|
#############################################################################
##
#W ctoline3.tbl GAP table library Thomas Breuer
##
## This file contains the ordinary character tables related to the
## linear group $L_3(4)$ of the ATLAS.
##
#H ctbllib history
#H ---------------
#H $Log: ctoline3.tbl,v $
#H Revision 4.43 2012/06/20 14:45:30 gap
#H added tables and fusions, as documented in ctbldiff.dat
#H TB
#H
#H Revision 4.42 2012/04/23 15:52:57 gap
#H corrected the table automorphisms of (2^2x3).L3(4).2_1
#H TB
#H
#H Revision 4.41 2012/03/28 13:08:58 gap
#H shortened too long history lines
#H TB
#H
#H Revision 4.40 2012/03/21 16:48:08 gap
#H - adjusted fusions 2.L3(4).2_3 -> 2.L3(4).(2^2)_{1*23},
#H 2.L3(4).2_3 -> 2.L3(4).(2^2)_{12*3} to the changed construction
#H
#H - encoded 2.L3(4).(2^2)_{1*23}, 2.L3(4).(2^2)_{12*3},
#H 2.L3(4).(2^2)_{1*2*3}, 2.L3(4).(2^2)_{1*23*}, 2.L3(4).(2^2)_{12*3*},
#H 2.L3(4).(2^2)_{1*2*3*} as isoclinic tables of other ones
#H
#H - encoded 4_1.L3(4).(2^2)_{123}, 4_1.L3(4).(2^2)_{1*23},
#H 4_1.L3(4).(2^2)_{12*3}, 4_1.L3(4).(2^2)_{123*},
#H 4_1.L3(4).(2^2)_{1*2*3}, 4_1.L3(4).(2^2)_{1*23*},
#H 4_1.L3(4).(2^2)_{12*3*}, 4_1.L3(4).(2^2)_{1*2*3*},
#H 4_2.L3(4).(2^2)_{123}, 4_2.L3(4).(2^2)_{1*23}, 4_2.L3(4).(2^2)_{12*3},
#H 4_2.L3(4).(2^2)_{123*}, 4_2.L3(4).(2^2)_{1*2*3},
#H 4_2.L3(4).(2^2)_{1*23*}, 4_2.L3(4).(2^2)_{12*3*},
#H 4_2.L3(4).(2^2)_{1*2*3*}, 6.L3(4).(2^2)_{123}, 6.L3(4).(2^2)_{1*23},
#H 6.L3(4).(2^2)_{12*3}, 6.L3(4).(2^2)_{123*}, 6.L3(4).(2^2)_{1*2*3},
#H 6.L3(4).(2^2)_{1*23*}, 6.L3(4).(2^2)_{12*3*}, 6.L3(4).(2^2)_{1*2*3*}
#H as MGA tables
#H
#H - corrected the V4G construction of (2^2x3).L3(4).2_1, 2^2.L3(4).2_1
#H (due to conditions imposed by Brauer tables)
#H
#H - corrected the GV4/GS3 construction of 2^2.L3(4).D12
#H (due to conditions imposed by Brauer tables)
#H
#H - encode 2^2.L3(4).2^2 as an MGA table
#H
#H - added several fusions
#H
#H TB
#H
#H Revision 4.38 2011/09/28 14:32:12 gap
#H removed revision entry and SET_TABLEFILENAME call
#H TB
#H
#H Revision 4.37 2010/12/01 17:41:05 gap
#H added factor fusion (2x12).L3(4) ->> (2x4).L3(4)
#H TB
#H
#H Revision 4.36 2010/09/15 08:05:28 gap
#H added the fusion (2^2x3).L3(4).3 -> L3(4).3
#H TB
#H
#H Revision 4.35 2010/05/05 13:20:01 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 4.34 2010/01/19 17:05:31 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 4.33 2009/04/22 12:39:02 gap
#H added missing maxes of He.2, ON.2, HN.2, Fi24, and B
#H TB
#H
#H Revision 4.32 2008/06/24 16:23:05 gap
#H added several fusions and names
#H TB
#H
#H Revision 4.31 2006/06/07 07:50:52 gap
#H added tables of (2x4).L3(4), 4^2.L3(4), (4^2x3).L3(4), (2x12).L3(4), and
#H (2^2x3).L3(4).3
#H TB
#H
#H Revision 4.30 2005/09/12 08:36:59 gap
#H added tables of 2^2.L3(4).2^2, 2^2.L3(4).6, 2^2.L3(4).D12
#H TB
#H
#H Revision 4.29 2005/09/07 12:57:23 gap
#H added tables of (2^2x3).L3(4).2_2 and (2^2x3).L3(4).2_3
#H TB
#H
#H Revision 4.28 2005/08/10 14:33:20 gap
#H corrected InfoText values concerning GV4 constructions,
#H added table of 2^2.L3(4).2_1 and related fusions
#H TB
#H
#H Revision 4.27 2005/04/27 07:39:18 gap
#H added fusion L3(4).2^2 -> HS.2
#H TB
#H
#H Revision 4.26 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 4.25 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 4.24 2003/06/20 15:02:57 gap
#H added several fusions
#H TB
#H
#H Revision 4.23 2003/06/10 16:19:06 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 4.22 2003/05/15 17:38:04 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 4.21 2003/03/07 15:53:34 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 4.20 2003/02/24 16:36:45 gap
#H added 2^2.L3(4).2_3, 2^2.L3(4).3, 2^2.L3(4).3.2_2, 2^2.L3(4).3.2_3
#H TB
#H
#H Revision 4.19 2003/01/27 10:03:59 gap
#H fixed two more fusions
#H TB
#H
#H Revision 4.18 2003/01/24 15:57:29 gap
#H replaced several fusions by ones that are compatible with Brauer tables
#H TB
#H
#H Revision 4.17 2003/01/21 16:25:31 gap
#H further standardizations of `InfoText' strings,
#H added and corrected `Maxes' infos,
#H added some fusions
#H TB
#H
#H Revision 4.16 2002/10/22 12:44:07 gap
#H added 215 factor fusions for cases <tbl> -> <tbl> / O_{<p>}(<tbl>)
#H (they make it possible to construct <p>-modular Brauer tables
#H for tables of the type [p^n].<fact> where the <p>-modular Brauer table
#H of <fact> is in the library)
#H TB
#H
#H Revision 4.15 2002/08/21 14:52:37 gap
#H added fusion L3(4).2_2 -> M22.2
#H TB
#H
#H Revision 4.14 2002/07/26 16:58:05 gap
#H added more missing table automorphisms,
#H removed a few inconvenient names such as `c2' for `Co2'
#H (note that `c2' is used for the cyclic group of order 2,
#H which occurs in direct product constructions ...)
#H TB
#H
#H Revision 4.13 2002/07/12 06:45:55 gap
#H further tidying up: removed `irredinfo' stuff, rearranged constructions
#H TB
#H
#H Revision 4.12 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 4.11 2002/03/25 18:08:01 gap
#H added a max info for 6.M22.2
#H TB
#H
#H Revision 4.10 2001/05/04 16:47:38 gap
#H first revision for ctbllib
#H
#H
#H tbl history (GAP 4)
#H -------------------
#H (Rev. 4.10 of ctbllib coincides with Rev. 4.9 of tbl in GAP 4)
#H
#H RCS file: /gap/CVS/GAP/4.0/tbl/ctoline3.tbl,v
#H Working file: ctoline3.tbl
#H head: 4.9
#H branch:
#H locks: strict
#H access list:
#H symbolic names:
#H GAP4R2: 4.5.0.6
#H GAP4R2PRE2: 4.5.0.4
#H GAP4R2PRE1: 4.5.0.2
#H GAP4R1: 4.4.0.2
#H keyword substitution: kv
#H total revisions: 11; selected revisions: 11
#H description:
#H ----------------------------
#H revision 4.9
#H date: 2000/12/27 15:01:30; author: gap; state: Exp; lines: +26 -2
#H added table of 2^2.L3(4).2_2
#H
#H TB
#H ----------------------------
#H revision 4.8
#H date: 2000/07/15 07:55:37; author: gap; state: Exp; lines: +3 -3
#H typos
#H
#H TB
#H ----------------------------
#H revision 4.7
#H date: 2000/07/08 10:07:46; author: gap; state: Exp; lines: +17 -2
#H added some maxes of 2.HS (not yet complete ...) and corresponding fusions
#H
#H TB
#H ----------------------------
#H revision 4.6
#H date: 2000/03/30 09:41:59; author: gap; state: Exp; lines: +47 -2
#H added table of (2^2x3).L3(4)
#H
#H TB
#H ----------------------------
#H revision 4.5
#H date: 1999/10/21 14:15:46; author: gap; state: Exp; lines: +6 -2
#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 4.4
#H date: 1999/07/14 11:39:38; author: gap; state: Exp; lines: +4 -3
#H cosmetic changes for the release ...
