Quellcode-Bibliothek ctounit1.tbl   Sprache: unbekannt

#############################################################################
##
#W  ctounit1.tbl                GAP table library               Thomas Breuer
##
##  This file contains the ordinary character tables of groups related to
##  the unitary group $U_4(3)$ of the ATLAS.
##
#H  ctbllib history
#H  ---------------
#H  $Log: ctounit1.tbl,v $
#H  Revision 4.47  2012/04/23 16:16:16  gap
#H  next step of consolidation:
#H
#H  - removed a few unnecessary duplicate tables,
#H    and changed some related fusions, names of maxes, table constructions
#H  - make sure that duplicate tables arise only via `ConstructPermuted'
#H    constructions
#H  - added some relative names
#H  - added fusions A11.2 -> A12.2, L2(11).2 -> A12.2, D8x2F4(2)'.2 -> B,
#H    L2(41) -> M, (A5xA12):2 -> A17,
#H  - added maxes of A12.2, L6(2), 2.M22.2
#H  - added table of QD16.2,
#H  - fixed the syntax of two `ALN' calls
#H      TB
#H
#H  Revision 4.46  2012/03/28 13:14:00  gap
#H  added table of 6_1.U4(3).2_2'
#H      TB
#H
#H  Revision 4.45  2012/03/12 17:01:48  gap
#H  omit the fourth argument of `ConstructV4G'
#H      TB
#H
#H  Revision 4.44  2012/03/02 08:19:35  gap
#H  - added the tables of 2.U4(3).(2^2)_{133},
#H  - encode some tables of 2.U4(3).(2^2)_{122} via `ConstructIsoclinic',
#H      TB
#H
#H  Revision 4.43  2012/01/30 08:32:04  gap
#H  removed #H entries from the headers
#H      TB
#H
#H  Revision 4.42  2011/09/28 14:17:09  gap
#H  - removed revision entry and SET_TABLEFILENAME call,
#H  - added fusion Isoclinic(2.U4(3).2_1) -> 3^6:2U4(3).2_1
#H      TB
#H
#H  Revision 4.41  2010/12/01 17:52:14  gap
#H  - tomfusion of "U4(3).2_1" needs the permutation (3,4)
#H  - fusion U4(3).2_3' -> U4(3).(2^2)_{133} is relative to the fusion
#H    U4(3).2_3 -> U4(3).(2^2)_{133} (w.r.t. the automorphism induced by
#H    U4(3).D8)
#H  - added tables of "(3^2x2).U4(3)" and "(3^2x4).U4(3)"
#H    (Eamonn had asked for them)
#H
#H      TB
#H
#H  Revision 4.40  2010/11/15 16:32:26  gap
#H  replaced some fusions to U4(3).2_3 by fusions to U4(3).2_3',
#H  added comments
#H      TB
#H
#H  Revision 4.39  2010/09/15 08:11:28  gap
#H  added the fusion 6_2.U4(3).2_3' -> U4(3).2_3',
#H  adjusted the mapping between the maxes and the corresponding information
#H  in the table of marks of U4(3) and U4(3).(2^2)_{133}
#H      TB
#H
#H  Revision 4.38  2010/05/05 13:20:09  gap
#H  - added many class fusions,
#H  - changed several class fusions according to consistency conditions,
#H    after systematic checks of consistency
#H    - with Brauer tables w.r.t. the restriction of characters,
#H    - of subgroup fusions with the corresponding subgroup fusions between
#H      proper factors where the factor fusions are stored,
#H    - of subgroup fusions from maximal subgroups with subgroup fusions of
#H      extensions inside automorphic extensions
#H
#H      TB
#H
#H  Revision 4.37  2010/01/19 17:05:35  gap
#H  added several tables of maximal subgroups of central extensions of
#H  simple groups (many of them were contributed by S. Dany)
#H      TB
#H
#H  Revision 4.36  2009/04/22 12:39:08  gap
#H  added missing maxes of He.2, ON.2, HN.2, Fi24, and B
#H      TB
#H
#H  Revision 4.35  2006/06/07 07:54:27  gap
#H  unified ConstructMixed and ConstructMGA (for better programmatic access)
#H      TB
#H
#H  Revision 4.34  2005/09/14 08:31:28  gap
#H  changed fusion 2.U4(3).2_2 -> O7(3) such that the fusion is compatible
#H  with 12_1.U4(3).2_2 -> 6.O7(3)
#H      TB
#H
#H  Revision 4.33  2005/08/10 14:39:55  gap
#H  corrected InfoText values of GV4 constructed tables
#H      TB
#H
#H  Revision 4.32  2004/11/24 15:20:20  gap
#H  added missing maxes of U4(3) --Max had asked for them--
#H  and their class fusions,
#H  fixed construction entry for "(2xA6).2^2",
#H  fixed fusion "2.U4(3).2_2' -> U4(3).2_2"
#H      TB
#H
#H  Revision 4.31  2004/08/31 12:33:34  gap
#H  added tables of 4.L2(25).2_3,
#H                  L2(49).2^2,
#H                  L2(81).2^2,
#H                  L2(81).(2x4),
#H                  3.L3(4).3.2_2,
#H                  L3(9).2^2,
#H                  L4(4).2^2,
#H                  2x2^3:L3(2)x2,
#H                  (2xA6).2^2,
#H                  2xL2(11).2,
#H                  S3xTh,
#H                  41:40,
#H                  7^(1+4):(3x2.S7),
#H                  7xL2(8),
#H                  (7xL2(8)).3,
#H                  O7(3)N3A,
#H                  O8+(3).2_1',
#H                  O8+(3).2_1'',
#H                  O8+(3).2_2',
#H                  O8+(3).(2^2)_{122},
#H                  S4(9),
#H                  S4(9).2_i,
#H                  2.U4(3).2_2',
#H                  2.U4(3).(2^2)_{133},
#H                  2.U4(3).D8,
#H                  3.U6(2).S3,
#H  added fusions 3.A6.2_i -> 3.A6.2^2,
#H                L2(49).2_i -> L2(49).2^2,
#H                L3(9).2_i -> L3(9).2^2,
#H                L4(4).2_i -> L4(4).2^2,
#H                G2(3) -> O7(3),
#H                L2(17) -> S8(2),
#H                2.L3(4).2_2 -> 2.M22.2
#H                3.L3(4).2_2 -> 3.L3(4).3.2_2
#H                3.L3(4).3 -> 3.L3(4).3.2_2
#H                2^5:S6 -> 2.M22.2
#H                O8+(3) -> O8+(3).2_1',
#H                O8+(3) -> O8+(3).2_1'',
#H                O8+(3) -> O8+(3).2_2',
#H                O8+(3) -> O8+(3).(2^2)_{122},
#H                O8+(3).2_1 -> O8+(3).(2^2)_{122},
#H                O8+(3).2_2 -> O8+(3).(2^2)_{122},
#H                2.U4(3) -> 2.U4(3).2_2',
#H                2.U4(3).2_1 -> 2.U4(3).(2^2)_{133},
#H                2.U4(3).2_2 -> O7(3),
#H                2.U4(3).2_2' -> U4(3).2_2,
#H                2.U4(3).2_3 -> 2.U4(3).(2^2)_{133},
#H                2.U4(3).2_3' -> 2.U4(3).(2^2)_{133},
#H                2.U4(3).4 -> 2.U4(3).D8,
#H                3.U6(2).2 -> 3.U6(2).S3,
#H                3.U6(2).3 -> 3.U6(2).S3,
#H  replaced table of psl(3,4):d12 by L3(4).D12,
#H  changed table of O8+(3).S4 to a construction table,
#H  changed encoding of the table of 12.A6.2_3,
#H  added maxes of Sz(8), Sz(8).3,
#H      TB
#H
#H  Revision 4.30  2004/03/30 08:55:58  gap
#H  (name change also in a factor fusion)
#H      TB
#H
#H  Revision 4.29  2004/03/30 08:05:55  gap
#H  unified tables `u4q3:2^2' and `U4(3).(2^2)_{133}'
#H      TB
#H
#H  Revision 4.28  2004/01/20 10:26:13  gap
#H  added several names of the forms `<name>C<class>', `<name>N<class>'
#H      TB
#H
#H  Revision 4.27  2003/10/06 07:18:17  gap
#H  added fusion 2.U4(3).(2^2)_{122} -> 2^2.U4(3).(2^2)_{122}
#H      TB
#H
#H  Revision 4.26  2003/07/28 15:31:22  gap
#H  added some fusions concerning maxes of 6.U6(2)
#H      TB
#H
#H  Revision 4.25  2003/06/10 16:19:16  gap
#H  store in several fusions between character tables to which subgroup number
#H  in the table of marks of the supergroup the subgroup belongs
#H  (in order to make the commutative diagrams testable)
#H      TB
#H
#H  Revision 4.24  2003/05/15 17:38:27  gap
#H  next step towards the closer connection to the library of tables of marks:
#H  added fusions tbl -> tom, adjusted fusions between character tables
#H  in order to make the diagrams commute, adjusted orderings of maxes
#H      TB
#H
#H  Revision 4.23  2003/01/14 17:28:50  gap
#H  changed `InfoText' values (for a better programmatic access)
#H  and replaced `ConstructDirectProduct' by `ConstructPermuted' where
#H  there is only one factor (again better programmatic handling)
#H      TB
#H
#H  Revision 4.22  2002/10/22 12:44:15  gap
#H  added 215 factor fusions for cases <tbl> -> <tbl> / O_{<p>}(<tbl>)
#H  (they make it possible to construct <p>-modular Brauer tables
#H  for tables of the type [p^n].<fact> where the <p>-modular Brauer table
#H  of <fact> is in the library)
#H      TB
#H
#H  Revision 4.21  2002/10/14 15:20:18  gap
#H  added two fusion texts
#H      TB
#H
#H  Revision 4.20  2002/09/23 15:07:22  gap
#H  changed comment of the fusion U4(3).2_2 -> Fi22
#H      TB
#H
#H  Revision 4.19  2002/09/18 15:22:02  gap
#H  changed the `text' components of many fusions,
#H  in order to use them as a status information (for evaluation)
#H      TB
#H
#H  Revision 4.18  2002/08/21 13:53:52  gap
#H  removed names of the form `c1m<n>', `c2m<n>', `c3m<n>'
#H      TB
#H
#H  Revision 4.17  2002/07/12 06:45:57  gap
#H  further tidying up: removed `irredinfo' stuff, rearranged constructions
#H      TB
#H
#H  Revision 4.16  2002/07/08 16:06:57  gap
#H  changed `construction' component from function (call) to list of function
#H  name and arguments
#H      TB
#H
#H  Revision 4.15  2001/05/04 16:50:33  gap
#H  first revision for ctbllib
#H
#H
#H  tbl history (GAP 4)
#H  -------------------
#H  (Rev. 4.15 of ctbllib coincides with Rev. 4.14 of tbl in GAP 4)
#H  
#H  RCS file: /gap/CVS/GAP/4.0/tbl/ctounit1.tbl,v
#H  Working file: ctounit1.tbl
#H  head: 4.14
#H  branch:
#H  locks: strict
#H  access list:
#H  symbolic names:
#H   GAP4R2: 4.12.0.6
#H   GAP4R2PRE2: 4.12.0.4
#H   GAP4R2PRE1: 4.12.0.2
#H   GAP4R1: 4.6.0.2
#H  keyword substitution: kv
#H  total revisions: 16; selected revisions: 16
#H  description:
#H  ----------------------------
#H  revision 4.14
#H  date: 2000/10/09 17:21:50;  author: gap;  state: Exp;  lines: +45 -44
#H  added tables of 3_1.U4(3).2_2' and F3+M9
#H  
#H      TB
#H  ----------------------------
#H  revision 4.13
#H  date: 2000/05/13 12:15:28;  author: gap;  state: Exp;  lines: +434 -2
#H  added some maxes of 6.Suz: [1,2,4,6,9,10,11,14,16]
#H  
#H      TB
#H  ----------------------------
#H  revision 4.12
#H  date: 1999/10/21 14:15:49;  author: gap;  state: Exp;  lines: +21 -3
#H  added many `tomidentifer' and `tomfusion' values, which yields a better
#H  interface between `tom' and `tbl';
#H  
#H  added maxes of McL.2,
#H  
#H  unified tables `J2.2M4', `2^(2+4):(3x3):2^2', `2^(2+4):(S3xS3)'.
#H  
#H      TB
#H  ----------------------------
#H  revision 4.11
#H  date: 1999/09/17 14:11:52;  author: gap;  state: Exp;  lines: +127 -69
#H  added maxes of 3.Suz.2
#H  
#H      TB
#H  ----------------------------
#H  revision 4.10
#H  date: 1999/09/14 13:30:12;  author: gap;  state: Exp;  lines: +2 -3
#H  added maxes of 3.Suz
#H  
#H      TB
#H  ----------------------------
#H  revision 4.9
#H  date: 1999/08/31 13:16:16;  author: gap;  state: Exp;  lines: +45 -2
#H  added missing tables and fusions of maximal subgroups of Suz.2
#H  
#H      TB
#H  ----------------------------
#H  revision 4.8
#H  date: 1999/08/23 10:26:59;  author: gap;  state: Exp;  lines: +6 -2
#H  unified tables of U3(5).S3 and U3(5).3.2
#H  (one CAS table, o ne ATLAS conformal table)
#H  
#H      TB
#H  ----------------------------
#H  revision 4.7
#H  date: 1999/08/18 13:59:08;  author: gap;  state: Exp;  lines: +73 -2
#H  added table of U4(3).(2^2)_{133}, and related fusions
#H  
#H      TB
#H  ----------------------------
#H  revision 4.6
#H  date: 1999/06/15 13:49:34;  author: gap;  state: Exp;  lines: +22 -2
#H  added table of 2.SuzM2 (request of a student)
#H  
#H      TB
#H  ----------------------------
#H  revision 4.5
#H  date: 1999/05/31 13:28:30;  author: gap;  state: Exp;  lines: +225 -9
#H  added table of 2.U4(3).(2^2)_{122}
#H  
#H      TB
#H  ----------------------------
#H  revision 4.4
#H  date: 1999/05/03 15:35:18;  author: gap;  state: Exp;  lines: +55 -11
#H  added tables of 2.U4(3).2_3' and 6_2.U4(3).2_3'
#H  (requested by a student in Aachen)
#H  
#H      TB
#H  ----------------------------
#H  revision 4.3
#H  date: 1997/11/25 15:46:01;  author: gap;  state: Exp;  lines: +12 -9
#H  first attempt to link the library of character tables and the
#H      library of tables of marks
#H          TB
#H  ----------------------------
#H  revision 4.2
#H  date: 1997/08/05 15:03:59;  author: gap;  state: Exp;  lines: +5 -5
#H  removed unnecessary (and ugly) `return' statements in the calls of
#H      `ConstructPermuted' and `ConstructSubdirect'
#H  ----------------------------
#H  revision 4.1
#H  date: 1997/07/17 15:48:15;  author: fceller;  state: Exp;  lines: +2 -2
#H  for version 4
#H  ----------------------------
#H  revision 1.2
#H  date: 1997/04/04 12:20:32;  author: sam;  state: Exp;  lines: +7 -23
#H  added 'ConstructPermuted', 'ConstructSubdirect',
#H  changed table constructions involving 'CharTable', 'RecFields'
#H      'Sort...' up to now
#H  ----------------------------
#H  revision 1.1
#H  date: 1996/10/21 16:02:03;  author: sam;  state: Exp;
#H  first proposal of the table library
#H  ==========================================================================
##

