Impressum ctounit4.tbl   Sprache: unbekannt

#############################################################################
##
#W  ctounit4.tbl                GAP table library               Thomas Breuer
##
##  This file contains the ordinary character tables related to the unitary
##  group $U_6(2)$ of the ATLAS.
##
#H  ctbllib history
#H  ---------------
#H  $Log: ctounit4.tbl,v $
#H  Revision 4.29  2012/03/12 17:01:48  gap
#H  omit the fourth argument of `ConstructV4G'
#H      TB
#H
#H  Revision 4.28  2012/03/02 08:20:42  gap
#H  added fusion 3.U6(2).3.2 -> U6(2).3.2
#H      TB
#H
#H  Revision 4.27  2012/01/30 08:32:05  gap
#H  removed #H entries from the headers
#H      TB
#H
#H  Revision 4.26  2012/01/26 11:18:40  gap
#H  added missing table automorphisms
#H      TB
#H
#H  Revision 4.25  2011/09/28 14:20:19  gap
#H  - removed revision entry and SET_TABLEFILENAME call,
#H  - added fusion (2^2x3).U6(2).2 -> 6.Fi22.2
#H      TB
#H
#H  Revision 4.24  2010/05/05 13:20:09  gap
#H  - added many class fusions,
#H  - changed several class fusions according to consistency conditions,
#H    after systematic checks of consistency
#H    - with Brauer tables w.r.t. the restriction of characters,
#H    - of subgroup fusions with the corresponding subgroup fusions between
#H      proper factors where the factor fusions are stored,
#H    - of subgroup fusions from maximal subgroups with subgroup fusions of
#H      extensions inside automorphic extensions
#H
#H      TB
#H
#H  Revision 4.23  2010/01/19 17:05:36  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 4.22  2009/01/12 17:33:58  gap
#H  added missing maxes of Fi22.2 and their fusions
#H      TB
#H
#H  Revision 4.21  2007/07/03 08:36:55  gap
#H  2.U6(2).2 is Fi22.2M2,
#H  adjusted the factor fusion (2^2x3).U6(2) -> 3.U6(2)
#H      TB
#H
#H  Revision 4.20  2005/10/19 12:59:44  gap
#H  added table of (2^2x3).U6(2).3
#H      TB
#H
#H  Revision 4.19  2005/09/12 08:34:45  gap
#H  added table of (2^2x3).U6(2).2
#H      TB
#H
#H  Revision 4.18  2005/08/10 14:38:27  gap
#H  added fusions (2^2x3).U6(2) -> 2.U6(2) and (2^2x3).U6(2) -> U6(2)
#H      TB
#H
#H  Revision 4.17  2004/08/31 12:33:34  gap
#H  added tables of 4.L2(25).2_3,
#H                  L2(49).2^2,
#H                  L2(81).2^2,
#H                  L2(81).(2x4),
#H                  3.L3(4).3.2_2,
#H                  L3(9).2^2,
#H                  L4(4).2^2,
#H                  2x2^3:L3(2)x2,
#H                  (2xA6).2^2,
#H                  2xL2(11).2,
#H                  S3xTh,
#H                  41:40,
#H                  7^(1+4):(3x2.S7),
#H                  7xL2(8),
#H                  (7xL2(8)).3,
#H                  O7(3)N3A,
#H                  O8+(3).2_1',
#H                  O8+(3).2_1'',
#H                  O8+(3).2_2',
#H                  O8+(3).(2^2)_{122},
#H                  S4(9),
#H                  S4(9).2_i,
#H                  2.U4(3).2_2',
#H                  2.U4(3).(2^2)_{133},
#H                  2.U4(3).D8,
#H                  3.U6(2).S3,
#H  added fusions 3.A6.2_i -> 3.A6.2^2,
#H                L2(49).2_i -> L2(49).2^2,
#H                L3(9).2_i -> L3(9).2^2,
#H                L4(4).2_i -> L4(4).2^2,
#H                G2(3) -> O7(3),
#H                L2(17) -> S8(2),
#H                2.L3(4).2_2 -> 2.M22.2
#H                3.L3(4).2_2 -> 3.L3(4).3.2_2
#H                3.L3(4).3 -> 3.L3(4).3.2_2
#H                2^5:S6 -> 2.M22.2
#H                O8+(3) -> O8+(3).2_1',
#H                O8+(3) -> O8+(3).2_1'',
#H                O8+(3) -> O8+(3).2_2',
#H                O8+(3) -> O8+(3).(2^2)_{122},
#H                O8+(3).2_1 -> O8+(3).(2^2)_{122},
#H                O8+(3).2_2 -> O8+(3).(2^2)_{122},
#H                2.U4(3) -> 2.U4(3).2_2',
#H                2.U4(3).2_1 -> 2.U4(3).(2^2)_{133},
#H                2.U4(3).2_2 -> O7(3),
#H                2.U4(3).2_2' -> U4(3).2_2,
#H                2.U4(3).2_3 -> 2.U4(3).(2^2)_{133},
#H                2.U4(3).2_3' -> 2.U4(3).(2^2)_{133},
#H                2.U4(3).4 -> 2.U4(3).D8,
#H                3.U6(2).2 -> 3.U6(2).S3,
#H                3.U6(2).3 -> 3.U6(2).S3,
#H  replaced table of psl(3,4):d12 by L3(4).D12,
#H  changed table of O8+(3).S4 to a construction table,
#H  changed encoding of the table of 12.A6.2_3,
#H  added maxes of Sz(8), Sz(8).3,
#H      TB
#H
#H  Revision 4.16  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 4.15  2002/10/22 12:44:16  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 4.14  2002/09/30 13:21:22  gap
#H  added fusions 2^2.U6(2).2 -> U6(2).2, 2^2.U6(2).3.2 -> U6(2).3.2
#H  (in order to make the automatic computation of the 2-modular table work)
#H      TB
#H
#H  Revision 4.13  2002/09/23 15:08:54  gap
#H  removed trailing blanks
#H      TB
#H
#H  Revision 4.12  2002/09/18 15:22:02  gap
#H  changed the `text' components of many fusions,
#H  in order to use them as a status information (for evaluation)
#H      TB
#H
#H  Revision 4.11  2002/08/21 13:53:52  gap
#H  removed names of the form `c1m<n>', `c2m<n>', `c3m<n>'
#H      TB
#H
#H  Revision 4.10  2002/07/12 06:45:57  gap
#H  further tidying up: removed `irredinfo' stuff, rearranged constructions
#H      TB
#H
#H  Revision 4.9  2002/07/08 16:06:57  gap
#H  changed `construction' component from function (call) to list of function
#H  name and arguments
#H      TB
#H
#H  Revision 4.8  2001/05/04 16:50:46  gap
#H  first revision for ctbllib
#H
#H
#H  tbl history (GAP 4)
#H  -------------------
#H  (Rev. 4.8 of ctbllib coincides with Rev. 4.7 of tbl in GAP 4)
#H  
#H  RCS file: /gap/CVS/GAP/4.0/tbl/ctounit4.tbl,v
#H  Working file: ctounit4.tbl
#H  head: 4.7
#H  branch:
#H  locks: strict
#H  access list:
#H  symbolic names:
#H   GAP4R2: 4.3.0.6
#H   GAP4R2PRE2: 4.3.0.4
#H   GAP4R2PRE1: 4.3.0.2
#H   GAP4R1: 4.2.0.2
#H  keyword substitution: kv
#H  total revisions: 9; selected revisions: 9
#H  description:
#H  ----------------------------
#H  revision 4.7
#H  date: 2000/04/03 11:06:50;  author: gap;  state: Exp;  lines: +21 -2
#H  added tables of 6.U6(2)M3 and (2^2x3).U6(2)M3 (constructed for Eamonn)
#H  
#H      TB
#H  ----------------------------
#H  revision 4.6
#H  date: 2000/03/30 12:39:35;  author: gap;  state: Exp;  lines: +4 -4
#H  inserted a crucial comma that had been lost for some strange reason
#H  
#H      TB
#H  ----------------------------
#H  revision 4.5
#H  date: 2000/03/13 16:24:09;  author: gap;  state: Exp;  lines: +236 -14
#H  added table of (2^2x3).U6(2)
#H  
#H      TB
#H  ----------------------------
#H  revision 4.4
#H  date: 2000/03/09 08:41:47;  author: gap;  state: Exp;  lines: +15 -5
#H  added fusion 6.U6(2) -> 3.Fi22 (needed for the construction of
#H  the table of (3x2^2).U6(2) < 6.Fi22)
#H  
#H      TB
#H  ----------------------------
#H  revision 4.3
#H  date: 1999/09/17 14:09:43;  author: gap;  state: Exp;  lines: +23 -491
#H  encoded table of `2^2.U6(2).S3' via `ConstructGS3'
#H  
#H      TB
#H  ----------------------------
#H  revision 4.2
#H  date: 1999/07/14 11:39:43;  author: gap;  state: Exp;  lines: +4 -3
#H  cosmetic changes for the release ...
#H  
#H      TB
#H  ----------------------------
#H  revision 4.1
#H  date: 1997/07/17 15:48:44;  author: fceller;  state: Exp;  lines: +2 -2
#H  for version 4
#H  ----------------------------
#H  revision 1.2
#H  date: 1997/04/03 15:47:05;  author: sam;  state: Exp;  lines: +4 -18
#H  improved a 'construction' component (now calls 'ConstructMGA'
#H      instead of several library functions)
#H  ----------------------------
#H  revision 1.1
#H  date: 1996/10/21 16:02:14;  author: sam;  state: Exp;
#H  first proposal of the table library
#H  ==========================================================================
##