#H
#H TB
#H ----------------------------
#H revision 4.3
#H date: 1998/03/11 08:05:21; author: gap; state: Exp; lines: +98 -109
#H mainly new fusions to tables of marks added
#H
#H TB
#H ----------------------------
#H revision 4.2
#H date: 1997/11/25 15:44:48; author: gap; state: Exp; lines: +16 -4
#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 15:40:11; author: fceller; state: Exp; lines: +2 -2
#H for version 4
#H ----------------------------
#H revision 1.2
#H date: 1997/04/04 17:14:27; author: sam; state: Exp; lines: +4 -22
#H removed last occurrency of 'CharTable' in the files,
#H fixed a typo
#H ----------------------------
#H revision 1.1
#H date: 1996/10/21 15:59:33; author: sam; state: Exp;
#H first proposal of the table library
#H ==========================================================================
##
MOT("12_1.L3(4)",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[241920,241920,241920,241920,241920,241920,241920,241920,241920,241920,241920,
241920,384,384,384,384,384,384,36,36,36,36,96,96,96,96,96,96,48,48,48,48,48,
48,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,84,
84,84,84,84,84,84,84,84,84,84,84,84,84,84,84,84,84,84,84,84,84,84,84],
[,[1,3,5,7,9,11,1,3,5,7,9,11,1,3,5,7,9,11,19,21,19,21,13,15,17,13,15,17,16,18,
14,16,18,14,47,49,51,53,55,57,47,49,51,53,55,57,35,37,39,41,43,45,35,37,39,41,
43,45,59,61,63,65,67,69,59,61,63,65,67,69,71,73,75,77,79,81,71,73,75,77,79,
81],[1,4,7,10,1,4,7,10,1,4,7,10,13,16,13,16,13,16,1,4,7,10,23,26,23,26,23,26,
29,29,29,32,32,32,47,50,53,56,47,50,53,56,47,50,53,56,35,38,41,44,35,38,41,44,
35,38,41,44,71,74,77,80,71,74,77,80,71,74,77,80,59,62,65,68,59,62,65,68,59,62,
65,68],,[1,6,11,4,9,2,7,12,5,10,3,8,13,18,17,16,15,14,19,20,21,22,23,28,27,26,
25,24,29,31,30,32,34,33,1,6,11,4,9,2,7,12,5,10,3,8,1,6,11,4,9,2,7,12,5,10,3,8,
71,76,81,74,79,72,77,82,75,80,73,78,59,64,69,62,67,60,65,70,63,68,61,66],,[1,
8,3,10,5,12,7,2,9,4,11,6,13,14,15,16,17,18,19,22,21,20,23,24,25,26,27,28,29,
30,31,32,33,34,47,54,49,56,51,58,53,48,55,50,57,52,35,42,37,44,39,46,41,36,43,
38,45,40,1,8,3,10,5,12,7,2,9,4,11,6,1,8,3,10,5,12,7,2,9,4,11,6]],
0,
[(59,71)(60,72)(61,73)(62,74)(63,75)(64,76)(65,77)(66,78)(67,79)(68,80)(69,81)
(70,82),(35,47)(36,48)(37,49)(38,50)(39,51)(40,52)(41,53)(42,54)(43,55)(44,56)
(45,57)(46,58),(29,32)(30,33)(31,34),( 2, 6)( 3,11)( 5, 9)( 8,12)(14,18)
(15,17)(24,28)(25,27)(30,31)(33,34)(36,40)(37,45)(39,43)(42,46)(48,52)(49,57)
(51,55)(54,58)(60,64)(61,69)(63,67)(66,70)(72,76)(73,81)(75,79)(78,82),( 2, 8)
( 4,10)( 6,12)(20,22)(36,42)(38,44)(40,46)(48,54)(50,56)(52,58)(60,66)(62,68)
(64,70)(72,78)(74,80)(76,82)],
["ConstructProj",[["L3(4)",[]],["2.L3(4)",[]],["3.L3(4)",[-1,-1,-1,-1,-13,-13,
11,11,-1]],["4_1.L3(4)",[-9,-9,-1,-1,15,15]],,["6.L3(4)",[-1,-1,11,11,-13,-13,
-1]],,,,,,["12_1.L3(4)",[[-55,-377,-433],[-55,-377,-433],[41,-209,-169],[41,
-209,-169],[-7,7,-1]]]]]);
ALF("12_1.L3(4)","L3(4)",[1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,4,4,
4,4,4,4,5,5,5,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,
9,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,10,10,10]);
ALF("12_1.L3(4)","2.L3(4)",[1,2,1,2,1,2,1,2,1,2,1,2,3,4,3,4,3,4,5,6,5,6,7,
8,7,8,7,8,9,9,9,10,10,10,11,12,11,12,11,12,11,12,11,12,11,12,13,14,13,14,
13,14,13,14,13,14,13,14,15,16,15,16,15,16,15,16,15,16,15,16,17,18,17,18,
17,18,17,18,17,18,17,18]);
ALF("12_1.L3(4)","4_1.L3(4)",[1,2,3,4,1,2,3,4,1,2,3,4,5,6,5,6,5,6,7,8,9,
10,11,12,11,12,11,12,13,13,13,14,14,14,15,16,17,18,15,16,17,18,15,16,17,
18,19,20,21,22,19,20,21,22,19,20,21,22,23,24,25,26,23,24,25,26,23,24,25,
26,27,28,29,30,27,28,29,30,27,28,29,30]);
ALF("12_1.L3(4)","3.L3(4)",[1,2,3,1,2,3,1,2,3,1,2,3,4,5,6,4,5,6,7,7,7,7,8,
9,10,8,9,10,11,12,13,14,15,16,17,18,19,17,18,19,17,18,19,17,18,19,20,21,
22,20,21,22,20,21,22,20,21,22,23,24,25,23,24,25,23,24,25,23,24,25,26,27,
28,26,27,28,26,27,28,26,27,28]);
ALF("12_1.L3(4)","6.L3(4)",[1,2,3,4,5,6,1,2,3,4,5,6,7,8,9,10,11,12,13,14,
13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,27,28,29,30,
31,32,33,34,35,36,37,38,33,34,35,36,37,38,39,40,41,42,43,44,39,40,41,42,
43,44,45,46,47,48,49,50,45,46,47,48,49,50]);
ALF("12_1.L3(4)","12_1.L3(4).2_1",[1,2,3,4,5,6,7,2,8,4,9,6,10,11,12,13,14,
15,16,17,18,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,
38,39,40,41,42,31,38,33,40,35,42,37,32,39,34,41,36,43,44,45,46,47,48,49,
50,51,52,53,54,43,50,45,52,47,54,49,44,51,46,53,48],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("12_1.L3(4)","12_1.L3(4).2_2",[1,2,3,4,5,6,7,6,5,4,3,2,8,9,10,11,10,9,
12,13,14,13,15,16,17,18,17,16,19,20,21,19,21,20,22,23,24,25,26,27,28,29,
30,31,32,33,22,33,32,31,30,29,28,27,26,25,24,23,34,35,36,37,38,39,40,39,
38,37,36,35,41,42,43,44,45,46,47,46,45,44,43,42],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);
ALF("12_1.L3(4)","12_1.L3(4).2_3",[1,2,3,4,5,2,6,7,5,8,3,7,9,10,11,12,11,
10,13,14,15,16,17,18,19,20,19,18,21,22,23,21,23,22,24,25,26,27,28,25,29,
30,28,31,26,30,32,33,34,35,36,33,37,38,36,39,34,38,40,41,42,43,44,45,46,
47,48,49,50,51,40,45,50,43,48,41,46,51,44,49,42,47],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);
ALF("12_1.L3(4)","12.M22",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,
19,20,21,22,23,24,25,26,27,28,29,30,31,29,30,31,32,33,34,35,36,37,38,39,
40,41,42,43,32,33,34,35,36,37,38,39,40,41,42,43,50,51,52,53,54,55,56,57,
58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
MOT("12_1.L3(4).2_1",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[483840,241920,483840,241920,483840,241920,483840,483840,483840,768,768,768,
768,768,768,72,36,72,192,192,192,192,192,192,96,96,96,96,96,96,60,60,60,60,60,
60,60,60,60,60,60,60,84,84,84,84,84,84,84,84,84,84,84,84,432,432,432,48,48,48,
36,36,48,48,48,48,48,48,48,48,48,48,48,48,48,48,48,48,48,48],
[,[1,3,5,7,8,9,1,5,8,1,3,5,7,8,9,16,18,16,10,12,14,10,12,14,13,15,11,13,15,11,
31,33,35,37,39,41,31,33,35,37,39,41,43,45,47,49,51,53,43,45,47,49,51,53,1,8,5,
10,12,14,16,16,19,21,23,19,21,23,25,27,26,25,27,26,28,30,29,28,30,29],[1,4,7,
4,1,4,7,1,7,10,13,10,13,10,13,1,4,7,19,22,19,22,19,22,25,25,25,28,28,28,31,40,
37,34,31,40,37,34,31,40,37,34,43,52,49,46,43,52,49,46,43,52,49,46,55,55,55,58,
58,58,55,55,63,66,63,66,63,66,72,69,72,69,72,69,78,75,78,75,78,75],,[1,6,9,4,
8,2,7,5,3,10,15,14,13,12,11,16,17,18,19,24,23,22,21,20,25,27,26,28,30,29,1,6,
9,4,8,2,7,6,5,4,3,2,43,54,53,52,51,50,49,48,47,46,45,44,55,57,56,58,60,59,61,
62,63,68,67,66,65,64,72,71,70,69,74,73,78,77,76,75,80,79],,[1,2,3,4,5,6,7,8,9,
10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,
36,37,38,39,40,41,42,1,2,3,4,5,6,7,2,8,4,9,6,55,56,57,58,59,60,61,62,63,64,65,
66,67,68,69,70,71,72,73,74,75,76,77,78,79,80]],
0,
[(69,72)(70,73)(71,74)(75,78)(76,79)(77,80),(63,66)(64,67)(65,68),(61,62),
(44,50)(46,52)(48,54),(32,38)(34,40)(36,42),(32,38)(34,40)(36,42)(44,50)
(46,52)(48,54),(32,38)(34,40)(36,42)(44,50)(46,52)(48,54)(69,72)(70,73)(71,74)
(75,78)(76,79)(77,80),( 2, 6)( 3, 9)( 5, 8)(11,15)(12,14)(20,24)(21,23)(26,27)
(29,30)(32,36)(33,41)(35,39)(38,42)(44,48)(45,53)(47,51)(50,54)(56,57)(59,60)
(64,68)(65,67)(70,74)(71,73)(76,80)(77,79),(25,28)(26,29)(27,30)(69,75)(70,76)
(71,77)(72,78)(73,79)(74,80)],
["ConstructMGA","12_1.L3(4)","6.L3(4).2_1",[[19,22],[20,21],[23,24],[25,26],
[27,30],[28,29],[63,69],[64,70],[65,67],[66,68],[71,77],[72,78],[73,75],[74,
76],[79,81],[80,82]],(25,31,37,43,49,55,61,67,27,33,39,45,51,57,63,69,29,35,
41,47,53,59,65)(26,32,38,44,50,56,62,68,28,34,40,46,52,58,64,70,30,36,42,48,
54,60,66)]);
ALF("12_1.L3(4).2_1","L3(4).2_1",[1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,4,4,
4,4,4,4,5,5,5,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,
