Quelle  ctoline3.tbl   Sprache: unbekannt

#############################################################################
##
#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
,-1,-1,-1,-1,-1,-1,-1],[1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-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,-2,2,2,0,0,0,0,6,6,2,2,0,0,0,
-1,-1,0,0,0,0,-2,2,2,0,0],
[TENSOR,[5,2]],
[TENSOR,[5,3]],
[TENSOR,[5,4]],[35,35,3,3,-1,-1,3,3,-1,0,0,0,0,1,1,1,1,1,1,-1,-1,7,7,-1,-1,1,
1,-1,0,0,5,5,-1,-1,1,1,1,0,0],
[TENSOR,[9,2]],
[TENSOR,[9,3]],
[TENSOR,[9,4]],[70,70,6,6,-2,-2,-2,-2,2,0,0,0,0,2,2,2,2,-2,-2,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[13,3]],[90,90,-6,-6,0,0,2,2,2,0,0,-1,-1,0,0,0,0,0,0,0,0,6,6,-2,-2,0,
0,2,-1,-1,0,0,0,0,0,0,0,0,0],
[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
,0,0,0,0,6,6,0,0,-2,-2,-2,1,1],
[TENSOR,[17,2]],[64,64,0,0,1,1,0,0,0,-1,-1,1,1,8,0,-1,-1,0,0,0,0,8,8,0,0,-1,
-1,0,1,1,4,4,1,1,0,0,0,-1,-1],
[TENSOR,[19,2]],
[TENSOR,[19,3]],
[TENSOR,[19,4]],[20,-20,4,-4,2,-2,4,-4,0,0,0,-1,1,0,0,0,0,0,0,0,0,8,-8,0,0,2,
-2,0,1,-1,0,0,0,0,0,0,0,0,0],
[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,
0,0,0,4,-4,-2,2,0,0,0,-1,1],
[TENSOR,[25,2]],[36,-36,4,-4,0,0,0,0,0,1,-1,1,-1,0,0,0,0,2,-2,0,0,6,-6,2,-2,0
,0,0,-1,1,6,-6,0,0,0,0,0,1,-1],
[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
,1,0,1,-1,4,-4,1,-1,0,0,0,-1,1],
[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]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[1,1,
1,1,1,1,1,1,1,1,1,1,1,-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,
0,-2,-2,2,0,0],
[TENSOR,[5,2]],
[TENSOR,[5,3]],
[TENSOR,[5,4]],[35,35,3,3,-1,-1,3,3,-1,0,0,0,0,1,1,1,1,-1,-1,7,-1,1,-1,-1,0,0
,5,-1,1,1,1,0,0],
[TENSOR,[9,2]],
[TENSOR,[9,3]],
[TENSOR,[9,4]],[70,70,6,6,-2,-2,-2,-2,2,0,0,0,0,2,2,2,-2,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0],
[TENSOR,[13,3]],[90,90,-6,-6,0,0,2,2,2,0,0,-1,-1,0,0,0,0,0,0,6,-2,0,2,2,-1,-1
,0,0,0,0,0,0,0],
[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
,6,0,-2,-2,-2,1,1],
[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,
E(7)+E(7)^2-E(7)^3+E(7)^4-E(7)^5-E(7)^6,0,0,0,0,0,0,0],
[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,
0,0,0,0,E(20)+E(20)^9-E(20)^13-E(20)^17,-E(20)-E(20)^9+E(20)^13+E(20)^17],
[TENSOR,[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)
( 44, 47)( 51, 52)( 55, 56)( 57, 63)( 58, 64)( 59, 62)( 60, 61)( 67, 68)
( 71, 72)( 73, 79)( 74, 80)( 75, 78)( 76, 77)( 83, 84)( 87, 88)( 89, 95)
( 90, 96)( 91, 94)( 92, 93)( 99,100)(103,104)(105,111)(106,112)(107,110)
(108,109)
,
(  2,  3)(  5,  9)(  6, 11)(  7, 10)(  8, 12)( 14, 15)( 18, 19)( 22, 23)
( 25, 29)( 26, 31)( 27, 30)( 28, 32)( 34, 35)( 37, 41)( 38, 42)( 39, 44)
( 40, 43)( 47, 48)( 50, 51)( 53, 57)( 54, 59)( 55, 58)( 56, 60)( 62, 63)
( 66, 67)( 69, 73)( 70, 75)( 71, 74)( 72, 76)( 78, 79)( 82, 83)( 85, 89)
( 86, 91)( 87, 90)( 88, 92)( 94, 95)( 98, 99)(101,105)(102,107)(103,106)
(104,108)(110,111)
],
["ConstructV4G","(2x4).L3(4)",(2,3,4)(5,11,14)(6,9,15)(7,10,13)(8,12,16)(18,
19,20)(22,23,24)(25,31,34)(26,29,35)(27,30,33)(28,32,36)(37,41,45)(38,42,46)
(39,43,48)(40,44,47)(50,51,52)(53,59,62)(54,57,63)(55,58,61)(56,60,64)(66,67,
68)(69,75,78)(70,73,79)(71,74,77)(72,76,80)(82,83,84)(85,91,94)(86,89,95)(87,
90,93)(88,92,96)(98,99,100)(101,107,110)(102,105,111)(103,106,109)(104,108,
112)]);
ALF("4^2.L3(4)","(2x4).L3(4)",[1,1,4,4,2,2,3,3,5,5,8,8,6,6,7,7,9,10,11,
12,13,13,16,16,14,14,15,15,17,17,20,20,18,18,19,19,21,22,23,24,25,25,26,
26,27,27,28,28,29,29,32,32,30,30,31,31,33,33,36,36,34,34,35,35,37,37,40,
40,38,38,39,39,41,41,44,44,42,42,43,43,45,45,48,48,46,46,47,47,49,49,52,
52,50,50,51,51,53,53,56,56,54,54,55,55,57,57,60,60,58,58,59,59]);

MOT("(4^2x3).L3(4)",
[
"constructed using `PossibleCharacterTablesOfTypeV4G'"
],
[967680,967680,967680,967680,967680,967680,967680,967680,967680,967680,967680,
967680,967680,967680,967680,967680,967680,967680,967680,967680,967680,967680,
967680,967680,967680,967680,967680,967680,967680,967680,967680,967680,967680,
967680,967680,967680,967680,967680,967680,967680,967680,967680,967680,967680,
967680,967680,967680,967680,768,768,768,768,768,768,768,768,768,768,768,768,
144,144,144,144,144,144,144,144,144,144,144,144,144,144,144,144,192,192,192,
192,192,192,192,192,192,192,192,192,192,192,192,192,192,192,192,192,192,192,
192,192,192,192,192,192,192,192,192,192,192,192,192,192,240,240,240,240,240,
240,240,240,240,240,240,240,240,240,240,240,240,240,240,240,240,240,240,240,
240,240,240,240,240,240,240,240,240,240,240,240,240,240,240,240,240,240,240,
240,240,240,240,240,240,240,240,240,240,240,240,240,240,240,240,240,240,240,
240,240,240,240,240,240,240,240,240,240,240,240,240,240,240,240,240,240,240,
240,240,240,240,240,240,240,240,240,240,240,240,240,240,240,336,336,336,336,
336,336,336,336,336,336,336,336,336,336,336,336,336,336,336,336,336,336,336,
336,336,336,336,336,336,336,336,336,336,336,336,336,336,336,336,336,336,336,
336,336,336,336,336,336,336,336,336,336,336,336,336,336,336,336,336,336,336,
336,336,336,336,336,336,336,336,336,336,336,336,336,336,336,336,336,336,336,
336,336,336,336,336,336,336,336,336,336,336,336,336,336,336,336],
[,[1,1,1,1,2,2,2,2,18,18,18,18,17,17,17,17,33,33,33,33,34,34,34,34,3,3,3,3,4,4
,4,4,20,20,20,20,19,19,19,19,35,35,35,35,36,36,36,36,1,2,18,17,33,34,3,4,20,19
,35,36,61,61,61,61,62,62,62,62,63,63,63,63,64,64,64,64,50,50,54,54,58,58,50,50
,54,54,58,58,55,55,55,55,59,59,59,59,51,51,51,51,56,56,56,56,60,60,60,60,52,52
,52,52,161,161,161,161,162,162,162,162,178,178,178,178,177,177,177,177,193,193
,193,193,194,194,194,194,163,163,163,163,164,164,164,164,180,180,180,180,179,
179,179,179,195,195,195,195,196,196,196,196,113,113,113,113,114,114,114,114,
130,130,130,130,129,129,129,129,145,145,145,145,146,146,146,146,115,115,115,
115,116,116,116,116,132,132,132,132,131,131,131,131,147,147,147,147,148,148,
148,148,209,209,209,209,210,210,210,210,226,226,226,226,225,225,225,225,241,
241,241,241,242,242,242,242,211,211,211,211,212,212,212,212,228,228,228,228,
227,227,227,227,243,243,243,243,244,244,244,244,257,257,257,257,258,258,258,
258,274,274,274,274,273,273,273,273,289,289,289,289,290,290,290,290,259,259,
259,259,260,260,260,260,276,276,276,276,275,275,275,275,291,291,291,291,292,
292,292,292],[1,2,3,4,6,5,8,7,25,26,27,28,29,30,31,32,4,3,2,1,7,8,5,6,27,28,25
,26,32,31,30,29,1,2,3,4,5,6,7,8,26,25,28,27,29,30,31,32,49,50,55,56,49,50,55,
56,49,50,55,56,1,2,3,4,5,6,7,8,25,26,27,28,29,30,31,32,77,78,83,84,78,77,84,83
,77,78,83,84,89,90,92,91,91,92,89,90,90,89,91,92,101,102,104,103,103,104,101,
102,102,101,103,104,161,162,163,164,166,165,168,167,185,186,187,188,189,190,
191,192,164,163,162,161,167,168,165,166,187,188,185,186,192,191,190,189,161,
162,163,164,165,166,167,168,186,185,188,187,189,190,191,192,113,114,115,116,
118,117,120,119,137,138,139,140,141,142,143,144,116,115,114,113,119,120,117,
118,139,140,137,138,144,143,142,141,113,114,115,116,117,118,119,120,138,137,
140,139,141,142,143,144,257,258,259,260,262,261,264,263,281,282,283,284,285,
286,287,288,260,259,258,257,263,264,261,262,283,284,281,282,288,287,286,285,
257,258,259,260,261,262,263,264,282,281,284,283,285,286,287,288,209,210,211,
212,214,213,216,215,233,234,235,236,237,238,239,240,212,211,210,209,215,216,
213,214,235,236,233,234,240,239,238,237,209,210,211,212,213,214,215,216,234,
233,236,235,237,238,239,240],,[1,2,3,4,5,6,7,8,42,41,44,43,45,46,47,48,36,35,
34,33,39,40,37,38,25,26,27,28,29,30,31,32,20,19,18,17,23,24,21,22,10,9,12,11,
13,14,15,16,49,50,59,60,57,58,55,56,53,54,51,52,61,62,63,64,65,66,67,68,69,70,
71,72,73,74,75,76,77,78,87,88,86,85,83,84,82,81,79,80,89,90,91,92,99,100,98,97
,96,95,93,94,101,102,103,104,111,112,110,109,108,107,105,106,1,2,3,4,5,6,7,8,
42,41,44,43,45,46,47,48,36,35,34,33,39,40,37,38,25,26,27,28,29,30,31,32,20,19,
18,17,23,24,21,22,10,9,12,11,13,14,15,16,1,2,3,4,5,6,7,8,42,41,44,43,45,46,47,
48,36,35,34,33,39,40,37,38,25,26,27,28,29,30,31,32,20,19,18,17,23,24,21,22,10,
9,12,11,13,14,15,16,257,258,259,260,261,262,263,264,298,297,300,299,301,302,
303,304,292,291,290,289,295,296,293,294,281,282,283,284,285,286,287,288,276,
275,274,273,279,280,277,278,266,265,268,267,269,270,271,272,209,210,211,212,
213,214,215,216,250,249,252,251,253,254,255,256,244,243,242,241,247,248,245,
246,233,234,235,236,237,238,239,240,228,227,226,225,231,232,229,230,218,217,
220,219,221,222,223,224],,[1,2,3,4,6,5,8,7,11,12,9,10,16,15,14,13,17,18,19,20,
22,21,24,23,27,28,25,26,32,31,30,29,33,34,35,36,38,37,40,39,43,44,41,42,48,47,
46,45,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,66,65,68,67,71,72,69,70,
76,75,74,73,77,78,80,79,81,82,84,83,85,86,88,87,89,90,92,91,94,93,95,96,97,98,
100,99,101,102,104,103,106,105,107,108,109,110,112,111,161,162,163,164,166,165
,168,167,171,172,169,170,176,175,174,173,177,178,179,180,182,181,184,183,187,
188,185,186,192,191,190,189,193,194,195,196,198,197,200,199,203,204,201,202,
208,207,206,205,113,114,115,116,118,117,120,119,123,124,121,122,128,127,126,
125,129,130,131,132,134,133,136,135,139,140,137,138,144,143,142,141,145,146,
147,148,150,149,152,151,155,156,153,154,160,159,158,157,1,2,3,4,6,5,8,7,11,12,
9,10,16,15,14,13,17,18,19,20,22,21,24,23,27,28,25,26,32,31,30,29,33,34,35,36,
38,37,40,39,43,44,41,42,48,47,46,45,1,2,3,4,6,5,8,7,11,12,9,10,16,15,14,13,17,
18,19,20,22,21,24,23,27,28,25,26,32,31,30,29,33,34,35,36,38,37,40,39,43,44,41,
42,48,47,46,45]],
0,
[
(209,257)(210,258)(211,259)(212,260)(213,261)(214,262)(215,263)(216,264)
(217,265)(218,266)(219,267)(220,268)(221,269)(222,270)(223,271)(224,272)
(225,273)(226,274)(227,275)(228,276)(229,277)(230,278)(231,279)(232,280)
(233,281)(234,282)(235,283)(236,284)(237,285)(238,286)(239,287)(240,288)
(241,289)(242,290)(243,291)(244,292)(245,293)(246,294)(247,295)(248,296)
(249,297)(250,298)(251,299)(252,300)(253,301)(254,302)(255,303)(256,304)
,
(113,161)(114,162)(115,163)(116,164)(117,165)(118,166)(119,167)(120,168)
(121,169)(122,170)(123,171)(124,172)(125,173)(126,174)(127,175)(128,176)
(129,177)(130,178)(131,179)(132,180)(133,181)(134,182)(135,183)(136,184)
(137,185)(138,186)(139,187)(140,188)(141,189)(142,190)(143,191)(144,192)
(145,193)(146,194)(147,195)(148,196)(149,197)(150,198)(151,199)(152,200)
(153,201)(154,202)(155,203)(156,204)(157,205)(158,206)(159,207)(160,208)
,
(  9, 42)( 10, 41)( 11, 44)( 12, 43)( 13, 45)( 14, 46)( 15, 47)( 16, 48)
( 17, 36)( 18, 35)( 19, 34)( 20, 33)( 21, 39)( 22, 40)( 23, 37)( 24, 38)
( 51, 59)( 52, 60)( 53, 57)( 54, 58)( 79, 87)( 80, 88)( 81, 86)( 82, 85)
( 93, 99)( 94,100)( 95, 98)( 96, 97)(105,111)(106,112)(107,110)(108,109)
(121,154)(122,153)(123,156)(124,155)(125,157)(126,158)(127,159)(128,160)
(129,148)(130,147)(131,146)(132,145)(133,151)(134,152)(135,149)(136,150)
(169,202)(170,201)(171,204)(172,203)(173,205)(174,206)(175,207)(176,208)
(177,196)(178,195)(179,194)(180,193)(181,199)(182,200)(183,197)(184,198)
(217,250)(218,249)(219,252)(220,251)(221,253)(222,254)(223,255)(224,256)
(225,244)(226,243)(227,242)(228,241)(229,247)(230,248)(231,245)(232,246)
(265,298)(266,297)(267,300)(268,299)(269,301)(270,302)(271,303)(272,304)
(273,292)(274,291)(275,290)(276,289)(277,295)(278,296)(279,293)(280,294)
,
(  5,  6)(  7,  8)(  9, 11)( 10, 12)( 13, 16)( 14, 15)( 21, 22)( 23, 24)
( 25, 27)( 26, 28)( 29, 32)( 30, 31)( 37, 38)( 39, 40)( 41, 43)( 42, 44)
( 45, 48)( 46, 47)( 65, 66)( 67, 68)( 69, 71)( 70, 72)( 73, 76)( 74, 75)
( 79, 80)( 83, 84)( 87, 88)( 91, 92)( 93, 94)( 99,100)(103,104)(105,106)
(111,112)(117,118)(119,120)(121,123)(122,124)(125,128)(126,127)(133,134)
(135,136)(137,139)(138,140)(141,144)(142,143)(149,150)(151,152)(153,155)
(154,156)(157,160)(158,159)(165,166)(167,168)(169,171)(170,172)(173,176)
(174,175)(181,182)(183,184)(185,187)(186,188)(189,192)(190,191)(197,198)
(199,200)(201,203)(202,204)(205,208)(206,207)(213,214)(215,216)(217,219)
(218,220)(221,224)(222,223)(229,230)(231,232)(233,235)(234,236)(237,240)
(238,239)(245,246)(247,248)(249,251)(250,252)(253,256)(254,255)(261,262)
(263,264)(265,267)(266,268)(269,272)(270,271)(277,278)(279,280)(281,283)
(282,284)(285,288)(286,287)(293,294)(295,296)(297,299)(298,300)(301,304)
(302,303)
,
(  3,  4)(  7,  8)(  9, 15)( 10, 16)( 11, 14)( 12, 13)( 17, 18)( 21, 22)
( 25, 31)( 26, 32)( 27, 30)( 28, 29)( 35, 36)( 39, 40)( 41, 48)( 42, 47)
( 43, 45)( 44, 46)( 51, 52)( 55, 56)( 59, 60)( 63, 64)( 67, 68)( 69, 75)
( 70, 76)( 71, 74)( 72, 73)( 89,101)( 90,102)( 91,104)( 92,103)( 93,106)
( 94,105)( 95,107)( 96,108)( 97,109)( 98,110)( 99,112)(100,111)(115,116)
(119,120)(121,127)(122,128)(123,126)(124,125)(129,130)(133,134)(137,143)
(138,144)(139,142)(140,141)(147,148)(151,152)(153,160)(154,159)(155,157)
(156,158)(163,164)(167,168)(169,175)(170,176)(171,174)(172,173)(177,178)
(181,182)(185,191)(186,192)(187,190)(188,189)(195,196)(199,200)(201,208)
(202,207)(203,205)(204,206)(211,212)(215,216)(217,223)(218,224)(219,222)
(220,221)(225,226)(229,230)(233,239)(234,240)(235,238)(236,237)(243,244)
(247,248)(249,256)(250,255)(251,253)(252,254)(259,260)(263,264)(265,271)
(266,272)(267,270)(268,269)(273,274)(277,278)(281,287)(282,288)(283,286)
(284,285)(291,292)(295,296)(297,304)(298,303)(299,301)(300,302)
,
(  2,  3)(  5, 25)(  6, 27)(  7, 26)(  8, 28)(  9, 23)( 10, 21)( 11, 24)
( 12, 22)( 13, 45)( 14, 47)( 15, 46)( 16, 48)( 17, 36)( 18, 34)( 19, 35)
( 20, 33)( 30, 31)( 37, 42)( 38, 44)( 39, 41)( 40, 43)( 50, 55)( 51, 54)
( 52, 60)( 53, 57)( 58, 59)( 62, 63)( 65, 69)( 66, 71)( 67, 70)( 68, 72)
( 74, 75)( 77, 89)( 78, 90)( 79,100)( 80, 99)( 81, 96)( 82, 95)( 83, 92)
( 84, 91)( 85, 98)( 86, 97)( 87, 94)( 88, 93)(103,104)(105,112)(106,111)
(107,110)(108,109)(114,115)(117,137)(118,139)(119,138)(120,140)(121,135)
(122,133)(123,136)(124,134)(125,157)(126,159)(127,158)(128,160)(129,148)
(130,146)(131,147)(132,145)(142,143)(149,154)(150,156)(151,153)(152,155)
(162,163)(165,185)(166,187)(167,186)(168,188)(169,183)(170,181)(171,184)
(172,182)(173,205)(174,207)(175,206)(176,208)(177,196)(178,194)(179,195)
(180,193)(190,191)(197,202)(198,204)(199,201)(200,203)(210,211)(213,233)
(214,235)(215,234)(216,236)(217,231)(218,229)(219,232)(220,230)(221,253)
(222,255)(223,254)(224,256)(225,244)(226,242)(227,243)(228,241)(238,239)
(245,250)(246,252)(247,249)(248,251)(258,259)(261,281)(262,283)(263,282)
(264,284)(265,279)(266,277)(267,280)(268,278)(269,301)(270,303)(271,302)
(272,304)(273,292)(274,290)(275,291)(276,289)(286,287)(293,298)(294,300)
(295,297)(296,299)
],
["ConstructV4G","(2x12).L3(4)",(2,3,4)(5,27,30)(6,25,31)(7,26,29)(8,28,32)(9,
15,38)(10,13,39)(11,14,37)(12,16,40)(17,19,18)(21,41,45)(22,43,48)(23,44,46)
(24,42,47)(34,35,36)(50,55,56)(51,52,58)(54,59,60)(62,63,64)(65,71,74)(66,69,
75)(67,70,73)(68,72,76)(77,89,101)(78,90,102)(79,93,106)(80,94,105)(81,97,109)
(82,98,110)(83,91,104)(84,92,103)(85,95,107)(86,96,108)(87,99,112)(88,100,111)
(114,115,116)(117,139,142)(118,137,143)(119,138,141)(120,140,144)(121,127,150)
(122,125,151)(123,126,149)(124,128,152)(129,131,130)(133,153,157)(134,155,160)
(135,156,158)(136,154,159)(146,147,148)(162,163,164)(165,187,190)(166,185,191)
(167,186,189)(168,188,192)(169,175,198)(170,173,199)(171,174,197)(172,176,200)
(177,179,178)(181,201,205)(182,203,208)(183,204,206)(184,202,207)(194,195,196)
(210,211,212)(213,235,238)(214,233,239)(215,234,237)(216,236,240)(217,223,246)
(218,221,247)(219,222,245)(220,224,248)(225,227,226)(229,249,253)(230,251,256)
(231,252,254)(232,250,255)(242,243,244)(258,259,260)(261,283,286)(262,281,287)
(263,282,285)(264,284,288)(265,271,294)(266,269,295)(267,270,293)(268,272,296)
(273,275,274)(277,297,301)(278,299,304)(279,300,302)(280,298,303)(290,291,292)
]);
ALF("(4^2x3).L3(4)","(2x12).L3(4)",[1,1,4,4,2,2,3,3,5,5,8,8,6,6,7,7,9,9,
12,12,10,10,11,11,13,13,16,16,14,14,15,15,17,17,20,20,18,18,19,19,21,21,
24,24,22,22,23,23,25,26,27,28,29,30,31,32,33,34,35,36,37,37,40,40,38,38,
39,39,41,41,44,44,42,42,43,43,45,46,47,48,49,50,51,52,53,54,55,56,57,57,
58,58,59,59,60,60,61,61,62,62,63,63,64,64,65,65,66,66,67,67,68,68,69,69,
72,72,70,70,71,71,73,73,76,76,74,74,75,75,77,77,80,80,78,78,79,79,81,81,
84,84,82,82,83,83,85,85,88,88,86,86,87,87,89,89,92,92,90,90,91,91,93,93,
96,96,94,94,95,95,97,97,100,100,98,98,99,99,101,101,104,104,102,102,103,
103,105,105,108,108,106,106,107,107,109,109,112,112,110,110,111,111,113,
113,116,116,114,114,115,115,117,117,120,120,118,118,119,119,121,121,124,
124,122,122,123,123,125,125,128,128,126,126,127,127,129,129,132,132,130,
130,131,131,133,133,136,136,134,134,135,135,137,137,140,140,138,138,139,
139,141,141,144,144,142,142,143,143,145,145,148,148,146,146,147,147,149,
149,152,152,150,150,151,151,153,153,156,156,154,154,155,155,157,157,160,
160,158,158,159,159,161,161,164,164,162,162,163,163]);

MOT("3.L3(4)",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[60480,60480,60480,192,192,192,9,48,48,48,48,48,48,48,48,48,15,15,15,15,15,15,
21,21,21,21,21,21],
[,[1,3,2,1,3,2,7,4,6,5,4,6,5,4,6,5,20,22,21,17,19,18,23,25,24,26,28,27],[1,1,
1,4,4,4,1,8,8,8,11,11,11,14,14,14,20,20,20,17,17,17,26,26,26,23,23,23],,[1,3,
2,4,6,5,7,8,10,9,11,13,12,14,16,15,1,3,2,1,3,2,26,28,27,23,25,24],,[1,2,3,4,5,
6,7,8,9,10,11,12,13,14,15,16,20,21,22,17,18,19,1,2,3,1,2,3]],
0,
[(23,26)(24,27)(25,28),(17,20)(18,21)(19,22),( 2, 3)( 5, 6)( 9,10)(12,13)
(15,16)(18,19)(21,22)(24,25)(27,28),(11,14)(12,15)(13,16),( 8,11)( 9,12)
(10,13)],
["ConstructProj",[["L3(4)",[]],,["3.L3(4)",[-1,-1,-1,-1,-13,-13,11,11,-1]]]]);
ARC("3.L3(4)","tomfusion",rec(name:="3.L3(4)",map:=[1,3,3,2,16,16,4,12,39,
39,13,37,37,14,38,38,15,55,55,15,55,55,18,72,72,18,72,72],text:=[
"fusion map is unique up to table autom."
],perm:=(4,5)));
ARC("3.L3(4)","maxes",["3x2^4:A5","3x2^4:A5","3.A6","3.L3(4)M4","3.L3(4)M5",
"3xL3(2)","3.L3(4)M7","3.L3(4)M8","3^(1+2)_+:Q8"]);
ALF("3.L3(4)","L3(4)",[1,1,1,2,2,2,3,4,4,4,5,5,5,6,6,6,7,7,7,8,8,8,9,9,9,
10,10,10]);
ALF("3.L3(4)","3.L3(4).2_1",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,
19,17,18,19,20,21,22,20,21,22],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("3.L3(4)","3.L3(4).2_2",[1,2,2,3,4,4,5,6,7,7,8,9,10,8,10,9,11,12,13,
11,13,12,14,15,15,16,17,17],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);
ALF("3.L3(4)","3.L3(4).2_3",[1,2,2,3,4,4,5,6,7,7,8,9,10,8,10,9,11,12,12,
13,14,14,15,16,17,15,17,16],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);
ALF("3.L3(4)","3.L3(4).3",[1,2,3,4,5,6,7,8,9,10,8,9,10,8,9,10,11,12,13,14,
15,16,17,18,19,20,21,22],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);
ALF("3.L3(4)","3.L3(4).6",[1,2,3,4,5,6,7,8,9,10,8,9,10,8,9,10,11,12,13,11,
12,13,14,15,16,14,15,16]);
ALF("3.L3(4)","3.M22",[1,2,3,4,5,6,7,8,9,10,11,12,13,11,12,13,14,15,16,14,
15,16,20,21,22,23,24,25],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);

MOT("3.L3(4).2^2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[241920,120960,768,384,36,192,96,96,96,96,30,15,42,21,864,432,96,48,36,48,24,
24,24,24,672,32,12,16,14,240,12,32,32,10],
[,[1,2,1,2,5,3,4,3,4,4,11,12,13,14,1,2,3,4,5,6,7,8,10,9,1,3,5,6,13,1,5,6,6,
11],[1,1,3,3,1,6,6,8,8,8,11,11,13,13,15,15,17,17,15,20,20,22,22,22,25,26,25,
28,29,30,30,32,33,34],,[1,2,3,4,5,6,7,8,10,9,1,2,13,14,15,16,17,18,19,20,21,
22,24,23,25,26,27,28,29,30,31,32,33,30],,[1,2,3,4,5,6,7,8,9,10,11,12,1,2,15,
16,17,18,19,20,21,22,23,24,25,26,27,28,25,30,31,32,33,34]],
0,
[( 9,10)(23,24)],
["ConstructMGA","3.L3(4).2_1","L3(4).2^2",[[15,17],[16,18],[19,25],[20,26],
[21,23],[22,24],[27,29],[28,30],[31,32],[33,34],[35,37],[36,38]],()]);
ALF("3.L3(4).2^2","L3(4).2^2",[1,1,2,2,3,4,4,5,5,5,6,6,7,7,8,8,9,9,10,11,
11,12,12,12,13,14,15,16,17,18,19,20,21,22]);
ALF("3.L3(4).2^2","G2(4).2",[1,4,2,11,5,6,18,7,19,20,9,22,13,24,25,28,26,
33,29,30,38,31,40,39,25,26,29,32,35,3,12,14,14,17],[
"fusion map is unique up to table autom."
]);
ALN("3.L3(4).2^2",["3.L3(4).V4"]);

MOT("3.L3(4).2_1",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[120960,120960,120960,384,384,384,18,96,96,96,96,96,96,96,96,96,15,15,15,21,
21,21,432,432,432,48,48,48,18,24,24,24,24,24,24,24,24,24],
[,[1,3,2,1,3,2,7,4,6,5,4,6,5,4,6,5,17,19,18,20,22,21,1,3,2,4,6,5,7,8,10,9,11,
13,12,14,16,15],[1,1,1,4,4,4,1,8,8,8,11,11,11,14,14,14,17,17,17,20,20,20,23,
23,23,26,26,26,23,30,30,30,33,33,33,36,36,36],,[1,3,2,4,6,5,7,8,10,9,11,13,12,
14,16,15,1,3,2,20,22,21,23,25,24,26,28,27,29,30,32,31,33,35,34,36,38,37],,[1,
2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,1,2,3,23,24,25,26,27,28,29,30,
31,32,33,34,35,36,37,38]],
0,
[( 2, 3)( 5, 6)( 9,10)(12,13)(15,16)(18,19)(21,22)(24,25)(27,28)(31,32)(34,35)
(37,38),(11,14)(12,15)(13,16)(33,36)(34,37)(35,38),( 8,11)( 9,12)(10,13)
(30,33)(31,34)(32,35)],
["ConstructProj",[["L3(4).2_1",[]],,["3.L3(4).2_1",[-1,-1,-1,-1,-1,-1,-1]]]]);
ALF("3.L3(4).2_1","L3(4).2_1",[1,1,1,2,2,2,3,4,4,4,5,5,5,6,6,6,7,7,7,8,8,
8,9,9,9,10,10,10,11,12,12,12,13,13,13,14,14,14]);
ALF("3.L3(4).2_1","3.L3(4).6",[1,2,3,4,5,6,7,8,9,10,8,9,10,8,9,10,11,12,
13,14,15,16,17,18,19,20,21,22,23,24,25,26,24,25,26,24,25,26]);
ALF("3.L3(4).2_1","3.L3(4).2^2",[1,2,2,3,4,4,5,6,7,7,8,9,10,8,10,9,11,12,
12,13,14,14,15,16,16,17,18,18,19,20,21,21,22,23,24,22,24,23],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("3.L3(4).2_1","3.U6(2)",[1,2,3,7,8,9,19,26,27,28,29,30,31,32,33,34,41,
42,43,66,67,68,10,11,12,38,39,40,65,72,73,74,75,76,77,78,79,80],[
"fusion map determined up to table aut. by compatibility\n",
"with factors"
]);

MOT("3.L3(4).2_2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[120960,60480,384,192,18,96,48,48,48,48,15,15,15,42,21,42,21,336,16,6,8,14,
14],
[,[1,2,1,2,5,3,4,3,4,4,11,12,13,14,15,16,17,1,3,5,6,14,16],[1,1,3,3,1,6,6,8,8,
8,11,11,11,16,16,14,14,18,19,18,21,23,22],,[1,2,3,4,5,6,7,8,10,9,1,2,2,16,17,
14,15,18,19,20,21,23,22],,[1,2,3,4,5,6,7,8,9,10,11,13,12,1,2,1,2,18,19,20,21,
18,18]],
0,
[(14,16)(15,17)(22,23),(12,13),( 9,10),( 9,10)(12,13)],
["ConstructMGA","3.L3(4)","L3(4).2_2",[[11,12],[13,16],[14,15],[17,18],[19,
20],[21,22],[23,26],[24,25],[27,28]],()]);
ALF("3.L3(4).2_2","L3(4).2_2",[1,1,2,2,3,4,4,5,5,5,6,6,6,7,7,8,8,9,10,11,
12,13,14]);
ALF("3.L3(4).2_2","3.L3(4).2^2",[1,2,3,4,5,6,7,8,9,10,11,12,12,13,14,13,
14,25,26,27,28,29,29]);
ALF("3.L3(4).2_2","3.L3(4).3.2_2",[1,2,3,4,5,6,7,6,7,7,8,9,10,11,12,13,14,
34,35,36,37,38,39],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);
ALF("3.L3(4).2_2","3.M22.2",[1,2,3,4,5,6,7,8,9,9,10,11,11,14,15,16,17,23,
26,27,28,31,32],[
"fusion map is unique up to table aut."
]);

MOT("3.L3(4).2_3",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[120960,60480,384,192,18,96,48,48,48,48,30,15,30,15,21,21,21,120,6,16,16,10,
10],
[,[1,2,1,2,5,3,4,3,4,4,13,14,11,12,15,17,16,1,5,6,6,13,11],[1,1,3,3,1,6,6,8,8,
8,13,13,11,11,15,15,15,18,18,20,21,23,22],,[1,2,3,4,5,6,7,8,10,9,1,2,1,2,15,
16,17,18,19,20,21,18,18],,[1,2,3,4,5,6,7,8,9,10,13,14,11,12,1,2,2,18,19,20,21,
23,22]],
0,
[(20,21),(16,17),(11,13)(12,14)(22,23),( 9,10),( 9,10)(16,17)],
["ConstructMGA","3.L3(4)","L3(4).2_3",[[11,12],[13,16],[14,15],[17,18],[19,
22],[20,21],[23,24],[25,26],[27,28]],()]);
ARC("3.L3(4).2_3","tomfusion",rec(name:="3.L3(4).2_3",map:=[1,5,3,17,4,11,48,
12,49,49,13,52,13,52,19,74,74,2,14,29,30,32,32],text:=[
"fusion map is unique up to table automorphisms"
]));
ALF("3.L3(4).2_3","L3(4).2_3",[1,1,2,2,3,4,4,5,5,5,6,6,7,7,8,8,8,9,10,11,
12,13,14]);
ALF("3.L3(4).2_3","3.L3(4).2^2",[1,2,3,4,5,6,7,8,9,10,11,12,11,12,13,14,
14,30,31,32,33,34,34],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables"
]);
ALF("3.L3(4).2_3","3.L3(4).3.2_3",[1,2,3,4,5,6,7,6,7,7,8,9,10,11,12,13,14,
34,35,36,37,38,39]);
ALF("3.L3(4).2_3","G2(4)",[1,4,2,13,5,6,22,7,23,24,9,27,10,28,15,31,32,3,
14,16,16,20,21],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables"
]);
ALN("3.L3(4).2_3",["G2(4)N3A"]);

