap
#H added table of 6_1.U4(3).2_2'
#H TB
#H
#H Revision 4.45 2012/03/12 17:01:48 gap
#H omit the fourth argument of `ConstructV4G'
#H TB
#H
#H Revision 4.44 2012/03/02 08:19:35 gap
#H - added the tables of 2.U4(3).(2^2)_{133},
#H - encode some tables of 2.U4(3).(2^2)_{122} via `ConstructIsoclinic',
#H TB
#H
#H Revision 4.43 2012/01/30 08:32:04 gap
#H removed #H entries from the headers
#H TB
#H
#H Revision 4.42 2011/09/28 14:17:09 gap
#H - removed revision entry and SET_TABLEFILENAME call,
#H - added fusion Isoclinic(2.U4(3).2_1) -> 3^6:2U4(3).2_1
#H TB
#H
#H Revision 4.41 2010/12/01 17:52:14 gap
#H - tomfusion of "U4(3).2_1" needs the permutation (3,4)
#H - fusion U4(3).2_3' -> U4(3).(2^2)_{133} is relative to the fusion
#H U4(3).2_3 -> U4(3).(2^2)_{133} (w.r.t. the automorphism induced by
#H U4(3).D8)
#H - added tables of "(3^2x2).U4(3)" and "(3^2x4).U4(3)"
#H (Eamonn had asked for them)
#H
#H TB
#H
#H Revision 4.40 2010/11/15 16:32:26 gap
#H replaced some fusions to U4(3).2_3 by fusions to U4(3).2_3',
#H added comments
#H TB
#H
#H Revision 4.39 2010/09/15 08:11:28 gap
#H added the fusion 6_2.U4(3).2_3' -> U4(3).2_3',
#H adjusted the mapping between the maxes and the corresponding information
#H in the table of marks of U4(3) and U4(3).(2^2)_{133}
#H TB
#H
#H Revision 4.38 2010/05/05 13:20:09 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 4.37 2010/01/19 17:05:35 gap
#H added several tables of maximal subgroups of central extensions of
#H simple groups (many of them were contributed by S. Dany)
#H TB
#H
#H Revision 4.36 2009/04/22 12:39:08 gap
#H added missing maxes of He.2, ON.2, HN.2, Fi24, and B
#H TB
#H
#H Revision 4.35 2006/06/07 07:54:27 gap
#H unified ConstructMixed and ConstructMGA (for better programmatic access)
#H TB
#H
#H Revision 4.34 2005/09/14 08:31:28 gap
#H changed fusion 2.U4(3).2_2 -> O7(3) such that the fusion is compatible
#H with 12_1.U4(3).2_2 -> 6.O7(3)
#H TB
#H
#H Revision 4.33 2005/08/10 14:39:55 gap
#H corrected InfoText values of GV4 constructed tables
#H TB
#H
#H Revision 4.32 2004/11/24 15:20:20 gap
#H added missing maxes of U4(3) --Max had asked for them--
#H and their class fusions,
#H fixed construction entry for "(2xA6).2^2",
#H fixed fusion "2.U4(3).2_2' -> U4(3).2_2"
#H TB
#H
#H Revision 4.31 2004/08/31 12:33:34 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 4.30 2004/03/30 08:55:58 gap
#H (name change also in a factor fusion)
#H TB
#H
#H Revision 4.29 2004/03/30 08:05:55 gap
#H unified tables `u4q3:2^2' and `U4(3).(2^2)_{133}'
#H TB
#H
#H Revision 4.28 2004/01/20 10:26:13 gap
#H added several names of the forms `<name>C<class>', `<name>N<class>'
#H TB
#H
#H Revision 4.27 2003/10/06 07:18:17 gap
#H added fusion 2.U4(3).(2^2)_{122} -> 2^2.U4(3).(2^2)_{122}
#H TB
#H
#H Revision 4.26 2003/07/28 15:31:22 gap
#H added some fusions concerning maxes of 6.U6(2)
#H TB
#H
#H Revision 4.25 2003/06/10 16:19:16 gap
#H store in several fusions between character tables to which subgroup number
#H in the table of marks of the supergroup the subgroup belongs
#H (in order to make the commutative diagrams testable)
#H TB
#H
#H Revision 4.24 2003/05/15 17:38:27 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 4.23 2003/01/14 17:28:50 gap
#H changed `InfoText' values (for a better programmatic access)
#H and replaced `ConstructDirectProduct' by `ConstructPermuted' where
#H there is only one factor (again better programmatic handling)
#H TB
#H
#H Revision 4.22 2002/10/22 12:44:15 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 4.21 2002/10/14 15:20:18 gap
#H added two fusion texts
#H TB
#H
#H Revision 4.20 2002/09/23 15:07:22 gap
#H changed comment of the fusion U4(3).2_2 -> Fi22
#H TB
#H
#H Revision 4.19 2002/09/18 15:22:02 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 4.18 2002/08/21 13:53:52 gap
#H removed names of the form `c1m<n>', `c2m<n>', `c3m<n>'
#H TB
#H
#H Revision 4.17 2002/07/12 06:45:57 gap
#H further tidying up: removed `irredinfo' stuff, rearranged constructions
#H TB
#H
#H Revision 4.16 2002/07/08 16:06:57 gap
#H changed `construction' component from function (call) to list of function
#H name and arguments
#H TB
#H
#H Revision 4.15 2001/05/04 16:50:33 gap
#H first revision for ctbllib
#H
#H
#H tbl history (GAP 4)
#H -------------------
#H (Rev. 4.15 of ctbllib coincides with Rev. 4.14 of tbl in GAP 4)
#H
#H RCS file: /gap/CVS/GAP/4.0/tbl/ctounit1.tbl,v
#H Working file: ctounit1.tbl
#H head: 4.14
#H branch:
#H locks: strict
#H access list:
#H symbolic names:
#H GAP4R2: 4.12.0.6
#H GAP4R2PRE2: 4.12.0.4
#H GAP4R2PRE1: 4.12.0.2
#H GAP4R1: 4.6.0.2
#H keyword substitution: kv
#H total revisions: 16; selected revisions: 16
#H description:
#H ----------------------------
#H revision 4.14
#H date: 2000/10/09 17:21:50; author: gap; state: Exp; lines: +45 -44
#H added tables of 3_1.U4(3).2_2' and F3+M9
#H
#H TB
#H ----------------------------
#H revision 4.13
#H date: 2000/05/13 12:15:28; author: gap; state: Exp; lines: +434 -2
#H added some maxes of 6.Suz: [1,2,4,6,9,10,11,14,16]
#H
#H TB
#H ----------------------------
#H revision 4.12
#H date: 1999/10/21 14:15:49; author: gap; state: Exp; lines: +21 -3
#H added many `tomidentifer' and `tomfusion' values, which yields a better
#H interface between `tom' and `tbl';
#H
#H added maxes of McL.2,
#H
#H unified tables `J2.2M4', `2^(2+4):(3x3):2^2', `2^(2+4):(S3xS3)'.
#H
#H TB
#H ----------------------------
#H revision 4.11
#H date: 1999/09/17 14:11:52; author: gap; state: Exp; lines: +127 -69
#H added maxes of 3.Suz.2
#H
#H TB
#H ----------------------------
#H revision 4.10
#H date: 1999/09/14 13:30:12; author: gap; state: Exp; lines: +2 -3
#H added maxes of 3.Suz
#H
#H TB
#H ----------------------------
#H revision 4.9
#H date: 1999/08/31 13:16:16; author: gap; state: Exp; lines: +45 -2
#H added missing tables and fusions of maximal subgroups of Suz.2
#H
#H TB
#H ----------------------------
#H revision 4.8
#H date: 1999/08/23 10:26:59; author: gap; state: Exp; lines: +6 -2
#H unified tables of U3(5).S3 and U3(5).3.2
#H (one CAS table, o ne ATLAS conformal table)
#H
#H TB
#H ----------------------------
#H revision 4.7
#H date: 1999/08/18 13:59:08; author: gap; state: Exp; lines: +73 -2
#H added table of U4(3).(2^2)_{133}, and related fusions
#H
#H TB
#H ----------------------------
#H revision 4.6
#H date: 1999/06/15 13:49:34; author: gap; state: Exp; lines: +22 -2
#H added table of 2.SuzM2 (request of a student)
#H
#H TB
#H ----------------------------
#H revision 4.5
#H date: 1999/05/31 13:28:30; author: gap; state: Exp; lines: +225 -9
#H added table of 2.U4(3).(2^2)_{122}
#H
#H TB
#H ----------------------------
#H revision 4.4
#H date: 1999/05/03 15:35:18; author: gap; state: Exp; lines: +55 -11
#H added tables of 2.U4(3).2_3' and 6_2.U4(3).2_3'
#H (requested by a student in Aachen)
#H
#H TB
#H ----------------------------
#H revision 4.3
#H date: 1997/11/25 15:46:01; author: gap; state: Exp; lines: +12 -9
#H first attempt to link the library of character tables and the
#H library of tables of marks
#H TB
#H ----------------------------
#H revision 4.2
#H date: 1997/08/05 15:03:59; author: gap; state: Exp; lines: +5 -5
#H removed unnecessary (and ugly) `return' statements in the calls of
#H `ConstructPermuted' and `ConstructSubdirect'
#H ----------------------------
#H revision 4.1