10,10,10,11,11,12,12,12,12,12,12,13,13,13,13,13,13,14,14,14,14,14,14]);
ALF("12_1.L3(4).2_1","2.L3(4).2_1",[1,2,1,2,1,2,1,1,1,3,4,3,4,3,4,5,6,5,7,
8,7,8,7,8,9,9,9,10,10,10,11,12,11,12,11,12,11,12,11,12,11,12,13,14,13,14,
13,14,13,14,13,14,13,14,15,15,15,16,16,16,17,18,19,20,19,20,19,20,21,22,
21,22,21,22,23,24,23,24,23,24]);
ALF("12_1.L3(4).2_1","4_1.L3(4).2_1",[1,2,3,2,1,2,3,1,3,4,5,4,5,4,5,6,7,8,
9,10,9,10,9,10,11,11,11,12,12,12,13,14,15,16,13,14,15,16,13,14,15,16,17,
18,19,20,17,18,19,20,17,18,19,20,21,21,21,22,22,22,23,24,25,26,25,26,25,
26,27,28,27,28,27,28,29,30,29,30,29,30]);
ALF("12_1.L3(4).2_1","3.L3(4).2_1",[1,2,3,1,2,3,1,3,2,4,5,6,4,5,6,7,7,7,8,
9,10,8,9,10,11,12,13,14,15,16,17,18,19,17,18,19,17,18,19,17,18,19,20,21,
22,20,21,22,20,21,22,20,21,22,23,24,25,26,27,28,29,29,30,31,32,30,31,32,
33,34,35,33,34,35,36,37,38,36,37,38]);
ALF("12_1.L3(4).2_1","6.L3(4).2_1",[1,2,3,4,5,6,1,3,5,7,8,9,10,11,12,13,
14,13,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,27,28,29,30,
31,32,33,34,35,36,37,38,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,
49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64]);
MOT("Isoclinic(12_1.L3(4).2_1)",
[
"isoclinic group of the 12_1.L3(4).2_1 given in the ATLAS"
],
0,
0,
0,
[(69,72)(70,73)(71,74)(75,78)(76,79)(77,80),(63,66)(64,67)(65,68),(61,62),(44,
50)(46,52)(48,54),(32,38)(34,40)(36,42),(25,28)(26,29)(27,30)(69,75)(70,76)
(71,77)(72,78)(73,79)(74,80),(2,6)(3,9)(5,8)(11,15)(12,14)(20,24)(21,23)(26,
27)(29,30)(32,36)(33,41)(35,39)(38,42)(44,48)(45,53)(47,51)(50,54)(56,57)(59,
60)(64,68)(65,67)(70,74)(71,73)(76,80)(77,79)],
["ConstructIsoclinic",[["12_1.L3(4).2_1"]]]);
ALF("Isoclinic(12_1.L3(4).2_1)","2.L3(4).2_1",[1,2,1,2,1,2,1,1,1,3,4,3,4,
3,4,5,6,5,7,8,7,8,7,8,9,9,9,10,10,10,11,12,11,12,11,12,11,12,11,12,11,12,
13,14,13,14,13,14,13,14,13,14,13,14,15,15,15,16,16,16,17,18,19,20,19,20,
19,20,21,22,21,22,21,22,23,24,23,24,23,24]);
MOT("12_1.L3(4).2_2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[483840,241920,241920,241920,241920,241920,483840,768,384,384,768,72,36,72,
192,96,96,192,48,48,48,60,60,60,60,60,60,60,60,60,60,60,60,168,84,84,84,84,84,
168,168,84,84,84,84,84,168,672,672,32,32,12,12,16,16,28,28,28,28],
[,[1,3,5,7,5,3,1,1,3,5,7,12,14,12,8,10,10,8,11,9,9,22,32,30,28,26,24,22,32,30,
28,26,24,34,36,38,40,38,36,34,41,43,45,47,45,43,41,1,1,8,8,12,12,18,18,34,34,
41,41],[1,4,7,4,1,4,7,8,11,8,11,1,4,7,15,18,15,18,19,19,19,22,31,28,25,22,31,
28,25,22,31,28,25,41,44,47,44,41,44,47,34,37,40,37,34,37,40,48,49,50,51,48,49,
55,54,58,59,56,57],,[1,6,3,4,5,2,7,8,9,10,11,12,13,14,15,16,17,18,19,21,20,1,
6,3,4,5,2,7,2,5,4,3,6,41,46,43,44,45,42,47,34,39,36,37,38,35,40,48,49,50,51,
52,53,54,55,58,59,56,57],,[1,6,3,4,5,2,7,8,9,10,11,12,13,14,15,16,17,18,19,20,
21,22,27,32,25,30,23,28,33,26,31,24,29,1,6,3,4,5,2,7,1,6,3,4,5,2,7,48,49,50,
51,52,53,55,54,48,49,48,49]],
0,
[(54,55),(34,41)(35,42)(36,43)(37,44)(38,45)(39,46)(40,47)(56,58)(57,59),
(23,33)(24,32)(25,31)(26,30)(27,29),(20,21),( 2, 6)(23,27)(24,32)(26,30)
(29,33)(35,39)(42,46),( 2, 6)(23,29)(25,31)(27,33)(35,39)(42,46),( 2, 6)
(23,29)(25,31)(27,33)(35,39)(42,46)(54,55),( 2, 6)(20,21)(23,27)(24,32)(26,30)
(29,33)(35,39)(42,46),(48,49)(50,51)(52,53)(56,57)(58,59)],
["ConstructMGA","12_1.L3(4)","2.L3(4).2_2",[[19,22],[20,21],[23,24],[25,26],
[27,28],[29,30],[31,32],[33,36],[34,35],[37,38],[39,40],[41,42],[43,46],[44,
45],[47,48],[49,50],[51,52],[53,56],[54,55],[57,58],[59,60],[61,62],[63,66],
[64,65],[67,70],[68,69],[71,78],[72,77],[73,76],[74,75],[79,82],[80,81]],()]);
ALF("12_1.L3(4).2_2","L3(4).2_2",[1,1,1,1,1,1,1,2,2,2,2,3,3,3,4,4,4,4,5,5,
5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,8,8,8,8,8,8,8,9,9,10,10,11,11,12,
12,13,13,14,14]);
ALF("12_1.L3(4).2_2","2.L3(4).2_2",[1,2,1,2,1,2,1,3,4,3,4,5,6,5,7,8,7,8,9,
9,9,10,11,10,11,10,11,10,11,10,11,10,11,12,13,12,13,12,13,12,14,15,14,15,
14,15,14,16,17,18,19,20,21,22,23,24,25,26,27]);
ALF("12_1.L3(4).2_2","4_1.L3(4).2_2",[1,2,3,2,1,2,3,4,5,4,5,6,7,8,9,10,9,
10,11,11,11,12,13,14,15,12,13,14,15,12,13,14,15,16,17,18,17,16,17,18,19,
20,21,20,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33]);
ALF("12_1.L3(4).2_2","3.L3(4).2_2",[1,2,2,1,2,2,1,3,4,4,3,5,5,5,6,7,7,6,8,
9,10,11,12,13,11,12,13,11,12,13,11,12,13,14,15,15,14,15,15,14,16,17,17,16,
17,17,16,18,18,19,19,20,20,21,21,22,22,23,23]);
ALF("12_1.L3(4).2_2","6.L3(4).2_2",[1,2,3,4,3,2,1,5,6,7,8,9,10,9,11,12,13,
14,15,16,17,18,19,20,21,22,23,18,19,20,21,22,23,24,25,26,27,26,25,24,28,
29,30,31,30,29,28,32,33,34,35,36,37,38,39,40,41,42,43]);
MOT("Isoclinic(12_1.L3(4).2_2)",
[
"isoclinic group of the 12_1.L3(4).2_2 given in the ATLAS"
],
0,
0,
0,
[(54,55),(48,49)(50,51)(52,53)(56,57)(58,59),(34,41)(35,42)(36,43)(37,44)(38,
45)(39,46)(40,47)(56,58)(57,59),(23,33)(24,32)(25,31)(26,30)(27,29),(20,21),
(2,6)(23,27)(24,32)(26,30)(29,33)(35,39)(42,46)],
["ConstructIsoclinic",[["12_1.L3(4).2_2"]]]);
ALF("Isoclinic(12_1.L3(4).2_2)","6.L3(4).2_2",[1,2,3,4,3,2,1,5,6,7,8,9,10,
9,11,12,13,14,15,16,17,18,19,20,21,22,23,18,19,20,21,22,23,24,25,26,27,26,
25,24,28,29,30,31,30,29,28,32,33,34,35,36,37,38,39,40,41,42,43]);
MOT("12_1.L3(4).2_3",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[483840,241920,241920,483840,241920,483840,241920,483840,768,384,384,768,72,
72,72,72,192,96,96,192,48,48,48,120,60,60,120,60,120,60,120,120,60,60,120,60,
120,60,120,84,84,84,84,84,84,84,84,84,84,84,84,480,480,480,480,24,24,24,24,32,
32,32,32,40,40,40,40,40,40,40,40],
[,[1,3,5,6,5,1,3,6,1,3,5,6,13,15,13,15,9,11,11,9,12,10,10,32,34,36,37,36,32,
34,37,24,26,28,29,28,24,26,29,40,42,44,46,48,50,40,42,44,46,48,50,1,6,1,6,13,
15,13,15,17,17,17,17,32,37,32,37,24,29,24,29],[1,4,6,8,1,6,8,4,9,12,9,12,1,4,
6,8,17,20,17,20,21,21,21,32,35,37,39,32,37,39,35,24,27,29,31,24,29,31,27,40,
43,46,49,40,43,46,49,40,43,46,49,52,55,54,53,52,55,54,53,61,60,63,62,68,71,70,
69,64,67,66,65],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,23,22,
1,2,3,4,5,6,7,8,1,2,3,4,5,6,7,8,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,
55,56,57,58,59,61,60,63,62,52,53,54,55,52,53,54,55],,[1,7,3,8,5,6,2,4,9,10,11,
12,13,16,15,14,17,18,19,20,21,22,23,32,38,34,39,36,37,33,35,24,30,26,31,28,29,
25,27,1,7,3,8,5,7,6,2,5,4,3,2,52,55,54,53,56,59,58,57,60,61,62,63,68,71,70,69,
64,67,66,65]],
0,
[(62,63),(60,61),(41,45)(42,50)(44,48)(47,51),(24,32)(25,33)(26,34)(27,35)
(28,36)(29,37)(30,38)(31,39)(64,68)(65,69)(66,70)(67,71),(22,23),(22,23)
(41,45)(42,50)(44,48)(47,51),( 2, 7)( 4, 8)(14,16)(25,30)(27,31)(33,38)(35,39)
(41,47)(43,49)(45,51)(53,55)(57,59)(65,67)(69,71),( 2, 7)( 4, 8)(14,16)(25,30)
(27,31)(33,38)(35,39)(41,47)(43,49)(45,51)(53,55)(57,59)(60,61)(62,63)(65,67)
(69,71),(52,54)(53,55)(56,58)(57,59)(64,66)(65,67)(68,70)(69,71)],
["ConstructMGA","12_1.L3(4)","4_1.L3(4).2_3",[[31,32],[33,36],[34,35],[37,
38],[39,42],[40,41],[43,44],[45,46],[47,48],[49,50],[51,52],[53,54],[55,56],
[57,60],[58,59],[61,62],[63,68],[64,67],[65,70],[66,69],[71,72],[73,74],[75,
76],[77,78],[79,80],[81,82]],()]);
ALF("12_1.L3(4).2_3","L3(4).2_3",[1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4,
5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,10,
10,10,10,11,11,12,12,13,13,13,13,14,14,14,14]);
ALF("12_1.L3(4).2_3","2.L3(4).2_3",[1,2,1,2,1,1,2,2,3,4,3,4,5,6,5,6,7,8,7,
8,9,9,9,10,11,10,11,10,10,11,11,12,13,12,13,12,12,13,13,14,15,14,15,14,15,
14,15,14,15,14,15,16,17,16,17,18,19,18,19,20,21,22,23,24,25,24,25,26,27,
26,27]);
ALF("12_1.L3(4).2_3","4_1.L3(4).2_3",[1,2,3,4,1,3,4,2,5,6,5,6,7,8,9,10,11,
12,11,12,13,13,13,14,15,16,17,14,16,17,15,18,19,20,21,18,20,21,19,22,23,
24,25,22,23,24,25,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,