MOT("2.U6(2)",
[
"origin: ATLAS of finite groups, tests: 1.o.r."
],
[18393661440,18393661440,26542080,26542080,294912,294912,36864,155520,155520,
93312,93312,3888,3888,55296,6144,3072,3072,1536,1536,1536,1536,256,60,60,
10368,10368,10368,10368,3456,3456,1152,1152,576,576,432,432,144,144,144,144,
14,14,64,64,64,32,32,108,108,108,108,54,54,20,20,22,22,22,22,864,864,288,288,
96,96,96,96,48,48,48,48,30,30,36,36,36,36],
[,[1,1,1,1,1,1,1,8,8,10,10,12,12,3,3,5,5,6,6,5,5,5,23,23,10,10,10,10,8,8,10,
10,8,8,12,12,12,12,12,12,41,41,15,16,16,18,19,50,50,48,48,52,52,23,23,58,58,
56,56,27,25,29,29,27,25,31,31,32,32,33,33,72,72,50,50,48,48],[1,2,3,4,5,6,7,1,
2,1,2,1,2,14,15,16,17,18,19,20,21,22,23,24,3,4,3,4,3,4,5,6,5,6,3,4,5,6,7,7,41,
42,43,44,45,46,47,10,11,10,11,10,11,54,55,56,57,58,59,14,14,14,14,15,15,16,17,
18,19,20,21,23,24,25,26,27,28],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,
19,20,21,22,1,2,27,28,25,26,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,
45,46,47,50,51,48,49,52,53,3,4,56,57,58,59,61,60,62,63,65,64,66,67,68,69,70,
71,8,9,76,77,74,75],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,
22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,1,2,43,44,45,46,47,
48,49,50,51,52,53,54,55,58,59,56,57,60,61,62,63,64,65,66,67,68,69,70,71,72,73,
74,75,76,77],,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,
24,27,28,25,26,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,50,51,
48,49,52,53,54,55,1,2,1,2,61,60,62,63,65,64,66,67,68,69,70,71,72,73,76,77,74,
75]],
0,
[(56,58)(57,59),(25,27)(26,28)(48,50)(49,51)(60,61)(64,65)(74,76)(75,77),
(18,19)(46,47)(68,69)],
["ConstructProj",[["U6(2)",[]],["2.U6(2)",[]]]]);
ARC("2.U6(2)","maxes",["2xU5(2)","2.2^(1+8)_+:U4(2)","2.U6(2)M3",
"2xU4(3).2_2","2.U4(3).2_2","2.U6(2)M6","2.2^(4+8):(S3xA5)","2xS6(2)",
"2.U6(2)M9","2.U6(2)M10","2xM22","2.M22","2.U6(2)M13","2xS3xU4(2)",
"2.(3^(1+4).[2^7.3])","2.L3(4).2_1"]);
ALF("2.U6(2)","U6(2)",[1,1,2,2,3,3,4,5,5,6,6,7,7,8,9,10,10,11,12,13,13,14,
15,15,16,16,17,17,18,18,19,19,20,20,21,21,22,22,23,23,24,24,25,26,26,27,
28,29,29,30,30,31,31,32,32,33,33,34,34,35,36,37,37,38,39,40,40,41,42,43,
43,44,44,45,45,46,46]);
ALF("2.U6(2)","2.U6(2).2",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,
18,19,20,21,22,23,24,25,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,
40,41,42,43,43,44,45,44,45,46,47,48,49,50,51,50,51,52,52,53,54,55,55,56,
57,58,58,59,60,61,62,63,64,63,64]);
ALF("2.U6(2)","Fi22",[1,2,3,2,3,4,4,5,15,6,16,7,19,9,11,9,11,12,12,13,10,
13,14,34,17,16,17,16,18,15,17,21,18,20,23,19,23,24,22,24,26,51,29,27,28,
30,30,31,55,31,56,32,57,35,34,36,61,37,62,38,38,39,40,45,45,38,45,42,43,
46,41,52,65,58,56,58,55],[
"fusion is unique up to table automorphisms"
]);
ALN("2.U6(2)",["2.U6(2).2M1","Fi22C2A","Fi22N2A"]);

MOT("2.U6(2).2",
[
"origin: ATLAS of finite groups"
],
[36787322880,36787322880,53084160,53084160,589824,589824,73728,311040,311040,
186624,186624,7776,7776,110592,12288,6144,6144,1536,3072,3072,512,120,120,
10368,10368,6912,6912,2304,2304,1152,1152,864,864,288,288,288,288,28,28,128,
128,128,32,108,108,108,108,40,40,22,22,864,576,576,96,192,192,48,96,96,60,60,
36,36,5806080,5806080,92160,92160,18432,18432,6144,6144,1536,1536,8640,8640,
2592,2592,576,576,432,432,144,144,384,384,192,128,128,120,120,40,40,576,576,
288,288,192,192,144,144,48,48,28,28,32,32,36,36,48,48,48,48,60,60],
[,[1,1,1,1,1,1,1,8,8,10,10,12,12,3,3,5,5,6,5,5,5,22,22,10,10,8,8,10,10,8,8,12,
12,12,12,12,12,38,38,15,16,16,18,44,44,46,46,22,22,50,50,24,26,26,24,28,28,29,
30,30,61,61,44,44,1,1,1,1,5,5,5,5,5,5,8,8,10,10,8,8,12,12,12,12,14,14,17,16,
16,22,22,22,22,30,30,28,28,30,30,34,34,34,34,38,38,40,40,46,46,53,53,57,57,61,
61],[1,2,3,4,5,6,7,1,2,1,2,1,2,14,15,16,17,18,19,20,21,22,23,3,4,3,4,5,6,5,6,
3,4,5,6,7,7,38,39,40,41,42,43,10,11,10,11,48,49,50,51,14,14,14,15,16,17,18,19,
20,22,23,24,25,65,66,67,68,69,70,71,72,73,74,65,66,65,66,67,68,65,66,67,68,85,
86,87,88,89,90,91,92,93,69,70,69,70,71,72,69,70,73,74,104,105,106,107,77,78,
85,86,87,87,90,91],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,1,
2,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,3,4,
50,51,52,53,54,55,56,57,58,59,60,8,9,63,64,65,66,67,68,69,70,71,72,73,74,75,
76,77,78,79,80,81,82,83,84,85,86,87,88,89,65,66,67,68,94,95,96,97,98,99,100,
101,102,103,104,105,107,106,108,109,110,111,113,112,75,76],,[1,2,3,4,5,6,7,8,
9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,
35,36,37,1,2,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,
61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,
87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,65,66,107,106,108,109,
110,111,113,112,114,115],,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,
20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,
46,47,48,49,1,2,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,
72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,
98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115]],
0,
[(112,113),(106,107),(106,107)(112,113),( 65, 66)( 67, 68)( 69, 70)( 71, 72)
( 73, 74)( 75, 76)( 77, 78)( 79, 80)( 81, 82)( 83, 84)( 85, 86)( 90, 91)
( 92, 93)( 94, 95)( 96, 97)( 98, 99)(100,101)(102,103)(104,105)(108,109)
(110,111)(114,115)],
["ConstructProj",[["U6(2).2",[]],["2.U6(2).2",[]]]]);
ALF("2.U6(2).2","U6(2).2",[1,1,2,2,3,3,4,5,5,6,6,7,7,8,9,10,10,11,12,12,
13,14,14,15,15,16,16,17,17,18,18,19,19,20,20,21,21,22,22,23,24,24,25,26,
26,27,27,28,28,29,29,30,31,31,32,33,33,34,35,35,36,36,37,37,38,38,39,39,
40,40,41,41,42,42,43,43,44,44,45,45,46,46,47,47,48,48,49,50,51,52,52,53,
53,54,54,55,55,56,56,57,57,58,58,59,59,60,61,62,62,63,63,64,64,65,65]);
ALF("2.U6(2).2","Fi22.2",[1,2,3,2,3,4,4,5,15,6,16,7,19,9,11,9,11,12,13,10,
13,14,34,17,16,18,15,17,21,18,20,23,19,23,24,22,24,26,48,29,27,28,30,31,
51,32,52,35,34,36,56,37,38,39,43,37,43,41,44,40,49,59,53,51,60,62,61,62,
65,63,65,64,65,66,68,71,70,74,73,71,72,78,77,78,80,79,81,79,80,83,84,85,
84,91,86,92,87,91,90,93,89,93,94,96,97,98,98,100,101,105,104,106,107,109,
110],[
"fusion map is unique up to table automorphisms"
]);

MOT("Isoclinic(2.U6(2).2)",
[
"isoclinic group of the 2.U6(2).2 given in the ATLAS"
],
0,
0,
0,
[(112,113),(106,107),(65,66)(67,68)(69,70)(71,72)(73,74)(75,76)(77,78)(79,80)
(81,82)(83,84)(85,86)(90,91)(92,93)(94,95)(96,97)(98,99)(100,101)(102,103)
(104,105)(108,109)(110,111)(114,115)],
["ConstructIsoclinic",[["2.U6(2).2"]]]);
ALF("Isoclinic(2.U6(2).2)","U6(2).2",[1,1,2,2,3,3,4,5,5,6,6,7,7,8,9,10,10,
11,12,12,13,14,14,15,15,16,16,17,17,18,18,19,19,20,20,21,21,22,22,23,24,
24,25,26,26,27,27,28,28,29,29,30,31,31,32,33,33,34,35,35,36,36,37,37,38,
38,39,39,40,40,41,41,42,42,43,43,44,44,45,45,46,46,47,47,48,48,49,50,51,
52,52,53,53,54,54,55,55,56,56,57,57,58,58,59,59,60,61,62,62,63,63,64,64,
65,65]);