#H date: 1997/07/17 15:48:15; author: fceller; state: Exp; lines: +2 -2
#H for version 4
#H ----------------------------
#H revision 1.2
#H date: 1997/04/04 12:20:32; author: sam; state: Exp; lines: +7 -23
#H added 'ConstructPermuted', 'ConstructSubdirect',
#H changed table constructions involving 'CharTable', 'RecFields'
#H 'Sort...' up to now
#H ----------------------------
#H revision 1.1
#H date: 1996/10/21 16:02:03; author: sam; state: Exp;
#H first proposal of the table library
#H ==========================================================================
##
MOT("12_1.U4(3)",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[39191040,39191040,39191040,39191040,39191040,39191040,39191040,39191040,
39191040,39191040,39191040,39191040,6912,6912,6912,6912,6912,6912,69984,69984,
69984,69984,69984,69984,69984,69984,69984,69984,69984,69984,11664,11664,11664,
11664,11664,11664,11664,11664,11664,11664,11664,11664,3888,3888,3888,3888,324,
324,324,324,1152,1152,1152,1152,1152,1152,1152,1152,1152,1152,1152,1152,48,48,
48,60,60,60,60,60,60,60,60,60,60,60,60,864,864,864,864,864,864,864,864,864,
864,864,864,216,216,216,216,216,216,216,216,216,216,216,216,84,84,84,84,84,84,
84,84,84,84,84,84,84,84,84,84,84,84,84,84,84,84,84,84,96,96,96,96,96,96,96,96,
96,96,96,96,324,324,324,324,324,324,324,324,324,324,324,324,324,324,324,324,
324,324,324,324,324,324,324,324,108,108,108,108,108,108,108,108,144,144,144,
144,144,144,144,144,144,144,144,144],
[,[1,3,5,7,9,11,1,3,5,7,9,11,1,3,5,7,9,11,19,21,23,25,27,29,19,21,23,25,27,29,
31,33,35,37,39,41,31,33,35,37,39,41,43,45,43,45,47,49,47,49,13,15,17,13,15,17,
13,15,17,13,15,17,16,18,14,66,68,70,72,74,76,66,68,70,72,74,76,19,21,23,25,27,
29,19,21,23,25,27,29,31,33,35,37,39,41,43,45,43,45,43,45,102,104,106,108,110,
112,102,104,106,108,110,112,114,116,118,120,122,124,114,116,118,120,122,124,
60,62,52,54,56,58,60,62,52,54,56,58,150,152,154,156,158,160,150,152,154,156,
158,160,138,140,142,144,146,148,138,140,142,144,146,148,166,168,166,168,162,
164,162,164,78,80,82,84,86,88,78,80,82,84,86,88],[1,4,7,10,1,4,7,10,1,4,7,10,
13,16,13,16,13,16,1,4,7,10,1,4,7,10,1,4,7,10,1,4,7,10,1,4,7,10,1,4,7,10,1,4,7,
10,1,4,7,10,51,54,57,60,51,54,57,60,51,54,57,60,63,63,63,66,69,72,75,66,69,72,
75,66,69,72,75,13,16,13,16,13,16,13,16,13,16,13,16,13,16,13,16,13,16,13,16,13,
16,13,16,114,117,120,123,114,117,120,123,114,117,120,123,102,105,108,111,102,
105,108,111,102,105,108,111,129,132,135,126,129,132,135,126,129,132,135,126,
27,30,21,24,27,30,21,24,27,30,21,24,23,26,29,20,23,26,29,20,23,26,29,20,19,22,
25,28,19,22,25,28,51,54,57,60,51,54,57,60,51,54,57,60],,[1,6,11,4,9,2,7,12,5,
10,3,8,13,18,17,16,15,14,19,24,29,22,27,20,25,30,23,28,21,26,31,36,41,34,39,
32,37,42,35,40,33,38,43,44,45,46,47,48,49,50,51,56,61,54,59,52,57,62,55,60,53,
58,63,65,64,1,6,11,4,9,2,7,12,5,10,3,8,78,83,88,81,86,79,84,89,82,87,80,85,90,
95,94,93,92,91,96,101,100,99,98,97,114,119,124,117,122,115,120,125,118,123,
116,121,102,107,112,105,110,103,108,113,106,111,104,109,126,131,136,129,134,
127,132,137,130,135,128,133,150,155,160,153,158,151,156,161,154,159,152,157,
138,143,148,141,146,139,144,149,142,147,140,145,166,167,168,169,162,163,164,
165,170,175,180,173,178,171,176,181,174,179,172,177],,[1,8,3,10,5,12,7,2,9,4,
11,6,13,14,15,16,17,18,19,26,21,28,23,30,25,20,27,22,29,24,31,38,33,40,35,42,
37,32,39,34,41,36,43,46,45,44,47,50,49,48,51,58,53,60,55,62,57,52,59,54,61,56,
63,64,65,66,73,68,75,70,77,72,67,74,69,76,71,78,85,80,87,82,89,84,79,86,81,88,
83,90,91,92,93,94,95,96,97,98,99,100,101,1,8,3,10,5,12,7,2,9,4,11,6,1,8,3,10,
5,12,7,2,9,4,11,6,129,136,131,126,133,128,135,130,137,132,127,134,138,145,140,
147,142,149,144,139,146,141,148,143,150,157,152,159,154,161,156,151,158,153,
160,155,162,165,164,163,166,169,168,167,170,177,172,179,174,181,176,171,178,
173,180,175]],
0,
[(162,166)(163,167)(164,168)(165,169),(102,114)(103,115)(104,116)(105,117)
(106,118)(107,119)(108,120)(109,121)(110,122)(111,123)(112,124)(113,125),
( 2, 6)( 3, 11)( 5, 9)( 8, 12)( 14, 18)( 15, 17)( 20, 24)( 21, 29)
( 23, 27)( 26, 30)( 32, 36)( 33, 41)( 35, 39)( 38, 42)( 52, 56)( 53, 61)
( 55, 59)( 58, 62)( 64, 65)( 67, 71)( 68, 76)( 70, 74)( 73, 77)( 79, 83)
( 80, 88)( 82, 86)( 85, 89)( 91, 95)( 92, 94)( 97,101)( 98,100)(103,107)
(104,112)(106,110)(109,113)(115,119)(116,124)(118,122)(121,125)(127,131)
(128,136)(130,134)(133,137)(138,150)(139,155)(140,160)(141,153)(142,158)
(143,151)(144,156)(145,161)(146,154)(147,159)(148,152)(149,157)(162,166)
(163,167)(164,168)(165,169)(171,175)(172,180)(174,178)(177,181),( 2, 8)
( 4, 10)( 6, 12)( 20, 26)( 22, 28)( 24, 30)( 32, 38)( 34, 40)( 36, 42)
( 44, 46)( 48, 50)( 52, 58)( 54, 60)( 56, 62)( 67, 73)( 69, 75)( 71, 77)
( 79, 85)( 81, 87)( 83, 89)(103,109)(105,111)(107,113)(115,121)(117,123)
(119,125)(126,129)(127,136)(128,131)(130,133)(132,135)(134,137)(139,145)
(141,147)(143,149)(151,157)(153,159)(155,161)(163,165)(167,169)(171,177)
(173,179)(175,181),( 2, 6)( 3, 11)( 5, 9)( 8, 12)( 14, 18)( 15, 17)
( 20, 24)( 21, 29)( 23, 27)( 26, 30)( 32, 36)( 33, 41)( 35, 39)( 38, 42)
( 52, 56)( 53, 61)( 55, 59)( 58, 62)( 64, 65)( 67, 71)( 68, 76)( 70, 74)
( 73, 77)( 79, 83)( 80, 88)( 82, 86)( 85, 89)( 91, 95)( 92, 94)( 97,101)
( 98,100)(103,107)(104,112)(106,110)(109,113)(115,119)(116,124)(118,122)
(121,125)(127,131)(128,136)(130,134)(133,137)(138,150)(139,155)(140,160)
(141,153)(142,158)(143,151)(144,156)(145,161)(146,154)(147,159)(148,152)
(149,157)(171,175)(172,180)(174,178)(177,181)],
["ConstructProj",[["U4(3)",[]],["2.U4(3)",[]],["3_1.U4(3)",[-1,-1,-1,-1,-1,-1,
-1,-1,-13,-13,-1,-1,-1,-1,-1,-1]],["4.U4(3)",[-1,-1,-1,7,7,7,7,-1,-1,-1,-1,-1,
15,15,-1,-1]],,["6_1.U4(3)",[-1,-1,-1,-1,-1,-13,-13,-1,-1,-1,-1,-7,-7,-1,
-1]],,,,,,["12_1.U4(3)",[[-7,7,-1],[-7,7,-1],[-7,7,-1],[-7,7,-1],[-7,7,-1],[
-7,7,-1],[-55,-377,-433],[-55,-377,-433],[-7,7,-1],[-7,7,-1],[-7,7,-1],[-7,7,
-1]]]]]);
ALF("12_1.U4(3)","U4(3)",[1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,
3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,
7,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,10,10,10,11,11,
11,11,11,11,12,12,12,12,12,12,13,13,13,13,13,13,13,13,13,13,13,13,14,14,
14,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,15,15,15,15,15,16,16,
16,16,16,16,16,16,16,16,16,16,17,17,17,17,17,17,17,17,17,17,17,17,18,18,
18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,20]);
ALF("12_1.U4(3)","2.U4(3)",[1,2,1,2,1,2,1,2,1,2,1,2,3,4,3,4,3,4,5,6,5,6,5,
6,5,6,5,6,5,6,7,8,7,8,7,8,7,8,7,8,7,8,9,10,9,10,11,12,11,12,13,14,13,14,
13,14,13,14,13,14,13,14,15,15,15,16,17,16,17,16,17,16,17,16,17,16,17,18,
19,18,19,18,19,18,19,18,19,18,19,20,21,20,21,20,21,22,23,22,23,22,23,24,
25,24,25,24,25,24,25,24,25,24,25,26,27,26,27,26,27,26,27,26,27,26,27,28,
29,28,29,28,29,28,29,28,29,28,29,30,31,30,31,30,31,30,31,30,31,30,31,32,
33,32,33,32,33,32,33,32,33,32,33,34,35,34,35,36,37,36,37,38,39,38,39,38,
39,38,39,38,39,38,39]);
ALF("12_1.U4(3)","4.U4(3)",[1,2,3,4,1,2,3,4,1,2,3,4,5,6,5,6,5,6,7,8,9,10,
7,8,9,10,7,8,9,10,11,12,13,14,11,12,13,14,11,12,13,14,15,16,17,18,19,20,
21,22,23,24,25,26,23,24,25,26,23,24,25,26,27,27,27,28,29,30,31,28,29,30,
31,28,29,30,31,32,33,34,35,32,33,34,35,32,33,34,35,36,37,36,37,36,37,38,
39,38,39,38,39,40,41,42,43,40,41,42,43,40,41,42,43,44,45,46,47,44,45,46,
47,44,45,46,47,48,49,50,51,48,49,50,51,48,49,50,51,52,53,54,55,52,53,54,