40,41,42,43,44,45]);
ALF("12_1.L3(4).2_3","3.L3(4).2_3",[1,2,2,1,2,1,2,1,3,4,4,3,5,5,5,5,6,7,7,
6,8,9,10,11,12,12,11,12,11,12,11,13,14,14,13,14,13,14,13,15,16,17,15,16,
17,15,16,17,15,16,17,18,18,18,18,19,19,19,19,20,20,21,21,22,22,22,22,23,
23,23,23]);
ALF("12_1.L3(4).2_3","6.L3(4).2_3",[1,2,3,4,3,1,2,4,5,6,7,8,9,10,9,10,11,
12,13,14,15,16,17,18,19,20,21,20,18,19,21,22,23,24,25,24,22,23,25,26,27,
28,29,30,31,26,27,28,29,30,31,32,33,32,33,34,35,34,35,36,37,38,39,40,41,
40,41,42,43,42,43]);
MOT("12_2.L3(4)",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[241920,241920,241920,241920,241920,241920,241920,241920,241920,241920,241920,
241920,384,384,384,384,384,384,36,36,36,36,192,192,192,192,192,192,192,192,
192,192,192,192,48,48,48,48,48,48,60,60,60,60,60,60,60,60,60,60,60,60,60,60,
60,60,60,60,60,60,60,60,60,60,84,84,84,84,84,84,84,84,84,84,84,84,84,84,84,84,
84,84,84,84,84,84,84,84],
[,[1,3,5,7,9,11,1,3,5,7,9,11,1,3,5,7,9,11,19,21,19,21,13,15,17,13,15,17,13,15,
17,13,15,17,16,18,14,16,18,14,53,55,57,59,61,63,53,55,57,59,61,63,41,43,45,47,
49,51,41,43,45,47,49,51,65,67,69,71,73,75,65,67,69,71,73,75,77,79,81,83,85,87,
77,79,81,83,85,87],[1,4,7,10,1,4,7,10,1,4,7,10,13,16,13,16,13,16,1,4,7,10,23,
26,29,32,23,26,29,32,23,26,29,32,35,35,35,38,38,38,53,56,59,62,53,56,59,62,53,
56,59,62,41,44,47,50,41,44,47,50,41,44,47,50,77,80,83,86,77,80,83,86,77,80,83,
86,65,68,71,74,65,68,71,74,65,68,71,74],,[1,6,11,4,9,2,7,12,5,10,3,8,13,18,17,
16,15,14,19,20,21,22,23,28,33,26,31,24,29,34,27,32,25,30,35,37,36,38,40,39,1,
6,11,4,9,2,7,12,5,10,3,8,1,6,11,4,9,2,7,12,5,10,3,8,77,82,87,80,85,78,83,88,
81,86,79,84,65,70,75,68,73,66,71,76,69,74,67,72],,[1,8,3,10,5,12,7,2,9,4,11,6,
13,14,15,16,17,18,19,22,21,20,23,30,25,32,27,34,29,24,31,26,33,28,35,36,37,38,
39,40,53,60,55,62,57,64,59,54,61,56,63,58,41,48,43,50,45,52,47,42,49,44,51,46,
1,8,3,10,5,12,7,2,9,4,11,6,1,8,3,10,5,12,7,2,9,4,11,6]],
0,
[(65,77)(66,78)(67,79)(68,80)(69,81)(70,82)(71,83)(72,84)(73,85)(74,86)(75,87)
(76,88),(41,53)(42,54)(43,55)(44,56)(45,57)(46,58)(47,59)(48,60)(49,61)(50,62)
(51,63)(52,64),(35,38)(36,39)(37,40),( 2, 6)( 3,11)( 5, 9)( 8,12)(14,18)
(15,17)(24,28)(25,33)(27,31)(30,34)(36,37)(39,40)(42,46)(43,51)(45,49)(48,52)
(54,58)(55,63)(57,61)(60,64)(66,70)(67,75)(69,73)(72,76)(78,82)(79,87)(81,85)
(84,88),( 2, 8)( 4,10)( 6,12)(20,22)(24,30)(26,32)(28,34)(42,48)(44,50)(46,52)
(54,60)(56,62)(58,64)(66,72)(68,74)(70,76)(78,84)(80,86)(82,88)],
["ConstructProj",[["L3(4)",[]],["2.L3(4)",[]],["3.L3(4)",[-1,-1,-1,-1,-13,-13,
11,11,-1]],["4_2.L3(4)",[-1,-9,-9,-1,-1,15,15]],,["6.L3(4)",[-1,-1,11,11,-13,
-13,-1]],,,,,,["12_2.L3(4)",[[-7,7,-1],[41,-209,-169],[41,-209,-169],[-55,
-377,-433],[-55,-377,-433],[-7,7,-1]]]]]);
ALF("12_2.L3(4)","L3(4)",[1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,4,4,
4,4,4,4,4,4,4,4,4,4,5,5,5,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,
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]);
ALF("12_2.L3(4)","2.L3(4)",[1,2,1,2,1,2,1,2,1,2,1,2,3,4,3,4,3,4,5,6,5,6,7,
8,7,8,7,8,7,8,7,8,7,8,9,9,9,10,10,10,11,12,11,12,11,12,11,12,11,12,11,12,
13,14,13,14,13,14,13,14,13,14,13,14,15,16,15,16,15,16,15,16,15,16,15,16,
17,18,17,18,17,18,17,18,17,18,17,18]);
ALF("12_2.L3(4)","4_2.L3(4)",[1,2,3,4,1,2,3,4,1,2,3,4,5,6,5,6,5,6,7,8,9,
10,11,12,13,14,11,12,13,14,11,12,13,14,15,15,15,16,16,16,17,18,19,20,17,
18,19,20,17,18,19,20,21,22,23,24,21,22,23,24,21,22,23,24,25,26,27,28,25,
26,27,28,25,26,27,28,29,30,31,32,29,30,31,32,29,30,31,32]);
ALF("12_2.L3(4)","3.L3(4)",[1,2,3,1,2,3,1,2,3,1,2,3,4,5,6,4,5,6,7,7,7,7,8,
9,10,8,9,10,8,9,10,8,9,10,11,12,13,14,15,16,17,18,19,17,18,19,17,18,19,17,
18,19,20,21,22,20,21,22,20,21,22,20,21,22,23,24,25,23,24,25,23,24,25,23,
24,25,26,27,28,26,27,28,26,27,28,26,27,28]);
ALF("12_2.L3(4)","6.L3(4)",[1,2,3,4,5,6,1,2,3,4,5,6,7,8,9,10,11,12,13,14,
13,14,15,16,17,18,19,20,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,
31,32,27,28,29,30,31,32,33,34,35,36,37,38,33,34,35,36,37,38,39,40,41,42,
43,44,39,40,41,42,43,44,45,46,47,48,49,50,45,46,47,48,49,50]);
ALF("12_2.L3(4)","12_2.L3(4).2_1",[1,2,3,4,5,6,7,2,8,4,9,6,10,11,12,13,14,
15,16,17,18,17,19,20,21,22,23,24,25,20,26,22,27,24,28,29,30,31,32,33,34,
35,36,37,38,39,40,41,42,43,44,45,34,41,36,43,38,45,40,35,42,37,44,39,46,
47,48,49,50,51,52,53,54,55,56,57,46,53,48,55,50,57,52,47,54,49,56,51],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);
ALF("12_2.L3(4)","12_2.L3(4).2_2",[1,2,3,4,5,2,6,7,5,8,3,7,9,10,11,12,11,
10,13,14,15,16,17,18,19,20,21,18,22,23,21,24,19,23,25,26,27,25,27,26,28,
29,30,31,32,33,34,35,36,37,38,39,28,33,38,31,36,29,34,39,32,37,30,35,40,
41,42,43,44,41,45,46,44,47,42,46,48,49,50,51,52,49,53,54,52,55,50,54],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);
ALF("12_2.L3(4)","12_2.L3(4).2_3",[1,2,3,4,5,6,7,6,5,4,3,2,8,9,10,11,10,9,
12,13,14,13,15,16,17,18,19,20,21,20,19,18,17,16,22,23,24,22,24,23,25,26,
27,28,29,30,31,30,29,28,27,26,32,33,34,35,36,37,38,37,36,35,34,33,39,40,
41,42,43,44,45,46,47,48,49,50,39,50,49,48,47,46,45,44,43,42,41,40],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);
MOT("12_2.L3(4).2_1",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[483840,241920,483840,241920,483840,241920,483840,483840,483840,768,768,768,
768,768,768,72,36,72,384,192,384,192,384,192,384,384,384,96,96,96,96,96,96,60,
60,60,60,60,60,60,60,60,60,60,60,84,84,84,84,84,84,84,84,84,84,84,84,432,432,
432,48,48,48,36,36,48,48,48,48,48,48,48,48,48,48,48,48,48,48,48,48,48,48],
[,[1,3,5,7,8,9,1,5,8,1,3,5,7,8,9,16,18,16,10,12,14,10,12,14,10,14,12,13,15,11,
13,15,11,34,36,38,40,42,44,34,36,38,40,42,44,46,48,50,52,54,56,46,48,50,52,54,
56,1,8,5,10,12,14,16,16,19,26,23,19,26,23,28,30,29,28,30,29,31,33,32,31,33,
32],[1,4,7,4,1,4,7,1,7,10,13,10,13,10,13,1,4,7,19,22,25,22,19,22,25,19,25,28,
28,28,31,31,31,34,43,40,37,34,43,40,37,34,43,40,37,46,55,52,49,46,55,52,49,46,
55,52,49,58,58,58,61,61,61,58,58,66,69,66,69,66,69,75,72,75,72,75,72,81,78,81,
78,81,78],,[1,6,9,4,8,2,7,5,3,10,15,14,13,12,11,16,17,18,19,24,27,22,26,20,25,
23,21,28,30,29,31,33,32,1,6,9,4,8,2,7,6,5,4,3,2,46,57,56,55,54,53,52,51,50,49,
48,47,58,60,59,61,63,62,64,65,66,71,70,69,68,67,75,74,73,72,77,76,81,80,79,78,
83,82],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,
27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,1,2,3,4,5,6,7,2,8,4,
9,6,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,
82,83]],
0,
[(72,75)(73,76)(74,77)(78,81)(79,82)(80,83),(66,69)(67,70)(68,71),(64,65),
(47,53)(49,55)(51,57),(35,41)(37,43)(39,45),(35,41)(37,43)(39,45)(47,53)
(49,55)(51,57),(35,41)(37,43)(39,45)(47,53)(49,55)(51,57)(72,75)(73,76)(74,77)
(78,81)(79,82)(80,83),( 2, 6)( 3, 9)( 5, 8)(11,15)(12,14)(20,24)(21,27)(23,26)
(29,30)(32,33)(35,39)(36,44)(38,42)(41,45)(47,51)(48,56)(50,54)(53,57)(59,60)
(62,63)(67,71)(68,70)(73,77)(74,76)(79,83)(80,82),(28,31)(29,32)(30,33)(72,78)
(73,79)(74,80)(75,81)(76,82)(77,83)],
["ConstructMGA","12_2.L3(4)","6.L3(4).2_1",[[19,20],[21,24],[22,23],[25,26],
[27,28],[29,32],[30,31],[65,67],[66,68],[69,75],[70,76],[71,73],[72,74],[77,
83],[78,84],[79,81],[80,82],[85,87],[86,88]],(25,32,39,46,53,60,67,27,34,41,
48,55,62,69,29,36,43,50,57,64,71,31,38,45,52,59,66,26,33,40,47,54,61,68,28,35,
42,49,56,63,70,30,37,44,51,58,65)]);
ALF("12_2.L3(4).2_1","L3(4).2_1",[1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,4,4,
4,4,4,4,4,4,4,5,5,5,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,
9,9,9,10,10,10,11,11,12,12,12,12,12,12,13,13,13,13,13,13,14,14,14,14,14,
14]);
ALF("12_2.L3(4).2_1","2.L3(4).2_1",[1,2,1,2,1,2,1,1,1,3,4,3,4,3,4,5,6,5,7,
8,7,8,7,8,7,7,7,9,9,9,10,10,10,11,12,11,12,11,12,11,12,11,12,11,12,13,14,