MOT("3.L3(4).3",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[181440,181440,181440,576,576,576,27,48,48,48,45,45,45,45,45,45,63,63,63,63,
63,63,540,540,540,540,540,540,63,63,36,36,36,36,36,36,45,45,45,45,45,45,45,45,
45,45,45,45,63,63,63,63,63,63,63,63,63,63,63,63],
[,[1,3,2,1,3,2,7,4,6,5,14,16,15,11,13,12,17,19,18,20,22,21,26,27,28,23,24,25,
30,29,26,27,28,23,24,25,46,47,48,43,44,45,40,41,42,37,38,39,52,53,54,49,50,51,
58,59,60,55,56,57],[1,1,1,4,4,4,1,8,8,8,14,14,14,11,11,11,20,20,20,17,17,17,1,
1,1,1,1,1,2,3,4,4,4,4,4,4,14,14,14,14,14,14,11,11,11,11,11,11,21,21,21,22,22,
22,18,18,18,19,19,19],,[1,3,2,4,6,5,7,8,10,9,1,3,2,1,3,2,20,22,21,17,19,18,26,
27,28,23,24,25,30,29,34,35,36,31,32,33,26,27,28,23,24,25,26,27,28,23,24,25,60,
58,59,57,55,56,54,52,53,51,49,50],,[1,2,3,4,5,6,7,8,9,10,14,15,16,11,12,13,1,
2,3,1,2,3,23,24,25,26,27,28,29,30,31,32,33,34,35,36,43,44,45,46,47,48,37,38,
39,40,41,42,29,29,29,30,30,30,29,29,29,30,30,30]],
0,
[(49,51,50)(52,54,53)(55,57,56)(58,60,59),(17,20)(18,21)(19,22)
(49,57,50,55,51,56)(52,60,53,58,54,59),(11,14)(12,15)(13,16)(37,43)(38,44)
(39,45)(40,46)(41,47)(42,48),( 2, 3)( 5, 6)( 9,10)(12,13)(15,16)(18,19)(21,22)
(23,26)(24,27)(25,28)(29,30)(31,34)(32,35)(33,36)(37,40)(38,41)(39,42)(43,46)
(44,47)(45,48)(49,54,50,52,51,53)(55,60,56,58,57,59),(23,24,25)(26,27,28)
(31,32,33)(34,35,36)(37,38,39)(40,41,42)(43,44,45)(46,47,48)],
["ConstructProj",[["L3(4).3",[]],,["3.L3(4).3",[-1,-1,-55,-55,11,11,-1]]]]);
ALF("3.L3(4).3","L3(4).3",[1,1,1,2,2,2,3,4,4,4,5,5,5,6,6,6,7,7,7,8,8,8,9,
9,9,10,10,10,11,12,13,13,13,14,14,14,15,15,15,16,16,16,17,17,17,18,18,18,
19,19,19,20,20,20,21,21,21,22,22,22]);
ALF("3.L3(4).3","3.L3(4).6",[1,2,3,4,5,6,7,8,9,10,11,12,13,11,12,13,14,15,
16,14,15,16,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,
41,42,43,44,45,46,47,48,49,50,51,52,47,48,49,50,51,52],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);
ALF("3.L3(4).3","3.L3(4).3.2_2",[1,2,2,3,4,4,5,6,7,7,8,9,10,8,10,9,11,12,
12,13,14,14,15,16,17,15,16,17,18,18,19,20,21,19,20,21,22,23,24,25,26,27,
25,26,27,22,23,24,28,29,30,28,29,30,31,32,33,31,32,33],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);
ALF("3.L3(4).3","3.L3(4).3.2_3",[1,2,2,3,4,4,5,6,7,7,8,9,9,10,11,11,12,13,
14,12,14,13,15,16,17,15,16,17,18,18,19,20,21,19,20,21,22,23,24,22,23,24,
25,26,27,25,26,27,28,29,30,31,32,33,31,32,33,28,29,30]);

MOT("Isoclinic(3.L3(4).3,1)",
[
"1st isoclinic group of the 3.L3(4).3 given in the ATLAS"
],
0,
0,
0,
[(2,3)(5,6)(9,10)(12,13)(15,16)(18,19)(21,22)(23,26,24,27,25,28)(29,30)(31,34,
32,35,33,36)(37,40,38,41,39,42)(43,46,44,47,45,48)(49,52,50,53,51,54)(55,58,
56,59,57,60),(49,50,51)(52,53,54)(55,56,57)(58,59,60),(23,24,25)(26,27,28)(31,
32,33)(34,35,36)(37,38,39)(40,41,42)(43,44,45)(46,47,48),(17,20)(18,21)(19,22)
(49,55)(50,56)(51,57)(52,58)(53,59)(54,60),(11,14)(12,15)(13,16)(37,43)(38,44)
(39,45)(40,46)(41,47)(42,48)],
["ConstructIsoclinic",[["3.L3(4).3"]],rec(k:=1)]);
ALF("Isoclinic(3.L3(4).3,1)","L3(4).3",[1,1,1,2,2,2,3,4,4,4,5,5,5,6,6,6,7,
7,7,8,8,8,9,9,9,10,10,10,11,12,13,13,13,14,14,14,15,15,15,16,16,16,17,17,
17,18,18,18,19,19,19,20,20,20,21,21,21,22,22,22]);

MOT("Isoclinic(3.L3(4).3,2)",
[
"2nd isoclinic group of the 3.L3(4).3 given in the ATLAS"
],
0,
0,
0,
[(2,3)(5,6)(9,10)(12,13)(15,16)(18,19)(21,22)(23,26,25,28,24,27)(29,30)(31,34,
33,36,32,35)(37,40,39,42,38,41)(43,46,45,48,44,47)(49,52,51,54,50,53)(55,58,
57,60,56,59),(49,50,51)(52,53,54)(55,56,57)(58,59,60),(23,24,25)(26,27,28)(31,
32,33)(34,35,36)(37,38,39)(40,41,42)(43,44,45)(46,47,48),(17,20)(18,21)(19,22)
(49,55)(50,56)(51,57)(52,58)(53,59)(54,60),(11,14)(12,15)(13,16)(37,43)(38,44)
(39,45)(40,46)(41,47)(42,48)],
["ConstructIsoclinic",[["3.L3(4).3"]],rec(k:=2)]);
ALF("Isoclinic(3.L3(4).3,2)","L3(4).3",[1,1,1,2,2,2,3,4,4,4,5,5,5,6,6,6,7,
7,7,8,8,8,9,9,9,10,10,10,11,12,13,13,13,14,14,14,15,15,15,16,16,16,17,17,
17,18,18,18,19,19,19,20,20,20,21,21,21,22,22,22]);

MOT("3.L3(4).6",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[362880,362880,362880,1152,1152,1152,54,96,96,96,45,45,45,63,63,63,1296,1296,
1296,144,144,144,54,24,24,24,1080,1080,1080,1080,1080,1080,126,126,72,72,72,
72,72,72,45,45,45,45,45,45,63,63,63,63,63,63,108,108,108,108,108,108,18,18,36,
36,36,36,36,36],
[,[1,3,2,1,3,2,7,4,6,5,11,13,12,14,16,15,1,3,2,4,6,5,7,8,10,9,30,31,32,27,28,
29,34,33,30,31,32,27,28,29,44,45,46,41,42,43,50,51,52,47,48,49,30,31,32,27,28,
29,34,33,38,39,40,35,36,37],[1,1,1,4,4,4,1,8,8,8,11,11,11,14,14,14,17,17,17,
20,20,20,17,24,24,24,1,1,1,1,1,1,2,3,4,4,4,4,4,4,11,11,11,11,11,11,15,15,15,
16,16,16,17,17,17,17,17,17,18,19,20,20,20,20,20,20],,[1,3,2,4,6,5,7,8,10,9,1,
3,2,14,16,15,17,19,18,20,22,21,23,24,26,25,30,31,32,27,28,29,34,33,38,39,40,
35,36,37,30,31,32,27,28,29,52,50,51,49,47,48,56,57,58,53,54,55,60,59,64,65,66,
61,62,63],,[1,2,3,4,5,6,7,8,9,10,11,12,13,1,2,3,17,18,19,20,21,22,23,24,25,26,
27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,33,33,33,34,34,34,
53,54,55,56,57,58,59,60,61,62,63,64,65,66]],
0,
[(47,49,48)(50,52,51),( 2, 3)( 5, 6)( 9,10)(12,13)(15,16)(18,19)(21,22)(25,26)
(27,30)(28,31)(29,32)(33,34)(35,38)(36,39)(37,40)(41,44)(42,45)(43,46)
(47,52,48,50,49,51)(53,56)(54,57)(55,58)(59,60)(61,64)(62,65)(63,66),
(27,28,29)(30,31,32)(35,36,37)(38,39,40)(41,42,43)(44,45,46)(53,54,55)
(56,57,58)(61,62,63)(64,65,66)],
["ConstructProj",[["L3(4).6",[]],,["3.L3(4).6",[-1,-1,-55,-1,-1]]]]);
ALF("3.L3(4).6","L3(4).6",[1,1,1,2,2,2,3,4,4,4,5,5,5,6,6,6,7,7,7,8,8,8,9,
10,10,10,11,11,11,12,12,12,13,14,15,15,15,16,16,16,17,17,17,18,18,18,19,
19,19,20,20,20,21,21,21,22,22,22,23,24,25,25,25,26,26,26]);

MOT("Isoclinic(3.L3(4).6,1)",
[
"1st isoclinic group of the 3.L3(4).6 given in the ATLAS"
],
0,
0,
0,
[(2,3)(5,6)(9,10)(12,13)(15,16)(18,19)(21,22)(25,26)(27,30,28,31,29,32)(33,34)
(35,38,36,39,37,40)(41,44,42,45,43,46)(47,50,48,51,49,52)(53,56,54,57,55,58)
(59,60)(61,64,62,65,63,66),(47,48,49)(50,51,52),(27,28,29)(30,31,32)(35,36,37)
(38,39,40)(41,42,43)(44,45,46)(53,54,55)(56,57,58)(61,62,63)(64,65,66)],
["ConstructIsoclinic",[["3.L3(4).6"]],rec(k:=1)]);
ALF("Isoclinic(3.L3(4).6,1)","L3(4).6",[1,1,1,2,2,2,3,4,4,4,5,5,5,6,6,6,7,
7,7,8,8,8,9,10,10,10,11,11,11,12,12,12,13,14,15,15,15,16,16,16,17,17,17,
18,18,18,19,19,19,20,20,20,21,21,21,22,22,22,23,24,25,25,25,26,26,26]);

MOT("Isoclinic(3.L3(4).6,2)",
[
"2nd isoclinic group of the 3.L3(4).6 given in the ATLAS"
],
0,
0,
0,
[(2,3)(5,6)(9,10)(12,13)(15,16)(18,19)(21,22)(25,26)(27,30,29,32,28,31)(33,34)
(35,38,37,40,36,39)(41,44,43,46,42,45)(47,50,49,52,48,51)(53,56,55,58,54,57)
(59,60)(61,64,63,66,62,65),(47,48,49)(50,51,52),(27,28,29)(30,31,32)(35,36,37)
(38,39,40)(41,42,43)(44,45,46)(53,54,55)(56,57,58)(61,62,63)(64,65,66)],
["ConstructIsoclinic",[["3.L3(4).6"]],rec(k:=2)]);
ALF("Isoclinic(3.L3(4).6,2)","L3(4).6",[1,1,1,2,2,2,3,4,4,4,5,5,5,6,6,6,7,
7,7,8,8,8,9,10,10,10,11,11,11,12,12,12,13,14,15,15,15,16,16,16,17,17,17,
18,18,18,19,19,19,20,20,20,21,21,21,22,22,22,23,24,25,25,25,26,26,26]);

MOT("4_1.L3(4)",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[80640,80640,80640,80640,128,128,36,36,36,36,32,32,16,16,20,20,20,20,20,20,20,
20,28,28,28,28,28,28,28,28],
[,[1,3,1,3,1,3,7,9,7,9,5,5,6,6,19,21,19,21,15,17,15,17,23,25,23,25,27,29,27,
29],[1,4,3,2,5,6,1,4,3,2,11,12,13,14,19,22,21,20,15,18,17,16,27,30,29,28,23,
26,25,24],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,1,2,3,4,1,2,3,4,27,28,29,30,23,
24,25,26],,[1,4,3,2,5,6,7,10,9,8,11,12,13,14,19,22,21,20,15,18,17,16,1,4,3,2,
1,4,3,2]],
0,
[(23,27)(24,28)(25,29)(26,30),(15,19)(16,20)(17,21)(18,22),(13,14),( 2, 4)
( 8,10)(16,18)(20,22)(24,26)(28,30)],
["ConstructProj",[["L3(4)",[]],["2.L3(4)",[]],,["4_1.L3(4)",[-9,-9,-1,-1,15,
15]]]]);
ALF("4_1.L3(4)","L3(4)",[1,1,1,1,2,2,3,3,3,3,4,4,5,6,7,7,7,7,8,8,8,8,9,9,
9,9,10,10,10,10]);
ALF("4_1.L3(4)","2.L3(4)",[1,2,1,2,3,4,5,6,5,6,7,8,9,10,11,12,11,12,13,14,
13,14,15,16,15,16,17,18,17,18]);
ALF("4_1.L3(4)","4_1.L3(4).2_1",[1,2,3,2,4,5,6,7,8,7,9,10,11,12,13,14,15,
16,13,16,15,14,17,18,19,20,17,20,19,18],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("4_1.L3(4)","4_1.L3(4).2_2",[1,2,3,2,4,5,6,7,8,7,9,10,11,11,12,13,14,
15,12,15,14,13,16,17,18,17,19,20,21,20],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("4_1.L3(4)","4_1.L3(4).2_3",[1,2,3,4,5,6,7,8,9,10,11,12,13,13,14,15,
16,17,18,19,20,21,22,23,24,25,22,23,24,25],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("4_1.L3(4)","Isoclinic(4_1.L3(4).2_1)",[1,2,3,2,4,5,6,7,8,7,9,10,11,
12,13,14,15,16,13,16,15,14,17,18,19,20,17,20,19,18]);
ALF("4_1.L3(4)","Isoclinic(4_1.L3(4).2_2)",[1,2,3,2,4,5,6,7,8,7,9,10,11,
11,12,13,14,15,12,15,14,13,16,17,18,17,19,20,21,20]);
ALF("4_1.L3(4)","4_1.L3(4).2_3*",[1,2,3,4,5,6,7,8,9,10,11,12,13,13,14,15,
16,17,18,19,20,21,22,23,24,25,22,23,24,25],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("4_1.L3(4)","4.M22",[1,2,3,4,5,6,7,8,9,10,11,12,13,13,14,15,16,17,14,
15,16,17,20,21,22,23,24,25,26,27],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);

MOT("4_1.L3(4).2_1",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[161280,80640,161280,256,256,72,36,72,64,64,32,32,20,20,20,20,28,28,28,28,144,
16,36,36,16,16,16,16,16,16],
[,[1,3,1,1,3,6,8,6,4,4,5,5,13,15,13,15,17,19,17,19,1,4,6,6,9,9,11,11,12,12],[
1,2,3,4,5,1,2,3,9,10,11,12,13,14,15,16,17,18,19,20,21,22,21,21,25,26,28,27,30,
29],,[1,2,3,4,5,6,7,8,9,10,11,12,1,2,3,2,17,20,19,18,21,22,23,24,25,26,28,27,
30,29],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,1,2,3,2,21,22,23,24,25,26,27,
28,29,30]],
0,
[(27,28)(29,30),(25,26),(23,24),(18,20),(14,16),(14,16)(18,20),(14,16)(18,20)
(27,28)(29,30),(11,12)(27,29)(28,30)],
["ConstructMGA","4_1.L3(4)","2.L3(4).2_1",[[19,22],[20,21],[23,24],[25,26],
[27,30],[28,29]],()]);
ALF("4_1.L3(4).2_1","L3(4).2_1",[1,1,1,2,2,3,3,3,4,4,5,6,7,7,7,7,8,8,8,8,
9,10,11,11,12,12,13,13,14,14]);
ALF("4_1.L3(4).2_1","2.L3(4).2_1",[1,2,1,3,4,5,6,5,7,8,9,10,11,12,11,12,
13,14,13,14,15,16,17,18,19,20,21,22,23,24]);
ALF("4_1.L3(4).2_1","4_1.L3(4).(2^2)_{123}",[1,2,3,4,5,6,7,8,9,10,11,11,
12,13,14,15,16,17,18,17,19,20,21,22,23,24,25,26,26,25]);
ALF("4_1.L3(4).2_1","4_1.L3(4).(2^2)_{12*3}",[1,2,3,4,5,6,7,8,9,10,11,11,
12,13,14,15,16,17,18,17,19,20,21,22,23,24,25,26,26,25]);
ALF("4_1.L3(4).2_1","4_1.L3(4).(2^2)_{123*}",[1,2,3,4,5,6,7,8,9,10,11,11,
12,13,14,15,16,17,18,17,19,20,21,21,22,22,23,24,23,24]);
ALF("4_1.L3(4).2_1","4_1.L3(4).(2^2)_{12*3*}",[1,2,3,4,5,6,7,8,9,10,11,11,
12,13,14,15,16,17,18,17,19,20,21,21,22,22,23,24,23,24]);

MOT("Isoclinic(4_1.L3(4).2_1)",
0,
0,
0,
0,
[(27,28)(29,30),(25,26),(23,24),(18,20),(14,16),(11,12)(27,29)(28,30)],
["ConstructIsoclinic",[["4_1.L3(4).2_1"]]]);
ALF("Isoclinic(4_1.L3(4).2_1)","4_1.L3(4).(2^2)_{1*23}",[1,2,3,4,5,6,7,8,
9,10,11,11,12,13,14,15,16,17,18,17,19,20,21,22,23,24,25,26,26,25]);
ALF("Isoclinic(4_1.L3(4).2_1)","4_1.L3(4).(2^2)_{1*2*3}",[1,2,3,4,5,6,7,8,
9,10,11,11,12,13,14,15,16,17,18,17,19,20,21,22,23,24,25,26,26,25]);
ALF("Isoclinic(4_1.L3(4).2_1)","4_1.L3(4).(2^2)_{1*23*}",[1,2,3,4,5,6,7,8,
9,10,11,11,12,13,14,15,16,17,18,17,19,20,21,21,22,22,23,24,23,24]);
ALF("Isoclinic(4_1.L3(4).2_1)","4_1.L3(4).(2^2)_{1*2*3*}",[1,2,3,4,5,6,7,
8,9,10,11,11,12,13,14,15,16,17,18,17,19,20,21,21,22,22,23,24,23,24]);
ALN("Isoclinic(4_1.L3(4).2_1)",["4_1.L3(4).2_1*"]);

MOT("4_1.L3(4).2_2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[161280,80640,161280,256,256,72,36,72,64,64,16,20,20,20,20,56,28,56,56,28,56,
672,672,32,32,12,12,16,16,28,28,28,28],
[,[1,3,1,1,3,6,8,6,4,4,5,12,14,12,14,16,18,16,19,21,19,1,1,4,4,6,6,10,10,16,
16,19,19],[1,2,3,4,5,1,2,3,9,10,11,12,13,14,15,19,20,21,16,17,18,22,23,24,25,
22,23,29,28,32,33,30,31],,[1,2,3,4,5,6,7,8,9,10,11,1,2,3,2,19,20,21,16,17,18,
22,23,24,25,26,27,28,29,32,33,30,31],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,1,
2,3,1,2,3,22,23,24,25,26,27,29,28,22,23,22,23]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[20,20,
20,4,4,2,2,2,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,6,6,2,2,0,0,0,0,-1,-1,-1,-1],
[TENSOR,[3,2]],[35,35,35,3,3,-1,-1,-1,3,3,-1,0,0,0,0,0,0,0,0,0,0,7,7,-1,-1,1,
1,-1,-1,0,0,0,0],
[TENSOR,[5,2]],[70,70,70,6,6,-2,-2,-2,-2,-2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0],[45,45,45,-3,-3,0,0,0,1,1,1,0,0,0,0,E(7)+E(7)^2+E(7)^4,
E(7)+E(7)^2+E(7)^4,E(7)+E(7)^2+E(7)^4,E(7)^3+E(7)^5+E(7)^6,
E(7)^3+E(7)^5+E(7)^6,E(7)^3+E(7)^5+E(7)^6,3,3,-1,-1,0,0,1,1,E(7)+E(7)^2+E(7)^4
 ,E(7)+E(7)^2+E(7)^4,E(7)^3+E(7)^5+E(7)^6,E(7)^3+E(7)^5+E(7)^6],
[TENSOR,[8,2]],
[GALOIS,[8,3]],
[TENSOR,[10,2]],[126,126,126,-2,-2,0,0,0,-2,-2,-2,1,1,1,1,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0],[64,64,64,0,0,1,1,1,0,0,0,-1,-1,-1,-1,1,1,1,1,1,1,8,8,0,0,-1,
-1,0,0,1,1,1,1],
[TENSOR,[13,2]],[10,-10,10,2,-2,1,-1,1,2,-2,0,0,0,0,0,E(7)+E(7)^2+E(7)^4,
-E(7)-E(7)^2-E(7)^4,E(7)+E(7)^2+E(7)^4,E(7)^3+E(7)^5+E(7)^6,
-E(7)^3-E(7)^5-E(7)^6,E(7)^3+E(7)^5+E(7)^6,4,-4,0,0,1,-1,0,0,
-E(7)-E(7)^2-E(7)^4,E(7)+E(7)^2+E(7)^4,-E(7)^3-E(7)^5-E(7)^6,
E(7)^3+E(7)^5+E(7)^6],
[TENSOR,[15,2]],
[GALOIS,[15,3]],
[TENSOR,[17,2]],[56,-56,56,-8,8,2,-2,2,0,0,0,1,-1,1,-1,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0],[36,-36,36,4,-4,0,0,0,0,0,0,1,-1,1,-1,1,-1,1,1,-1,1,6,-6,2,-2,
0,0,0,0,-1,1,-1,1],
[TENSOR,[20,2]],[64,-64,64,0,0,1,-1,1,0,0,0,-1,1,-1,1,1,-1,1,1,-1,1,8,-8,0,0,
-1,1,0,0,1,-1,1,-1],
[TENSOR,[22,2]],[70,-70,70,-2,2,-2,2,-2,2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,2*E(4),-2*E(4),0,0,0,0],
[TENSOR,[24,2]],[90,-90,90,2,-2,0,0,0,-2,2,0,0,0,0,0,-1,1,-1,-1,1,-1,6,-6,-2,
2,0,0,0,0,-1,1,-1,1],
[TENSOR,[26,2]],[16,0,-16,0,0,-2,0,2,0,0,0,1,-E(20)-E(20)^9+E(20)^13+E(20)^17,
-1,E(20)+E(20)^9-E(20)^13-E(20)^17,2,0,-2,2,0,-2,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[28,11]],[112,0,-112,0,0,4,0,-4,0,0,0,2,0,-2,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0],[128,0,-128,0,0,2,0,-2,0,0,0,-2,0,2,0,2,0,-2,2,0,-2,0,0,0,0,0,
0,0,0,0,0,0,0],[160,0,-160,0,0,-2,0,2,0,0,0,0,0,0,0,2*E(7)+2*E(7)^2+2*E(7)^4,
0,-2*E(7)-2*E(7)^2-2*E(7)^4,2*E(7)^3+2*E(7)^5+2*E(7)^6,0,-2*E(7)^3-2*E(7)^5
 -2*E(7)^6,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[32,3]]],
[(28,29),(16,19)(17,20)(18,21)(30,32)(31,33),(13,15),(13,15)(28,29),(22,23)
(24,25)(26,27)(30,31)(32,33)]);
ALF("4_1.L3(4).2_2","L3(4).2_2",[1,1,1,2,2,3,3,3,4,4,5,6,6,6,6,7,7,7,8,8,
8,9,9,10,10,11,11,12,12,13,13,14,14]);
ALF("4_1.L3(4).2_2","2.L3(4).2_2",[1,2,1,3,4,5,6,5,7,8,9,10,11,10,11,12,
13,12,14,15,14,16,17,18,19,20,21,22,23,24,25,26,27]);
ALF("4_1.L3(4).2_2","4_1.L3(4).(2^2)_{123}",[1,2,3,4,5,6,7,8,9,10,11,12,
13,14,15,16,17,18,16,17,18,27,28,29,30,31,32,33,33,34,35,34,35]);
ALF("4_1.L3(4).2_2","4_1.L3(4).(2^2)_{1*23}",[1,2,3,4,5,6,7,8,9,10,11,12,
13,14,15,16,17,18,16,17,18,27,28,29,30,31,32,33,33,34,35,34,35]);
ALF("4_1.L3(4).2_2","4_1.L3(4).(2^2)_{123*}",[1,2,3,4,5,6,7,8,9,10,11,12,
13,14,15,16,17,18,16,17,18,25,25,26,26,27,27,28,29,30,31,31,30]);
ALF("4_1.L3(4).2_2","4_1.L3(4).(2^2)_{1*23*}",[1,2,3,4,5,6,7,8,9,10,11,12,
13,14,15,16,17,18,16,17,18,25,25,26,26,27,27,28,29,30,31,31,30]);

MOT("Isoclinic(4_1.L3(4).2_2)",
0,
0,
0,
0,
[(28,29),(13,15),(22,23)(24,25)(26,27)(30,31)(32,33),(16,19)(17,20)(18,21)
(30,32)(31,33)],
["ConstructIsoclinic",[["4_1.L3(4).2_2"]]]);
ALF("Isoclinic(4_1.L3(4).2_2)","4_1.L3(4).(2^2)_{12*3}",[1,2,3,4,5,6,7,8,
9,10,11,12,13,14,15,16,17,18,16,17,18,27,28,29,30,31,32,33,33,34,35,34,35]);
ALF("Isoclinic(4_1.L3(4).2_2)","4_1.L3(4).(2^2)_{1*2*3}",[1,2,3,4,5,6,7,8,
9,10,11,12,13,14,15,16,17,18,16,17,18,27,28,29,30,31,32,33,33,34,35,34,35]);
ALF("Isoclinic(4_1.L3(4).2_2)","4_1.L3(4).(2^2)_{12*3*}",[1,2,3,4,5,6,7,8,
9,10,11,12,13,14,15,16,17,18,16,17,18,25,25,26,26,27,27,28,29,30,31,31,30]);
ALF("Isoclinic(4_1.L3(4).2_2)","4_1.L3(4).(2^2)_{1*2*3*}",[1,2,3,4,5,6,7,
8,9,10,11,12,13,14,15,16,17,18,16,17,18,25,25,26,26,27,27,28,29,30,31,31,
30]);
ALN("Isoclinic(4_1.L3(4).2_2)",["4_1.L3(4).2_2*"]);

MOT("4_1.L3(4).2_3",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[161280,161280,161280,161280,256,256,72,72,72,72,64,64,16,40,40,40,40,40,40,
40,40,28,28,28,28,480,480,480,480,24,24,24,24,32,32,32,32,40,40,40,40,40,40,
40,40],
[,[1,3,1,3,1,3,7,9,7,9,5,5,6,18,20,18,20,14,16,14,16,22,24,22,24,1,3,1,3,7,9,
7,9,11,11,11,11,18,20,18,20,14,16,14,16],[1,4,3,2,5,6,1,4,3,2,11,12,13,18,21,
20,19,14,17,16,15,22,25,24,23,26,29,28,27,26,29,28,27,35,34,37,36,42,45,44,43,
38,41,40,39],,[1,2,3,4,5,6,7,8,9,10,11,12,13,1,2,3,4,1,2,3,4,22,23,24,25,26,
27,28,29,30,31,32,33,35,34,37,36,26,27,28,29,26,27,28,29],,[1,4,3,2,5,6,7,10,
9,8,11,12,13,18,21,20,19,14,17,16,15,1,4,3,2,26,29,28,27,30,33,32,31,34,35,36,
37,42,45,44,43,38,41,40,39]],
0,
[(36,37),(34,35),(14,18)(15,19)(16,20)(17,21)(38,42)(39,43)(40,44)(41,45),
( 2, 4)( 8,10)(15,17)(19,21)(23,25)(27,29)(31,33)(39,41)(43,45),( 2, 4)( 8,10)
(15,17)(19,21)(23,25)(27,29)(31,33)(34,35)(36,37)(39,41)(43,45),(26,28)(27,29)
(30,32)(31,33)(38,40)(39,41)(42,44)(43,45)],
["ConstructProj",[["L3(4).2_3",[]],["2.L3(4).2_3",[]],,["4_1.L3(4).2_3",[-9,
-9,-1,-1,-1]]]]);
ALF("4_1.L3(4).2_3","L3(4).2_3",[1,1,1,1,2,2,3,3,3,3,4,4,5,6,6,6,6,7,7,7,
7,8,8,8,8,9,9,9,9,10,10,10,10,11,11,12,12,13,13,13,13,14,14,14,14]);
ALF("4_1.L3(4).2_3","2.L3(4).2_3",[1,2,1,2,3,4,5,6,5,6,7,8,9,10,11,10,11,
12,13,12,13,14,15,14,15,16,17,16,17,18,19,18,19,20,21,22,23,24,25,24,25,
26,27,26,27]);
ALF("4_1.L3(4).2_3","4_1.L3(4).(2^2)_{123}",[1,2,3,2,4,5,6,7,8,7,9,10,11,
12,13,14,15,12,15,14,13,16,17,18,17,36,37,38,37,39,40,41,40,42,42,43,44,
45,46,47,48,45,48,47,46]);
ALF("4_1.L3(4).2_3","4_1.L3(4).(2^2)_{1*23}",[1,2,3,2,4,5,6,7,8,7,9,10,11,
12,13,14,15,12,15,14,13,16,17,18,17,36,37,36,38,39,40,39,41,42,42,43,44,
45,46,47,48,47,46,45,48]);
ALF("4_1.L3(4).2_3","4_1.L3(4).(2^2)_{12*3}",[1,2,3,2,4,5,6,7,8,7,9,10,11,
12,13,14,15,12,15,14,13,16,17,18,17,36,37,36,38,39,40,39,41,42,42,43,44,
45,46,47,48,47,46,45,48]);
ALF("4_1.L3(4).2_3","4_1.L3(4).(2^2)_{1*2*3}",[1,2,3,2,4,5,6,7,8,7,9,10,
11,12,13,14,15,12,15,14,13,16,17,18,17,36,37,38,37,39,40,41,40,42,42,43,
44,45,46,47,48,45,48,47,46]);

MOT("4_1.L3(4).2_3*",
0,
0,
0,
0,
[(36,37),(34,35),(26,28)(27,29)(30,32)(31,33)(38,40)(39,41)(42,44)(43,45),
(14,18)(15,19)(16,20)(17,21)(38,42)(39,43)(40,44)(41,45),(2,4)(8,10)(15,17)
(19,21)(23,25)(26,27)(28,29)(30,31)(32,33)(38,39)(40,41)(42,43)(44,45)],
["ConstructIsoclinic",[["4_1.L3(4).2_3"]],[1..4]]);
ALF("4_1.L3(4).2_3*","Isoclinic(2.L3(4).2_3)",[1,2,1,2,3,4,5,6,5,6,7,8,9,
10,11,10,11,12,13,12,13,14,15,14,15,16,17,16,17,18,19,18,19,20,21,22,23,
24,25,24,25,26,27,26,27]);
ALF("4_1.L3(4).2_3*","4_1.L3(4).(2^2)_{123*}",[1,2,3,2,4,5,6,7,8,7,9,10,
11,12,13,14,15,12,15,14,13,16,17,18,17,32,33,33,32,34,35,35,34,36,37,38,
38,39,40,41,42,42,41,40,39]);
ALF("4_1.L3(4).2_3*","4_1.L3(4).(2^2)_{1*23*}",[1,2,3,2,4,5,6,7,8,7,9,10,
11,12,13,14,15,12,15,14,13,16,17,18,17,32,32,33,33,34,34,35,35,36,37,38,
38,39,40,41,42,40,39,42,41]);
ALF("4_1.L3(4).2_3*","4_1.L3(4).(2^2)_{12*3*}",[1,2,3,2,4,5,6,7,8,7,9,10,
11,12,13,14,15,12,15,14,13,16,17,18,17,32,32,33,33,34,34,35,35,36,37,38,
38,39,40,41,42,40,39,42,41]);
ALF("4_1.L3(4).2_3*","4_1.L3(4).(2^2)_{1*2*3*}",[1,2,3,2,4,5,6,7,8,7,9,10,
11,12,13,14,15,12,15,14,13,16,17,18,17,32,33,33,32,34,35,35,34,36,37,38,
38,39,40,41,42,42,41,40,39]);

MOT("4_1.L3(4).(2^2)_{123}",
[
"constructed using `PossibleCharacterTablesOfTypeMGA'"
],
[322560,161280,322560,512,512,144,72,144,128,128,32,40,40,40,40,56,28,56,288,
32,72,72,32,32,16,16,1344,1344,64,64,24,24,16,28,28,960,480,960,48,24,48,32,64
,64,40,40,40,40],
[,[1,3,1,1,3,6,8,6,4,4,5,12,14,12,14,16,18,16,1,4,6,6,9,9,11,11,1,1,4,4,6,6,10
,16,16,1,3,1,6,8,6,9,9,9,12,14,12,14],[1,2,3,4,5,1,2,3,9,10,11,12,13,14,15,16,
17,18,19,20,19,19,23,24,26,25,27,28,29,30,27,28,33,34,35,36,37,38,36,37,38,42,
44,43,45,46,47,48],,[1,2,3,4,5,6,7,8,9,10,11,1,2,3,2,16,17,18,19,20,21,22,23,
24,26,25,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,44,43,36,37,38,37],,[
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,1,2,3,19,20,21,22,23,24,25,26,27,28,29,30,
31,32,33,27,28,36,37,38,39,40,41,42,43,44,45,46,47,48]],
0,
[(25,26)(43,44),(21,22)(23,24)(27,28)(29,30)(31,32)(34,35)(43,44),
(13,15)(46,48),(36,38)(39,41)(45,47)(46,48)],
["ConstructMGA","4_1.L3(4).2_3","2.L3(4).(2^2)_{123}",[[28,34],[29,35],[30,32]
,[31,33],[36,38],[37,39],[40,42],[41,43],[44,45]],()]);
ALF("4_1.L3(4).(2^2)_{123}","L3(4).2^2",[1,1,1,2,2,3,3,3,4,4,5,6,6,6,6,7,
7,7,8,9,10,10,11,11,12,12,13,13,14,14,15,15,16,17,17,18,18,18,19,19,19,20,
21,21,22,22,22,22]);
ALF("4_1.L3(4).(2^2)_{123}","2.L3(4).(2^2)_{123}",[1,2,1,3,4,5,6,5,7,8,9,
10,11,10,11,12,13,12,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,
31,32,31,33,34,33,35,36,37,38,39,38,39]);