55,52,53,54,55,56,57,58,59,56,57,58,59,56,57,58,59,60,61,62,63,64,65,66,
67,68,69,70,71,68,69,70,71,68,69,70,71]);
ALF("12_1.U4(3)","3_1.U4(3)",[1,2,3,1,2,3,1,2,3,1,2,3,4,5,6,4,5,6,7,8,9,7,
8,9,7,8,9,7,8,9,10,11,12,10,11,12,10,11,12,10,11,12,13,13,13,13,14,14,14,
14,15,16,17,15,16,17,15,16,17,15,16,17,18,19,20,21,22,23,21,22,23,21,22,
23,21,22,23,24,25,26,24,25,26,24,25,26,24,25,26,27,28,29,27,28,29,30,31,
32,30,31,32,33,34,35,33,34,35,33,34,35,33,34,35,36,37,38,36,37,38,36,37,
38,36,37,38,39,40,41,39,40,41,39,40,41,39,40,41,42,43,44,42,43,44,42,43,
44,42,43,44,45,46,47,45,46,47,45,46,47,45,46,47,48,48,48,48,49,49,49,49,
50,51,52,50,51,52,50,51,52,50,51,52]);
ALF("12_1.U4(3)","6_1.U4(3)",[1,2,3,4,5,6,1,2,3,4,5,6,7,8,9,10,11,12,13,
14,15,16,17,18,13,14,15,16,17,18,19,20,21,22,23,24,19,20,21,22,23,24,25,
26,25,26,27,28,27,28,29,30,31,32,33,34,29,30,31,32,33,34,35,36,37,38,39,
40,41,42,43,38,39,40,41,42,43,44,45,46,47,48,49,44,45,46,47,48,49,50,51,
52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,62,63,64,65,66,67,68,69,
70,71,72,73,68,69,70,71,72,73,74,75,76,77,78,79,74,75,76,77,78,79,80,81,
82,83,84,85,80,81,82,83,84,85,86,87,88,89,90,91,86,87,88,89,90,91,92,93,
92,93,94,95,94,95,96,97,98,99,100,101,96,97,98,99,100,101]);
ALF("12_1.U4(3)","12_1.U4(3).2_1",[1,2,3,4,5,2,6,7,5,8,3,7,9,10,11,12,11,
10,13,14,15,16,17,14,18,19,17,20,15,19,21,22,23,24,25,22,26,27,25,28,23,
27,29,30,31,32,33,34,35,36,37,38,39,40,41,38,42,43,41,44,39,43,45,46,46,
47,48,49,50,51,48,52,53,51,54,49,53,55,56,57,58,59,56,60,61,59,62,57,61,
63,64,65,66,65,64,67,68,69,70,69,68,71,72,73,74,75,72,76,77,75,78,73,77,
79,80,81,82,83,80,84,85,83,86,81,85,87,88,89,90,91,88,92,93,91,94,89,93,
95,96,97,98,99,100,101,102,103,104,105,106,95,100,105,98,103,96,101,106,
99,104,97,102,107,108,109,110,107,108,109,110,111,112,113,114,115,112,116,
117,115,118,113,117],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);
ALF("12_1.U4(3)","12_1.U4(3).2_2",[1,2,3,4,5,6,7,2,8,4,9,6,10,11,12,13,14,
15,16,17,18,19,20,21,22,17,23,19,24,21,25,26,27,28,29,30,31,26,32,28,33,
30,34,35,36,35,37,38,39,38,40,41,42,43,44,45,46,41,47,43,48,45,49,50,51,
52,53,54,55,56,57,58,53,59,55,60,57,61,62,63,64,65,66,67,62,68,64,69,66,
70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,
82,89,84,91,86,93,88,83,90,85,92,87,94,95,96,94,97,96,98,97,99,98,95,99,
100,101,102,103,104,105,106,101,107,103,108,105,109,110,111,112,113,114,
115,110,116,112,117,114,118,119,120,121,118,121,120,119,122,123,124,125,
126,127,128,123,129,125,130,127],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);
ALF("12_1.U4(3)","12_1.U4(3).2_2'",[1,2,3,4,5,6,7,6,5,4,3,2,8,9,10,11,10,
9,12,13,14,15,16,17,18,17,16,15,14,13,19,20,21,22,23,24,25,24,23,22,21,20,
26,27,28,27,29,30,31,30,32,33,34,35,36,37,38,37,36,35,34,33,39,40,40,41,
42,43,44,45,46,47,46,45,44,43,42,48,49,50,51,52,53,54,53,52,51,50,49,55,
56,57,58,57,56,59,60,61,62,61,60,63,64,65,66,67,68,69,70,71,72,73,74,63,
74,73,72,71,70,69,68,67,66,65,64,75,76,76,75,77,78,79,80,80,79,78,77,81,
82,83,84,85,86,87,88,89,90,91,92,81,92,91,90,89,88,87,86,85,84,83,82,93,
94,95,94,96,97,98,97,99,100,101,102,103,104,105,104,103,102,101,100]);
MOT("12_1.U4(3).2_1",
[
"origin: ATLAS of finite groups, tests: 1.o.r."
],
[78382080,39191040,39191040,78382080,39191040,78382080,39191040,78382080,
13824,6912,6912,13824,139968,69984,69984,139968,69984,139968,69984,139968,
23328,11664,11664,23328,11664,23328,11664,23328,7776,7776,7776,7776,648,648,
648,648,2304,1152,1152,2304,1152,2304,1152,2304,96,48,120,60,60,120,60,120,60,
120,1728,864,864,1728,864,1728,864,1728,432,216,216,432,432,216,216,432,168,
84,84,168,84,168,84,168,168,84,84,168,84,168,84,168,192,96,96,192,96,192,96,
192,324,324,324,324,324,324,324,324,324,324,324,324,108,108,108,108,288,144,
144,288,144,288,144,288,48384,48384,48384,48384,2880,2880,4608,4608,4608,4608,
128,864,864,864,864,72,72,72,72,72,72,72,72,64,64,64,64,40,40,40,40,576,576,
576,576,576,576,576,576,144,144,144,144,144,144,144,144,56,56,56,56,56,56,56,
56],
[,[1,3,5,6,5,1,3,6,1,3,5,6,13,15,17,18,17,13,15,18,21,23,25,26,25,21,23,26,29,
31,29,31,33,35,33,35,9,11,11,9,11,9,11,9,12,10,47,49,51,52,51,47,49,52,13,15,
17,18,17,13,15,18,21,23,25,26,29,31,29,31,71,73,75,76,75,71,73,76,79,81,83,84,
83,79,81,84,44,43,38,40,38,44,43,40,95,105,103,101,99,97,95,105,103,101,99,97,
107,109,107,109,55,57,59,60,59,55,57,60,1,6,1,6,8,4,9,9,9,9,9,13,18,13,18,28,
24,30,32,33,35,33,35,40,44,40,44,54,50,54,50,55,60,55,60,60,55,60,55,63,63,63,
63,67,67,67,67,71,76,71,76,79,84,79,84],[1,4,6,8,1,6,8,4,9,12,9,12,1,4,6,8,1,
6,8,4,1,4,6,8,1,6,8,4,1,4,6,8,1,4,6,8,37,40,42,44,37,42,44,40,45,45,47,50,52,
54,47,52,54,50,9,12,9,12,9,9,12,12,9,12,9,12,9,12,9,12,79,82,84,86,79,84,86,
82,71,74,76,78,71,76,78,74,90,92,94,87,90,94,87,92,17,19,15,14,17,19,15,14,17,
19,15,14,13,16,18,20,37,40,42,44,37,42,44,40,119,122,121,120,124,123,128,127,
126,125,129,119,122,121,120,124,123,124,123,119,122,121,120,145,144,143,142,
149,148,147,146,128,127,126,125,128,127,126,125,128,127,126,125,128,127,126,
125,170,173,172,171,166,169,168,167],,[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,
43,44,45,46,1,2,3,4,5,6,7,8,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,
79,80,81,82,83,84,85,86,71,72,73,74,75,76,77,78,87,88,89,90,91,92,93,94,95,96,
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,
136,137,138,139,140,141,142,143,144,145,123,124,123,124,150,151,152,153,154,
155,156,157,158,159,160,161,162,163,164,165,170,171,172,173,166,167,168,
169],,[1,7,3,8,5,6,2,4,9,10,11,12,13,19,15,20,17,18,14,16,21,27,23,28,25,26,
22,24,29,32,31,30,33,36,35,34,37,43,39,44,41,42,38,40,45,46,47,53,49,54,51,52,
48,50,55,61,57,62,59,60,56,58,63,64,65,66,67,68,69,70,1,7,3,8,5,6,2,4,1,7,3,8,
5,6,2,4,90,89,88,87,93,94,91,92,95,102,97,104,99,106,101,96,103,98,105,100,
107,110,109,108,111,117,113,118,115,116,112,114,119,122,121,120,124,123,128,
127,126,125,129,130,133,132,131,135,134,137,136,138,141,140,139,145,144,143,
142,147,146,149,148,157,156,155,154,153,152,151,150,161,160,159,158,165,164,
163,162,119,122,121,120,119,122,121,120]],
0,
[(146,148)(147,149),( 71, 79)( 72, 80)( 73, 81)( 74, 82)( 75, 83)( 76, 84)
( 77, 85)( 78, 86)(166,170)(167,171)(168,172)(169,173),( 2, 7)( 4, 8)
( 14, 19)( 16, 20)( 22, 27)( 24, 28)( 30, 32)( 34, 36)( 38, 43)( 40, 44)
( 48, 53)( 50, 54)( 56, 61)( 58, 62)( 72, 77)( 74, 78)( 80, 85)( 82, 86)
( 87, 90)( 88, 89)( 91, 93)( 92, 94)( 96,102)( 98,104)(100,106)(108,110)
(112,117)(114,118)(120,122)(123,124)(125,128)(126,127)(131,133)(134,135)
(136,137)(139,141)(142,145)(143,144)(146,147)(148,149)(150,157)(151,156)
(152,155)(153,154)(158,161)(159,160)(162,165)(163,164)(167,169)(171,173),
( 2, 7)( 4, 8)( 14, 19)( 16, 20)( 22, 27)( 24, 28)( 30, 32)( 34, 36)
( 38, 43)( 40, 44)( 48, 53)( 50, 54)( 56, 61)( 58, 62)( 72, 77)( 74, 78)
( 80, 85)( 82, 86)( 87, 90)( 88, 89)( 91, 93)( 92, 94)( 96,102)( 98,104)
(100,106)(108,110)(112,117)(114,118)(120,122)(123,124)(125,128)(126,127)
(131,133)(134,135)(136,137)(139,141)(142,145)(143,144)(146,149)(147,148)
(150,157)(151,156)(152,155)(153,154)(158,161)(159,160)(162,165)(163,164)
(167,169)(171,173),(119,121)(120,122)(125,127)(126,128)(130,132)(131,133)
(138,140)(139,141)(142,144)(143,145)(150,152)(151,153)(154,156)(155,157)
(158,160)(159,161)(162,164)(163,165)(166,168)(167,169)(170,172)(171,173)],
["ConstructMGA","12_1.U4(3)","4.U4(3).2_1",