13,14,13,14,13,14,13,14,13,14,15,15,15,16,16,16,17,18,19,20,19,20,19,20,
21,22,21,22,21,22,23,24,23,24,23,24]);
ALF("12_2.L3(4).2_1","4_2.L3(4).2_1",[1,2,3,2,1,2,3,1,3,4,5,4,5,4,5,6,7,8,
9,10,11,10,9,10,11,9,11,12,12,12,13,13,13,14,15,16,17,14,15,16,17,14,15,
16,17,18,19,20,21,18,19,20,21,18,19,20,21,22,22,22,23,23,23,24,25,26,27,
26,27,26,27,28,29,28,29,28,29,30,31,30,31,30,31]);
ALF("12_2.L3(4).2_1","3.L3(4).2_1",[1,2,3,1,2,3,1,3,2,4,5,6,4,5,6,7,7,7,8,
9,10,8,9,10,8,10,9,11,12,13,14,15,16,17,18,19,17,18,19,17,18,19,17,18,19,
20,21,22,20,21,22,20,21,22,20,21,22,23,24,25,26,27,28,29,29,30,31,32,30,
31,32,33,34,35,33,34,35,36,37,38,36,37,38]);
ALF("12_2.L3(4).2_1","6.L3(4).2_1",[1,2,3,4,5,6,1,3,5,7,8,9,10,11,12,13,
14,13,15,16,17,18,19,20,15,17,19,21,22,23,24,25,26,27,28,29,30,31,32,27,
28,29,30,31,32,33,34,35,36,37,38,33,34,35,36,37,38,39,40,41,42,43,44,45,
46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64]);
ALF("12_2.L3(4).2_1","3.ON",[1,9,6,8,2,10,4,3,5,4,12,6,11,5,13,7,36,17,11,
12,10,11,12,13,8,13,9,24,25,26,27,28,29,14,64,32,66,15,65,30,67,16,63,31,
68,18,73,39,69,19,74,37,70,20,72,38,71,4,5,6,11,12,13,17,17,24,28,26,27,
25,29,42,46,44,45,43,47,48,52,50,51,49,53],[
"compatible with 4_2.L3(4).2_1 -> ON"
]);
MOT("Isoclinic(12_2.L3(4).2_1)",
[
"isoclinic group of the 12_2.L3(4).2_1 given in the ATLAS"
],
0,
0,
0,
[(72,75)(73,76)(74,77)(78,81)(79,82)(80,83),(66,69)(67,70)(68,71),(64,65),(47,
53)(49,55)(51,57),(35,41)(37,43)(39,45),(28,31)(29,32)(30,33)(72,78)(73,79)
(74,80)(75,81)(76,82)(77,83),(2,6)(3,9)(5,8)(11,15)(12,14)(20,24)(21,27)(23,
26)(29,30)(32,33)(35,39)(36,44)(38,42)(41,45)(47,51)(48,56)(50,54)(53,57)(59,
60)(62,63)(67,71)(68,70)(73,77)(74,76)(79,83)(80,82)],
["ConstructIsoclinic",[["12_2.L3(4).2_1"]]]);
ALF("Isoclinic(12_2.L3(4).2_1)","2.L3(4).2_1",[1,2,1,2,1,2,1,1,1,3,4,3,4,
3,4,5,6,5,7,8,7,8,7,8,7,7,7,9,9,9,10,10,10,11,12,11,12,11,12,11,12,11,12,
11,12,13,14,13,14,13,14,13,14,13,14,13,14,15,15,15,16,16,16,17,18,19,20,
19,20,19,20,21,22,21,22,21,22,23,24,23,24,23,24]);
MOT("12_2.L3(4).2_2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[483840,241920,241920,483840,241920,483840,241920,483840,768,384,384,768,72,
72,72,72,384,192,192,384,192,384,192,384,48,48,48,60,60,60,60,60,60,60,60,60,
60,60,60,168,84,84,168,84,168,84,168,168,84,84,168,84,168,84,168,1344,1344,
1344,1344,32,32,24,24,24,24,32,32,32,32,56,56,56,56,56,56,56,56],
[,[1,3,5,6,5,1,3,6,1,3,5,6,13,15,13,15,9,11,11,9,11,9,11,9,12,10,10,28,38,36,
34,32,30,28,38,36,34,32,30,40,42,44,45,44,40,42,45,48,50,52,53,52,48,50,53,1,
6,1,6,9,9,13,15,13,15,20,24,20,24,40,45,40,45,48,53,48,53],[1,4,6,8,1,6,8,4,9,
12,9,12,1,4,6,8,17,20,22,24,17,22,24,20,25,25,25,28,31,34,37,28,31,34,37,28,
31,34,37,48,51,53,55,48,53,55,51,40,43,45,47,40,45,47,43,56,59,58,57,60,61,56,
59,58,57,69,68,67,66,74,77,76,75,70,73,72,71],,[1,2,3,4,5,6,7,8,9,10,11,12,13,
14,15,16,17,18,19,20,21,22,23,24,25,27,26,1,2,3,4,5,2,6,7,5,8,3,7,48,49,50,51,
52,53,54,55,40,41,42,43,44,45,46,47,56,57,58,59,60,61,62,63,64,65,66,67,68,69,
74,75,76,77,70,71,72,73],,[1,7,3,8,5,6,2,4,9,10,11,12,13,16,15,14,17,23,19,24,
21,22,18,20,25,26,27,28,39,38,37,36,35,34,33,32,31,30,29,1,7,3,8,5,6,2,4,1,7,
3,8,5,6,2,4,56,59,58,57,60,61,62,65,64,63,69,68,67,66,56,59,58,57,56,59,58,
57]],
0,
[(40,48)(41,49)(42,50)(43,51)(44,52)(45,53)(46,54)(47,55)(70,74)(71,75)(72,76)
(73,77),(29,33)(30,38)(32,36)(35,39),(26,27),(26,27)(29,33)(30,38)(32,36)
(35,39),( 2, 7)( 4, 8)(14,16)(18,23)(20,24)(29,35)(31,37)(33,39)(41,46)(43,47)
(49,54)(51,55)(57,59)(63,65)(66,69)(67,68)(71,73)(75,77),(56,58)(57,59)(62,64)
(63,65)(66,68)(67,69)(70,72)(71,73)(74,76)(75,77)],
["ConstructMGA","12_2.L3(4)","4_2.L3(4).2_2",[[33,34],[35,38],[36,37],[39,
40],[41,42],[43,44],[45,48],[46,47],[49,50],[51,52],[53,54],[55,58],[56,57],
[59,60],[61,62],[63,64],[65,66],[67,68],[69,74],[70,73],[71,76],[72,75],[77,
78],[79,80],[81,82],[83,84],[85,86],[87,88]],()]);
ALF("12_2.L3(4).2_2","L3(4).2_2",[1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4,
4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,9,9,
9,9,10,10,11,11,11,11,12,12,12,12,13,13,13,13,14,14,14,14]);
ALF("12_2.L3(4).2_2","2.L3(4).2_2",[1,2,1,2,1,1,2,2,3,4,3,4,5,6,5,6,7,8,7,
8,7,7,8,8,9,9,9,10,11,10,11,10,11,10,11,10,11,10,11,12,13,12,13,12,12,13,
13,14,15,14,15,14,14,15,15,16,17,16,17,18,19,20,21,20,21,22,23,22,23,24,
25,24,25,26,27,26,27]);
ALF("12_2.L3(4).2_2","4_2.L3(4).2_2",[1,2,3,4,1,3,4,2,5,6,5,6,7,8,9,10,11,
12,13,14,11,13,14,12,15,15,15,16,17,18,19,16,17,18,19,16,17,18,19,20,21,
22,23,20,22,23,21,24,25,26,27,24,26,27,25,28,29,30,31,32,33,34,35,36,37,
38,39,40,41,42,43,44,45,46,47,48,49]);
ALF("12_2.L3(4).2_2","3.L3(4).2_2",[1,2,2,1,2,1,2,1,3,4,4,3,5,5,5,5,6,7,7,
6,7,6,7,6,8,9,10,11,12,13,11,12,13,11,12,13,11,12,13,14,15,15,14,15,14,15,
14,16,17,17,16,17,16,17,16,18,18,18,18,19,19,20,20,20,20,21,21,21,21,22,
22,22,22,23,23,23,23]);
ALF("12_2.L3(4).2_2","6.L3(4).2_2",[1,2,3,4,3,1,2,4,5,6,7,8,9,10,9,10,11,
12,13,14,13,11,12,14,15,16,17,18,19,20,21,22,23,18,19,20,21,22,23,24,25,
26,27,26,24,25,27,28,29,30,31,30,28,29,31,32,33,32,33,34,35,36,37,36,37,
38,39,38,39,40,41,40,41,42,43,42,43]);
MOT("12_2.L3(4).2_3",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]\n",
"2nd power map determined in 4_2.L3(4).2_3 (see there)"
],
[483840,241920,241920,241920,241920,241920,483840,768,384,384,768,72,36,72,
384,192,192,192,192,192,384,48,48,48,120,60,60,60,60,60,120,120,60,60,60,60,
60,120,84,84,84,84,84,84,84,84,84,84,84,84,240,240,12,12,32,32,32,32,20,20,20,
20],
[,[1,3,5,7,5,3,1,1,3,5,7,12,14,12,8,10,10,8,10,10,8,11,9,9,32,34,36,38,36,34,
32,25,27,29,31,29,27,25,39,41,43,45,47,49,39,41,43,45,47,49,1,1,12,12,21,21,
15,15,32,32,25,25],[1,4,7,4,1,4,7,8,11,8,11,1,4,7,15,18,21,18,15,18,21,22,22,
22,32,35,38,35,32,35,38,25,28,31,28,25,28,31,39,48,45,42,39,48,45,42,39,48,45,
42,51,52,51,52,56,55,58,57,61,62,59,60],,[1,6,3,4,5,2,7,8,9,10,11,12,13,14,15,
20,17,18,19,16,21,22,24,23,1,6,3,4,5,2,7,1,6,3,4,5,2,7,39,46,41,48,43,50,45,
40,47,42,49,44,51,52,53,54,56,55,58,57,51,52,51,52],,[1,6,3,4,5,2,7,8,9,10,11,
12,13,14,15,20,17,18,19,16,21,22,23,24,32,37,34,35,36,33,38,25,30,27,28,29,26,
31,1,6,3,4,5,2,7,2,5,4,3,6,51,52,53,54,55,56,57,58,61,62,59,60]],
0,
[(57,58),(55,56),(40,50)(41,49)(42,48)(43,47)(44,46),(25,32)(26,33)(27,34)
(28,35)(29,36)(30,37)(31,38)(59,61)(60,62),(23,24),( 2, 6)(16,20)(26,30)
(33,37)(40,46)(42,48)(44,50),( 2, 6)(16,20)(26,30)(33,37)(40,46)(42,48)(44,50)
(55,56)(57,58),( 2, 6)(16,20)(23,24)(26,30)(33,37)(40,44)(41,49)(43,47)
(46,50),(51,52)(53,54)(59,60)(61,62)],
["ConstructMGA","12_2.L3(4)","2.L3(4).2_3",[[19,20],[21,22],[23,24],[25,26],
[27,28],[29,32],[30,31],[33,34],[35,38],[36,37],[39,40],[41,44],[42,43],[45,
46],[47,48],[49,50],[51,52],[53,54],[55,56],[57,58],[59,62],[60,61],[63,64],
[65,68],[66,67],[69,72],[70,71],[73,76],[74,75],[77,84],[78,83],[79,82],[80,
81],[85,88],[86,87]],()]);
ALF("12_2.L3(4).2_3","L3(4).2_3",[1,1,1,1,1,1,1,2,2,2,2,3,3,3,4,4,4,4,4,4,
4,5,5,5,6,6,6,6,6,6,6,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,10,11,
11,12,12,13,13,14,14]);
ALF("12_2.L3(4).2_3","2.L3(4).2_3",[1,2,1,2,1,2,1,3,4,3,4,5,6,5,7,8,7,8,7,
8,7,9,9,9,10,11,10,11,10,11,10,12,13,12,13,12,13,12,14,15,14,15,14,15,14,
15,14,15,14,15,16,17,18,19,20,21,22,23,24,25,26,27]);
ALF("12_2.L3(4).2_3","4_2.L3(4).2_3",[1,2,3,2,1,2,3,4,5,4,5,6,7,8,9,10,11,
10,9,10,11,12,12,12,13,14,15,14,13,14,15,16,17,18,17,16,17,18,19,20,21,22,
19,20,21,22,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34]);
ALF("12_2.L3(4).2_3","3.L3(4).2_3",[1,2,2,1,2,2,1,3,4,4,3,5,5,5,6,7,7,6,7,
7,6,8,9,10,11,12,12,11,12,12,11,13,14,14,13,14,14,13,15,16,17,15,16,17,15,