MOT("2^2.U6(2)",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11]"
],
[36787322880,36787322880,36787322880,36787322880,53084160,53084160,53084160,
53084160,589824,589824,589824,589824,36864,311040,311040,311040,311040,186624,
186624,186624,186624,7776,7776,7776,7776,55296,6144,3072,3072,3072,3072,3072,
3072,3072,3072,3072,3072,256,120,120,120,120,20736,20736,20736,20736,20736,
20736,20736,20736,6912,6912,6912,6912,2304,2304,2304,2304,1152,1152,1152,1152,
864,864,864,864,288,288,288,288,288,288,288,288,28,28,28,28,64,64,64,64,64,64,
64,216,216,216,216,216,216,216,216,108,108,108,108,40,40,40,40,44,44,44,44,44,
44,44,44,864,864,576,576,576,576,96,96,96,96,96,96,96,96,96,96,96,96,60,60,60,
60,72,72,72,72,72,72,72,72],
[,[1,1,1,1,1,1,1,1,1,1,1,1,1,14,14,14,14,18,18,18,18,22,22,22,22,5,5,10,10,11,
11,12,12,9,9,9,9,9,39,39,39,39,18,18,18,18,18,18,18,18,14,14,14,14,18,18,18,
18,14,14,14,14,22,22,22,22,22,22,22,22,22,22,22,22,75,75,75,75,27,28,28,30,30,
32,32,90,90,90,90,86,86,86,86,94,94,94,94,39,39,39,39,106,106,106,106,102,102,
102,102,47,43,51,51,51,51,47,43,56,56,57,57,58,58,59,59,59,59,128,128,128,128,
90,90,90,90,86,86,86,86],[1,2,3,4,5,6,7,8,9,10,11,12,13,1,2,3,4,1,2,3,4,1,2,3,
4,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,5,6,7,8,5,6,7,8,5,6,7,8,
9,10,11,12,9,10,11,12,5,6,7,8,9,10,11,12,13,13,13,13,75,76,77,78,79,80,81,82,
83,84,85,18,19,20,21,18,19,20,21,18,19,20,21,98,99,100,101,102,103,104,105,
106,107,108,109,26,26,26,26,26,26,27,27,28,29,30,31,32,33,34,35,36,37,39,40,
41,42,43,44,45,46,47,48,49,50],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,
19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,1,2,3,4,47,48,49,
50,43,44,45,46,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,
72,73,74,75,76,77,78,79,80,81,82,83,84,85,90,91,92,93,86,87,88,89,94,95,96,97,
5,6,7,8,102,103,104,105,106,107,108,109,111,110,112,113,114,115,117,116,118,
119,120,121,122,123,124,125,126,127,14,15,16,17,136,137,138,139,132,133,134,
135],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,
27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,
53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,1,2,3,4,79,
80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,106,107,
108,109,102,103,104,105,110,111,112,113,114,115,116,117,118,119,120,121,122,
123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139],,,,[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,
31,32,33,34,35,36,37,38,39,40,41,42,47,48,49,50,43,44,45,46,51,52,53,54,55,56,
57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,
83,84,85,90,91,92,93,86,87,88,89,94,95,96,97,98,99,100,101,1,2,3,4,1,2,3,4,
111,110,112,113,114,115,117,116,118,119,120,121,122,123,124,125,126,127,128,
129,130,131,136,137,138,139,132,133,134,135]],
0,
[(102,106)(103,107)(104,108)(105,109),( 43, 47)( 44, 48)( 45, 49)( 46, 50)
( 86, 90)( 87, 91)( 88, 92)( 89, 93)(110,111)(116,117)(132,136)(133,137)
(134,138)(135,139),(  3,  4)(  7,  8)( 11, 12)( 16, 17)( 20, 21)( 24, 25)
( 30, 32)( 31, 33)( 36, 37)( 41, 42)( 45, 46)( 49, 50)( 53, 54)( 57, 58)
( 61, 62)( 65, 66)( 69, 70)( 73, 74)( 77, 78)( 82, 84)( 83, 85)( 88, 89)
( 92, 93)( 96, 97)(100,101)(104,105)(108,109)(114,115)(120,122)(121,123)
(126,127)(130,131)(134,135)(138,139),(  2,  3)(  6,  7)( 10, 11)( 15, 16)
( 19, 20)( 23, 24)( 28, 30)( 29, 31)( 35, 36)( 40, 41)( 44, 45)( 48, 49)
( 52, 53)( 56, 57)( 60, 61)( 64, 65)( 68, 69)( 72, 73)( 76, 77)( 80, 82)
( 81, 83)( 87, 88)( 91, 92)( 95, 96)( 99,100)(103,104)(107,108)(113,114)
(118,120)(119,121)(125,126)(129,130)(133,134)(137,138)],
["ConstructV4G","2.U6(2)",(  2,  3,  4)(  6,  7,  8)( 10, 11, 12)
    ( 15, 16, 17)( 19, 20, 21)( 23, 24, 25)( 28, 30, 32)( 29, 31, 33)( 35,
    36, 37)( 40, 41, 42)( 44, 45, 46)( 48, 49, 50)( 52, 53, 54)( 56, 57, 58)
    ( 60, 61, 62)( 64, 65, 66)( 68, 69, 70)( 72, 73, 74)( 76, 77, 78)( 80,
    82, 84)( 81, 83, 85)( 87, 88, 89)( 91, 92, 93)( 95, 96, 97)( 99,100,101)
    (103,104,105)(107,108,109)(113,114,115)(118,120,122)(119,121,123)(125,126,
    127)(129,130,131)(133,134,135)(137,138,139)]);
ALF("2^2.U6(2)","2.U6(2)",[1,1,2,2,3,3,4,4,5,5,6,6,7,8,8,9,9,10,10,11,11,
12,12,13,13,14,15,16,17,18,18,19,19,20,20,21,21,22,23,23,24,24,25,25,26,
26,27,27,28,28,29,29,30,30,31,31,32,32,33,33,34,34,35,35,36,36,37,37,38,
38,39,39,40,40,41,41,42,42,43,44,45,46,46,47,47,48,48,49,49,50,50,51,51,
52,52,53,53,54,54,55,55,56,56,57,57,58,58,59,59,60,61,62,62,63,63,64,65,
66,67,68,68,69,69,70,70,71,71,72,72,73,73,74,74,75,75,76,76,77,77]);
ALF("2^2.U6(2)","U6(2)",[1,1,1,1,2,2,2,2,3,3,3,3,4,5,5,5,5,6,6,6,6,7,7,7,
7,8,9,10,10,11,11,12,12,13,13,13,13,14,15,15,15,15,16,16,16,16,17,17,17,
17,18,18,18,18,19,19,19,19,20,20,20,20,21,21,21,21,22,22,22,22,23,23,23,
23,24,24,24,24,25,26,26,27,27,28,28,29,29,29,29,30,30,30,30,31,31,31,31,
32,32,32,32,33,33,33,33,34,34,34,34,35,36,37,37,37,37,38,39,40,40,41,41,
42,42,43,43,43,43,44,44,44,44,45,45,45,45,46,46,46,46]);
ALF("2^2.U6(2)","2^2.U6(2).3",[1,2,2,2,3,4,4,4,5,6,6,6,7,8,9,9,9,10,11,11,
11,12,13,13,13,14,15,16,17,16,17,16,17,18,19,19,19,20,21,22,22,22,23,24,
24,24,25,26,26,26,27,28,28,28,29,30,30,30,31,32,32,32,33,34,34,34,35,36,
36,36,37,38,38,38,39,40,40,40,41,42,43,42,43,42,43,44,45,45,45,46,47,47,
47,48,49,49,49,50,51,51,51,52,53,53,53,54,55,55,55,56,57,58,59,59,59,60,
61,62,63,62,63,62,63,64,65,65,65,66,67,67,67,68,69,69,69,70,71,71,71],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);
ALF("2^2.U6(2)","2^2.U6(2).2",[1,2,3,3,4,5,6,6,7,8,9,9,10,11,12,13,13,14,
15,16,16,17,18,19,19,20,21,22,23,24,25,24,25,26,27,28,28,29,30,31,32,32,
33,34,35,36,33,34,36,35,37,38,39,39,40,41,42,42,43,44,45,45,46,47,48,48,
49,50,51,51,52,53,54,54,55,56,57,57,58,59,60,61,62,61,62,63,64,65,66,63,
64,66,65,67,68,69,69,70,71,72,72,73,74,75,76,73,74,76,75,77,77,78,79,80,
80,81,81,82,83,84,85,84,85,86,87,88,88,89,90,91,91,92,93,94,95,92,93,95,
94],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("2^2.U6(2)","2.Fi22",[1,2,3,4,6,5,4,3,5,6,7,7,7,8,9,25,26,10,11,27,28,
12,13,33,34,16,19,16,19,20,21,20,21,22,22,18,17,22,23,24,59,60,30,29,28,
27,30,29,28,27,32,31,26,25,29,30,36,37,31,32,35,35,41,40,34,33,40,41,42,
43,39,38,43,42,46,47,89,90,50,48,49,52,51,51,52,53,54,95,96,53,54,97,98,
55,56,99,100,62,61,60,59,63,64,107,108,65,66,109,110,67,67,68,69,70,70,79,
79,67,79,74,73,76,75,80,80,72,71,91,92,113,114,102,101,98,97,102,101,96,
95],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALN("2^2.U6(2)",["V4.U6(2)"]);

MOT("2^2.U6(2).2",
[
"origin: ATLAS of finite groups,\n",
"3rd maximal subgroup of Fi23"
],
[73574645760,73574645760,36787322880,106168320,106168320,53084160,1179648,
1179648,589824,73728,622080,622080,311040,373248,373248,186624,15552,15552,
7776,110592,12288,6144,6144,3072,3072,6144,6144,3072,512,240,240,120,20736,
20736,20736,20736,13824,13824,6912,4608,4608,2304,2304,2304,1152,1728,1728,
864,576,576,288,576,576,288,56,56,28,128,128,128,64,64,216,216,216,216,216,
216,108,80,80,40,44,44,44,44,864,1152,1152,576,96,192,192,96,96,192,192,96,
120,120,60,72,72,72,72,5806080,5806080,92160,92160,18432,18432,6144,6144,1536,
1536,8640,8640,2592,2592,576,576,432,432,144,144,384,384,192,128,128,120,120,
40,40,576,576,288,288,192,192,144,144,48,48,28,28,32,32,36,36,48,48,48,48,60,
60],
[,[1,1,1,1,1,1,1,1,1,1,11,11,11,14,14,14,17,17,17,4,4,8,8,9,9,7,7,7,7,30,30,
30,14,14,14,14,11,11,11,14,14,14,11,11,11,17,17,17,17,17,17,17,17,17,55,55,55,
21,22,22,24,24,63,63,63,63,67,67,67,30,30,30,73,73,73,73,33,37,37,37,33,41,41,
42,42,43,43,43,89,89,89,63,63,63,63,1,2,1,2,7,8,7,8,7,8,11,12,14,15,11,12,17,
18,17,18,20,20,23,22,22,30,31,30,31,43,44,40,41,43,44,49,50,49,50,55,56,58,58,
67,68,78,79,83,83,89,90],[1,2,3,4,5,6,7,8,9,10,1,2,3,1,2,3,1,2,3,20,21,22,23,
24,25,26,27,28,29,30,31,32,4,5,6,6,4,5,6,7,8,9,7,8,9,4,5,6,7,8,9,10,10,10,55,
56,57,58,59,60,61,62,14,15,16,16,14,15,16,70,71,72,73,74,75,76,20,20,20,20,21,
22,23,24,25,26,27,28,30,31,32,33,34,35,36,96,97,98,99,100,101,102,103,104,105,
96,97,96,97,98,99,96,97,98,99,116,117,118,119,120,121,122,123,124,100,101,100,
101,102,103,100,101,104,105,135,136,137,138,108,109,116,117,118,118,121,
122],,[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,
27,28,29,1,2,3,33,34,36,35,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,
54,55,56,57,58,59,60,61,62,63,64,66,65,67,68,69,4,5,6,73,74,75,76,77,78,79,80,
81,82,83,84,85,86,87,88,11,12,13,92,93,95,94,96,97,98,99,100,101,102,103,104,
105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,96,97,98,99,
125,126,127,128,129,130,131,132,133,134,135,136,138,137,139,140,141,142,144,
143,106,107],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,
25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,
51,52,53,54,1,2,3,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,76,75,77,
78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,
103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,
122,123,124,125,126,127,128,129,130,131,132,133,134,96,97,138,137,139,140,141,
142,144,143,145,146],,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,
21,22,23,24,25,26,27,28,29,30,31,32,33,34,36,35,37,38,39,40,41,42,43,44,45,46,
47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,66,65,67,68,69,70,71,72,
1,2,3,3,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,95,94,96,97,98,99,
100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,
119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,
138,139,140,141,142,143,144,145,146]],
0,
[(143,144),(137,138),(137,138)(143,144),(75,76),( 35, 36)( 65, 66)( 94, 95)
(143,144)],
["ConstructMGA","2^2.U6(2)","2.U6(2).2",
 [[78,109],[79,110],[80,111],[81,112],[82,113],[83,114],[84,115],[85,117],
  [86,116],[87,118],[88,119],[89,121],[90,120],[91,122],[92,123],[93,124],
  [94,125],[95,127],[96,126],[97,128],[98,129],[99,130],[100,131],[101,132],
  [102,133],[103,135],[104,134],[105,136],[106,137],[107,138],[108,139]],()]);
ALF("2^2.U6(2).2","2.U6(2).2",[1,1,2,3,3,4,5,5,6,7,8,8,9,10,10,11,12,12,
13,14,15,16,17,18,18,19,19,20,21,22,22,23,24,24,25,25,26,26,27,28,28,29,
30,30,31,32,32,33,34,34,35,36,36,37,38,38,39,40,41,42,43,43,44,44,45,45,
46,46,47,48,48,49,50,50,51,51,52,53,53,54,55,56,57,58,58,59,59,60,61,61,
62,63,63,64,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,
84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,
106,107,108,109,110,111,112,113,114,115]);
ALF("2^2.U6(2).2","U6(2).2",[1,1,1,2,2,2,3,3,3,4,5,5,5,6,6,6,7,7,7,8,9,10,
10,11,11,12,12,12,13,14,14,14,15,15,15,15,16,16,16,17,17,17,18,18,18,19,
19,19,20,20,20,21,21,21,22,22,22,23,24,24,25,25,26,26,26,26,27,27,27,28,
28,28,29,29,29,29,30,31,31,31,32,33,33,34,34,35,35,35,36,36,36,37,37,37,
37,38,38,39,39,40,40,41,41,42,42,43,43,44,44,45,45,46,46,47,47,48,48,49,
50,51,52,52,53,53,54,54,55,55,56,56,57,57,58,58,59,59,60,61,62,62,63,63,
64,64,65,65]);
ALF("2^2.U6(2).2","2^2.U6(2).3.2",[1,2,2,3,4,4,5,6,6,7,8,9,9,10,11,11,12,
13,13,14,15,16,17,16,17,18,19,19,20,21,22,22,23,24,24,24,25,26,26,27,28,
28,29,30,30,31,32,32,33,34,34,35,36,36,37,38,38,39,40,41,40,41,42,43,43,
43,44,45,45,46,47,47,48,49,49,49,50,51,52,52,53,54,55,54,55,56,57,57,58,
59,59,60,61,61,61,99,100,101,102,103,104,105,106,107,108,109,110,111,112,
113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,
131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,
149],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("2^2.U6(2).2","Fi23",[1,3,2,4,2,3,3,4,4,4,5,16,14,6,17,15,7,24,18,10,
12,10,12,10,12,11,9,11,11,13,39,38,21,15,17,17,22,14,16,17,19,21,16,22,22,
26,18,24,24,25,26,20,26,25,29,60,59,32,30,31,31,30,35,71,66,66,34,70,67,
40,38,39,41,77,78,79,46,44,48,48,52,43,47,46,52,50,42,50,61,89,90,68,66,
71,71,3,9,4,11,9,10,11,10,11,12,16,42,17,45,22,50,24,51,26,55,31,30,32,31,
30,39,74,40,75,42,44,45,43,50,48,51,49,55,53,60,88,63,64,70,94,82,84,83,
83,89,98],[
"fusion map is unique up to table automorphisms"
]);
ALN("2^2.U6(2).2",["Fi23C2B","Fi23N2B"]);