[ [ 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, 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 ] ]
, ()]);
ALF("12_1.U4(3).2_1","U4(3).2_1",[1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,
4,4,4,4,4,4,4,4,5,5,5,5,6,6,6,6,7,7,7,7,7,7,7,7,8,8,9,9,9,9,9,9,9,9,10,10,
10,10,10,10,10,10,11,11,11,11,12,12,12,12,13,13,13,13,13,13,13,13,14,14,
14,14,14,14,14,14,15,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,
16,16,17,17,17,17,18,18,18,18,18,18,18,18,19,19,19,19,20,20,21,21,21,21,
22,23,23,23,23,24,24,25,25,26,26,26,26,27,27,27,27,28,28,28,28,29,29,29,
29,30,30,30,30,31,31,31,31,32,32,32,32,33,33,33,33,34,34,34,34]);
ALF("12_1.U4(3).2_1","2.U4(3).2_1",[1,2,1,2,1,1,2,2,3,4,3,4,5,6,5,6,5,5,6,
6,7,8,7,8,7,7,8,8,9,10,9,10,11,12,11,12,13,14,13,14,13,13,14,14,15,15,16,
17,16,17,16,16,17,17,18,19,18,19,18,18,19,19,20,21,20,21,22,23,22,23,24,
25,24,25,24,24,25,25,26,27,26,27,26,26,27,27,28,29,28,29,28,28,29,29,30,
31,30,31,30,31,30,31,30,31,30,31,32,33,32,33,34,35,34,35,34,34,35,35,36,
37,36,37,38,39,40,41,40,41,42,43,44,43,44,45,46,47,48,49,50,49,50,51,52,
51,52,53,54,53,54,55,56,55,56,57,58,57,58,59,60,59,60,61,62,61,62,63,64,
63,64,65,66,65,66]);
ALF("12_1.U4(3).2_1","4.U4(3).2_1",[1,2,3,4,1,3,4,2,5,6,5,6,7,8,9,10,7,9,
10,8,11,12,13,14,11,13,14,12,15,16,17,18,19,20,21,22,23,24,25,26,23,25,26,
24,27,27,28,29,30,31,28,30,31,29,32,33,34,35,32,34,35,33,36,37,36,37,38,
39,38,39,40,41,42,43,40,42,43,41,44,45,46,47,44,46,47,45,48,49,50,51,48,
50,51,49,52,53,54,55,52,53,54,55,52,53,54,55,56,57,58,59,60,61,62,63,60,
62,63,61,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,
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]);
ALF("12_1.U4(3).2_1","3_1.U4(3).2_1",[1,2,2,1,2,1,2,1,3,4,4,3,5,6,6,5,6,5,
6,5,7,8,8,7,8,7,8,7,9,9,9,9,10,10,10,10,11,12,12,11,12,11,12,11,13,14,15,
16,16,15,16,15,16,15,17,18,18,17,18,17,18,17,19,20,20,19,21,22,22,21,23,
24,24,23,24,23,24,23,25,26,26,25,26,25,26,25,27,28,28,27,28,27,28,27,29,
30,31,29,30,31,29,30,31,29,30,31,32,32,32,32,33,34,34,33,34,33,34,33,35,
35,35,35,36,36,37,37,37,37,38,39,39,39,39,40,40,41,41,42,42,42,42,43,43,
43,43,44,44,44,44,45,45,45,45,46,46,46,46,47,47,47,47,48,48,48,48,49,49,
49,49,50,50,50,50]);
ALF("12_1.U4(3).2_1","6_1.U4(3).2_1",[1,2,3,4,3,1,2,4,5,6,7,8,9,10,11,12,
11,9,10,12,13,14,15,16,15,13,14,16,17,18,17,18,19,20,19,20,21,22,23,24,23,
21,22,24,25,26,27,28,29,30,29,27,28,30,31,32,33,34,33,31,32,34,35,36,37,
38,39,40,41,42,43,44,45,46,45,43,44,46,47,48,49,50,49,47,48,50,51,52,53,
54,53,51,52,54,55,56,57,58,59,60,55,56,57,58,59,60,61,62,61,62,63,64,65,
66,65,63,64,66,67,68,67,68,69,70,71,72,71,72,73,74,75,74,75,76,77,78,79,
80,81,80,81,82,83,82,83,84,85,84,85,86,87,86,87,88,89,88,89,90,91,90,91,
92,93,92,93,94,95,94,95,96,97,96,97]);
MOT("12_1.U4(3).2_2",
[
"origin: ATLAS of finite groups, tests: 1.o.r."
],
[78382080,39191040,78382080,39191040,78382080,39191040,78382080,78382080,
78382080,13824,13824,13824,13824,13824,13824,139968,69984,139968,69984,139968,
69984,139968,139968,139968,23328,11664,23328,11664,23328,11664,23328,23328,
23328,7776,3888,7776,648,324,648,2304,1152,2304,1152,2304,1152,2304,2304,2304,
96,96,96,120,60,120,60,120,60,120,120,120,1728,864,1728,864,1728,864,1728,
1728,1728,432,432,432,432,432,432,432,432,432,432,432,432,84,84,84,84,84,84,
84,84,84,84,84,84,96,96,96,96,96,96,648,324,648,324,648,324,648,648,648,648,
324,648,324,648,324,648,648,648,108,108,108,108,288,144,288,144,288,144,288,
288,288,311040,311040,311040,311040,311040,311040,3456,3456,3456,576,576,576,
576,576,576,576,576,576,7776,7776,7776,7776,7776,7776,7776,7776,7776,7776,
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48,48,48,60,60,60,60,60,60,144,144,144,144,144,144,72,72,72,72,72,72,108,108,
108,108,108,108,108,108,108,108,108,108],
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60,52,56,59,16,18,20,22,23,24,16,20,23,25,27,29,31,32,33,34,36,34,36,34,36,82,
84,86,88,90,92,82,84,86,88,90,92,43,45,41,45,43,41,109,111,113,115,116,117,
109,113,116,100,102,104,106,107,108,100,104,107,118,120,118,120,61,63,65,67,
68,69,61,65,68,7,3,9,7,3,9,1,8,5,10,12,14,13,15,11,13,15,11,22,18,24,22,18,24,
22,18,24,22,18,24,36,36,36,36,36,36,31,27,33,31,27,33,34,34,37,37,40,47,44,58,
54,60,58,54,60,67,63,69,67,63,69,73,75,71,73,75,71,115,111,117,115,111,117,
106,102,108,106,102,108],[1,4,7,4,1,4,7,1,7,10,13,10,13,10,13,1,4,7,4,1,4,7,1,
7,1,4,7,4,1,4,7,1,7,1,4,7,1,4,7,40,43,46,43,40,43,46,40,46,49,49,49,52,55,58,
55,52,55,58,52,58,10,13,10,13,10,13,10,10,10,10,13,10,13,10,13,10,13,10,13,10,
13,82,91,88,85,82,91,88,85,82,91,88,85,94,98,98,94,98,94,23,21,18,21,23,21,18,
23,18,20,17,24,17,20,17,24,20,24,16,19,22,19,40,43,46,43,40,43,46,40,46,131,
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134,131,134,137,137,137,137,177,177,177,180,183,180,183,180,183,140,140,140,
140,140,140,143,146,143,146,143,146,151,154,151,154,151,154,159,156,159,156,
159,156],,[1,6,9,4,8,2,7,5,3,10,15,14,13,12,11,16,21,24,19,23,17,22,20,18,25,
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130,125,129,123,128,126,124,131,136,135,134,133,132,137,139,138,140,142,141,
143,148,147,146,145,144,155,160,159,158,157,156,149,154,153,152,151,150,161,
166,165,164,163,162,167,172,171,170,169,168,173,174,175,176,177,179,178,131,
136,135,134,133,132,189,188,187,186,191,190,192,197,196,195,194,193,204,209,
208,207,206,205,198,203,202,201,200,199],,[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,
67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,1,2,3,4,5,6,7,2,8,4,9,6,94,95,96,
97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,
117,118,121,120,119,122,123,124,125,126,127,128,129,130,131,132,133,134,135,
136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,
155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,
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]],
0,
[(175,176),(119,121),(83,89)(85,91)(87,93),( 83, 89)( 85, 91)( 87, 93)
(119,121),( 2, 6)( 3, 9)( 5, 8)( 11, 15)( 12, 14)( 17, 21)( 18, 24)
( 20, 23)( 26, 30)( 27, 33)( 29, 32)( 41, 45)( 42, 48)( 44, 47)( 50, 51)
( 53, 57)( 54, 60)( 56, 59)( 62, 66)( 63, 69)( 65, 68)( 71, 75)( 72, 74)
( 77, 81)( 78, 80)( 83, 87)( 84, 92)( 86, 90)( 89, 93)( 95, 96)( 97, 99)
(100,109)(101,114)(102,117)(103,112)(104,116)(105,110)(106,115)(107,113)
(108,111)(119,121)(123,127)(124,130)(126,129)(132,136)(133,135)(138,139)
(141,142)(144,148)(145,147)(149,155)(150,160)(151,159)(152,158)(153,157)
(154,156)(162,166)(163,165)(168,172)(169,171)(178,179)(181,185)(182,184)
(186,189)(187,188)(190,191)(193,197)(194,196)(198,204)(199,209)(200,208)
(201,207)(202,206)(203,205),( 2, 6)( 3, 9)( 5, 8)( 11, 15)( 12, 14)
( 17, 21)( 18, 24)( 20, 23)( 26, 30)( 27, 33)( 29, 32)( 41, 45)( 42, 48)
( 44, 47)( 50, 51)( 53, 57)( 54, 60)( 56, 59)( 62, 66)( 63, 69)( 65, 68)
( 71, 75)( 72, 74)( 77, 81)( 78, 80)( 83, 87)( 84, 92)( 86, 90)( 89, 93)
( 95, 96)( 97, 99)(100,109)(101,114)(102,117)(103,112)(104,116)(105,110)
(106,115)(107,113)(108,111)(123,127)(124,130)(126,129)(132,136)(133,135)
(138,139)(141,142)(144,148)(145,147)(149,155)(150,160)(151,159)(152,158)
(153,157)(154,156)(162,166)(163,165)(168,172)(169,171)(178,179)(181,185)
(182,184)(186,189)(187,188)(190,191)(193,197)(194,196)(198,204)(199,209)
(200,208)(201,207)(202,206)(203,205),(131,134)(132,135)(133,136)(143,146)
(144,147)(145,148)(149,152)(150,153)(151,154)(155,158)(156,159)(157,160)