MOT("12_1.U4(3)",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[39191040,39191040,39191040,39191040,39191040,39191040,39191040,39191040,
39191040,39191040,39191040,39191040,6912,6912,6912,6912,6912,6912,69984,69984,
69984,69984,69984,69984,69984,69984,69984,69984,69984,69984,11664,11664,11664,
11664,11664,11664,11664,11664,11664,11664,11664,11664,3888,3888,3888,3888,324,
324,324,324,1152,1152,1152,1152,1152,1152,1152,1152,1152,1152,1152,1152,48,48,
48,60,60,60,60,60,60,60,60,60,60,60,60,864,864,864,864,864,864,864,864,864,
864,864,864,216,216,216,216,216,216,216,216,216,216,216,216,84,84,84,84,84,84,
84,84,84,84,84,84,84,84,84,84,84,84,84,84,84,84,84,84,96,96,96,96,96,96,96,96,
96,96,96,96,324,324,324,324,324,324,324,324,324,324,324,324,324,324,324,324,
324,324,324,324,324,324,324,324,108,108,108,108,108,108,108,108,144,144,144,
144,144,144,144,144,144,144,144,144],
[,[1,3,5,7,9,11,1,3,5,7,9,11,1,3,5,7,9,11,19,21,23,25,27,29,19,21,23,25,27,29,
31,33,35,37,39,41,31,33,35,37,39,41,43,45,43,45,47,49,47,49,13,15,17,13,15,17,
13,15,17,13,15,17,16,18,14,66,68,70,72,74,76,66,68,70,72,74,76,19,21,23,25,27,
29,19,21,23,25,27,29,31,33,35,37,39,41,43,45,43,45,43,45,102,104,106,108,110,
112,102,104,106,108,110,112,114,116,118,120,122,124,114,116,118,120,122,124,
60,62,52,54,56,58,60,62,52,54,56,58,150,152,154,156,158,160,150,152,154,156,
158,160,138,140,142,144,146,148,138,140,142,144,146,148,166,168,166,168,162,
164,162,164,78,80,82,84,86,88,78,80,82,84,86,88],[1,4,7,10,1,4,7,10,1,4,7,10,
13,16,13,16,13,16,1,4,7,10,1,4,7,10,1,4,7,10,1,4,7,10,1,4,7,10,1,4,7,10,1,4,7,
10,1,4,7,10,51,54,57,60,51,54,57,60,51,54,57,60,63,63,63,66,69,72,75,66,69,72,
75,66,69,72,75,13,16,13,16,13,16,13,16,13,16,13,16,13,16,13,16,13,16,13,16,13,
16,13,16,114,117,120,123,114,117,120,123,114,117,120,123,102,105,108,111,102,
105,108,111,102,105,108,111,129,132,135,126,129,132,135,126,129,132,135,126,
27,30,21,24,27,30,21,24,27,30,21,24,23,26,29,20,23,26,29,20,23,26,29,20,19,22,
25,28,19,22,25,28,51,54,57,60,51,54,57,60,51,54,57,60],,[1,6,11,4,9,2,7,12,5,
10,3,8,13,18,17,16,15,14,19,24,29,22,27,20,25,30,23,28,21,26,31,36,41,34,39,
32,37,42,35,40,33,38,43,44,45,46,47,48,49,50,51,56,61,54,59,52,57,62,55,60,53,
58,63,65,64,1,6,11,4,9,2,7,12,5,10,3,8,78,83,88,81,86,79,84,89,82,87,80,85,90,
95,94,93,92,91,96,101,100,99,98,97,114,119,124,117,122,115,120,125,118,123,
116,121,102,107,112,105,110,103,108,113,106,111,104,109,126,131,136,129,134,
127,132,137,130,135,128,133,150,155,160,153,158,151,156,161,154,159,152,157,
138,143,148,141,146,139,144,149,142,147,140,145,166,167,168,169,162,163,164,
165,170,175,180,173,178,171,176,181,174,179,172,177],,[1,8,3,10,5,12,7,2,9,4,
11,6,13,14,15,16,17,18,19,26,21,28,23,30,25,20,27,22,29,24,31,38,33,40,35,42,
37,32,39,34,41,36,43,46,45,44,47,50,49,48,51,58,53,60,55,62,57,52,59,54,61,56,
63,64,65,66,73,68,75,70,77,72,67,74,69,76,71,78,85,80,87,82,89,84,79,86,81,88,
83,90,91,92,93,94,95,96,97,98,99,100,101,1,8,3,10,5,12,7,2,9,4,11,6,1,8,3,10,
5,12,7,2,9,4,11,6,129,136,131,126,133,128,135,130,137,132,127,134,138,145,140,
147,142,149,144,139,146,141,148,143,150,157,152,159,154,161,156,151,158,153,
160,155,162,165,164,163,166,169,168,167,170,177,172,179,174,181,176,171,178,
173,180,175]],
0,
[(162,166)(163,167)(164,168)(165,169),(102,114)(103,115)(104,116)(105,117)
(106,118)(107,119)(108,120)(109,121)(110,122)(111,123)(112,124)(113,125),
(  2,  6)(  3, 11)(  5,  9)(  8, 12)( 14, 18)( 15, 17)( 20, 24)( 21, 29)
( 23, 27)( 26, 30)( 32, 36)( 33, 41)( 35, 39)( 38, 42)( 52, 56)( 53, 61)
( 55, 59)( 58, 62)( 64, 65)( 67, 71)( 68, 76)( 70, 74)( 73, 77)( 79, 83)
( 80, 88)( 82, 86)( 85, 89)( 91, 95)( 92, 94)( 97,101)( 98,100)(103,107)
(104,112)(106,110)(109,113)(115,119)(116,124)(118,122)(121,125)(127,131)
(128,136)(130,134)(133,137)(138,150)(139,155)(140,160)(141,153)(142,158)
(143,151)(144,156)(145,161)(146,154)(147,159)(148,152)(149,157)(162,166)
(163,167)(164,168)(165,169)(171,175)(172,180)(174,178)(177,181),(  2,  8)
(  4, 10)(  6, 12)( 20, 26)( 22, 28)( 24, 30)( 32, 38)( 34, 40)( 36, 42)
( 44, 46)( 48, 50)( 52, 58)( 54, 60)( 56, 62)( 67, 73)( 69, 75)( 71, 77)
( 79, 85)( 81, 87)( 83, 89)(103,109)(105,111)(107,113)(115,121)(117,123)
(119,125)(126,129)(127,136)(128,131)(130,133)(132,135)(134,137)(139,145)
(141,147)(143,149)(151,157)(153,159)(155,161)(163,165)(167,169)(171,177)
(173,179)(175,181),(  2,  6)(  3, 11)(  5,  9)(  8, 12)( 14, 18)( 15, 17)
( 20, 24)( 21, 29)( 23, 27)( 26, 30)( 32, 36)( 33, 41)( 35, 39)( 38, 42)
( 52, 56)( 53, 61)( 55, 59)( 58, 62)( 64, 65)( 67, 71)( 68, 76)( 70, 74)
( 73, 77)( 79, 83)( 80, 88)( 82, 86)( 85, 89)( 91, 95)( 92, 94)( 97,101)
( 98,100)(103,107)(104,112)(106,110)(109,113)(115,119)(116,124)(118,122)
(121,125)(127,131)(128,136)(130,134)(133,137)(138,150)(139,155)(140,160)
(141,153)(142,158)(143,151)(144,156)(145,161)(146,154)(147,159)(148,152)
(149,157)(171,175)(172,180)(174,178)(177,181)],
["ConstructProj",[["U4(3)",[]],["2.U4(3)",[]],["3_1.U4(3)",[-1,-1,-1,-1,-1,-1,
-1,-1,-13,-13,-1,-1,-1,-1,-1,-1]],["4.U4(3)",[-1,-1,-1,7,7,7,7,-1,-1,-1,-1,-1,
15,15,-1,-1]],,["6_1.U4(3)",[-1,-1,-1,-1,-1,-13,-13,-1,-1,-1,-1,-7,-7,-1,
-1]],,,,,,["12_1.U4(3)",[[-7,7,-1],[-7,7,-1],[-7,7,-1],[-7,7,-1],[-7,7,-1],[
-7,7,-1],[-55,-377,-433],[-55,-377,-433],[-7,7,-1],[-7,7,-1],[-7,7,-1],[-7,7,
-1]]]]]);
ALF("12_1.U4(3)","U4(3)",[1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,
3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,
7,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,10,10,10,11,11,
11,11,11,11,12,12,12,12,12,12,13,13,13,13,13,13,13,13,13,13,13,13,14,14,
14,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,15,15,15,15,15,16,16,
16,16,16,16,16,16,16,16,16,16,17,17,17,17,17,17,17,17,17,17,17,17,18,18,
18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,20]);
ALF("12_1.U4(3)","2.U4(3)",[1,2,1,2,1,2,1,2,1,2,1,2,3,4,3,4,3,4,5,6,5,6,5,
6,5,6,5,6,5,6,7,8,7,8,7,8,7,8,7,8,7,8,9,10,9,10,11,12,11,12,13,14,13,14,
13,14,13,14,13,14,13,14,15,15,15,16,17,16,17,16,17,16,17,16,17,16,17,18,
19,18,19,18,19,18,19,18,19,18,19,20,21,20,21,20,21,22,23,22,23,22,23,24,
25,24,25,24,25,24,25,24,25,24,25,26,27,26,27,26,27,26,27,26,27,26,27,28,
29,28,29,28,29,28,29,28,29,28,29,30,31,30,31,30,31,30,31,30,31,30,31,32,
33,32,33,32,33,32,33,32,33,32,33,34,35,34,35,36,37,36,37,38,39,38,39,38,
39,38,39,38,39,38,39]);
ALF("12_1.U4(3)","4.U4(3)",[1,2,3,4,1,2,3,4,1,2,3,4,5,6,5,6,5,6,7,8,9,10,
7,8,9,10,7,8,9,10,11,12,13,14,11,12,13,14,11,12,13,14,15,16,17,18,19,20,
21,22,23,24,25,26,23,24,25,26,23,24,25,26,27,27,27,28,29,30,31,28,29,30,
31,28,29,30,31,32,33,34,35,32,33,34,35,32,33,34,35,36,37,36,37,36,37,38,
39,38,39,38,39,40,41,42,43,40,41,42,43,40,41,42,43,44,45,46,47,44,45,46,
47,44,45,46,47,48,49,50,51,48,49,50,51,48,49,50,51,52,53,54,55,52,53,54,
55,52,53,54,55,56,57,58,59,56,57,58,59,56,57,58,59,60,61,62,63,64,65,66,
67,68,69,70,71,68,69,70,71,68,69,70,71]);
ALF("12_1.U4(3)","3_1.U4(3)",[1,2,3,1,2,3,1,2,3,1,2,3,4,5,6,4,5,6,7,8,9,7,
8,9,7,8,9,7,8,9,10,11,12,10,11,12,10,11,12,10,11,12,13,13,13,13,14,14,14,
14,15,16,17,15,16,17,15,16,17,15,16,17,18,19,20,21,22,23,21,22,23,21,22,
23,21,22,23,24,25,26,24,25,26,24,25,26,24,25,26,27,28,29,27,28,29,30,31,
32,30,31,32,33,34,35,33,34,35,33,34,35,33,34,35,36,37,38,36,37,38,36,37,
38,36,37,38,39,40,41,39,40,41,39,40,41,39,40,41,42,43,44,42,43,44,42,43,
44,42,43,44,45,46,47,45,46,47,45,46,47,45,46,47,48,48,48,48,49,49,49,49,
50,51,52,50,51,52,50,51,52,50,51,52]);
ALF("12_1.U4(3)","6_1.U4(3)",[1,2,3,4,5,6,1,2,3,4,5,6,7,8,9,10,11,12,13,
14,15,16,17,18,13,14,15,16,17,18,19,20,21,22,23,24,19,20,21,22,23,24,25,
26,25,26,27,28,27,28,29,30,31,32,33,34,29,30,31,32,33,34,35,36,37,38,39,
40,41,42,43,38,39,40,41,42,43,44,45,46,47,48,49,44,45,46,47,48,49,50,51,
52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,62,63,64,65,66,67,68,69,
70,71,72,73,68,69,70,71,72,73,74,75,76,77,78,79,74,75,76,77,78,79,80,81,
82,83,84,85,80,81,82,83,84,85,86,87,88,89,90,91,86,87,88,89,90,91,92,93,
92,93,94,95,94,95,96,97,98,99,100,101,96,97,98,99,100,101]);
ALF("12_1.U4(3)","12_1.U4(3).2_1",[1,2,3,4,5,2,6,7,5,8,3,7,9,10,11,12,11,
10,13,14,15,16,17,14,18,19,17,20,15,19,21,22,23,24,25,22,26,27,25,28,23,
27,29,30,31,32,33,34,35,36,37,38,39,40,41,38,42,43,41,44,39,43,45,46,46,
47,48,49,50,51,48,52,53,51,54,49,53,55,56,57,58,59,56,60,61,59,62,57,61,
63,64,65,66,65,64,67,68,69,70,69,68,71,72,73,74,75,72,76,77,75,78,73,77,
79,80,81,82,83,80,84,85,83,86,81,85,87,88,89,90,91,88,92,93,91,94,89,93,
95,96,97,98,99,100,101,102,103,104,105,106,95,100,105,98,103,96,101,106,
99,104,97,102,107,108,109,110,107,108,109,110,111,112,113,114,115,112,116,
117,115,118,113,117],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);
ALF("12_1.U4(3)","12_1.U4(3).2_2",[1,2,3,4,5,6,7,2,8,4,9,6,10,11,12,13,14,
15,16,17,18,19,20,21,22,17,23,19,24,21,25,26,27,28,29,30,31,26,32,28,33,
30,34,35,36,35,37,38,39,38,40,41,42,43,44,45,46,41,47,43,48,45,49,50,51,
52,53,54,55,56,57,58,53,59,55,60,57,61,62,63,64,65,66,67,62,68,64,69,66,
70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,
82,89,84,91,86,93,88,83,90,85,92,87,94,95,96,94,97,96,98,97,99,98,95,99,
100,101,102,103,104,105,106,101,107,103,108,105,109,110,111,112,113,114,
115,110,116,112,117,114,118,119,120,121,118,121,120,119,122,123,124,125,
126,127,128,123,129,125,130,127],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);
ALF("12_1.U4(3)","12_1.U4(3).2_2'",[1,2,3,4,5,6,7,6,5,4,3,2,8,9,10,11,10,
9,12,13,14,15,16,17,18,17,16,15,14,13,19,20,21,22,23,24,25,24,23,22,21,20,
26,27,28,27,29,30,31,30,32,33,34,35,36,37,38,37,36,35,34,33,39,40,40,41,
42,43,44,45,46,47,46,45,44,43,42,48,49,50,51,52,53,54,53,52,51,50,49,55,
56,57,58,57,56,59,60,61,62,61,60,63,64,65,66,67,68,69,70,71,72,73,74,63,
74,73,72,71,70,69,68,67,66,65,64,75,76,76,75,77,78,79,80,80,79,78,77,81,
82,83,84,85,86,87,88,89,90,91,92,81,92,91,90,89,88,87,86,85,84,83,82,93,
94,95,94,96,97,98,97,99,100,101,102,103,104,105,104,103,102,101,100]);

MOT("12_1.U4(3).2_1",
[
"origin: ATLAS of finite groups, tests: 1.o.r."
],
[78382080,39191040,39191040,78382080,39191040,78382080,39191040,78382080,
13824,6912,6912,13824,139968,69984,69984,139968,69984,139968,69984,139968,
23328,11664,11664,23328,11664,23328,11664,23328,7776,7776,7776,7776,648,648,
648,648,2304,1152,1152,2304,1152,2304,1152,2304,96,48,120,60,60,120,60,120,60,
120,1728,864,864,1728,864,1728,864,1728,432,216,216,432,432,216,216,432,168,
84,84,168,84,168,84,168,168,84,84,168,84,168,84,168,192,96,96,192,96,192,96,
192,324,324,324,324,324,324,324,324,324,324,324,324,108,108,108,108,288,144,
144,288,144,288,144,288,48384,48384,48384,48384,2880,2880,4608,4608,4608,4608,
128,864,864,864,864,72,72,72,72,72,72,72,72,64,64,64,64,40,40,40,40,576,576,
576,576,576,576,576,576,144,144,144,144,144,144,144,144,56,56,56,56,56,56,56,
56],
[,[1,3,5,6,5,1,3,6,1,3,5,6,13,15,17,18,17,13,15,18,21,23,25,26,25,21,23,26,29,
31,29,31,33,35,33,35,9,11,11,9,11,9,11,9,12,10,47,49,51,52,51,47,49,52,13,15,
17,18,17,13,15,18,21,23,25,26,29,31,29,31,71,73,75,76,75,71,73,76,79,81,83,84,
83,79,81,84,44,43,38,40,38,44,43,40,95,105,103,101,99,97,95,105,103,101,99,97,
107,109,107,109,55,57,59,60,59,55,57,60,1,6,1,6,8,4,9,9,9,9,9,13,18,13,18,28,
24,30,32,33,35,33,35,40,44,40,44,54,50,54,50,55,60,55,60,60,55,60,55,63,63,63,
63,67,67,67,67,71,76,71,76,79,84,79,84],[1,4,6,8,1,6,8,4,9,12,9,12,1,4,6,8,1,
6,8,4,1,4,6,8,1,6,8,4,1,4,6,8,1,4,6,8,37,40,42,44,37,42,44,40,45,45,47,50,52,
54,47,52,54,50,9,12,9,12,9,9,12,12,9,12,9,12,9,12,9,12,79,82,84,86,79,84,86,
82,71,74,76,78,71,76,78,74,90,92,94,87,90,94,87,92,17,19,15,14,17,19,15,14,17,
19,15,14,13,16,18,20,37,40,42,44,37,42,44,40,119,122,121,120,124,123,128,127,
126,125,129,119,122,121,120,124,123,124,123,119,122,121,120,145,144,143,142,
149,148,147,146,128,127,126,125,128,127,126,125,128,127,126,125,128,127,126,
125,170,173,172,171,166,169,168,167],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,
17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,
43,44,45,46,1,2,3,4,5,6,7,8,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,
79,80,81,82,83,84,85,86,71,72,73,74,75,76,77,78,87,88,89,90,91,92,93,94,95,96,
97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,
117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,
136,137,138,139,140,141,142,143,144,145,123,124,123,124,150,151,152,153,154,
155,156,157,158,159,160,161,162,163,164,165,170,171,172,173,166,167,168,
169],,[1,7,3,8,5,6,2,4,9,10,11,12,13,19,15,20,17,18,14,16,21,27,23,28,25,26,
22,24,29,32,31,30,33,36,35,34,37,43,39,44,41,42,38,40,45,46,47,53,49,54,51,52,
48,50,55,61,57,62,59,60,56,58,63,64,65,66,67,68,69,70,1,7,3,8,5,6,2,4,1,7,3,8,
5,6,2,4,90,89,88,87,93,94,91,92,95,102,97,104,99,106,101,96,103,98,105,100,
107,110,109,108,111,117,113,118,115,116,112,114,119,122,121,120,124,123,128,
127,126,125,129,130,133,132,131,135,134,137,136,138,141,140,139,145,144,143,
142,147,146,149,148,157,156,155,154,153,152,151,150,161,160,159,158,165,164,
163,162,119,122,121,120,119,122,121,120]],
0,
[(146,148)(147,149),( 71, 79)( 72, 80)( 73, 81)( 74, 82)( 75, 83)( 76, 84)
( 77, 85)( 78, 86)(166,170)(167,171)(168,172)(169,173),(  2,  7)(  4,  8)
( 14, 19)( 16, 20)( 22, 27)( 24, 28)( 30, 32)( 34, 36)( 38, 43)( 40, 44)
( 48, 53)( 50, 54)( 56, 61)( 58, 62)( 72, 77)( 74, 78)( 80, 85)( 82, 86)
( 87, 90)( 88, 89)( 91, 93)( 92, 94)( 96,102)( 98,104)(100,106)(108,110)
(112,117)(114,118)(120,122)(123,124)(125,128)(126,127)(131,133)(134,135)
(136,137)(139,141)(142,145)(143,144)(146,147)(148,149)(150,157)(151,156)
(152,155)(153,154)(158,161)(159,160)(162,165)(163,164)(167,169)(171,173),
(  2,  7)(  4,  8)( 14, 19)( 16, 20)( 22, 27)( 24, 28)( 30, 32)( 34, 36)
( 38, 43)( 40, 44)( 48, 53)( 50, 54)( 56, 61)( 58, 62)( 72, 77)( 74, 78)
( 80, 85)( 82, 86)( 87, 90)( 88, 89)( 91, 93)( 92, 94)( 96,102)( 98,104)
(100,106)(108,110)(112,117)(114,118)(120,122)(123,124)(125,128)(126,127)
(131,133)(134,135)(136,137)(139,141)(142,145)(143,144)(146,149)(147,148)
(150,157)(151,156)(152,155)(153,154)(158,161)(159,160)(162,165)(163,164)
(167,169)(171,173),(119,121)(120,122)(125,127)(126,128)(130,132)(131,133)
(138,140)(139,141)(142,144)(143,145)(150,152)(151,153)(154,156)(155,157)
(158,160)(159,161)(162,164)(163,165)(166,168)(167,169)(170,172)(171,173)],
["ConstructMGA","12_1.U4(3)","4.U4(3).2_1",
     [ [ 72, 73 ], [ 74, 75 ], [ 76, 77 ], [ 78, 79 ], [ 80, 81 ],
        [ 82, 83 ], [ 84, 85 ], [ 86, 87 ], [ 88, 89 ], [ 90, 91 ],
        [ 92, 93 ], [ 94, 95 ], [ 96, 97 ], [ 98, 99 ], [ 100, 101 ],
        [ 102, 103 ], [ 104, 105 ], [ 106, 107 ], [ 108, 109 ], [ 110, 111 ],
        [ 112, 113 ], [ 114, 115 ], [ 116, 117 ], [ 118, 119 ], [ 120, 121 ],
        [ 122, 123 ], [ 124, 125 ], [ 126, 127 ], [ 128, 129 ], [ 130, 131 ],
        [ 132, 133 ], [ 134, 135 ], [ 136, 137 ], [ 138, 139 ], [ 140, 141 ],
        [ 142, 143 ], [ 144, 145 ], [ 146, 147 ], [ 148, 149 ], [ 150, 151 ],
        [ 152, 153 ], [ 154, 155 ], [ 156, 157 ], [ 158, 159 ], [ 160, 161 ],
        [ 162, 163 ], [ 164, 165 ], [ 166, 167 ], [ 168, 169 ], [ 170, 171 ],
        [ 172, 173 ], [ 174, 175 ], [ 176, 177 ], [ 178, 179 ], [ 180, 181 ] ]
      , ()]);
ALF("12_1.U4(3).2_1","U4(3).2_1",[1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,
4,4,4,4,4,4,4,4,5,5,5,5,6,6,6,6,7,7,7,7,7,7,7,7,8,8,9,9,9,9,9,9,9,9,10,10,
10,10,10,10,10,10,11,11,11,11,12,12,12,12,13,13,13,13,13,13,13,13,14,14,
14,14,14,14,14,14,15,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,
16,16,17,17,17,17,18,18,18,18,18,18,18,18,19,19,19,19,20,20,21,21,21,21,
22,23,23,23,23,24,24,25,25,26,26,26,26,27,27,27,27,28,28,28,28,29,29,29,
29,30,30,30,30,31,31,31,31,32,32,32,32,33,33,33,33,34,34,34,34]);
ALF("12_1.U4(3).2_1","2.U4(3).2_1",[1,2,1,2,1,1,2,2,3,4,3,4,5,6,5,6,5,5,6,
6,7,8,7,8,7,7,8,8,9,10,9,10,11,12,11,12,13,14,13,14,13,13,14,14,15,15,16,
17,16,17,16,16,17,17,18,19,18,19,18,18,19,19,20,21,20,21,22,23,22,23,24,
25,24,25,24,24,25,25,26,27,26,27,26,26,27,27,28,29,28,29,28,28,29,29,30,
31,30,31,30,31,30,31,30,31,30,31,32,33,32,33,34,35,34,35,34,34,35,35,36,
37,36,37,38,39,40,41,40,41,42,43,44,43,44,45,46,47,48,49,50,49,50,51,52,
51,52,53,54,53,54,55,56,55,56,57,58,57,58,59,60,59,60,61,62,61,62,63,64,
63,64,65,66,65,66]);
ALF("12_1.U4(3).2_1","4.U4(3).2_1",[1,2,3,4,1,3,4,2,5,6,5,6,7,8,9,10,7,9,
10,8,11,12,13,14,11,13,14,12,15,16,17,18,19,20,21,22,23,24,25,26,23,25,26,
24,27,27,28,29,30,31,28,30,31,29,32,33,34,35,32,34,35,33,36,37,36,37,38,
39,38,39,40,41,42,43,40,42,43,41,44,45,46,47,44,46,47,45,48,49,50,51,48,
50,51,49,52,53,54,55,52,53,54,55,52,53,54,55,56,57,58,59,60,61,62,63,60,
62,63,61,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,
85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,
107,108,109,110,111,112,113,114,115,116,117,118]);
ALF("12_1.U4(3).2_1","3_1.U4(3).2_1",[1,2,2,1,2,1,2,1,3,4,4,3,5,6,6,5,6,5,
6,5,7,8,8,7,8,7,8,7,9,9,9,9,10,10,10,10,11,12,12,11,12,11,12,11,13,14,15,
16,16,15,16,15,16,15,17,18,18,17,18,17,18,17,19,20,20,19,21,22,22,21,23,
24,24,23,24,23,24,23,25,26,26,25,26,25,26,25,27,28,28,27,28,27,28,27,29,
30,31,29,30,31,29,30,31,29,30,31,32,32,32,32,33,34,34,33,34,33,34,33,35,
35,35,35,36,36,37,37,37,37,38,39,39,39,39,40,40,41,41,42,42,42,42,43,43,
43,43,44,44,44,44,45,45,45,45,46,46,46,46,47,47,47,47,48,48,48,48,49,49,
49,49,50,50,50,50]);
ALF("12_1.U4(3).2_1","6_1.U4(3).2_1",[1,2,3,4,3,1,2,4,5,6,7,8,9,10,11,12,
11,9,10,12,13,14,15,16,15,13,14,16,17,18,17,18,19,20,19,20,21,22,23,24,23,
21,22,24,25,26,27,28,29,30,29,27,28,30,31,32,33,34,33,31,32,34,35,36,37,
38,39,40,41,42,43,44,45,46,45,43,44,46,47,48,49,50,49,47,48,50,51,52,53,
54,53,51,52,54,55,56,57,58,59,60,55,56,57,58,59,60,61,62,61,62,63,64,65,
66,65,63,64,66,67,68,67,68,69,70,71,72,71,72,73,74,75,74,75,76,77,78,79,
80,81,80,81,82,83,82,83,84,85,84,85,86,87,86,87,88,89,88,89,90,91,90,91,
92,93,92,93,94,95,94,95,96,97,96,97]);