MOT("2^2.U6(2).3",
[
"origin: ATLAS of finite groups"
],
[110361968640,36787322880,159252480,53084160,1769472,589824,110592,933120,
311040,559872,186624,23328,7776,165888,18432,3072,3072,9216,3072,768,360,120,
62208,20736,62208,20736,20736,6912,6912,2304,3456,1152,2592,864,864,288,864,
288,84,28,192,64,64,648,216,648,216,324,108,120,40,132,44,132,44,2592,2592,
1728,576,288,288,96,96,288,96,180,60,216,72,216,72,41057280,41057280,466560,
466560,11664,11664,4536,4536,248832,248832,155520,155520,13824,13824,10368,
10368,3888,3888,3456,3456,1728,1728,1296,1296,576,576,432,432,72,72,1944,1944,
243,243,162,162,3456,3456,1152,1152,864,864,288,288,288,288,216,216,144,144,
72,72,48,48,90,90,45,45,216,216,54,54,21,21,48,48,30,30,33,33,33,33,36,36],
[,[1,1,1,1,1,1,1,8,8,10,10,12,12,3,3,6,6,5,5,5,21,21,10,10,10,10,8,8,10,10,8,
8,12,12,12,12,12,12,39,39,15,16,16,46,46,44,44,48,48,21,21,54,54,52,52,25,23,
27,27,25,23,30,30,31,31,66,66,46,46,44,44,73,72,75,74,77,76,79,78,73,72,75,74,
73,72,75,74,77,76,75,74,75,74,77,76,75,74,77,76,79,78,103,102,105,104,107,106,
81,80,81,80,87,86,85,84,87,86,95,94,93,92,95,94,93,92,127,126,129,128,103,102,
107,106,135,134,111,110,127,126,143,142,141,140,131,130],[1,2,3,4,5,6,7,1,2,1,
2,1,2,14,15,16,17,18,19,20,21,22,3,4,3,4,3,4,5,6,5,6,3,4,5,6,7,7,39,40,41,42,
43,10,11,10,11,10,11,50,51,52,53,54,55,14,14,14,14,15,15,16,17,18,19,21,22,23,
24,25,26,1,1,1,1,1,1,1,1,3,3,3,3,5,5,3,3,3,3,5,5,5,5,3,3,7,7,5,5,7,7,10,10,10,
10,10,10,14,14,15,15,14,14,18,18,15,15,14,14,18,18,15,15,20,20,21,21,21,21,23,
25,25,23,39,39,41,41,50,50,52,52,54,54,56,57],,[1,2,3,4,5,6,7,8,9,10,11,12,13,
14,15,16,17,18,19,20,1,2,25,26,23,24,27,28,29,30,31,32,33,34,35,36,37,38,39,
40,41,42,43,46,47,44,45,48,49,3,4,52,53,54,55,57,56,58,59,61,60,62,63,64,65,8,
9,70,71,68,69,73,72,75,74,77,76,79,78,81,80,83,82,85,84,87,86,89,88,91,90,93,
92,95,94,97,96,99,98,101,100,103,102,105,104,107,106,109,108,111,110,113,112,
115,114,117,116,119,118,121,120,123,122,125,124,75,74,73,72,131,130,133,132,
135,134,137,136,83,82,141,140,143,142,145,144],,[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,
1,2,41,42,43,44,45,46,47,48,49,50,51,54,55,52,53,56,57,58,59,60,61,62,63,64,
65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,
91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,
112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,
131,132,133,78,79,136,137,138,139,142,143,140,141,144,145],,,,[1,2,3,4,5,6,7,
8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,25,26,23,24,27,28,29,30,31,32,33,
34,35,36,37,38,39,40,41,42,43,46,47,44,45,48,49,50,51,1,2,1,2,57,56,58,59,61,
60,62,63,64,65,66,67,70,71,68,69,73,72,75,74,77,76,79,78,81,80,83,82,85,84,87,
86,89,88,91,90,93,92,95,94,97,96,99,98,101,100,103,102,105,104,107,106,109,
108,111,110,113,112,115,114,117,116,119,118,121,120,123,122,125,124,127,126,
129,128,131,130,133,132,135,134,137,136,139,138,73,72,73,72,145,144]],
0,
[( 52, 54)( 53, 55)(140,142)(141,143),( 23, 25)( 24, 26)( 44, 46)( 45, 47)
( 56, 57)( 60, 61)( 68, 70)( 69, 71)( 72, 73)( 74, 75)( 76, 77)( 78, 79)
( 80, 81)( 82, 83)( 84, 85)( 86, 87)( 88, 89)( 90, 91)( 92, 93)( 94, 95)
( 96, 97)( 98, 99)(100,101)(102,103)(104,105)(106,107)(108,109)(110,111)
(112,113)(114,115)(116,117)(118,119)(120,121)(122,123)(124,125)(126,127)
(128,129)(130,131)(132,133)(134,135)(136,137)(138,139)(140,141)(142,143)
(144,145)],
["ConstructMGA","2^2.U6(2)","U6(2).3",
[[47,78,109],[48,79,110],[49,80,111],[50,81,112],[51,82,113],[52,83,114],
[53,84,115],[54,85,116],[55,86,117],[56,87,118],[57,88,119],[58,89,120],
[59,90,121],[60,91,122],[61,92,123],[62,93,124],[63,94,125],[64,95,126],
[65,96,127],[66,97,128],[67,98,129],[68,99,130],[69,100,131],[70,101,132],
[71,102,133],[72,103,134],[73,104,135],[74,105,136],[75,106,137],[76,107,138],
[77,108,139]],()]);
ALF("2^2.U6(2).3","U6(2).3",[1,1,2,2,3,3,4,5,5,6,6,7,7,8,9,10,10,11,11,12,
13,13,14,14,15,15,16,16,17,17,18,18,19,19,20,20,21,21,22,22,23,24,24,25,
25,26,26,27,27,28,28,29,29,30,30,31,32,33,33,34,35,36,36,37,37,38,38,39,
39,40,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,
62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,
86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,
108,109,110,111,112,113,114]);
ALF("2^2.U6(2).3","2^2.U6(2).3.2",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,
17,18,19,20,21,22,23,24,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,
39,40,41,42,43,42,43,44,45,46,47,48,49,48,49,50,50,51,52,53,53,54,55,56,
57,58,59,60,61,60,61,62,62,63,63,64,64,65,65,66,66,67,67,68,68,69,69,70,
70,71,71,72,72,73,73,74,74,75,75,76,76,77,77,78,78,79,79,80,80,81,81,82,
82,83,83,84,84,85,85,86,86,87,87,88,88,89,89,90,90,91,91,92,92,93,93,94,
94,95,95,96,97,97,96,98,98],[
"fusion map is unique up to table autom.,\n",
"unique map that is compatible with Brauer tables"
]);
ALN("2^2.U6(2).3",["V4.U6(2).3"]);