(161,164)(162,165)(163,166)(167,170)(168,171)(169,172)(173,174)(180,183)
(181,184)(182,185)(186,189)(187,190)(188,191)(192,195)(193,196)(194,197)
(198,201)(199,202)(200,203)(204,207)(205,208)(206,209)],
["ConstructMGA","12_1.U4(3)","6_1.U4(3).2_2",
[ [ 40, 41 ], [ 42, 43 ], [ 44, 45 ], [ 46, 47 ], [ 48, 49 ],
[ 50, 53 ], [ 51, 52 ], [ 54, 55 ], [ 56, 57 ], [ 58, 59 ],
[ 60, 61 ], [ 62, 63 ], [ 64, 67 ], [ 65, 66 ], [ 68, 69 ],
[ 70, 71 ], [ 134, 136 ], [ 135, 137 ], [ 138, 140 ], [ 139, 141 ],
[ 142, 144 ], [ 143, 145 ], [ 146, 148 ], [ 147, 149 ], [ 150, 152 ],
[ 151, 153 ], [ 154, 156 ], [ 155, 157 ], [ 158, 164 ], [ 159, 165 ],
[ 160, 162 ], [ 161, 163 ], [ 166, 168 ], [ 167, 169 ], [ 170, 172 ],
[ 171, 173 ], [ 174, 176 ], [ 175, 177 ], [ 178, 180 ], [ 179, 181 ] ]
, ( 64, 80, 96,112,128,144,160,176, 70, 86,102,118,134,150,166,182, 76,
92,108,124,140,156,172, 66, 82, 98,114,130,146,162,178, 72, 88,104,
120,136,152,168,184, 78, 94,110,126,142,158,174, 68, 84,100,116,132,
148,164,180, 74, 90,106,122,138,154,170)( 65, 81, 97,113,129,145,161,
177, 71, 87,103,119,135,151,167,183, 77, 93,109,125,141,157,173, 67,
83, 99,115,131,147,163,179, 73, 89,105,121,137,153,169,185, 79, 95,
111,127,143,159,175, 69, 85,101,117,133,149,165,181, 75, 91,107,123,
139,155,171)]);
ALF("12_1.U4(3).2_2","U4(3).2_2",[1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,
3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,6,6,6,7,7,7,7,7,7,7,7,7,8,8,8,9,9,9,9,9,9,
9,9,9,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,12,12,12,12,12,12,13,
13,13,13,13,13,13,13,13,13,13,13,14,14,14,14,14,14,15,15,15,15,15,15,15,
15,15,16,16,16,16,16,16,16,16,16,17,17,17,17,18,18,18,18,18,18,18,18,18,
19,19,19,19,19,19,20,20,20,21,21,21,22,22,22,22,22,22,23,23,23,23,23,23,
24,24,24,24,24,24,25,25,25,25,25,25,26,26,26,26,26,26,27,27,28,28,29,29,
29,30,30,30,30,30,30,31,31,31,31,31,31,32,32,32,32,32,32,33,33,33,33,33,
33,34,34,34,34,34,34]);
ALF("12_1.U4(3).2_2","2.U4(3).2_2",[1,2,1,2,1,2,1,1,1,3,4,3,4,3,4,5,6,5,6,
5,6,5,5,5,7,8,7,8,7,8,7,7,7,9,10,9,11,12,11,13,14,13,14,13,14,13,13,13,15,
15,15,16,17,16,17,16,17,16,16,16,18,19,18,19,18,19,18,18,18,20,21,20,21,
20,21,22,23,22,23,22,23,24,25,24,25,24,25,24,25,24,25,24,25,26,26,26,26,
26,26,27,28,27,28,27,28,27,27,27,29,30,29,30,29,30,29,29,29,31,32,31,32,
33,34,33,34,33,34,33,33,33,35,36,35,36,35,36,37,37,37,38,38,38,39,40,39,
40,39,40,41,42,41,42,41,42,43,44,43,44,43,44,45,46,45,46,45,46,47,48,47,
48,47,48,49,50,51,52,53,53,53,54,55,54,55,54,55,56,57,56,57,56,57,58,59,
58,59,58,59,60,61,60,61,60,61,62,63,62,63,62,63]);
ALF("12_1.U4(3).2_2","4.U4(3).2_2",[1,2,3,2,1,2,3,1,3,4,5,4,5,4,5,6,7,8,7,
6,7,8,6,8,9,10,11,10,9,10,11,9,11,12,13,14,15,16,17,18,19,20,19,18,19,20,
18,20,21,21,21,22,23,24,23,22,23,24,22,24,25,26,27,26,25,26,27,25,27,28,
29,28,29,28,29,30,31,30,31,30,31,32,33,34,35,32,33,34,35,32,33,34,35,36,
37,37,36,37,36,38,39,40,39,38,39,40,38,40,41,42,43,42,41,42,43,41,43,44,
45,46,47,48,49,50,49,48,49,50,48,50,51,52,51,52,51,52,53,53,53,54,54,54,
55,56,55,56,55,56,57,58,57,58,57,58,59,60,59,60,59,60,61,62,61,62,61,62,
63,64,63,64,63,64,65,66,67,68,69,69,69,70,71,70,71,70,71,72,73,72,73,72,
73,74,75,74,75,74,75,76,77,76,77,76,77,78,79,78,79,78,79]);
ALF("12_1.U4(3).2_2","3_1.U4(3).2_2",[1,2,3,1,2,3,1,3,2,4,5,6,4,5,6,7,8,9,
7,8,9,7,9,8,10,11,12,10,11,12,10,12,11,13,13,13,14,14,14,15,16,17,15,16,
17,15,17,16,18,19,20,21,22,23,21,22,23,21,23,22,24,25,26,24,25,26,24,26,
25,27,28,29,27,28,29,30,31,32,30,31,32,33,34,35,33,34,35,33,34,35,33,34,
35,36,37,38,37,36,38,39,40,41,39,40,41,39,41,40,42,43,44,42,43,44,42,44,
43,45,45,45,45,46,47,48,46,47,48,46,48,47,49,50,51,49,50,51,52,53,54,55,
56,57,58,59,60,58,59,60,61,62,63,61,62,63,64,65,66,64,65,66,67,68,69,67,
68,69,70,71,72,70,71,72,73,73,74,74,75,76,77,78,79,80,78,79,80,81,82,83,
81,82,83,84,85,86,84,85,86,87,88,89,87,88,89,90,91,92,90,91,92]);
ALF("12_1.U4(3).2_2","6_1.U4(3).2_2",[1,2,3,4,5,6,1,3,5,7,8,9,10,11,12,13,
14,15,16,17,18,13,15,17,19,20,21,22,23,24,19,21,23,25,26,25,27,28,27,29,
30,31,32,33,34,29,31,33,35,36,37,38,39,40,41,42,43,38,40,42,44,45,46,47,
48,49,44,46,48,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,62,
63,64,65,66,67,68,69,70,69,68,70,71,72,73,74,75,76,71,73,75,77,78,79,80,
81,82,77,79,81,83,84,83,84,85,86,87,88,89,90,85,87,89,91,92,93,94,95,96,
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,
152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169]);
ALF("12_1.U4(3).2_2","6.O7(3)",[1,8,6,7,5,9,4,3,2,13,11,15,10,14,12,16,56,
17,55,16,57,17,16,17,18,59,23,58,22,60,21,20,19,24,61,25,30,78,31,37,44,
42,43,41,45,40,39,38,46,47,48,49,118,54,117,53,119,52,51,50,70,63,69,62,
70,64,69,70,69,74,72,76,71,75,73,77,67,77,66,77,68,87,153,92,152,91,157,
90,156,89,155,88,154,96,97,101,100,99,98,106,169,105,168,104,167,103,102,
107,104,164,103,166,102,165,107,106,105,108,170,109,171,122,131,123,130,
122,132,123,122,123,7,11,9,10,8,12,13,14,15,43,44,45,34,47,36,46,35,48,57,
64,56,63,55,62,56,62,55,64,57,63,61,67,61,66,61,68,58,72,60,71,59,73,65,
77,83,84,93,94,95,117,115,119,114,118,116,131,130,130,132,132,131,127,138,
129,137,128,139,165,174,164,173,166,172,169,172,168,174,167,173],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);
MOT("Isoclinic(12_1.U4(3).2_2)",
[
"isoclinic group of the 12_1.U4(3).2_2 given in the ATLAS"
],
0,
0,
0,
[(175,176),(131,134)(132,135)(133,136)(143,146)(144,147)(145,148)(149,152)
(150,153)(151,154)(155,158)(156,159)(157,160)(161,164)(162,165)(163,166)(167,
170)(168,171)(169,172)(173,174)(180,183)(181,184)(182,185)(186,189)(187,190)
(188,191)(192,195)(193,196)(194,197)(198,201)(199,202)(200,203)(204,207)(205,
208)(206,209),(119,121),(83,89)(85,91)(87,93),(2,6)(3,9)(5,8)(11,15)(12,14)
(17,21)(18,24)(20,23)(26,30)(27,33)(29,32)(41,45)(42,48)(44,47)(50,51)(53,57)
(54,60)(56,59)(62,66)(63,69)(65,68)(71,75)(72,74)(77,81)(78,80)(83,87)(84,92)
(86,90)(89,93)(95,96)(97,99)(100,109)(101,114)(102,117)(103,112)(104,116)(105,
110)(106,115)(107,113)(108,111)(123,127)(124,130)(126,129)(132,136)(133,135)
(138,139)(141,142)(144,148)(145,147)(149,155)(150,160)(151,159)(152,158)(153,
157)(154,156)(162,166)(163,165)(168,172)(169,171)(178,179)(181,185)(182,184)
(186,189)(187,188)(190,191)(193,197)(194,196)(198,204)(199,209)(200,208)(201,
207)(202,206)(203,205)],
["ConstructIsoclinic",[["12_1.U4(3).2_2"]]]);
ALF("Isoclinic(12_1.U4(3).2_2)","2.U4(3).2_2",[1,2,1,2,1,2,1,1,1,3,4,3,4,
3,4,5,6,5,6,5,6,5,5,5,7,8,7,8,7,8,7,7,7,9,10,9,11,12,11,13,14,13,14,13,14,
13,13,13,15,15,15,16,17,16,17,16,17,16,16,16,18,19,18,19,18,19,18,18,18,
20,21,20,21,20,21,22,23,22,23,22,23,24,25,24,25,24,25,24,25,24,25,24,25,
26,26,26,26,26,26,27,28,27,28,27,28,27,27,27,29,30,29,30,29,30,29,29,29,
31,32,31,32,33,34,33,34,33,34,33,33,33,35,36,35,36,35,36,37,37,37,38,38,
38,39,40,39,40,39,40,41,42,41,42,41,42,43,44,43,44,43,44,45,46,45,46,45,
46,47,48,47,48,47,48,49,50,51,52,53,53,53,54,55,54,55,54,55,56,57,56,57,
56,57,58,59,58,59,58,59,60,61,60,61,60,61,62,63,62,63,62,63]);
MOT("12_1.U4(3).2_2'",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7],\n",
"constructed using `PossibleCharacterTablesOfTypeMGA'"
],
[78382080,39191040,39191040,39191040,39191040,39191040,78382080,13824,6912,
6912,13824,139968,69984,69984,69984,69984,69984,139968,23328,11664,11664,11664
,11664,11664,23328,7776,3888,7776,648,324,648,2304,1152,1152,1152,1152,1152,