MOT("4_1.L3(4).(2^2)_{1*23}",
[
"constructed using `PossibleCharacterTablesOfTypeMGA'"
],
[322560,161280,322560,512,512,144,72,144,128,128,32,40,40,40,40,56,28,56,288,
32,72,72,32,32,16,16,1344,1344,64,64,24,24,16,28,28,480,960,960,24,48,48,32,64
,64,40,40,40,40],
[,[1,3,1,1,3,6,8,6,4,4,5,12,14,12,14,16,18,16,3,4,8,8,9,9,11,11,1,1,4,4,6,6,10
,16,16,1,3,3,6,8,8,9,9,9,12,14,12,14],[1,2,3,4,5,1,2,3,9,10,11,12,13,14,15,16,
17,18,19,20,19,19,23,24,26,25,27,28,29,30,27,28,33,34,35,36,38,37,36,38,37,42,
44,43,47,48,45,46],,[1,2,3,4,5,6,7,8,9,10,11,1,2,3,2,16,17,18,19,20,21,22,23,
24,26,25,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,44,43,36,37,36,38],,[
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,1,2,3,19,20,21,22,23,24,25,26,27,28,29,30,
31,32,33,27,28,36,38,37,39,41,40,42,43,44,47,48,45,46]],
0,
[(25,26)(43,44),(21,22)(23,24)(27,28)(29,30)(31,32)(34,35)(43,44),
(13,15)(45,47),(37,38)(40,41)(45,47)(46,48)],
["ConstructMGA","4_1.L3(4).2_3","2.L3(4).(2^2)_{123}",[[28,35],[29,34],[30,33]
,[31,32],[36,39],[37,38],[40,43],[41,42],[44,45]],()]);
ALF("4_1.L3(4).(2^2)_{1*23}","L3(4).2^2",[1,1,1,2,2,3,3,3,4,4,5,6,6,6,6,7,
7,7,8,9,10,10,11,11,12,12,13,13,14,14,15,15,16,17,17,18,18,18,19,19,19,20,
21,21,22,22,22,22]);
ALF("4_1.L3(4).(2^2)_{1*23}","2.L3(4).(2^2)_{123}",[1,2,1,3,4,5,6,5,7,8,9,
10,11,10,11,12,13,12,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,
31,32,32,33,34,34,35,36,37,38,39,38,39]);

MOT("4_1.L3(4).(2^2)_{12*3}",
[
"constructed using `PossibleCharacterTablesOfTypeMGA'"
],
[322560,161280,322560,512,512,144,72,144,128,128,32,40,40,40,40,56,28,56,288,
32,72,72,32,32,16,16,1344,1344,64,64,24,24,16,28,28,480,960,960,24,48,48,32,64
,64,40,40,40,40],
[,[1,3,1,1,3,6,8,6,4,4,5,12,14,12,14,16,18,16,1,4,6,6,9,9,11,11,3,3,4,4,8,8,10
,18,18,1,3,3,6,8,8,9,9,9,12,14,12,14],[1,2,3,4,5,1,2,3,9,10,11,12,13,14,15,16,
17,18,19,20,19,19,23,24,26,25,27,28,29,30,27,28,33,34,35,36,38,37,36,38,37,42,
44,43,47,48,45,46],,[1,2,3,4,5,6,7,8,9,10,11,1,2,3,2,16,17,18,19,20,21,22,23,
24,26,25,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,44,43,36,37,36,38],,[
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,1,2,3,19,20,21,22,23,24,25,26,27,28,29,30,
31,32,33,27,28,36,38,37,39,41,40,42,43,44,47,48,45,46]],
0,
[(25,26)(43,44),(21,22)(23,24)(27,28)(29,30)(31,32)(34,35)(43,44),
(13,15)(45,47),(37,38)(40,41)(45,47)(46,48)],
["ConstructMGA","4_1.L3(4).2_3","2.L3(4).(2^2)_{123}",[[28,35],[29,34],[30,33]
,[31,32],[36,39],[37,38],[40,43],[41,42],[44,45]],()]);
ALF("4_1.L3(4).(2^2)_{12*3}","L3(4).2^2",[1,1,1,2,2,3,3,3,4,4,5,6,6,6,6,7,
7,7,8,9,10,10,11,11,12,12,13,13,14,14,15,15,16,17,17,18,18,18,19,19,19,20,
21,21,22,22,22,22]);
ALF("4_1.L3(4).(2^2)_{12*3}","2.L3(4).(2^2)_{123}",[1,2,1,3,4,5,6,5,7,8,9,
10,11,10,11,12,13,12,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,
31,32,32,33,34,34,35,36,37,38,39,38,39]);

MOT("4_1.L3(4).(2^2)_{123*}",
[
"constructed using `PossibleCharacterTablesOfTypeMGA'"
],
[322560,161280,322560,512,512,144,72,144,128,128,32,40,40,40,40,56,28,56,288,
32,36,16,16,16,672,32,12,32,32,28,28,480,480,24,24,64,64,32,40,40,40,40],
[,[1,3,1,1,3,6,8,6,4,4,5,12,14,12,14,16,18,16,1,4,6,9,11,11,1,4,6,10,10,16,16,
2,2,7,7,10,10,10,15,13,15,13],[1,2,3,4,5,1,2,3,9,10,11,12,13,14,15,16,17,18,19
,20,19,22,24,23,25,26,25,29,28,31,30,33,32,33,32,36,37,38,41,42,39,40],,[1,2,3
,4,5,6,7,8,9,10,11,1,2,3,2,16,17,18,19,20,21,22,24,23,25,26,27,28,29,31,30,33,
32,35,34,37,36,38,33,32,32,33],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,1,2,3,19,
20,21,22,23,24,25,26,27,29,28,25,25,32,33,34,35,37,36,38,39,40,41,42]],
0,
[(30,31),(28,29)(36,37),(23,24)(36,37),(32,33)(34,35)(39,41)(40,42),
(13,15)(39,42)(40,41)],
["ConstructMGA","4_1.L3(4).2_3*","2.L3(4).(2^2)_{123*}",[[28,34],[29,35],[30,
32],[31,33],[36,38],[37,39],[40,42],[41,43],[44,45]],()]);
ALF("4_1.L3(4).(2^2)_{123*}","L3(4).2^2",[1,1,1,2,2,3,3,3,4,4,5,6,6,6,6,7,
7,7,8,9,10,11,12,12,13,14,15,16,16,17,17,18,18,19,19,20,20,21,22,22,22,22]);
ALF("4_1.L3(4).(2^2)_{123*}","2.L3(4).(2^2)_{123*}",[1,2,1,3,4,5,6,5,7,8,
9,10,11,10,11,12,13,12,14,15,16,17,18,19,20,21,22,23,24,25,26,27,27,28,28,
29,30,31,32,33,32,33]);

MOT("4_1.L3(4).(2^2)_{1*2*3}",
[
"constructed using `PossibleCharacterTablesOfTypeMGA'"
],
[322560,161280,322560,512,512,144,72,144,128,128,32,40,40,40,40,56,28,56,288,
32,72,72,32,32,16,16,1344,1344,64,64,24,24,16,28,28,960,480,960,48,24,48,32,64
,64,40,40,40,40],
[,[1,3,1,1,3,6,8,6,4,4,5,12,14,12,14,16,18,16,3,4,8,8,9,9,11,11,3,3,4,4,8,8,10
,18,18,1,3,1,6,8,6,9,9,9,12,14,12,14],[1,2,3,4,5,1,2,3,9,10,11,12,13,14,15,16,
17,18,19,20,19,19,23,24,26,25,27,28,29,30,27,28,33,34,35,36,37,38,36,37,38,42,
44,43,45,46,47,48],,[1,2,3,4,5,6,7,8,9,10,11,1,2,3,2,16,17,18,19,20,21,22,23,
24,26,25,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,44,43,36,37,38,37],,[
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,1,2,3,19,20,21,22,23,24,25,26,27,28,29,30,
31,32,33,27,28,36,37,38,39,40,41,42,43,44,45,46,47,48]],
0,
[(25,26)(43,44),(21,22)(23,24)(27,28)(29,30)(31,32)(34,35)(43,44),
(13,15)(46,48),(36,38)(39,41)(45,47)(46,48)],
["ConstructMGA","4_1.L3(4).2_3","2.L3(4).(2^2)_{123}",[[28,34],[29,35],[30,32]
,[31,33],[36,38],[37,39],[40,42],[41,43],[44,45]],()]);
ALF("4_1.L3(4).(2^2)_{1*2*3}","L3(4).2^2",[1,1,1,2,2,3,3,3,4,4,5,6,6,6,6,
7,7,7,8,9,10,10,11,11,12,12,13,13,14,14,15,15,16,17,17,18,18,18,19,19,19,
20,21,21,22,22,22,22]);
ALF("4_1.L3(4).(2^2)_{1*2*3}","2.L3(4).(2^2)_{123}",[1,2,1,3,4,5,6,5,7,8,
9,10,11,10,11,12,13,12,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,
31,32,31,33,34,33,35,36,37,38,39,38,39]);

MOT("4_1.L3(4).(2^2)_{1*23*}",
[
"constructed using `PossibleCharacterTablesOfTypeMGA'"
],
[322560,161280,322560,512,512,144,72,144,128,128,32,40,40,40,40,56,28,56,288,
32,36,16,16,16,672,32,12,32,32,28,28,480,480,24,24,64,64,32,40,40,40,40],
[,[1,3,1,1,3,6,8,6,4,4,5,12,14,12,14,16,18,16,3,4,8,9,11,11,1,4,6,10,10,16,16,
2,2,7,7,10,10,10,15,13,15,13],[1,2,3,4,5,1,2,3,9,10,11,12,13,14,15,16,17,18,19
,20,19,22,24,23,25,26,25,29,28,31,30,32,33,32,33,36,37,38,39,40,41,42],,[1,2,3
,4,5,6,7,8,9,10,11,1,2,3,2,16,17,18,19,20,21,22,24,23,25,26,27,28,29,31,30,33,
32,35,34,37,36,38,33,33,32,32],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,1,2,3,19,
20,21,22,23,24,25,26,27,29,28,25,25,33,32,35,34,37,36,38,41,42,39,40]],
0,
[(30,31),(28,29)(36,37),(23,24)(36,37),(32,33)(34,35)(39,41)(40,42),
(13,15)(39,40)(41,42)],
["ConstructMGA","4_1.L3(4).2_3*","2.L3(4).(2^2)_{123*}",[[28,35],[29,34],[30,
33],[31,32],[36,39],[37,38],[40,43],[41,42],[44,45]],()]);
ALF("4_1.L3(4).(2^2)_{1*23*}","2.L3(4).(2^2)_{123*}",[1,2,1,3,4,5,6,5,7,8,
9,10,11,10,11,12,13,12,14,15,16,17,18,19,20,21,22,23,24,25,26,27,27,28,28,
29,30,31,32,33,32,33]);
ALF("4_1.L3(4).(2^2)_{1*23*}","L3(4).2^2",[1,1,1,2,2,3,3,3,4,4,5,6,6,6,6,
7,7,7,8,9,10,11,12,12,13,14,15,16,16,17,17,18,18,19,19,20,20,21,22,22,22,
22]);

MOT("4_1.L3(4).(2^2)_{12*3*}",
[
"constructed using `PossibleCharacterTablesOfTypeMGA'"
],
[322560,161280,322560,512,512,144,72,144,128,128,32,40,40,40,40,56,28,56,288,
32,36,16,16,16,672,32,12,32,32,28,28,480,480,24,24,64,64,32,40,40,40,40],
[,[1,3,1,1,3,6,8,6,4,4,5,12,14,12,14,16,18,16,1,4,6,9,11,11,3,4,8,10,10,18,18,
2,2,7,7,10,10,10,15,13,15,13],[1,2,3,4,5,1,2,3,9,10,11,12,13,14,15,16,17,18,19
,20,19,22,24,23,25,26,25,29,28,31,30,32,33,32,33,36,37,38,39,40,41,42],,[1,2,3
,4,5,6,7,8,9,10,11,1,2,3,2,16,17,18,19,20,21,22,24,23,25,26,27,28,29,31,30,33,
32,35,34,37,36,38,33,33,32,32],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,1,2,3,19,
20,21,22,23,24,25,26,27,29,28,25,25,33,32,35,34,37,36,38,41,42,39,40]],
0,
[(30,31),(28,29)(36,37),(23,24)(36,37),(32,33)(34,35)(39,41)(40,42),
(13,15)(39,40)(41,42)],
["ConstructMGA","4_1.L3(4).2_3*","2.L3(4).(2^2)_{123*}",[[28,35],[29,34],[30,
33],[31,32],[36,39],[37,38],[40,43],[41,42],[44,45]],()]);
ALF("4_1.L3(4).(2^2)_{12*3*}","2.L3(4).(2^2)_{123*}",[1,2,1,3,4,5,6,5,7,8,
9,10,11,10,11,12,13,12,14,15,16,17,18,19,20,21,22,23,24,25,26,27,27,28,28,
29,30,31,32,33,32,33]);
ALF("4_1.L3(4).(2^2)_{12*3*}","L3(4).2^2",[1,1,1,2,2,3,3,3,4,4,5,6,6,6,6,
7,7,7,8,9,10,11,12,12,13,14,15,16,16,17,17,18,18,19,19,20,20,21,22,22,22,
22]);

MOT("4_1.L3(4).(2^2)_{1*2*3*}",
[
"constructed using `PossibleCharacterTablesOfTypeMGA'"
],
[322560,161280,322560,512,512,144,72,144,128,128,32,40,40,40,40,56,28,56,288,
32,36,16,16,16,672,32,12,32,32,28,28,480,480,24,24,64,64,32,40,40,40,40],
[,[1,3,1,1,3,6,8,6,4,4,5,12,14,12,14,16,18,16,3,4,8,9,11,11,3,4,8,10,10,18,18,
2,2,7,7,10,10,10,15,13,15,13],[1,2,3,4,5,1,2,3,9,10,11,12,13,14,15,16,17,18,19
,20,19,22,24,23,25,26,25,29,28,31,30,33,32,33,32,36,37,38,41,42,39,40],,[1,2,3
,4,5,6,7,8,9,10,11,1,2,3,2,16,17,18,19,20,21,22,24,23,25,26,27,28,29,31,30,33,
32,35,34,37,36,38,33,32,32,33],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,1,2,3,19,
20,21,22,23,24,25,26,27,29,28,25,25,32,33,34,35,37,36,38,39,40,41,42]],
0,
[(30,31),(28,29)(36,37),(23,24)(36,37),(32,33)(34,35)(39,41)(40,42),
(13,15)(39,42)(40,41)],
["ConstructMGA","4_1.L3(4).2_3*","2.L3(4).(2^2)_{123*}",[[28,34],[29,35],[30,
32],[31,33],[36,38],[37,39],[40,42],[41,43],[44,45]],()]);
ALF("4_1.L3(4).(2^2)_{1*2*3*}","L3(4).2^2",[1,1,1,2,2,3,3,3,4,4,5,6,6,6,6,
7,7,7,8,9,10,11,12,12,13,14,15,16,16,17,17,18,18,19,19,20,20,21,22,22,22,
22]);
ALF("4_1.L3(4).(2^2)_{1*2*3*}","2.L3(4).(2^2)_{123*}",[1,2,1,3,4,5,6,5,7,
8,9,10,11,10,11,12,13,12,14,15,16,17,18,19,20,21,22,23,24,25,26,27,27,28,
28,29,30,31,32,33,32,33]);

MOT("4_2.L3(4)",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[80640,80640,80640,80640,128,128,36,36,36,36,64,64,64,64,16,16,20,20,20,20,20,
20,20,20,28,28,28,28,28,28,28,28],
[,[1,3,1,3,1,3,7,9,7,9,5,5,5,5,6,6,21,23,21,23,17,19,17,19,25,27,25,27,29,31,
29,31],[1,4,3,2,5,6,1,4,3,2,11,14,13,12,15,16,21,24,23,22,17,20,19,18,29,32,
31,30,25,28,27,26],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,1,2,3,4,1,2,3,4,
29,30,31,32,25,26,27,28],,[1,4,3,2,5,6,7,10,9,8,11,14,13,12,15,16,21,24,23,22,
17,20,19,18,1,4,3,2,1,4,3,2]],
0,
[(25,29)(26,30)(27,31)(28,32),(17,21)(18,22)(19,23)(20,24),(15,16),( 2, 4)
( 8,10)(12,14)(18,20)(22,24)(26,28)(30,32)],
["ConstructProj",[["L3(4)",[]],["2.L3(4)",[]],,["4_2.L3(4)",[-1,-9,-9,-1,-1,
15,15]]]]);
ALF("4_2.L3(4)","L3(4)",[1,1,1,1,2,2,3,3,3,3,4,4,4,4,5,6,7,7,7,7,8,8,8,8,
9,9,9,9,10,10,10,10]);
ALF("4_2.L3(4)","2.L3(4)",[1,2,1,2,3,4,5,6,5,6,7,8,7,8,9,10,11,12,11,12,
13,14,13,14,15,16,15,16,17,18,17,18]);
ALF("4_2.L3(4)","4_2.L3(4).2_1",[1,2,3,2,4,5,6,7,8,7,9,10,11,10,12,13,14,
15,16,17,14,17,16,15,18,19,20,21,18,21,20,19],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);
ALF("4_2.L3(4)","4_2.L3(4).2_2",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,15,
16,17,18,19,16,17,18,19,20,21,22,23,24,25,26,27],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);
ALF("4_2.L3(4)","4_2.L3(4).2_3",[1,2,3,2,4,5,6,7,8,7,9,10,11,10,12,12,13,
14,15,14,16,17,18,17,19,20,21,22,19,22,21,20],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);
ALF("4_2.L3(4)","Isoclinic(4_2.L3(4).2_1)",[1,2,3,2,4,5,6,7,8,7,9,10,11,
10,12,13,14,15,16,17,14,17,16,15,18,19,20,21,18,21,20,19],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables"
]);
ALF("4_2.L3(4)","4_2.L3(4).2_2*",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,15,
16,17,18,19,16,17,18,19,20,21,22,23,24,25,26,27],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);
ALF("4_2.L3(4)","Isoclinic(4_2.L3(4).2_3)",[1,2,3,2,4,5,6,7,8,7,9,10,11,
10,12,12,13,14,15,14,16,17,18,17,19,20,21,22,19,22,21,20],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables"
]);

MOT("4_2.L3(4).2_1",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[161280,80640,161280,256,256,72,36,72,128,64,128,32,32,20,20,20,20,28,28,28,
28,144,16,36,36,16,16,16,16,16,16],
[,[1,3,1,1,3,6,8,6,4,4,4,5,5,14,16,14,16,18,20,18,20,1,4,6,6,9,9,12,12,13,
13],[1,2,3,4,5,1,2,3,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,22,22,26,27,
29,28,31,30],,[1,2,3,4,5,6,7,8,9,10,11,12,13,1,2,3,2,18,21,20,19,22,23,24,25,
26,27,29,28,31,30],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,1,2,3,2,22,23,
24,25,26,27,28,29,30,31]],
0,
[(28,29)(30,31),(26,27),(24,25),(19,21),(15,17),(15,17)(19,21),(15,17)(19,21)
(28,29)(30,31),(12,13)(28,30)(29,31)],
["ConstructMGA","4_2.L3(4)","2.L3(4).2_1",[[19,20],[21,24],[22,23],[25,26],
[27,28],[29,32],[30,31]],()]);
ALF("4_2.L3(4).2_1","L3(4).2_1",[1,1,1,2,2,3,3,3,4,4,4,5,6,7,7,7,7,8,8,8,
8,9,10,11,11,12,12,13,13,14,14]);
ALF("4_2.L3(4).2_1","2.L3(4).2_1",[1,2,1,3,4,5,6,5,7,8,7,9,10,11,12,11,12,
13,14,13,14,15,16,17,18,19,20,21,22,23,24]);
ALF("4_2.L3(4).2_1","4_2.L3(4).(2^2)_{123}",[1,2,3,4,5,6,7,8,9,10,11,12,
12,13,14,15,14,16,17,18,19,20,21,22,23,24,25,26,27,27,26]);
ALF("4_2.L3(4).2_1","4_2.L3(4).(2^2)_{12*3}",[1,2,3,4,5,6,7,8,9,10,11,12,
12,13,14,15,14,16,17,18,19,20,21,22,22,23,23,24,25,24,25]);
ALF("4_2.L3(4).2_1","4_2.L3(4).(2^2)_{123*}",[1,2,3,4,5,6,7,8,9,10,11,12,
12,13,14,15,14,16,17,18,19,20,21,22,23,24,25,26,27,27,26]);
ALF("4_2.L3(4).2_1","4_2.L3(4).(2^2)_{12*3*}",[1,2,3,4,5,6,7,8,9,10,11,12,
12,13,14,15,14,16,17,18,19,20,21,22,22,23,23,24,25,24,25]);
ALF("4_2.L3(4).2_1","ON",[1,4,2,2,5,3,14,7,5,5,4,10,11,6,25,12,26,8,28,15,
27,2,5,7,7,10,11,18,19,20,21],[
"fusion map is unique up to table automorphisms,\n",
"compatible with Brauer tables"
]);
ALN("4_2.L3(4).2_1",["ONC2A","ONN2A","ONN4A"]);

MOT("Isoclinic(4_2.L3(4).2_1)",
0,
0,
0,
0,
[(28,29)(30,31),(26,27),(24,25),(19,21),(15,17),(15,17)(19,21),
(12,13)(28,30)(29,31)],
["ConstructIsoclinic",[["4_2.L3(4).2_1"]]]);
ALF("Isoclinic(4_2.L3(4).2_1)","4_2.L3(4).(2^2)_{1*23}",[1,2,3,4,5,6,7,8,
9,10,11,12,12,13,14,15,14,16,17,18,19,20,21,22,23,24,25,26,27,27,26]);
ALF("Isoclinic(4_2.L3(4).2_1)","4_2.L3(4).(2^2)_{1*2*3}",[1,2,3,4,5,6,7,8,
9,10,11,12,12,13,14,15,14,16,17,18,19,20,21,22,22,23,23,24,25,24,25]);
ALF("Isoclinic(4_2.L3(4).2_1)","4_2.L3(4).(2^2)_{1*23*}",[1,2,3,4,5,6,7,8,
9,10,11,12,12,13,14,15,14,16,17,18,19,20,21,22,23,24,25,26,27,27,26]);
ALF("Isoclinic(4_2.L3(4).2_1)","4_2.L3(4).(2^2)_{1*2*3*}",[1,2,3,4,5,6,7,
8,9,10,11,12,12,13,14,15,14,16,17,18,19,20,21,22,22,23,23,24,25,24,25]);
ALN("Isoclinic(4_2.L3(4).2_1)",["4_2.L3(4).2_1*"]);

MOT("4_2.L3(4).2_2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[161280,161280,161280,161280,256,256,72,72,72,72,128,128,128,128,16,20,20,20,
20,56,56,56,56,56,56,56,56,1344,1344,1344,1344,32,32,24,24,24,24,32,32,32,32,
56,56,56,56,56,56,56,56],
[,[1,3,1,3,1,3,7,9,7,9,5,5,5,5,6,16,18,16,18,20,22,20,22,24,26,24,26,1,3,1,3,
5,5,7,9,7,9,14,12,14,12,20,22,20,22,24,26,24,26],[1,4,3,2,5,6,1,4,3,2,11,14,
13,12,15,16,19,18,17,24,27,26,25,20,23,22,21,28,31,30,29,32,33,28,31,30,29,41,
40,39,38,46,49,48,47,42,45,44,43],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,1,2,3,
4,24,25,26,27,20,21,22,23,28,29,30,31,32,33,34,35,36,37,38,39,40,41,46,47,48,
49,42,43,44,45],,[1,4,3,2,5,6,7,10,9,8,11,14,13,12,15,16,19,18,17,1,4,3,2,1,4,
3,2,28,31,30,29,32,33,34,37,36,35,41,40,39,38,28,31,30,29,28,31,30,29]],
0,
[(20,24)(21,25)(22,26)(23,27)(42,46)(43,47)(44,48)(45,49),( 2, 4)( 8,10)
(12,14)(17,19)(21,23)(25,27)(29,31)(35,37)(38,41)(39,40)(43,45)(47,49),(28,30)
(29,31)(34,36)(35,37)(38,40)(39,41)(42,44)(43,45)(46,48)(47,49)],
["ConstructProj",[["L3(4).2_2",[]],["2.L3(4).2_2",[]],,["4_2.L3(4).2_2",[-1,
-1,-1,-1,15,15]]]]);
ALF("4_2.L3(4).2_2","L3(4).2_2",[1,1,1,1,2,2,3,3,3,3,4,4,4,4,5,6,6,6,6,7,
7,7,7,8,8,8,8,9,9,9,9,10,10,11,11,11,11,12,12,12,12,13,13,13,13,14,14,14,
14]);
ALF("4_2.L3(4).2_2","2.L3(4).2_2",[1,2,1,2,3,4,5,6,5,6,7,8,7,8,9,10,11,10,
11,12,13,12,13,14,15,14,15,16,17,16,17,18,19,20,21,20,21,22,23,22,23,24,
25,24,25,26,27,26,27]);
ALF("4_2.L3(4).2_2","4_2.L3(4).(2^2)_{123}",[1,2,3,2,4,5,6,7,8,7,9,10,11,
10,12,13,14,15,14,16,17,18,19,16,19,18,17,28,29,30,29,31,32,33,34,35,34,
36,37,37,36,38,39,40,41,38,41,40,39]);
ALF("4_2.L3(4).2_2","4_2.L3(4).(2^2)_{1*23}",[1,2,3,2,4,5,6,7,8,7,9,10,11,
10,12,13,14,15,14,16,17,18,19,16,19,18,17,28,29,28,30,31,32,33,34,33,35,
36,36,37,37,38,39,40,41,40,39,38,41]);
ALF("4_2.L3(4).2_2","4_2.L3(4).(2^2)_{123*}",[1,2,3,2,4,5,6,7,8,7,9,10,11,
10,12,13,14,15,14,16,17,18,19,16,19,18,17,28,29,28,30,31,32,33,34,33,35,
36,36,37,37,38,39,40,41,40,39,38,41]);
ALF("4_2.L3(4).2_2","4_2.L3(4).(2^2)_{1*23*}",[1,2,3,2,4,5,6,7,8,7,9,10,
11,10,12,13,14,15,14,16,17,18,19,16,19,18,17,28,29,30,29,31,32,33,34,35,
34,36,37,37,36,38,39,40,41,38,41,40,39]);

MOT("4_2.L3(4).2_2*",
0,
0,
0,
0,
[(28,30)(29,31)(34,36)(35,37)(38,40)(39,41)(42,44)(43,45)(46,48)(47,49),(20,
24)(21,25)(22,26)(23,27)(42,46)(43,47)(44,48)(45,49),(2,4)(8,10)(12,14)(17,19)
(21,23)(25,27)(28,29)(30,31)(32,33)(34,35)(36,37)(39,41)(42,43)(44,45)(46,47)
(48,49)],
["ConstructIsoclinic",[["4_2.L3(4).2_2"]],[1..4]]);
ALF("4_2.L3(4).2_2*","Isoclinic(2.L3(4).2_2)",[1,2,1,2,3,4,5,6,5,6,7,8,7,
8,9,10,11,10,11,12,13,12,13,14,15,14,15,16,17,16,17,18,19,20,21,20,21,22,
23,22,23,24,25,24,25,26,27,26,27]);
ALF("4_2.L3(4).2_2*","4_2.L3(4).(2^2)_{12*3}",[1,2,3,2,4,5,6,7,8,7,9,10,
11,10,12,13,14,15,14,16,17,18,19,16,19,18,17,26,27,27,26,28,28,29,30,30,
29,31,32,31,33,34,35,36,37,37,36,35,34]);
ALF("4_2.L3(4).2_2*","4_2.L3(4).(2^2)_{1*2*3}",[1,2,3,2,4,5,6,7,8,7,9,10,
11,10,12,13,14,15,14,16,17,18,19,16,19,18,17,26,26,27,27,28,28,29,29,30,
30,31,32,33,32,34,35,36,37,35,34,37,36]);
ALF("4_2.L3(4).2_2*","4_2.L3(4).(2^2)_{12*3*}",[1,2,3,2,4,5,6,7,8,7,9,10,
11,10,12,13,14,15,14,16,17,18,19,16,19,18,17,26,26,27,27,28,28,29,29,30,
30,31,32,33,32,34,35,36,37,35,34,37,36]);
ALF("4_2.L3(4).2_2*","4_2.L3(4).(2^2)_{1*2*3*}",[1,2,3,2,4,5,6,7,8,7,9,10,
11,10,12,13,14,15,14,16,17,18,19,16,19,18,17,26,27,27,26,28,28,29,30,30,
29,31,32,31,33,34,35,36,37,37,36,35,34]);

MOT("4_2.L3(4).2_3",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]\n",
"2nd power map determined by fusion into 4.U4(3).2_3"
],
[161280,80640,161280,256,256,72,36,72,128,64,128,16,40,20,40,40,20,40,28,28,
28,28,240,240,12,12,32,32,32,32,20,20,20,20],
[,[1,3,1,1,3,6,8,6,4,4,4,5,16,18,16,13,15,13,19,21,19,21,1,1,6,6,11,11,9,9,16,
16,13,13],[1,2,3,4,5,1,2,3,9,10,11,12,16,17,18,13,14,15,19,20,21,22,23,24,23,
24,28,27,30,29,33,34,31,32],,[1,2,3,4,5,6,7,8,9,10,11,12,1,2,3,1,2,3,19,22,21,
20,23,24,25,26,28,27,30,29,23,24,23,24],,[1,2,3,4,5,6,7,8,9,10,11,12,16,17,18,
13,14,15,1,2,3,2,23,24,25,26,27,28,29,30,33,34,31,32]],
0,
[(29,30),(27,28),(20,22),(20,22)(27,28)(29,30),(13,16)(14,17)(15,18)(31,33)
(32,34),(23,24)(25,26)(31,32)(33,34)],
["ConstructMGA","4_2.L3(4)","2.L3(4).2_3",[[19,20],[21,22],[23,24],[25,26],
[27,28],[29,32],[30,31]],()]);
ALF("4_2.L3(4).2_3","L3(4).2_3",[1,1,1,2,2,3,3,3,4,4,4,5,6,6,6,7,7,7,8,8,
8,8,9,9,10,10,11,11,12,12,13,13,14,14]);
ALF("4_2.L3(4).2_3","2.L3(4).2_3",[1,2,1,3,4,5,6,5,7,8,7,9,10,11,10,12,13,
12,14,15,14,15,16,17,18,19,20,21,22,23,24,25,26,27]);
ALF("4_2.L3(4).2_3","4_2.L3(4).(2^2)_{123}",[1,2,3,4,5,6,7,8,9,10,11,12,
13,14,15,13,14,15,16,17,18,19,42,43,44,45,46,46,47,48,49,50,49,50]);
ALF("4_2.L3(4).2_3","4_2.L3(4).(2^2)_{1*23}",[1,2,3,4,5,6,7,8,9,10,11,12,
13,14,15,13,14,15,16,17,18,19,42,43,44,45,46,46,47,48,49,50,49,50]);
ALF("4_2.L3(4).2_3","4_2.L3(4).(2^2)_{12*3}",[1,2,3,4,5,6,7,8,9,10,11,12,
13,14,15,13,14,15,16,17,18,19,38,38,39,39,40,41,42,42,43,44,44,43]);
ALF("4_2.L3(4).2_3","4_2.L3(4).(2^2)_{1*2*3}",[1,2,3,4,5,6,7,8,9,10,11,12,
13,14,15,13,14,15,16,17,18,19,38,38,39,39,40,41,42,42,43,44,44,43]);
ALF("4_2.L3(4).2_3","4.U4(3).2_3",[1,2,3,4,5,13,14,15,16,17,18,19,20,21,
22,20,21,22,28,29,30,31,45,45,47,48,49,50,51,51,55,54,54,55],[
"fusion is unique up to table automorphisms,\n",
"compatible with Brauer tables"
]);

MOT("Isoclinic(4_2.L3(4).2_3)",
0,
0,
0,
0,
[(29,30),(27,28)(29,30),(20,22),(13,16)(14,17)(15,18)(31,33)(32,34),
(23,24)(25,26)(31,32)(33,34)],
["ConstructIsoclinic",[["4_2.L3(4).2_3"]]]);
ALF("Isoclinic(4_2.L3(4).2_3)","4_2.L3(4).(2^2)_{123*}",[1,2,3,4,5,6,7,8,
9,10,11,12,13,14,15,13,14,15,16,17,18,19,42,43,44,45,46,46,47,48,49,50,49,
50]);
ALF("Isoclinic(4_2.L3(4).2_3)","4_2.L3(4).(2^2)_{1*23*}",[1,2,3,4,5,6,7,8,
9,10,11,12,13,14,15,13,14,15,16,17,18,19,42,43,44,45,46,46,47,48,49,50,49,
50]);
ALF("Isoclinic(4_2.L3(4).2_3)","4_2.L3(4).(2^2)_{12*3*}",[1,2,3,4,5,6,7,8,
9,10,11,12,13,14,15,13,14,15,16,17,18,19,38,38,39,39,40,41,42,42,43,44,44,
43]);
ALF("Isoclinic(4_2.L3(4).2_3)","4_2.L3(4).(2^2)_{1*2*3*}",[1,2,3,4,5,6,7,
8,9,10,11,12,13,14,15,13,14,15,16,17,18,19,38,38,39,39,40,41,42,42,43,44,
44,43]);
ALN("Isoclinic(4_2.L3(4).2_3)",["4_2.L3(4).2_3*"]);

MOT("4_2.L3(4).(2^2)_{123}",
[
"constructed using `PossibleCharacterTablesOfTypeMGA'"
],
[322560,161280,322560,512,512,144,72,144,256,128,256,32,40,20,40,56,56,56,56,
288,32,72,72,32,32,16,16,2688,1344,2688,64,64,48,24,48,32,32,56,56,56,56,480,
480,24,24,32,64,64,20,20],
[,[1,3,1,1,3,6,8,6,4,4,4,5,13,15,13,16,18,16,18,1,4,6,6,9,9,12,12,1,3,1,4,4,6,
8,6,10,10,16,18,16,18,1,1,6,6,11,9,9,13,13],[1,2,3,4,5,1,2,3,9,10,11,12,13,14,
15,16,17,18,19,20,21,20,20,24,25,27,26,28,29,30,31,32,28,29,30,36,37,38,39,40,
41,42,43,42,43,46,48,47,49,50],,[1,2,3,4,5,6,7,8,9,10,11,12,1,2,3,16,19,18,17,
20,21,22,23,24,25,27,26,28,29,30,31,32,33,34,35,36,37,38,41,40,39,42,43,44,45,
46,48,47,42,43],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,1,2,3,2,20,21,22,23,24,
25,26,27,28,29,30,31,32,33,34,35,36,37,28,29,30,29,42,43,44,45,46,47,48,49,50]
],
0,
[(26,27)(47,48),(22,23)(24,25)(42,43)(44,45)(49,50),(17,19)(39,41),
(17,19)(28,30)(33,35)(36,37)(38,40)],
["ConstructMGA","4_2.L3(4).2_2","2.L3(4).(2^2)_{123}",[[28,30],[29,31],[32,33]
,[34,36],[35,37],[38,40],[39,41],[42,48],[43,49],[44,46],[45,47]],()]);
ALF("4_2.L3(4).(2^2)_{123}","L3(4).2^2",[1,1,1,2,2,3,3,3,4,4,4,5,6,6,6,7,
7,7,7,8,9,10,10,11,11,12,12,13,13,13,14,14,15,15,15,16,16,17,17,17,17,18,
18,19,19,20,21,21,22,22]);
ALF("4_2.L3(4).(2^2)_{123}","2.L3(4).(2^2)_{123}",[1,2,1,3,4,5,6,5,7,8,7,
9,10,11,10,12,13,12,13,14,15,16,17,18,19,20,21,22,23,22,24,25,26,27,26,28,
28,29,30,29,30,31,32,33,34,35,36,37,38,39]);