MOT("2^2.U6(2).3.2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11]"
],
[220723937280,73574645760,318504960,106168320,3538944,1179648,221184,1866240,
622080,1119744,373248,46656,15552,331776,36864,6144,6144,18432,6144,1536,720,
240,62208,20736,41472,13824,13824,4608,6912,2304,5184,1728,1728,576,1728,576,
168,56,384,128,128,648,216,648,216,240,80,132,44,2592,3456,1152,288,192,192,
576,192,360,120,216,72,41057280,466560,11664,4536,248832,155520,13824,10368,
3888,3456,1728,1296,576,432,72,1944,243,162,3456,1152,864,288,288,216,144,72,
48,90,45,216,54,21,48,30,33,33,36,5806080,5806080,92160,92160,18432,18432,
6144,6144,1536,1536,8640,8640,2592,2592,576,576,432,432,144,144,384,384,192,
128,128,120,120,40,40,576,576,288,288,192,192,144,144,48,48,28,28,32,32,36,36,
48,48,48,48,60,60],
[,[1,1,1,1,1,1,1,8,8,10,10,12,12,3,3,6,6,5,5,5,21,21,10,10,8,8,10,10,8,8,12,
12,12,12,12,12,37,37,15,16,16,42,42,44,44,21,21,48,48,23,25,25,23,28,28,29,29,
58,58,42,42,62,63,64,65,62,63,62,63,64,63,63,64,63,64,65,77,78,79,66,66,69,68,
69,73,72,73,72,89,90,77,79,93,81,89,96,97,91,1,2,1,2,5,6,5,6,5,6,8,9,10,11,8,
9,12,13,12,13,14,14,17,16,16,21,22,21,22,29,30,27,28,29,30,33,34,33,34,37,38,
39,39,44,45,51,52,55,55,58,59],[1,2,3,4,5,6,7,1,2,1,2,1,2,14,15,16,17,18,19,
20,21,22,3,4,3,4,5,6,5,6,3,4,5,6,7,7,37,38,39,40,41,10,11,10,11,46,47,48,49,
14,14,14,15,16,17,18,19,21,22,23,24,1,1,1,1,3,3,5,3,3,5,5,3,7,5,7,10,10,10,14,
15,14,18,15,14,18,15,20,21,21,23,23,37,39,46,48,48,50,99,100,101,102,103,104,
105,106,107,108,99,100,99,100,101,102,99,100,101,102,119,120,121,122,123,124,
125,126,127,103,104,103,104,105,106,103,104,107,108,138,139,140,141,111,112,
119,120,121,121,124,125],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,
1,2,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,3,4,
48,49,50,51,52,53,54,55,56,57,8,9,60,61,62,63,64,65,66,67,68,69,70,71,72,73,
74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,63,62,91,92,93,94,67,97,96,98,99,
100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,
119,120,121,122,123,99,100,101,102,128,129,130,131,132,133,134,135,136,137,
138,139,141,140,142,143,144,145,147,146,109,110],,[1,2,3,4,5,6,7,8,9,10,11,12,
13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,1,2,
39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,
65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,
91,92,65,94,95,97,96,98,99,100,101,102,103,104,105,106,107,108,109,110,111,
112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,
131,132,133,134,135,136,137,99,100,141,140,142,143,144,145,147,146,148,
149],,,,[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,
27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,1,2,50,51,52,
53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,
79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,62,62,98,99,100,101,102,
103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,
122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,
141,142,143,144,145,146,147,148,149]],
0,
[(146,147),(140,141),(140,141)(146,147),(96,97),( 96, 97)(146,147)],
["ConstructGS3","2^2.U6(2).2","2^2.U6(2).3",
[18,19,39,40,43,44,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,
85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,
108,109,110,111,112,113,114,115],[[2,3],[5,6],[8,9],[11,12],[14,15],[17,18],
[20,21],[23,24],[25,28],[27,29],[26,30],[33,34],[36,37],[38,41],[40,42],[39,
43],[45,46],[48,49],[51,52],[54,55],[56,59],[58,60],[57,61],[63,64],[66,67],
[69,72],[71,73],[70,74],[77,78],[80,81],[83,84],[86,87],[89,90],[91,94],[93,
95],[92,96],[98,99],[100,103],[102,104],[101,105],[107,108],[110,111],[113,
114]],[[1,1],[4,3],[7,5],[10,7],[13,9],[16,11],[19,13],[22,15],[32,21],[35,
23],[44,26],[47,28],[50,30],[53,32],[62,35],[65,37],[76,46],[79,48],[82,50],
[85,52],[88,54],[97,57],[106,60],[109,62],[112,64]],
(  1, 28,121, 40,133, 68, 32,125, 46,139, 77, 51,144, 91, 84, 63, 21,114, 22,
115, 23,116, 30,123, 43,136, 73, 41,134, 70, 36,129, 55,148, 97, 93, 87, 75,
 47,140, 79, 52,145, 92, 83, 64, 24,117, 31,124, 45,138, 76, 50,143, 86, 72,
 37,130, 57,  3, 60, 12,105,  8,101,  2, 29,122, 42,135, 71, 38,131, 58,  6,
 66, 27,120, 39,132, 67, 26,119, 34,127, 49,142, 85, 69, 35,128, 54,147, 95,
 90, 82, 62, 18,111, 17,110, 16,109, 14,107, 11,104,  7,100)(  4, 61, 15,108,
 13,106, 10,103,  5, 65, 25,118, 33,126, 48,141, 80, 56,149, 98, 96, 89, 81,
 59,  9,102)( 19,112)( 20,113)( 44,137, 74)( 53,146, 94, 88, 78)]);
ALF("2^2.U6(2).3.2","U6(2).3.2",[1,1,2,2,3,3,4,5,5,6,6,7,7,8,9,10,10,11,
11,12,13,13,14,14,15,15,16,16,17,17,18,18,19,19,20,20,21,21,22,23,23,24,
24,25,25,26,26,27,27,28,29,29,30,31,31,32,32,33,33,34,34,35,36,37,38,39,
40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,
64,65,66,67,68,69,70,71,72,72,73,73,74,74,75,75,76,76,77,77,78,78,79,79,
80,80,81,81,82,82,83,84,85,86,86,87,87,88,88,89,89,90,90,91,91,92,92,93,
93,94,95,96,96,97,97,98,98,99,99]);
ALF("2^2.U6(2).3.2","F3+",[1,2,3,2,2,3,3,4,13,5,15,6,18,9,11,9,11,10,10,
10,12,35,17,15,16,13,15,17,13,16,21,18,18,21,14,21,24,52,27,26,26,31,60,
30,62,36,35,37,73,39,38,40,45,39,45,41,41,54,90,59,60,5,6,7,8,17,14,15,21,
20,18,18,22,21,19,23,29,32,33,39,45,42,44,48,43,49,50,49,56,55,61,63,70,
80,91,92,93,97,2,10,3,10,10,9,10,9,10,11,13,41,15,44,16,41,18,49,21,49,26,
26,27,26,26,35,67,36,67,41,38,44,39,41,40,49,42,49,48,52,87,57,57,62,98,
76,77,80,80,90,108],[
"fusion map is unique up to table automorphisms"
]);
ALN("2^2.U6(2).3.2",["2^2.U6(2):S3"]);

MOT("3.U6(2)",
[
"origin: ATLAS of finite groups, tests: 1.o.r."
],
[27590492160,27590492160,27590492160,39813120,39813120,39813120,442368,442368,
442368,110592,110592,110592,233280,233280,233280,139968,139968,139968,1944,
165888,165888,165888,18432,18432,18432,4608,4608,4608,4608,4608,4608,4608,
4608,4608,2304,2304,2304,768,768,768,90,90,90,15552,15552,15552,15552,15552,
15552,5184,5184,5184,1728,1728,1728,864,864,864,648,648,648,216,216,216,72,21,
21,21,192,192,192,96,96,96,96,96,96,96,96,96,162,162,162,162,162,162,27,30,30,
30,33,33,33,33,33,33,2592,2592,2592,2592,2592,2592,432,432,432,288,288,288,
288,288,288,144,144,144,144,144,144,144,144,144,72,72,72,45,45,45,54,54,54,54,
54,54],
[,[1,3,2,1,3,2,1,3,2,1,3,2,13,15,14,16,18,17,19,4,6,5,4,6,5,7,9,8,7,9,8,7,9,8,
7,9,8,7,9,8,41,43,42,16,18,17,16,18,17,13,15,14,16,18,17,13,15,14,19,19,19,19,
19,19,19,66,68,67,23,25,24,26,28,27,29,31,30,32,34,33,84,86,85,81,83,82,87,41,
43,42,94,96,95,91,93,92,47,49,48,44,46,45,50,52,51,47,49,48,44,46,45,53,55,54,
53,55,54,53,55,54,56,58,57,124,126,125,84,86,85,81,83,82],[1,1,1,4,4,4,7,7,7,
10,10,10,1,1,1,1,1,1,1,20,20,20,23,23,23,26,26,26,29,29,29,32,32,32,35,35,35,
38,38,38,41,41,41,4,4,4,4,4,4,4,4,4,7,7,7,7,7,7,4,4,4,7,7,7,10,66,66,66,69,69,
69,72,72,72,75,75,75,78,78,78,17,17,17,18,18,18,16,88,88,88,91,91,91,94,94,94,
20,20,20,20,20,20,20,20,20,23,23,23,23,23,23,26,26,26,29,29,29,32,32,32,35,35,
35,41,41,41,45,45,45,49,49,49],,[1,3,2,4,6,5,7,9,8,10,12,11,13,15,14,16,18,17,
19,20,22,21,23,25,24,26,28,27,29,31,30,32,34,33,35,37,36,38,40,39,1,3,2,47,49,
48,44,46,45,50,52,51,53,55,54,56,58,57,59,61,60,62,64,63,65,66,68,67,69,71,70,
72,74,73,75,77,76,78,80,79,84,86,85,81,83,82,87,4,6,5,91,93,92,94,96,95,100,
102,101,97,99,98,103,105,104,109,111,110,106,108,107,112,114,113,115,117,116,
118,120,119,121,123,122,13,15,14,130,132,131,127,129,128],,[1,2,3,4,5,6,7,8,9,
10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,
36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,
62,63,64,65,1,2,3,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,
89,90,94,95,96,91,92,93,97,98,99,100,101,102,103,104,105,106,107,108,109,110,
111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,
130,131,132],,,,[1,3,2,4,6,5,7,9,8,10,12,11,13,15,14,16,18,17,19,20,22,21,23,
25,24,26,28,27,29,31,30,32,34,33,35,37,36,38,40,39,41,43,42,47,49,48,44,46,45,
50,52,51,53,55,54,56,58,57,59,61,60,62,64,63,65,66,68,67,69,71,70,72,74,73,75,
77,76,78,80,79,84,86,85,81,83,82,87,88,90,89,1,3,2,1,3,2,100,102,101,97,99,98,
103,105,104,109,111,110,106,108,107,112,114,113,115,117,116,118,120,119,121,
123,122,124,126,125,130,132,131,127,129,128]],
0,
[(91,94)(92,95)(93,96),(  2,  3)(  5,  6)(  8,  9)( 11, 12)( 14, 15)( 17, 18)
( 21, 22)( 24, 25)( 27, 28)( 30, 31)( 33, 34)( 36, 37)( 39, 40)( 42, 43)
( 44, 47)( 45, 49)( 46, 48)( 51, 52)( 54, 55)( 57, 58)( 60, 61)( 63, 64)
( 67, 68)( 70, 71)( 73, 74)( 76, 77)( 79, 80)( 81, 84)( 82, 86)( 83, 85)
( 89, 90)( 92, 93)( 95, 96)( 97,100)( 98,102)( 99,101)(104,105)(106,109)
(107,111)(108,110)(113,114)(116,117)(119,120)(122,123)(125,126)(127,130)
(128,132)(129,131),( 29, 32)( 30, 33)( 31, 34)( 75, 78)( 76, 79)( 77, 80)
(115,118)(116,119)(117,120),( 26, 29)( 27, 30)( 28, 31)( 72, 75)( 73, 76)
( 74, 77)(112,115)(113,116)(114,117)],
["ConstructProj",[["U6(2)",[]],,["3.U6(2)",[-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
23,23,-1,-1,-1,-1]]]]);
ARC("3.U6(2)","maxes",["3xU5(2)","3x2^(1+8)_+:U4(2)","3.U6(2)M3",
"3_1.U4(3).2_2","3.U6(2)M5","3.U6(2)M6","3x2^(4+8):(S3xA5)","3xS6(2)",
"3.U6(2)M9","3.U6(2)M10","3.M22","3.U6(2)M12","3.U6(2)M13","3xS3xU4(2)",
"3.(3^(1+4).[2^7.3])","3.L3(4).2_1"]);
ALF("3.U6(2)","U6(2)",[1,1,1,2,2,2,3,3,3,4,4,4,5,5,5,6,6,6,7,8,8,8,9,9,9,
10,10,10,11,11,11,12,12,12,13,13,13,14,14,14,15,15,15,16,16,16,17,17,17,
18,18,18,19,19,19,20,20,20,21,21,21,22,22,22,23,24,24,24,25,25,25,26,26,
26,27,27,27,28,28,28,29,29,29,30,30,30,31,32,32,32,33,33,33,34,34,34,35,
35,35,36,36,36,37,37,37,38,38,38,39,39,39,40,40,40,41,41,41,42,42,42,43,
43,43,44,44,44,45,45,45,46,46,46]);
ALF("3.U6(2)","3.U6(2).2",[1,2,2,3,4,4,5,6,6,7,8,8,9,10,10,11,12,12,13,14,
15,15,16,17,17,18,19,19,20,21,22,20,22,21,23,24,24,25,26,26,27,28,28,29,
30,31,29,31,30,32,33,33,34,35,35,36,37,37,38,39,39,40,41,41,42,43,44,44,
45,46,46,47,48,48,49,50,51,49,51,50,52,53,54,52,54,53,55,56,57,57,58,59,
60,58,60,59,61,62,63,61,63,62,64,65,65,66,67,68,66,68,67,69,70,70,71,72,
73,71,73,72,74,75,75,76,77,77,78,79,80,78,80,79],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);
ALF("3.U6(2)","3.U6(2).3",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,
19,20,21,22,23,24,25,26,27,28,26,27,28,26,27,28,29,30,31,32,33,34,35,36,
37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,
61,62,63,64,65,66,67,68,66,67,68,66,67,68,69,70,71,72,73,74,75,76,77,78,
79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,
102,100,101,102,100,101,102,103,104,105,106,107,108,109,110,111,112,113,
114],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);