2304,96,48,120,60,60,60,60,60,120,1728,864,864,864,864,864,1728,432,216,216,
432,432,216,216,432,84,84,84,84,84,84,84,84,84,84,84,84,96,96,96,96,96,96,324,
324,324,324,324,324,324,324,324,324,324,324,216,108,216,216,108,216,288,144,
144,144,144,144,288,103680,103680,1152,192,192,192,2592,2592,2592,2592,432,432
,216,216,144,144,36,36,16,20,20,48,48,24,24,36,36,36,36],
[,[1,3,5,7,5,3,1,1,3,5,7,12,14,16,18,16,14,12,19,21,23,25,23,21,19,26,28,26,29
,31,29,8,10,10,8,10,10,8,11,9,41,43,45,47,45,43,41,12,14,16,18,16,14,12,19,21,
23,25,26,28,26,28,63,65,67,69,71,73,63,65,67,69,71,73,35,33,37,37,35,33,81,91,
89,87,85,83,81,91,89,87,85,83,96,98,96,93,95,93,48,50,52,54,52,50,48,7,7,1,8,
11,11,18,18,18,18,25,25,28,28,19,19,29,29,32,47,47,54,54,62,62,98,98,95,95],[1
,4,7,4,1,4,7,8,11,8,11,1,4,7,4,1,4,7,1,4,7,4,1,4,7,1,4,7,1,4,7,32,35,38,35,32,
35,38,39,39,41,44,47,44,41,44,47,8,11,8,11,8,11,8,8,11,8,11,8,11,8,11,63,72,69
,66,63,72,69,66,63,72,69,66,75,79,75,79,79,75,16,13,14,17,16,13,14,17,16,13,14
,17,12,15,18,12,15,18,32,35,38,35,32,35,38,106,107,108,109,110,111,106,107,106
,107,106,107,106,107,108,108,108,108,124,125,126,109,109,110,111,112,113,114,
115],,[1,6,3,4,5,2,7,8,9,10,11,12,17,14,15,16,13,18,19,24,21,22,23,20,25,26,27
,28,29,30,31,32,37,34,35,36,33,38,39,40,1,6,3,4,5,2,7,48,53,50,51,52,49,54,55,
56,57,58,59,60,61,62,63,70,65,72,67,74,69,64,71,66,73,68,75,78,80,76,79,77,81,
88,83,90,85,92,87,82,89,84,91,86,96,97,98,93,94,95,99,104,101,102,103,100,105,
106,107,108,109,110,111,114,115,112,113,116,117,118,119,120,121,122,123,124,
106,107,128,127,129,130,133,134,131,132],,[1,6,3,4,5,2,7,8,9,10,11,12,17,14,15
,16,13,18,19,24,21,22,23,20,25,26,27,28,29,30,31,32,37,34,35,36,33,38,39,40,41
,46,43,44,45,42,47,48,53,50,51,52,49,54,55,56,57,58,59,60,61,62,1,6,3,4,5,2,7,
2,5,4,3,6,75,78,80,76,79,77,81,88,83,90,85,92,87,82,89,84,91,86,93,94,95,96,97
,98,99,104,101,102,103,100,105,106,107,108,109,110,111,112,113,114,115,116,117
,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134]],
0,
[(122,123),(64,74)(65,73)(66,72)(67,71)(68,70),(93,96)(94,97)(95,98)(106,107)(
110,111)(112,115)(113,114)(116,117)(118,119)(120,121)(125,126)(129,130)(131,
134)(132,133),(93,96)(94,97)(95,98)(112,114)(113,115)(127,128)(131,133)(132,
134),(2,6)(13,17)(20,24)(33,37)(42,46)(49,53)(64,68)(65,73)(67,71)(70,74)(76,
78)(77,80)(82,88)(84,90)(86,92)(93,96)(94,97)(95,98)(100,104)(106,107)(110,111
)(112,115)(113,114)(116,117)(118,119)(120,121)(125,126)(129,130)(131,134)(132,
133)],
["ConstructMGA","12_1.U4(3)","2.U4(3).2_2'",[[40,41],[42,43],[44,45],[46,49],[
47,48],[50,51],[52,53],[54,55],[56,57],[58,59],[60,61],[62,63],[64,67],[65,66]
,[68,69],[70,71],[72,73],[74,75],[76,77],[78,79],[80,81],[82,83],[84,85],[86,
87],[88,91],[89,90],[92,93],[94,95],[96,97],[98,99],[100,101],[102,103],[104,
105],[106,107],[108,109],[110,111],[112,113],[114,117],[115,116],[118,119],[
120,121],[122,123],[124,125],[126,129],[127,128],[130,131],[132,133],[134,137]
,[135,136],[138,141],[139,140],[142,145],[143,144],[146,149],[147,148],[150,
153],[151,152],[154,157],[155,156],[158,165],[159,164],[160,163],[161,162],[
166,169],[167,168],[170,173],[171,172],[174,177],[175,176],[178,181],[179,180]
],()]);
ALF("12_1.U4(3).2_2'","U4(3).2_2'",[1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,4,
4,4,4,4,4,4,5,5,5,6,6,6,7,7,7,7,7,7,7,8,8,9,9,9,9,9,9,9,10,10,10,10,10,10,
10,11,11,11,11,12,12,12,12,13,13,13,13,13,13,13,13,13,13,13,13,14,14,14,
14,14,14,15,15,15,15,15,15,15,15,15,15,15,15,16,16,16,17,17,17,18,18,18,
18,18,18,18,19,19,20,21,22,22,23,23,24,24,25,25,26,26,27,27,28,28,29,30,
30,31,31,32,32,33,33,34,34]);
ALF("12_1.U4(3).2_2'","2.U4(3).2_2'",[1,2,1,2,1,2,1,3,4,3,4,5,6,5,6,5,6,5,
7,8,7,8,7,8,7,9,10,9,11,12,11,13,14,13,14,13,14,13,15,15,16,17,16,17,16,
17,16,18,19,18,19,18,19,18,20,21,20,21,22,23,22,23,24,25,24,25,24,25,24,
25,24,25,24,25,26,26,26,26,26,26,27,28,27,28,27,28,27,28,27,28,27,28,29,
30,29,31,32,31,33,34,33,34,33,34,33,35,36,37,38,39,40,41,42,43,44,45,46,
47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63]);
ALF("12_1.U4(3).2_2'","4.U4(3).2_2",[1,2,3,2,1,2,3,4,5,4,5,6,7,8,7,6,7,8,
12,13,14,13,12,13,14,9,10,11,15,16,17,18,19,20,19,18,19,20,21,21,22,23,24,
23,22,23,24,25,26,27,26,25,26,27,30,31,30,31,28,29,28,29,32,33,34,35,32,
33,34,35,32,33,34,35,36,37,36,37,37,36,44,45,46,47,44,45,46,47,44,45,46,
47,38,39,40,41,42,43,48,49,50,49,48,49,50,51,52,53,54,55,56,57,58,59,60,
61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79]);
ALF("12_1.U4(3).2_2'","3_1.U4(3).2_2'",[1,2,2,1,2,2,1,3,4,4,3,5,6,6,5,6,6,
5,7,8,8,7,8,8,7,9,9,9,10,10,10,11,12,12,11,12,12,11,13,14,15,16,16,15,16,
16,15,17,18,18,17,18,18,17,19,20,20,19,21,22,22,21,23,24,25,23,24,25,23,
24,25,23,24,25,26,27,27,27,26,27,28,29,30,28,29,30,28,29,30,28,29,30,31,
31,31,32,32,32,33,34,34,33,34,34,33,35,35,36,37,38,38,39,39,40,40,41,41,
42,42,43,43,44,44,45,46,46,47,47,48,48,49,49,50,50]);
ALF("12_1.U4(3).2_2'","6_1.U4(3).2_2'",[1,2,3,4,3,2,1,5,6,7,8,9,10,11,12,
11,10,9,13,14,15,16,15,14,13,17,18,17,19,20,19,21,22,23,24,23,22,21,25,26,
27,28,29,30,29,28,27,31,32,33,34,33,32,31,35,36,37,38,39,40,41,42,43,44,
45,46,47,48,43,44,45,46,47,48,49,50,51,51,49,50,52,53,54,55,56,57,52,53,
54,55,56,57,58,59,58,60,61,60,62,63,64,65,64,63,62,66,67,68,69,70,71,72,
73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94]);
MOT("Isoclinic(12_1.U4(3).2_2')",
[
"isoclinic group of the 12_1.U4(3).2_2' given in the ATLAS"
],
0,
0,
0,
[(122,123),(106,107)(110,111)(112,113)(114,115)(116,117)(118,119)(120,121)
(125,126)(127,128)(129,130)(131,132)(133,134),(93,96)(94,97)(95,98)(112,114)
(113,115)(127,128)(131,133)(132,134),(64,74)(65,73)(66,72)(67,71)(68,70),(2,6)
(13,17)(20,24)(33,37)(42,46)(49,53)(64,68)(65,73)(67,71)(70,74)(76,78)(77,80)
(82,88)(84,90)(86,92)(100,104)],
["ConstructIsoclinic",[["12_1.U4(3).2_2'"]]]);
ALF("Isoclinic(12_1.U4(3).2_2')","6_1.U4(3).2_2'",[1,2,3,4,3,2,1,5,6,7,8,
9,10,11,12,11,10,9,13,14,15,16,15,14,13,17,18,17,19,20,19,21,22,23,24,23,
22,21,25,26,27,28,29,30,29,28,27,31,32,33,34,33,32,31,35,36,37,38,39,40,
41,42,43,44,45,46,47,48,43,44,45,46,47,48,49,50,51,51,49,50,52,53,54,55,
56,57,52,53,54,55,56,57,58,59,58,60,61,60,62,63,64,65,64,63,62,66,67,68,
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]);
MOT("12_2.U4(3)",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3]\n",
"3rd power map determined only up to matrix automorphisms\n",
"(138,142)(139,143)(140,144)(141,145), (130,134)(131,135)(132,136)(133,137)"
],
[39191040,39191040,39191040,39191040,39191040,39191040,39191040,39191040,
39191040,39191040,39191040,39191040,6912,6912,6912,6912,6912,6912,69984,69984,
69984,69984,69984,69984,69984,69984,69984,69984,69984,69984,3888,3888,3888,
3888,3888,3888,3888,3888,324,324,324,324,1152,1152,1152,1152,1152,1152,1152,
1152,1152,1152,1152,1152,48,48,48,60,60,60,60,60,60,60,60,60,60,60,60,864,864,
864,864,864,864,864,864,864,864,864,864,216,216,216,216,216,216,216,216,216,
216,216,216,84,84,84,84,84,84,84,84,84,84,84,84,84,84,84,84,84,84,84,84,84,84,
84,84,96,96,96,96,96,96,96,96,96,96,96,96,108,108,108,108,108,108,108,108,108,
108,108,108,108,108,108,108,144,144,144,144,144,144,144,144,144,144,144,144],
[,[1,3,5,7,9,11,1,3,5,7,9,11,1,3,5,7,9,11,19,21,23,25,27,29,19,21,23,25,27,29,
31,33,31,33,35,37,35,37,39,41,39,41,13,15,17,13,15,17,13,15,17,13,15,17,16,18,