MOT("12_1.U4(3).2_2",
[
"origin: ATLAS of finite groups, tests: 1.o.r."
],
[78382080,39191040,78382080,39191040,78382080,39191040,78382080,78382080,
78382080,13824,13824,13824,13824,13824,13824,139968,69984,139968,69984,139968,
69984,139968,139968,139968,23328,11664,23328,11664,23328,11664,23328,23328,
23328,7776,3888,7776,648,324,648,2304,1152,2304,1152,2304,1152,2304,2304,2304,
96,96,96,120,60,120,60,120,60,120,120,120,1728,864,1728,864,1728,864,1728,
1728,1728,432,432,432,432,432,432,432,432,432,432,432,432,84,84,84,84,84,84,
84,84,84,84,84,84,96,96,96,96,96,96,648,324,648,324,648,324,648,648,648,648,
324,648,324,648,324,648,648,648,108,108,108,108,288,144,288,144,288,144,288,
288,288,311040,311040,311040,311040,311040,311040,3456,3456,3456,576,576,576,
576,576,576,576,576,576,7776,7776,7776,7776,7776,7776,7776,7776,7776,7776,
7776,7776,1296,1296,1296,1296,1296,1296,648,648,648,648,648,648,144,144,36,36,
48,48,48,60,60,60,60,60,60,144,144,144,144,144,144,72,72,72,72,72,72,108,108,
108,108,108,108,108,108,108,108,108,108],
[,[1,3,5,7,8,9,1,5,8,1,3,5,7,8,9,16,18,20,22,23,24,16,20,23,25,27,29,31,32,33,
25,29,32,34,36,34,37,39,37,10,12,14,10,12,14,10,14,12,13,15,11,52,54,56,58,59,
60,52,56,59,16,18,20,22,23,24,16,20,23,25,27,29,31,32,33,34,36,34,36,34,36,82,
84,86,88,90,92,82,84,86,88,90,92,43,45,41,45,43,41,109,111,113,115,116,117,
109,113,116,100,102,104,106,107,108,100,104,107,118,120,118,120,61,63,65,67,
68,69,61,65,68,7,3,9,7,3,9,1,8,5,10,12,14,13,15,11,13,15,11,22,18,24,22,18,24,
22,18,24,22,18,24,36,36,36,36,36,36,31,27,33,31,27,33,34,34,37,37,40,47,44,58,
54,60,58,54,60,67,63,69,67,63,69,73,75,71,73,75,71,115,111,117,115,111,117,
106,102,108,106,102,108],[1,4,7,4,1,4,7,1,7,10,13,10,13,10,13,1,4,7,4,1,4,7,1,
7,1,4,7,4,1,4,7,1,7,1,4,7,1,4,7,40,43,46,43,40,43,46,40,46,49,49,49,52,55,58,
55,52,55,58,52,58,10,13,10,13,10,13,10,10,10,10,13,10,13,10,13,10,13,10,13,10,
13,82,91,88,85,82,91,88,85,82,91,88,85,94,98,98,94,98,94,23,21,18,21,23,21,18,
23,18,20,17,24,17,20,17,24,20,24,16,19,22,19,40,43,46,43,40,43,46,40,46,131,
134,131,134,131,134,137,137,137,140,140,140,143,146,143,146,143,146,131,134,
131,134,131,134,131,134,131,134,131,134,131,134,131,134,131,134,131,134,131,
134,131,134,137,137,137,137,177,177,177,180,183,180,183,180,183,140,140,140,
140,140,140,143,146,143,146,143,146,151,154,151,154,151,154,159,156,159,156,
159,156],,[1,6,9,4,8,2,7,5,3,10,15,14,13,12,11,16,21,24,19,23,17,22,20,18,25,
30,33,28,32,26,31,29,27,34,35,36,37,38,39,40,45,48,43,47,41,46,44,42,49,51,50,
1,6,9,4,8,2,7,5,3,61,66,69,64,68,62,67,65,63,70,75,74,73,72,71,76,81,80,79,78,
77,82,93,92,91,90,89,88,87,86,85,84,83,94,96,95,99,98,97,109,114,117,112,116,
110,115,113,111,100,105,108,103,107,101,106,104,102,118,121,120,119,122,127,
130,125,129,123,128,126,124,131,136,135,134,133,132,137,139,138,140,142,141,
143,148,147,146,145,144,155,160,159,158,157,156,149,154,153,152,151,150,161,
166,165,164,163,162,167,172,171,170,169,168,173,174,175,176,177,179,178,131,
136,135,134,133,132,189,188,187,186,191,190,192,197,196,195,194,193,204,209,
208,207,206,205,198,203,202,201,200,199],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,
15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,
41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,
67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,1,2,3,4,5,6,7,2,8,4,9,6,94,95,96,
97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,
117,118,121,120,119,122,123,124,125,126,127,128,129,130,131,132,133,134,135,
136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,
155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,
174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,
193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209]],
0,
[(175,176),(119,121),(83,89)(85,91)(87,93),( 83, 89)( 85, 91)( 87, 93)
(119,121),(  2,  6)(  3,  9)(  5,  8)( 11, 15)( 12, 14)( 17, 21)( 18, 24)
( 20, 23)( 26, 30)( 27, 33)( 29, 32)( 41, 45)( 42, 48)( 44, 47)( 50, 51)
( 53, 57)( 54, 60)( 56, 59)( 62, 66)( 63, 69)( 65, 68)( 71, 75)( 72, 74)
( 77, 81)( 78, 80)( 83, 87)( 84, 92)( 86, 90)( 89, 93)( 95, 96)( 97, 99)
(100,109)(101,114)(102,117)(103,112)(104,116)(105,110)(106,115)(107,113)
(108,111)(119,121)(123,127)(124,130)(126,129)(132,136)(133,135)(138,139)
(141,142)(144,148)(145,147)(149,155)(150,160)(151,159)(152,158)(153,157)
(154,156)(162,166)(163,165)(168,172)(169,171)(178,179)(181,185)(182,184)
(186,189)(187,188)(190,191)(193,197)(194,196)(198,204)(199,209)(200,208)
(201,207)(202,206)(203,205),(  2,  6)(  3,  9)(  5,  8)( 11, 15)( 12, 14)
( 17, 21)( 18, 24)( 20, 23)( 26, 30)( 27, 33)( 29, 32)( 41, 45)( 42, 48)
( 44, 47)( 50, 51)( 53, 57)( 54, 60)( 56, 59)( 62, 66)( 63, 69)( 65, 68)
( 71, 75)( 72, 74)( 77, 81)( 78, 80)( 83, 87)( 84, 92)( 86, 90)( 89, 93)
( 95, 96)( 97, 99)(100,109)(101,114)(102,117)(103,112)(104,116)(105,110)
(106,115)(107,113)(108,111)(123,127)(124,130)(126,129)(132,136)(133,135)
(138,139)(141,142)(144,148)(145,147)(149,155)(150,160)(151,159)(152,158)
(153,157)(154,156)(162,166)(163,165)(168,172)(169,171)(178,179)(181,185)
(182,184)(186,189)(187,188)(190,191)(193,197)(194,196)(198,204)(199,209)
(200,208)(201,207)(202,206)(203,205),(131,134)(132,135)(133,136)(143,146)
(144,147)(145,148)(149,152)(150,153)(151,154)(155,158)(156,159)(157,160)
(161,164)(162,165)(163,166)(167,170)(168,171)(169,172)(173,174)(180,183)
(181,184)(182,185)(186,189)(187,190)(188,191)(192,195)(193,196)(194,197)
(198,201)(199,202)(200,203)(204,207)(205,208)(206,209)],
["ConstructMGA","12_1.U4(3)","6_1.U4(3).2_2",
     [ [ 40, 41 ], [ 42, 43 ], [ 44, 45 ], [ 46, 47 ], [ 48, 49 ],
        [ 50, 53 ], [ 51, 52 ], [ 54, 55 ], [ 56, 57 ], [ 58, 59 ],
        [ 60, 61 ], [ 62, 63 ], [ 64, 67 ], [ 65, 66 ], [ 68, 69 ],
        [ 70, 71 ], [ 134, 136 ], [ 135, 137 ], [ 138, 140 ], [ 139, 141 ],
        [ 142, 144 ], [ 143, 145 ], [ 146, 148 ], [ 147, 149 ], [ 150, 152 ],
        [ 151, 153 ], [ 154, 156 ], [ 155, 157 ], [ 158, 164 ], [ 159, 165 ],
        [ 160, 162 ], [ 161, 163 ], [ 166, 168 ], [ 167, 169 ], [ 170, 172 ],
        [ 171, 173 ], [ 174, 176 ], [ 175, 177 ], [ 178, 180 ], [ 179, 181 ] ]
      , ( 64, 80, 96,112,128,144,160,176, 70, 86,102,118,134,150,166,182, 76,
        92,108,124,140,156,172, 66, 82, 98,114,130,146,162,178, 72, 88,104,
       120,136,152,168,184, 78, 94,110,126,142,158,174, 68, 84,100,116,132,
       148,164,180, 74, 90,106,122,138,154,170)( 65, 81, 97,113,129,145,161,
       177, 71, 87,103,119,135,151,167,183, 77, 93,109,125,141,157,173, 67,
        83, 99,115,131,147,163,179, 73, 89,105,121,137,153,169,185, 79, 95,
       111,127,143,159,175, 69, 85,101,117,133,149,165,181, 75, 91,107,123,
       139,155,171)]);
ALF("12_1.U4(3).2_2","U4(3).2_2",[1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,
3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,6,6,6,7,7,7,7,7,7,7,7,7,8,8,8,9,9,9,9,9,9,
9,9,9,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,12,12,12,12,12,12,13,
13,13,13,13,13,13,13,13,13,13,13,14,14,14,14,14,14,15,15,15,15,15,15,15,
15,15,16,16,16,16,16,16,16,16,16,17,17,17,17,18,18,18,18,18,18,18,18,18,
19,19,19,19,19,19,20,20,20,21,21,21,22,22,22,22,22,22,23,23,23,23,23,23,
24,24,24,24,24,24,25,25,25,25,25,25,26,26,26,26,26,26,27,27,28,28,29,29,
29,30,30,30,30,30,30,31,31,31,31,31,31,32,32,32,32,32,32,33,33,33,33,33,
33,34,34,34,34,34,34]);
ALF("12_1.U4(3).2_2","2.U4(3).2_2",[1,2,1,2,1,2,1,1,1,3,4,3,4,3,4,5,6,5,6,
5,6,5,5,5,7,8,7,8,7,8,7,7,7,9,10,9,11,12,11,13,14,13,14,13,14,13,13,13,15,
15,15,16,17,16,17,16,17,16,16,16,18,19,18,19,18,19,18,18,18,20,21,20,21,
20,21,22,23,22,23,22,23,24,25,24,25,24,25,24,25,24,25,24,25,26,26,26,26,
26,26,27,28,27,28,27,28,27,27,27,29,30,29,30,29,30,29,29,29,31,32,31,32,
33,34,33,34,33,34,33,33,33,35,36,35,36,35,36,37,37,37,38,38,38,39,40,39,
40,39,40,41,42,41,42,41,42,43,44,43,44,43,44,45,46,45,46,45,46,47,48,47,
48,47,48,49,50,51,52,53,53,53,54,55,54,55,54,55,56,57,56,57,56,57,58,59,
58,59,58,59,60,61,60,61,60,61,62,63,62,63,62,63]);
ALF("12_1.U4(3).2_2","4.U4(3).2_2",[1,2,3,2,1,2,3,1,3,4,5,4,5,4,5,6,7,8,7,
6,7,8,6,8,9,10,11,10,9,10,11,9,11,12,13,14,15,16,17,18,19,20,19,18,19,20,
18,20,21,21,21,22,23,24,23,22,23,24,22,24,25,26,27,26,25,26,27,25,27,28,
29,28,29,28,29,30,31,30,31,30,31,32,33,34,35,32,33,34,35,32,33,34,35,36,
37,37,36,37,36,38,39,40,39,38,39,40,38,40,41,42,43,42,41,42,43,41,43,44,
45,46,47,48,49,50,49,48,49,50,48,50,51,52,51,52,51,52,53,53,53,54,54,54,
55,56,55,56,55,56,57,58,57,58,57,58,59,60,59,60,59,60,61,62,61,62,61,62,
63,64,63,64,63,64,65,66,67,68,69,69,69,70,71,70,71,70,71,72,73,72,73,72,
73,74,75,74,75,74,75,76,77,76,77,76,77,78,79,78,79,78,79]);
ALF("12_1.U4(3).2_2","3_1.U4(3).2_2",[1,2,3,1,2,3,1,3,2,4,5,6,4,5,6,7,8,9,
7,8,9,7,9,8,10,11,12,10,11,12,10,12,11,13,13,13,14,14,14,15,16,17,15,16,
17,15,17,16,18,19,20,21,22,23,21,22,23,21,23,22,24,25,26,24,25,26,24,26,
25,27,28,29,27,28,29,30,31,32,30,31,32,33,34,35,33,34,35,33,34,35,33,34,
35,36,37,38,37,36,38,39,40,41,39,40,41,39,41,40,42,43,44,42,43,44,42,44,
43,45,45,45,45,46,47,48,46,47,48,46,48,47,49,50,51,49,50,51,52,53,54,55,
56,57,58,59,60,58,59,60,61,62,63,61,62,63,64,65,66,64,65,66,67,68,69,67,
68,69,70,71,72,70,71,72,73,73,74,74,75,76,77,78,79,80,78,79,80,81,82,83,
81,82,83,84,85,86,84,85,86,87,88,89,87,88,89,90,91,92,90,91,92]);
ALF("12_1.U4(3).2_2","6_1.U4(3).2_2",[1,2,3,4,5,6,1,3,5,7,8,9,10,11,12,13,
14,15,16,17,18,13,15,17,19,20,21,22,23,24,19,21,23,25,26,25,27,28,27,29,
30,31,32,33,34,29,31,33,35,36,37,38,39,40,41,42,43,38,40,42,44,45,46,47,
48,49,44,46,48,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,62,
63,64,65,66,67,68,69,70,69,68,70,71,72,73,74,75,76,71,73,75,77,78,79,80,
81,82,77,79,81,83,84,83,84,85,86,87,88,89,90,85,87,89,91,92,93,94,95,96,
97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,
116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,
134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,
152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169]);
ALF("12_1.U4(3).2_2","6.O7(3)",[1,8,6,7,5,9,4,3,2,13,11,15,10,14,12,16,56,
17,55,16,57,17,16,17,18,59,23,58,22,60,21,20,19,24,61,25,30,78,31,37,44,
42,43,41,45,40,39,38,46,47,48,49,118,54,117,53,119,52,51,50,70,63,69,62,
70,64,69,70,69,74,72,76,71,75,73,77,67,77,66,77,68,87,153,92,152,91,157,
90,156,89,155,88,154,96,97,101,100,99,98,106,169,105,168,104,167,103,102,
107,104,164,103,166,102,165,107,106,105,108,170,109,171,122,131,123,130,
122,132,123,122,123,7,11,9,10,8,12,13,14,15,43,44,45,34,47,36,46,35,48,57,
64,56,63,55,62,56,62,55,64,57,63,61,67,61,66,61,68,58,72,60,71,59,73,65,
77,83,84,93,94,95,117,115,119,114,118,116,131,130,130,132,132,131,127,138,
129,137,128,139,165,174,164,173,166,172,169,172,168,174,167,173],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);

MOT("Isoclinic(12_1.U4(3).2_2)",
[
"isoclinic group of the 12_1.U4(3).2_2 given in the ATLAS"
],
0,
0,
0,
[(175,176),(131,134)(132,135)(133,136)(143,146)(144,147)(145,148)(149,152)
(150,153)(151,154)(155,158)(156,159)(157,160)(161,164)(162,165)(163,166)(167,
170)(168,171)(169,172)(173,174)(180,183)(181,184)(182,185)(186,189)(187,190)
(188,191)(192,195)(193,196)(194,197)(198,201)(199,202)(200,203)(204,207)(205,
208)(206,209),(119,121),(83,89)(85,91)(87,93),(2,6)(3,9)(5,8)(11,15)(12,14)
(17,21)(18,24)(20,23)(26,30)(27,33)(29,32)(41,45)(42,48)(44,47)(50,51)(53,57)
(54,60)(56,59)(62,66)(63,69)(65,68)(71,75)(72,74)(77,81)(78,80)(83,87)(84,92)
(86,90)(89,93)(95,96)(97,99)(100,109)(101,114)(102,117)(103,112)(104,116)(105,
110)(106,115)(107,113)(108,111)(123,127)(124,130)(126,129)(132,136)(133,135)
(138,139)(141,142)(144,148)(145,147)(149,155)(150,160)(151,159)(152,158)(153,
157)(154,156)(162,166)(163,165)(168,172)(169,171)(178,179)(181,185)(182,184)
(186,189)(187,188)(190,191)(193,197)(194,196)(198,204)(199,209)(200,208)(201,
207)(202,206)(203,205)],
["ConstructIsoclinic",[["12_1.U4(3).2_2"]]]);
ALF("Isoclinic(12_1.U4(3).2_2)","2.U4(3).2_2",[1,2,1,2,1,2,1,1,1,3,4,3,4,
3,4,5,6,5,6,5,6,5,5,5,7,8,7,8,7,8,7,7,7,9,10,9,11,12,11,13,14,13,14,13,14,
13,13,13,15,15,15,16,17,16,17,16,17,16,16,16,18,19,18,19,18,19,18,18,18,
20,21,20,21,20,21,22,23,22,23,22,23,24,25,24,25,24,25,24,25,24,25,24,25,
26,26,26,26,26,26,27,28,27,28,27,28,27,27,27,29,30,29,30,29,30,29,29,29,
31,32,31,32,33,34,33,34,33,34,33,33,33,35,36,35,36,35,36,37,37,37,38,38,
38,39,40,39,40,39,40,41,42,41,42,41,42,43,44,43,44,43,44,45,46,45,46,45,
46,47,48,47,48,47,48,49,50,51,52,53,53,53,54,55,54,55,54,55,56,57,56,57,
56,57,58,59,58,59,58,59,60,61,60,61,60,61,62,63,62,63,62,63]);