MOT("3.U6(2).2",
[
"origin: ATLAS of finite groups"
],
[55180984320,27590492160,79626240,39813120,884736,442368,221184,110592,466560,
233280,279936,139968,3888,331776,165888,36864,18432,9216,4608,4608,4608,4608,
4608,2304,1536,768,180,90,15552,15552,15552,10368,5184,3456,1728,1728,864,
1296,648,432,216,144,42,21,384,192,192,96,96,96,96,162,162,162,54,60,30,33,33,
33,2592,2592,2592,864,432,288,288,288,288,144,144,144,144,144,72,90,45,54,54,
54,2903040,46080,9216,3072,768,4320,1296,288,216,72,192,192,128,128,60,20,288,
144,96,72,24,14,32,32,18,24,24,30],
[,[1,2,1,2,1,2,1,2,9,10,11,12,13,3,4,3,4,5,6,5,6,6,5,6,5,6,27,28,11,12,12,9,
10,11,12,9,10,13,13,13,13,13,43,44,16,17,18,19,20,22,21,52,53,54,55,27,28,58,
59,60,29,30,31,32,33,29,30,31,34,35,34,35,35,36,37,76,77,52,53,54,1,1,5,5,5,9,
11,9,13,13,14,18,18,18,27,27,36,34,36,40,40,43,45,45,55,64,69,76],[1,1,3,3,5,
5,7,7,1,1,1,1,1,14,14,16,16,18,18,20,20,20,23,23,25,25,27,27,3,3,3,3,3,5,5,5,
5,3,3,5,5,7,43,43,45,45,47,47,49,49,49,12,12,12,11,56,56,58,58,58,14,14,14,14,
14,16,16,16,18,18,20,20,20,23,23,27,27,30,30,30,81,82,83,84,85,81,81,82,81,82,
91,92,93,94,95,96,83,83,84,83,85,102,103,104,87,91,92,95],,[1,2,3,4,5,6,7,8,9,
10,11,12,13,14,15,16,17,18,19,20,22,21,23,24,25,26,1,2,29,30,31,32,33,34,35,
36,37,38,39,40,41,42,43,44,45,46,47,48,49,51,50,52,53,54,55,3,4,58,60,59,61,
62,63,64,65,66,67,68,69,70,71,73,72,74,75,9,10,78,79,80,81,82,83,84,85,86,87,
88,89,90,91,92,93,94,81,82,97,98,99,100,101,102,104,103,105,106,107,86],,[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,
31,32,33,34,35,36,37,38,39,40,41,42,1,2,45,46,47,48,49,50,51,52,53,54,55,56,
57,58,60,59,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,
83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,81,104,103,105,106,
107,108],,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,22,21,23,24,
25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,51,
50,52,53,54,55,56,57,1,2,2,61,62,63,64,65,66,67,68,69,70,71,73,72,74,75,76,77,
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]],
0,
[(103,104),(59,60),(21,22)(50,51)(72,73),(21,22)(50,51)(59,60)(72,73)],
["ConstructMGA","3.U6(2)","U6(2).2",
     [ [ 47, 48 ], [ 49, 50 ], [ 51, 52 ], [ 53, 54 ], [ 55, 56 ],
        [ 57, 58 ], [ 59, 60 ], [ 61, 62 ], [ 63, 66 ], [ 64, 65 ],
        [ 67, 68 ], [ 69, 70 ], [ 71, 72 ], [ 73, 74 ], [ 75, 76 ],
        [ 77, 78 ], [ 79, 82 ], [ 80, 81 ], [ 83, 84 ], [ 85, 86 ],
        [ 87, 88 ], [ 89, 90 ], [ 91, 92 ], [ 93, 94 ], [ 95, 96 ],
        [ 97, 98 ], [ 99, 100 ], [ 101, 102 ], [ 103, 104 ], [ 105, 108 ],
        [ 106, 107 ], [ 109, 110 ], [ 111, 112 ], [ 113, 114 ], [ 115, 116 ],
        [ 117, 118 ], [ 119, 120 ], [ 121, 124 ], [ 122, 123 ], [ 125, 126 ],
        [ 127, 128 ], [ 129, 130 ], [ 131, 132 ] ], ()]);
ALF("3.U6(2).2","U6(2).2",[1,1,2,2,3,3,4,4,5,5,6,6,7,8,8,9,9,10,10,11,11,
11,12,12,13,13,14,14,15,15,15,16,16,17,17,18,18,19,19,20,20,21,22,22,23,
23,24,24,25,25,25,26,26,26,27,28,28,29,29,29,30,30,30,31,31,32,32,32,33,
33,34,34,34,35,35,36,36,37,37,37,38,39,40,41,42,43,44,45,46,47,48,49,50,
51,52,53,54,55,56,57,58,59,60,61,62,63,64,65]);
ALF("3.U6(2).2","3.U6(2).3.2",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,
18,19,18,19,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,
39,40,41,42,43,44,45,44,45,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,
60,61,62,63,64,63,64,64,65,66,67,68,69,70,71,177,178,179,180,181,182,183,
184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,
202,203,204]);