14,58,60,62,64,66,68,58,60,62,64,66,68,19,21,23,25,27,29,19,21,23,25,27,29,31,
33,31,33,31,33,35,37,35,37,35,37,94,96,98,100,102,104,94,96,98,100,102,104,
106,108,110,112,114,116,106,108,110,112,114,116,52,54,44,46,48,50,52,54,44,46,
48,50,134,136,134,136,130,132,130,132,142,144,142,144,138,140,138,140,70,72,
74,76,78,80,70,72,74,76,78,80],[1,4,7,10,1,4,7,10,1,4,7,10,13,16,13,16,13,16,
1,4,7,10,1,4,7,10,1,4,7,10,1,4,7,10,1,4,7,10,1,4,7,10,43,46,49,52,43,46,49,52,
43,46,49,52,55,55,55,58,61,64,67,58,61,64,67,58,61,64,67,13,16,13,16,13,16,13,
16,13,16,13,16,13,16,13,16,13,16,13,16,13,16,13,16,106,109,112,115,106,109,
112,115,106,109,112,115,94,97,100,103,94,97,100,103,94,97,100,103,121,124,127,
118,121,124,127,118,121,124,127,118,27,30,21,24,23,26,29,20,27,30,21,24,23,26,
29,20,43,46,49,52,43,46,49,52,43,46,49,52],,[1,6,11,4,9,2,7,12,5,10,3,8,13,18,
17,16,15,14,19,24,29,22,27,20,25,30,23,28,21,26,31,32,33,34,35,36,37,38,39,40,
41,42,43,48,53,46,51,44,49,54,47,52,45,50,55,57,56,1,6,11,4,9,2,7,12,5,10,3,8,
70,75,80,73,78,71,76,81,74,79,72,77,82,87,86,85,84,83,88,93,92,91,90,89,106,
111,116,109,114,107,112,117,110,115,108,113,94,99,104,97,102,95,100,105,98,
103,96,101,118,123,128,121,126,119,124,129,122,127,120,125,134,135,136,137,
130,131,132,133,142,143,144,145,138,139,140,141,146,151,156,149,154,147,152,
157,150,155,148,153],,[1,8,3,10,5,12,7,2,9,4,11,6,13,14,15,16,17,18,19,26,21,
28,23,30,25,20,27,22,29,24,31,34,33,32,35,38,37,36,39,42,41,40,43,50,45,52,47,
54,49,44,51,46,53,48,55,56,57,58,65,60,67,62,69,64,59,66,61,68,63,70,77,72,79,
74,81,76,71,78,73,80,75,82,83,84,85,86,87,88,89,90,91,92,93,1,8,3,10,5,12,7,2,
9,4,11,6,1,8,3,10,5,12,7,2,9,4,11,6,121,128,123,118,125,120,127,122,129,124,
119,126,130,133,132,131,134,137,136,135,138,141,140,139,142,145,144,143,146,
153,148,155,150,157,152,147,154,149,156,151]],
0,
[( 94,106)( 95,107)( 96,108)( 97,109)( 98,110)( 99,111)(100,112)(101,113)
(102,114)(103,115)(104,116)(105,117),( 2, 6)( 3, 11)( 5, 9)( 8, 12)
( 14, 18)( 15, 17)( 20, 24)( 21, 29)( 23, 27)( 26, 30)( 44, 48)( 45, 53)
( 47, 51)( 50, 54)( 56, 57)( 59, 63)( 60, 68)( 62, 66)( 65, 69)( 71, 75)
( 72, 80)( 74, 78)( 77, 81)( 83, 87)( 84, 86)( 89, 93)( 90, 92)( 95, 99)
( 96,104)( 98,102)(101,105)(107,111)(108,116)(110,114)(113,117)(119,123)
(120,128)(122,126)(125,129)(130,134)(131,135)(132,136)(133,137)(138,142)
(139,143)(140,144)(141,145)(147,151)(148,156)(150,154)(153,157),( 2, 8)
( 4, 10)( 6, 12)( 20, 26)( 22, 28)( 24, 30)( 32, 34)( 36, 38)( 40, 42)
( 44, 50)( 46, 52)( 48, 54)( 59, 65)( 61, 67)( 63, 69)( 71, 77)( 73, 79)
( 75, 81)( 95,101)( 97,103)( 99,105)(107,113)(109,115)(111,117)(118,121)
(119,128)(120,123)(122,125)(124,127)(126,129)(131,133)(135,137)(139,141)
(143,145)(147,153)(149,155)(151,157),( 31, 35)( 32, 36)( 33, 37)( 34, 38)
( 82, 88)( 83, 89)( 84, 90)( 85, 91)( 86, 92)( 87, 93)(130,138)(131,139)
(132,140)(133,141)(134,142)(135,143)(136,144)(137,145)],
["ConstructProj",[["U4(3)",[]],["2.U4(3)",[]],["3_2.U4(3)",[-1,-13,-13,-1,-1,
-1,-1,-1,-1,-1,-1,-1,-1]],["4.U4(3)",[-1,-1,-1,7,7,7,7,-1,-1,-1,-1,-1,15,15,
-1,-1]],,["6_2.U4(3)",[-1,-1,-1,-7,-7,-13,-13,-1,-1,-1,-1,
-1]],,,,,,["12_2.U4(3)",[[-7,7,-1],[-7,7,-1],[-55,-377,-433],[-55,-377,-433],[
-7,7,-1],[-7,7,-1],[-7,7,-1],[-7,7,-1],[-7,7,-1]]]]]);
ALF("12_2.U4(3)","U4(3)",[1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,
3,3,3,3,3,3,4,4,4,4,5,5,5,5,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,9,9,9,9,
9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,12,
12,12,12,12,12,13,13,13,13,13,13,13,13,13,13,13,13,14,14,14,14,14,14,14,
14,14,14,14,14,15,15,15,15,15,15,15,15,15,15,15,15,16,16,16,16,17,17,17,
17,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,20]);
ALF("12_2.U4(3)","2.U4(3)",[1,2,1,2,1,2,1,2,1,2,1,2,3,4,3,4,3,4,5,6,5,6,5,
6,5,6,5,6,5,6,7,8,7,8,9,10,9,10,11,12,11,12,13,14,13,14,13,14,13,14,13,14,
13,14,15,15,15,16,17,16,17,16,17,16,17,16,17,16,17,18,19,18,19,18,19,18,
19,18,19,18,19,20,21,20,21,20,21,22,23,22,23,22,23,24,25,24,25,24,25,24,
25,24,25,24,25,26,27,26,27,26,27,26,27,26,27,26,27,28,29,28,29,28,29,28,
29,28,29,28,29,30,31,30,31,32,33,32,33,34,35,34,35,36,37,36,37,38,39,38,
39,38,39,38,39,38,39,38,39]);
ALF("12_2.U4(3)","4.U4(3)",[1,2,3,4,1,2,3,4,1,2,3,4,5,6,5,6,5,6,7,8,9,10,
7,8,9,10,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,23,24,
25,26,23,24,25,26,27,27,27,28,29,30,31,28,29,30,31,28,29,30,31,32,33,34,
35,32,33,34,35,32,33,34,35,36,37,36,37,36,37,38,39,38,39,38,39,40,41,42,
43,40,41,42,43,40,41,42,43,44,45,46,47,44,45,46,47,44,45,46,47,48,49,50,
51,48,49,50,51,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,
67,68,69,70,71,68,69,70,71,68,69,70,71]);
ALF("12_2.U4(3)","3_2.U4(3)",[1,2,3,1,2,3,1,2,3,1,2,3,4,5,6,4,5,6,7,8,9,7,
8,9,7,8,9,7,8,9,10,10,10,10,11,11,11,11,12,12,12,12,13,14,15,13,14,15,13,
14,15,13,14,15,16,17,18,19,20,21,19,20,21,19,20,21,19,20,21,22,23,24,22,
23,24,22,23,24,22,23,24,25,26,27,25,26,27,28,29,30,28,29,30,31,32,33,31,
32,33,31,32,33,31,32,33,34,35,36,34,35,36,34,35,36,34,35,36,37,38,39,37,
38,39,37,38,39,37,38,39,40,40,40,40,41,41,41,41,42,42,42,42,43,43,43,43,
44,45,46,44,45,46,44,45,46,44,45,46]);
ALF("12_2.U4(3)","6_2.U4(3)",[1,2,3,4,5,6,1,2,3,4,5,6,7,8,9,10,11,12,13,
14,15,16,17,18,13,14,15,16,17,18,19,20,19,20,21,22,21,22,23,24,23,24,25,
26,27,28,29,30,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,34,35,36,37,
38,39,40,41,42,43,44,45,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,
56,57,58,59,60,61,62,63,58,59,60,61,62,63,64,65,66,67,68,69,64,65,66,67,
68,69,70,71,72,73,74,75,70,71,72,73,74,75,76,77,76,77,78,79,78,79,80,81,
80,81,82,83,82,83,84,85,86,87,88,89,84,85,86,87,88,89]);
ALF("12_2.U4(3)","12_2.U4(3).2_1",[1,2,3,4,5,2,6,7,5,8,3,7,9,10,11,12,11,
10,13,14,15,16,17,14,18,19,17,20,15,19,21,22,23,24,25,26,27,28,29,30,31,
32,33,34,35,36,37,34,38,39,37,40,35,39,41,42,42,43,44,45,46,47,44,48,49,
47,50,45,49,51,52,53,54,55,52,56,57,55,58,53,57,59,60,61,62,61,60,63,64,
65,66,65,64,67,68,69,70,71,68,72,73,71,74,69,73,75,76,77,78,79,76,80,81,
79,82,77,81,83,84,85,86,87,84,88,89,87,90,85,89,91,92,93,94,91,92,93,94,
95,96,97,98,95,96,97,98,99,100,101,102,103,100,104,105,103,106,101,105],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);
ALF("12_2.U4(3)","12_2.U4(3).2_3",[1,2,3,4,5,6,7,2,8,4,9,6,10,11,12,13,14,
15,16,17,18,19,20,21,22,17,23,19,24,21,25,26,27,28,25,28,27,26,29,30,31,
30,32,33,34,35,36,37,38,33,39,35,40,37,41,42,43,44,45,46,47,48,49,50,45,
51,47,52,49,53,54,55,56,57,58,59,54,60,56,61,58,62,63,64,65,66,67,62,63,
64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,68,75,70,77,72,79,74,69,
76,71,78,73,80,81,82,80,83,82,84,83,85,84,81,85,86,87,88,89,90,91,92,93,
86,89,88,87,90,93,92,91,94,95,96,97,98,99,100,95,101,97,102,99],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);
ALF("12_2.U4(3)","12_2.U4(3).2_3'",[1,2,3,4,5,6,7,6,5,4,3,2,8,9,10,11,10,
9,12,13,14,15,16,17,18,17,16,15,14,13,19,20,21,22,19,22,21,20,23,24,25,24,
26,27,28,29,30,31,32,31,30,29,28,27,33,34,34,35,36,37,38,39,40,41,40,39,
38,37,36,42,43,44,45,46,47,48,47,46,45,44,43,49,50,51,52,53,54,49,54,53,
52,51,50,55,56,57,58,59,60,61,62,63,64,65,66,55,66,65,64,63,62,61,60,59,
58,57,56,67,68,68,67,69,70,71,72,72,71,70,69,73,74,75,76,77,78,79,80,77,
80,79,78,73,76,75,74,81,82,83,84,85,86,87,86,85,84,83,82]);
MOT("12_2.U4(3).2_1",
[
"origin: ATLAS of finite groups, tests: 1.o.r."