16,17,15,16,17,18,18,19,19,20,20,21,21,22,22,23,23]);
ALF("12_2.L3(4).2_3","6.L3(4).2_3",[1,2,3,4,3,2,1,5,6,7,8,9,10,9,11,12,13,
14,13,12,11,15,16,17,18,19,20,21,20,19,18,22,23,24,25,24,23,22,26,27,28,
29,30,31,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43]);
MOT("Isoclinic(12_2.L3(4).2_3)",
[
"isoclinic group of the 12_2.L3(4).2_3 given in the ATLAS"
],
0,
0,
0,
[(57,58),(55,56),(51,52)(53,54)(59,60)(61,62),(25,32)(26,33)(27,34)(28,35)(29,
36)(30,37)(31,38)(59,61)(60,62),(23,24),(2,6)(16,20)(26,30)(33,37)(40,44)(41,
49)(43,47)(46,50),(2,6)(16,20)(26,30)(33,37)(40,46)(42,48)(44,50)],
["ConstructIsoclinic",[["12_2.L3(4).2_3"]]]);
ALF("Isoclinic(12_2.L3(4).2_3)","6.L3(4).2_3",[1,2,3,4,3,2,1,5,6,7,8,9,10,
9,11,12,13,14,13,12,11,15,16,17,18,19,20,21,20,19,18,22,23,24,25,24,23,22,
26,27,28,29,30,31,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43]);
MOT("2.L3(4)",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[40320,40320,128,128,18,18,32,32,16,16,10,10,10,10,14,14,14,14],
[,[1,1,1,1,5,5,3,3,4,4,13,13,11,11,15,15,17,17],[1,2,3,4,1,2,7,8,9,10,13,14,
11,12,17,18,15,16],,[1,2,3,4,5,6,7,8,9,10,1,2,1,2,17,18,15,16],,[1,2,3,4,5,6,
7,8,9,10,13,14,11,12,1,2,1,2]],
0,
[(15,17)(16,18),(11,13)(12,14),( 9,10)],
["ConstructProj",[["L3(4)",[]],["2.L3(4)",[]]]]);
ARC("2.L3(4)","maxes",["P1/G2/L1/V1/ext2","P1/G2/L1/V1/ext2","2xA6",
"2.L3(4)M4","2.L3(4)M5","2xL3(2)","2.L3(4)M7","2.L3(4)M8",
"Isoclinic(2x3^2:Q8)"]);
ALF("2.L3(4)","L3(4)",[1,1,2,2,3,3,4,4,5,6,7,7,8,8,9,9,10,10]);
ALF("2.L3(4)","2.L3(4).2_1",[1,2,3,4,5,6,7,8,9,10,11,12,11,12,13,14,13,14],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("2.L3(4)","Isoclinic(2.L3(4).2_1)",[1,2,3,4,5,6,7,8,9,10,11,12,11,12,
13,14,13,14],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("2.L3(4)","2.L3(4).2_2",[1,2,3,4,5,6,7,8,9,9,10,11,10,11,12,13,14,15],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("2.L3(4)","Isoclinic(2.L3(4).2_2)",[1,2,3,4,5,6,7,8,9,9,10,11,10,11,
12,13,14,15]);
ALF("2.L3(4)","2.L3(4).2_3",[1,2,3,4,5,6,7,8,9,9,10,11,12,13,14,15,14,15],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("2.L3(4)","Isoclinic(2.L3(4).2_3)",[1,2,3,4,5,6,7,8,9,9,10,11,12,13,
14,15,14,15]);
ALF("2.L3(4)","2.M22",[1,2,3,4,5,6,7,8,9,9,10,11,10,11,14,15,16,17],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
MOT("2.L3(4).2_1",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[80640,80640,256,256,36,36,64,64,32,32,10,10,14,14,144,16,36,36,16,16,16,16,
16,16],
[,[1,1,1,1,5,5,3,3,4,4,11,11,13,13,1,3,5,5,7,7,9,9,10,10],[1,2,3,4,1,2,7,8,9,
10,11,12,13,14,15,16,15,15,19,20,22,21,24,23],,[1,2,3,4,5,6,7,8,9,10,1,2,13,
14,15,16,17,18,19,20,22,21,24,23],,[1,2,3,4,5,6,7,8,9,10,11,12,1,2,15,16,17,
18,19,20,21,22,23,24]],
0,
[(21,22)(23,24),(19,20),(17,18),( 9,10)(21,23)(22,24)],
["ConstructProj",[["L3(4).2_1",[]],["2.L3(4).2_1",[]]]]);
ALF("2.L3(4).2_1","L3(4).2_1",[1,1,2,2,3,3,4,4,5,6,7,7,8,8,9,10,11,11,12,
12,13,13,14,14]);
ALF("2.L3(4).2_1","2.L3(4).(2^2)_{123}",[1,2,3,4,5,6,7,8,9,9,10,11,12,13,
14,15,16,17,18,19,20,21,21,20]);
ALF("2.L3(4).2_1","2.L3(4).(2^2)_{12*3}",[1,2,3,4,5,6,7,8,9,9,10,11,12,13,
14,15,16,16,17,17,18,19,18,19]);
ALF("2.L3(4).2_1","2.L3(4).(2^2)_{123*}",[1,2,3,4,5,6,7,8,9,9,10,11,12,13,
14,15,16,16,17,17,18,19,18,19]);
ALF("2.L3(4).2_1","2.L3(4).(2^2)_{12*3*}",[1,2,3,4,5,6,7,8,9,9,10,11,12,
13,14,15,16,17,18,19,20,21,21,20]);
ALF("2.L3(4).2_1","2.U6(2)",[1,2,5,6,12,13,16,17,18,19,23,24,41,42,7,22,
39,40,44,45,46,46,47,47],[
"fusion map determined up to table aut. by compatibility\n",
"with factors"
]);
MOT("Isoclinic(2.L3(4).2_1)",
[
"4th maximal subgroup of 2.HS"
],
0,
0,
0,
[(21,22)(23,24),(19,20),(17,18),(9,10)(21,23)(22,24)],
["ConstructIsoclinic",[["2.L3(4).2_1"]]]);
ALF("Isoclinic(2.L3(4).2_1)","L3(4).2_1",[1,1,2,2,3,3,4,4,5,6,7,7,8,8,9,
10,11,11,12,12,13,13,14,14]);
ALF("Isoclinic(2.L3(4).2_1)","2.L3(4).(2^2)_{1*23}",[1,2,3,4,5,6,7,8,9,9,
10,11,12,13,14,15,16,16,17,17,18,19,18,19]);
ALF("Isoclinic(2.L3(4).2_1)","2.L3(4).(2^2)_{1*2*3}",[1,2,3,4,5,6,7,8,9,9,
10,11,12,13,14,15,16,17,18,19,20,21,21,20]);
ALF("Isoclinic(2.L3(4).2_1)","2.L3(4).(2^2)_{1*23*}",[1,2,3,4,5,6,7,8,9,9,
10,11,12,13,14,15,16,17,18,19,20,21,21,20]);
ALF("Isoclinic(2.L3(4).2_1)","2.L3(4).(2^2)_{1*2*3*}",[1,2,3,4,5,6,7,8,9,
9,10,11,12,13,14,15,16,16,17,17,18,19,18,19]);
ALF("Isoclinic(2.L3(4).2_1)","2.HS",[1,2,4,3,6,7,10,10,11,11,16,17,22,23,
5,11,18,19,24,25,26,26,27,27],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);
ALN("Isoclinic(2.L3(4).2_1)",["2.L3(4).2_1*"]);
MOT("2.L3(4).2_2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[80640,80640,256,256,36,36,64,64,16,10,10,28,28,28,28,672,672,32,32,12,12,16,
16,28,28,28,28],
[,[1,1,1,1,5,5,3,3,4,10,10,12,12,14,14,1,1,3,3,5,5,8,8,12,12,14,14],[1,2,3,4,
1,2,7,8,9,10,11,14,15,12,13,16,17,18,19,16,17,23,22,26,27,24,25],,[1,2,3,4,5,
6,7,8,9,1,2,14,15,12,13,16,17,18,19,20,21,22,23,26,27,24,25],,[1,2,3,4,5,6,7,
8,9,10,11,1,2,1,2,16,17,18,19,20,21,23,22,16,17,16,17]],
0,
[(22,23),(12,14)(13,15)(24,26)(25,27),(16,17)(18,19)(20,21)(24,25)(26,27)],
["ConstructProj",[["L3(4).2_2",[]],["2.L3(4).2_2",[]]]]);
ALF("2.L3(4).2_2","L3(4).2_2",[1,1,2,2,3,3,4,4,5,6,6,7,7,8,8,9,9,10,10,11,
11,12,12,13,13,14,14]);
ALF("2.L3(4).2_2","2.M22.2",[1,2,3,4,5,6,7,8,9,10,11,14,15,16,17,21,22,26,
26,27,28,29,29,34,35,36,37],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("2.L3(4).2_2","2.L3(4).(2^2)_{123}",[1,2,3,4,5,6,7,8,9,10,11,12,13,12,
13,22,23,24,25,26,27,28,28,29,30,29,30]);
ALF("2.L3(4).2_2","2.L3(4).(2^2)_{1*23}",[1,2,3,4,5,6,7,8,9,10,11,12,13,
12,13,20,20,21,21,22,22,23,24,25,26,26,25]);
ALF("2.L3(4).2_2","2.L3(4).(2^2)_{123*}",[1,2,3,4,5,6,7,8,9,10,11,12,13,
12,13,20,20,21,21,22,22,23,24,25,26,26,25]);
ALF("2.L3(4).2_2","2.L3(4).(2^2)_{1*23*}",[1,2,3,4,5,6,7,8,9,10,11,12,13,
12,13,22,23,24,25,26,27,28,28,29,30,29,30]);
MOT("Isoclinic(2.L3(4).2_2)",
0,
0,
0,
0,
[(22,23),(16,17)(18,19)(20,21)(24,25)(26,27),(12,14)(13,15)(24,26)(25,27)],
["ConstructIsoclinic",[["2.L3(4).2_2"]]]);
ALF("Isoclinic(2.L3(4).2_2)","2.L3(4).(2^2)_{12*3}",[1,2,3,4,5,6,7,8,9,10,
11,12,13,12,13,20,20,21,21,22,22,23,24,25,26,26,25]);
ALF("Isoclinic(2.L3(4).2_2)","2.L3(4).(2^2)_{1*2*3}",[1,2,3,4,5,6,7,8,9,
10,11,12,13,12,13,22,23,24,25,26,27,28,28,29,30,29,30]);
ALF("Isoclinic(2.L3(4).2_2)","2.L3(4).(2^2)_{12*3*}",[1,2,3,4,5,6,7,8,9,
10,11,12,13,12,13,22,23,24,25,26,27,28,28,29,30,29,30]);
ALF("Isoclinic(2.L3(4).2_2)","2.L3(4).(2^2)_{1*2*3*}",[1,2,3,4,5,6,7,8,9,
10,11,12,13,12,13,20,20,21,21,22,22,23,24,25,26,26,25]);
ALN("Isoclinic(2.L3(4).2_2)",["2.L3(4).2_2*"]);
MOT("2.L3(4).2_3",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[80640,80640,256,256,36,36,64,64,16,20,20,20,20,14,14,240,240,12,12,32,32,32,
32,20,20,20,20],
[,[1,1,1,1,5,5,3,3,4,12,12,10,10,14,14,1,1,5,5,7,7,7,7,12,12,10,10],[1,2,3,4,
1,2,7,8,9,12,13,10,11,14,15,16,17,16,17,21,20,23,22,26,27,24,25],,[1,2,3,4,5,
6,7,8,9,1,2,1,2,14,15,16,17,18,19,21,20,23,22,16,17,16,17],,[1,2,3,4,5,6,7,8,
9,12,13,10,11,1,2,16,17,18,19,20,21,22,23,26,27,24,25]],
0,
[(22,23),(20,21),(20,21)(22,23),(10,12)(11,13)(24,26)(25,27),(16,17)(18,19)
(24,25)(26,27)],
["ConstructProj",[["L3(4).2_3",[]],["2.L3(4).2_3",[]]]]);
ALF("2.L3(4).2_3","L3(4).2_3",[1,1,2,2,3,3,4,4,5,6,6,7,7,8,8,9,9,10,10,11,
11,12,12,13,13,14,14]);
ALF("2.L3(4).2_3","2.L3(4).(2^2)_{123}",[1,2,3,4,5,6,7,8,9,10,11,10,11,12,
13,31,32,33,34,35,35,36,37,38,39,38,39]);
ALF("2.L3(4).2_3","2.L3(4).(2^2)_{1*23}",[1,2,3,4,5,6,7,8,9,10,11,10,11,
12,13,27,27,28,28,30,29,31,31,32,33,33,32]);
ALF("2.L3(4).2_3","2.L3(4).(2^2)_{12*3}",[1,2,3,4,5,6,7,8,9,10,11,10,11,
12,13,27,27,28,28,30,29,31,31,32,33,33,32]);