MOT("4_2.L3(4).(2^2)_{1*23}",
[
"constructed using `PossibleCharacterTablesOfTypeMGA'"
],
[322560,161280,322560,512,512,144,72,144,256,128,256,32,40,20,40,56,56,56,56,
288,32,72,72,32,32,16,16,1344,2688,2688,64,64,24,48,48,32,32,56,56,56,56,480,
480,24,24,32,64,64,20,20],
[,[1,3,1,1,3,6,8,6,4,4,4,5,13,15,13,16,18,16,18,3,4,8,8,11,11,12,12,1,3,3,4,4,
6,8,8,10,10,16,18,16,18,1,1,6,6,11,9,9,13,13],[1,2,3,4,5,1,2,3,9,10,11,12,13,
14,15,16,17,18,19,20,21,20,20,24,25,27,26,28,30,29,31,32,28,30,29,37,36,40,41,
38,39,42,43,42,43,46,48,47,49,50],,[1,2,3,4,5,6,7,8,9,10,11,12,1,2,3,16,19,18,
17,20,21,22,23,24,25,27,26,28,29,30,31,32,33,34,35,36,37,40,39,38,41,42,43,44,
45,46,48,47,42,43],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,1,2,3,2,20,21,22,23,
24,25,26,27,28,30,29,31,32,33,35,34,37,36,28,30,28,29,42,43,44,45,46,47,48,49,
50]],
0,
[(26,27)(47,48),(22,23)(24,25)(42,43)(44,45)(49,50),(17,19)(38,40),
(17,19)(29,30)(34,35)(36,37)(39,41)],
["ConstructMGA","4_2.L3(4).2_2","2.L3(4).(2^2)_{123}",[[28,31],[29,30],[32,33]
,[34,37],[35,36],[38,41],[39,40],[42,49],[43,48],[44,47],[45,46]],()]);
ALF("4_2.L3(4).(2^2)_{1*23}","L3(4).2^2",[1,1,1,2,2,3,3,3,4,4,4,5,6,6,6,7,
7,7,7,8,9,10,10,11,11,12,12,13,13,13,14,14,15,15,15,16,16,17,17,17,17,18,
18,19,19,20,21,21,22,22]);
ALF("4_2.L3(4).(2^2)_{1*23}","2.L3(4).(2^2)_{123}",[1,2,1,3,4,5,6,5,7,8,7,
9,10,11,10,12,13,12,13,14,15,16,17,18,19,20,21,22,23,23,24,25,26,27,27,28,
28,29,30,29,30,31,32,33,34,35,36,37,38,39]);

MOT("4_2.L3(4).(2^2)_{12*3}",
[
"constructed using `PossibleCharacterTablesOfTypeMGA',\n",
"3rd maximal subgroup of ON.2"
],
[322560,161280,322560,512,512,144,72,144,256,128,256,32,40,20,40,56,56,56,56,
288,32,36,16,16,16,1344,1344,32,24,24,32,64,64,56,56,56,56,240,12,64,64,32,20,
20],
[,[1,3,1,1,3,6,8,6,4,4,4,5,13,15,13,16,18,16,18,1,4,6,9,12,12,2,2,5,7,7,9,11,
11,17,19,17,19,1,6,11,11,9,13,13],[1,2,3,4,5,1,2,3,9,10,11,12,13,14,15,16,17,
18,19,20,21,20,23,25,24,27,26,28,27,26,31,33,32,36,37,34,35,38,38,41,40,42,44,
43],,[1,2,3,4,5,6,7,8,9,10,11,12,1,2,3,16,19,18,17,20,21,22,23,25,24,27,26,28,
30,29,31,33,32,35,34,37,36,38,39,41,40,42,38,38],,[1,2,3,4,5,6,7,8,9,10,11,12,
13,14,15,1,2,3,2,20,21,22,23,24,25,26,27,28,29,30,31,32,33,26,27,27,26,38,39,
40,41,42,44,43]],
0,
[(43,44),(24,25)(40,41),(26,27)(29,30)(32,33)(34,36)(35,37),
(17,19)(34,37)(35,36)],
["ConstructMGA","4_2.L3(4).2_2*","2.L3(4).(2^2)_{12*3}",[[28,30],[29,31],[32,
33],[34,36],[35,37],[38,40],[39,41],[42,48],[43,49],[44,46],[45,47]],()]);
ALF("4_2.L3(4).(2^2)_{12*3}","L3(4).2^2",[1,1,1,2,2,3,3,3,4,4,4,5,6,6,6,7,
7,7,7,8,9,10,11,12,12,13,13,14,15,15,16,16,16,17,17,17,17,18,19,20,20,21,
22,22]);
ALF("4_2.L3(4).(2^2)_{12*3}","2.L3(4).(2^2)_{12*3}",[1,2,1,3,4,5,6,5,7,8,
7,9,10,11,10,12,13,12,13,14,15,16,17,18,19,20,20,21,22,22,23,24,24,25,26,
25,26,27,28,30,29,31,32,33]);
ALF("4_2.L3(4).(2^2)_{12*3}","ON.2",[1,4,2,2,5,3,13,7,5,5,4,10,6,22,11,8,
24,14,23,2,5,7,10,17,18,28,29,30,35,36,30,28,29,44,43,45,42,26,27,29,28,
30,31,32],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables"
]);

MOT("4_2.L3(4).(2^2)_{123*}",
[
"constructed using `PossibleCharacterTablesOfTypeMGA'"
],
[322560,161280,322560,512,512,144,72,144,256,128,256,32,40,20,40,56,56,56,56,
288,32,72,72,32,32,16,16,1344,2688,2688,64,64,24,48,48,32,32,56,56,56,56,480,
480,24,24,32,64,64,20,20],
[,[1,3,1,1,3,6,8,6,4,4,4,5,13,15,13,16,18,16,18,1,4,6,6,9,9,12,12,1,3,3,4,4,6,
8,8,10,10,16,18,16,18,3,3,8,8,9,11,11,15,15],[1,2,3,4,5,1,2,3,9,10,11,12,13,14
,15,16,17,18,19,20,21,20,20,24,25,27,26,28,30,29,31,32,28,30,29,37,36,40,41,38
,39,42,43,42,43,46,48,47,49,50],,[1,2,3,4,5,6,7,8,9,10,11,12,1,2,3,16,19,18,17
,20,21,22,23,24,25,27,26,28,29,30,31,32,33,34,35,36,37,40,39,38,41,42,43,44,45
,46,48,47,42,43],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,1,2,3,2,20,21,22,23,24,
25,26,27,28,30,29,31,32,33,35,34,37,36,28,30,28,29,42,43,44,45,46,47,48,49,50]
],
0,
[(26,27)(47,48),(22,23)(24,25)(42,43)(44,45)(49,50),(17,19)(38,40),
(17,19)(29,30)(34,35)(36,37)(39,41)],
["ConstructMGA","4_2.L3(4).2_2","2.L3(4).(2^2)_{123}",[[28,31],[29,30],[32,33]
,[34,37],[35,36],[38,41],[39,40],[42,49],[43,48],[44,47],[45,46]],()]);
ALF("4_2.L3(4).(2^2)_{123*}","L3(4).2^2",[1,1,1,2,2,3,3,3,4,4,4,5,6,6,6,7,
7,7,7,8,9,10,10,11,11,12,12,13,13,13,14,14,15,15,15,16,16,17,17,17,17,18,
18,19,19,20,21,21,22,22]);
ALF("4_2.L3(4).(2^2)_{123*}","2.L3(4).(2^2)_{123}",[1,2,1,3,4,5,6,5,7,8,7,
9,10,11,10,12,13,12,13,14,15,16,17,18,19,20,21,22,23,23,24,25,26,27,27,28,
28,29,30,29,30,31,32,33,34,35,36,37,38,39]);

MOT("4_2.L3(4).(2^2)_{1*2*3}",
[
"constructed using `PossibleCharacterTablesOfTypeMGA'"
],
[322560,161280,322560,512,512,144,72,144,256,128,256,32,40,20,40,56,56,56,56,
288,32,36,16,16,16,1344,1344,32,24,24,64,32,64,56,56,56,56,240,12,64,64,32,20,
20],
[,[1,3,1,1,3,6,8,6,4,4,4,5,13,15,13,16,18,16,18,3,4,8,11,12,12,2,2,5,7,7,9,11,
9,17,19,17,19,1,6,11,11,9,13,13],[1,2,3,4,5,1,2,3,9,10,11,12,13,14,15,16,17,18
,19,20,21,20,23,25,24,26,27,28,26,27,31,32,33,34,35,36,37,38,38,41,40,42,44,43
],,[1,2,3,4,5,6,7,8,9,10,11,12,1,2,3,16,19,18,17,20,21,22,23,25,24,27,26,28,30
,29,33,32,31,37,36,35,34,38,39,41,40,42,38,38],,[1,2,3,4,5,6,7,8,9,10,11,12,13
,14,15,1,2,3,2,20,21,22,23,24,25,27,26,28,30,29,33,32,31,27,27,26,26,38,39,40,
41,42,44,43]],
0,
[(43,44),(24,25)(40,41),(26,27)(29,30)(31,33)(34,36)(35,37),
(17,19)(34,35)(36,37)],
["ConstructMGA","4_2.L3(4).2_2*","2.L3(4).(2^2)_{12*3}",[[28,31],[29,30],[32,
33],[34,37],[35,36],[38,41],[39,40],[42,49],[43,48],[44,47],[45,46]],()]);
ALF("4_2.L3(4).(2^2)_{1*2*3}","L3(4).2^2",[1,1,1,2,2,3,3,3,4,4,4,5,6,6,6,
7,7,7,7,8,9,10,11,12,12,13,13,14,15,15,16,16,16,17,17,17,17,18,19,20,20,
21,22,22]);
ALF("4_2.L3(4).(2^2)_{1*2*3}","2.L3(4).(2^2)_{12*3}",[1,2,1,3,4,5,6,5,7,8,
7,9,10,11,10,12,13,12,13,14,15,16,17,18,19,20,20,21,22,22,23,24,23,25,26,
25,26,27,28,30,29,31,32,33]);

MOT("4_2.L3(4).(2^2)_{1*23*}",
[
"constructed using `PossibleCharacterTablesOfTypeMGA'"
],
[322560,161280,322560,512,512,144,72,144,256,128,256,32,40,20,40,56,56,56,56,
288,32,72,72,32,32,16,16,2688,1344,2688,64,64,48,24,48,32,32,56,56,56,56,480,
480,24,24,32,64,64,20,20],
[,[1,3,1,1,3,6,8,6,4,4,4,5,13,15,13,16,18,16,18,3,4,8,8,11,11,12,12,1,3,1,4,4,
6,8,6,10,10,16,18,16,18,3,3,8,8,9,11,11,15,15],[1,2,3,4,5,1,2,3,9,10,11,12,13,
14,15,16,17,18,19,20,21,20,20,24,25,27,26,28,29,30,31,32,28,29,30,36,37,38,39,
40,41,42,43,42,43,46,48,47,49,50],,[1,2,3,4,5,6,7,8,9,10,11,12,1,2,3,16,19,18,
17,20,21,22,23,24,25,27,26,28,29,30,31,32,33,34,35,36,37,38,41,40,39,42,43,44,
45,46,48,47,42,43],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,1,2,3,2,20,21,22,23,
24,25,26,27,28,29,30,31,32,33,34,35,36,37,28,29,30,29,42,43,44,45,46,47,48,49,
50]],
0,
[(26,27)(47,48),(22,23)(24,25)(42,43)(44,45)(49,50),(17,19)(39,41),
(17,19)(28,30)(33,35)(36,37)(38,40)],
["ConstructMGA","4_2.L3(4).2_2","2.L3(4).(2^2)_{123}",[[28,30],[29,31],[32,33]
,[34,36],[35,37],[38,40],[39,41],[42,48],[43,49],[44,46],[45,47]],()]);
ALF("4_2.L3(4).(2^2)_{1*23*}","L3(4).2^2",[1,1,1,2,2,3,3,3,4,4,4,5,6,6,6,
7,7,7,7,8,9,10,10,11,11,12,12,13,13,13,14,14,15,15,15,16,16,17,17,17,17,
18,18,19,19,20,21,21,22,22]);
ALF("4_2.L3(4).(2^2)_{1*23*}","2.L3(4).(2^2)_{123}",[1,2,1,3,4,5,6,5,7,8,
7,9,10,11,10,12,13,12,13,14,15,16,17,18,19,20,21,22,23,22,24,25,26,27,26,
28,28,29,30,29,30,31,32,33,34,35,36,37,38,39]);

MOT("4_2.L3(4).(2^2)_{12*3*}",
[
"constructed using `PossibleCharacterTablesOfTypeMGA'"
],
[322560,161280,322560,512,512,144,72,144,256,128,256,32,40,20,40,56,56,56,56,
288,32,36,16,16,16,1344,1344,32,24,24,64,32,64,56,56,56,56,240,12,64,64,32,20,
20],
[,[1,3,1,1,3,6,8,6,4,4,4,5,13,15,13,16,18,16,18,1,4,6,9,12,12,2,2,5,7,7,9,11,9
,17,19,17,19,3,8,9,9,11,15,15],[1,2,3,4,5,1,2,3,9,10,11,12,13,14,15,16,17,18,
19,20,21,20,23,25,24,26,27,28,26,27,31,32,33,34,35,36,37,38,38,41,40,42,44,43]
,,[1,2,3,4,5,6,7,8,9,10,11,12,1,2,3,16,19,18,17,20,21,22,23,25,24,27,26,28,30,
29,33,32,31,37,36,35,34,38,39,41,40,42,38,38],,[1,2,3,4,5,6,7,8,9,10,11,12,13,
14,15,1,2,3,2,20,21,22,23,24,25,27,26,28,30,29,33,32,31,27,27,26,26,38,39,40,
41,42,44,43]],
0,
[(43,44),(24,25)(40,41),(26,27)(29,30)(31,33)(34,36)(35,37),
(17,19)(34,35)(36,37)],
["ConstructMGA","4_2.L3(4).2_2*","2.L3(4).(2^2)_{12*3}",[[28,31],[29,30],[32,
33],[34,37],[35,36],[38,41],[39,40],[42,49],[43,48],[44,47],[45,46]],()]);
ALF("4_2.L3(4).(2^2)_{12*3*}","L3(4).2^2",[1,1,1,2,2,3,3,3,4,4,4,5,6,6,6,
7,7,7,7,8,9,10,11,12,12,13,13,14,15,15,16,16,16,17,17,17,17,18,19,20,20,
21,22,22]);
ALF("4_2.L3(4).(2^2)_{12*3*}","2.L3(4).(2^2)_{12*3}",[1,2,1,3,4,5,6,5,7,8,
7,9,10,11,10,12,13,12,13,14,15,16,17,18,19,20,20,21,22,22,23,24,23,25,26,
25,26,27,28,30,29,31,32,33]);

MOT("4_2.L3(4).(2^2)_{1*2*3*}",
[
"constructed using `PossibleCharacterTablesOfTypeMGA'"
],
[322560,161280,322560,512,512,144,72,144,256,128,256,32,40,20,40,56,56,56,56,
288,32,36,16,16,16,1344,1344,32,24,24,32,64,64,56,56,56,56,240,12,64,64,32,20,
20],
[,[1,3,1,1,3,6,8,6,4,4,4,5,13,15,13,16,18,16,18,3,4,8,11,12,12,2,2,5,7,7,9,11,
11,17,19,17,19,3,8,9,9,11,15,15],[1,2,3,4,5,1,2,3,9,10,11,12,13,14,15,16,17,18
,19,20,21,20,23,25,24,27,26,28,27,26,31,33,32,36,37,34,35,38,38,41,40,42,44,43
],,[1,2,3,4,5,6,7,8,9,10,11,12,1,2,3,16,19,18,17,20,21,22,23,25,24,27,26,28,30
,29,31,33,32,35,34,37,36,38,39,41,40,42,38,38],,[1,2,3,4,5,6,7,8,9,10,11,12,13
,14,15,1,2,3,2,20,21,22,23,24,25,26,27,28,29,30,31,32,33,26,27,27,26,38,39,40,
41,42,44,43]],
0,
[(43,44),(24,25)(40,41),(26,27)(29,30)(32,33)(34,36)(35,37),
(17,19)(34,37)(35,36)],
["ConstructMGA","4_2.L3(4).2_2*","2.L3(4).(2^2)_{12*3}",[[28,30],[29,31],[32,
33],[34,36],[35,37],[38,40],[39,41],[42,48],[43,49],[44,46],[45,47]],()]);
ALF("4_2.L3(4).(2^2)_{1*2*3*}","L3(4).2^2",[1,1,1,2,2,3,3,3,4,4,4,5,6,6,6,
7,7,7,7,8,9,10,11,12,12,13,13,14,15,15,16,16,16,17,17,17,17,18,19,20,20,
21,22,22]);
ALF("4_2.L3(4).(2^2)_{1*2*3*}","2.L3(4).(2^2)_{12*3}",[1,2,1,3,4,5,6,5,7,
8,7,9,10,11,10,12,13,12,13,14,15,16,17,18,19,20,20,21,22,22,23,24,24,25,
26,25,26,27,28,30,29,31,32,33]);

MOT("6.L3(4)",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[120960,120960,120960,120960,120960,120960,384,384,384,384,384,384,18,18,96,
96,96,96,96,96,48,48,48,48,48,48,30,30,30,30,30,30,30,30,30,30,30,30,42,42,42,
42,42,42,42,42,42,42,42,42],
[,[1,3,5,1,3,5,1,3,5,1,3,5,13,13,7,9,11,7,9,11,10,12,8,10,12,8,33,35,37,33,35,
37,27,29,31,27,29,31,39,41,43,39,41,43,45,47,49,45,47,49],[1,4,1,4,1,4,7,10,7,
10,7,10,1,4,15,18,15,18,15,18,21,21,21,24,24,24,33,36,33,36,33,36,27,30,27,30,
27,30,45,48,45,48,45,48,39,42,39,42,39,42],,[1,6,5,4,3,2,7,12,11,10,9,8,13,14,
15,20,19,18,17,16,21,23,22,24,26,25,1,6,5,4,3,2,1,6,5,4,3,2,45,50,49,48,47,46,
39,44,43,42,41,40],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,
23,24,25,26,33,34,35,36,37,38,27,28,29,30,31,32,1,2,3,4,5,6,1,2,3,4,5,6]],
0,
[(39,45)(40,46)(41,47)(42,48)(43,49)(44,50),(27,33)(28,34)(29,35)(30,36)
(31,37)(32,38),( 2, 6)( 3, 5)( 8,12)( 9,11)(16,20)(17,19)(22,23)(25,26)(28,32)
(29,31)(34,38)(35,37)(40,44)(41,43)(46,50)(47,49),(21,24)(22,25)(23,26)],
["ConstructProj",[["L3(4)",[]],["2.L3(4)",[]],["3.L3(4)",[-1,-1,-1,-1,-13,-13,
11,11,-1]],,,["6.L3(4)",[-1,-1,11,11,-13,-13,-1]]]]);
ALF("6.L3(4)","L3(4)",[1,1,1,1,1,1,2,2,2,2,2,2,3,3,4,4,4,4,4,4,5,5,5,6,6,
6,7,7,7,7,7,7,8,8,8,8,8,8,9,9,9,9,9,9,10,10,10,10,10,10]);
ALF("6.L3(4)","2.L3(4)",[1,2,1,2,1,2,3,4,3,4,3,4,5,6,7,8,7,8,7,8,9,9,9,10,
10,10,11,12,11,12,11,12,13,14,13,14,13,14,15,16,15,16,15,16,17,18,17,18,
17,18]);
ALF("6.L3(4)","3.L3(4)",[1,2,3,1,2,3,4,5,6,4,5,6,7,7,8,9,10,8,9,10,11,12,
13,14,15,16,17,18,19,17,18,19,20,21,22,20,21,22,23,24,25,23,24,25,26,27,
28,26,27,28]);
ALF("6.L3(4)","6.L3(4).2_1",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,
19,20,21,22,23,24,25,26,27,28,29,30,31,32,27,28,29,30,31,32,33,34,35,36,
37,38,33,34,35,36,37,38],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("6.L3(4)","6.L3(4).2_2",[1,2,3,4,3,2,5,6,7,8,7,6,9,10,11,12,13,14,13,
12,15,16,17,15,17,16,18,19,20,21,22,23,18,23,22,21,20,19,24,25,26,27,26,
25,28,29,30,31,30,29],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);
ALF("6.L3(4)","6.L3(4).2_3",[1,2,3,4,3,2,5,6,7,8,7,6,9,10,11,12,13,14,13,
12,15,16,17,15,17,16,18,19,20,21,20,19,22,23,24,25,24,23,26,27,28,29,30,
31,26,31,30,29,28,27],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);
ALF("6.L3(4)","Isoclinic(6.L3(4).2_1)",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,
15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,27,28,29,30,31,32,
33,34,35,36,37,38,33,34,35,36,37,38]);
ALF("6.L3(4)","Isoclinic(6.L3(4).2_2)",[1,2,3,4,3,2,5,6,7,8,7,6,9,10,11,
12,13,14,13,12,15,16,17,15,17,16,18,19,20,21,22,23,18,23,22,21,20,19,24,
25,26,27,26,25,28,29,30,31,30,29],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables"
]);
ALF("6.L3(4)","Isoclinic(6.L3(4).2_3)",[1,2,3,4,3,2,5,6,7,8,7,6,9,10,11,
12,13,14,13,12,15,16,17,15,17,16,18,19,20,21,20,19,22,23,24,25,24,23,26,
27,28,29,30,31,26,31,30,29,28,27],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);
ALF("6.L3(4)","6.M22",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,
21,22,23,21,22,23,24,25,26,27,28,29,24,25,26,27,28,29,36,37,38,39,40,41,
42,43,44,45,46,47],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);

MOT("6.L3(4).2_1",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[241920,241920,241920,241920,241920,241920,768,768,768,768,768,768,36,36,192,
192,192,192,192,192,96,96,96,96,96,96,30,30,30,30,30,30,42,42,42,42,42,42,432,
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],
[,[1,3,5,1,3,5,1,3,5,1,3,5,13,13,7,9,11,7,9,11,10,12,8,10,12,8,27,29,31,27,29,
31,33,35,37,33,35,37,1,3,5,7,9,11,13,13,15,17,19,15,17,19,21,23,22,21,23,22,
24,26,25,24,26,25],[1,4,1,4,1,4,7,10,7,10,7,10,1,4,15,18,15,18,15,18,21,21,21,
24,24,24,27,30,27,30,27,30,33,36,33,36,33,36,39,39,39,42,42,42,39,39,47,50,47,
50,47,50,56,53,56,53,56,53,62,59,62,59,62,59],,[1,6,5,4,3,2,7,12,11,10,9,8,13,
14,15,20,19,18,17,16,21,23,22,24,26,25,1,6,5,4,3,2,33,38,37,36,35,34,39,41,40,
42,44,43,45,46,47,52,51,50,49,48,56,55,54,53,58,57,62,61,60,59,64,63],,[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,
32,1,2,3,4,5,6,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,
60,61,62,63,64]],
0,
[(53,56)(54,57)(55,58)(59,62)(60,63)(61,64),(47,50)(48,51)(49,52),(45,46),
( 2, 6)( 3, 5)( 8,12)( 9,11)(16,20)(17,19)(22,23)(25,26)(28,32)(29,31)(34,38)
(35,37)(40,41)(43,44)(48,52)(49,51)(54,58)(55,57)(60,64)(61,63),(21,24)(22,25)
(23,26)(53,59)(54,60)(55,61)(56,62)(57,63)(58,64)],
["ConstructProj",[["L3(4).2_1",[]],["2.L3(4).2_1",[]],["3.L3(4).2_1",[-1,-1,
-1,-1,-1,-1,-1]],,,["6.L3(4).2_1",[17,-1,-1,-1,17]]]]);
ALF("6.L3(4).2_1","L3(4).2_1",[1,1,1,1,1,1,2,2,2,2,2,2,3,3,4,4,4,4,4,4,5,
5,5,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,9,9,10,10,10,11,11,12,12,12,12,12,12,
13,13,13,13,13,13,14,14,14,14,14,14]);
ALF("6.L3(4).2_1","2.L3(4).2_1",[1,2,1,2,1,2,3,4,3,4,3,4,5,6,7,8,7,8,7,8,
9,9,9,10,10,10,11,12,11,12,11,12,13,14,13,14,13,14,15,15,15,16,16,16,17,
18,19,20,19,20,19,20,21,22,21,22,21,22,23,24,23,24,23,24]);
ALF("6.L3(4).2_1","3.L3(4).2_1",[1,2,3,1,2,3,4,5,6,4,5,6,7,7,8,9,10,8,9,
10,11,12,13,14,15,16,17,18,19,17,18,19,20,21,22,20,21,22,23,24,25,26,27,
28,29,29,30,31,32,30,31,32,33,34,35,33,34,35,36,37,38,36,37,38]);
ALF("6.L3(4).2_1","6.L3(4).(2^2)_{123}",[1,2,3,4,3,2,5,6,7,8,7,6,9,10,11,
12,13,14,13,12,15,16,17,15,17,16,18,19,20,21,20,19,22,23,24,25,24,23,26,
27,27,28,29,29,30,31,32,33,34,35,34,33,36,37,38,39,40,41,39,38,37,36,41,
40]);
ALF("6.L3(4).2_1","6.L3(4).(2^2)_{12*3}",[1,2,3,4,3,2,5,6,7,8,7,6,9,10,11,
12,13,14,13,12,15,16,17,15,17,16,18,19,20,21,20,19,22,23,24,25,24,23,26,
27,27,28,29,29,30,30,31,32,32,31,33,33,34,35,36,37,38,39,34,39,38,37,36,
35]);
ALF("6.L3(4).2_1","6.L3(4).(2^2)_{123*}",[1,2,3,4,3,2,5,6,7,8,7,6,9,10,11,
12,13,14,13,12,15,16,17,15,17,16,18,19,20,21,20,19,22,23,24,25,24,23,26,
27,27,28,29,29,30,30,31,32,32,31,33,33,34,35,36,37,38,39,34,39,38,37,36,
35]);
ALF("6.L3(4).2_1","6.L3(4).(2^2)_{12*3*}",[1,2,3,4,3,2,5,6,7,8,7,6,9,10,
11,12,13,14,13,12,15,16,17,15,17,16,18,19,20,21,20,19,22,23,24,25,24,23,
26,27,27,28,29,29,30,31,32,33,34,35,34,33,36,37,38,39,40,41,39,38,37,36,
41,40]);
ALF("6.L3(4).2_1","6.U6(2)",[1,2,3,4,5,6,13,14,15,16,17,18,34,35,42,43,44,
45,46,47,48,49,50,51,52,53,63,64,65,66,67,68,113,114,115,116,117,118,19,
20,21,60,61,62,111,112,122,123,124,125,126,127,128,129,130,128,129,130,
131,132,133,131,132,133],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);

MOT("Isoclinic(6.L3(4).2_1)",
0,
0,
0,
0,
[(53,56)(54,57)(55,58)(59,62)(60,63)(61,64),(47,50)(48,51)(49,52),(45,46),
(21,24)(22,25)(23,26)(53,59)(54,60)(55,61)(56,62)(57,63)(58,64),(2,6)(3,5)
(8,12)(9,11)(16,20)(17,19)(22,23)(25,26)(28,32)(29,31)(34,38)(35,37)(40,41)
(43,44)(48,52)(49,51)(54,58)(55,57)(60,64)(61,63)],
["ConstructIsoclinic",[["6.L3(4).2_1"]]]);
ALF("Isoclinic(6.L3(4).2_1)","Isoclinic(2.L3(4).2_1)",[1,2,1,2,1,2,3,4,3,
4,3,4,5,6,7,8,7,8,7,8,9,9,9,10,10,10,11,12,11,12,11,12,13,14,13,14,13,14,
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("Isoclinic(6.L3(4).2_1)","6.L3(4).(2^2)_{1*23}",[1,2,3,4,3,2,5,6,7,8,
7,6,9,10,11,12,13,14,13,12,15,16,17,15,17,16,18,19,20,21,20,19,22,23,24,
25,24,23,26,27,27,28,29,29,30,30,31,32,32,31,33,33,34,35,36,37,38,39,34,
39,38,37,36,35]);
ALF("Isoclinic(6.L3(4).2_1)","6.L3(4).(2^2)_{1*2*3}",[1,2,3,4,3,2,5,6,7,8,
7,6,9,10,11,12,13,14,13,12,15,16,17,15,17,16,18,19,20,21,20,19,22,23,24,
25,24,23,26,27,27,28,29,29,30,31,32,33,34,35,34,33,36,37,38,39,40,41,39,
38,37,36,41,40]);
ALF("Isoclinic(6.L3(4).2_1)","6.L3(4).(2^2)_{1*23*}",[1,2,3,4,3,2,5,6,7,8,
7,6,9,10,11,12,13,14,13,12,15,16,17,15,17,16,18,19,20,21,20,19,22,23,24,
25,24,23,26,27,27,28,29,29,30,31,32,33,34,35,34,33,36,37,38,39,40,41,39,
38,37,36,41,40]);
ALF("Isoclinic(6.L3(4).2_1)","6.L3(4).(2^2)_{1*2*3*}",[1,2,3,4,3,2,5,6,7,
8,7,6,9,10,11,12,13,14,13,12,15,16,17,15,17,16,18,19,20,21,20,19,22,23,24,
25,24,23,26,27,27,28,29,29,30,30,31,32,32,31,33,33,34,35,36,37,38,39,34,
39,38,37,36,35]);
ALN("Isoclinic(6.L3(4).2_1)",["6.L3(4).2_1*"]);

MOT("6.L3(4).2_2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[241920,120960,120960,241920,768,384,384,768,36,36,192,96,96,192,48,48,48,30,
30,30,30,30,30,84,42,42,84,84,42,42,84,672,672,32,32,12,12,16,16,28,28,28,28],
[,[1,3,3,1,1,3,3,1,9,9,5,7,7,5,8,6,6,18,22,20,18,22,20,24,26,26,24,28,30,30,
28,1,1,5,5,9,9,14,14,24,24,28,28],[1,4,1,4,5,8,5,8,1,4,11,14,11,14,15,15,15,
18,21,18,21,18,21,28,31,28,31,24,27,24,27,32,33,34,35,32,33,39,38,42,43,40,
41],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,17,16,1,2,3,4,3,2,28,29,30,31,24,25,
26,27,32,33,34,35,36,37,38,39,42,43,40,41],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,
15,16,17,18,23,22,21,20,19,1,2,3,4,1,2,3,4,32,33,34,35,36,37,39,38,32,33,32,
33]],
0,
[(38,39),(24,28)(25,29)(26,30)(27,31)(40,42)(41,43),(19,23)(20,22),(16,17),
(16,17)(19,23)(20,22),(32,33)(34,35)(36,37)(40,41)(42,43)],
["ConstructMGA","6.L3(4)","2.L3(4).2_2",[[19,20],[21,24],[22,23],[25,26],
[27,28],[29,30],[31,34],[32,33],[35,36],[37,38],[39,40],[41,44],[42,43],[45,
46],[47,48],[49,50]],()]);
ALF("6.L3(4).2_2","L3(4).2_2",[1,1,1,1,2,2,2,2,3,3,4,4,4,4,5,5,5,6,6,6,6,
6,6,7,7,7,7,8,8,8,8,9,9,10,10,11,11,12,12,13,13,14,14]);
ALF("6.L3(4).2_2","2.L3(4).2_2",[1,2,1,2,3,4,3,4,5,6,7,8,7,8,9,9,9,10,11,
10,11,10,11,12,13,12,13,14,15,14,15,16,17,18,19,20,21,22,23,24,25,26,27]);
ALF("6.L3(4).2_2","3.L3(4).2_2",[1,2,2,1,3,4,4,3,5,5,6,7,7,6,8,9,10,11,12,
13,11,12,13,14,15,15,14,16,17,17,16,18,18,19,19,20,20,21,21,22,22,23,23]);
ALF("6.L3(4).2_2","6.L3(4).(2^2)_{123}",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,
15,16,17,18,19,20,21,20,19,22,23,24,25,22,23,24,25,42,43,44,45,46,47,48,
48,49,50,49,50]);
ALF("6.L3(4).2_2","6.L3(4).(2^2)_{1*23}",[1,2,3,4,5,6,7,8,9,10,11,12,13,
14,15,16,17,18,19,20,21,20,19,22,23,24,25,22,23,24,25,40,40,41,41,42,42,
43,44,45,46,46,45]);
ALF("6.L3(4).2_2","6.L3(4).(2^2)_{123*}",[1,2,3,4,5,6,7,8,9,10,11,12,13,
14,15,16,17,18,19,20,21,20,19,22,23,24,25,22,23,24,25,40,40,41,41,42,42,
43,44,45,46,46,45]);
ALF("6.L3(4).2_2","6.L3(4).(2^2)_{1*23*}",[1,2,3,4,5,6,7,8,9,10,11,12,13,
14,15,16,17,18,19,20,21,20,19,22,23,24,25,22,23,24,25,42,43,44,45,46,47,
48,48,49,50,49,50]);
ALF("6.L3(4).2_2","6.M22.2",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,16,17,
18,19,20,19,18,25,26,27,28,29,30,31,32,42,43,47,47,48,49,50,50,55,56,57,
58],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALN("6.L3(4).2_2",["6.M22.2M2"]);