MOT("12_1.U4(3).2_2'",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7],\n",
"constructed using `PossibleCharacterTablesOfTypeMGA'"
],
[78382080,39191040,39191040,39191040,39191040,39191040,78382080,13824,6912,
6912,13824,139968,69984,69984,69984,69984,69984,139968,23328,11664,11664,11664
,11664,11664,23328,7776,3888,7776,648,324,648,2304,1152,1152,1152,1152,1152,
2304,96,48,120,60,60,60,60,60,120,1728,864,864,864,864,864,1728,432,216,216,
432,432,216,216,432,84,84,84,84,84,84,84,84,84,84,84,84,96,96,96,96,96,96,324,
324,324,324,324,324,324,324,324,324,324,324,216,108,216,216,108,216,288,144,
144,144,144,144,288,103680,103680,1152,192,192,192,2592,2592,2592,2592,432,432
,216,216,144,144,36,36,16,20,20,48,48,24,24,36,36,36,36],
[,[1,3,5,7,5,3,1,1,3,5,7,12,14,16,18,16,14,12,19,21,23,25,23,21,19,26,28,26,29
,31,29,8,10,10,8,10,10,8,11,9,41,43,45,47,45,43,41,12,14,16,18,16,14,12,19,21,
23,25,26,28,26,28,63,65,67,69,71,73,63,65,67,69,71,73,35,33,37,37,35,33,81,91,
89,87,85,83,81,91,89,87,85,83,96,98,96,93,95,93,48,50,52,54,52,50,48,7,7,1,8,
11,11,18,18,18,18,25,25,28,28,19,19,29,29,32,47,47,54,54,62,62,98,98,95,95],[1
,4,7,4,1,4,7,8,11,8,11,1,4,7,4,1,4,7,1,4,7,4,1,4,7,1,4,7,1,4,7,32,35,38,35,32,
35,38,39,39,41,44,47,44,41,44,47,8,11,8,11,8,11,8,8,11,8,11,8,11,8,11,63,72,69
,66,63,72,69,66,63,72,69,66,75,79,75,79,79,75,16,13,14,17,16,13,14,17,16,13,14
,17,12,15,18,12,15,18,32,35,38,35,32,35,38,106,107,108,109,110,111,106,107,106
,107,106,107,106,107,108,108,108,108,124,125,126,109,109,110,111,112,113,114,
115],,[1,6,3,4,5,2,7,8,9,10,11,12,17,14,15,16,13,18,19,24,21,22,23,20,25,26,27
,28,29,30,31,32,37,34,35,36,33,38,39,40,1,6,3,4,5,2,7,48,53,50,51,52,49,54,55,
56,57,58,59,60,61,62,63,70,65,72,67,74,69,64,71,66,73,68,75,78,80,76,79,77,81,
88,83,90,85,92,87,82,89,84,91,86,96,97,98,93,94,95,99,104,101,102,103,100,105,
106,107,108,109,110,111,114,115,112,113,116,117,118,119,120,121,122,123,124,
106,107,128,127,129,130,133,134,131,132],,[1,6,3,4,5,2,7,8,9,10,11,12,17,14,15
,16,13,18,19,24,21,22,23,20,25,26,27,28,29,30,31,32,37,34,35,36,33,38,39,40,41
,46,43,44,45,42,47,48,53,50,51,52,49,54,55,56,57,58,59,60,61,62,1,6,3,4,5,2,7,
2,5,4,3,6,75,78,80,76,79,77,81,88,83,90,85,92,87,82,89,84,91,86,93,94,95,96,97
,98,99,104,101,102,103,100,105,106,107,108,109,110,111,112,113,114,115,116,117
,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134]],
0,
[(122,123),(64,74)(65,73)(66,72)(67,71)(68,70),(93,96)(94,97)(95,98)(106,107)(
110,111)(112,115)(113,114)(116,117)(118,119)(120,121)(125,126)(129,130)(131,
134)(132,133),(93,96)(94,97)(95,98)(112,114)(113,115)(127,128)(131,133)(132,
134),(2,6)(13,17)(20,24)(33,37)(42,46)(49,53)(64,68)(65,73)(67,71)(70,74)(76,
78)(77,80)(82,88)(84,90)(86,92)(93,96)(94,97)(95,98)(100,104)(106,107)(110,111
)(112,115)(113,114)(116,117)(118,119)(120,121)(125,126)(129,130)(131,134)(132,
133)],
["ConstructMGA","12_1.U4(3)","2.U4(3).2_2'",[[40,41],[42,43],[44,45],[46,49],[
47,48],[50,51],[52,53],[54,55],[56,57],[58,59],[60,61],[62,63],[64,67],[65,66]
,[68,69],[70,71],[72,73],[74,75],[76,77],[78,79],[80,81],[82,83],[84,85],[86,
87],[88,91],[89,90],[92,93],[94,95],[96,97],[98,99],[100,101],[102,103],[104,
105],[106,107],[108,109],[110,111],[112,113],[114,117],[115,116],[118,119],[
120,121],[122,123],[124,125],[126,129],[127,128],[130,131],[132,133],[134,137]
,[135,136],[138,141],[139,140],[142,145],[143,144],[146,149],[147,148],[150,
153],[151,152],[154,157],[155,156],[158,165],[159,164],[160,163],[161,162],[
166,169],[167,168],[170,173],[171,172],[174,177],[175,176],[178,181],[179,180]
],()]);
ALF("12_1.U4(3).2_2'","U4(3).2_2'",[1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,4,
4,4,4,4,4,4,5,5,5,6,6,6,7,7,7,7,7,7,7,8,8,9,9,9,9,9,9,9,10,10,10,10,10,10,
10,11,11,11,11,12,12,12,12,13,13,13,13,13,13,13,13,13,13,13,13,14,14,14,
14,14,14,15,15,15,15,15,15,15,15,15,15,15,15,16,16,16,17,17,17,18,18,18,
18,18,18,18,19,19,20,21,22,22,23,23,24,24,25,25,26,26,27,27,28,28,29,30,
30,31,31,32,32,33,33,34,34]);
ALF("12_1.U4(3).2_2'","2.U4(3).2_2'",[1,2,1,2,1,2,1,3,4,3,4,5,6,5,6,5,6,5,
7,8,7,8,7,8,7,9,10,9,11,12,11,13,14,13,14,13,14,13,15,15,16,17,16,17,16,
17,16,18,19,18,19,18,19,18,20,21,20,21,22,23,22,23,24,25,24,25,24,25,24,
25,24,25,24,25,26,26,26,26,26,26,27,28,27,28,27,28,27,28,27,28,27,28,29,
30,29,31,32,31,33,34,33,34,33,34,33,35,36,37,38,39,40,41,42,43,44,45,46,
47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63]);
ALF("12_1.U4(3).2_2'","4.U4(3).2_2",[1,2,3,2,1,2,3,4,5,4,5,6,7,8,7,6,7,8,
12,13,14,13,12,13,14,9,10,11,15,16,17,18,19,20,19,18,19,20,21,21,22,23,24,
23,22,23,24,25,26,27,26,25,26,27,30,31,30,31,28,29,28,29,32,33,34,35,32,
33,34,35,32,33,34,35,36,37,36,37,37,36,44,45,46,47,44,45,46,47,44,45,46,
47,38,39,40,41,42,43,48,49,50,49,48,49,50,51,52,53,54,55,56,57,58,59,60,
61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79]);
ALF("12_1.U4(3).2_2'","3_1.U4(3).2_2'",[1,2,2,1,2,2,1,3,4,4,3,5,6,6,5,6,6,
5,7,8,8,7,8,8,7,9,9,9,10,10,10,11,12,12,11,12,12,11,13,14,15,16,16,15,16,
16,15,17,18,18,17,18,18,17,19,20,20,19,21,22,22,21,23,24,25,23,24,25,23,
24,25,23,24,25,26,27,27,27,26,27,28,29,30,28,29,30,28,29,30,28,29,30,31,
31,31,32,32,32,33,34,34,33,34,34,33,35,35,36,37,38,38,39,39,40,40,41,41,
42,42,43,43,44,44,45,46,46,47,47,48,48,49,49,50,50]);
ALF("12_1.U4(3).2_2'","6_1.U4(3).2_2'",[1,2,3,4,3,2,1,5,6,7,8,9,10,11,12,
11,10,9,13,14,15,16,15,14,13,17,18,17,19,20,19,21,22,23,24,23,22,21,25,26,
27,28,29,30,29,28,27,31,32,33,34,33,32,31,35,36,37,38,39,40,41,42,43,44,
45,46,47,48,43,44,45,46,47,48,49,50,51,51,49,50,52,53,54,55,56,57,52,53,
54,55,56,57,58,59,58,60,61,60,62,63,64,65,64,63,62,66,67,68,69,70,71,72,
73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94]);

MOT("Isoclinic(12_1.U4(3).2_2')",
[
"isoclinic group of the 12_1.U4(3).2_2' given in the ATLAS"
],
0,
0,
0,
[(122,123),(106,107)(110,111)(112,113)(114,115)(116,117)(118,119)(120,121)
(125,126)(127,128)(129,130)(131,132)(133,134),(93,96)(94,97)(95,98)(112,114)
(113,115)(127,128)(131,133)(132,134),(64,74)(65,73)(66,72)(67,71)(68,70),(2,6)
(13,17)(20,24)(33,37)(42,46)(49,53)(64,68)(65,73)(67,71)(70,74)(76,78)(77,80)
(82,88)(84,90)(86,92)(100,104)],
["ConstructIsoclinic",[["12_1.U4(3).2_2'"]]]);
ALF("Isoclinic(12_1.U4(3).2_2')","6_1.U4(3).2_2'",[1,2,3,4,3,2,1,5,6,7,8,
9,10,11,12,11,10,9,13,14,15,16,15,14,13,17,18,17,19,20,19,21,22,23,24,23,
22,21,25,26,27,28,29,30,29,28,27,31,32,33,34,33,32,31,35,36,37,38,39,40,
41,42,43,44,45,46,47,48,43,44,45,46,47,48,49,50,51,51,49,50,52,53,54,55,
56,57,52,53,54,55,56,57,58,59,58,60,61,60,62,63,64,65,64,63,62,66,67,68,
69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,
93,94]);

MOT("12_2.U4(3)",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3]\n",
"3rd power map determined only up to matrix automorphisms\n",
"(138,142)(139,143)(140,144)(141,145), (130,134)(131,135)(132,136)(133,137)"
],
[39191040,39191040,39191040,39191040,39191040,39191040,39191040,39191040,
39191040,39191040,39191040,39191040,6912,6912,6912,6912,6912,6912,69984,69984,
69984,69984,69984,69984,69984,69984,69984,69984,69984,69984,3888,3888,3888,
3888,3888,3888,3888,3888,324,324,324,324,1152,1152,1152,1152,1152,1152,1152,
1152,1152,1152,1152,1152,48,48,48,60,60,60,60,60,60,60,60,60,60,60,60,864,864,
864,864,864,864,864,864,864,864,864,864,216,216,216,216,216,216,216,216,216,
216,216,216,84,84,84,84,84,84,84,84,84,84,84,84,84,84,84,84,84,84,84,84,84,84,
84,84,96,96,96,96,96,96,96,96,96,96,96,96,108,108,108,108,108,108,108,108,108,
108,108,108,108,108,108,108,144,144,144,144,144,144,144,144,144,144,144,144],
[,[1,3,5,7,9,11,1,3,5,7,9,11,1,3,5,7,9,11,19,21,23,25,27,29,19,21,23,25,27,29,
31,33,31,33,35,37,35,37,39,41,39,41,13,15,17,13,15,17,13,15,17,13,15,17,16,18,
14,58,60,62,64,66,68,58,60,62,64,66,68,19,21,23,25,27,29,19,21,23,25,27,29,31,
33,31,33,31,33,35,37,35,37,35,37,94,96,98,100,102,104,94,96,98,100,102,104,
106,108,110,112,114,116,106,108,110,112,114,116,52,54,44,46,48,50,52,54,44,46,
48,50,134,136,134,136,130,132,130,132,142,144,142,144,138,140,138,140,70,72,
74,76,78,80,70,72,74,76,78,80],[1,4,7,10,1,4,7,10,1,4,7,10,13,16,13,16,13,16,
1,4,7,10,1,4,7,10,1,4,7,10,1,4,7,10,1,4,7,10,1,4,7,10,43,46,49,52,43,46,49,52,
43,46,49,52,55,55,55,58,61,64,67,58,61,64,67,58,61,64,67,13,16,13,16,13,16,13,
16,13,16,13,16,13,16,13,16,13,16,13,16,13,16,13,16,106,109,112,115,106,109,
112,115,106,109,112,115,94,97,100,103,94,97,100,103,94,97,100,103,121,124,127,
118,121,124,127,118,121,124,127,118,27,30,21,24,23,26,29,20,27,30,21,24,23,26,
29,20,43,46,49,52,43,46,49,52,43,46,49,52],,[1,6,11,4,9,2,7,12,5,10,3,8,13,18,
17,16,15,14,19,24,29,22,27,20,25,30,23,28,21,26,31,32,33,34,35,36,37,38,39,40,
41,42,43,48,53,46,51,44,49,54,47,52,45,50,55,57,56,1,6,11,4,9,2,7,12,5,10,3,8,
70,75,80,73,78,71,76,81,74,79,72,77,82,87,86,85,84,83,88,93,92,91,90,89,106,
111,116,109,114,107,112,117,110,115,108,113,94,99,104,97,102,95,100,105,98,
103,96,101,118,123,128,121,126,119,124,129,122,127,120,125,134,135,136,137,
130,131,132,133,142,143,144,145,138,139,140,141,146,151,156,149,154,147,152,
157,150,155,148,153],,[1,8,3,10,5,12,7,2,9,4,11,6,13,14,15,16,17,18,19,26,21,
28,23,30,25,20,27,22,29,24,31,34,33,32,35,38,37,36,39,42,41,40,43,50,45,52,47,
54,49,44,51,46,53,48,55,56,57,58,65,60,67,62,69,64,59,66,61,68,63,70,77,72,79,
74,81,76,71,78,73,80,75,82,83,84,85,86,87,88,89,90,91,92,93,1,8,3,10,5,12,7,2,
9,4,11,6,1,8,3,10,5,12,7,2,9,4,11,6,121,128,123,118,125,120,127,122,129,124,
119,126,130,133,132,131,134,137,136,135,138,141,140,139,142,145,144,143,146,
153,148,155,150,157,152,147,154,149,156,151]],
0,
[( 94,106)( 95,107)( 96,108)( 97,109)( 98,110)( 99,111)(100,112)(101,113)
(102,114)(103,115)(104,116)(105,117),(  2,  6)(  3, 11)(  5,  9)(  8, 12)
( 14, 18)( 15, 17)( 20, 24)( 21, 29)( 23, 27)( 26, 30)( 44, 48)( 45, 53)
( 47, 51)( 50, 54)( 56, 57)( 59, 63)( 60, 68)( 62, 66)( 65, 69)( 71, 75)
( 72, 80)( 74, 78)( 77, 81)( 83, 87)( 84, 86)( 89, 93)( 90, 92)( 95, 99)
( 96,104)( 98,102)(101,105)(107,111)(108,116)(110,114)(113,117)(119,123)
(120,128)(122,126)(125,129)(130,134)(131,135)(132,136)(133,137)(138,142)
(139,143)(140,144)(141,145)(147,151)(148,156)(150,154)(153,157),(  2,  8)
(  4, 10)(  6, 12)( 20, 26)( 22, 28)( 24, 30)( 32, 34)( 36, 38)( 40, 42)
( 44, 50)( 46, 52)( 48, 54)( 59, 65)( 61, 67)( 63, 69)( 71, 77)( 73, 79)
( 75, 81)( 95,101)( 97,103)( 99,105)(107,113)(109,115)(111,117)(118,121)
(119,128)(120,123)(122,125)(124,127)(126,129)(131,133)(135,137)(139,141)
(143,145)(147,153)(149,155)(151,157),( 31, 35)( 32, 36)( 33, 37)( 34, 38)
( 82, 88)( 83, 89)( 84, 90)( 85, 91)( 86, 92)( 87, 93)(130,138)(131,139)
(132,140)(133,141)(134,142)(135,143)(136,144)(137,145)],
["ConstructProj",[["U4(3)",[]],["2.U4(3)",[]],["3_2.U4(3)",[-1,-13,-13,-1,-1,
-1,-1,-1,-1,-1,-1,-1,-1]],["4.U4(3)",[-1,-1,-1,7,7,7,7,-1,-1,-1,-1,-1,15,15,
-1,-1]],,["6_2.U4(3)",[-1,-1,-1,-7,-7,-13,-13,-1,-1,-1,-1,
-1]],,,,,,["12_2.U4(3)",[[-7,7,-1],[-7,7,-1],[-55,-377,-433],[-55,-377,-433],[
-7,7,-1],[-7,7,-1],[-7,7,-1],[-7,7,-1],[-7,7,-1]]]]]);
ALF("12_2.U4(3)","U4(3)",[1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,
3,3,3,3,3,3,4,4,4,4,5,5,5,5,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,9,9,9,9,
9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,12,
12,12,12,12,12,13,13,13,13,13,13,13,13,13,13,13,13,14,14,14,14,14,14,14,
14,14,14,14,14,15,15,15,15,15,15,15,15,15,15,15,15,16,16,16,16,17,17,17,
17,18,18,18,18,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,20]);
ALF("12_2.U4(3)","2.U4(3)",[1,2,1,2,1,2,1,2,1,2,1,2,3,4,3,4,3,4,5,6,5,6,5,
6,5,6,5,6,5,6,7,8,7,8,9,10,9,10,11,12,11,12,13,14,13,14,13,14,13,14,13,14,
13,14,15,15,15,16,17,16,17,16,17,16,17,16,17,16,17,18,19,18,19,18,19,18,
19,18,19,18,19,20,21,20,21,20,21,22,23,22,23,22,23,24,25,24,25,24,25,24,
25,24,25,24,25,26,27,26,27,26,27,26,27,26,27,26,27,28,29,28,29,28,29,28,
29,28,29,28,29,30,31,30,31,32,33,32,33,34,35,34,35,36,37,36,37,38,39,38,
39,38,39,38,39,38,39,38,39]);
ALF("12_2.U4(3)","4.U4(3)",[1,2,3,4,1,2,3,4,1,2,3,4,5,6,5,6,5,6,7,8,9,10,
7,8,9,10,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,23,24,
25,26,23,24,25,26,27,27,27,28,29,30,31,28,29,30,31,28,29,30,31,32,33,34,
35,32,33,34,35,32,33,34,35,36,37,36,37,36,37,38,39,38,39,38,39,40,41,42,
43,40,41,42,43,40,41,42,43,44,45,46,47,44,45,46,47,44,45,46,47,48,49,50,
51,48,49,50,51,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,
67,68,69,70,71,68,69,70,71,68,69,70,71]);
ALF("12_2.U4(3)","3_2.U4(3)",[1,2,3,1,2,3,1,2,3,1,2,3,4,5,6,4,5,6,7,8,9,7,
8,9,7,8,9,7,8,9,10,10,10,10,11,11,11,11,12,12,12,12,13,14,15,13,14,15,13,
14,15,13,14,15,16,17,18,19,20,21,19,20,21,19,20,21,19,20,21,22,23,24,22,
23,24,22,23,24,22,23,24,25,26,27,25,26,27,28,29,30,28,29,30,31,32,33,31,
32,33,31,32,33,31,32,33,34,35,36,34,35,36,34,35,36,34,35,36,37,38,39,37,
38,39,37,38,39,37,38,39,40,40,40,40,41,41,41,41,42,42,42,42,43,43,43,43,
44,45,46,44,45,46,44,45,46,44,45,46]);
ALF("12_2.U4(3)","6_2.U4(3)",[1,2,3,4,5,6,1,2,3,4,5,6,7,8,9,10,11,12,13,
14,15,16,17,18,13,14,15,16,17,18,19,20,19,20,21,22,21,22,23,24,23,24,25,
26,27,28,29,30,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,34,35,36,37,
38,39,40,41,42,43,44,45,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,
56,57,58,59,60,61,62,63,58,59,60,61,62,63,64,65,66,67,68,69,64,65,66,67,
68,69,70,71,72,73,74,75,70,71,72,73,74,75,76,77,76,77,78,79,78,79,80,81,
80,81,82,83,82,83,84,85,86,87,88,89,84,85,86,87,88,89]);
ALF("12_2.U4(3)","12_2.U4(3).2_1",[1,2,3,4,5,2,6,7,5,8,3,7,9,10,11,12,11,
10,13,14,15,16,17,14,18,19,17,20,15,19,21,22,23,24,25,26,27,28,29,30,31,
32,33,34,35,36,37,34,38,39,37,40,35,39,41,42,42,43,44,45,46,47,44,48,49,
47,50,45,49,51,52,53,54,55,52,56,57,55,58,53,57,59,60,61,62,61,60,63,64,
65,66,65,64,67,68,69,70,71,68,72,73,71,74,69,73,75,76,77,78,79,76,80,81,
79,82,77,81,83,84,85,86,87,84,88,89,87,90,85,89,91,92,93,94,91,92,93,94,
95,96,97,98,95,96,97,98,99,100,101,102,103,100,104,105,103,106,101,105],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);
ALF("12_2.U4(3)","12_2.U4(3).2_3",[1,2,3,4,5,6,7,2,8,4,9,6,10,11,12,13,14,
15,16,17,18,19,20,21,22,17,23,19,24,21,25,26,27,28,25,28,27,26,29,30,31,
30,32,33,34,35,36,37,38,33,39,35,40,37,41,42,43,44,45,46,47,48,49,50,45,
51,47,52,49,53,54,55,56,57,58,59,54,60,56,61,58,62,63,64,65,66,67,62,63,
64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,68,75,70,77,72,79,74,69,
76,71,78,73,80,81,82,80,83,82,84,83,85,84,81,85,86,87,88,89,90,91,92,93,
86,89,88,87,90,93,92,91,94,95,96,97,98,99,100,95,101,97,102,99],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);
ALF("12_2.U4(3)","12_2.U4(3).2_3'",[1,2,3,4,5,6,7,6,5,4,3,2,8,9,10,11,10,
9,12,13,14,15,16,17,18,17,16,15,14,13,19,20,21,22,19,22,21,20,23,24,25,24,
26,27,28,29,30,31,32,31,30,29,28,27,33,34,34,35,36,37,38,39,40,41,40,39,
38,37,36,42,43,44,45,46,47,48,47,46,45,44,43,49,50,51,52,53,54,49,54,53,
52,51,50,55,56,57,58,59,60,61,62,63,64,65,66,55,66,65,64,63,62,61,60,59,
58,57,56,67,68,68,67,69,70,71,72,72,71,70,69,73,74,75,76,77,78,79,80,77,
80,79,78,73,76,75,74,81,82,83,84,85,86,87,86,85,84,83,82]);