MOT("3.U6(2).3",
[
"origin: ATLAS of finite groups"
],
[82771476480,82771476480,82771476480,119439360,119439360,119439360,1327104,
1327104,1327104,331776,331776,331776,699840,699840,699840,419904,419904,
419904,5832,497664,497664,497664,55296,55296,55296,4608,4608,4608,6912,6912,
6912,2304,2304,2304,270,270,270,46656,46656,46656,46656,46656,46656,15552,
15552,15552,5184,5184,5184,2592,2592,2592,1944,1944,1944,648,648,648,216,63,
63,63,576,576,576,96,96,96,486,486,486,486,486,486,81,90,90,90,99,99,99,99,99,
99,7776,7776,7776,7776,7776,7776,1296,1296,1296,864,864,864,864,864,864,144,
144,144,216,216,216,135,135,135,162,162,162,162,162,162,123171840,123171840,
123171840,123171840,123171840,123171840,1399680,1399680,1399680,1399680,
1399680,1399680,34992,34992,34992,34992,34992,34992,4536,4536,746496,746496,
746496,746496,746496,746496,466560,466560,466560,466560,466560,466560,41472,
41472,41472,41472,41472,41472,31104,31104,31104,31104,31104,31104,11664,11664,
11664,11664,11664,11664,10368,10368,10368,10368,10368,10368,5184,5184,5184,
5184,5184,5184,3888,3888,3888,3888,3888,3888,1728,1728,1728,1728,1728,1728,
1296,1296,1296,1296,1296,1296,72,72,5832,5832,5832,5832,5832,5832,243,243,486,
486,486,486,486,486,10368,10368,10368,10368,10368,10368,3456,3456,3456,3456,
3456,3456,2592,2592,2592,2592,2592,2592,864,864,864,864,864,864,864,864,864,
864,864,864,648,648,648,648,648,648,432,432,432,432,432,432,216,216,216,216,
216,216,144,144,144,144,144,144,270,270,270,270,270,270,135,135,135,135,135,
135,648,648,648,648,648,648,162,162,162,162,162,162,63,63,63,63,63,63,144,144,
144,144,144,144,90,90,90,90,90,90,99,99,99,99,99,99,99,99,99,99,99,99,108,108,
108,108,108,108],
[,[1,3,2,1,3,2,1,3,2,1,3,2,13,15,14,16,18,17,19,4,6,5,4,6,5,7,9,8,7,9,8,7,9,8,
35,37,36,16,18,17,16,18,17,13,15,14,16,18,17,13,15,14,19,19,19,19,19,19,19,60,
62,61,23,25,24,26,28,27,72,74,73,69,71,70,75,35,37,36,82,84,83,79,81,80,41,43,
42,38,40,39,44,46,45,41,43,42,38,40,39,47,49,48,50,52,51,106,108,107,72,74,73,
69,71,70,118,119,120,115,116,117,124,125,126,121,122,123,130,131,132,127,128,
129,134,133,118,119,120,115,116,117,124,125,126,121,122,123,118,119,120,115,
116,117,124,125,126,121,122,123,130,131,132,127,128,129,124,125,126,121,122,
123,124,125,126,121,122,123,130,131,132,127,128,129,124,125,126,121,122,123,
130,131,132,127,128,129,134,133,200,201,202,197,198,199,204,203,208,209,210,
205,206,207,138,139,140,135,136,137,138,139,140,135,136,137,156,157,158,153,
154,155,150,151,152,147,148,149,156,157,158,153,154,155,180,181,182,177,178,
179,174,175,176,171,172,173,180,181,182,177,178,179,174,175,176,171,172,173,
268,269,270,265,266,267,274,275,276,271,272,273,200,201,202,197,198,199,208,
209,210,205,206,207,292,293,294,289,290,291,220,221,222,217,218,219,268,269,
270,265,266,267,316,317,318,313,314,315,310,311,312,307,308,309,280,281,282,
277,278,279],[1,1,1,4,4,4,7,7,7,10,10,10,1,1,1,1,1,1,1,20,20,20,23,23,23,26,
26,26,29,29,29,32,32,32,35,35,35,4,4,4,4,4,4,4,4,4,7,7,7,7,7,7,4,4,4,7,7,7,10,
60,60,60,63,63,63,66,66,66,17,17,17,18,18,18,16,76,76,76,79,79,79,82,82,82,20,
20,20,20,20,20,20,20,20,23,23,23,23,23,23,26,26,26,29,29,29,35,35,35,39,39,39,
43,43,43,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,3,4,4,4,4,4,4,4,4,4,4,4,4,7,7,
7,7,7,7,4,4,4,4,4,4,4,4,4,4,4,4,7,7,7,7,7,7,7,7,7,7,7,7,4,4,4,4,4,4,10,10,10,
10,10,10,7,7,7,7,7,7,11,12,17,17,17,18,18,18,17,18,18,18,18,17,17,17,20,20,20,
20,20,20,23,23,23,23,23,23,20,20,20,20,20,20,29,29,29,29,29,29,23,23,23,23,23,
23,20,20,20,20,20,20,29,29,29,29,29,29,23,23,23,23,23,23,32,32,32,32,32,32,35,
35,35,35,35,35,35,35,35,35,35,35,39,39,39,43,43,43,43,43,43,39,39,39,61,61,61,
62,62,62,63,63,63,63,63,63,76,76,76,76,76,76,79,79,79,79,79,79,82,82,82,82,82,
82,86,86,86,90,90,90],,[1,3,2,4,6,5,7,9,8,10,12,11,13,15,14,16,18,17,19,20,22,
21,23,25,24,26,28,27,29,31,30,32,34,33,1,3,2,41,43,42,38,40,39,44,46,45,47,49,
48,50,52,51,53,55,54,56,58,57,59,60,62,61,63,65,64,66,68,67,72,74,73,69,71,70,
75,4,6,5,79,81,80,82,84,83,88,90,89,85,87,86,91,93,92,97,99,98,94,96,95,100,
102,101,103,105,104,13,15,14,112,114,113,109,111,110,118,119,120,115,116,117,
124,125,126,121,122,123,130,131,132,127,128,129,134,133,138,139,140,135,136,
137,144,145,146,141,142,143,150,151,152,147,148,149,156,157,158,153,154,155,
162,163,164,159,160,161,168,169,170,165,166,167,174,175,176,171,172,173,180,
181,182,177,178,179,186,187,188,183,184,185,192,193,194,189,190,191,196,195,
200,201,202,197,198,199,204,203,208,209,210,205,206,207,214,215,216,211,212,
213,220,221,222,217,218,219,226,227,228,223,224,225,232,233,234,229,230,231,
238,239,240,235,236,237,244,245,246,241,242,243,250,251,252,247,248,249,256,
257,258,253,254,255,262,263,264,259,260,261,124,125,126,121,122,123,118,119,
120,115,116,117,280,281,282,277,278,279,286,287,288,283,284,285,294,292,293,
291,289,290,298,299,300,295,296,297,144,145,146,141,142,143,310,311,312,307,
308,309,316,317,318,313,314,315,322,323,324,319,320,321],,[1,2,3,4,5,6,7,8,9,
10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,
36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,1,2,3,
63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,82,83,84,79,80,81,85,86,87,88,
89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,
111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,
130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,
149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,
168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,
187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,
206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,
225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,
244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,
263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,
282,283,284,285,286,287,288,133,133,133,134,134,134,295,296,297,298,299,300,
301,302,303,304,305,306,313,314,315,316,317,318,307,308,309,310,311,312,319,
320,321,322,323,324],,,,[1,3,2,4,6,5,7,9,8,10,12,11,13,15,14,16,18,17,19,20,
22,21,23,25,24,26,28,27,29,31,30,32,34,33,35,37,36,41,43,42,38,40,39,44,46,45,
47,49,48,50,52,51,53,55,54,56,58,57,59,60,62,61,63,65,64,66,68,67,72,74,73,69,
71,70,75,76,78,77,1,3,2,1,3,2,88,90,89,85,87,86,91,93,92,97,99,98,94,96,95,
100,102,101,103,105,104,106,108,107,112,114,113,109,111,110,118,119,120,115,
116,117,124,125,126,121,122,123,130,131,132,127,128,129,134,133,138,139,140,
135,136,137,144,145,146,141,142,143,150,151,152,147,148,149,156,157,158,153,
154,155,162,163,164,159,160,161,168,169,170,165,166,167,174,175,176,171,172,
173,180,181,182,177,178,179,186,187,188,183,184,185,192,193,194,189,190,191,
196,195,200,201,202,197,198,199,204,203,208,209,210,205,206,207,214,215,216,
211,212,213,220,221,222,217,218,219,226,227,228,223,224,225,232,233,234,229,
230,231,238,239,240,235,236,237,244,245,246,241,242,243,250,251,252,247,248,
249,256,257,258,253,254,255,262,263,264,259,260,261,268,269,270,265,266,267,
274,275,276,271,272,273,280,281,282,277,278,279,286,287,288,283,284,285,293,
294,292,290,291,289,298,299,300,295,296,297,304,305,306,301,302,303,118,119,
120,115,116,117,118,119,120,115,116,117,322,323,324,319,320,321]],
0,
[(289,291,290)(292,294,293),( 79, 82)( 80, 83)( 81, 84)(307,313)(308,314)
(309,315)(310,316)(311,317)(312,318),(  2,  3)(  5,  6)(  8,  9)( 11, 12)
( 14, 15)( 17, 18)( 21, 22)( 24, 25)( 27, 28)( 30, 31)( 33, 34)( 36, 37)
( 38, 41)( 39, 43)( 40, 42)( 45, 46)( 48, 49)( 51, 52)( 54, 55)( 57, 58)
( 61, 62)( 64, 65)( 67, 68)( 69, 72)( 70, 74)( 71, 73)( 77, 78)( 80, 81)
( 83, 84)( 85, 88)( 86, 90)( 87, 89)( 92, 93)( 94, 97)( 95, 99)( 96, 98)
(101,102)(104,105)(107,108)(109,112)(110,114)(111,113)(115,118)(116,119)
(117,120)(121,124)(122,125)(123,126)(127,130)(128,131)(129,132)(133,134)
(135,138)(136,139)(137,140)(141,144)(142,145)(143,146)(147,150)(148,151)
(149,152)(153,156)(154,157)(155,158)(159,162)(160,163)(161,164)(165,168)
(166,169)(167,170)(171,174)(172,175)(173,176)(177,180)(178,181)(179,182)
(183,186)(184,187)(185,188)(189,192)(190,193)(191,194)(195,196)(197,200)
(198,201)(199,202)(203,204)(205,208)(206,209)(207,210)(211,214)(212,215)
(213,216)(217,220)(218,221)(219,222)(223,226)(224,227)(225,228)(229,232)
(230,233)(231,234)(235,238)(236,239)(237,240)(241,244)(242,245)(243,246)
(247,250)(248,251)(249,252)(253,256)(254,257)(255,258)(259,262)(260,263)
(261,264)(265,268)(266,269)(267,270)(271,274)(272,275)(273,276)(277,280)
(278,281)(279,282)(283,286)(284,287)(285,288)(289,294,290,292,291,293)
(295,298)(296,299)(297,300)(301,304)(302,305)(303,306)(307,310)(308,311)
(309,312)(313,316)(314,317)(315,318)(319,322)(320,323)(321,324),(115,116,117)
(118,119,120)(121,122,123)(124,125,126)(127,128,129)(130,131,132)(135,136,137)
(138,139,140)(141,142,143)(144,145,146)(147,148,149)(150,151,152)(153,154,155)
(156,157,158)(159,160,161)(162,163,164)(165,166,167)(168,169,170)(171,172,173)
(174,175,176)(177,178,179)(180,181,182)(183,184,185)(186,187,188)(189,190,191)
(192,193,194)(197,198,199)(200,201,202)(205,206,207)(208,209,210)(211,212,213)
(214,215,216)(217,218,219)(220,221,222)(223,224,225)(226,227,228)(229,230,231)
(232,233,234)(235,236,237)(238,239,240)(241,242,243)(244,245,246)(247,248,249)
(250,251,252)(253,254,255)(256,257,258)(259,260,261)(262,263,264)(265,266,267)
(268,269,270)(271,272,273)(274,275,276)(277,278,279)(280,281,282)(283,284,285)
(286,287,288)(295,296,297)(298,299,300)(301,302,303)(304,305,306)(307,308,309)
(310,311,312)(313,314,315)(316,317,318)(319,320,321)(322,323,324)],
["ConstructProj",[["U6(2).3",[]],,["3.U6(2).3",[-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,23,23,-1,-1,-1,
-55]]]]);
ALF("3.U6(2).3","U6(2).3",[1,1,1,2,2,2,3,3,3,4,4,4,5,5,5,6,6,6,7,8,8,8,9,
9,9,10,10,10,11,11,11,12,12,12,13,13,13,14,14,14,15,15,15,16,16,16,17,17,
17,18,18,18,19,19,19,20,20,20,21,22,22,22,23,23,23,24,24,24,25,25,25,26,
26,26,27,28,28,28,29,29,29,30,30,30,31,31,31,32,32,32,33,33,33,34,34,34,
35,35,35,36,36,36,37,37,37,38,38,38,39,39,39,40,40,40,41,41,41,42,42,42,
43,43,43,44,44,44,45,45,45,46,46,46,47,48,49,49,49,50,50,50,51,51,51,52,
52,52,53,53,53,54,54,54,55,55,55,56,56,56,57,57,57,58,58,58,59,59,59,60,
60,60,61,61,61,62,62,62,63,63,63,64,64,64,65,65,65,66,66,66,67,67,67,68,
68,68,69,70,71,71,71,72,72,72,73,74,75,75,75,76,76,76,77,77,77,78,78,78,
79,79,79,80,80,80,81,81,81,82,82,82,83,83,83,84,84,84,85,85,85,86,86,86,
87,87,87,88,88,88,89,89,89,90,90,90,91,91,91,92,92,92,93,93,93,94,94,94,
95,95,95,96,96,96,97,97,97,98,98,98,99,99,99,100,100,100,101,101,101,102,
102,102,103,103,103,104,104,104,105,105,105,106,106,106,107,107,107,108,
108,108,109,109,109,110,110,110,111,111,111,112,112,112,113,113,113,114,
114,114]);
ALF("3.U6(2).3","3.U6(2).3.2",[1,2,2,3,4,4,5,6,6,7,8,8,9,10,10,11,12,12,13,
14,15,15,16,17,17,18,19,19,20,21,21,22,23,23,24,25,25,26,27,28,26,28,27,
29,30,30,31,32,32,33,34,34,35,36,36,37,38,38,39,40,41,41,42,43,43,44,45,
45,46,47,48,46,48,47,49,50,51,51,52,53,54,52,54,53,55,56,57,55,57,56,58,
59,59,60,61,62,60,62,61,63,64,64,65,66,66,67,68,68,69,70,71,69,71,70,72,
73,74,72,73,74,75,76,77,75,76,77,78,79,80,78,79,80,81,81,82,83,84,82,83,
84,85,86,87,85,86,87,88,89,90,88,89,90,91,92,93,91,92,93,94,95,96,94,95,
96,97,98,99,97,98,99,100,101,102,100,101,102,103,104,105,103,104,105,106,
107,108,106,107,108,109,110,111,109,110,111,112,112,113,114,115,113,114,
115,116,116,117,118,119,117,118,119,120,121,122,120,121,122,123,124,125,
123,124,125,126,127,128,126,127,128,129,130,131,129,130,131,132,133,134,
132,133,134,135,136,137,135,136,137,138,139,140,138,139,140,141,142,143,
141,142,143,144,145,146,144,145,146,147,148,149,147,148,149,150,151,152,
150,151,152,153,154,155,153,154,155,156,157,158,156,157,158,159,160,161,
159,160,161,162,163,164,162,163,164,165,166,167,165,166,167,168,169,170,
171,172,173,171,172,173,168,169,170,174,175,176,174,175,176]);