MOT("Isoclinic(6.L3(4).2_2)",
0,
0,
0,
0,
[(38,39),(19,23)(20,22),(16,17),(32,33)(34,35)(36,37)(40,41)(42,43),
(24,28)(25,29)(26,30)(27,31)(40,42)(41,43)],
["ConstructIsoclinic",[["6.L3(4).2_2"]]]);
ALF("Isoclinic(6.L3(4).2_2)","6.L3(4).(2^2)_{12*3}",[1,2,3,4,5,6,7,8,9,10,
11,12,13,14,15,16,17,18,19,20,21,20,19,22,23,24,25,22,23,24,25,40,40,41,
41,42,42,43,44,45,46,46,45]);
ALF("Isoclinic(6.L3(4).2_2)","6.L3(4).(2^2)_{1*2*3}",[1,2,3,4,5,6,7,8,9,
10,11,12,13,14,15,16,17,18,19,20,21,20,19,22,23,24,25,22,23,24,25,42,43,
44,45,46,47,48,48,49,50,49,50]);
ALF("Isoclinic(6.L3(4).2_2)","6.L3(4).(2^2)_{12*3*}",[1,2,3,4,5,6,7,8,9,
10,11,12,13,14,15,16,17,18,19,20,21,20,19,22,23,24,25,22,23,24,25,42,43,
44,45,46,47,48,48,49,50,49,50]);
ALF("Isoclinic(6.L3(4).2_2)","6.L3(4).(2^2)_{1*2*3*}",[1,2,3,4,5,6,7,8,9,
10,11,12,13,14,15,16,17,18,19,20,21,20,19,22,23,24,25,22,23,24,25,40,40,
41,41,42,42,43,44,45,46,46,45]);
ALN("Isoclinic(6.L3(4).2_2)",["6.L3(4).2_2*"]);

MOT("6.L3(4).2_3",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[241920,120960,120960,241920,768,384,384,768,36,36,192,96,96,192,48,48,48,60,
30,30,60,60,30,30,60,42,42,42,42,42,42,240,240,12,12,32,32,32,32,20,20,20,20],
[,[1,3,3,1,1,3,3,1,9,9,5,7,7,5,8,6,6,22,24,24,22,18,20,20,18,26,28,30,26,28,
30,1,1,9,9,11,11,11,11,22,22,18,18],[1,4,1,4,5,8,5,8,1,4,11,14,11,14,15,15,15,
22,25,22,25,18,21,18,21,26,29,26,29,26,29,32,33,32,33,37,36,39,38,42,43,40,
41],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,17,16,1,2,3,4,1,2,3,4,26,27,28,29,
30,31,32,33,34,35,37,36,39,38,32,33,32,33],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,
15,16,17,22,23,24,25,18,19,20,21,1,2,3,4,3,2,32,33,34,35,36,37,38,39,42,43,40,
41]],
0,
[(38,39),(36,37),(36,37)(38,39),(27,31)(28,30),(18,22)(19,23)(20,24)(21,25)
(40,42)(41,43),(16,17),(16,17)(27,31)(28,30),(32,33)(34,35)(40,41)(42,43)],
["ConstructMGA","6.L3(4)","2.L3(4).2_3",[[19,20],[21,24],[22,23],[25,26],
[27,30],[28,29],[31,32],[33,34],[35,36],[37,38],[39,40],[41,42],[43,44],[45,
48],[46,47],[49,50]],()]);
ALF("6.L3(4).2_3","L3(4).2_3",[1,1,1,1,2,2,2,2,3,3,4,4,4,4,5,5,5,6,6,6,6,
7,7,7,7,8,8,8,8,8,8,9,9,10,10,11,11,12,12,13,13,14,14]);
ALF("6.L3(4).2_3","2.L3(4).2_3",[1,2,1,2,3,4,3,4,5,6,7,8,7,8,9,9,9,10,11,
10,11,12,13,12,13,14,15,14,15,14,15,16,17,18,19,20,21,22,23,24,25,26,27]);
ALF("6.L3(4).2_3","3.L3(4).2_3",[1,2,2,1,3,4,4,3,5,5,6,7,7,6,8,9,10,11,12,
12,11,13,14,14,13,15,16,17,15,16,17,18,18,19,19,20,20,21,21,22,22,23,23]);
ALF("6.L3(4).2_3","6.L3(4).(2^2)_{123}",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,
15,16,17,18,19,20,21,18,19,20,21,22,23,24,25,24,23,51,52,53,54,55,55,56,
57,58,59,58,59]);
ALF("6.L3(4).2_3","6.L3(4).(2^2)_{1*23}",[1,2,3,4,5,6,7,8,9,10,11,12,13,
14,15,16,17,18,19,20,21,18,19,20,21,22,23,24,25,24,23,47,47,48,48,49,50,
51,51,52,53,53,52]);
ALF("6.L3(4).2_3","6.L3(4).(2^2)_{12*3}",[1,2,3,4,5,6,7,8,9,10,11,12,13,
14,15,16,17,18,19,20,21,18,19,20,21,22,23,24,25,24,23,47,47,48,48,49,50,
51,51,52,53,53,52]);
ALF("6.L3(4).2_3","6.L3(4).(2^2)_{1*2*3}",[1,2,3,4,5,6,7,8,9,10,11,12,13,
14,15,16,17,18,19,20,21,18,19,20,21,22,23,24,25,24,23,51,52,53,54,55,55,
56,57,58,59,58,59]);

MOT("Isoclinic(6.L3(4).2_3)",
0,
0,
0,
0,
[(38,39),(36,37)(38,39),(32,33)(34,35)(36,37)(38,39)(40,41)(42,43),
(27,31)(28,30),(18,22)(19,23)(20,24)(21,25)(40,42)(41,43),(16,17),
(16,17)(27,31)(28,30)],
["ConstructIsoclinic",[["6.L3(4).2_3"]]]);
ALF("Isoclinic(6.L3(4).2_3)","3.L3(4).2_3",[1,2,2,1,3,4,4,3,5,5,6,7,7,6,8,
9,10,11,12,12,11,13,14,14,13,15,16,17,15,16,17,18,18,19,19,20,20,21,21,22,
22,23,23]);
ALF("Isoclinic(6.L3(4).2_3)","6.L3(4).(2^2)_{123*}",[1,2,3,4,5,6,7,8,9,10,
11,12,13,14,15,16,17,18,19,20,21,18,19,20,21,22,23,24,25,24,23,47,47,48,
48,49,50,51,51,52,53,53,52]);
ALF("Isoclinic(6.L3(4).2_3)","6.L3(4).(2^2)_{1*23*}",[1,2,3,4,5,6,7,8,9,
10,11,12,13,14,15,16,17,18,19,20,21,18,19,20,21,22,23,24,25,24,23,51,52,
53,54,55,55,56,57,58,59,58,59]);
ALF("Isoclinic(6.L3(4).2_3)","6.L3(4).(2^2)_{12*3*}",[1,2,3,4,5,6,7,8,9,
10,11,12,13,14,15,16,17,18,19,20,21,18,19,20,21,22,23,24,25,24,23,51,52,
53,54,55,55,56,57,58,59,58,59]);
ALF("Isoclinic(6.L3(4).2_3)","6.L3(4).(2^2)_{1*2*3*}",[1,2,3,4,5,6,7,8,9,
10,11,12,13,14,15,16,17,18,19,20,21,18,19,20,21,22,23,24,25,24,23,47,47,
48,48,49,50,51,51,52,53,53,52]);
ALF("Isoclinic(6.L3(4).2_3)","2.G2(4)",[1,7,6,2,3,23,22,4,8,9,11,36,37,10,
12,38,39,14,45,44,15,16,47,46,17,25,53,54,26,52,55,5,5,24,24,27,27,27,27,
34,34,35,35],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);
ALN("Isoclinic(6.L3(4).2_3)",["6.L3(4).2_3*"]);

MOT("6.L3(4).(2^2)_{123}",
[
"constructed using `PossibleCharacterTablesOfTypeMGA'"
],
[483840,241920,241920,483840,1536,768,768,1536,72,72,384,192,192,384,96,96,96,
60,30,30,60,84,42,42,84,864,432,96,48,72,72,96,48,48,96,48,48,48,48,48,48,1344
,1344,64,64,24,24,16,28,28,480,480,24,24,32,64,64,20,20],
[,[1,3,3,1,1,3,3,1,9,9,5,7,7,5,8,6,6,18,20,20,18,22,24,24,22,1,3,5,7,9,9,11,13
,13,11,15,17,16,15,17,16,1,1,5,5,9,9,14,22,22,1,1,9,9,11,11,11,18,18],[1,4,1,4
,5,8,5,8,1,4,11,14,11,14,15,15,15,18,21,18,21,22,25,22,25,26,26,28,28,26,26,32
,35,32,35,39,36,39,36,39,36,42,43,44,45,42,43,48,49,50,51,52,51,52,55,57,56,58
,59],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,17,16,1,2,3,4,22,23,24,25,26,27,28,
29,30,31,32,33,34,35,39,38,37,36,41,40,42,43,44,45,46,47,48,49,50,51,52,53,54,
55,57,56,51,52],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,1,2,3,
4,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,42,43,
51,52,53,54,55,56,57,58,59]],
0,
[(36,39)(37,40)(38,41)(56,57),(16,17)(36,39)(37,38)(40,41)(56,57),
(42,43)(44,45)(46,47)(49,50)(51,52)(53,54)(56,57)(58,59),
(30,31)(32,35)(33,34)(51,52)(53,54)(58,59)],
["ConstructMGA","6.L3(4).2_1","2.L3(4).(2^2)_{123}",[[25,27],[26,28],[29,35],[
30,36],[31,33],[32,34],[37,39],[38,40],[41,42],[43,44],[45,47],[46,48],[49,52]
,[50,51],[53,55],[54,56],[57,58],[59,60],[61,63],[62,64]],()]);
ALF("6.L3(4).(2^2)_{123}","2.L3(4).(2^2)_{123}",[1,2,1,2,3,4,3,4,5,6,7,8,
7,8,9,9,9,10,11,10,11,12,13,12,13,14,14,15,15,16,17,18,19,18,19,20,21,
20,21,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39]);
ALF("6.L3(4).(2^2)_{123}","6.U6(2).2",[1,2,3,4,9,10,11,12,23,24,29,30,31,
32,33,34,35,42,43,44,45,74,75,76,77,13,14,40,41,72,73,80,81,82,83,84,85,
86,84,85,86,136,137,143,142,152,153,158,175,176,138,139,154,155,159,160,
160,163,164]);

MOT("6.L3(4).(2^2)_{1*23}",
[
"constructed using `PossibleCharacterTablesOfTypeMGA'"
],
[483840,241920,241920,483840,1536,768,768,1536,72,72,384,192,192,384,96,96,96,
60,30,30,60,84,42,42,84,864,432,96,48,36,48,48,48,48,48,48,48,48,48,672,32,12,
32,32,28,28,240,12,64,64,32,20,20],
[,[1,3,3,1,1,3,3,1,9,9,5,7,7,5,8,6,6,18,20,20,18,22,24,24,22,4,2,8,6,10,14,12,
12,15,17,16,15,17,16,1,5,9,14,14,22,22,1,9,11,11,11,18,18],[1,4,1,4,5,8,5,8,1,
4,11,14,11,14,15,15,15,18,21,18,21,22,25,22,25,26,26,28,28,26,31,31,31,34,37,
34,37,34,37,40,41,40,44,43,46,45,47,47,50,49,51,53,52],,[1,2,3,4,5,6,7,8,9,10,
11,12,13,14,15,17,16,1,2,3,4,22,23,24,25,26,27,28,29,30,31,33,32,37,36,35,34,
39,38,40,41,42,43,44,46,45,47,48,50,49,51,47,47],,[1,2,3,4,5,6,7,8,9,10,11,12,
13,14,15,16,17,18,19,20,21,1,2,3,4,26,27,28,29,30,31,33,32,37,38,39,34,35,36,
40,41,42,44,43,40,40,47,48,49,50,51,53,52]],
0,
[(52,53),(45,46),(32,33),(43,44)(49,50),(34,37)(35,38)(36,39)(43,44),
(16,17)(34,37)(35,36)(38,39)(43,44)],
["ConstructMGA","Isoclinic(6.L3(4).2_1)","2.L3(4).(2^2)_{1*23}",[[25,27],[26,
28],[29,35],[30,36],[31,33],[32,34],[37,39],[38,40],[41,42],[43,44],[45,47],[
46,48],[49,51],[50,52],[53,56],[54,55],[57,58],[59,60],[61,64],[62,63]],()]);
ALF("6.L3(4).(2^2)_{1*23}","2.L3(4).(2^2)_{1*23}",[1,2,1,2,3,4,3,4,5,6,7,
8,7,8,9,9,9,10,11,10,11,12,13,12,13,14,14,15,15,16,17,17,17,18,19,18,19,
18,19,20,21,22,23,24,25,26,27,28,30,29,31,32,33]);

MOT("6.L3(4).(2^2)_{12*3}",
[
"constructed using `PossibleCharacterTablesOfTypeMGA'"
],
[483840,241920,241920,483840,1536,768,768,1536,72,72,384,192,192,384,96,96,96,
60,30,30,60,84,42,42,84,864,432,96,48,36,48,48,48,48,48,48,48,48,48,672,32,12,
32,32,28,28,240,12,64,64,32,20,20],
[,[1,3,3,1,1,3,3,1,9,9,5,7,7,5,8,6,6,18,20,20,18,22,24,24,22,1,3,5,7,9,11,13,
13,15,17,16,15,17,16,4,8,10,11,11,25,25,1,9,11,11,11,18,18],[1,4,1,4,5,8,5,8,1
,4,11,14,11,14,15,15,15,18,21,18,21,22,25,22,25,26,26,28,28,26,31,31,31,37,34,
37,34,37,34,40,41,40,43,44,45,46,47,47,50,49,51,53,52],,[1,2,3,4,5,6,7,8,9,10,
11,12,13,14,15,17,16,1,2,3,4,22,23,24,25,26,27,28,29,30,31,33,32,37,36,35,34,
39,38,40,41,42,43,44,46,45,47,48,50,49,51,47,47],,[1,2,3,4,5,6,7,8,9,10,11,12,
13,14,15,16,17,18,19,20,21,1,2,3,4,26,27,28,29,30,31,32,33,34,35,36,37,38,39,
40,41,42,43,44,40,40,47,48,49,50,51,53,52]],
0,
[(52,53),(45,46),(32,33),(43,44)(49,50),(34,37)(35,38)(36,39)(43,44),
(16,17)(34,37)(35,36)(38,39)(43,44)],
["ConstructMGA","6.L3(4).2_1","2.L3(4).(2^2)_{12*3}",[[25,27],[26,28],[29,35],
[30,36],[31,33],[32,34],[37,39],[38,40],[41,42],[43,44],[45,47],[46,48],[49,51
],[50,52],[53,56],[54,55],[57,58],[59,60],[61,64],[62,63]],()]);
ALF("6.L3(4).(2^2)_{12*3}","2.L3(4).(2^2)_{12*3}",[1,2,1,2,3,4,3,4,5,6,7,
8,7,8,9,9,9,10,11,10,11,12,13,12,13,14,14,15,15,16,17,17,17,18,19,18,19,
18,19,20,21,22,23,24,25,26,27,28,30,29,31,32,33]);

MOT("6.L3(4).(2^2)_{123*}",
[
"constructed using `PossibleCharacterTablesOfTypeMGA'"
],
[483840,241920,241920,483840,1536,768,768,1536,72,72,384,192,192,384,96,96,96,
60,30,30,60,84,42,42,84,864,432,96,48,36,48,48,48,48,48,48,48,48,48,672,32,12,
32,32,28,28,240,12,64,64,32,20,20],
[,[1,3,3,1,1,3,3,1,9,9,5,7,7,5,8,6,6,18,20,20,18,22,24,24,22,1,3,5,7,9,11,13,
13,15,17,16,15,17,16,1,5,9,14,14,22,22,4,10,14,14,14,21,21],[1,4,1,4,5,8,5,8,1
,4,11,14,11,14,15,15,15,18,21,18,21,22,25,22,25,26,26,28,28,26,31,31,31,37,34,
37,34,37,34,40,41,40,44,43,46,45,47,47,49,50,51,52,53],,[1,2,3,4,5,6,7,8,9,10,
11,12,13,14,15,17,16,1,2,3,4,22,23,24,25,26,27,28,29,30,31,33,32,37,36,35,34,
39,38,40,41,42,43,44,46,45,47,48,50,49,51,47,47],,[1,2,3,4,5,6,7,8,9,10,11,12,
13,14,15,16,17,18,19,20,21,1,2,3,4,26,27,28,29,30,31,32,33,34,35,36,37,38,39,
40,41,42,44,43,40,40,47,48,50,49,51,52,53]],
0,
[(52,53),(45,46),(32,33),(43,44)(49,50),(34,37)(35,38)(36,39)(43,44),
(16,17)(34,37)(35,36)(38,39)(43,44)],
["ConstructMGA","6.L3(4).2_1","2.L3(4).(2^2)_{123*}",[[25,27],[26,28],[29,35],
[30,36],[31,33],[32,34],[37,39],[38,40],[41,42],[43,44],[45,47],[46,48],[49,51
],[50,52],[53,56],[54,55],[57,58],[59,60],[61,64],[62,63]],()]);
ALF("6.L3(4).(2^2)_{123*}","2.L3(4).(2^2)_{123*}",[1,2,1,2,3,4,3,4,5,6,7,
8,7,8,9,9,9,10,11,10,11,12,13,12,13,14,14,15,15,16,17,17,17,18,19,18,19,
18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33]);
ALF("6.L3(4).(2^2)_{123*}","2.G2(4).2",[1,7,6,2,3,19,18,4,8,9,11,29,30,10,
12,31,32,14,36,35,15,21,40,39,22,41,45,42,51,46,47,60,61,48,65,62,49,64,
63,41,42,46,50,50,54,55,5,20,23,23,23,28,28],[
"fusion map is unique up to table aut."
]);

MOT("6.L3(4).(2^2)_{1*2*3}",
[
"constructed using `PossibleCharacterTablesOfTypeMGA'"
],
[483840,241920,241920,483840,1536,768,768,1536,72,72,384,192,192,384,96,96,96,
60,30,30,60,84,42,42,84,864,432,96,48,72,72,96,48,48,96,48,48,48,48,48,48,1344
,1344,64,64,24,24,16,28,28,480,480,24,24,32,64,64,20,20],
[,[1,3,3,1,1,3,3,1,9,9,5,7,7,5,8,6,6,18,20,20,18,22,24,24,22,4,2,8,6,10,10,14,
12,12,14,15,17,16,15,17,16,4,4,8,8,10,10,11,25,25,1,1,9,9,11,11,11,18,18],[1,4
,1,4,5,8,5,8,1,4,11,14,11,14,15,15,15,18,21,18,21,22,25,22,25,26,26,28,28,26,
26,35,32,35,32,36,39,36,39,36,39,43,42,45,44,43,42,48,50,49,51,52,51,52,55,57,
56,58,59],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,17,16,1,2,3,4,22,23,24,25,26,
27,28,29,30,31,32,33,34,35,39,38,37,36,41,40,42,43,44,45,46,47,48,49,50,51,52,
53,54,55,57,56,51,52],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,
1,2,3,4,26,27,28,29,31,30,35,34,33,32,39,40,41,36,37,38,43,42,45,44,47,46,48,
43,42,51,52,53,54,55,56,57,58,59]],
0,
[(36,39)(37,40)(38,41)(56,57),(16,17)(36,39)(37,38)(40,41)(56,57),
(42,43)(44,45)(46,47)(49,50)(51,52)(53,54)(56,57)(58,59),
(30,31)(32,35)(33,34)(51,52)(53,54)(58,59)],
["ConstructMGA","Isoclinic(6.L3(4).2_1)","2.L3(4).(2^2)_{1*2*3}",[[25,27],[26,
28],[29,35],[30,36],[31,33],[32,34],[37,39],[38,40],[41,42],[43,44],[45,47],[
46,48],[49,52],[50,51],[53,55],[54,56],[57,58],[59,60],[61,63],[62,64]],()]);
ALF("6.L3(4).(2^2)_{1*2*3}","2.L3(4).(2^2)_{1*2*3}",[1,2,1,2,3,4,3,4,5,6,
7,8,7,8,9,9,9,10,11,10,11,12,13,12,13,14,14,15,15,16,17,18,19,18,19,20,
21,20,21,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39]);

MOT("6.L3(4).(2^2)_{1*23*}",
[
"constructed using `PossibleCharacterTablesOfTypeMGA'"
],
[483840,241920,241920,483840,1536,768,768,1536,72,72,384,192,192,384,96,96,96,
60,30,30,60,84,42,42,84,864,432,96,48,72,72,96,48,48,96,48,48,48,48,48,48,1344
,1344,64,64,24,24,16,28,28,480,480,24,24,32,64,64,20,20],
[,[1,3,3,1,1,3,3,1,9,9,5,7,7,5,8,6,6,18,20,20,18,22,24,24,22,4,2,8,6,10,10,14,
12,12,14,15,17,16,15,17,16,1,1,5,5,9,9,14,22,22,4,4,10,10,14,14,14,21,21],[1,4
,1,4,5,8,5,8,1,4,11,14,11,14,15,15,15,18,21,18,21,22,25,22,25,26,26,28,28,26,
26,35,32,35,32,36,39,36,39,36,39,42,43,44,45,42,43,48,49,50,52,51,52,51,55,56,
57,59,58],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,17,16,1,2,3,4,22,23,24,25,26,
27,28,29,30,31,32,33,34,35,39,38,37,36,41,40,42,43,44,45,46,47,48,49,50,51,52,
53,54,55,57,56,51,52],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,
1,2,3,4,26,27,28,29,31,30,35,34,33,32,39,40,41,36,37,38,42,43,44,45,46,47,48,
42,43,52,51,54,53,55,57,56,59,58]],
0,
[(36,39)(37,40)(38,41)(56,57),(16,17)(36,39)(37,38)(40,41)(56,57),
(42,43)(44,45)(46,47)(49,50)(51,52)(53,54)(56,57)(58,59),
(30,31)(32,35)(33,34)(51,52)(53,54)(58,59)],
["ConstructMGA","Isoclinic(6.L3(4).2_1)","2.L3(4).(2^2)_{1*23*}",[[25,27],[26,
28],[29,35],[30,36],[31,33],[32,34],[37,39],[38,40],[41,42],[43,44],[45,47],[
46,48],[49,52],[50,51],[53,55],[54,56],[57,58],[59,60],[61,63],[62,64]],()]);
ALF("6.L3(4).(2^2)_{1*23*}","2.L3(4).(2^2)_{1*23*}",[1,2,1,2,3,4,3,4,5,6,
7,8,7,8,9,9,9,10,11,10,11,12,13,12,13,14,14,15,15,16,17,18,19,18,19,20,
21,20,21,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39]);

MOT("6.L3(4).(2^2)_{12*3*}",
[
"constructed using `PossibleCharacterTablesOfTypeMGA'"
],
[483840,241920,241920,483840,1536,768,768,1536,72,72,384,192,192,384,96,96,96,
60,30,30,60,84,42,42,84,864,432,96,48,72,72,96,48,48,96,48,48,48,48,48,48,1344
,1344,64,64,24,24,16,28,28,480,480,24,24,32,64,64,20,20],
[,[1,3,3,1,1,3,3,1,9,9,5,7,7,5,8,6,6,18,20,20,18,22,24,24,22,1,3,5,7,9,9,11,13
,13,11,15,17,16,15,17,16,4,4,8,8,10,10,11,25,25,4,4,10,10,14,14,14,21,21],[1,4
,1,4,5,8,5,8,1,4,11,14,11,14,15,15,15,18,21,18,21,22,25,22,25,26,26,28,28,26,
26,32,35,32,35,39,36,39,36,39,36,43,42,45,44,43,42,48,50,49,52,51,52,51,55,56,
57,59,58],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,17,16,1,2,3,4,22,23,24,25,26,
27,28,29,30,31,32,33,34,35,39,38,37,36,41,40,42,43,44,45,46,47,48,49,50,51,52,
53,54,55,57,56,51,52],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,
1,2,3,4,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,43,42,45,44,47,46,48,
43,42,52,51,54,53,55,57,56,59,58]],
0,
[(36,39)(37,40)(38,41)(56,57),(16,17)(36,39)(37,38)(40,41)(56,57),
(42,43)(44,45)(46,47)(49,50)(51,52)(53,54)(56,57)(58,59),
(30,31)(32,35)(33,34)(51,52)(53,54)(58,59)],
["ConstructMGA","6.L3(4).2_1","2.L3(4).(2^2)_{12*3*}",[[25,27],[26,28],[29,35]
,[30,36],[31,33],[32,34],[37,39],[38,40],[41,42],[43,44],[45,47],[46,48],[49,
52],[50,51],[53,55],[54,56],[57,58],[59,60],[61,63],[62,64]],()]);
ALF("6.L3(4).(2^2)_{12*3*}","2.L3(4).(2^2)_{12*3*}",[1,2,1,2,3,4,3,4,5,6,
7,8,7,8,9,9,9,10,11,10,11,12,13,12,13,14,14,15,15,16,17,18,19,18,19,20,
21,20,21,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39]);

MOT("6.L3(4).(2^2)_{1*2*3*}",
[
"constructed using `PossibleCharacterTablesOfTypeMGA'"
],
[483840,241920,241920,483840,1536,768,768,1536,72,72,384,192,192,384,96,96,96,
60,30,30,60,84,42,42,84,864,432,96,48,36,48,48,48,48,48,48,48,48,48,672,32,12,
32,32,28,28,240,12,64,64,32,20,20],
[,[1,3,3,1,1,3,3,1,9,9,5,7,7,5,8,6,6,18,20,20,18,22,24,24,22,4,2,8,6,10,14,12,
12,15,17,16,15,17,16,4,8,10,11,11,25,25,4,10,14,14,14,21,21],[1,4,1,4,5,8,5,8,
1,4,11,14,11,14,15,15,15,18,21,18,21,22,25,22,25,26,26,28,28,26,31,31,31,34,37
,34,37,34,37,40,41,40,43,44,45,46,47,47,49,50,51,52,53],,[1,2,3,4,5,6,7,8,9,10
,11,12,13,14,15,17,16,1,2,3,4,22,23,24,25,26,27,28,29,30,31,33,32,37,36,35,34,
39,38,40,41,42,43,44,46,45,47,48,50,49,51,47,47],,[1,2,3,4,5,6,7,8,9,10,11,12,
13,14,15,16,17,18,19,20,21,1,2,3,4,26,27,28,29,30,31,33,32,37,38,39,34,35,36,
40,41,42,43,44,40,40,47,48,50,49,51,52,53]],
0,
[(52,53),(45,46),(32,33),(43,44)(49,50),(34,37)(35,38)(36,39)(43,44),
(16,17)(34,37)(35,36)(38,39)(43,44)],
["ConstructMGA","Isoclinic(6.L3(4).2_1)","2.L3(4).(2^2)_{1*2*3*}",[[25,27],[26
,28],[29,35],[30,36],[31,33],[32,34],[37,39],[38,40],[41,42],[43,44],[45,47],[
46,48],[49,51],[50,52],[53,56],[54,55],[57,58],[59,60],[61,64],[62,63]],()]);
ALF("6.L3(4).(2^2)_{1*2*3*}","2.L3(4).(2^2)_{1*2*3*}",[1,2,1,2,3,4,3,4,5,
6,7,8,7,8,9,9,9,10,11,10,11,12,13,12,13,14,14,15,15,16,17,17,17,18,19,
18,19,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33]);

MOT("(2x12).L3(4)",
[
"constructed using `PossibleCharacterTablesOfTypeV4G'"
],
[483840,483840,483840,483840,483840,483840,483840,483840,483840,483840,483840,
483840,483840,483840,483840,483840,483840,483840,483840,483840,483840,483840,
483840,483840,768,768,768,768,768,768,768,768,768,768,768,768,72,72,72,72,72,
72,72,72,192,192,192,192,192,192,192,192,192,192,192,192,96,96,96,96,96,96,96,
96,96,96,96,96,120,120,120,120,120,120,120,120,120,120,120,120,120,120,120,120
,120,120,120,120,120,120,120,120,120,120,120,120,120,120,120,120,120,120,120,
120,120,120,120,120,120,120,120,120,120,120,120,120,168,168,168,168,168,168,
168,168,168,168,168,168,168,168,168,168,168,168,168,168,168,168,168,168,168,
168,168,168,168,168,168,168,168,168,168,168,168,168,168,168,168,168,168,168,
168,168,168,168],
[,[1,1,1,1,9,9,9,9,17,17,17,17,4,4,4,4,12,12,12,12,20,20,20,20,1,1,9,9,17,17,4
,4,12,12,20,20,37,37,37,37,40,40,40,40,26,26,30,30,34,34,26,26,30,30,34,34,31,
31,35,35,27,27,32,32,36,36,28,28,93,93,93,93,101,101,101,101,109,109,109,109,
96,96,96,96,104,104,104,104,112,112,112,112,69,69,69,69,77,77,77,77,85,85,85,
85,72,72,72,72,80,80,80,80,88,88,88,88,117,117,117,117,125,125,125,125,133,133
,133,133,120,120,120,120,128,128,128,128,136,136,136,136,141,141,141,141,149,
149,149,149,157,157,157,157,144,144,144,144,152,152,152,152,160,160,160,160],[
1,2,3,4,13,14,15,16,4,3,2,1,16,15,14,13,1,2,3,4,13,14,15,16,25,26,31,32,25,26,
31,32,25,26,31,32,1,2,3,4,13,14,15,16,45,46,51,52,46,45,52,51,45,46,51,52,57,
58,58,57,57,58,63,64,64,63,63,64,93,94,95,96,105,106,107,108,96,95,94,93,108,
107,106,105,93,94,95,96,105,106,107,108,69,70,71,72,81,82,83,84,72,71,70,69,84
,83,82,81,69,70,71,72,81,82,83,84,141,142,143,144,153,154,155,156,144,143,142,
141,156,155,154,153,141,142,143,144,153,154,155,156,117,118,119,120,129,130,
131,132,120,119,118,117,132,131,130,129,117,118,119,120,129,130,131,132],,[1,2
,3,4,21,22,23,24,20,19,18,17,13,14,15,16,12,11,10,9,5,6,7,8,25,26,35,36,33,34,
31,32,29,30,27,28,37,38,39,40,41,42,43,44,45,46,55,56,54,53,51,52,50,49,47,48,
57,58,62,61,60,59,63,64,68,67,66,65,1,2,3,4,21,22,23,24,20,19,18,17,13,14,15,
16,12,11,10,9,5,6,7,8,1,2,3,4,21,22,23,24,20,19,18,17,13,14,15,16,12,11,10,9,5
,6,7,8,141,142,143,144,161,162,163,164,160,159,158,157,153,154,155,156,152,151
,150,149,145,146,147,148,117,118,119,120,137,138,139,140,136,135,134,133,129,
130,131,132,128,127,126,125,121,122,123,124],,[1,2,3,4,8,7,6,5,9,10,11,12,16,
15,14,13,17,18,19,20,24,23,22,21,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,
40,44,43,42,41,45,46,48,47,49,50,52,51,53,54,56,55,57,58,59,60,61,62,63,64,65,
66,67,68,93,94,95,96,100,99,98,97,101,102,103,104,108,107,106,105,109,110,111,
112,116,115,114,113,69,70,71,72,76,75,74,73,77,78,79,80,84,83,82,81,85,86,87,
88,92,91,90,89,1,2,3,4,8,7,6,5,9,10,11,12,16,15,14,13,17,18,19,20,24,23,22,21,
1,2,3,4,8,7,6,5,9,10,11,12,16,15,14,13,17,18,19,20,24,23,22,21]],
0,
[
(117,141)(118,142)(119,143)(120,144)(121,145)(122,146)(123,147)(124,148)
(125,149)(126,150)(127,151)(128,152)(129,153)(130,154)(131,155)(132,156)
(133,157)(134,158)(135,159)(136,160)(137,161)(138,162)(139,163)(140,164)
,
( 69, 93)( 70, 94)( 71, 95)( 72, 96)( 73, 97)( 74, 98)( 75, 99)( 76,100)
( 77,101)( 78,102)( 79,103)( 80,104)( 81,105)( 82,106)( 83,107)( 84,108)
( 85,109)( 86,110)( 87,111)( 88,112)( 89,113)( 90,114)( 91,115)( 92,116)
,
(  5,  6)(  7,  8)( 13, 14)( 15, 16)( 21, 22)( 23, 24)( 27, 28)( 31, 32)
( 35, 36)( 41, 42)( 43, 44)( 47, 48)( 51, 52)( 55, 56)( 57, 63)( 58, 64)
( 59, 65)( 60, 66)( 61, 67)( 62, 68)( 73, 74)( 75, 76)( 81, 82)( 83, 84)
( 89, 90)( 91, 92)( 97, 98)( 99,100)(105,106)(107,108)(113,114)(115,116)
(121,122)(123,124)(129,130)(131,132)(137,138)(139,140)(145,146)(147,148)
(153,154)(155,156)(161,162)(163,164)
,
(  5,  7)(  6,  8)( 13, 15)( 14, 16)( 21, 23)( 22, 24)( 27, 28)( 31, 32)
( 35, 36)( 41, 43)( 42, 44)( 57, 63)( 58, 64)( 59, 65)( 60, 66)( 61, 67)
( 62, 68)( 73, 75)( 74, 76)( 81, 83)( 82, 84)( 89, 91)( 90, 92)( 97, 99)
( 98,100)(105,107)(106,108)(113,115)(114,116)(121,123)(122,124)(129,131)
(130,132)(137,139)(138,140)(145,147)(146,148)(153,155)(154,156)(161,163)
(162,164)
,
(  5, 21)(  6, 22)(  7, 23)(  8, 24)(  9, 20)( 10, 19)( 11, 18)( 12, 17)
( 27, 35)( 28, 36)( 29, 33)( 30, 34)( 47, 55)( 48, 56)( 49, 54)( 50, 53)
( 59, 62)( 60, 61)( 65, 68)( 66, 67)( 73, 89)( 74, 90)( 75, 91)( 76, 92)
( 77, 88)( 78, 87)( 79, 86)( 80, 85)( 97,113)( 98,114)( 99,115)(100,116)
(101,112)(102,111)(103,110)(104,109)(121,137)(122,138)(123,139)(124,140)
(125,136)(126,135)(127,134)(128,133)(145,161)(146,162)(147,163)(148,164)
(149,160)(150,159)(151,158)(152,157)
],
["ConstructV4G",["12_1.L3(4)","12_2.L3(4)","(2^2x3).L3(4)"]]);
ALF("(2x12).L3(4)","12_1.L3(4)",[1,1,7,7,2,2,8,8,3,3,9,9,4,4,10,10,5,5,11,
11,6,6,12,12,13,13,14,14,15,15,16,16,17,17,18,18,19,19,21,21,20,20,22,22,
23,23,24,24,25,25,26,26,27,27,28,28,29,29,30,30,31,31,32,32,33,33,34,34,
35,35,41,41,36,36,42,42,37,37,43,43,38,38,44,44,39,39,45,45,40,40,46,46,
47,47,53,53,48,48,54,54,49,49,55,55,50,50,56,56,51,51,57,57,52,52,58,58,
59,59,65,65,60,60,66,66,61,61,67,67,62,62,68,68,63,63,69,69,64,64,70,70,
71,71,77,77,72,72,78,78,73,73,79,79,74,74,80,80,75,75,81,81,76,76,82,82]);
ALF("(2x12).L3(4)","12_2.L3(4)",[1,7,1,7,2,8,2,8,3,9,3,9,4,10,4,10,5,11,5,
11,6,12,6,12,13,13,14,14,15,15,16,16,17,17,18,18,19,21,19,21,20,22,20,22,
23,29,24,30,25,31,26,32,27,33,28,34,35,35,36,36,37,37,38,38,39,39,40,40,
41,47,41,47,42,48,42,48,43,49,43,49,44,50,44,50,45,51,45,51,46,52,46,52,
53,59,53,59,54,60,54,60,55,61,55,61,56,62,56,62,57,63,57,63,58,64,58,64,
65,71,65,71,66,72,66,72,67,73,67,73,68,74,68,74,69,75,69,75,70,76,70,76,
77,83,77,83,78,84,78,84,79,85,79,85,80,86,80,86,81,87,81,87,82,88,82,88]);
ALF("(2x12).L3(4)","(2^2x3).L3(4)",[1,2,2,1,3,4,4,3,5,6,6,5,7,8,8,7,9,10,
10,9,11,12,12,11,13,14,15,16,17,18,19,20,21,22,23,24,25,26,26,25,27,28,28,
27,29,29,30,30,31,31,32,32,33,33,34,34,35,36,37,38,39,40,41,42,43,44,45,
46,47,48,48,47,49,50,50,49,51,52,52,51,53,54,54,53,55,56,56,55,57,58,58,
57,59,60,60,59,61,62,62,61,63,64,64,63,65,66,66,65,67,68,68,67,69,70,70,
69,71,72,72,71,73,74,74,73,75,76,76,75,77,78,78,77,79,80,80,79,81,82,82,
81,83,84,84,83,85,86,86,85,87,88,88,87,89,90,90,89,91,92,92,91,93,94,94,
93]);
ALF("(2x12).L3(4)","(2x4).L3(4)",[1,2,3,4,5,6,7,8,4,3,2,1,8,7,6,5,1,2,3,4,
5,6,7,8,9,10,11,12,9,10,11,12,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,
24,22,21,24,23,21,22,23,24,25,26,26,25,25,26,27,28,28,27,27,28,29,30,31,
32,33,34,35,36,32,31,30,29,36,35,34,33,29,30,31,32,33,34,35,36,37,38,39,
40,41,42,43,44,40,39,38,37,44,43,42,41,37,38,39,40,41,42,43,44,45,46,47,
48,49,50,51,52,48,47,46,45,52,51,50,49,45,46,47,48,49,50,51,52,53,54,55,
56,57,58,59,60,56,55,54,53,60,59,58,57,53,54,55,56,57,58,59,60]);