MOT("12_2.U4(3).2_1",
[
"origin: ATLAS of finite groups, tests: 1.o.r."
],
[78382080,39191040,39191040,78382080,39191040,78382080,39191040,78382080,
13824,6912,6912,13824,139968,69984,69984,139968,69984,139968,69984,139968,
7776,7776,7776,7776,7776,7776,7776,7776,648,648,648,648,2304,1152,1152,2304,
1152,2304,1152,2304,96,48,120,60,60,120,60,120,60,120,1728,864,864,1728,864,
1728,864,1728,432,216,216,432,432,216,216,432,168,84,84,168,84,168,84,168,168,
84,84,168,84,168,84,168,192,96,96,192,96,192,96,192,108,108,108,108,108,108,
108,108,288,144,144,288,144,288,144,288,48384,48384,48384,48384,2880,2880,
4608,4608,4608,4608,128,864,864,864,864,72,72,72,72,72,72,72,72,64,64,64,64,
40,40,40,40,576,576,576,576,576,576,576,576,144,144,144,144,144,144,144,144,
56,56,56,56,56,56,56,56],
[,[1,3,5,6,5,1,3,6,1,3,5,6,13,15,17,18,17,13,15,18,21,23,21,23,25,27,25,27,29,
31,29,31,9,11,11,9,11,9,11,9,12,10,43,45,47,48,47,43,45,48,13,15,17,18,17,13,
15,18,21,23,21,23,25,27,25,27,67,69,71,72,71,67,69,72,75,77,79,80,79,75,77,80,
40,39,34,36,34,40,39,36,91,93,91,93,95,97,95,97,51,53,55,56,55,51,53,56,1,6,1,
6,8,4,9,9,9,9,9,13,18,13,18,22,24,26,28,29,31,29,31,36,40,36,40,50,46,50,46,
51,56,51,56,56,51,56,51,59,59,59,59,63,63,63,63,67,72,67,72,75,80,75,80],[1,4,
6,8,1,6,8,4,9,12,9,12,1,4,6,8,1,6,8,4,1,4,6,8,1,4,6,8,1,4,6,8,33,36,38,40,33,
38,40,36,41,41,43,46,48,50,43,48,50,46,9,12,9,12,9,9,12,12,9,12,9,12,9,12,9,
12,75,78,80,82,75,80,82,78,67,70,72,74,67,72,74,70,86,88,90,83,86,90,83,88,17,
19,15,14,17,19,15,14,33,36,38,40,33,38,40,36,107,110,109,108,112,111,116,115,
114,113,117,107,110,109,108,112,111,112,111,107,110,109,108,133,132,131,130,
137,136,135,134,116,115,114,113,116,115,114,113,116,115,114,113,116,115,114,
113,158,161,160,159,154,157,156,155],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,
17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,
1,2,3,4,5,6,7,8,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,75,76,77,78,
79,80,81,82,67,68,69,70,71,72,73,74,83,84,85,86,87,88,89,90,91,92,93,94,95,96,
97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,
117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,111,112,
111,112,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,158,
159,160,161,154,155,156,157],,[1,7,3,8,5,6,2,4,9,10,11,12,13,19,15,20,17,18,
14,16,21,24,23,22,25,28,27,26,29,32,31,30,33,39,35,40,37,38,34,36,41,42,43,49,
45,50,47,48,44,46,51,57,53,58,55,56,52,54,59,60,61,62,63,64,65,66,1,7,3,8,5,6,
2,4,1,7,3,8,5,6,2,4,86,85,84,83,89,90,87,88,91,94,93,92,95,98,97,96,99,105,
101,106,103,104,100,102,107,110,109,108,112,111,116,115,114,113,117,118,121,
120,119,123,122,125,124,126,129,128,127,133,132,131,130,135,134,137,136,145,
144,143,142,141,140,139,138,149,148,147,146,153,152,151,150,107,110,109,108,
107,110,109,108]],
0,
[(134,136)(135,137),( 67, 75)( 68, 76)( 69, 77)( 70, 78)( 71, 79)( 72, 80)
( 73, 81)( 74, 82)(154,158)(155,159)(156,160)(157,161),(  2,  7)(  4,  8)
( 14, 19)( 16, 20)( 22, 24)( 26, 28)( 30, 32)( 34, 39)( 36, 40)( 44, 49)
( 46, 50)( 52, 57)( 54, 58)( 68, 73)( 70, 74)( 76, 81)( 78, 82)( 83, 86)
( 84, 85)( 87, 89)( 88, 90)( 92, 94)( 96, 98)(100,105)(102,106)(108,110)
(111,112)(113,116)(114,115)(119,121)(122,123)(124,125)(127,129)(130,133)
(131,132)(134,135)(136,137)(138,145)(139,144)(140,143)(141,142)(146,149)
(147,148)(150,153)(151,152)(155,157)(159,161),(  2,  7)(  4,  8)( 14, 19)
( 16, 20)( 22, 24)( 26, 28)( 30, 32)( 34, 39)( 36, 40)( 44, 49)( 46, 50)
( 52, 57)( 54, 58)( 68, 73)( 70, 74)( 76, 81)( 78, 82)( 83, 86)( 84, 85)
( 87, 89)( 88, 90)( 92, 94)( 96, 98)(100,105)(102,106)(108,110)(111,112)
(113,116)(114,115)(119,121)(122,123)(124,125)(127,129)(130,133)(131,132)
(134,137)(135,136)(138,145)(139,144)(140,143)(141,142)(146,149)(147,148)
(150,153)(151,152)(155,157)(159,161),(107,109)(108,110)(113,115)(114,116)
(118,120)(119,121)(126,128)(127,129)(130,132)(131,133)(138,140)(139,141)
(142,144)(143,145)(146,148)(147,149)(150,152)(151,153)(154,156)(155,157)
(158,160)(159,161),( 21, 25)( 22, 26)( 23, 27)( 24, 28)( 59, 63)( 60, 64)
( 61, 65)( 62, 66)( 91, 95)( 92, 96)( 93, 97)( 94, 98)(122,124)(123,125)
(146,150)(147,151)(148,152)(149,153)],
["ConstructMGA","12_2.U4(3)","4.U4(3).2_1",
     [ [ 72, 73 ], [ 74, 75 ], [ 76, 77 ], [ 78, 79 ], [ 80, 81 ],
        [ 82, 83 ], [ 84, 85 ], [ 86, 87 ], [ 88, 89 ], [ 90, 91 ],
        [ 92, 93 ], [ 94, 95 ], [ 96, 97 ], [ 98, 99 ], [ 100, 101 ],
        [ 102, 103 ], [ 104, 105 ], [ 106, 107 ], [ 108, 109 ], [ 110, 111 ],
        [ 112, 113 ], [ 114, 115 ], [ 116, 117 ], [ 118, 119 ], [ 120, 121 ],
        [ 122, 123 ], [ 124, 125 ], [ 126, 127 ], [ 128, 129 ], [ 130, 131 ],
        [ 132, 133 ], [ 134, 135 ], [ 136, 137 ], [ 138, 139 ], [ 140, 141 ],
        [ 142, 143 ], [ 144, 145 ], [ 146, 147 ], [ 148, 149 ], [ 150, 151 ],
        [ 152, 153 ], [ 154, 155 ], [ 156, 157 ] ], ()]);
ALF("12_2.U4(3).2_1","U4(3).2_1",[1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,
4,4,4,4,5,5,5,5,6,6,6,6,7,7,7,7,7,7,7,7,8,8,9,9,9,9,9,9,9,9,10,10,10,10,
10,10,10,10,11,11,11,11,12,12,12,12,13,13,13,13,13,13,13,13,14,14,14,14,
14,14,14,14,15,15,15,15,15,15,15,15,16,16,16,16,17,17,17,17,18,18,18,18,
18,18,18,18,19,19,19,19,20,20,21,21,21,21,22,23,23,23,23,24,24,25,25,26,
26,26,26,27,27,27,27,28,28,28,28,29,29,29,29,30,30,30,30,31,31,31,31,32,
32,32,32,33,33,33,33,34,34,34,34]);
ALF("12_2.U4(3).2_1","2.U4(3).2_1",[1,2,1,2,1,1,2,2,3,4,3,4,5,6,5,6,5,5,6,
6,7,8,7,8,9,10,9,10,11,12,11,12,13,14,13,14,13,13,14,14,15,15,16,17,16,17,
16,16,17,17,18,19,18,19,18,18,19,19,20,21,20,21,22,23,22,23,24,25,24,25,
24,24,25,25,26,27,26,27,26,26,27,27,28,29,28,29,28,28,29,29,30,31,30,31,
32,33,32,33,34,35,34,35,34,34,35,35,36,37,36,37,38,39,40,41,40,41,42,43,
44,43,44,45,46,47,48,49,50,49,50,51,52,51,52,53,54,53,54,55,56,55,56,57,
58,57,58,59,60,59,60,61,62,61,62,63,64,63,64,65,66,65,66]);
ALF("12_2.U4(3).2_1","4.U4(3).2_1",[1,2,3,4,1,3,4,2,5,6,5,6,7,8,9,10,7,9,
10,8,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,23,25,26,24,27,27,28,
29,30,31,28,30,31,29,32,33,34,35,32,34,35,33,36,37,36,37,38,39,38,39,40,
41,42,43,40,42,43,41,44,45,46,47,44,46,47,45,48,49,50,51,48,50,51,49,52,
53,54,55,56,57,58,59,60,61,62,63,60,62,63,61,64,65,66,67,68,69,70,71,72,
73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,
97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,
116,117,118]);
ALF("12_2.U4(3).2_1","3_2.U4(3).2_1",[1,2,2,1,2,1,2,1,3,4,4,3,5,6,6,5,6,5,
6,5,7,7,7,7,8,8,8,8,9,9,9,9,10,11,11,10,11,10,11,10,12,13,14,15,15,14,15,
14,15,14,16,17,17,16,17,16,17,16,18,19,19,18,20,21,21,20,22,23,23,22,23,
22,23,22,24,25,25,24,25,24,25,24,26,27,27,26,27,26,27,26,28,28,28,28,29,
29,29,29,30,31,31,30,31,30,31,30,32,32,32,32,33,33,34,34,34,34,35,36,36,
36,36,37,37,38,38,39,39,39,39,40,40,40,40,41,41,41,41,42,42,42,42,43,43,
43,43,44,44,44,44,45,45,45,45,46,46,46,46,47,47,47,47]);
ALF("12_2.U4(3).2_1","6_2.U4(3).2_1",[1,2,3,4,3,1,2,4,5,6,7,8,9,10,11,12,
11,9,10,12,13,14,13,14,15,16,15,16,17,18,17,18,19,20,21,22,21,19,20,22,23,
24,25,26,27,28,27,25,26,28,29,30,31,32,31,29,30,32,33,34,35,36,37,38,39,
40,41,42,43,44,43,41,42,44,45,46,47,48,47,45,46,48,49,50,51,52,51,49,50,
52,53,54,53,54,55,56,55,56,57,58,59,60,59,57,58,60,61,62,61,62,63,64,65,
66,65,66,67,68,69,68,69,70,71,72,73,74,75,74,75,76,77,76,77,78,79,78,79,
80,81,80,81,82,83,82,83,84,85,84,85,86,87,86,87,88,89,88,89,90,91,90,91]);

MOT("12_2.U4(3).2_3",
[
"origin: ATLAS of finite groups, tests: 1.o.r.,\n",
"3rd power map determined only up to matrix automorphism\n",
"(86,90)(88,92)(87,91)(89,93)"
],
[78382080,39191040,78382080,39191040,78382080,39191040,78382080,78382080,
78382080,13824,13824,13824,13824,13824,13824,139968,69984,139968,69984,139968,
69984,139968,139968,139968,3888,3888,3888,3888,648,324,648,2304,1152,2304,
1152,2304,1152,2304,2304,2304,96,96,96,120,60,120,60,120,60,120,120,120,1728,
864,1728,864,1728,864,1728,1728,1728,216,216,216,216,216,216,84,84,84,84,84,
84,84,84,84,84,84,84,96,96,96,96,96,96,108,108,108,108,108,108,108,108,288,
144,288,144,288,144,288,288,288,4320,4320,4320,288,288,288,36,36,576,576,576,
576,576,576,96,96,96,48,48,48,48,48,48,60,60,60,60,60,60,72,72,72,72,72,72,
144,144,144,144,144,144,144,144,144,144,144,144],
[,[1,3,5,7,8,9,1,5,8,1,3,5,7,8,9,16,18,20,22,23,24,16,20,23,25,27,25,27,29,31,
29,10,12,14,10,12,14,10,14,12,13,15,11,44,46,48,50,51,52,44,48,51,16,18,20,22,
23,24,16,20,23,25,27,25,27,25,27,68,70,72,74,76,78,68,70,72,74,76,78,35,37,33,
37,35,33,90,92,90,92,86,88,86,88,53,55,57,59,60,61,53,57,60,1,8,5,10,12,14,29,
29,38,34,40,38,34,40,32,39,36,41,43,42,41,43,42,44,51,48,44,51,48,59,55,61,59,
55,61,100,96,102,100,96,102,100,96,102,100,96,102],[1,4,7,4,1,4,7,1,7,10,13,
10,13,10,13,1,4,7,4,1,4,7,1,7,1,4,7,4,1,4,7,32,35,38,35,32,35,38,32,38,41,41,
41,44,47,50,47,44,47,50,44,50,10,13,10,13,10,13,10,10,10,10,13,10,13,10,13,68,
77,74,71,68,77,74,71,68,77,74,71,80,84,84,80,84,80,23,21,18,21,20,17,24,17,32,
35,38,35,32,35,38,32,38,103,103,103,106,106,106,103,103,114,111,114,111,114,
111,117,117,117,123,120,123,120,123,120,129,126,129,126,129,126,106,106,106,
106,106,106,114,111,114,111,114,111,114,111,114,111,114,111],,[1,6,9,4,8,2,7,
5,3,10,15,14,13,12,11,16,21,24,19,23,17,22,20,18,25,26,27,28,29,30,31,32,37,
40,35,39,33,38,36,34,41,43,42,1,6,9,4,8,2,7,5,3,53,58,61,56,60,54,59,57,55,62,
67,66,65,64,63,68,79,78,77,76,75,74,73,72,71,70,69,80,82,81,85,84,83,90,91,92,
93,86,87,88,89,94,99,102,97,101,95,100,98,96,103,105,104,106,108,107,109,110,
114,113,112,111,116,115,117,119,118,123,122,121,120,125,124,103,105,104,103,
105,104,135,134,133,132,137,136,141,140,139,138,143,142,147,146,145,144,149,
148],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,28,
27,26,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,
53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,1,2,3,4,5,6,7,2,8,4,9,6,80,81,82,
83,84,85,86,89,88,87,90,93,92,91,94,95,96,97,98,99,100,101,102,103,104,105,
106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,
125,129,130,131,126,127,128,132,133,134,135,136,137,138,139,140,141,142,143,
144,145,146,147,148,149]],
0,
[(126,129)(127,130)(128,131),(109,110),(69,75)(71,77)(73,79),(26,28)(87,89)
(91,93),(26,28)(69,75)(71,77)(73,79)(87,89)(91,93),( 26, 28)( 69, 75)( 71, 77)
( 73, 79)( 87, 89)( 91, 93)(111,114)(112,115)(113,116)(120,123)(121,124)
(122,125)(138,147)(139,148)(140,149)(141,144)(142,145)(143,146),(  2,  6)
(  3,  9)(  5,  8)( 11, 15)( 12, 14)( 17, 21)( 18, 24)( 20, 23)( 33, 37)
( 34, 40)( 36, 39)( 42, 43)( 45, 49)( 46, 52)( 48, 51)( 54, 58)( 55, 61)
( 57, 60)( 63, 67)( 64, 66)( 69, 73)( 70, 78)( 72, 76)( 75, 79)( 81, 82)
( 83, 85)( 86, 90)( 87, 91)( 88, 92)( 89, 93)( 95, 99)( 96,102)( 98,101)
(104,105)(107,108)(112,116)(113,115)(118,119)(121,125)(122,124)(127,131)
(128,130)(132,135)(133,134)(136,137)(138,144)(139,149)(140,148)(141,147)
(142,146)(143,145),(111,114)(112,115)(113,116)(120,123)(121,124)(122,125)
(138,147)(139,148)(140,149)(141,144)(142,145)(143,146),(111,114)(112,115)
(113,116)(120,123)(121,124)(122,125)(132,135)(133,136)(134,137)(138,141)
(139,142)(140,143)(144,147)(145,148)(146,149)],
["ConstructMGA","12_2.U4(3)","6_2.U4(3).2_3",
     [ [ 40, 41 ], [ 42, 43 ], [ 44, 45 ], [ 46, 51 ], [ 47, 50 ],
        [ 48, 53 ], [ 49, 52 ], [ 54, 55 ], [ 56, 59 ], [ 57, 58 ],
        [ 60, 61 ], [ 62, 63 ], [ 64, 67 ], [ 65, 66 ], [ 68, 69 ],
        [ 70, 71 ], [ 122, 124 ], [ 123, 125 ], [ 126, 128 ], [ 127, 129 ],
        [ 130, 136 ], [ 131, 137 ], [ 132, 134 ], [ 133, 135 ], [ 138, 140 ],
        [ 139, 141 ], [ 142, 144 ], [ 143, 145 ], [ 146, 148 ], [ 147, 149 ],
        [ 150, 152 ], [ 151, 153 ], [ 154, 156 ], [ 155, 157 ] ],
     ( 46, 62, 78, 94,110,126, 56, 72, 88,104,120, 50, 66, 82, 98,114,130, 60,
       76, 92,108,124, 54, 70, 86,102,118, 48, 64, 80, 96,112,128, 58, 74, 90,
       106,122, 52, 68, 84,100,116)( 47, 63, 79, 95,111,127, 57, 73, 89,105,
       121, 51, 67, 83, 99,115,131, 61, 77, 93,109,125, 55, 71, 87,103,119,
        49, 65, 81, 97,113,129, 59, 75, 91,107,123, 53, 69, 85,101,117)]);
ALF("12_2.U4(3).2_3","U4(3).2_3",[1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,
3,3,3,3,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,7,7,7,8,8,8,8,8,8,8,8,8,9,9,9,9,9,
9,9,9,9,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,11,11,11,12,12,12,12,
12,12,13,13,13,13,14,14,14,14,15,15,15,15,15,15,15,15,15,16,16,16,17,17,
17,18,18,19,19,19,19,19,19,20,20,20,21,21,21,21,21,21,22,22,22,22,22,22,
23,23,23,23,23,23,24,24,24,24,24,24,25,25,25,25,25,25]);
ALF("12_2.U4(3).2_3","2.U4(3).2_3",[1,2,1,2,1,2,1,1,1,3,4,3,4,3,4,5,6,5,6,
5,6,5,5,5,7,8,7,8,9,10,9,11,12,11,12,11,12,11,11,11,13,13,13,14,15,14,15,
14,15,14,14,14,16,17,16,17,16,17,16,16,16,18,19,18,19,18,19,20,21,20,21,
20,21,20,21,20,21,20,21,22,22,22,22,22,22,23,24,23,24,25,26,25,26,27,28,
27,28,27,28,27,27,27,29,29,29,30,30,30,31,32,33,34,33,34,33,34,35,35,35,
36,37,36,37,36,37,38,39,38,39,38,39,40,41,40,41,40,41,42,43,42,43,42,43,
44,45,44,45,44,45]);
ALF("12_2.U4(3).2_3","4.U4(3).2_3",[1,2,3,2,1,2,3,1,3,4,5,4,5,4,5,6,7,8,7,
6,7,8,6,8,9,10,11,12,13,14,15,16,17,18,17,16,17,18,16,18,19,19,19,20,21,
22,21,20,21,22,20,22,23,24,25,24,23,24,25,23,25,26,27,26,27,26,27,28,29,
30,31,28,29,30,31,28,29,30,31,32,33,33,32,33,32,34,35,36,37,38,39,40,41,
42,43,44,43,42,43,44,42,44,45,45,45,46,46,46,47,48,49,50,49,50,49,50,51,
51,51,52,53,52,53,52,53,54,55,54,55,54,55,56,57,56,57,56,57,58,59,58,59,
58,59,60,61,60,61,60,61]);
ALF("12_2.U4(3).2_3","3_2.U4(3).2_3",[1,2,3,1,2,3,1,3,2,4,5,6,4,5,6,7,8,9,
7,8,9,7,9,8,10,10,10,10,11,11,11,12,13,14,12,13,14,12,14,13,15,16,17,18,
19,20,18,19,20,18,20,19,21,22,23,21,22,23,21,23,22,24,25,26,24,25,26,27,
28,29,27,28,29,27,28,29,27,28,29,30,31,32,31,30,32,33,33,33,33,34,34,34,
34,35,36,37,35,36,37,35,37,36,38,39,40,41,42,43,44,44,45,46,47,45,46,47,
48,49,50,51,52,53,51,52,53,54,55,56,54,55,56,57,58,59,57,58,59,60,61,62,
60,61,62,63,64,65,63,64,65]);
ALF("12_2.U4(3).2_3","6_2.U4(3).2_3",[1,2,3,4,5,6,1,3,5,7,8,9,10,11,12,13,
14,15,16,17,18,13,15,17,19,20,19,20,21,22,21,23,24,25,26,27,28,23,25,27,
29,30,31,32,33,34,35,36,37,32,34,36,38,39,40,41,42,43,38,40,42,44,45,46,
47,48,49,50,51,52,53,54,55,50,51,52,53,54,55,56,57,58,57,56,58,59,60,59,
60,61,62,61,62,63,64,65,66,67,68,63,65,67,69,70,71,72,73,74,75,76,77,78,
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]);