MOT("Isoclinic(3.U6(2).3,1)",
[
"1st isoclinic group of the 3.U6(2).3 given in the ATLAS"
],
0,
0,
0,
[(2,3)(5,6)(8,9)(11,12)(14,15)(17,18)(21,22)(24,25)(27,28)(30,31)(33,34)(36,
37)(38,41)(39,43)(40,42)(45,46)(48,49)(51,52)(54,55)(57,58)(61,62)(64,65)(67,
68)(69,72)(70,74)(71,73)(77,78)(80,81)(83,84)(85,88)(86,90)(87,89)(92,93)(94,
97)(95,99)(96,98)(101,102)(104,105)(107,108)(109,112)(110,114)(111,113)(115,
118,116,119,117,120)(121,124,122,125,123,126)(127,130,128,131,129,132)(133,
134)(135,138,136,139,137,140)(141,144,142,145,143,146)(147,150,148,151,149,
152)(153,156,154,157,155,158)(159,162,160,163,161,164)(165,168,166,169,167,
170)(171,174,172,175,173,176)(177,180,178,181,179,182)(183,186,184,187,185,
188)(189,192,190,193,191,194)(195,196)(197,200,198,201,199,202)(203,204)(205,
208,206,209,207,210)(211,214,212,215,213,216)(217,220,218,221,219,222)(223,
226,224,227,225,228)(229,232,230,233,231,234)(235,238,236,239,237,240)(241,
244,242,245,243,246)(247,250,248,251,249,252)(253,256,254,257,255,258)(259,
262,260,263,261,264)(265,268,266,269,267,270)(271,274,272,275,273,276)(277,
280,278,281,279,282)(283,286,284,287,285,288)(289,292,290,293,291,294)(295,
298,296,299,297,300)(301,304,302,305,303,306)(307,310,308,311,309,312)(313,
316,314,317,315,318)(319,322,320,323,321,324),(289,290,291)(292,293,294),(115,
116,117)(118,119,120)(121,122,123)(124,125,126)(127,128,129)(130,131,132)(135,
136,137)(138,139,140)(141,142,143)(144,145,146)(147,148,149)(150,151,152)(153,
154,155)(156,157,158)(159,160,161)(162,163,164)(165,166,167)(168,169,170)(171,
172,173)(174,175,176)(177,178,179)(180,181,182)(183,184,185)(186,187,188)(189,
190,191)(192,193,194)(197,198,199)(200,201,202)(205,206,207)(208,209,210)(211,
212,213)(214,215,216)(217,218,219)(220,221,222)(223,224,225)(226,227,228)(229,
230,231)(232,233,234)(235,236,237)(238,239,240)(241,242,243)(244,245,246)(247,
248,249)(250,251,252)(253,254,255)(256,257,258)(259,260,261)(262,263,264)(265,
266,267)(268,269,270)(271,272,273)(274,275,276)(277,278,279)(280,281,282)(283,
284,285)(286,287,288)(295,296,297)(298,299,300)(301,302,303)(304,305,306)(307,
308,309)(310,311,312)(313,314,315)(316,317,318)(319,320,321)(322,323,324),(79,
82)(80,83)(81,84)(307,313)(308,314)(309,315)(310,316)(311,317)(312,318)],
["ConstructIsoclinic",[["3.U6(2).3"]],rec(k:=1)]);
ALF("Isoclinic(3.U6(2).3,1)","U6(2).3",[1,1,1,2,2,2,3,3,3,4,4,4,5,5,5,6,6,
6,7,8,8,8,9,9,9,10,10,10,11,11,11,12,12,12,13,13,13,14,14,14,15,15,15,16,
16,16,17,17,17,18,18,18,19,19,19,20,20,20,21,22,22,22,23,23,23,24,24,24,
25,25,25,26,26,26,27,28,28,28,29,29,29,30,30,30,31,31,31,32,32,32,33,33,
33,34,34,34,35,35,35,36,36,36,37,37,37,38,38,38,39,39,39,40,40,40,41,41,
41,42,42,42,43,43,43,44,44,44,45,45,45,46,46,46,47,48,49,49,49,50,50,50,
51,51,51,52,52,52,53,53,53,54,54,54,55,55,55,56,56,56,57,57,57,58,58,58,
59,59,59,60,60,60,61,61,61,62,62,62,63,63,63,64,64,64,65,65,65,66,66,66,
67,67,67,68,68,68,69,70,71,71,71,72,72,72,73,74,75,75,75,76,76,76,77,77,
77,78,78,78,79,79,79,80,80,80,81,81,81,82,82,82,83,83,83,84,84,84,85,85,
85,86,86,86,87,87,87,88,88,88,89,89,89,90,90,90,91,91,91,92,92,92,93,93,
93,94,94,94,95,95,95,96,96,96,97,97,97,98,98,98,99,99,99,100,100,100,101,
101,101,102,102,102,103,103,103,104,104,104,105,105,105,106,106,106,107,
107,107,108,108,108,109,109,109,110,110,110,111,111,111,112,112,112,113,
113,113,114,114,114]);

MOT("Isoclinic(3.U6(2).3,2)",
[
"2nd isoclinic group of the 3.U6(2).3 given in the ATLAS"
],
0,
0,
0,
[(2,3)(5,6)(8,9)(11,12)(14,15)(17,18)(21,22)(24,25)(27,28)(30,31)(33,34)(36,
37)(38,41)(39,43)(40,42)(45,46)(48,49)(51,52)(54,55)(57,58)(61,62)(64,65)(67,
68)(69,72)(70,74)(71,73)(77,78)(80,81)(83,84)(85,88)(86,90)(87,89)(92,93)(94,
97)(95,99)(96,98)(101,102)(104,105)(107,108)(109,112)(110,114)(111,113)(115,
118,117,120,116,119)(121,124,123,126,122,125)(127,130,129,132,128,131)(133,
134)(135,138,137,140,136,139)(141,144,143,146,142,145)(147,150,149,152,148,
151)(153,156,155,158,154,157)(159,162,161,164,160,163)(165,168,167,170,166,
169)(171,174,173,176,172,175)(177,180,179,182,178,181)(183,186,185,188,184,
187)(189,192,191,194,190,193)(195,196)(197,200,199,202,198,201)(203,204)(205,
208,207,210,206,209)(211,214,213,216,212,215)(217,220,219,222,218,221)(223,
226,225,228,224,227)(229,232,231,234,230,233)(235,238,237,240,236,239)(241,
244,243,246,242,245)(247,250,249,252,248,251)(253,256,255,258,254,257)(259,
262,261,264,260,263)(265,268,267,270,266,269)(271,274,273,276,272,275)(277,
280,279,282,278,281)(283,286,285,288,284,287)(289,292,291,294,290,293)(295,
298,297,300,296,299)(301,304,303,306,302,305)(307,310,309,312,308,311)(313,
316,315,318,314,317)(319,322,321,324,320,323),(289,290,291)(292,293,294),(115,
116,117)(118,119,120)(121,122,123)(124,125,126)(127,128,129)(130,131,132)(135,
136,137)(138,139,140)(141,142,143)(144,145,146)(147,148,149)(150,151,152)(153,
154,155)(156,157,158)(159,160,161)(162,163,164)(165,166,167)(168,169,170)(171,
172,173)(174,175,176)(177,178,179)(180,181,182)(183,184,185)(186,187,188)(189,
190,191)(192,193,194)(197,198,199)(200,201,202)(205,206,207)(208,209,210)(211,
212,213)(214,215,216)(217,218,219)(220,221,222)(223,224,225)(226,227,228)(229,
230,231)(232,233,234)(235,236,237)(238,239,240)(241,242,243)(244,245,246)(247,
248,249)(250,251,252)(253,254,255)(256,257,258)(259,260,261)(262,263,264)(265,
266,267)(268,269,270)(271,272,273)(274,275,276)(277,278,279)(280,281,282)(283,
284,285)(286,287,288)(295,296,297)(298,299,300)(301,302,303)(304,305,306)(307,
308,309)(310,311,312)(313,314,315)(316,317,318)(319,320,321)(322,323,324),(79,
82)(80,83)(81,84)(307,313)(308,314)(309,315)(310,316)(311,317)(312,318)],
["ConstructIsoclinic",[["3.U6(2).3"]],rec(k:=2)]);
ALF("Isoclinic(3.U6(2).3,2)","U6(2).3",[1,1,1,2,2,2,3,3,3,4,4,4,5,5,5,6,6,
6,7,8,8,8,9,9,9,10,10,10,11,11,11,12,12,12,13,13,13,14,14,14,15,15,15,16,
16,16,17,17,17,18,18,18,19,19,19,20,20,20,21,22,22,22,23,23,23,24,24,24,
25,25,25,26,26,26,27,28,28,28,29,29,29,30,30,30,31,31,31,32,32,32,33,33,
33,34,34,34,35,35,35,36,36,36,37,37,37,38,38,38,39,39,39,40,40,40,41,41,
41,42,42,42,43,43,43,44,44,44,45,45,45,46,46,46,47,48,49,49,49,50,50,50,
51,51,51,52,52,52,53,53,53,54,54,54,55,55,55,56,56,56,57,57,57,58,58,58,
59,59,59,60,60,60,61,61,61,62,62,62,63,63,63,64,64,64,65,65,65,66,66,66,
67,67,67,68,68,68,69,70,71,71,71,72,72,72,73,74,75,75,75,76,76,76,77,77,
77,78,78,78,79,79,79,80,80,80,81,81,81,82,82,82,83,83,83,84,84,84,85,85,
85,86,86,86,87,87,87,88,88,88,89,89,89,90,90,90,91,91,91,92,92,92,93,93,
93,94,94,94,95,95,95,96,96,96,97,97,97,98,98,98,99,99,99,100,100,100,101,
101,101,102,102,102,103,103,103,104,104,104,105,105,105,106,106,106,107,
107,107,108,108,108,109,109,109,110,110,110,111,111,111,112,112,112,113,
113,113,114,114,114]);

MOT("6.U6(2)",
[
--> --------------------

--> maximum size reached

--> --------------------