MOT("L3(4)",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[20160,64,9,16,16,16,5,5,7,7],
[,[1,1,3,2,2,2,8,7,9,10],[1,2,1,4,5,6,8,7,10,9],,[1,2,3,4,5,6,1,1,10,9],,[1,2,
3,4,5,6,8,7,1,1]],
[[1,1,1,1,1,1,1,1,1,1],[20,4,2,0,0,0,0,0,-1,-1],[35,3,-1,3,-1,-1,0,0,0,0],[35,
3,-1,-1,3,-1,0,0,0,0],[35,3,-1,-1,-1,3,0,0,0,0],[45,-3,0,1,1,1,0,0,
E(7)+E(7)^2+E(7)^4,E(7)^3+E(7)^5+E(7)^6],
[GALOIS,[6,3]],[63,-1,0,-1,-1,-1,-E(5)-E(5)^4,-E(5)^2-E(5)^3,0,0],
[GALOIS,[8,2]],[64,0,1,0,0,0,-1,-1,1,1]],
[( 9,10),(7,8),(5,6),(4,5)]);
ARC("L3(4)","CAS",[rec(name:="psl(3,4)",
permchars:=(8,9),
permclasses:=())]);
ARC("L3(4)","projectives",["2.L3(4)",[[10,2,1,2,0,0,0,0,E(7)+E(7)^2+E(7)^4,
E(7)^3+E(7)^5+E(7)^6],
[GALOIS,[1,3]],[28,-4,1,0,0,0,-E(5)-E(5)^4,-E(5)^2-E(5)^3,0,0],
[GALOIS,[3,2]],[36,4,0,0,0,0,1,1,1,1],[64,0,1,0,0,0,-1,-1,1,1],[70,-2,-2,2,0,
0,0,0,0,0],[90,2,0,-2,0,0,0,0,-1,-1]],"3.L3(4)",[[15,-1,0,3,-1,-1,0,0,1,1],[
15,-1,0,-1,3,-1,0,0,1,1],[15,-1,0,-1,-1,3,0,0,1,1],[21,5,0,1,1,1,1,1,0,0],[45,
-3,0,1,1,1,0,0,E(7)+E(7)^2+E(7)^4,E(7)^3+E(7)^5+E(7)^6],
[GALOIS,[5,3]],[63,-1,0,-1,-1,-1,-E(5)-E(5)^4,-E(5)^2-E(5)^3,0,0],
[GALOIS,[7,2]],[84,4,0,0,0,0,-1,-1,0,0]],"6.L3(4)",[[6,-2,0,2,0,0,1,1,-1,-1],[
36,4,0,0,0,0,1,1,1,1],[42,2,0,2,0,0,E(5)+E(5)^4,E(5)^2+E(5)^3,0,0],
[GALOIS,[3,2]],[60,-4,0,0,0,0,0,0,-E(7)-E(7)^2-E(7)^4,-E(7)^3-E(7)^5-E(7)^6],
[GALOIS,[5,3]],[90,2,0,-2,0,0,0,0,-1,-1]],"4_1.L3(4)",[[8,0,-1,0,0,0,
-E(5)-E(5)^4,-E(5)^2-E(5)^3,1,1],
[GALOIS,[1,2]],[56,0,2,0,0,0,1,1,0,0],[64,0,1,0,0,0,-1,-1,1,1],[80,0,-1,0,0,0,
0,0,E(7)+E(7)^2+E(7)^4,E(7)^3+E(7)^5+E(7)^6],
[GALOIS,[5,3]]],"4_2.L3(4)",[[20,0,2,2,0,0,0,0,-1,-1],[28,0,1,-2,0,0,
-E(5)-E(5)^4,-E(5)^2-E(5)^3,0,0],
[GALOIS,[2,2]],[36,0,0,2,0,0,1,1,1,1],[64,0,1,0,0,0,-1,-1,1,1],[80,0,-1,0,0,0,
0,0,E(7)+E(7)^2+E(7)^4,E(7)^3+E(7)^5+E(7)^6],
[GALOIS,[6,3]]],"12_1.L3(4)",[[24,0,0,0,0,0,-1,-1,E(7)+E(7)^2+E(7)^4,
E(7)^3+E(7)^5+E(7)^6],
[GALOIS,[1,3]],[48,0,0,0,0,0,-E(5)-E(5)^4,-E(5)^2-E(5)^3,-1,-1],
[GALOIS,[3,2]],[120,0,0,0,0,0,0,0,1,1]],"12_2.L3(4)",[[36,0,0,2,0,0,1,1,1,1],[
48,0,0,0,0,0,-E(5)-E(5)^4,-E(5)^2-E(5)^3,-1,-1],
[GALOIS,[2,2]],[60,0,0,-2,0,0,0,0,-E(7)-E(7)^2-E(7)^4,-E(7)^3-E(7)^5-E(7)^6],
[GALOIS,[4,3]],[84,0,0,2,0,0,-1,-1,0,0]],]);
ARC("L3(4)","isSimple",true);
ARC("L3(4)","extInfo",["(3x4^2)","D12"]);
ARC("L3(4)","tomfusion",rec(name:="L3(4)",map:=[1,2,3,4,5,6,14,14,16,16],
text:=[
"fusion map is unique up to table autom."
],
perm:=(4,5)(6,7)));
ARC("L3(4)","maxes",["2^4:A5","2^4:A5","A6","L3(4)M4","L3(4)M5","L3(2)",
"L3(4)M7","L3(4)M8","3^2:Q8"]);
ALF("L3(4)","L3(4).2_1",[1,2,3,4,5,6,7,7,8,8],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("L3(4)","L3(4).2_2",[1,2,3,4,5,5,6,6,7,8]);
ALF("L3(4)","L3(4).2_3",[1,2,3,4,5,5,6,7,8,8]);
ALF("L3(4)","L3(4).3",[1,2,3,4,4,4,5,6,7,8]);
ALF("L3(4)","L3(4).6",[1,2,3,4,4,4,5,5,6,6]);
ALF("L3(4)","M22",[1,2,3,4,5,5,6,6,8,9],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("L3(4)","U4(3)",[1,2,6,7,8,8,9,9,13,14],[
"fusion map is unique up to table autom."
],"tom:376");
ALF("L3(4)","2^9.L3(4)",[1,5,14,18,22,26,30,32,34,35],[
"fusion map is unique up to table automorphisms"
]);
ALN("L3(4)",["psl(3,4)","M21"]);

MOT("L3(4).2^2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[80640,256,36,64,32,10,14,288,32,36,16,8,672,32,12,16,14,240,12,32,32,10],
[,[1,1,3,2,2,6,7,1,2,3,4,5,1,2,3,4,7,1,3,4,4,6],[1,2,1,4,5,6,7,8,9,8,11,12,13,
14,13,16,17,18,18,20,21,22],,[1,2,3,4,5,1,7,8,9,10,11,12,13,14,15,16,17,18,19,
20,21,18],,[1,2,3,4,5,6,1,8,9,10,11,12,13,14,15,16,13,18,19,20,21,22]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,
-1,-1,-1,-1,-1,-1,-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]],[20,4,2,0,0,0,-1,2,-2,2,0,0,6,2,0,0,-1,0,0,-2,2,0],
[TENSOR,[5,2]],
[TENSOR,[5,3]],
[TENSOR,[5,4]],[35,3,-1,3,-1,0,0,1,1,1,1,-1,7,-1,1,-1,0,5,-1,1,1,0],
[TENSOR,[9,2]],
[TENSOR,[9,3]],
[TENSOR,[9,4]],[70,6,-2,-2,2,0,0,2,2,2,-2,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[13,3]],[90,-6,0,2,2,0,-1,0,0,0,0,0,6,-2,0,2,-1,0,0,0,0,0],
[TENSOR,[15,2]],[126,-2,0,-2,-2,1,0,0,0,0,0,0,0,0,0,0,0,6,0,-2,-2,1],
[TENSOR,[17,2]],[64,0,1,0,0,-1,1,8,0,-1,0,0,8,0,-1,0,1,4,1,0,0,-1],
[TENSOR,[19,2]],
[TENSOR,[19,3]],
[TENSOR,[19,4]]],
[]);
ARC("L3(4).2^2","tomfusion",rec(name:="L3(4).2^2",map:=[1,4,6,9,14,18,26,3,15,
21,49,57,2,12,22,50,74,5,25,36,30,61],text:=[
"fusion map is unique"
]));
ALF("L3(4).2^2","L3(4).D12",[1,2,3,4,4,5,6,7,8,9,10,10,19,20,21,22,23,24,
25,26,27,28],[
"fusion map is unique"
]);
ALF("L3(4).2^2","HS.2",[1,2,4,6,7,10,13,3,7,11,14,15,22,24,28,30,35,23,29,
30,31,33],[
"fusion map is unique"
]);
ALF("L3(4).2^2","McL.2",[1,2,4,5,5,7,10,20,21,22,24,24,2,5,9,11,17,20,22,24,
23,25],[
"fusion map is unique"
]);
ALF("L3(4).2^2","U4(3).(2^2)_{133}",[1,2,5,6,7,8,11,36,37,38,40,41,15,18,
21,22,26,27,29,30,31,33],[
"fusion map is unique up to table autom."
],"tom:1783");
ALF("L3(4).2^2","U6(2).2",[1,3,7,10,11,14,22,4,13,21,24,25,38,41,46,49,59,
39,47,50,51,53],[
"fusion map is unique"
]);
ALN("L3(4).2^2",["L3(4).V4"]);

MOT("U4(3).(2^2)_{133}M6",
[
"6th maximal subgroup of U4(3).(2^2)_{133},\n",
"differs from U4(3).(2^2)_{133}M5 only by fusion map"
],
0,
0,
0,
0,
["ConstructPermuted",["L3(4).2^2"]]);
ALF("U4(3).(2^2)_{133}M6","U4(3).(2^2)_{133}",[1,2,5,6,7,8,11,27,28,29,31,
32,15,18,21,22,26,36,38,39,40,42],[
"fusion L3(4).2^2 -> U4(3).(2^2)_{133} mapped under U4(3).D8"
]);

MOT("L3(4).2_1",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[40320,128,18,32,32,32,5,7,144,16,18,8,8,8],
[,[1,1,3,2,2,2,7,8,1,2,3,4,5,6],[1,2,1,4,5,6,7,8,9,10,9,12,13,14],,[1,2,3,4,5,
6,1,8,9,10,11,12,13,14],,[1,2,3,4,5,6,7,1,9,10,11,12,13,14]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1],[20,4,2,0,
0,0,0,-1,2,-2,2,0,0,0],
[TENSOR,[3,2]],[35,3,-1,3,-1,-1,0,0,1,1,1,1,-1,-1],
[TENSOR,[5,2]],[35,3,-1,-1,3,-1,0,0,1,1,1,-1,1,-1],
[TENSOR,[7,2]],[35,3,-1,-1,-1,3,0,0,1,1,1,-1,-1,1],
[TENSOR,[9,2]],[90,-6,0,2,2,2,0,-1,0,0,0,0,0,0],[126,-2,0,-2,-2,-2,1,0,0,0,0,
0,0,0],[64,0,1,0,0,0,-1,1,8,0,-1,0,0,0],
[TENSOR,[13,2]]],
[( 5, 6)(13,14),( 4, 5)(12,13)]);
ARC("L3(4).2_1","CAS",[rec(name:="psl(3,4).2",
permchars:=( 6, 8, 9, 7)(11,13)(12,14),
permclasses:=())]);
ARC("L3(4).2_1","projectives",["2.L3(4).2_1",[[20,4,2,4,0,0,0,-1,0,0,0,0,0,
0],[56,-8,2,0,0,0,1,0,0,0,0,0,0,0],[36,4,0,0,0,0,1,1,0,0,0,2,0,0],[64,0,1,0,0,
0,-1,1,0,0,3,0,0,0],[70,-2,-2,2,0,0,0,0,0,0,0,0,E(8)-E(8)^3,E(8)-E(8)^3],[90,
2,0,-2,0,0,0,-1,0,0,0,0,E(8)-E(8)^3,-E(8)+E(8)^3]],"3.L3(4).2_1",[[15,-1,0,3,
-1,-1,0,1,3,-1,0,1,-1,-1],[15,-1,0,-1,3,-1,0,1,3,-1,0,-1,1,-1],[15,-1,0,-1,-1,
3,0,1,3,-1,0,-1,-1,1],[21,5,0,1,1,1,1,0,3,-1,0,1,1,1],[90,-6,0,2,2,2,0,-1,0,0,
0,0,0,0],[126,-2,0,-2,-2,-2,1,0,0,0,0,0,0,0],[84,4,0,0,0,0,-1,0,6,2,0,0,0,
0]],"6.L3(4).2_1",[[6,-2,0,2,0,0,1,-1,0,0,0,0,E(8)-E(8)^3,E(8)-E(8)^3],[36,4,
0,0,0,0,1,1,0,0,0,2,0,0],[84,4,0,4,0,0,-1,0,0,0,0,0,0,0],[120,-8,0,0,0,0,0,1,
0,0,0,0,0,0],[90,2,0,-2,0,0,0,-1,0,0,0,0,E(8)-E(8)^3,-E(8)+E(8)^3]],]);
ARC("L3(4).2_1","tomfusion",rec(name:="L3(4).2_1",map:=[1,3,4,9,10,11,14,18,2,
13,15,35,29,37],text:=[
"unique fusion map compatible with AtlasRep"
]));
ALF("L3(4).2_1","L3(4).6",[1,2,3,4,4,4,5,6,7,8,9,10,10,10]);
ALF("L3(4).2_1","HS",[1,2,4,6,7,7,10,13,3,7,11,14,15,16],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("L3(4).2_1","L3(4).2^2",[1,2,3,4,5,5,6,7,8,9,10,11,12,12]);
ALF("L3(4).2_1","U4(3).2_3",[1,2,5,6,7,7,8,11,16,17,18,20,21,21],[
"fusion map is unique up to table autom."
]);
ALF("L3(4).2_1","U6(2)",[1,3,7,10,11,12,15,24,4,14,23,26,27,28],[
"fusion determined up to table aut. by embedding L3(4).6 -> U6(2).3"
]);
ALN("L3(4).2_1",["psl(3,4).2"]);

MOT("L3(4).2_2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[40320,128,18,32,16,5,14,14,336,16,6,8,14,14],
[,[1,1,3,2,2,6,7,8,1,2,3,4,7,8],[1,2,1,4,5,6,8,7,9,10,9,12,14,13],,[1,2,3,4,5,
1,8,7,9,10,11,12,14,13],,[1,2,3,4,5,6,1,1,9,10,11,12,9,9]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1],[20,4,2,0,
0,0,-1,-1,6,2,0,0,-1,-1],
[TENSOR,[3,2]],[35,3,-1,3,-1,0,0,0,7,-1,1,-1,0,0],
[TENSOR,[5,2]],[70,6,-2,-2,2,0,0,0,0,0,0,0,0,0],[45,-3,0,1,1,0,
E(7)+E(7)^2+E(7)^4,E(7)^3+E(7)^5+E(7)^6,3,-1,0,1,E(7)+E(7)^2+E(7)^4,
E(7)^3+E(7)^5+E(7)^6],
[TENSOR,[8,2]],
[GALOIS,[8,3]],
[TENSOR,[10,2]],[126,-2,0,-2,-2,1,0,0,0,0,0,0,0,0],[64,0,1,0,0,-1,1,1,8,0,-1,
0,1,1],
[TENSOR,[13,2]]],
[( 7, 8)(13,14)]);
ARC("L3(4).2_2","CAS",[rec(name:="psl(3,4):2",
permchars:=( 7,13,11,10, 8)(12,14),
permclasses:=(),
text:=[
"maximal subgroup of sporadic simple Mathieu group m23.\n",
"test: 1.OR, JAMES, JAMES,n=3,\n",
"and restricted characters decompose properly.\n",
""])]);
ARC("L3(4).2_2","projectives",["2.L3(4).2_2",[[10,2,1,2,0,0,E(7)+E(7)^2+E(7)^4
 ,E(7)^3+E(7)^5+E(7)^6,4,0,1,0,-E(7)-E(7)^2-E(7)^4,-E(7)^3-E(7)^5-E(7)^6],
[GALOIS,[1,3]],[56,-8,2,0,0,1,0,0,0,0,0,0,0,0],[36,4,0,0,0,1,1,1,6,2,0,0,-1,
-1],[64,0,1,0,0,-1,1,1,8,0,-1,0,1,1],[70,-2,-2,2,0,0,0,0,0,0,0,2*E(4),0,0],[
90,2,0,-2,0,0,-1,-1,6,-2,0,0,-1,-1]],"4_2.L3(4).2_2",[[20,0,2,2,0,0,-1,-1,6,0,
0,1+E(4),-1,-1],[56,0,2,-4,0,1,0,0,0,0,0,0,0,0],[36,0,0,2,0,1,1,1,6,0,0,
-1-E(4),-1,-1],[64,0,1,0,0,-1,1,1,8,0,-1,0,1,1],[80,0,-1,0,0,0,
E(7)+E(7)^2+E(7)^4,E(7)^3+E(7)^5+E(7)^6,4,0,1,0,-E(7)-E(7)^2-E(7)^4,
-E(7)^3-E(7)^5-E(7)^6],
[GALOIS,[5,3]]],]);
ARC("L3(4).2_2","tomfusion",rec(name:="L3(4).2_2",map:=[1,3,4,10,12,14,18,18,
2,13,16,30,45,45],text:=[
"fusion map is unique"
]));
ALF("L3(4).2_2","McL",[1,2,4,5,5,7,10,11,2,5,9,12,19,20],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("L3(4).2_2","M22.2",[1,2,3,4,5,6,8,9,12,15,16,17,20,21],[
"fusion map is unique up to table autom."
]);
ALF("L3(4).2_2","M23",[1,2,3,4,4,5,7,8,2,4,6,9,12,13],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("L3(4).2_2","L3(4).3.2_2",[1,2,3,4,4,5,6,7,15,16,17,18,19,20]);
ALF("L3(4).2_2","L3(4).2^2",[1,2,3,4,5,6,7,7,13,14,15,16,17,17]);
ALF("L3(4).2_2","U4(3).2_1",[1,2,6,7,8,9,13,14,19,22,26,27,33,34],[
"fusion map is unique up to table autom."
]);
ALN("L3(4).2_2",["psl(3,4):2"]);

MOT("L3(4).2_3",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[40320,128,18,32,16,10,10,7,120,6,16,16,10,10],
[,[1,1,3,2,2,7,6,8,1,3,4,4,7,6],[1,2,1,4,5,7,6,8,9,9,11,12,14,13],,[1,2,3,4,5,
1,1,8,9,10,11,12,9,9],,[1,2,3,4,5,7,6,1,9,10,11,12,14,13]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1],[20,4,2,0,
0,0,0,-1,0,0,-2,2,0,0],
[TENSOR,[3,2]],[35,3,-1,3,-1,0,0,0,5,-1,1,1,0,0],
[TENSOR,[5,2]],[70,6,-2,-2,2,0,0,0,0,0,0,0,0,0],[90,-6,0,2,2,0,0,-1,0,0,0,0,0,
0],[63,-1,0,-1,-1,-E(5)-E(5)^4,-E(5)^2-E(5)^3,0,3,0,-1,-1,-E(5)-E(5)^4,
-E(5)^2-E(5)^3],
[TENSOR,[9,2]],
[GALOIS,[9,2]],
[TENSOR,[11,2]],[64,0,1,0,0,-1,-1,1,4,1,0,0,-1,-1],
[TENSOR,[13,2]]],
[(11,12),( 6, 7)(13,14)]);
ARC("L3(4).2_3","projectives",["2.L3(4).2_3",[[20,4,2,4,0,0,0,-1,0,0,0,0,0,
0],[28,-4,1,0,0,-E(5)-E(5)^4,-E(5)^2-E(5)^3,0,2,-1,0,0,E(5)+E(5)^4,
E(5)^2+E(5)^3],
[GALOIS,[2,2]],[36,4,0,0,0,1,1,1,6,0,0,0,1,1],[64,0,1,0,0,-1,-1,1,4,1,0,0,-1,
-1],[70,-2,-2,2,0,0,0,0,0,0,2*E(8)-2*E(8)^3,0,0,0],[90,2,0,-2,0,0,0,-1,0,0,0,
2*E(8)-2*E(8)^3,0,0]],"4_1.L3(4).2_3",[[8,0,-1,0,0,-E(5)-E(5)^4,
-E(5)^2-E(5)^3,1,2,-1,0,0,E(5)+E(5)^4,E(5)^2+E(5)^3],
[GALOIS,[1,2]],[56,0,2,0,0,1,1,0,6,0,0,0,1,1],[64,0,1,0,0,-1,-1,1,4,1,0,0,-1,
-1],[160,0,-2,0,0,0,0,-1,0,0,0,0,0,0]],]);
ARC("L3(4).2_3","tomfusion",rec(name:="L3(4).2_3",map:=[1,2,4,9,10,12,12,16,3,
14,21,22,30,30],text:=[
"fusion map is unique up to table automorphisms"
]));
ALF("L3(4).2_3","L3(4).3.2_3",[1,2,3,4,4,5,6,7,15,16,17,18,19,20],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables"
]);
ALF("L3(4).2_3","L3(4).2^2",[1,2,3,4,5,6,6,7,18,19,20,21,22,22],[
"fusion map is unique up to table autom.,\n",
"unique map that is compatible with Brauer tables"
]);
ALF("L3(4).2_3","U4(3).2_3",[1,2,5,6,7,8,8,11,16,18,19,20,22,22],[
"fusion map is unique up to table autom.,\n",
"unique map that is compatible with Brauer tables"
]);

MOT("L3(4).3",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[60480,192,27,16,15,15,21,21,180,180,63,63,12,12,15,15,15,15,21,21,21,21],
[,[1,1,3,2,6,5,7,8,10,9,12,11,10,9,18,17,16,15,20,19,22,21],[1,2,1,4,6,5,8,7,
1,1,1,1,2,2,6,6,5,5,8,8,7,7],,[1,2,3,4,1,1,8,7,10,9,12,11,14,13,10,9,10,9,22,
21,20,19],,[1,2,3,4,6,5,1,1,9,10,11,12,13,14,17,18,15,16,11,12,11,12]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,E(3),E(3)^2,
E(3),E(3)^2,E(3),E(3)^2,E(3),E(3)^2,E(3),E(3)^2,E(3),E(3)^2,E(3),E(3)^2],
[TENSOR,[2,2]],[20,4,2,0,0,0,-1,-1,5,5,-1,-1,1,1,0,0,0,0,-1,-1,-1,-1],
[TENSOR,[4,2]],
[TENSOR,[4,3]],[105,9,-3,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[45,-3,0,1,0,
0,E(7)+E(7)^2+E(7)^4,E(7)^3+E(7)^5+E(7)^6,0,0,3,3,0,0,0,0,0,0,
E(7)+E(7)^2+E(7)^4,E(7)+E(7)^2+E(7)^4,E(7)^3+E(7)^5+E(7)^6,
E(7)^3+E(7)^5+E(7)^6],
[TENSOR,[8,2]],
[TENSOR,[8,3]],
[GALOIS,[8,3]],
[TENSOR,[11,2]],
[TENSOR,[11,3]],[63,-1,0,-1,-E(5)-E(5)^4,-E(5)^2-E(5)^3,0,0,3,3,0,0,-1,-1,
-E(5)-E(5)^4,-E(5)-E(5)^4,-E(5)^2-E(5)^3,-E(5)^2-E(5)^3,0,0,0,0],
[TENSOR,[14,2]],
[TENSOR,[14,3]],
[GALOIS,[14,2]],
[TENSOR,[17,2]],
[TENSOR,[17,3]],[64,0,1,0,-1,-1,1,1,4,4,1,1,0,0,-1,-1,-1,-1,1,1,1,1],
[TENSOR,[20,2]],
[TENSOR,[20,3]]],
[( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22),( 7, 8)(19,21)(20,22),
( 5, 6)(15,17)(16,18)]);
ARC("L3(4).3","projectives",["3.L3(4).3",[[45,-3,0,1,0,0,3,3,0,0,0,0,0,0,0,0,
0,0,0,0,0,0],[21,5,0,1,1,1,0,0,5*E(3)+E(3)^2,E(3)+5*E(3)^2,0,0,-1,-1,E(3)^2,
E(3),E(3)^2,E(3),0,0,0,0],[45,-3,0,1,0,0,E(7)+E(7)^2+E(7)^4,
E(7)^3+E(7)^5+E(7)^6,0,0,0,0,0,0,0,0,0,0,E(63)+E(63)^4-E(63)^37-E(63)^58,
E(63)^8-E(63)^23+E(63)^32-E(63)^44,-E(63)^19+E(63)^31-E(63)^40+E(63)^55,
-E(63)^5-E(63)^26+E(63)^59+E(63)^62],
[GALOIS,[3,31]],[63,-1,0,-1,-E(5)-E(5)^4,-E(5)^2-E(5)^3,0,0,3,3,0,0,-1,-1,
-E(5)-E(5)^4,-E(5)-E(5)^4,-E(5)^2-E(5)^3,-E(5)^2-E(5)^3,0,0,0,0],
[GALOIS,[5,2]],[84,4,0,0,-1,-1,0,0,-E(3)-5*E(3)^2,-5*E(3)-E(3)^2,0,0,1,1,
-E(3),-E(3)^2,-E(3),-E(3)^2,0,0,0,0]],]);
ARC("L3(4).3","tomfusion",rec(name:="L3(4).3",map:=[1,2,5,9,10,10,13,13,3,
3,4,4,12,12,29,29,29,29,41,41,41,41],text:=[
"fusion map is unique"
]));
ALF("L3(4).3","L3(4).6",[1,2,3,4,5,5,6,6,11,12,13,14,15,16,17,18,17,18,19,
20,19,20]);
ALF("L3(4).3","L3(4).3.2_2",[1,2,3,4,5,5,6,7,8,8,9,9,10,10,11,12,12,11,13,
13,14,14],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables"
]);
ALF("L3(4).3","L3(4).3.2_3",[1,2,3,4,5,6,7,7,8,8,9,9,10,10,11,11,12,12,13,
14,14,13],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables"
]);
ALF("L3(4).3","3D4(4)",[1,3,4,8,11,12,18,18,5,5,4,4,14,14,46,46,45,45,68,
69,69,68],[
"fusion map is unique up to table automorphisms"
]);

MOT("L3(4).3.2_2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[120960,384,54,32,15,42,42,180,63,12,15,15,21,21,336,16,6,8,14,14],
[,[1,1,3,2,5,6,7,8,9,8,11,12,13,14,1,2,3,4,6,7],[1,2,1,4,5,7,6,1,1,2,5,5,7,6,
15,16,15,18,20,19],,[1,2,3,4,1,7,6,8,9,10,8,8,14,13,15,16,17,18,20,19],,[1,2,
3,4,5,1,1,8,9,10,12,11,9,9,15,16,17,18,15,15]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,
-1,-1,-1,-1],[2,2,2,2,2,2,2,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0],[20,4,2,0,0,-1,
-1,5,-1,1,0,0,-1,-1,6,2,0,0,-1,-1],
[TENSOR,[4,2]],[40,8,4,0,0,-2,-2,-5,1,-1,0,0,1,1,0,0,0,0,0,0],[105,9,-3,1,0,0,
0,0,0,0,0,0,0,0,7,-1,1,-1,0,0],
[TENSOR,[7,2]],[45,-3,0,1,0,E(7)+E(7)^2+E(7)^4,E(7)^3+E(7)^5+E(7)^6,0,3,0,0,0,
E(7)+E(7)^2+E(7)^4,E(7)^3+E(7)^5+E(7)^6,3,-1,0,1,E(7)+E(7)^2+E(7)^4,
E(7)^3+E(7)^5+E(7)^6],
[TENSOR,[9,2]],[90,-6,0,2,0,2*E(7)+2*E(7)^2+2*E(7)^4,2*E(7)^3+2*E(7)^5
 +2*E(7)^6,0,-3,0,0,0,-E(7)-E(7)^2-E(7)^4,-E(7)^3-E(7)^5-E(7)^6,0,0,0,0,0,0],
[GALOIS,[9,3]],
[TENSOR,[12,2]],
[GALOIS,[11,3]],[126,-2,0,-2,1,0,0,6,0,-2,1,1,0,0,0,0,0,0,0,0],[126,-2,0,-2,1,
0,0,-3,0,1,-E(15)-E(15)^2-E(15)^4-E(15)^8,-E(15)^7-E(15)^11-E(15)^13-E(15)^14,
0,0,0,0,0,0,0,0],
[GALOIS,[16,7]],[64,0,1,0,-1,1,1,4,1,0,-1,-1,1,1,8,0,-1,0,1,1],
[TENSOR,[18,2]],[128,0,2,0,-2,2,2,-4,-1,0,1,1,-1,-1,0,0,0,0,0,0]],
[(11,12),( 6, 7)(13,14)(19,20)]);
ARC("L3(4).3.2_2","CAS",[rec(name:="psl(3,4):s3",
permchars:=( 7,15,17,18,11,13,10, 9)( 8,16,19,12),
permclasses:=( 3, 5, 7,10, 8)( 4, 6, 9)(13,14),
text:=[
"origin: CAS library,\n",
"names:= psl(3,4):s3, m21.s3\n",
" order: 120,960 = 2^7 . 3^3 . 5 . 7\n",
" number of classes: 20\n",
" source: todd,j.a.\n",
"        a representation of the mathieu-group m24\n",
"        as a collineation group\n",
"        ann.mat.pura appl (4) 71\n",
"        (1966),199-238\n",
" comments: psl(3,4):s3 is maximal subgroup of m24\n",
" test: orth.1, min, sym(3)\n",
""])]);
ARC("L3(4).3.2_2","tomfusion",rec(name:="L3(4).3.2_2",map:=[1,2,6,10,13,
20,20,4,5,18,51,51,77,77,3,12,19,36,50,50],text:=[
"fusion map is unique"
]));
ALF("L3(4).3.2_2","M24",[1,2,4,7,9,12,13,4,5,10,21,22,23,24,2,7,10,14,19,
20],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("L3(4).3.2_2","L3(4).D12",[1,2,3,4,5,6,6,11,12,13,14,14,15,15,19,20,
21,22,23,23],[
"fusion map is unique"
]);
ALN("L3(4).3.2_2",["psl(3,4):s3"]);

MOT("L3(4).3.2_3",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[120960,384,54,32,30,30,21,180,63,12,15,15,21,21,120,6,16,16,10,10],
[,[1,1,3,2,6,5,7,8,9,8,12,11,14,13,1,3,4,4,6,5],[1,2,1,4,6,5,7,1,1,2,6,5,7,7,
15,15,17,18,20,19],,[1,2,3,4,1,1,7,8,9,10,8,8,13,14,15,16,17,18,15,15],,[1,2,
3,4,6,5,1,8,9,10,12,11,9,9,15,16,17,18,20,19]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,
-1,-1,-1,-1],[2,2,2,2,2,2,2,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0],[20,4,2,0,0,0,
-1,5,-1,1,0,0,-1,-1,0,0,-2,2,0,0],
[TENSOR,[4,2]],[40,8,4,0,0,0,-2,-5,1,-1,0,0,1,1,0,0,0,0,0,0],[105,9,-3,1,0,0,
0,0,0,0,0,0,0,0,5,-1,1,1,0,0],
[TENSOR,[7,2]],[90,-6,0,2,0,0,-1,0,-3,0,0,0,E(21)^2+E(21)^8+E(21)^10+E(21)^11
 +E(21)^13+E(21)^19,E(21)+E(21)^4+E(21)^5+E(21)^16+E(21)^17+E(21)^20,0,0,0,0,
0,0],
[GALOIS,[9,2]],[90,-6,0,2,0,0,-1,0,6,0,0,0,-1,-1,0,0,0,0,0,0],[63,-1,0,-1,
-E(5)-E(5)^4,-E(5)^2-E(5)^3,0,3,0,-1,-E(5)-E(5)^4,-E(5)^2-E(5)^3,0,0,3,0,-1,
-1,-E(5)-E(5)^4,-E(5)^2-E(5)^3],
[TENSOR,[12,2]],[126,-2,0,-2,-2*E(5)-2*E(5)^4,-2*E(5)^2-2*E(5)^3,0,-3,0,1,
E(5)+E(5)^4,E(5)^2+E(5)^3,0,0,0,0,0,0,0,0],
[GALOIS,[12,2]],
[TENSOR,[15,2]],
[GALOIS,[14,2]],[64,0,1,0,-1,-1,1,4,1,0,-1,-1,1,1,4,1,0,0,-1,-1],
[TENSOR,[18,2]],[128,0,2,0,-2,-2,2,-4,-1,0,1,1,-1,-1,0,0,0,0,0,0]],
[(17,18),(13,14),( 5, 6)(11,12)(19,20)]);
ARC("L3(4).3.2_3","tomfusion",rec(name:="L3(4).3.2_3",map:=[1,2,6,9,11,11,19,
4,5,16,43,43,62,62,3,18,24,25,34,34],text:=[
"fusion map is unique up to table autom."
]));
ALF("L3(4).3.2_3","L3(4).D12",[1,2,3,4,5,5,6,11,12,13,14,14,15,15,24,25,
26,27,28,28],[
"fusion map is unique up to table autom.,\n",
"unique map that is compatible with Brauer tables"
]);