MOT("Isoclinic(12_2.U4(3).2_3)",
[
"isoclinic group of the 12_2.U4(3).2_3 given in the ATLAS"
],
0,
0,
0,
[(132,135)(133,136)(134,137)(138,144)(139,145)(140,146)(141,147)(142,148)(143,
149),(126,129)(127,130)(128,131),(111,114)(112,115)(113,116)(120,123)(121,124)
(122,125)(138,147)(139,148)(140,149)(141,144)(142,145)(143,146),(109,110),(69,
75)(71,77)(73,79),(26,28)(87,89)(91,93),(2,6)(3,9)(5,8)(11,15)(12,14)(17,21)
(18,24)(20,23)(33,37)(34,40)(36,39)(42,43)(45,49)(46,52)(48,51)(54,58)(55,61)
(57,60)(63,67)(64,66)(69,73)(70,78)(72,76)(75,79)(81,82)(83,85)(86,90)(87,91)
(88,92)(89,93)(95,99)(96,102)(98,101)(104,105)(107,108)(112,116)(113,115)(118,
119)(121,125)(122,124)(127,131)(128,130)(132,135)(133,134)(136,137)(138,144)
(139,149)(140,148)(141,147)(142,146)(143,145)],
["ConstructIsoclinic",[["12_2.U4(3).2_3"]]]);
ALF("Isoclinic(12_2.U4(3).2_3)","2.U4(3).2_3",[1,2,1,2,1,2,1,1,1,3,4,3,4,
3,4,5,6,5,6,5,6,5,5,5,7,8,7,8,9,10,9,11,12,11,12,11,12,11,11,11,13,13,13,
14,15,14,15,14,15,14,14,14,16,17,16,17,16,17,16,16,16,18,19,18,19,18,19,
20,21,20,21,20,21,20,21,20,21,20,21,22,22,22,22,22,22,23,24,23,24,25,26,
25,26,27,28,27,28,27,28,27,27,27,29,29,29,30,30,30,31,32,33,34,33,34,33,
34,35,35,35,36,37,36,37,36,37,38,39,38,39,38,39,40,41,40,41,40,41,42,43,
42,43,42,43,44,45,44,45,44,45]);

MOT("12_2.U4(3).2_3'",
[
"origin: ATLAS of finite groups, tests: 1.o.r.,\n",
"constructed using `PossibleCharacterTablesOfTypeMGA',\n",
"3rd power map determined only up to matrix automorphism\n",
"(20,22)(74,76)(78,80)"
],
[78382080,39191040,39191040,39191040,39191040,39191040,78382080,13824,6912,
6912,13824,139968,69984,69984,69984,69984,69984,139968,3888,3888,3888,3888,648
,324,648,2304,1152,1152,1152,1152,1152,2304,96,48,120,60,60,60,60,60,120,1728,
864,864,864,864,864,1728,216,216,216,216,216,216,84,84,84,84,84,84,84,84,84,84
,84,84,96,96,96,96,96,96,108,108,108,108,108,108,108,108,288,144,144,144,144,
144,288,1440,96,36,36,192,192,32,16,16,20,20,24,24,48,48,48,48],
[,[1,3,5,7,5,3,1,1,3,5,7,12,14,16,18,16,14,12,19,21,19,21,23,25,23,8,10,10,8,
10,10,8,11,9,35,37,39,41,39,37,35,12,14,16,18,16,14,12,19,21,19,21,19,21,55,57
,59,61,63,65,55,57,59,61,63,65,29,27,31,31,29,27,77,79,77,79,73,75,73,75,42,44
,46,48,46,44,42,1,8,23,23,32,32,26,33,33,35,35,48,48,87,87,87,87],[1,4,7,4,1,4
,7,8,11,8,11,1,4,7,4,1,4,7,1,4,7,4,1,4,7,26,29,32,29,26,29,32,33,33,35,38,41,
38,35,38,41,8,11,8,11,8,11,8,8,11,8,11,8,11,55,64,61,58,55,64,61,58,55,64,61,
58,67,71,67,71,71,67,16,13,14,17,16,17,14,13,26,29,32,29,26,29,32,88,89,88,88,
93,92,94,96,95,98,97,89,89,93,92,93,92],,[1,6,3,4,5,2,7,8,9,10,11,12,17,14,15,
16,13,18,19,20,21,22,23,24,25,26,31,28,29,30,27,32,33,34,1,6,3,4,5,2,7,42,47,
44,45,46,43,48,49,54,53,52,51,50,55,62,57,64,59,66,61,56,63,58,65,60,67,70,72,
68,71,69,77,78,79,80,73,74,75,76,81,86,83,84,85,82,87,88,89,90,91,93,92,94,96,
95,88,88,100,99,102,101,104,103],,[1,6,3,4,5,2,7,8,9,10,11,12,17,14,15,16,13,
18,19,22,21,20,23,24,25,26,31,28,29,30,27,32,33,34,35,40,37,38,39,36,41,42,47,
44,45,46,43,48,49,50,51,52,53,54,1,6,3,4,5,2,7,2,5,4,3,6,67,70,72,68,71,69,73,
76,75,74,77,80,79,78,81,86,83,84,85,82,87,88,89,90,91,92,93,94,95,96,98,97,99,
100,101,102,103,104]],
0,
[(97,98),(90,91),(56,66)(57,65)(58,64)(59,63)(60,62),(50,54)(51,53),(20,22)(73
,77)(74,80)(75,79)(76,78),(92,93)(95,96)(101,104)(102,103),(99,100)(101,103)(
102,104),(2,6)(13,17)(27,31)(36,40)(43,47)(56,60)(57,65)(59,63)(62,66)(68,70)(
69,72)(73,77)(74,78)(75,79)(76,80)(82,86)(92,93)(95,96)(101,104)(102,103)],
["ConstructMGA","12_2.U4(3)","2.U4(3).2_3'",[[40,41],[42,43],[44,45],[46,53],[
47,52],[48,51],[49,50],[54,55],[56,59],[57,58],[60,61],[62,63],[64,67],[65,66]
,[68,69],[70,71],[72,73],[74,77],[75,76],[78,79],[80,81],[82,83],[84,87],[85,
86],[88,89],[90,91],[92,93],[94,95],[96,97],[98,99],[100,103],[101,102],[104,
107],[105,106],[108,111],[109,110],[112,113],[114,115],[116,117],[118,119],[
120,121],[122,125],[123,124],[126,129],[127,128],[130,137],[131,136],[132,135]
,[133,134],[138,141],[139,140],[142,145],[143,144],[146,149],[147,148],[150,
153],[151,152],[154,157],[155,156]],()]);
ALF("12_2.U4(3).2_3'","U4(3).2_3'",[1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,4,
4,4,4,5,5,5,6,6,6,6,6,6,6,7,7,8,8,8,8,8,8,8,9,9,9,9,9,9,9,10,10,10,10,10,
10,11,11,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,13,13,13,13,14,
14,14,14,15,15,15,15,15,15,15,16,17,18,18,19,19,20,21,21,22,22,23,23,24,
24,25,25]);
ALF("12_2.U4(3).2_3'","2.U4(3).2_3'",[1,2,1,2,1,2,1,3,4,3,4,5,6,5,6,5,6,5,
7,8,7,8,9,10,9,11,12,11,12,11,12,11,13,13,14,15,14,15,14,15,14,16,17,16,
17,16,17,16,18,19,18,19,18,19,20,21,20,21,20,21,20,21,20,21,20,21,22,22,
22,22,22,22,23,24,23,24,25,26,25,26,27,28,27,28,27,28,27,29,30,31,32,33,
34,35,36,37,38,39,40,41,42,43,44,45]);
ALF("12_2.U4(3).2_3'","4.U4(3).2_3",[1,2,3,2,1,2,3,4,5,4,5,6,7,8,7,6,7,8,
9,10,11,12,13,14,15,16,17,18,17,16,17,18,19,19,20,21,22,21,20,21,22,23,24,
25,24,23,24,25,26,27,26,27,26,27,28,29,30,31,28,29,30,31,28,29,30,31,32,
33,32,33,33,32,34,35,36,37,38,39,40,41,42,43,44,43,42,43,44,45,46,47,48,
49,50,51,52,53,54,55,56,57,58,59,60,61]);
ALF("12_2.U4(3).2_3'","3_2.U4(3).2_3'",[1,2,2,1,2,2,1,3,4,4,3,5,6,6,5,6,6,
5,7,7,7,7,8,8,8,9,10,10,9,10,10,9,11,12,13,14,14,13,14,14,13,15,16,16,15,
16,16,15,17,18,19,17,18,19,20,21,22,20,21,22,20,21,22,20,21,22,23,24,24,
24,23,24,25,25,25,25,26,26,26,26,27,28,28,27,28,28,27,29,30,31,31,32,32,
33,34,34,35,35,36,36,37,37,38,38]);
ALF("12_2.U4(3).2_3'","6_2.U4(3).2_3'",[1,2,3,4,3,2,1,5,6,7,8,9,10,11,12,
11,10,9,13,14,13,14,15,16,15,17,18,19,20,19,18,17,21,22,23,24,25,26,25,24,
23,27,28,29,30,29,28,27,31,32,33,34,35,36,37,38,39,40,41,42,37,38,39,40,
41,42,43,44,45,45,43,44,46,47,46,47,48,49,48,49,50,51,52,53,52,51,50,54,
55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70]);

MOT("Isoclinic(12_2.U4(3).2_3')",
[
"isoclinic group of the 12_2.U4(3).2_3' given in the ATLAS"
],
0,
0,
0,
[(99,100)(101,103)(102,104),(97,98),(92,93)(95,96)(99,100)(101,102)(103,104),
(90,91),(56,66)(57,65)(58,64)(59,63)(60,62),(50,54)(51,53),(20,22)(73,77)(74,
80)(75,79)(76,78)(97,98),(2,6)(13,17)(27,31)(36,40)(43,47)(56,60)(57,65)(59,
63)(62,66)(68,70)(69,72)(73,77)(74,78)(75,79)(76,80)(82,86)(92,93)(95,96)(97,
98)(101,104)(102,103)],
["ConstructIsoclinic",[["12_2.U4(3).2_3'"]]]);
ALF("Isoclinic(12_2.U4(3).2_3')","6_2.U4(3).2_3'",[1,2,3,4,3,2,1,5,6,7,8,
9,10,11,12,11,10,9,13,14,13,14,15,16,15,17,18,19,20,19,18,17,21,22,23,24,
25,26,25,24,23,27,28,29,30,29,28,27,31,32,33,34,35,36,37,38,39,40,41,42,
37,38,39,40,41,42,43,44,45,45,43,44,46,47,46,47,48,49,48,49,50,51,52,53,
52,51,50,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70]);

MOT("2.U4(3)",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[6531840,6531840,2304,2304,11664,11664,1944,1944,1944,1944,162,162,192,192,16,
10,10,144,144,72,72,72,72,14,14,14,14,16,16,54,54,54,54,54,54,54,54,24,24],
[,[1,1,1,1,5,5,7,7,9,9,11,11,3,3,4,16,16,5,5,7,7,9,9,24,24,26,26,14,14,32,32,
30,30,36,36,34,34,18,18],[1,2,3,4,1,2,1,2,1,2,1,2,13,14,15,16,17,3,4,3,4,3,4,
26,27,24,25,29,28,5,6,5,6,5,6,5,6,13,14],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,
15,1,2,18,19,20,21,22,23,26,27,24,25,28,29,32,33,30,31,36,37,34,35,38,39],,[1,
2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,1,2,1,2,29,28,30,31,
32,33,34,35,36,37,38,39]],
0,
[(30,32)(31,33)(34,36)(35,37),(28,29),(24,26)(25,27),(34,36)(35,37),( 7, 9)
( 8,10)(20,22)(21,23)(30,34)(31,35)(32,36)(33,37)],
["ConstructProj",[["U4(3)",[]],["2.U4(3)",[]]]]);
ALF("2.U4(3)","U4(3)",[1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,9,9,10,10,11,11,12,
12,13,13,14,14,15,15,16,16,17,17,18,18,19,19,20,20]);
ALF("2.U4(3)","2.U4(3).2_1",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,
19,20,21,22,23,24,25,26,27,28,29,30,31,30,31,32,33,32,33,34,35],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);
ALF("2.U4(3)","2.U4(3).2_2",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,
19,20,21,22,23,24,25,24,25,26,26,27,28,29,30,31,32,31,32,33,34],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("2.U4(3)","2.U4(3).2_2'",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,
18,19,20,21,22,23,24,25,24,25,26,26,27,28,27,28,29,30,31,32,33,34],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("2.U4(3)","2.U4(3).2_3",[1,2,3,4,5,6,7,8,7,8,9,10,11,12,13,14,15,16,
17,18,19,18,19,20,21,20,21,22,22,23,24,25,26,23,24,25,26,27,28],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("2.U4(3)","2.U4(3).2_3'",[1,2,3,4,5,6,7,8,7,8,9,10,11,12,13,14,15,16,
17,18,19,18,19,20,21,20,21,22,22,23,24,25,26,25,26,23,24,27,28],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]); # exactly this map is required for constructing 6_2.U4(3).2_3'
ALF("2.U4(3)","Isoclinic(2.U4(3).2_1)",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,
15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,30,31,32,33,32,33,34,
35],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables"
]);
ALF("2.U4(3)","Isoclinic(2.U4(3).2_2)",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,
15,16,17,18,19,20,21,22,23,24,25,24,25,26,26,27,28,29,30,31,32,31,32,33,
34]);
ALF("2.U4(3)","Isoclinic(2.U4(3).2_2')",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,
15,16,17,18,19,20,21,22,23,24,25,24,25,26,26,27,28,27,28,29,30,31,32,33,
34]);
ALF("2.U4(3)","Isoclinic(2.U4(3).2_3)",[1,2,3,4,5,6,7,8,7,8,9,10,11,12,13,
14,15,16,17,18,19,18,19,20,21,20,21,22,22,23,24,25,26,23,24,25,26,27,28]);
ALF("2.U4(3)","Isoclinic(2.U4(3).2_3')",[1,2,3,4,5,6,7,8,7,8,9,10,11,12,
13,14,15,16,17,18,19,18,19,20,21,20,21,22,22,23,24,25,26,25,26,23,24,27,
28]);
ALF("2.U4(3)","2.U4(3).4",[1,2,3,4,5,6,7,8,7,8,9,10,11,12,13,14,15,16,17,
18,19,18,19,20,21,22,23,24,25,26,27,26,27,26,27,26,27,28,29],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);

MOT("2.U4(3).2_1",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[13063680,13063680,4608,4608,23328,23328,3888,3888,3888,3888,324,324,384,384,
32,20,20,288,288,144,144,144,144,28,28,28,28,32,32,54,54,54,54,48,48,24192,
24192,2880,2880,2304,2304,128,432,432,72,72,72,72,36,36,32,32,20,20,288,288,
288,288,72,72,72,72,28,28,28,28],
[,[1,1,1,1,5,5,7,7,9,9,11,11,3,3,4,16,16,5,5,7,7,9,9,24,24,26,26,14,14,30,30,
32,32,18,18,1,1,2,2,3,3,3,5,5,8,8,10,10,11,11,14,14,17,17,18,18,18,18,20,20,
22,22,24,24,26,26],[1,2,3,4,1,2,1,2,1,2,1,2,13,14,15,16,17,3,4,3,4,3,4,26,27,
24,25,29,28,5,6,5,6,13,14,36,37,39,38,41,40,42,36,37,39,38,39,38,36,37,52,51,
54,53,41,40,41,40,41,40,41,40,65,66,63,64],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,
15,1,2,18,19,20,21,22,23,26,27,24,25,28,29,30,31,32,33,34,35,36,37,38,39,40,
41,42,43,44,45,46,47,48,49,50,51,52,38,39,55,56,57,58,59,60,61,62,65,66,63,
64],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,1,2,1,2,29,
28,30,31,32,33,34,35,36,37,39,38,41,40,42,43,44,46,45,48,47,49,50,52,51,54,53,
58,57,56,55,60,59,62,61,36,37,36,37]],
0,
[(28,29)(38,39)(40,41)(45,46)(47,48)(51,52)(53,54)(55,58)(56,57)(59,60)
(61,62),(28,29)(36,37)(43,44)(49,50)(55,57)(56,58)(63,64)(65,66),(24,26)
(25,27)(63,65)(64,66),(36,37)(38,39)(40,41)(43,44)(45,46)(47,48)(49,50)(51,52)
(53,54)(55,56)(57,58)(59,60)(61,62)(63,64)(65,66),( 7, 9)( 8,10)(20,22)(21,23)
(30,32)(31,33)(45,47)(46,48)(59,61)(60,62)],
["ConstructProj",[["U4(3).2_1",[]],["2.U4(3).2_1",[]]]]);
ALF("2.U4(3).2_1","U4(3).2_1",[1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,9,9,10,10,11,
11,12,12,13,13,14,14,15,15,16,16,17,17,18,18,19,19,20,20,21,21,22,23,23,
24,24,25,25,26,26,27,27,28,28,29,29,30,30,31,31,32,32,33,33,34,34]);
ALF("2.U4(3).2_1","2.U4(3).4",[1,2,3,4,5,6,7,8,7,8,9,10,11,12,13,14,15,16,
17,18,19,18,19,20,21,22,23,24,25,26,27,26,27,28,29,30,31,32,33,34,35,36,
37,38,39,40,39,40,41,42,43,44,45,46,47,48,49,50,51,52,51,52,53,54,55,56],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);
ALF("2.U4(3).2_1","2.U4(3).(2^2)_{122}",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,
15,16,17,18,19,20,21,22,23,24,25,24,25,26,26,27,28,29,30,31,32,33,34,35,
35,36,36,37,38,39,40,40,41,41,42,43,44,44,45,45,46,47,47,46,48,48,49,49,
50,51,50,51],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("2.U4(3).2_1","2.U4(3).(2^2)_{12*2}",[1,2,3,4,5,6,7,8,9,10,11,12,13,
14,15,16,17,18,19,20,21,22,23,24,25,24,25,26,26,27,28,29,30,31,32,33,33,
34,35,36,37,38,39,39,40,41,42,43,44,44,45,46,47,48,49,50,49,50,51,52,53,
54,55,56,56,55]);
ALF("2.U4(3).2_1","2.U4(3).(2^2)_{12*2*}",[1,2,3,4,5,6,7,8,9,10,11,12,13,
14,15,16,17,18,19,20,21,22,23,24,25,24,25,26,26,27,28,29,30,31,32,33,34,
35,35,36,36,37,38,39,40,40,41,41,42,43,44,44,45,45,46,47,47,46,48,48,49,
49,50,51,50,51]);
ALF("2.U4(3).2_1","2.U4(3).(2^2)_{133}",[1,2,3,4,5,6,7,8,7,8,9,10,11,12,
13,14,15,16,17,18,19,18,19,20,21,20,21,22,22,23,24,23,24,25,26,27,28,29,
29,30,30,31,32,33,34,35,35,34,36,37,38,38,39,39,40,41,41,40,42,43,43,42,
44,45,44,45]);
ALF("2.U4(3).2_1","2.U4(3).(2^2)_{13*3}",[1,2,3,4,5,6,7,8,7,8,9,10,11,12,
13,14,15,16,17,18,19,18,19,20,21,20,21,22,22,23,24,23,24,25,26,27,27,28,
29,30,31,32,33,33,34,35,34,35,36,36,37,38,39,40,41,42,41,42,43,44,43,44,
45,46,46,45]);
ALF("2.U4(3).2_1","2.U4(3).(2^2)_{13*3*}",[1,2,3,4,5,6,7,8,7,8,9,10,11,12,
13,14,15,16,17,18,19,18,19,20,21,20,21,22,22,23,24,23,24,25,26,27,28,29,
29,30,30,31,32,33,34,35,35,34,36,37,38,38,39,39,40,41,41,40,42,43,43,42,
44,45,44,45]);