ALF("2.L3(4).2_3","2.L3(4).(2^2)_{1*2*3}",[1,2,3,4,5,6,7,8,9,10,11,10,11,
12,13,31,32,33,34,35,35,36,37,38,39,38,39]);
MOT("Isoclinic(2.L3(4).2_3)",
0,
0,
0,
0,
[(22,23),(20,21)(22,23),(16,17)(18,19)(20,21)(22,23)(24,25)(26,27),
(10,12)(11,13)(24,26)(25,27)],
["ConstructIsoclinic",[["2.L3(4).2_3"]]]);
ALF("Isoclinic(2.L3(4).2_3)","2.L3(4).(2^2)_{123*}",[1,2,3,4,5,6,7,8,9,10,
11,10,11,12,13,27,27,28,28,29,30,31,31,32,33,33,32]);
ALF("Isoclinic(2.L3(4).2_3)","2.L3(4).(2^2)_{1*23*}",[1,2,3,4,5,6,7,8,9,
10,11,10,11,12,13,31,32,33,34,35,35,36,37,38,39,38,39]);
ALF("Isoclinic(2.L3(4).2_3)","2.L3(4).(2^2)_{12*3*}",[1,2,3,4,5,6,7,8,9,
10,11,10,11,12,13,31,32,33,34,35,35,36,37,38,39,38,39]);
ALF("Isoclinic(2.L3(4).2_3)","2.L3(4).(2^2)_{1*2*3*}",[1,2,3,4,5,6,7,8,9,
10,11,10,11,12,13,27,27,28,28,29,30,31,31,32,33,33,32]);
ALN("Isoclinic(2.L3(4).2_3)",["2.L3(4).2_3*"]);
MOT("2.L3(4).(2^2)_{123}",
[
"constructed using `PossibleCharacterTablesOfTypeGV4'"
],
[161280,161280,512,512,72,72,128,128,32,20,20,28,28,288,32,72,72,32,32,16,16,
1344,1344,64,64,24,24,16,28,28,480,480,24,24,32,64,64,20,20],
[,[1,1,1,1,5,5,3,3,4,10,10,12,12,1,3,5,5,7,7,9,9,1,1,3,3,5,5,8,12,12,1,1,5,5,7
,7,7,10,10],[1,2,3,4,1,2,7,8,9,10,11,12,13,14,15,14,14,18,19,21,20,22,23,24,25
,22,23,28,29,30,31,32,31,32,35,37,36,38,39],,[1,2,3,4,5,6,7,8,9,1,2,12,13,14,
15,16,17,18,19,21,20,22,23,24,25,26,27,28,29,30,31,32,33,34,35,37,36,31,32],,[
1,2,3,4,5,6,7,8,9,10,11,1,2,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,22,23
,31,32,33,34,35,36,37,38,39]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1
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[TENSOR,[27,2]],
[TENSOR,[27,3]],
[TENSOR,[27,4]],[64,-64,0,0,1,-1,0,0,0,-1,1,1,-1,0,0,3,-3,0,0,0,0,8,-8,0,0,-1
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[TENSOR,[31,2]],
[TENSOR,[31,3]],
[TENSOR,[31,4]],[140,-140,-4,4,-4,4,4,-4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0],[90,-90,2,-2,0,0,-2,2,0,0,0,-1,1,0,0,0,0,0,0,
E(8)-E(8)^3,-E(8)+E(8)^3,6,-6,-2,2,0,0,0,-1,1,0,0,0,0,0,2*E(8)-2*E(8)^3,
-2*E(8)+2*E(8)^3,0,0],
[TENSOR,[36,2]],
[TENSOR,[36,3]],
[TENSOR,[36,4]]],
[(20,21)(36,37),(16,17)(18,19)(31,32)(33,34)(38,39),
(16,17)(18,19)(22,23)(24,25)(26,27)(29,30)(36,37)]);
ALF("2.L3(4).(2^2)_{123}","L3(4).2^2",[1,1,2,2,3,3,4,4,5,6,6,7,7,8,9,10,
10,11,11,12,12,13,13,14,14,15,15,16,17,17,18,18,19,19,20,21,21,22,22]);
ALF("2.L3(4).(2^2)_{123}","2.U6(2).2",[1,2,5,6,12,13,16,17,18,22,23,38,39,
7,21,36,37,41,42,43,43,65,66,72,71,81,82,87,104,105,67,68,83,84,88,89,89,
92,93]);
MOT("2.L3(4).(2^2)_{1*23}",
[
"constructed using `PossibleCharacterTablesOfTypeGV4'"
],
0,
0,
0,
[(32,33),(25,26),(23,24)(29,30),(18,19)(29,30)],
["ConstructIsoclinic",[["2.L3(4).(2^2)_{123*}"]],[1,2,3,4,5,6,7,8,9,10,11,12,
13,20,21,22,23,24,25,26]]);
ALF("2.L3(4).(2^2)_{1*23}","L3(4).2^2",[1,1,2,2,3,3,4,4,5,6,6,7,7,8,9,10,
11,12,12,13,14,15,16,16,17,17,18,19,20,20,21,22,22]);
ALF("2.L3(4).(2^2)_{1*23}","2.HS.2",[1,2,4,3,6,7,9,9,10,15,16,20,21,5,10,
17,22,23,23,34,36,40,42,42,48,49,35,41,42,42,43,45,46],[
"fusion map is unique up to table autom.",
]);
ALN("2.L3(4).(2^2)_{1*23}",["2.HS.2M3"]);
MOT("2.L3(4).(2^2)_{12*3}",
[
"constructed using `PossibleCharacterTablesOfTypeGV4'"
],
0,
0,
0,
[(32,33),(25,26),(23,24)(29,30),(18,19)(29,30)],
["ConstructIsoclinic",[["2.L3(4).(2^2)_{123*}"]],[1..19]]);
ALF("2.L3(4).(2^2)_{12*3}","L3(4).2^2",[1,1,2,2,3,3,4,4,5,6,6,7,7,8,9,10,
11,12,12,13,14,15,16,16,17,17,18,19,20,20,21,22,22]);
MOT("2.L3(4).(2^2)_{123*}",
[
"constructed using `PossibleCharacterTablesOfTypeGV4'"
],
[161280,161280,512,512,72,72,128,128,32,20,20,28,28,288,32,36,16,16,16,672,32,
12,32,32,28,28,240,12,64,64,32,20,20],
[,[1,1,1,1,5,5,3,3,4,10,10,12,12,1,3,5,7,9,9,1,3,5,8,8,12,12,2,6,8,8,8,11,11],
[1,2,3,4,1,2,7,8,9,10,11,12,13,14,15,14,17,19,18,20,21,20,24,23,26,25,27,27,29
,30,31,32,33],,[1,2,3,4,5,6,7,8,9,1,2,12,13,14,15,16,17,19,18,20,21,22,23,24,
26,25,27,28,30,29,31,27,27],,[1,2,3,4,5,6,7,8,9,10,11,1,2,14,15,16,17,18,19,20
,21,22,24,23,20,20,27,28,30,29,31,32,33]],
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1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[1,1,
1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1],
[TENSOR,[2,3]],[20,20,4,4,2,2,0,0,0,0,0,-1,-1,2,-2,2,0,0,0,6,2,0,0,0,-1,-1,0,
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[TENSOR,[5,2]],
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[TENSOR,[9,2]],
[TENSOR,[9,3]],
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[TENSOR,[15,2]],[126,126,-2,-2,0,0,-2,-2,-2,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
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[TENSOR,[17,2]],[64,64,0,0,1,1,0,0,0,-1,-1,1,1,8,0,-1,0,0,0,8,0,-1,0,0,1,1,4,
1,0,0,0,-1,-1],
[TENSOR,[19,2]],
[TENSOR,[19,3]],
[TENSOR,[19,4]],[20,-20,4,-4,2,-2,4,-4,0,0,0,-1,1,0,0,0,0,0,0,0,0,0,0,0,
-E(7)-E(7)^2+E(7)^3-E(7)^4+E(7)^5+E(7)^6,
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[TENSOR,[23,2]],[56,-56,-8,8,2,-2,0,0,0,1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
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[TENSOR,[25,2]],[72,-72,8,-8,0,0,0,0,0,2,-2,2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0],[128,-128,0,0,2,-2,0,0,0,-2,2,2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0],[70,-70,-2,2,-2,2,2,-2,0,0,0,0,0,0,0,0,0,E(8)-E(8)^3,-E(8)+E(8)^3,0
,0,0,2*E(4),-2*E(4),0,0,0,0,2*E(8)+2*E(8)^3,-2*E(8)-2*E(8)^3,0,0,0],
[TENSOR,[29,2]],
[TENSOR,[29,3]],
[TENSOR,[29,4]],[180,-180,4,-4,0,0,-4,4,0,0,0,-2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0]],
[(32,33),(25,26),(23,24)(29,30),(18,19)(29,30)]);
ALF("2.L3(4).(2^2)_{123*}","L3(4).2^2",[1,1,2,2,3,3,4,4,5,6,6,7,7,8,9,10,
11,12,12,13,14,15,16,16,17,17,18,19,20,20,21,22,22]);
MOT("2.L3(4).(2^2)_{1*2*3}",
[
"constructed using `PossibleCharacterTablesOfTypeGV4'"
],
0,
0,
0,
[(20,21)(36,37),(16,17)(18,19)(31,32)(33,34)(38,39),
(16,17)(18,19)(22,23)(24,25)(26,27)(29,30)(36,37)],
["ConstructIsoclinic",[["2.L3(4).(2^2)_{123}"]],[1,2,3,4,5,6,7,8,9,10,11,12,
13,31,32,33,34,35,36,37,38,39]]);
ALF("2.L3(4).(2^2)_{1*2*3}","L3(4).2^2",[1,1,2,2,3,3,4,4,5,6,6,7,7,8,9,10,
10,11,11,12,12,13,13,14,14,15,15,16,17,17,18,18,19,19,20,21,21,22,22]);
MOT("2.L3(4).(2^2)_{1*23*}",
[
"constructed using `PossibleCharacterTablesOfTypeGV4'"
],
0,
0,
0,
[(20,21)(36,37),(16,17)(18,19)(31,32)(33,34)(38,39),
(16,17)(18,19)(22,23)(24,25)(26,27)(29,30)(36,37)],
["ConstructIsoclinic",[["2.L3(4).(2^2)_{123}"]],[1,2,3,4,5,6,7,8,9,10,11,12,
13,22,23,24,25,26,27,28,29,30]]);
ALF("2.L3(4).(2^2)_{1*23*}","L3(4).2^2",[1,1,2,2,3,3,4,4,5,6,6,7,7,8,9,10,
10,11,11,12,12,13,13,14,14,15,15,16,17,17,18,18,19,19,20,21,21,22,22]);
MOT("2.L3(4).(2^2)_{12*3*}",
[
"constructed using `PossibleCharacterTablesOfTypeGV4'"
],
0,
0,
0,
[(20,21)(36,37),(16,17)(18,19)(31,32)(33,34)(38,39),
(16,17)(18,19)(22,23)(24,25)(26,27)(29,30)(36,37)],
["ConstructIsoclinic",[["2.L3(4).(2^2)_{123}"]],[1..21]]);
ALF("2.L3(4).(2^2)_{12*3*}","L3(4).2^2",[1,1,2,2,3,3,4,4,5,6,6,7,7,8,9,10,
10,11,11,12,12,13,13,14,14,15,15,16,17,17,18,18,19,19,20,21,21,22,22]);
MOT("2.L3(4).(2^2)_{1*2*3*}",
[
"constructed using `PossibleCharacterTablesOfTypeGV4'"
],
0,
0,
0,
[(32,33),(25,26),(23,24)(29,30),(18,19)(29,30)],
["ConstructIsoclinic",[["2.L3(4).(2^2)_{123*}"]],[1,2,3,4,5,6,7,8,9,10,11,12,
13,27,28,29,30,31,32,33]]);
ALF("2.L3(4).(2^2)_{1*2*3*}","L3(4).2^2",[1,1,2,2,3,3,4,4,5,6,6,7,7,8,9,
10,11,12,12,13,14,15,16,16,17,17,18,19,20,20,21,22,22]);
ALF("2.L3(4).(2^2)_{1*2*3*}","Isoclinic(2.HS.2)",[1,2,4,3,6,7,9,9,10,15,
16,20,21,5,10,17,22,23,23,34,36,40,42,42,48,49,35,41,42,42,43,45,46],[
"fusion map is unique up to table autom."