MOT("L3(4).6",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[120960,384,54,32,15,21,432,48,54,8,360,360,126,126,24,24,15,15,21,21,36,36,
18,18,12,12],
[,[1,1,3,2,5,6,1,2,3,4,12,11,14,13,12,11,18,17,20,19,12,11,14,13,16,15],[1,2,
1,4,5,6,7,8,7,10,1,1,1,1,2,2,5,5,6,6,7,7,7,7,8,8],,[1,2,3,4,1,6,7,8,9,10,12,
11,14,13,16,15,12,11,20,19,22,21,24,23,26,25],,[1,2,3,4,5,1,7,8,9,10,11,12,13,
14,15,16,17,18,13,14,21,22,23,24,25,26]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,-1,-1,-1,
-1,E(3),E(3)^2,E(3),E(3)^2,E(3),E(3)^2,E(3),E(3)^2,E(3),E(3)^2,-E(3),-E(3)^2,
-E(3),-E(3)^2,-E(3),-E(3)^2],
[TENSOR,[2,2]],
[TENSOR,[2,3]],
[TENSOR,[2,4]],
[TENSOR,[2,5]],[20,4,2,0,0,-1,2,-2,2,0,5,5,-1,-1,1,1,0,0,-1,-1,-1,-1,-1,-1,1,
1],
[TENSOR,[7,2]],
[TENSOR,[7,3]],
[TENSOR,[7,4]],
[TENSOR,[7,5]],
[TENSOR,[7,6]],[105,9,-3,1,0,0,3,3,3,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[13,2]],[90,-6,0,2,0,-1,0,0,0,0,0,0,6,6,0,0,0,0,-1,-1,0,0,0,0,0,0],
[TENSOR,[15,2]],
[TENSOR,[15,3]],[126,-2,0,-2,1,0,0,0,0,0,6,6,0,0,-2,-2,1,1,0,0,0,0,0,0,0,0],
[TENSOR,[18,2]],
[TENSOR,[18,3]],[64,0,1,0,-1,1,8,0,-1,0,4,4,1,1,0,0,-1,-1,1,1,2,2,-1,-1,0,0],
[TENSOR,[21,2]],
[TENSOR,[21,3]],
[TENSOR,[21,4]],
[TENSOR,[21,5]],
[TENSOR,[21,6]]],
[(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)]);
ARC("L3(4).6","projectives",["3.L3(4).6",[[45,-3,0,1,0,3,9,-3,0,-1,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0],[21,5,0,1,1,0,3,-1,0,1,5*E(3)+E(3)^2,E(3)+5*E(3)^2,0,0,
-1,-1,E(3)^2,E(3),0,0,-E(3)+E(3)^2,E(3)-E(3)^2,0,0,-1,-1],[90,-6,0,2,0,-1,0,0,
0,0,0,0,0,0,0,0,0,0,E(63)+E(63)^4-E(63)^19+E(63)^31-E(63)^37-E(63)^40+E(63)^55
 -E(63)^58,-E(63)^5+E(63)^8-E(63)^23-E(63)^26+E(63)^32-E(63)^44+E(63)^59
 +E(63)^62,0,0,0,0,0,0],[126,-2,0,-2,1,0,0,0,0,0,6,6,0,0,-2,-2,1,1,0,0,0,0,0,
0,0,0],[84,4,0,0,-1,0,6,2,0,0,-E(3)-5*E(3)^2,-5*E(3)-E(3)^2,0,0,1,1,-E(3),
-E(3)^2,0,0,E(3)-E(3)^2,-E(3)+E(3)^2,0,0,-1,-1]],]);
ARC("L3(4).6","tomfusion",rec(name:="L3(4).6",map:=[1,3,6,11,12,19,2,9,13,
28,4,4,5,5,17,17,41,41,62,62,14,14,18,18,38,38],text:=[
"fusion map is unique"
]));
ALF("L3(4).6","L3(4).D12",[1,2,3,4,5,6,7,8,9,10,11,11,12,12,13,13,14,14,
15,15,16,16,17,17,18,18],[
"fusion map is unique"
]);

MOT("L3(4).D12",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7],\n",
"constructions: Aut(L3(4))"
],
[241920,768,108,64,30,42,864,96,108,16,360,126,24,15,21,36,18,12,672,32,12,16,
14,240,12,32,32,10],
[,[1,1,3,2,5,6,1,2,3,4,11,12,11,14,15,11,12,13,1,2,3,4,6,1,3,4,4,5],[1,2,1,4,5
,6,7,8,7,10,1,1,2,5,6,7,7,8,19,20,19,22,23,24,24,26,27,28],,[1,2,3,4,1,6,7,8,9
,10,11,12,13,11,15,16,17,18,19,20,21,22,23,24,25,26,27,24],,[1,2,3,4,5,1,7,8,9
,10,11,12,13,14,12,16,17,18,19,20,21,22,19,24,25,26,27,28]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[2,2,2,2,2,2,-2,-2,-2,-2,-1,
-1,-1,-1,-1,1,1,1,0,0,0,0,0,0,0,0,0,0],[2,2,2,2,2,2,2,2,2,2,-1,-1,-1,-1,-1,-1,
-1,-1,0,0,0,0,0,0,0,0,0,0],[1,1,1,1,1,1,-1,-1,-1,-1,1,1,1,1,1,-1,-1,-1,1,1,1,1
,1,-1,-1,-1,-1,-1],
[TENSOR,[2,5]],[20,4,2,0,0,-1,2,-2,2,0,5,-1,1,0,-1,-1,-1,1,6,2,0,0,-1,0,0,-2,
2,0],
[TENSOR,[7,2]],[40,8,4,0,0,-2,-4,4,-4,0,-5,1,-1,0,1,-1,-1,1,0,0,0,0,0,0,0,0,0
,0],
[TENSOR,[9,5]],
[TENSOR,[7,5]],
[TENSOR,[7,6]],[105,9,-3,1,0,0,3,3,3,-1,0,0,0,0,0,0,0,0,7,-1,1,-1,0,5,-1,1,1,
0],
[TENSOR,[13,2]],
[TENSOR,[13,5]],
[TENSOR,[13,6]],[90,-6,0,2,0,-1,0,0,0,0,0,6,0,0,-1,0,0,0,6,-2,0,2,-1,0,0,0,0,
0],
[TENSOR,[17,2]],[180,-12,0,4,0,-2,0,0,0,0,0,-6,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,
0],[126,-2,0,-2,1,0,0,0,0,0,6,0,-2,1,0,0,0,0,0,0,0,0,0,6,0,-2,-2,1],
[TENSOR,[20,2]],[252,-4,0,-4,2,0,0,0,0,0,-6,0,2,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,
0],[64,0,1,0,-1,1,8,0,-1,0,4,1,0,-1,1,2,-1,0,8,0,-1,0,1,4,1,0,0,-1],
[TENSOR,[23,2]],[128,0,2,0,-2,2,-16,0,2,0,-4,-1,0,1,-1,2,-1,0,0,0,0,0,0,0,0,0
,0,0],
[TENSOR,[25,5]],
[TENSOR,[23,5]],
[TENSOR,[23,6]]],
[]);
ARC("L3(4).D12","maxes",["L3(4).3.2_3","L3(4).6","L3(4).3.2_2","L3(4).2^2",
"2^(2+4):(S3xS3)","2x3^2.2.S4","S5xS3","S3x7:6"]);
ALF("L3(4).D12","Co3",[1,2,5,8,10,16,3,7,14,18,5,6,13,31,35,14,15,28,2,8,
13,19,29,3,14,18,17,23],[
"fusion map is unique, compatible with that on the CAS table"
]);
ARC("L3(4).D12","tomfusion",rec(name:="L3(4).D12",map:=[1,3,8,16,18,34,2,
15,28,59,6,7,30,90,151,29,31,86,5,17,32,60,89,4,33,58,57,66],text:=[
"fusion map is unique"
]));
ARC("L3(4).D12","CAS",[rec(name:="psl(3,4):d12",
permchars:=(3,6,4,5)(9,12,10,11)(14,15)(25,28,26,27),
permclasses:=(11,14,17,12,15,18,13,16),
text:=[
"origin: CAS library,\n",
"maximal subgroup of Co3,\n",
"Source: Atlas.\n",
"Test: JAMES, JAMES,n=3,\n",
"and restricted characters decompose properly.\n",
""])]);
ALN("L3(4).D12",["psl(3,4):d12","pls(3,4):d12"]);

MOT("(2^2x3).L3(4)",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow"
],
[241920,241920,241920,241920,241920,241920,241920,241920,241920,241920,241920,
241920,768,768,768,768,768,768,768,768,768,768,768,768,36,36,36,36,96,96,96,
96,96,96,96,96,96,96,96,96,96,96,96,96,96,96,60,60,60,60,60,60,60,60,60,60,60,
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],
[,[1,1,5,5,9,9,1,1,5,5,9,9,1,1,5,5,9,9,1,1,5,5,9,9,25,25,25,25,14,18,22,14,18,
22,19,19,23,23,15,15,20,20,24,24,16,16,59,59,63,63,67,67,59,59,63,63,67,67,47,
47,51,51,55,55,47,47,51,51,55,55,71,71,75,75,79,79,71,71,75,75,79,79,83,83,87,
87,91,91,83,83,87,87,91,91],[1,2,7,8,1,2,7,8,1,2,7,8,13,14,19,20,13,14,19,20,
13,14,19,20,1,2,7,8,29,32,29,32,29,32,35,36,36,35,35,36,41,42,42,41,41,42,59,
60,65,66,59,60,65,66,59,60,65,66,47,48,53,54,47,48,53,54,47,48,53,54,83,84,89,
90,83,84,89,90,83,84,89,90,71,72,77,78,71,72,77,78,71,72,77,78],,[1,2,11,12,9,
10,7,8,5,6,3,4,13,14,23,24,21,22,19,20,17,18,15,16,25,26,27,28,29,34,33,32,31,
30,35,36,40,39,38,37,41,42,46,45,44,43,1,2,11,12,9,10,7,8,5,6,3,4,1,2,11,12,9,
10,7,8,5,6,3,4,83,84,93,94,91,92,89,90,87,88,85,86,71,72,81,82,79,80,77,78,75,
76,73,74],,[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,
26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,59,60,61,62,63,
64,65,66,67,68,69,70,47,48,49,50,51,52,53,54,55,56,57,58,1,2,3,4,5,6,7,8,9,10,
11,12,1,2,3,4,5,6,7,8,9,10,11,12]],
0,
[(71,83)(72,84)(73,85)(74,86)(75,87)(76,88)(77,89)(78,90)(79,91)(80,92)(81,93)
(82,94),(47,59)(48,60)(49,61)(50,62)(51,63)(52,64)(53,65)(54,66)(55,67)(56,68)
(57,69)(58,70),( 3,11)( 4,12)( 5, 9)( 6,10)(15,23)(16,24)(17,21)(18,22)(30,34)
(31,33)(37,40)(38,39)(43,46)(44,45)(49,57)(50,58)(51,55)(52,56)(61,69)(62,70)
(63,67)(64,68)(73,81)(74,82)(75,79)(76,80)(85,93)(86,94)(87,91)(88,92),( 3, 4)
( 7, 8)(11,12)(15,16)(19,20)(23,24)(27,28)(35,41)(36,42)(37,43)(38,44)(39,45)
(40,46)(49,50)(53,54)(57,58)(61,62)(65,66)(69,70)(73,74)(77,78)(81,82)(85,86)
(89,90)(93,94),( 2, 7, 8)( 3, 4,10)( 6,11,12)(14,19,20)(15,16,22)(18,23,24)
(26,27,28)(29,35,41)(30,37,43)(31,39,45)(32,36,42)(33,38,44)(34,40,46)
(48,53,54)(49,50,56)(52,57,58)(60,65,66)(61,62,68)(64,69,70)(72,77,78)
(73,74,80)(76,81,82)(84,89,90)(85,86,92)(88,93,94)],
["ConstructV4G","6.L3(4)",( 2, 7, 8)( 3, 4,10)( 6,11,12)(14,19,
20)(15,16,22)(18,23,24)(26,27,28)(29,35,41)(30,37,43)(31,39,45)(32,36,42)(33,
38,44)(34,40,46)(48,53,54)(49,50,56)(52,57,58)(60,65,66)(61,62,68)(64,69,70)
(72,77,78)(73,74,80)(76,81,82)(84,89,90)(85,86,92)(88,93,94)]);
ALF("(2^2x3).L3(4)","6.L3(4)",[1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,9,10,10,
11,11,12,12,13,13,14,14,15,16,17,18,19,20,21,21,22,22,23,23,24,24,25,25,
26,26,27,27,28,28,29,29,30,30,31,31,32,32,33,33,34,34,35,35,36,36,37,37,
38,38,39,39,40,40,41,41,42,42,43,43,44,44,45,45,46,46,47,47,48,48,49,49,
50,50]);
ALF("(2^2x3).L3(4)","3.L3(4)",[1,1,2,2,3,3,1,1,2,2,3,3,4,4,5,5,6,6,4,4,5,
5,6,6,7,7,7,7,8,9,10,8,9,10,11,11,12,12,13,13,14,14,15,15,16,16,17,17,18,
18,19,19,17,17,18,18,19,19,20,20,21,21,22,22,20,20,21,21,22,22,23,23,24,
24,25,25,23,23,24,24,25,25,26,26,27,27,28,28,26,26,27,27,28,28]);
ALF("(2^2x3).L3(4)","2^2.L3(4)",[1,2,3,4,1,2,3,4,1,2,3,4,5,6,7,8,5,6,7,8,
5,6,7,8,9,10,11,12,13,14,13,14,13,14,15,16,16,15,15,16,17,18,18,17,17,18,
19,20,21,22,19,20,21,22,19,20,21,22,23,24,25,26,23,24,25,26,23,24,25,26,
27,28,29,30,27,28,29,30,27,28,29,30,31,32,33,34,31,32,33,34,31,32,33,34]);
ALF("(2^2x3).L3(4)","2.L3(4)",[1,1,2,2,1,1,2,2,1,1,2,2,3,3,4,4,3,3,4,4,3,
3,4,4,5,5,6,6,7,8,7,8,7,8,9,9,9,9,9,9,10,10,10,10,10,10,11,11,12,12,11,11,
12,12,11,11,12,12,13,13,14,14,13,13,14,14,13,13,14,14,15,15,16,16,15,15,
16,16,15,15,16,16,17,17,18,18,17,17,18,18,17,17,18,18]);
ALF("(2^2x3).L3(4)","L3(4)",[1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,
2,2,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,8,
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("(2^2x3).L3(4)","(2^2x3).L3(4).2_2",[1,2,3,4,5,6,7,7,5,6,4,3,8,9,10,
11,12,13,14,14,12,13,11,10,15,16,17,17,18,19,20,21,20,19,22,23,24,25,26,
27,22,23,27,26,25,24,28,29,30,31,32,33,34,35,36,37,38,39,28,29,39,38,36,
37,35,34,32,33,31,30,40,41,42,43,44,45,46,46,44,45,43,42,47,48,49,50,51,
52,53,53,51,52,50,49],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);
ALF("(2^2x3).L3(4)","(2^2x3).L3(4).2_3",[1,2,3,4,5,6,7,7,5,6,4,3,8,9,10,
11,12,13,14,14,12,13,11,10,15,16,17,17,18,19,20,21,20,19,22,23,24,25,26,
27,22,23,27,26,25,24,28,29,30,31,32,33,34,34,32,33,31,30,35,36,37,38,39,
40,41,41,39,40,38,37,42,43,44,45,46,47,48,49,50,51,52,53,42,43,53,52,50,
51,49,48,46,47,45,44],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);
ALF("(2^2x3).L3(4)","(2^2x3).L3(4).3",[1,2,3,3,4,5,2,2,6,3,5,5,7,8,9,9,10,
11,8,8,12,9,11,11,13,14,14,14,15,16,17,18,19,20,15,18,16,19,17,20,15,18,
16,19,17,20,21,22,23,23,24,25,22,22,26,23,25,25,27,28,29,29,30,31,28,28,
32,29,31,31,33,34,35,35,36,37,34,34,38,35,37,37,39,40,41,41,42,43,40,40,
44,41,43,43],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);

MOT("(2^2x3).L3(4).2_1",
[
"constructed using `PossibleCharacterTablesOfTypeV4G'"
],
[483840,483840,483840,483840,483840,483840,483840,483840,483840,483840,483840,
483840,1536,1536,1536,1536,1536,1536,1536,1536,1536,1536,1536,1536,72,72,72,72
,192,192,192,192,192,192,192,192,192,192,192,192,192,192,192,192,192,192,60,60
,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
,48,48,48,72,72,72,72,96,96,96,96,96,96,96,96,96,96,96,96,96,96,96,96,96,96,96
,96,96,96,96,96,96,96,96,96,96,96,96,96,96,96,96,96],
[,[1,1,1,1,9,9,9,9,8,8,8,8,1,1,1,1,9,9,9,9,8,8,8,8,25,25,25,25,14,14,22,22,19,
19,15,15,23,23,18,18,16,16,24,24,17,17,47,47,47,47,55,55,55,55,54,54,54,54,59,
59,59,59,67,67,67,67,66,66,66,66,1,9,8,13,21,20,25,25,25,25,29,29,29,29,33,33,
33,33,32,32,32,32,35,35,35,35,39,39,39,39,38,38,38,38,41,41,41,41,45,45,45,45,
44,44,44,44],[1,2,3,4,4,3,2,1,1,2,3,4,13,14,15,16,16,15,14,13,13,14,15,16,1,2,
3,4,29,30,30,29,29,30,35,36,36,35,35,36,41,42,42,41,41,42,47,48,49,50,50,49,48
,47,47,48,49,50,59,60,61,62,62,61,60,59,59,60,61,62,71,71,71,74,74,74,71,71,71
,71,82,81,84,83,83,84,81,82,82,81,84,83,95,96,93,94,94,93,96,95,95,96,93,94,
108,107,106,105,105,106,107,108,108,107,106,105],,[1,2,3,4,12,11,10,9,8,7,6,5,
13,14,15,16,24,23,22,21,20,19,18,17,25,26,27,28,29,30,34,33,32,31,35,36,40,39,
38,37,41,42,46,45,44,43,1,2,3,4,12,11,10,9,8,7,6,5,59,60,61,62,70,69,68,67,66,
65,64,63,71,73,72,74,76,75,77,78,79,80,82,81,84,83,91,92,89,90,87,88,85,86,95,
96,93,94,102,101,104,103,98,97,100,99,108,107,106,105,113,114,115,116,109,110,
111,112],,[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,
52,53,54,55,56,57,58,1,2,3,4,5,6,7,8,9,10,11,12,71,72,73,74,75,76,77,78,79,80,
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]],
0,
[(77,79)(78,80)(93,96)(94,95)(97,100)(98,99)(101,104)(102,103)(105,107)(106,
108)(109,111)(110,112)(113,115)(114,116),(2,3)(6,7)(10,11)(14,15)(18,19)(22,
23)(26,27)(29,35)(30,36)(31,37)(32,38)(33,39)(34,40)(48,49)(52,53)(56,57)(60,
61)(64,65)(68,69)(77,79,80,78)(81,93,84,96)(82,95,83,94)(85,97,88,100)(86,99,
87,98)(89,101,92,104)(90,103,91,102)(105,106,108,107)(109,110,112,111)(113,
114,116,115),(2,3,4)(5,10,6,12,7,11)(8,9)(14,15,16)(17,22,18,24,19,23)(20,21)
(26,27,28)(29,35,41)(30,36,42)(31,40,43,34,37,46)(32,39,44,33,38,45)(48,49,50)
(51,56,52,58,53,57)(54,55)(60,61,62)(63,68,64,70,65,69)(66,67)(72,73)(75,76)
(77,80,79)(81,96,105,82,94,108)(83,93,106,84,95,107)(85,103,110,91,100,114)
(86,101,111,92,98,115)(87,102,109,89,97,113)(88,104,112,90,99,116)],
[ "ConstructV4G", "6.L3(4).2_1", (2,3,4)(5,7,6)(10,11,12)(14,15,16)(17,19,
    18)(22,23,24)(26,27,28)(29,35,41)(30,36,42)(31,37,43)(32,38,44)(33,39,
    45)(34,40,46)(48,49,50)(51,53,52)(56,57,58)(60,61,62)(63,65,64)(68,69,
    70)(78,79,80)(81,93,108)(82,95,105)(83,96,107)(84,94,106)(85,99,111)(86,
    97,110)(87,98,112)(88,100,109)(89,101,116)(90,103,113)(91,104,115)(92,102,
    114)]);
ALF("(2^2x3).L3(4).2_1","6.L3(4).2_1",[1,1,4,4,2,2,5,5,3,3,6,6,7,7,10,10,
8,8,11,11,9,9,12,12,13,13,14,14,15,18,16,19,17,20,21,21,22,22,23,23,24,24,
25,25,26,26,27,27,30,30,28,28,31,31,29,29,32,32,33,33,36,36,34,34,37,37,
35,35,38,38,39,40,41,42,43,44,45,45,46,46,47,47,50,50,48,48,51,51,49,49,
52,52,53,53,56,56,54,54,57,57,55,55,58,58,59,59,62,62,60,60,63,63,61,61,
64,64]);

MOT("(2^2x3).L3(4).2_2",
[
"constructed using `PossibleCharacterTablesOfTypeMGA'"
],
[483840,483840,241920,241920,241920,241920,241920,1536,1536,768,768,768,768,
768,72,72,36,192,96,96,192,96,96,96,96,96,96,60,60,60,60,60,60,60,60,60,60,60,
60,168,168,84,84,84,84,84,168,168,84,84,84,84,84,672,672,32,32,12,12,16,16,28,
28,28,28],
[,[1,1,5,5,5,5,1,1,1,5,5,5,5,1,15,15,15,9,13,13,9,14,14,11,11,10,10,28,28,36,
36,32,32,28,28,36,36,32,32,40,40,44,44,44,44,40,47,47,51,51,51,51,47,1,2,9,8,
15,16,21,21,40,41,47,48],[1,2,7,7,1,2,7,8,9,14,14,8,9,14,1,2,7,18,21,18,21,22,
23,23,22,22,23,28,29,35,34,28,29,35,34,28,29,35,34,47,48,53,53,47,48,53,40,41,
46,46,40,41,46,54,55,56,57,54,55,61,60,64,65,62,63],,[1,2,4,3,5,6,7,8,9,11,10,
12,13,14,15,16,17,18,19,20,21,22,23,27,26,25,24,1,2,4,3,5,6,7,7,5,6,3,4,47,48,
50,49,51,52,53,40,41,43,42,44,45,46,54,55,56,57,58,59,60,61,64,65,62,63],,[1,2
,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,39,
38,36,37,35,34,32,33,31,30,1,2,3,4,5,6,7,1,2,3,4,5,6,7,54,55,56,57,58,59,61,60
,54,55,54,55]],
0,
[(60,61),(30,39)(31,38)(32,36)(33,37)(34,35),
(40,47)(41,48)(42,49)(43,50)(44,51)(45,52)(46,53)(62,64)(63,65),
( 3, 4)(10,11)(24,27)(25,26)(30,31)(34,35)(38,39)(40,47)(41,48)(42,50)(43,49)
(44,51)(45,52)(46,53)(62,64)(63,65)
],
["ConstructMGA","(2^2x3).L3(4)","2^2.L3(4).2_2",[[19,20],[21,24],[22,23],[25,
26],[27,28],[29,30],[31,34],[32,33],[35,36],[37,38],[39,40],[41,44],[42,43],[
45,46],[47,48],[49,50],[59,82],[60,81],[61,84],[62,83],[63,88],[64,87],[65,86]
,[66,85],[67,90],[68,89],[69,92],[70,91],[71,94],[72,93]],()]);
ALF("(2^2x3).L3(4).2_2","L3(4).2_2",[1,1,1,1,1,1,1,2,2,2,2,2,2,2,3,3,3,4,
4,4,4,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,8,8,8,8,8,8,8,9,9,
10,10,11,11,12,12,13,13,14,14]);
ALF("(2^2x3).L3(4).2_2","2.L3(4).2_2",[1,1,2,2,1,1,2,3,3,4,4,3,3,4,5,5,6,
7,8,7,8,9,9,9,9,9,9,10,10,11,11,10,10,11,11,10,10,11,11,12,12,13,13,12,12,
13,14,14,15,15,14,14,15,16,17,18,19,20,21,22,23,24,25,26,27]);
ALF("(2^2x3).L3(4).2_2","3.L3(4).2_2",[1,1,2,2,2,2,1,3,3,4,4,4,4,3,5,5,5,
6,7,7,6,8,8,9,9,10,10,11,11,12,12,13,13,11,11,12,12,13,13,14,14,15,15,15,
15,14,16,16,17,17,17,17,16,18,18,19,19,20,20,21,21,22,22,23,23]);
ALF("(2^2x3).L3(4).2_2","6.L3(4).2_2",[1,1,2,2,3,3,4,5,5,6,6,7,7,8,9,9,
10,11,12,13,14,15,15,16,16,17,17,18,18,19,19,20,20,21,21,22,22,23,23,24,
24,25,25,26,26,27,28,28,29,29,30,30,31,32,33,34,35,36,37,38,39,40,41,42,
43]);
ALF("(2^2x3).L3(4).2_2","2^2.L3(4).2_2",[1,2,3,3,1,2,3,4,5,6,6,4,5,6,7,8,
9,10,11,10,11,12,13,13,12,12,13,14,15,16,17,14,15,16,17,14,15,16,17,18,19,
20,20,18,19,20,21,22,23,23,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35]);

MOT("(2^2x3).L3(4).2_3",
[
"constructed using `PossibleCharacterTablesOfTypeMGA'"
],
[483840,483840,241920,241920,241920,241920,241920,1536,1536,768,768,768,768,
768,72,72,36,192,96,96,192,96,96,96,96,96,96,120,120,60,60,60,60,60,120,120,60
,60,60,60,60,84,84,84,84,84,84,84,84,84,84,84,84,240,240,12,12,32,32,32,32,20,
20,20,20],
[,[1,1,5,5,5,5,1,1,1,5,5,5,5,1,15,15,15,9,13,13,9,14,14,11,11,10,10,35,35,39,
39,39,39,35,28,28,32,32,32,32,28,42,42,46,46,50,50,42,42,46,46,50,50,1,2,15,16
,18,18,18,18,35,36,28,29],[1,2,7,7,1,2,7,8,9,14,14,8,9,14,1,2,7,18,21,18,21,22
,23,23,22,22,23,35,36,41,41,35,36,41,28,29,34,34,28,29,34,42,43,49,48,42,43,49
,48,42,43,49,48,54,55,54,55,59,58,61,60,64,65,62,63],,[1,2,4,3,5,6,7,8,9,11,10
,12,13,14,15,16,17,18,19,20,21,22,23,27,26,25,24,1,2,4,3,5,6,7,1,2,4,3,5,6,7,
42,43,45,44,46,47,49,48,50,51,53,52,54,55,56,57,59,58,61,60,54,55,54,55],,[1,2
,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,35,36,37,
38,39,40,41,28,29,30,31,32,33,34,1,2,3,4,5,6,7,7,5,6,4,3,54,55,56,57,58,59,60,
61,64,65,62,63]],
0,
[(60,61),(58,59),(44,53)(45,52)(46,50)(47,51)(48,49),
(28,35)(29,36)(30,37)(31,38)(32,39)(33,40)(34,41)(62,64)(63,65),
( 3, 4)(10,11)(24,27)(25,26)(28,35)(29,36)(30,38)(31,37)(32,39)(33,40)(34,41)
(44,45)(48,49)(52,53)(62,64)(63,65)
],
["ConstructMGA","(2^2x3).L3(4)","2^2.L3(4).2_3",[[19,20],[21,24],[22,23],[25,
26],[27,30],[28,29],[31,32],[33,34],[35,36],[37,38],[39,40],[41,42],[43,44],[
45,48],[46,47],[49,50],[59,82],[60,81],[61,84],[62,83],[63,86],[64,85],[65,88]
,[66,87],[67,92],[68,91],[69,90],[70,89],[71,94],[72,93]],()]);
ALF("(2^2x3).L3(4).2_3","L3(4).2_3",[1,1,1,1,1,1,1,2,2,2,2,2,2,2,3,3,3,4,
4,4,4,5,5,5,5,5,5,6,6,6,6,6,6,6,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,9,9,
10,10,11,11,12,12,13,13,14,14]);
ALF("(2^2x3).L3(4).2_3","2.L3(4).2_3",[1,1,2,2,1,1,2,3,3,4,4,3,3,4,5,5,6,
7,8,7,8,9,9,9,9,9,9,10,10,11,11,10,10,11,12,12,13,13,12,12,13,14,14,15,15,
14,14,15,15,14,14,15,15,16,17,18,19,20,21,22,23,24,25,26,27]);
ALF("(2^2x3).L3(4).2_3","3.L3(4).2_3",[1,1,2,2,2,2,1,3,3,4,4,4,4,3,5,5,5,
6,7,7,6,8,8,9,9,10,10,11,11,12,12,12,12,11,13,13,14,14,14,14,13,15,15,16,
16,17,17,15,15,16,16,17,17,18,18,19,19,20,20,21,21,22,22,23,23]);
ALF("(2^2x3).L3(4).2_3","6.L3(4).2_3",[1,1,2,2,3,3,4,5,5,6,6,7,7,8,9,9,
10,11,12,13,14,15,15,16,16,17,17,18,18,19,19,20,20,21,22,22,23,23,24,24,
25,26,26,27,27,28,28,29,29,30,30,31,31,32,33,34,35,36,37,38,39,40,41,42,
43]);
ALF("(2^2x3).L3(4).2_3","2^2.L3(4).2_3",[1,2,3,3,1,2,3,4,5,6,6,4,5,6,7,8,
9,10,11,10,11,12,13,13,12,12,13,14,15,16,16,14,15,16,17,18,19,19,17,18,19,
20,21,22,23,20,21,22,23,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35]);

MOT("(2^2x3).L3(4).3",
[
"constructed using `PossibleCharacterTablesOfTypeMGA'"
],
[725760,241920,241920,725760,241920,725760,2304,768,768,2304,768,2304,108,36,
96,96,96,96,96,96,180,60,60,180,60,180,180,60,60,180,60,180,252,84,84,252,84,
252,252,84,84,252,84,252,540,540,540,540,540,540,63,63,36,36,36,36,36,36,45,45
,45,45,45,45,45,45,45,45,45,45,63,63,63,63,63,63,63,63,63,63,63,63],
[,[1,1,4,6,6,4,1,1,4,6,6,4,13,13,8,11,9,8,11,9,27,27,30,32,32,30,21,21,24,26,
26,24,33,33,36,38,38,36,39,39,42,44,44,42,48,49,50,45,46,47,52,51,48,49,50,45,
46,47,68,69,70,65,66,67,62,63,64,59,60,61,74,75,76,71,72,73,80,81,82,77,78,79]
,[1,2,2,1,2,1,7,8,8,7,8,7,1,2,15,18,15,18,15,18,27,28,28,27,28,27,21,22,22,21,
22,21,39,40,40,39,40,39,33,34,34,33,34,33,1,1,1,1,1,1,6,4,7,7,7,7,7,7,27,27,27
,27,27,27,21,21,21,21,21,21,44,44,44,42,42,42,38,38,38,36,36,36],,[1,2,5,6,3,4
,7,8,11,12,9,10,13,14,15,20,19,18,17,16,1,2,5,6,3,4,1,2,5,6,3,4,39,40,43,44,41
,42,33,34,37,38,35,36,48,49,50,45,46,47,52,51,56,57,58,53,54,55,48,49,50,45,46
,47,48,49,50,45,46,47,82,80,81,79,77,78,76,74,75,73,71,72],,[1,2,3,4,5,6,7,8,9
,10,11,12,13,14,15,16,17,18,19,20,27,28,29,30,31,32,21,22,23,24,25,26,1,2,3,4,
5,6,1,2,3,4,5,6,45,46,47,48,49,50,51,52,53,54,55,56,57,58,65,66,67,68,69,70,59
,60,61,62,63,64,51,51,51,52,52,52,51,51,51,52,52,52]],
0,
[
(45,46,47)(48,49,50)(53,54,55)(56,57,58)(59,60,61)(62,63,64)(65,66,67)
(68,69,70)
,
(21,27)(22,28)(23,29)(24,30)(25,31)(26,32)(59,65)(60,66)(61,67)(62,68)(63,69)
(64,70)
,
(33,39)(34,40)(35,41)(36,42)(37,43)(38,44)(71,78,73,77,72,79)(74,81,76,80,75,
 82)
,
( 3, 5)( 4, 6)( 9,11)(10,12)(16,20)(17,19)(23,25)(24,26)(29,31)(30,32)(33,39)
(34,40)(35,43)(36,44)(37,41)(38,42)(45,48)(46,49)(47,50)(51,52)(53,56)(54,57)
(55,58)(59,62)(60,63)(61,64)(65,68)(66,69)(67,70)(71,81,73,80,72,82)
(74,78,76,77,75,79)
],
["ConstructMGA","(2^2x3).L3(4)","3.L3(4).3",[[11,51,73],[12,52,74],[13,53,75],
[14,54,76],[15,55,77],[16,56,78],[17,57,79],[18,58,80],[37,59,81],[38,60,82],[
39,61,83],[40,62,84],[41,63,85],[42,64,86],[43,65,87],[44,66,88],[45,67,89],[
46,68,90],[47,69,91],[48,70,92],[49,71,93],[50,72,94]],(23,31,39,47,55,63,25,
33,41,49,57,65,27,35,43,51,59,67,29,37,45,53,61)(24,32,40,48,56,64,26,34,42,
50,58,66,28,36,44,52,60,68,30,38,46,54,62)]);
ALF("(2^2x3).L3(4).3","L3(4).3",[1,1,1,1,1,1,2,2,2,2,2,2,3,3,4,4,4,4,4,4,
5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,9,9,10,10,10,11,12,13,
13,13,14,14,14,15,15,15,16,16,16,17,17,17,18,18,18,19,19,19,20,20,20,21,
21,21,22,22,22]);
ALF("(2^2x3).L3(4).3","3.L3(4).3",[1,1,2,3,3,2,4,4,5,6,6,5,7,7,8,9,10,8,9,
10,11,11,12,13,13,12,14,14,15,16,16,15,17,17,18,19,19,18,20,20,21,22,22,
21,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,
46,47,48,49,50,51,52,53,54,55,56,57,58,59,60]);
ALF("(2^2x3).L3(4).3","2^2.L3(4).3",[1,2,2,1,2,1,3,4,4,3,4,3,5,6,7,8,7,8,
7,8,9,10,10,9,10,9,11,12,12,11,12,11,13,14,14,13,14,13,15,16,16,15,16,15,
17,17,17,18,18,18,19,20,21,21,21,22,22,22,23,23,23,24,24,24,25,25,25,26,
26,26,27,27,27,28,28,28,29,29,29,30,30,30]);