MOT("Isoclinic(2.U4(3).2_1)",
0,
0,
0,
0,
[(28,29)(36,37)(43,44)(49,50)(55,57)(56,58)(63,64)(65,66),
(24,26)(25,27)(63,65)(64,66),
( 7, 9)( 8,10)(20,22)(21,23)(30,32)(31,33)(45,47)(46,48)(59,61)(60,62),
(28,29)(38,39)(40,41)(45,46)(47,48)(51,52)(53,54)(55,58)(56,57)(59,60)(61,62)
],
["ConstructIsoclinic",[["2.U4(3).2_1"]]]);
ALF("Isoclinic(2.U4(3).2_1)","2.U4(3).(2^2)_{1*22}",[1,2,3,4,5,6,7,8,9,10,
11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,24,25,26,26,27,28,29,30,31,
32,33,33,34,35,36,37,38,39,39,40,41,42,43,44,44,45,46,47,48,49,50,49,50,
51,52,53,54,55,56,56,55]);
ALF("Isoclinic(2.U4(3).2_1)","2.U4(3).(2^2)_{1*2*2}",[1,2,3,4,5,6,7,8,9,
10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,24,25,26,26,27,28,29,30,
31,32,33,34,35,35,36,36,37,38,39,40,40,41,41,42,43,44,44,45,45,46,47,47,
46,48,48,49,49,50,51,50,51]);
ALF("Isoclinic(2.U4(3).2_1)","2.U4(3).(2^2)_{1*2*2*}",[1,2,3,4,5,6,7,8,9,
10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,24,25,26,26,27,28,29,30,
31,32,33,33,34,35,36,37,38,39,39,40,41,42,43,44,44,45,46,47,48,49,50,49,
50,51,52,53,54,55,56,56,55]);
ALF("Isoclinic(2.U4(3).2_1)","2.U4(3).(2^2)_{1*33}",[1,2,3,4,5,6,7,8,7,8,
9,10,11,12,13,14,15,16,17,18,19,18,19,20,21,20,21,22,22,23,24,23,24,25,26,
27,27,28,29,30,31,32,33,33,34,35,34,35,36,36,37,38,39,40,41,42,41,42,43,
44,43,44,45,46,46,45]);
ALF("Isoclinic(2.U4(3).2_1)","2.U4(3).(2^2)_{1*3*3}",[1,2,3,4,5,6,7,8,7,8,
9,10,11,12,13,14,15,16,17,18,19,18,19,20,21,20,21,22,22,23,24,23,24,25,26,
27,28,29,29,30,30,31,32,33,34,35,35,34,36,37,38,38,39,39,40,41,41,40,42,
43,43,42,44,45,44,45]);
ALF("Isoclinic(2.U4(3).2_1)","2.U4(3).(2^2)_{1*3*3*}",[1,2,3,4,5,6,7,8,7,
8,9,10,11,12,13,14,15,16,17,18,19,18,19,20,21,20,21,22,22,23,24,23,24,25,
26,27,27,28,29,30,31,32,33,33,34,35,34,35,36,36,37,38,39,40,41,42,41,42,
43,44,43,44,45,46,46,45]);
ALF("Isoclinic(2.U4(3).2_1)","3^6:2U4(3).2_1",[1,5,6,9,13,17,18,23,24,29,
30,33,34,37,38,42,47,48,51,53,56,59,62,65,66,67,68,69,70,71,74,75,78,79,
82,83,84,85,89,93,97,98,101,102,103,107,110,114,117,118,119,122,123,128,
129,131,132,134,135,138,139,142,143,144,145,146],[
"fusion map is unique up to table automorphisms"
]);
ALN("Isoclinic(2.U4(3).2_1)",["2.U4(3).2_1*"]);

MOT("2.U4(3).2_2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[13063680,13063680,4608,4608,23328,23328,3888,3888,3888,3888,324,324,384,384,
32,20,20,288,288,144,144,144,144,14,14,16,108,108,108,108,54,54,48,48,103680,
103680,1152,192,192,192,2592,2592,2592,2592,432,432,216,216,144,144,36,36,16,
20,20,48,48,24,24,36,36,36,36],
[,[1,1,1,1,5,5,7,7,9,9,11,11,3,3,4,16,16,5,5,7,7,9,9,24,24,14,29,29,27,27,31,
31,18,18,1,1,1,3,4,4,5,5,5,5,9,9,7,7,9,9,11,11,13,16,16,18,18,21,21,29,29,27,
27],[1,2,3,4,1,2,1,2,1,2,1,2,13,14,15,16,17,3,4,3,4,3,4,24,25,26,5,6,5,6,5,6,
13,14,35,36,37,38,39,40,35,36,35,36,35,36,35,36,37,37,37,37,53,54,55,38,38,39,
40,41,42,43,44],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,1,2,18,19,20,21,22,23,
24,25,26,29,30,27,28,31,32,33,34,35,36,37,38,39,40,43,44,41,42,45,46,47,48,49,
50,51,52,53,35,36,57,56,58,59,62,63,60,61],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,
15,16,17,18,19,20,21,22,23,1,2,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,
41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63]],
0,
[(51,52),(27,29)(28,30)(41,43)(42,44)(56,57)(60,62)(61,63),(35,36)(39,40)
(41,42)(43,44)(45,46)(47,48)(49,50)(54,55)(56,57)(58,59)(60,61)(62,63)],
["ConstructProj",[["U4(3).2_2",[]],["2.U4(3).2_2",[]]]]);
ALF("2.U4(3).2_2","U4(3).2_2",[1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,9,9,10,10,11,
11,12,12,13,13,14,15,15,16,16,17,17,18,18,19,19,20,21,22,22,23,23,24,24,
25,25,26,26,27,27,28,28,29,30,30,31,31,32,32,33,33,34,34]);
ALF("2.U4(3).2_2","2.U4(3).(2^2)_{122}",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,
15,16,17,18,19,20,21,22,23,24,25,26,27,28,27,28,29,30,31,32,52,52,53,54,
55,55,56,57,57,56,58,58,59,59,60,60,61,62,63,64,64,65,66,67,67,68,69,69,
68],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("2.U4(3).2_2","2.U4(3).(2^2)_{1*22}",[1,2,3,4,5,6,7,8,9,10,11,12,13,
14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,27,28,29,30,31,32,57,58,59,
60,61,62,63,64,63,64,65,66,67,68,69,70,71,71,72,73,74,75,75,76,77,78,79,
78,79]);
ALF("2.U4(3).2_2","O7(3)",[1,2,4,3,5,17,6,18,7,19,10,27,13,14,15,16,41,23,
20,25,24,26,22,33,52,35,36,55,36,54,37,56,43,46,2,3,4,14,12,15,17,20,17,
20,19,22,18,24,21,26,30,31,34,41,40,46,46,45,49,54,57,55,57]);
ALF("2.U4(3).2_2","2.U6(2)",[1,2,6,5,10,11,8,9,12,13,12,13,18,18,22,23,24,
32,31,34,33,38,37,41,42,46,48,49,50,51,52,53,68,68,3,4,7,18,20,21,25,26,
27,28,35,36,29,30,40,39,40,39,46,54,55,68,68,70,71,74,75,76,77],[
"fusion map is unique up to table automorphisms"
]);
ALN("2.U4(3).2_2",["O7(3)C2A","O7(3)N2A"]);

MOT("Isoclinic(2.U4(3).2_2)",
0,
0,
0,
0,
[(51,52),
(35,36)(39,40)(41,42)(43,44)(45,46)(47,48)(49,50)(54,55)(56,57)(58,59)(60,61)
(62,63)
,(27,29)(28,30)(41,43)(42,44)(56,57)(60,62)(61,63)],
["ConstructIsoclinic",[["2.U4(3).2_2"]]]);
ALF("Isoclinic(2.U4(3).2_2)","2.U4(3).(2^2)_{12*2}",[1,2,3,4,5,6,7,8,9,10,
11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,27,28,29,30,31,32,
58,57,59,60,62,61,64,63,64,63,66,65,68,67,70,69,71,71,72,74,73,75,75,77,
76,79,78,79,78]);
ALF("Isoclinic(2.U4(3).2_2)","2.U4(3).(2^2)_{1*2*2}",[1,2,3,4,5,6,7,8,9,
10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,27,28,29,30,31,
32,52,52,53,54,55,55,56,57,57,56,58,58,59,59,60,60,62,61,63,64,64,65,66,
67,67,68,69,69,68]);
ALF("Isoclinic(2.U4(3).2_2)","2.U4(3).(2^2)_{12*2*}",[1,2,3,4,5,6,7,8,9,
10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,27,28,29,30,31,
32,52,52,53,54,55,55,56,57,57,56,58,58,59,59,60,60,61,62,63,64,64,65,66,
67,67,68,69,69,68]);
ALF("Isoclinic(2.U4(3).2_2)","2.U4(3).(2^2)_{1*2*2*}",[1,2,3,4,5,6,7,8,9,
10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,27,28,29,30,31,
32,57,58,59,60,61,62,63,64,63,64,65,66,67,68,69,70,71,71,72,73,74,75,75,
76,77,78,79,78,79]);
ALN("Isoclinic(2.U4(3).2_2)",["2.U4(3).2_2*"]);

MOT("2.U4(3).2_2'",
0,
0,
0,
0,
0,
["ConstructPermuted",["2.U4(3).2_2"],(7,9)(8,10)(20,22)(21,23)(27,29,31)
(28,30,32),(5,7)(6,8)(17,18,19,20,21)(22,24)(23,25)(37,39)(38,40)(43,44,
45,46,47)(51,53)(52,54)]);
ALF("2.U4(3).2_2'","U4(3).2_2'",[1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,9,9,10,10,
11,11,12,12,13,13,14,15,15,16,16,17,17,18,18,19,19,20,21,22,22,23,23,24,
24,25,25,26,26,27,27,28,28,29,30,30,31,31,32,32,33,33,34,34]);
ALF("2.U4(3).2_2'","2.U4(3).(2^2)_{122}",[1,2,3,4,5,6,7,8,9,10,11,12,13,
14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,29,30,31,32,70,70,71,
72,73,73,74,75,75,74,76,76,77,77,78,78,80,79,81,82,82,83,84,85,85,86,87,
87,86]);
ALF("2.U4(3).2_2'","2.U4(3).(2^2)_{12*2}",[1,2,3,4,5,6,7,8,9,10,11,12,13,
14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,29,30,31,32,80,81,82,
83,84,85,86,87,86,87,88,89,90,91,92,93,94,94,95,96,97,98,98,99,100,101,
102,101,102]);
ALF("2.U4(3).2_2'","2.U4(3).(2^2)_{1*22}",[1,2,3,4,5,6,7,8,9,10,11,12,13,
14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,29,30,31,32,80,81,82,
83,84,85,86,87,86,87,88,89,90,91,92,93,94,94,95,96,97,98,98,99,100,101,
102,101,102]);
ALF("2.U4(3).2_2'","2.U4(3).(2^2)_{1*2*2}",[1,2,3,4,5,6,7,8,9,10,11,12,13,
14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,29,30,31,32,70,70,71,
72,73,73,74,75,75,74,76,76,77,77,78,78,79,80,81,82,82,83,84,85,85,86,87,
87,86]);

MOT("Isoclinic(2.U4(3).2_2')",
0,
0,
0,
0,
0,
["ConstructPermuted",["Isoclinic(2.U4(3).2_2)"],(7,9)(8,10)(20,22)(21,23)(27,
29,31)(28,30,32),(5,7)(6,8)(17,18,19,20,21)(22,24)(23,25)(37,39)(38,40)(43,44,
45,46,47)(51,53)(52,54)]);
ALF("Isoclinic(2.U4(3).2_2')","2.U4(3).(2^2)_{12*2*}",[1,2,3,4,5,6,7,8,9,
10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,29,30,31,
32,70,70,71,72,73,73,74,75,75,74,76,76,77,77,78,78,80,79,81,82,82,83,84,
85,85,86,87,87,86]);
ALF("Isoclinic(2.U4(3).2_2')","2.U4(3).(2^2)_{1*2*2*}",[1,2,3,4,5,6,7,8,9,
10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,29,30,31,
32,80,81,82,83,84,85,86,87,86,87,88,89,90,91,92,93,94,94,95,96,97,98,98,
99,100,101,102,101,102]);
ALN("Isoclinic(2.U4(3).2_2')",["2.U4(3).2_2'*"]);

MOT("2.U4(3).2_3",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[13063680,13063680,4608,4608,23328,23328,1944,1944,324,324,384,384,32,20,20,
288,288,72,72,14,14,16,54,54,54,54,48,48,1440,96,36,36,192,192,32,16,16,20,20,
24,24,48,48,48,48],
[,[1,1,1,1,5,5,7,7,9,9,3,3,4,14,14,5,5,7,7,20,20,12,25,25,23,23,16,16,1,3,9,9,
11,11,11,13,13,14,14,16,16,27,27,27,27],[1,2,3,4,1,2,1,2,1,2,11,12,13,14,15,3,
4,3,4,20,21,22,5,6,5,6,11,12,29,30,29,29,34,33,35,37,36,39,38,30,30,34,33,34,
33],,[1,2,3,4,5,6,7,8,9,10,11,12,13,1,2,16,17,18,19,20,21,22,25,26,23,24,27,
28,29,30,31,32,34,33,35,37,36,29,29,41,40,43,42,45,44],,[1,2,3,4,5,6,7,8,9,10,
11,12,13,14,15,16,17,18,19,1,2,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,
37,39,38,40,41,42,43,44,45]],
0,
[(40,41)(42,44)(43,45),(38,39),(33,34)(36,37)(42,45)(43,44),(31,32),(23,25)
(24,26)(40,41)(42,44)(43,45),(23,25)(24,26)],
["ConstructProj",[["U4(3).2_3",[]],["2.U4(3).2_3",[]]]]);
ALF("2.U4(3).2_3","U4(3).2_3",[1,1,2,2,3,3,4,4,5,5,6,6,7,8,8,9,9,10,10,11,
11,12,13,13,14,14,15,15,16,17,18,18,19,19,20,21,21,22,22,23,23,24,24,25,
25]);
ALF("2.U4(3).2_3","2.U4(3).(2^2)_{133}",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,
15,16,17,18,19,20,21,22,23,24,23,24,25,26,46,47,48,49,50,50,51,52,52,53,
53,54,55,56,57,57,56]);
ALF("2.U4(3).2_3","2.U4(3).(2^2)_{1*33}",[1,2,3,4,5,6,7,8,9,10,11,12,13,
14,15,16,17,18,19,20,21,22,23,24,23,24,25,26,47,48,49,49,50,51,52,53,54,
55,56,57,57,58,59,58,59]);

MOT("Isoclinic(2.U4(3).2_3)",
0,
0,
0,
0,
[(40,41)(42,44)(43,45),(38,39),(33,34)(36,37)(40,41)(42,43)(44,45),(31,32),
(23,25)(24,26)],
["ConstructIsoclinic",[["2.U4(3).2_3"]]]);
ALF("Isoclinic(2.U4(3).2_3)","2.U4(3).(2^2)_{13*3}",[1,2,3,4,5,6,7,8,9,10,
11,12,13,14,15,16,17,18,19,20,21,22,23,24,23,24,25,26,47,48,49,49,50,51,
52,53,54,56,55,57,57,58,59,58,59]);
ALF("Isoclinic(2.U4(3).2_3)","2.U4(3).(2^2)_{1*3*3}",[1,2,3,4,5,6,7,8,9,
10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,23,24,25,26,46,47,48,49,50,
50,51,52,52,53,53,54,55,56,57,57,56]);
ALF("Isoclinic(2.U4(3).2_3)","2.U4(3).(2^2)_{13*3*}",[1,2,3,4,5,6,7,8,9,
10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,23,24,25,26,46,47,48,49,50,
50,51,52,52,53,53,54,55,56,57,57,56]);
ALF("Isoclinic(2.U4(3).2_3)","2.U4(3).(2^2)_{1*3*3*}",[1,2,3,4,5,6,7,8,9,
10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,23,24,25,26,47,48,49,49,50,
51,52,53,54,55,56,57,57,58,59,58,59]);
ALN("Isoclinic(2.U4(3).2_3)",["2.U4(3).2_3*"]);

MOT("2.U4(3).2_3'",
0,
0,
0,
0,
0,
["ConstructPermuted",["2.U4(3).2_3"],(),()]);
ALF("2.U4(3).2_3'","U4(3).2_3'",[1,1,2,2,3,3,4,4,5,5,6,6,7,8,8,9,9,10,10,
11,11,12,13,13,14,14,15,15,16,17,18,18,19,19,20,21,21,22,22,23,23,24,24,
25,25]);
ALF("2.U4(3).2_3'","2.U4(3).(2^2)_{133}",[1,2,3,4,5,6,7,8,9,10,11,12,13,
14,15,16,17,18,19,20,21,22,23,24,23,24,25,26,58,59,60,61,62,62,63,64,64,
65,65,66,67,68,69,69,68]);
ALF("2.U4(3).2_3'","2.U4(3).(2^2)_{1*33}",[1,2,3,4,5,6,7,8,9,10,11,12,13,
14,15,16,17,18,19,20,21,22,23,24,23,24,25,26,60,61,62,62,63,64,65,66,67,
68,69,70,70,71,72,71,72]);
ALF("2.U4(3).2_3'","2.U4(3).(2^2)_{13*3}",[1,2,3,4,5,6,7,8,9,10,11,12,13,
14,15,16,17,18,19,20,21,22,23,24,23,24,25,26,60,61,62,62,64,63,65,67,66,
68,69,70,70,72,71,72,71]);
ALF("2.U4(3).2_3'","2.U4(3).(2^2)_{1*3*3}",[1,2,3,4,5,6,7,8,9,10,11,12,13,
14,15,16,17,18,19,20,21,22,23,24,23,24,25,26,58,59,60,61,62,62,63,64,64,
65,65,66,67,68,69,69,68]);

MOT("Isoclinic(2.U4(3).2_3')",
0,
0,
0,
0,
0,
["ConstructPermuted",["Isoclinic(2.U4(3).2_3)"],(),()]);
ALF("Isoclinic(2.U4(3).2_3')","2.U4(3).(2^2)_{13*3*}",[1,2,3,4,5,6,7,8,9,
10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,23,24,25,26,58,59,60,61,62,
62,63,64,64,65,65,66,67,68,69,69,68]);
ALF("Isoclinic(2.U4(3).2_3')","2.U4(3).(2^2)_{1*3*3*}",[1,2,3,4,5,6,7,8,9,
10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,23,24,25,26,60,61,62,62,63,
64,65,66,67,68,69,70,70,71,72,71,72]);
ALN("Isoclinic(2.U4(3).2_3')",["2.U4(3).2_3'*"]);

MOT("2.U4(3).4",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[26127360,26127360,9216,9216,46656,46656,3888,3888,648,648,768,768,64,40,40,
576,576,144,144,56,56,56,56,64,64,54,54,96,96,48384,48384,5760,5760,4608,4608,
256,864,864,72,72,72,72,64,64,40,40,576,576,576,576,72,72,56,56,56,56,48384,
48384,48384,48384,768,768,768,768,80,80,384,384,384,384,128,128,128,128,864,
864,864,864,96,96,96,96,72,72,72,72,40,40,40,40,48,48,48,48,56,56,56,56,56,56,
56,56],
[,[1,1,1,1,5,5,7,7,9,9,3,3,4,14,14,5,5,7,7,20,20,22,22,12,12,26,26,16,16,1,1,
2,2,3,3,3,5,5,8,8,9,9,12,12,15,15,16,16,16,16,18,18,20,20,22,22,30,30,30,30,
30,30,30,30,32,33,34,34,35,35,35,35,34,34,37,37,37,37,37,37,37,37,41,41,41,41,
45,45,46,46,47,47,50,50,53,53,53,53,55,55,55,55],[1,2,3,4,1,2,1,2,1,2,11,12,
13,14,15,3,4,3,4,22,23,20,21,25,24,5,6,11,12,30,31,33,32,35,34,36,30,31,33,32,
30,31,44,43,46,45,35,34,35,34,35,34,55,56,53,54,59,60,57,58,63,64,61,62,66,65,
69,70,67,68,73,74,71,72,59,60,57,58,63,64,61,62,59,60,57,58,89,90,87,88,69,70,
67,68,101,102,99,100,97,98,95,96],,[1,2,3,4,5,6,7,8,9,10,11,12,13,1,2,16,17,
18,19,22,23,20,21,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,
44,32,33,47,48,49,50,51,52,55,56,53,54,57,58,59,60,61,62,63,64,65,66,67,68,69,
70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,65,65,66,66,91,92,93,94,99,
100,101,102,95,96,97,98],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,1,
2,1,2,25,24,26,27,28,29,30,31,33,32,35,34,36,37,38,40,39,41,42,44,43,46,45,50,
49,48,47,52,51,30,31,30,31,59,60,57,58,63,64,61,62,66,65,69,70,67,68,73,74,71,
72,77,78,75,76,81,82,79,80,85,86,83,84,90,89,88,87,93,94,91,92,59,60,57,58,59,
60,57,58]],
0,
[(87,88)(89,90),( 57, 58)( 59, 60)( 61, 62)( 63, 64)( 67, 68)( 69, 70)
( 71, 72)( 73, 74)( 75, 76)( 77, 78)( 79, 80)( 81, 82)( 83, 84)( 85, 86)
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["ConstructProj",[["U4(3).4",[]],["2.U4(3).4",[]]]]);
ALF("2.U4(3).4","U4(3).4",[1,1,2,2,3,3,4,4,5,5,6,6,7,8,8,9,9,10,10,11,11,
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49,50,50,51,51,52,52,53,53]);
ALF("2.U4(3).4","2.U4(3).D8",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,
18,19,20,21,20,21,22,22,23,24,25,26,27,28,29,29,30,30,31,32,33,34,34,35,
36,37,37,38,38,39,40,40,39,41,41,42,43,42,43,44,45,44,45,46,47,46,47,48,
48,49,50,49,50,51,52,51,52,53,54,53,54,55,56,55,56,57,58,57,58,59,60,59,
60,61,62,61,62,63,64,65,66,65,66,63,64]);