]);
MOT("2^2.L3(4)",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[80640,80640,80640,80640,256,256,256,256,36,36,36,36,32,32,32,32,32,32,20,20,
20,20,20,20,20,20,28,28,28,28,28,28,28,28],
[,[1,1,1,1,1,1,1,1,9,9,9,9,6,6,7,7,8,8,23,23,23,23,19,19,19,19,27,27,27,27,31,
31,31,31],[1,2,3,4,5,6,7,8,1,2,3,4,13,14,15,16,17,18,23,24,25,26,19,20,21,22,
31,32,33,34,27,28,29,30],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,1,2,3,
4,1,2,3,4,31,32,33,34,27,28,29,30],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,
17,18,23,24,25,26,19,20,21,22,1,2,3,4,1,2,3,4]],
0,
[(27,31)(28,32)(29,33)(30,34),(19,23)(20,24)(21,25)(22,26),( 3, 4)( 7, 8)
(11,12)(15,17)(16,18)(21,22)(25,26)(29,30)(33,34),( 2, 3)( 6, 7)(10,11)(13,15)
(14,16)(20,21)(24,25)(28,29)(32,33)],
["ConstructV4G","2.L3(4)",( 2, 3, 4)( 6, 7, 8)(10,11,12)
(13,15,17)(14,16,18)(20,21,22)(24,25,26)(28,29,30)(32,33,34)]);
ARC("2^2.L3(4)","maxes",["P1/G3/L2/V1/ext2","P1/G3/L2/V1/ext2","2^2xA6",
"2^2.L3(4)M4","2^2.L3(4)M5","2^2xL2(7)","2^2.L3(4)M7","2^2.L3(4)M8",
"2^2.(3^2:Q8)"]);
ARC("2^2.L3(4)","tomfusion",rec(name:="2^2.L3(4)",map:=[1,2,3,4,6,8,7,5,9,
61,60,62,55,56,57,58,54,53,59,247,248,246,59,247,248,246,67,267,268,269,
67,267,268,269],text:=[
"fusion map is unique up to table autom."
],perm:=(3,5,4)(7,8)));
ALF("2^2.L3(4)","2.L3(4)",[1,1,2,2,3,3,4,4,5,5,6,6,7,8,9,9,10,10,11,11,12,
12,13,13,14,14,15,15,16,16,17,17,18,18]);
ALF("2^2.L3(4)","2^2.L3(4).2_1",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,
17,18,19,20,21,22,19,20,21,22,23,24,25,26,23,24,25,26],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("2^2.L3(4)","2^2.L3(4).2_2",[1,2,3,3,4,5,6,6,7,8,9,9,10,11,12,13,12,
13,14,15,16,17,14,15,17,16,18,19,20,20,21,22,23,23],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("2^2.L3(4)","2^2.L3(4).2_3",[1,2,3,3,4,5,6,6,7,8,9,9,10,11,12,13,12,
13,14,15,16,16,17,18,19,19,20,21,22,23,20,21,23,22],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("2^2.L3(4)","2^2.L3(4).3",[1,2,2,2,3,4,4,4,5,6,6,6,7,8,7,8,7,8,9,10,
10,10,11,12,12,12,13,14,14,14,15,16,16,16],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("2^2.L3(4)","L3(4)",[1,1,1,1,2,2,2,2,3,3,3,3,4,4,5,5,6,6,7,7,7,7,8,8,
8,8,9,9,9,9,10,10,10,10]);
ALN("2^2.L3(4)",["V4.L3(4)"]);
MOT("(2x4).L3(4)",
[
"constructed using `PossibleCharacterTablesOfTypeV4G'"
],
[161280,161280,161280,161280,161280,161280,161280,161280,256,256,256,256,72,72
,72,72,72,72,72,72,64,64,64,64,32,32,32,32,40,40,40,40,40,40,40,40,40,40,40,40
,40,40,40,40,56,56,56,56,56,56,56,56,56,56,56,56,56,56,56,56],
[,[1,1,1,1,4,4,4,4,1,1,4,4,13,13,13,13,16,16,16,16,10,10,10,10,11,11,12,12,37,
37,37,37,40,40,40,40,29,29,29,29,32,32,32,32,45,45,45,45,48,48,48,48,53,53,53,
53,56,56,56,56],[1,2,3,4,8,7,6,5,9,10,11,12,1,2,3,4,8,7,6,5,21,22,24,23,25,26,
27,28,37,38,39,40,44,43,42,41,29,30,31,32,36,35,34,33,53,54,55,56,60,59,58,57,
45,46,47,48,52,51,50,49],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,
21,22,23,24,25,26,27,28,1,2,3,4,5,6,7,8,1,2,3,4,5,6,7,8,53,54,55,56,57,58,59,
60,45,46,47,48,49,50,51,52],,[1,2,3,4,8,7,6,5,9,10,11,12,13,14,15,16,20,19,18,
17,21,22,24,23,25,26,27,28,37,38,39,40,44,43,42,41,29,30,31,32,36,35,34,33,1,2
,3,4,8,7,6,5,1,2,3,4,8,7,6,5]],
0,
[(29,37)(30,38)(31,39)(32,40)(33,41)(34,42)(35,43)(36,44),
(45,53)(46,54)(47,55)(48,56)(49,57)(50,58)(51,59)(52,60),
( 5, 6)( 7, 8)(11,12)(17,18)(19,20)(23,24)(25,27)(26,28)(33,34)(35,36)(41,42)
(43,44)(49,50)(51,52)(57,58)(59,60)
,
( 5, 7)( 6, 8)(11,12)(17,19)(18,20)(25,27)(26,28)(33,35)(34,36)(41,43)(42,44)
(49,51)(50,52)(57,59)(58,60)
],
["ConstructV4G",["4_1.L3(4)","4_2.L3(4)","2^2.L3(4)"]]);
ALF("(2x4).L3(4)","4_1.L3(4)",[1,1,3,3,2,2,4,4,5,5,6,6,7,7,9,9,8,8,10,10,
11,11,12,12,13,13,14,14,15,15,17,17,16,16,18,18,19,19,21,21,20,20,22,22,
23,23,25,25,24,24,26,26,27,27,29,29,28,28,30,30]);
ALF("(2x4).L3(4)","4_2.L3(4)",[1,3,1,3,2,4,2,4,5,5,6,6,7,9,7,9,8,10,8,10,
11,13,12,14,15,15,16,16,17,19,17,19,18,20,18,20,21,23,21,23,22,24,22,24,
25,27,25,27,26,28,26,28,29,31,29,31,30,32,30,32]);
ALF("(2x4).L3(4)","2^2.L3(4)",[1,2,2,1,3,4,4,3,5,6,7,8,9,10,10,9,11,12,12,
11,13,13,14,14,15,16,17,18,19,20,20,19,21,22,22,21,23,24,24,23,25,26,26,
25,27,28,28,27,29,30,30,29,31,32,32,31,33,34,34,33]);
MOT("4^2.L3(4)",
[
"constructed using `PossibleCharacterTablesOfTypeV4G'"
],
[322560,322560,322560,322560,322560,322560,322560,322560,322560,322560,322560,
322560,322560,322560,322560,322560,256,256,256,256,144,144,144,144,144,144,144
,144,144,144,144,144,144,144,144,144,64,64,64,64,64,64,64,64,64,64,64,64,80,80
,80,80,80,80,80,80,80,80,80,80,80,80,80,80,80,80,80,80,80,80,80,80,80,80,80,80
,80,80,80,80,112,112,112,112,112,112,112,112,112,112,112,112,112,112,112,112,
112,112,112,112,112,112,112,112,112,112,112,112,112,112,112,112],
[,[1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4,1,2,3,4,21,21,21,21,22,22,22,22,23,23,23,23
,24,24,24,24,18,18,18,18,19,19,19,19,20,20,20,20,65,65,65,65,66,66,66,66,67,67
,67,67,68,68,68,68,49,49,49,49,50,50,50,50,51,51,51,51,52,52,52,52,81,81,81,81
,82,82,82,82,83,83,83,83,84,84,84,84,97,97,97,97,98,98,98,98,99,99,99,99,100,
100,100,100],[1,2,3,4,6,5,8,7,11,12,9,10,16,15,14,13,17,18,19,20,1,2,3,4,6,5,8
,7,11,12,9,10,16,15,14,13,37,38,40,39,41,42,44,43,45,46,48,47,65,66,67,68,70,
69,72,71,75,76,73,74,80,79,78,77,49,50,51,52,54,53,56,55,59,60,57,58,64,63,62,
61,97,98,99,100,102,101,104,103,107,108,105,106,112,111,110,109,81,82,83,84,86
,85,88,87,91,92,89,90,96,95,94,93],,[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
,44,45,46,47,48,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,1,2,3,4,5,6,7,8,9,10,11
,12,13,14,15,16,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,
81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96],,[1,2,3,4,6,5,8,7,11,12,9,10,
16,15,14,13,17,18,19,20,21,22,23,24,26,25,28,27,31,32,29,30,36,35,34,33,37,38,
40,39,41,42,44,43,45,46,48,47,65,66,67,68,70,69,72,71,75,76,73,74,80,79,78,77,
49,50,51,52,54,53,56,55,59,60,57,58,64,63,62,61,1,2,3,4,6,5,8,7,11,12,9,10,16,
15,14,13,1,2,3,4,6,5,8,7,11,12,9,10,16,15,14,13]],
0,
[
(49,65)(50,66)(51,67)(52,68)(53,69)(54,70)(55,71)(56,72)(57,73)(58,74)(59,75)
(60,76)(61,77)(62,78)(63,79)(64,80)
,
( 81, 97)( 82, 98)( 83, 99)( 84,100)( 85,101)( 86,102)( 87,103)( 88,104)
( 89,105)( 90,106)( 91,107)( 92,108)( 93,109)( 94,110)( 95,111)( 96,112)
,
( 5, 6)( 7, 8)( 9, 11)( 10, 12)( 13, 16)( 14, 15)( 25, 26)( 27, 28)
( 29, 31)( 30, 32)( 33, 36)( 34, 35)( 39, 40)( 43, 44)( 47, 48)( 53, 54)
( 55, 56)( 57, 59)( 58, 60)( 61, 64)( 62, 63)( 69, 70)( 71, 72)( 73, 75)
( 74, 76)( 77, 80)( 78, 79)( 85, 86)( 87, 88)( 89, 91)( 90, 92)( 93, 96)
( 94, 95)(101,102)(103,104)(105,107)(106,108)(109,112)(110,111)
,
( 3, 4)( 7, 8)( 9, 15)( 10, 16)( 11, 14)( 12, 13)( 19, 20)( 23, 24)
( 27, 28)( 29, 35)( 30, 36)( 31, 34)( 32, 33)( 41, 45)( 42, 46)( 43, 48)
--> --------------------
--> maximum size reached
--> --------------------
[ Dauer der Verarbeitung: 0.31 Sekunden
(vorverarbeitet)
]
|