MOT("2^2.L3(4).2_1",
[
"constructed using `PossibleCharacterTablesOfTypeV4G'"
],
[161280,161280,161280,161280,512,512,512,512,72,72,72,72,64,64,64,64,64,64,20,
20,20,20,28,28,28,28,144,16,72,72,72,72,32,32,32,32,32,32,32,32,32,32,32,32],
[,[1,1,1,1,1,1,1,1,9,9,9,9,6,6,7,7,8,8,19,19,19,19,23,23,23,23,1,5,9,9,9,9,13,
13,13,13,15,15,15,15,17,17,17,17],[1,2,3,4,5,6,7,8,1,2,3,4,13,14,15,16,17,18,
19,20,21,22,23,24,25,26,27,28,27,27,27,27,34,33,36,35,39,40,37,38,44,43,42,41]
,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,1,2,3,4,23,24,25,26,27,28,29,
30,31,32,34,33,36,35,39,40,37,38,44,43,42,41],,[1,2,3,4,5,6,7,8,9,10,11,12,13,
14,15,16,17,18,19,20,21,22,1,2,3,4,27,28,29,30,31,32,33,34,35,36,37,38,39,40,
41,42,43,44]],
0,
[(29,30)(31,32),(29,31)(30,32),(37,40)(38,39)(41,43)(42,44),
(33,34)(35,36)(37,38)(39,40)(41,42)(43,44),(33,35)(34,36)(37,38)(39,40),
( 3, 4)( 7, 8)(11,12)(15,17)(16,18)(21,22)(25,26)(31,32)(35,36)(37,42)(38,41)
(39,43)(40,44)
,
( 2, 3)( 6, 7)(10,11)(13,15)(14,16)(20,21)(24,25)(30,31)(33,37)(34,39)(35,38)
(36,40)(42,43)
],
["ConstructV4G","2.L3(4).2_1",
( 2, 3, 4)( 6, 7, 8)(10,11,12)(13,15,17)(14,16,18)(20,21,22)(24,25,26)
(30,31,32)(33,37,44)(34,39,41)(35,40,43)(36,38,42)
]);
ALF("2^2.L3(4).2_1","2.L3(4).2_1",[1,1,2,2,3,3,4,4,5,5,6,6,7,8,9,9,10,10,
11,11,12,12,13,13,14,14,15,16,17,17,18,18,19,19,20,20,21,21,22,22,23, 23,
24,24]);
ALF("2^2.L3(4).2_1","L3(4).2_1",[1,1,1,1,2,2,2,2,3,3,3,3,4,4,5,5,6,6,7,7,
7,7,8,8,8,8,9,10,11,11,11,11,12,12,12,12,13,13,13,13,14,14,14,14]);
ALF("2^2.L3(4).2_1","2^2.L3(4).2^2",[1,2,3,3,4,5,6,6,7,8,9,9,10,11,12,13,
12,13,14,15,16,16,17,18,19,19,20,21,22,23,24,24,25,26,27,27,28,29,30,31,
30,31,29,28]);
ALF("2^2.L3(4).2_1","2^2.L3(4).6",[1,2,2,2,3,4,4,4,5,6,6,6,7,8,7,8,7,8,9,
10,10,10,11,12,12,12,13,14,15,16,16,16,17,18,19,20,17,20,18,19,18,20,19,
17],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables"
]);

MOT("2^2.L3(4).2_2",
[
"origin: ATLAS of Finite Groups"
],
[161280,161280,80640,512,512,256,72,72,36,64,64,32,32,20,20,20,20,56,56,28,56,
56,28,672,672,32,32,12,12,16,16,28,28,28,28],
[,[1,1,1,1,1,1,7,7,7,5,5,6,6,14,14,14,14,18,18,18,21,21,21,1,2,5,4,7,8,11,11,
18,19,21,22],[1,2,3,4,5,6,1,2,3,10,11,12,13,14,15,17,16,21,22,23,18,19,20,24,
25,26,27,24,25,31,30,34,35,32,33],,[1,2,3,4,5,6,7,8,9,10,11,12,13,1,2,3,3,21,
22,23,18,19,20,24,25,26,27,28,29,30,31,34,35,32,33],,[1,2,3,4,5,6,7,8,9,10,11,
12,13,14,15,17,16,1,2,3,1,2,3,24,25,26,27,28,29,31,30,24,25,24,25]],
0,
[(30,31),(18,21)(19,22)(20,23)(32,34)(33,35),
(16,17)(18,21)(19,22)(20,23)(32,34)(33,35)],
["ConstructMGA","2^2.L3(4)","2.L3(4).2_2",[[19,27],[20,28],[21,30],[22,29],
[23,31],[24,32],[25,33],[26,34]],()]);
ARC("2^2.L3(4).2_2","maxes",["2^2.L3(4)","M24C2B","M24C2B","2^2.S6",
"D8xL3(2)","2^2.(3^2:Q8.2)"]);
ARC("2^2.L3(4).2_2","tomfusion",rec(name:="2^2.L3(4).2_2",map:=[1,4,2,6,7,
3,8,48,49,43,41,44,45,47,194,195,195,55,212,214,55,212,214,5,40,46,42,50,
211,189,189,213,481,213,481],text:=[
"fusion map is unique"
]));
ALF("2^2.L3(4).2_2","2^2.L3(4).3.2_2",[1,2,2,3,4,4,5,6,6,7,8,7,8,9,10,10,
10,11,12,12,13,14,14,22,23,24,25,26,27,28,29,30,31,32,33],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);
ALF("2^2.L3(4).2_2","2.L3(4).2_2",[1,1,2,3,3,4,5,5,6,7,8,9,9,10,10,11,11,
12,12,13,14,14,15,16,17,18,19,20,21,22,23,24,25,26,27]);
ALF("2^2.L3(4).2_2","L3(4).2_2",[1,1,1,2,2,2,3,3,3,4,4,5,5,6,6,6,6,7,7,7,
8,8,8,9,9,10,10,11,11,12,12,13,13,14,14]);
ALF("2^2.L3(4).2_2","2^2.L3(4).2^2",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,
16,16,17,18,19,17,18,19,32,33,34,35,36,37,38,38,39,40,39,40]);
ALF("2^2.L3(4).2_2","2^2.psl(3,4).s3",[1,2,2,3,4,4,5,6,6,7,8,7,8,9,10,10,
10,11,12,12,13,14,14,22,23,25,24,26,27,28,29,30,31,32,33],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);

MOT("2^2.L3(4).2_3",
[
"origin: ATLAS of Finite Groups"
],
[161280,161280,80640,512,512,256,72,72,36,64,64,32,32,40,40,20,40,40,20,28,28,
28,28,240,240,12,12,32,32,32,32,20,20,20,20],
[,[1,1,1,1,1,1,7,7,7,5,5,6,6,17,17,17,14,14,14,20,20,20,20,1,2,7,8,10,10,10,10
,17,18,14,15],[1,2,3,4,5,6,1,2,3,10,11,12,13,17,18,19,14,15,16,20,21,23,22,24,
25,24,25,29,28,31,30,34,35,32,33],,[1,2,3,4,5,6,7,8,9,10,11,12,13,1,2,3,1,2,3,
20,21,23,22,24,25,26,27,29,28,31,30,24,25,24,25],,[1,2,3,4,5,6,7,8,9,10,11,12,
13,17,18,19,14,15,16,1,2,3,3,24,25,26,27,28,29,30,31,34,35,32,33]],
0,
[(30,31),(28,29),(22,23),(14,17)(15,18)(16,19)(32,34)(33,35)],
["ConstructMGA","2^2.L3(4)","2.L3(4).2_3",[[19,28],[20,27],[21,29],[22,30],
[23,31],[24,32],[25,33],[26,34]],()]);
ALF("2^2.L3(4).2_3","2^2.L3(4).3.2_3",[1,2,2,3,4,4,5,6,6,7,8,7,8,9,10,10,
11,12,12,13,14,14,14,22,23,24,25,26,27,28,29,30,31,32,33],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);
ALF("2^2.L3(4).2_3","2.L3(4).2_3",[1,1,2,3,3,4,5,5,6,7,8,9,9,10,10,11,12,
12,13,14,14,15,15,16,17,18,19,20,21,22,23,24,25,26,27]);
ALF("2^2.L3(4).2_3","L3(4).2_3",[1,1,1,2,2,2,3,3,3,4,4,5,5,6,6,6,7,7,7,8,
8,8,8,9,9,10,10,11,11,12,12,13,13,14,14]);
ALF("2^2.L3(4).2_3","2^2.L3(4).2^2",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,
16,14,15,16,17,18,19,19,41,42,43,44,45,45,46,47,48,49,48,49],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);

MOT("2^2.L3(4).3",
[
"origin: ATLAS of Finite Groups"
],
[241920,80640,768,256,108,36,32,32,60,20,60,20,84,28,84,28,180,180,63,63,12,12
,15,15,15,15,21,21,21,21],
[,[1,1,1,1,5,5,4,4,11,11,9,9,13,13,15,15,18,17,20,19,18,17,26,25,24,23,28,27,
30,29],[1,2,3,4,1,2,7,8,11,12,9,10,15,16,13,14,1,1,1,1,3,3,11,11,9,9,15,15,13,
13],,[1,2,3,4,5,6,7,8,1,2,1,2,15,16,13,14,18,17,20,19,22,21,18,17,18,17,30,29,
28,27],,[1,2,3,4,5,6,7,8,11,12,9,10,1,2,1,2,17,18,19,20,21,22,25,26,23,24,19,
20,19,20]],
0,
[(13,15)(14,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,30)(28,29),(13,15)(14,
16)(27,29)(28,30),(9,11)(10,12)(13,15)(14,16)(17,18)(19,20)(21,22)(23,26)(24,
25)(27,30)(28,29)],
["ConstructMGA","2^2.L3(4)","L3(4).3",[[11,19,27],[12,20,28],[13,21,29],[14,
22,30],[15,23,31],[16,24,32],[17,25,33],[18,26,34]],()]);
ARC("2^2.L3(4).3","maxes",["2^2.L3(4)","2^6:(3xA5)","2^6:(3xA5)",
"2^2.(3^2:2A4)","A4x7:3"]);
ARC("2^2.L3(4).3","tomfusion",rec(name:="2^2.L3(4).3",map:=[1,2,3,4,5,28,
26,25,27,103,27,103,32,117,32,117,6,6,7,7,29,29,118,118,118,118,212,212,
212,212],text:=[
"fusion map is unique"
]));
ALF("2^2.L3(4).3","2^2.L3(4).3.2_2",[1,2,3,4,5,6,7,8,9,10,9,10,11,12,13,
14,15,15,16,16,17,17,18,19,19,18,20,20,21,21],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);
ALF("2^2.L3(4).3","L3(4).3",[1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,10,11,12,
13,14,15,16,17,18,19,20,21,22]);
ALF("2^2.L3(4).3","2^2.L3(4).3.2_3",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,13,
14,15,15,16,16,17,17,18,18,19,19,20,21,21,20],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);
ALF("2^2.L3(4).3","2^2.L3(4).6",[1,2,3,4,5,6,7,8,9,10,9,10,11,12,11,12,21,
22,23,24,25,26,27,28,27,28,29,30,29,30]);
ALF("2^2.L3(4).3","2^2.psl(3,4).s3",[1,2,3,4,5,6,7,8,9,10,9,10,11,12,13,
14,15,15,16,16,17,17,18,19,19,18,21,21,20,20],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);

MOT("2^2.L3(4).3.2_2",
[
"origin: ATLAS of Finite Groups"
],
[483840,161280,1536,512,216,72,64,64,60,20,168,56,168,56,180,63,12,15,15,21,21
,672,672,32,32,12,12,16,16,28,28,28,28],
[,[1,1,1,1,5,5,4,4,9,9,11,11,13,13,15,16,15,18,19,20,21,1,2,4,3,5,6,8,8,11,12,
13,14],[1,2,3,4,1,2,7,8,9,10,13,14,11,12,1,1,3,9,9,13,11,22,23,24,25,22,23,29,
28,32,33,30,31],,[1,2,3,4,5,6,7,8,1,2,13,14,11,12,15,16,17,15,15,21,20,22,23,
24,25,26,27,28,29,32,33,30,31],,[1,2,3,4,5,6,7,8,9,10,1,2,1,2,15,16,17,19,18,
16,16,22,23,24,25,26,27,29,28,22,23,22,23]],
0,
[(28,29),(18,19),(11,13)(12,14)(20,21)(30,32)(31,33)],
["ConstructGS3","2^2.L3(4).2_2","2^2.L3(4).3",[5,6,15,16,17,18,19,20,21,22,23,
24,25,26,27],[[2,3],[5,6],[9,10],[12,13],[14,17],[16,18],[15,19],[21,22]],[[1,
1],[4,3],[8,8],[11,10],[20,13]],(1,7,25,2,8,26,4,22,16,3,21,17,6,24)(5,23,20,
15,33,19,14,32,18,11,29,10,28,9,27)(12,30)(13,31)]);
ALF("2^2.L3(4).3.2_2","L3(4).3.2_2",[1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,9,10,
11,12,13,14,15,15,16,16,17,17,18,18,19,19,20,20]);
ALF("2^2.L3(4).3.2_2","2^2.L3(4).D12",[1,2,3,4,5,6,7,8,9,10,11,12,11,12,
20,21,22,23,23,24,24,28,29,30,31,32,33,34,34,35,36,35,36]);

MOT("2^2.L3(4).3.2_3",
[
"origin: ATLAS of Finite Groups"
],
[483840,161280,1536,512,216,72,64,64,120,40,120,40,84,28,180,63,12,15,15,21,21
,240,240,12,12,32,32,32,32,20,20,20,20],
[,[1,1,1,1,5,5,4,4,11,11,9,9,13,13,15,16,15,19,18,21,20,1,2,5,6,7,7,7,7,11,12,
9,10],[1,2,3,4,1,2,7,8,11,12,9,10,13,14,1,1,3,11,9,13,13,22,23,22,23,27,26,29,
28,32,33,30,31],,[1,2,3,4,5,6,7,8,1,2,1,2,13,14,15,16,17,15,15,20,21,22,23,24,
25,27,26,29,28,22,23,22,23],,[1,2,3,4,5,6,7,8,11,12,9,10,1,2,15,16,17,19,18,16
,16,22,23,24,25,26,27,28,29,32,33,30,31]],
0,
[(28,29),(26,27),(20,21),(9,11)(10,12)(18,19)(30,32)(31,33)],
["ConstructGS3","2^2.L3(4).2_3","2^2.L3(4).3",[5,6,15,16,17,18,19,20,21,22,23,
24,25,26,27],[[2,3],[5,6],[8,11],[10,12],[9,13],[15,16],[18,19],[21,22]],[[1,
1],[4,3],[14,9],[17,11],[20,13]],(1,7,25,2,8,26,4,22,17,6,24)(3,21,14,32,18,9,
27,5,23,20,10,28,12,30,15,33,19,11,29,13,31,16)]);
ALF("2^2.L3(4).3.2_3","L3(4).3.2_3",[1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,9,10,
11,12,13,14,15,15,16,16,17,17,18,18,19,19,20,20]);
ALF("2^2.L3(4).3.2_3","2^2.L3(4).D12",[1,2,3,4,5,6,7,8,9,10,9,10,11,12,20,
21,22,23,23,24,24,37,38,39,40,41,41,42,43,44,45,44,45]);

MOT("3.L3(4).3.2_2",
[
"origin: ATLAS of Finite Groups"
],
[362880,181440,1152,576,54,96,48,45,45,45,126,63,126,63,540,540,540,63,36,36,
36,45,45,45,45,45,45,63,63,63,63,63,63,336,16,6,8,14,14],
[,[1,2,1,2,5,3,4,8,9,10,11,12,13,14,15,16,17,18,15,16,17,22,23,24,25,26,27,28,
29,30,31,32,33,1,3,5,6,11,13],[1,1,3,3,1,6,6,8,8,8,13,13,11,11,1,1,1,2,3,3,3,8
,8,8,8,8,8,14,14,14,12,12,12,34,35,34,37,39,38],,[1,2,3,4,5,6,7,1,2,2,13,14,11
,12,15,16,17,18,19,20,21,15,16,17,15,16,17,33,31,32,30,28,29,34,35,36,37,39,38
],,[1,2,3,4,5,6,7,8,10,9,1,2,1,2,15,16,17,18,19,20,21,25,26,27,22,23,24,18,18,
18,18,18,18,34,35,36,37,34,34]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1
,-1,-1,-1],[2,2,2,2,2,2,2,2,2,2,2,2,2,2,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1
,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0],[20,20,4,4,2,0,0,0,0,0,-1,-1,-1,-1,5,5,5,-1,1,
1,1,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,6,2,0,0,-1,-1],
[TENSOR,[4,2]],[40,40,8,8,4,0,0,0,0,0,-2,-2,-2,-2,-5,-5,-5,1,-1,-1,-1,0,0,0,0
,0,0,1,1,1,1,1,1,0,0,0,0,0,0],[105,105,9,9,-3,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,7,-1,1,-1,0,0],
[TENSOR,[7,2]],[45,45,-3,-3,0,1,1,0,0,0,E(7)+E(7)^2+E(7)^4,E(7)+E(7)^2+E(7)^4
,E(7)^3+E(7)^5+E(7)^6,E(7)^3+E(7)^5+E(7)^6,0,0,0,3,0,0,0,0,0,0,0,0,0,
E(7)+E(7)^2+E(7)^4,E(7)+E(7)^2+E(7)^4,E(7)+E(7)^2+E(7)^4,E(7)^3+E(7)^5+E(7)^6,
E(7)^3+E(7)^5+E(7)^6,E(7)^3+E(7)^5+E(7)^6,3,-1,0,1,E(7)+E(7)^2+E(7)^4,
E(7)^3+E(7)^5+E(7)^6],
[TENSOR,[9,2]],[90,90,-6,-6,0,2,2,0,0,0,2*E(7)+2*E(7)^2+2*E(7)^4,
2*E(7)+2*E(7)^2+2*E(7)^4,2*E(7)^3+2*E(7)^5+2*E(7)^6,2*E(7)^3+2*E(7)^5+2*E(7)^6
,0,0,0,-3,0,0,0,0,0,0,0,0,0,-E(7)-E(7)^2-E(7)^4,-E(7)-E(7)^2-E(7)^4,
-E(7)-E(7)^2-E(7)^4,-E(7)^3-E(7)^5-E(7)^6,-E(7)^3-E(7)^5-E(7)^6,
-E(7)^3-E(7)^5-E(7)^6,0,0,0,0,0,0],
[GALOIS,[9,3]],
[TENSOR,[12,2]],
[GALOIS,[11,3]],[126,126,-2,-2,0,-2,-2,1,1,1,0,0,0,0,6,6,6,0,-2,-2,-2,1,1,1,1
,1,1,0,0,0,0,0,0,0,0,0,0,0,0],[126,126,-2,-2,0,-2,-2,1,1,1,0,0,0,0,-3,-3,-3,0,
1,1,1,-E(15)-E(15)^2-E(15)^4-E(15)^8,-E(15)-E(15)^2-E(15)^4-E(15)^8,
-E(15)-E(15)^2-E(15)^4-E(15)^8,-E(15)^7-E(15)^11-E(15)^13-E(15)^14,
-E(15)^7-E(15)^11-E(15)^13-E(15)^14,-E(15)^7-E(15)^11-E(15)^13-E(15)^14,0,0,0,
0,0,0,0,0,0,0,0,0],
[GALOIS,[16,7]],[64,64,0,0,1,0,0,-1,-1,-1,1,1,1,1,4,4,4,1,0,0,0,-1,-1,-1,-1,
-1,-1,1,1,1,1,1,1,8,0,-1,0,1,1],
[TENSOR,[18,2]],[128,128,0,0,2,0,0,-2,-2,-2,2,2,2,2,-4,-4,-4,-1,0,0,0,1,1,1,1
,1,1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0],[90,-45,-6,3,0,2,-1,0,0,0,6,-3,6,-3,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[42,-21,10,-5,0,2,-1,2,-1,-1,0,0,
0,0,-6,-3,9,0,-2,1,1,-1,2,-1,-1,2,-1,0,0,0,0,0,0,0,0,0,0,0,0],[42,-21,10,-5,0,
2,-1,2,-1,-1,0,0,0,0,-3,9,-6,0,1,1,-2,2,-1,-1,2,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0]
,[42,-21,10,-5,0,2,-1,2,-1,-1,0,0,0,0,9,-6,-3,0,1,-2,1,-1,-1,2,-1,-1,2,0,0,0,0
,0,0,0,0,0,0,0,0],[90,-45,-6,3,0,2,-1,0,0,0,2*E(7)+2*E(7)^2+2*E(7)^4,
-E(7)-E(7)^2-E(7)^4,2*E(7)^3+2*E(7)^5+2*E(7)^6,-E(7)^3-E(7)^5-E(7)^6,0,0,0,0,0
,0,0,0,0,0,0,0,0,
E(63)+E(63)^4+E(63)^8-E(63)^23+E(63)^32-E(63)^37-E(63)^44-E(63)^58,
-E(63)^4+E(63)^22-E(63)^32+E(63)^37+E(63)^44-E(63)^46+E(63)^50-E(63)^53,
-E(63)-E(63)^8-E(63)^22+E(63)^23+E(63)^46-E(63)^50+E(63)^53+E(63)^58,
-E(63)^5-E(63)^19-E(63)^26+E(63)^31-E(63)^40+E(63)^55+E(63)^59+E(63)^62,
-E(63)^10+E(63)^13-E(63)^17+E(63)^19+E(63)^26-E(63)^31+E(63)^41-E(63)^59,
E(63)^5+E(63)^10-E(63)^13+E(63)^17+E(63)^40-E(63)^41-E(63)^55-E(63)^62,0,0,0,0
,0,0],
[GALOIS,[25,11]],
[GALOIS,[25,23]],
[GALOIS,[25,31]],
[GALOIS,[25,13]],
[GALOIS,[25,5]],[126,-63,-2,1,0,-2,1,1,-E(15)-E(15)^2-E(15)^4-E(15)^8,
-E(15)^7-E(15)^11-E(15)^13-E(15)^14,0,0,0,0,6,-3,-3,0,-2,1,1,1,
-E(15)-E(15)^2-E(15)^4-E(15)^8,-E(15)^7-E(15)^11-E(15)^13-E(15)^14,1,
-E(15)^7-E(15)^11-E(15)^13-E(15)^14,-E(15)-E(15)^2-E(15)^4-E(15)^8,0,0,0,0,0,0
,0,0,0,0,0,0],[126,-63,-2,1,0,-2,1,1,-E(15)-E(15)^2-E(15)^4-E(15)^8,
-E(15)^7-E(15)^11-E(15)^13-E(15)^14,0,0,0,0,-3,-3,6,0,1,1,-2,
-E(15)-E(15)^2-E(15)^4-E(15)^8,-E(15)^7-E(15)^11-E(15)^13-E(15)^14,1,
-E(15)^7-E(15)^11-E(15)^13-E(15)^14,-E(15)-E(15)^2-E(15)^4-E(15)^8,1,0,0,0,0,0
,0,0,0,0,0,0,0],[126,-63,-2,1,0,-2,1,1,-E(15)-E(15)^2-E(15)^4-E(15)^8,
-E(15)^7-E(15)^11-E(15)^13-E(15)^14,0,0,0,0,-3,6,-3,0,1,-2,1,
-E(15)^7-E(15)^11-E(15)^13-E(15)^14,1,-E(15)-E(15)^2-E(15)^4-E(15)^8,
-E(15)-E(15)^2-E(15)^4-E(15)^8,1,-E(15)^7-E(15)^11-E(15)^13-E(15)^14,0,0,0,0,0
,0,0,0,0,0,0,0],
[GALOIS,[31,7]],
[GALOIS,[33,7]],
[GALOIS,[32,7]],[168,-84,8,-4,0,0,0,-2,1,1,0,0,0,0,6,-9,3,0,2,-1,-1,1,1,-2,1,
1,-2,0,0,0,0,0,0,0,0,0,0,0,0],[168,-84,8,-4,0,0,0,-2,1,1,0,0,0,0,-9,3,6,0,-1,
-1,2,1,-2,1,1,-2,1,0,0,0,0,0,0,0,0,0,0,0,0],[168,-84,8,-4,0,0,0,-2,1,1,0,0,0,0
,3,6,-9,0,-1,2,-1,-2,1,1,-2,1,1,0,0,0,0,0,0,0,0,0,0,0,0]],
[(15,16,17)(19,20,21)(22,23,24)(25,26,27),
(11,13)(12,14)(28,33,29,31,30,32)(38,39),( 9,10)(22,25)(23,26)(24,27),
( 9,10)(22,25)(23,26)(24,27)(28,30,29)(31,33,32),(28,30,29)(31,33,32)]);
ALF("3.L3(4).3.2_2","L3(4).3.2_2",[1,1,2,2,3,4,4,5,5,5,6,6,7,7,8,8,8,9,10,
10,10,11,11,11,12,12,12,13,13,13,14,14,14,15,16,17,18,19,20]);
ALF("3.L3(4).3.2_2","L6(2)",[1,5,3,14,7,10,29,13,39,40,20,41,21,42,5,7,6,
27,14,18,17,39,37,38,40,36,38,57,55,59,58,56,60,4,12,19,26,32,33],[
"fusion map is unique up to table autom.,\n",
"representative compatible with Brauer tables"
]);

MOT("3.L3(4).3.2_3",
[
"constructed using `CharacterTableOfTypeGS3'"
],
[362880,181440,1152,576,54,96,48,90,45,90,45,63,63,63,540,540,540,63,36,36,36,
45,45,45,45,45,45,63,63,63,63,63,63,120,6,16,16,10,10],
[,[1,2,1,2,5,3,4,10,11,8,9,12,14,13,15,16,17,18,15,16,17,25,26,27,22,23,24,31,
32,33,28,29,30,1,5,6,6,10,8],[1,1,3,3,1,6,6,10,10,8,8,12,12,12,1,1,1,2,3,3,3,
10,10,10,8,8,8,14,14,14,13,13,13,34,34,36,37,39,38],,[1,2,3,4,5,6,7,1,2,1,2,12
,13,14,15,16,17,18,19,20,21,15,16,17,15,16,17,30,28,29,33,31,32,34,35,36,37,34
,34],,[1,2,3,4,5,6,7,10,11,8,9,1,2,2,15,16,17,18,19,20,21,25,26,27,22,23,24,18
,18,18,18,18,18,34,35,36,37,39,38]],
0,
[(36,37),(15,16,17)(19,20,21)(22,23,24)(25,26,27),(8,10)(9,11)(22,25)(23,26)(
24,27)(38,39),(28,29,30)(31,32,33),(13,14)(28,31)(29,32)(30,33)],
["ConstructGS3","3.L3(4).2_3","3.L3(4).3",[5,6,15],[[2,3],[5,6],[8,11],[10,12]
,[9,13],[15,16],[18,19],[21,22],[25,28],[27,29],[26,30],[34,37],[36,38],[35,39
],[31,40],[33,41],[32,42],[43,46],[45,47],[44,48],[49,52],[51,53],[50,54],[55,
58],[57,59],[56,60]],[[1,1],[4,3],[14,9],[17,11],[20,13]],(1,7,11,20,26,35,13,
24,34,12,22,33,5,6,9,14,23,32,4,3,21,31,2,8,10,17,29,38,18,25,36,15,28,39,19,
27,37,16,30)]);
ALF("3.L3(4).3.2_3","L3(4).3.2_3",[1,1,2,2,3,4,4,5,5,6,6,7,7,7,8,8,8,9,10,
10,10,11,11,11,12,12,12,13,13,13,14,14,14,15,16,17,18,19,20]);

MOT("2^2.L3(4).2^2",
[
"constructed using `PossibleCharacterTablesOfTypeMGA'"
],
[322560,322560,161280,1024,1024,512,144,144,72,128,128,64,64,40,40,20,56,56,28
,288,32,144,144,72,64,64,32,32,32,32,32,1344,1344,64,64,24,24,16,28,28,480,480
,24,24,32,64,64,20,20],
[,[1,1,1,1,1,1,7,7,7,5,5,6,6,14,14,14,17,17,17,1,4,7,7,7,10,10,10,12,12,12,12,
1,2,5,4,7,8,11,17,18,1,2,7,8,10,10,10,14,15],[1,2,3,4,5,6,1,2,3,10,11,12,13,14
,15,16,17,18,19,20,21,20,20,20,26,25,27,30,31,28,29,32,33,34,35,32,33,38,39,40
,41,42,41,42,45,47,46,48,49],,[1,2,3,4,5,6,7,8,9,10,11,12,13,1,2,3,17,18,19,20
,21,22,23,24,26,25,27,30,31,28,29,32,33,34,35,36,37,38,39,40,41,42,43,44,45,47
,46,41,42],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,1,2,3,20,21,22,23,24,25,26
,27,28,29,30,31,32,33,34,35,36,37,38,32,33,41,42,43,44,45,46,47,48,49]],
0,
[(25,26)(28,29)(30,31),(28,31)(29,30)(46,47),(22,23)(28,31)(29,30)(46,47)],
["ConstructMGA","2^2.L3(4).2_1","2.L3(4).(2^2)_{123}",[[25,35],[26,36],[27,37]
,[28,38],[29,39],[30,40],[31,42],[32,41],[33,43],[34,44]],()]);
ALF("2^2.L3(4).2^2","2.L3(4).(2^2)_{123}",[1,1,2,3,3,4,5,5,6,7,8,9,9,10,
10,11,12,12,13,14,15,16,16,17,18,18,19,20,20,21,21,22,23,24,25,26,27,28,
29,30,31,32,33,34,35,36,37,38,39]);
ALF("2^2.L3(4).2^2","L3(4).2^2",[1,1,1,2,2,2,3,3,3,4,4,5,5,6,6,6,7,7,7,8,
9,10,10,10,11,11,11,12,12,12,12,13,13,14,14,15,15,16,17,17,18,18,19,19,20,
21,21,22,22]);
ALF("2^2.L3(4).2^2","2^2.L3(4).D12",[1,2,2,3,4,4,5,6,6,7,8,7,8,9,10,10,11,
12,12,13,14,15,16,16,17,18,19,17,19,18,19,28,29,30,31,32,33,34,35,36,37,
38,39,40,41,42,43,44,45]);

MOT("2^2.L3(4).6",
[
"constructed using `PossibleCharacterTablesOfTypeMGA'"
],
[483840,161280,1536,512,216,72,64,64,60,20,84,28,432,48,216,72,32,32,32,32,360
,360,126,126,24,24,15,15,21,21,36,36,18,18,12,12],
[,[1,1,1,1,5,5,4,4,9,9,11,11,1,3,5,5,7,7,7,7,22,21,24,23,22,21,28,27,30,29,22,
21,24,23,26,25],[1,2,3,4,1,2,7,8,9,10,11,12,13,14,13,13,18,17,20,19,1,1,1,1,3,
3,9,9,11,11,13,13,13,13,14,14],,[1,2,3,4,5,6,7,8,1,2,11,12,13,14,15,16,18,17,
20,19,22,21,24,23,26,25,22,21,30,29,32,31,34,33,36,35],,[1,2,3,4,5,6,7,8,9,10,
1,2,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,23,24,31,32,33,34,35,36]],
0,
[(19,20),(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36),
(17,18)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36)],
["ConstructMGA","2^2.L3(4).2_1","L3(4).6",[[15,25,35],[16,26,36],[17,27,37],[
18,28,38],[19,29,39],[20,30,40],[21,31,41],[22,32,42],[23,33,43],[24,34,44]],
()]);
ALF("2^2.L3(4).6","L3(4).6",[1,1,2,2,3,3,4,4,5,5,6,6,7,8,9,9,10,10,10,
10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26]);
ALF("2^2.L3(4).6","2^2.L3(4).D12",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,
17,18,19,19,20,20,21,21,22,22,23,23,24,24,25,25,26,26,27,27]);

MOT("2^2.L3(4).D12",
[
"constructed using `CharacterTableOfTypeGS3'"
],
[967680,322560,3072,1024,432,144,128,128,120,40,168,56,864,96,432,144,64,64,32
,360,126,24,15,21,36,18,12,1344,1344,64,64,24,24,16,28,28,480,480,24,24,32,64,
64,20,20],
[,[1,1,1,1,5,5,4,4,9,9,11,11,1,3,5,5,7,7,7,20,21,20,23,24,20,21,22,1,2,4,3,5,6
,8,11,12,1,2,5,6,7,7,7,9,10],[1,2,3,4,1,2,7,8,9,10,11,12,13,14,13,13,18,17,19,
1,1,3,9,11,13,13,14,28,29,30,31,28,29,34,35,36,37,38,37,38,41,43,42,44,45],,[1
,2,3,4,5,6,7,8,1,2,11,12,13,14,15,16,18,17,19,20,21,22,20,24,25,26,27,28,29,30
,31,32,33,34,35,36,37,38,39,40,41,43,42,37,38],,[1,2,3,4,5,6,7,8,9,10,1,2,13,
14,15,16,17,18,19,20,21,22,23,21,25,26,27,28,29,30,31,32,33,34,28,29,37,38,39,
40,41,42,43,44,45]],
0,
[(17,18)(42,43)],
["ConstructGS3","2^2.L3(4).2^2","2^2.L3(4).6",[9,10,11,12,23,24,25,26,27,28,29
,30,31,32,33,34,35,36,37,38,39],[[3,5],[2,6],[9,11],[8,12],[16,17],[19,20],[23
,25],[22,26]],[[1,1],[4,3],[7,5],[10,7],[15,15],[18,17],[21,19],[24,21]],
( 1,13,37,12,36,11,35, 8,32, 5,29,25, 9,33, 6,30)( 2,14,38,17,41,21,45,28,26,
 19,43,24,10,34, 7,31)( 3,15,39,18,42,23)( 4,16,40,20,44,27,22)
]);
ALF("2^2.L3(4).D12","L3(4).D12",[1,1,2,2,3,3,4,4,5,5,6,6,7,8,9,9,10,10,10,
11,12,13,14,15,16,17,18,19,19,20,20,21,21,22,23,23,24,24,25,25,26,27,27,
28,28]);
ALF("2^2.L3(4).D12","He.2",[1,2,2,3,4,10,7,8,9,16,12,19,27,28,29,30,32,33,
34,4,5,10,21,25,30,31,36,2,6,7,6,10,17,15,19,26,27,28,30,36,34,33,32,35,
40]);

LIBTABLE.LOADSTATUS.ctoline3:="userloaded";

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