],
[78382080,39191040,39191040,78382080,39191040,78382080,39191040,78382080,
13824,6912,6912,13824,139968,69984,69984,139968,69984,139968,69984,139968,
7776,7776,7776,7776,7776,7776,7776,7776,648,648,648,648,2304,1152,1152,2304,
1152,2304,1152,2304,96,48,120,60,60,120,60,120,60,120,1728,864,864,1728,864,
1728,864,1728,432,216,216,432,432,216,216,432,168,84,84,168,84,168,84,168,168,
84,84,168,84,168,84,168,192,96,96,192,96,192,96,192,108,108,108,108,108,108,
108,108,288,144,144,288,144,288,144,288,48384,48384,48384,48384,2880,2880,
4608,4608,4608,4608,128,864,864,864,864,72,72,72,72,72,72,72,72,64,64,64,64,
40,40,40,40,576,576,576,576,576,576,576,576,144,144,144,144,144,144,144,144,
56,56,56,56,56,56,56,56],
[,[1,3,5,6,5,1,3,6,1,3,5,6,13,15,17,18,17,13,15,18,21,23,21,23,25,27,25,27,29,
31,29,31,9,11,11,9,11,9,11,9,12,10,43,45,47,48,47,43,45,48,13,15,17,18,17,13,
15,18,21,23,21,23,25,27,25,27,67,69,71,72,71,67,69,72,75,77,79,80,79,75,77,80,
40,39,34,36,34,40,39,36,91,93,91,93,95,97,95,97,51,53,55,56,55,51,53,56,1,6,1,
6,8,4,9,9,9,9,9,13,18,13,18,22,24,26,28,29,31,29,31,36,40,36,40,50,46,50,46,
51,56,51,56,56,51,56,51,59,59,59,59,63,63,63,63,67,72,67,72,75,80,75,80],[1,4,
6,8,1,6,8,4,9,12,9,12,1,4,6,8,1,6,8,4,1,4,6,8,1,4,6,8,1,4,6,8,33,36,38,40,33,
38,40,36,41,41,43,46,48,50,43,48,50,46,9,12,9,12,9,9,12,12,9,12,9,12,9,12,9,
12,75,78,80,82,75,80,82,78,67,70,72,74,67,72,74,70,86,88,90,83,86,90,83,88,17,
19,15,14,17,19,15,14,33,36,38,40,33,38,40,36,107,110,109,108,112,111,116,115,
114,113,117,107,110,109,108,112,111,112,111,107,110,109,108,133,132,131,130,
137,136,135,134,116,115,114,113,116,115,114,113,116,115,114,113,116,115,114,
113,158,161,160,159,154,157,156,155],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,
17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,
1,2,3,4,5,6,7,8,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,75,76,77,78,
79,80,81,82,67,68,69,70,71,72,73,74,83,84,85,86,87,88,89,90,91,92,93,94,95,96,
97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,
117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,111,112,
111,112,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,158,
159,160,161,154,155,156,157],,[1,7,3,8,5,6,2,4,9,10,11,12,13,19,15,20,17,18,
14,16,21,24,23,22,25,28,27,26,29,32,31,30,33,39,35,40,37,38,34,36,41,42,43,49,
45,50,47,48,44,46,51,57,53,58,55,56,52,54,59,60,61,62,63,64,65,66,1,7,3,8,5,6,
2,4,1,7,3,8,5,6,2,4,86,85,84,83,89,90,87,88,91,94,93,92,95,98,97,96,99,105,
101,106,103,104,100,102,107,110,109,108,112,111,116,115,114,113,117,118,121,
120,119,123,122,125,124,126,129,128,127,133,132,131,130,135,134,137,136,145,
144,143,142,141,140,139,138,149,148,147,146,153,152,151,150,107,110,109,108,
107,110,109,108]],
0,
[(134,136)(135,137),( 67, 75)( 68, 76)( 69, 77)( 70, 78)( 71, 79)( 72, 80)
( 73, 81)( 74, 82)(154,158)(155,159)(156,160)(157,161),( 2, 7)( 4, 8)
( 14, 19)( 16, 20)( 22, 24)( 26, 28)( 30, 32)( 34, 39)( 36, 40)( 44, 49)
( 46, 50)( 52, 57)( 54, 58)( 68, 73)( 70, 74)( 76, 81)( 78, 82)( 83, 86)
( 84, 85)( 87, 89)( 88, 90)( 92, 94)( 96, 98)(100,105)(102,106)(108,110)
(111,112)(113,116)(114,115)(119,121)(122,123)(124,125)(127,129)(130,133)
(131,132)(134,135)(136,137)(138,145)(139,144)(140,143)(141,142)(146,149)
(147,148)(150,153)(151,152)(155,157)(159,161),( 2, 7)( 4, 8)( 14, 19)
( 16, 20)( 22, 24)( 26, 28)( 30, 32)( 34, 39)( 36, 40)( 44, 49)( 46, 50)
( 52, 57)( 54, 58)( 68, 73)( 70, 74)( 76, 81)( 78, 82)( 83, 86)( 84, 85)
( 87, 89)( 88, 90)( 92, 94)( 96, 98)(100,105)(102,106)(108,110)(111,112)
(113,116)(114,115)(119,121)(122,123)(124,125)(127,129)(130,133)(131,132)
(134,137)(135,136)(138,145)(139,144)(140,143)(141,142)(146,149)(147,148)
(150,153)(151,152)(155,157)(159,161),(107,109)(108,110)(113,115)(114,116)
(118,120)(119,121)(126,128)(127,129)(130,132)(131,133)(138,140)(139,141)
(142,144)(143,145)(146,148)(147,149)(150,152)(151,153)(154,156)(155,157)
(158,160)(159,161),( 21, 25)( 22, 26)( 23, 27)( 24, 28)( 59, 63)( 60, 64)
( 61, 65)( 62, 66)( 91, 95)( 92, 96)( 93, 97)( 94, 98)(122,124)(123,125)
(146,150)(147,151)(148,152)(149,153)],
["ConstructMGA","12_2.U4(3)","4.U4(3).2_1",
[ [ 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, 151 ],
[ 152, 153 ], [ 154, 155 ], [ 156, 157 ] ], ()]);
ALF("12_2.U4(3).2_1","U4(3).2_1",[1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,
4,4,4,4,5,5,5,5,6,6,6,6,7,7,7,7,7,7,7,7,8,8,9,9,9,9,9,9,9,9,10,10,10,10,
10,10,10,10,11,11,11,11,12,12,12,12,13,13,13,13,13,13,13,13,14,14,14,14,
14,14,14,14,15,15,15,15,15,15,15,15,16,16,16,16,17,17,17,17,18,18,18,18,
18,18,18,18,19,19,19,19,20,20,21,21,21,21,22,23,23,23,23,24,24,25,25,26,
26,26,26,27,27,27,27,28,28,28,28,29,29,29,29,30,30,30,30,31,31,31,31,32,
32,32,32,33,33,33,33,34,34,34,34]);
ALF("12_2.U4(3).2_1","2.U4(3).2_1",[1,2,1,2,1,1,2,2,3,4,3,4,5,6,5,6,5,5,6,
6,7,8,7,8,9,10,9,10,11,12,11,12,13,14,13,14,13,13,14,14,15,15,16,17,16,17,
16,16,17,17,18,19,18,19,18,18,19,19,20,21,20,21,22,23,22,23,24,25,24,25,
24,24,25,25,26,27,26,27,26,26,27,27,28,29,28,29,28,28,29,29,30,31,30,31,
32,33,32,33,34,35,34,35,34,34,35,35,36,37,36,37,38,39,40,41,40,41,42,43,
44,43,44,45,46,47,48,49,50,49,50,51,52,51,52,53,54,53,54,55,56,55,56,57,
58,57,58,59,60,59,60,61,62,61,62,63,64,63,64,65,66,65,66]);
ALF("12_2.U4(3).2_1","4.U4(3).2_1",[1,2,3,4,1,3,4,2,5,6,5,6,7,8,9,10,7,9,
10,8,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,23,25,26,24,27,27,28,
29,30,31,28,30,31,29,32,33,34,35,32,34,35,33,36,37,36,37,38,39,38,39,40,
41,42,43,40,42,43,41,44,45,46,47,44,46,47,45,48,49,50,51,48,50,51,49,52,
53,54,55,56,57,58,59,60,61,62,63,60,62,63,61,64,65,66,67,68,69,70,71,72,
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]);
ALF("12_2.U4(3).2_1","3_2.U4(3).2_1",[1,2,2,1,2,1,2,1,3,4,4,3,5,6,6,5,6,5,
6,5,7,7,7,7,8,8,8,8,9,9,9,9,10,11,11,10,11,10,11,10,12,13,14,15,15,14,15,
14,15,14,16,17,17,16,17,16,17,16,18,19,19,18,20,21,21,20,22,23,23,22,23,
22,23,22,24,25,25,24,25,24,25,24,26,27,27,26,27,26,27,26,28,28,28,28,29,
29,29,29,30,31,31,30,31,30,31,30,32,32,32,32,33,33,34,34,34,34,35,36,36,
36,36,37,37,38,38,39,39,39,39,40,40,40,40,41,41,41,41,42,42,42,42,43,43,
43,43,44,44,44,44,45,45,45,45,46,46,46,46,47,47,47,47]);
ALF("12_2.U4(3).2_1","6_2.U4(3).2_1",[1,2,3,4,3,1,2,4,5,6,7,8,9,10,11,12,
11,9,10,12,13,14,13,14,15,16,15,16,17,18,17,18,19,20,21,22,21,19,20,22,23,
24,25,26,27,28,27,25,26,28,29,30,31,32,31,29,30,32,33,34,35,36,37,38,39,
40,41,42,43,44,43,41,42,44,45,46,47,48,47,45,46,48,49,50,51,52,51,49,50,
52,53,54,53,54,55,56,55,56,57,58,59,60,59,57,58,60,61,62,61,62,63,64,65,
66,65,66,67,68,69,68,69,70,71,72,73,74,75,74,75,76,77,76,77,78,79,78,79,
80,81,80,81,82,83,82,83,84,85,84,85,86,87,86,87,88,89,88,89,90,91,90,91]);
--> --------------------
--> maximum size reached
--> --------------------