MOT("2.U4(3).(2^2)_{122}",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
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192,2592,2592,432,216,144,72,72,32,20,96,96,24,36,36,103680,2304,384,192,2592,
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ALF("2.U4(3).(2^2)_{122}","U4(3).(2^2)_{122}",[1,1,2,2,3,3,4,4,5,5,6,6,7,
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ALF("2.U4(3).(2^2)_{122}","O8+(3)",[1,2,5,2,6,27,7,31,10,34,17,43,19,23,
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"fusion map is unique up to table automorphisms"
]);
ALF("2.U4(3).(2^2)_{122}","2^2.U4(3).(2^2)_{122}",[1,2,3,4,5,6,7,8,9,10,
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141,142,142,143,144,145,145,146,147,147]);
ALF("2.U4(3).(2^2)_{122}","2.U4(3).D8",[1,2,3,4,5,6,7,8,7,8,9,10,11,12,13,
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ALN("2.U4(3).(2^2)_{122}",["O8+(3)C2A","O8+(3)N2A"]);

MOT("2.U4(3).(2^2)_{1*22}",
[
"constructed using `PossibleCharacterTablesOfTypeGV4'"
],
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3,-3,0,0,0,0,-1,1,0,-1,1,0,0],
[TENSOR,[80,2]],
[TENSOR,[80,3]],
[TENSOR,[80,4]],[504,-504,-8,8,18,-18,-9,9,18,-18,0,0,0,0,0,-1,1,-2,2,1,-1,-2
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[TENSOR,[84,2]],
[TENSOR,[84,3]],
[TENSOR,[84,4]],[1080,-1080,24,-24,-54,54,0,0,0,0,0,0,8,-8,0,0,0,-6,6,0,0,0,0
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[TENSOR,[89,2]],
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[TENSOR,[93,2]],
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E(28)^3-E(28)^11-E(28)^15+E(28)^19-E(28)^23+E(28)^27,0,0,0,0,0,0,0,0,0,0,0,0,0
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0,0,0,0,-1,1,0,0,0,1,-1],
[TENSOR,[99,2]],
[TENSOR,[99,3]],
[TENSOR,[99,4]]],
[(55,56),
( 34, 35)( 36, 37)( 40, 41)( 42, 43)( 45, 46)( 47, 48)( 49, 50)( 51, 52)
( 53, 54)( 80, 81)( 84, 85)( 86, 87)( 88, 89)( 90, 91)( 92, 93)( 96, 97)
( 99,100)(101,102)
,
( 34, 35)( 36, 37)( 40, 41)( 42, 43)( 45, 46)( 47, 48)( 49, 50)( 51, 52)
( 53, 54)( 57, 58)( 61, 62)( 63, 64)( 65, 66)( 67, 68)( 69, 70)( 73, 74)
( 76, 77)( 78, 79)
,
(  7,  9)(  8, 10)( 20, 22)( 21, 23)( 27, 29)( 28, 30)( 40, 42)( 41, 43)
( 51, 53)( 52, 54)( 57, 80)( 58, 81)( 59, 82)( 60, 83)( 61, 84)( 62, 85)
( 63, 86)( 64, 87)( 65, 88)( 66, 89)( 67, 90)( 68, 91)( 69, 92)( 70, 93)
( 71, 94)( 72, 95)( 73, 96)( 74, 97)( 75, 98)( 76, 99)( 77,100)( 78,101)
( 79,102)
]);
ALF("2.U4(3).(2^2)_{1*22}","U4(3).(2^2)_{122}",[1,1,2,2,3,3,4,4,5,5,6,6,7,
7,8,9,9,10,10,11,11,12,12,13,13,14,15,15,16,16,17,17,18,19,19,20,20,21,22,
23,23,24,24,25,26,26,27,27,28,28,29,29,30,30,31,31,32,32,33,34,35,35,36,
36,37,37,38,38,39,39,40,41,42,42,43,44,44,45,45,46,46,47,48,49,49,50,50,
51,51,52,52,53,53,54,55,56,56,57,58,58,59,59]);
ALF("2.U4(3).(2^2)_{1*22}","O7(3).2",[1,2,4,3,5,16,6,17,7,18,9,26,12,13,
14,15,37,22,19,24,23,25,21,30,47,32,33,49,34,50,39,42,57,54,55,58,56,59,
80,66,67,69,68,87,74,73,77,75,82,78,84,81,83,79,95,96,2,3,4,13,11,14,16,
19,18,21,17,23,20,25,28,31,37,36,42,41,44,49,51,54,53,55,60,59,58,65,61,
66,62,69,63,67,64,71,74,77,76,86,85,83,90,89]);

MOT("2.U4(3).(2^2)_{12*2}",
[
"constructed using `PossibleCharacterTablesOfTypeGV4'"
],
0,
0,
0,
[(55,56),
(34,35)(36,37)(40,41)(42,43)(45,46)(47,48)(49,50)(51,52)(53,54)(57,58)(61,62)
(63,64)(65,66)(67,68)(69,70)(73,74)(76,77)(78,79)
,
( 57, 58)( 61, 62)( 63, 64)( 65, 66)( 67, 68)( 69, 70)( 73, 74)( 76, 77)
( 78, 79)( 80, 81)( 84, 85)( 86, 87)( 88, 89)( 90, 91)( 92, 93)( 96, 97)
( 99,100)(101,102)
],
["ConstructIsoclinic",[["2.U4(3).(2^2)_{1*22}"]],[1,2,3,4,5,6,7,8,9,10,11,12,
13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,80,81,82,83,84,85,
86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102],(57,58)(61,62)(63,64)
(65,66)(67,68)(69,70)(73,74)(76,77)(78,79),(61,64)(62,63)(65,68)(66,67)(69,72)
(70,71)(73,74)(78,79)(80,83)(81,82)(84,87)(85,86)(89,92)(90,91)(93,96)(94,95)
(97,98)(99,102)(100,101)]);
ALF("2.U4(3).(2^2)_{12*2}","U4(3).(2^2)_{122}",[1,1,2,2,3,3,4,4,5,5,6,6,7,
7,8,9,9,10,10,11,11,12,12,13,13,14,15,15,16,16,17,17,18,19,19,20,20,21,22,
23,23,24,24,25,26,26,27,27,28,28,29,29,30,30,31,31,32,32,33,34,35,35,36,
36,37,37,38,38,39,39,40,41,42,42,43,44,44,45,45,46,46,47,48,49,49,50,50,
51,51,52,52,53,53,54,55,56,56,57,58,58,59,59]);

MOT("2.U4(3).(2^2)_{1*2*2}",
[
"constructed using `PossibleCharacterTablesOfTypeGV4'"
],
0,
0,
0,
[(61,62)(79,80),(56,57)(65,66)(68,69)(74,75)(83,84)(86,87),
(33,34)(38,39)(42,43)(46,47)(50,51)(56,57)(61,62)(65,66)(68,69)],
["ConstructIsoclinic",[["2.U4(3).(2^2)_{122}"]],[1,2,3,4,5,6,7,8,9,10,11,12,
13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,70,71,72,73,74,75,
76,77,78,79,80,81,82,83,84,85,86,87],(61,62),(35,36)(69,70)(71,72)(79,80)]);
ALF("2.U4(3).(2^2)_{1*2*2}","U4(3).(2^2)_{122}",[1,1,2,2,3,3,4,4,5,5,6,6,
7,7,8,9,9,10,10,11,11,12,12,13,13,14,15,15,16,16,17,17,18,18,19,20,21,22,
22,23,24,25,25,26,27,28,28,29,30,31,31,32,33,34,35,36,36,37,38,39,40,40,
41,42,43,43,44,45,45,46,47,48,49,50,50,51,52,53,54,54,55,56,57,57,58,59,
59]);

MOT("2.U4(3).(2^2)_{12*2*}",
[
"constructed using `PossibleCharacterTablesOfTypeGV4'"
],
0,
0,
0,
[(61,62)(79,80),(56,57)(65,66)(68,69)(74,75)(83,84)(86,87),
(33,34)(38,39)(42,43)(46,47)(50,51)(74,75)(79,80)(83,84)(86,87),
( 7, 9)( 8,10)(20,22)(21,23)(27,29)(28,30)(40,41)(48,49)(52,70)(53,71)(54,72)
(55,73)(56,74)(57,75)(58,76)(59,77)(60,78)(61,79)(62,80)(63,81)(64,82)(65,83)
(66,84)(67,85)(68,86)(69,87)
],
["ConstructIsoclinic",[["2.U4(3).(2^2)_{122}"]],[1..51]]);
ALF("2.U4(3).(2^2)_{12*2*}","U4(3).(2^2)_{122}",[1,1,2,2,3,3,4,4,5,5,6,6,
7,7,8,9,9,10,10,11,11,12,12,13,13,14,15,15,16,16,17,17,18,18,19,20,21,22,
22,23,24,25,25,26,27,28,28,29,30,31,31,32,33,34,35,36,36,37,38,39,40,40,
41,42,43,43,44,45,45,46,47,48,49,50,50,51,52,53,54,54,55,56,57,57,58,59,
59]);

MOT("2.U4(3).(2^2)_{1*2*2*}",
[
"constructed using `PossibleCharacterTablesOfTypeGV4'"
],
0,
0,
0,
[(55,56),
( 34, 35)( 36, 37)( 40, 41)( 42, 43)( 45, 46)( 47, 48)( 49, 50)( 51, 52)
( 53, 54)( 80, 81)( 84, 85)( 86, 87)( 88, 89)( 90, 91)( 92, 93)( 96, 97)
( 99,100)(101,102)
,
( 34, 35)( 36, 37)( 40, 41)( 42, 43)( 45, 46)( 47, 48)( 49, 50)( 51, 52)
( 53, 54)( 57, 58)( 61, 62)( 63, 64)( 65, 66)( 67, 68)( 69, 70)( 73, 74)
( 76, 77)( 78, 79)
,
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( 51, 53)( 52, 54)( 57, 80)( 58, 81)( 59, 82)( 60, 83)( 61, 84)( 62, 85)
( 63, 86)( 64, 87)( 65, 88)( 66, 89)( 67, 90)( 68, 91)( 69, 92)( 70, 93)
( 71, 94)( 72, 95)( 73, 96)( 74, 97)( 75, 98)( 76, 99)( 77,100)( 78,101)
( 79,102)
],
["ConstructIsoclinic",[["2.U4(3).(2^2)_{1*22}"]],[1..56]]);
ALF("2.U4(3).(2^2)_{1*2*2*}","U4(3).(2^2)_{122}",[1,1,2,2,3,3,4,4,5,5,6,6,
7,7,8,9,9,10,10,11,11,12,12,13,13,14,15,15,16,16,17,17,18,19,19,20,20,21,
22,23,23,24,24,25,26,26,27,27,28,28,29,29,30,30,31,31,32,32,33,34,35,35,
36,36,37,37,38,38,39,39,40,41,42,42,43,44,44,45,45,46,46,47,48,49,49,50,
50,51,51,52,52,53,53,54,55,56,56,57,58,58,59,59]);

MOT("2.U4(3).(2^2)_{133}",
[
"constructed using `PossibleCharacterTablesOfTypeGV4'"
],
[26127360,26127360,9216,9216,46656,46656,3888,3888,648,648,768,768,64,40,40,
576,576,144,144,28,28,32,54,54,96,96,48384,48384,2880,2304,256,864,864,72,72,
72,72,32,20,288,288,72,72,28,28,2880,192,72,72,192,64,16,20,48,48,48,48,2880,
192,72,72,192,64,16,20,48,48,48,48],
[,[1,1,1,1,5,5,7,7,9,9,3,3,4,14,14,5,5,7,7,20,20,12,23,23,16,16,1,1,2,3,3,5,5,
8,8,9,9,12,15,16,16,18,18,20,20,1,3,9,9,11,11,13,14,16,16,25,25,1,3,9,9,11,11,
13,14,16,16,25,25],[1,2,3,4,1,2,1,2,1,2,11,12,13,14,15,3,4,3,4,20,21,22,5,6,11
,12,27,28,29,30,31,27,28,29,29,27,28,38,39,30,30,30,30,44,45,46,47,46,46,50,51
,52,53,47,47,50,50,58,59,58,58,62,63,64,65,59,59,62,62],,[1,2,3,4,5,6,7,8,9,10
,11,12,13,1,2,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,
37,38,29,40,41,42,43,44,45,46,47,48,49,50,51,52,46,55,54,57,56,58,59,60,61,62,
63,64,58,67,66,69,68],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,1,2,22
,23,24,25,26,27,28,29,30,31,32,33,35,34,36,37,38,39,40,41,43,42,27,28,46,47,48
,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69]],
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1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1
,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1
,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1
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(58,71)(59,72)
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ALF("2.U4(3).(2^2)_{1*33}","U4(3).(2^2)_{133}",[1,1,2,2,3,3,4,4,5,5,6,6,7,
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39,40,41,41,42,42,43,44,44]);

MOT("2.U4(3).(2^2)_{13*3}",
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],
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,
["ConstructIsoclinic",[["2.U4(3).(2^2)_{1*33}"]],[1,2,3,4,5,6,7,8,9,10,11,12,
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ALF("2.U4(3).(2^2)_{13*3}","U4(3).(2^2)_{133}",[1,1,2,2,3,3,4,4,5,5,6,6,7,
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39,40,41,41,42,42,43,44,44]);

MOT("2.U4(3).(2^2)_{1*3*3}",
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],
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0,
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(27,28)(32,33)(36,37)(40,41)(44,45)(48,49)(54,55)(56,57)],
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13,14,15,16,17,18,19,20,21,22,23,24,25,26,58,59,60,61,62,63,64,65,66,67,68,
69]]);
ALF("2.U4(3).(2^2)_{1*3*3}","U4(3).(2^2)_{133}",[1,1,2,2,3,3,4,4,5,5,6,6,
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40,41,42,43,43,44,44]);

MOT("2.U4(3).(2^2)_{13*3*}",
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"constructed using `PossibleCharacterTablesOfTypeGV4'"
],
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(57,69)
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ALF("2.U4(3).(2^2)_{13*3*}","U4(3).(2^2)_{133}",[1,1,2,2,3,3,4,4,5,5,6,6,
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40,41,42,43,43,44,44]);

MOT("2.U4(3).(2^2)_{1*3*3*}",
[
"constructed using `PossibleCharacterTablesOfTypeGV4'"
],
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0,
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(58,71)(59,72)
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ALF("2.U4(3).(2^2)_{1*3*3*}","U4(3).(2^2)_{133}",[1,1,2,2,3,3,4,4,5,5,6,6,
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MOT("2.U4(3).D8",
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"constructed using `PossibleCharacterTablesOfTypeGV4'"
],
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[(76,77)(87,88),(63,65)(64,66),(59,60),(71,72)(80,81)(83,84)(93,94)(95,96),
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MOT("O8+(3)M16",
[
"16th maximal subgroup of O8+(3),\n",
"differs from O8+(3)M15 only by fusion map"
],
0,
0,
0,
0,
["ConstructPermuted",["2.U4(3).(2^2)_{122}"]]);
ALF("O8+(3)M16","O8+(3)",[1,3,5,3,6,28,8,32,11,35,17,44,19,23,21,25,73,30,
28,38,32,41,35,55,98,57,59,107,62,110,76,84,2,4,21,19,23,27,29,90,93,43,
45,57,113,77,75,79,82,97,99,3,5,23,21,28,28,35,32,41,51,53,56,73,84,84,90,
107,107,3,5,23,21,28,28,32,35,38,52,50,56,73,84,84,93,110,110],[
"fusion map is unique up to table automorphisms,\n",
"equal to the map from O8+(3)M15, mapped under an outer autom."
]);
ALF("O8+(3)M16","U4(3).(2^2)_{122}",[1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,9,9,10,
10,11,11,12,12,13,13,14,15,15,16,16,17,17,18,18,19,20,21,22,22,23,24,25,
25,26,27,28,28,29,30,31,31,32,33,34,35,36,36,37,38,39,40,40,41,42,43,43,
44,45,45,46,47,48,49,50,50,51,52,53,54,54,55,56,57,57,58,59,59]);

MOT("O8+(3)M17",
[
"17th maximal subgroup of O8+(3),\n",
"differs from O8+(3)M15 only by fusion map"
],
0,
0,
0,
0,
["ConstructPermuted",["2.U4(3).(2^2)_{122}"]]);
ALF("O8+(3)M17","O8+(3)",[1,4,5,4,6,29,9,33,12,36,17,45,19,23,22,26,74,30,
29,39,33,42,36,55,99,57,60,108,63,111,77,84,2,3,22,19,23,27,28,91,94,43,
44,57,114,76,75,80,83,97,98,4,5,23,22,29,29,36,33,42,51,52,56,74,84,84,91,
108,108,4,5,23,22,29,29,33,36,39,53,50,56,74,84,84,94,111,111],[
"fusion map is unique up to table automorphisms,\n",
"equal to the map from O8+(3)M15, mapped under an outer autom."
]);
ALF("O8+(3)M17","U4(3).(2^2)_{122}",[1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,9,9,10,
10,11,11,12,12,13,13,14,15,15,16,16,17,17,18,18,19,20,21,22,22,23,24,25,
25,26,27,28,28,29,30,31,31,32,33,34,35,36,36,37,38,39,40,40,41,42,43,43,
44,45,45,46,47,48,49,50,50,51,52,53,54,54,55,56,57,57,58,59,59]);

MOT("3^2.U4(3)",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[29393280,29393280,29393280,29393280,29393280,29393280,29393280,29393280,
29393280,10368,10368,10368,10368,10368,10368,10368,10368,10368,52488,52488,
52488,52488,52488,52488,52488,52488,52488,2916,2916,2916,2916,2916,2916,81,864
,864,864,864,864,864,864,864,864,144,144,144,144,144,144,144,144,144,45,45,45,
45,45,45,45,45,45,648,648,648,648,648,648,648,648,648,324,324,324,324,324,324,
324,324,324,324,324,324,324,324,324,324,324,324,63,63,63,63,63,63,63,63,63,63,
63,63,63,63,63,63,63,63,72,72,72,72,72,72,72,72,72,81,81,81,81,81,81,81,81,81,
81,81,81,108,108,108,108,108,108,108,108,108],
[,[1,3,2,7,9,8,4,6,5,1,3,2,7,9,8,4,6,5,19,21,20,25,27,26,22,24,23,28,30,29,32,
31,33,34,10,12,11,16,18,17,13,15,14,10,12,11,16,18,17,13,15,14,53,55,54,59,61,
60,56,58,57,19,21,20,25,27,26,22,24,23,28,30,29,28,30,29,28,30,29,33,32,31,31,
33,32,32,31,33,89,91,90,95,97,96,92,94,93,98,100,99,104,106,105,101,103,102,35
,37,36,41,43,42,38,40,39,119,121,120,116,118,117,126,125,127,123,122,124,62,64
,63,68,70,69,65,67,66],[1,1,1,1,1,1,1,1,1,10,10,10,10,10,10,10,10,10,1,1,1,1,1
,1,1,1,1,1,1,1,1,1,1,1,35,35,35,35,35,35,35,35,35,44,44,44,44,44,44,44,44,44,
53,53,53,53,53,53,53,53,53,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,
10,10,10,10,10,10,10,10,10,10,98,98,98,98,98,98,98,98,98,89,89,89,89,89,89,89,
89,89,107,107,107,107,107,107,107,107,107,27,27,27,23,23,23,25,25,25,22,22,22,
35,35,35,35,35,35,35,35,35],,[1,3,2,7,9,8,4,6,5,10,12,11,16,18,17,13,15,14,19,
21,20,25,27,26,22,24,23,28,30,29,32,31,33,34,35,37,36,41,43,42,38,40,39,44,46,
45,50,52,51,47,49,48,1,3,2,7,9,8,4,6,5,62,64,63,68,70,69,65,67,66,71,73,72,77,
79,78,74,76,75,80,82,81,86,88,87,83,85,84,98,100,99,104,106,105,101,103,102,89
,91,90,95,97,96,92,94,93,107,109,108,113,115,114,110,112,111,119,121,120,116,
118,117,126,125,127,123,122,124,128,130,129,134,136,135,131,133,132],,[1,2,3,4
,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,
32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,
58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,
84,85,86,87,88,1,2,3,4,5,6,7,8,9,1,2,3,4,5,6,7,8,9,107,108,109,110,111,112,113
,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,
133,134,135,136]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[21,21,21,21,21,21,21,21,21,5,5,5,5,5
,5,5,5,5,-6,-6,-6,-6,-6,-6,-6,-6,-6,3,3,3,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
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-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,-2,-2,-2,-2,-2,-2,-2,-2,-2],[35,35,35,35,35,35,
35,35,35,3,3,3,3,3,3,3,3,3,8,8,8,8,8,8,8,8,8,8,8,8,-1,-1,-1,-1,3,3,3,3,3,3,3,3
,3,-1,-1,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,3,3,3,3,3,3,3,3,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,
-1,-1,-1,2,2,2,2,2,2,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0],[35,35,35,35,35,35,
35,35,35,3,3,3,3,3,3,3,3,3,8,8,8,8,8,8,8,8,8,-1,-1,-1,8,8,8,-1,3,3,3,3,3,3,3,3
,3,-1,-1,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,3,3,3,3,3,3,
3,3,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,-1,-1,2,2,2,2,2,2,0,0,0,0,0,0,0,0,0],[90,90,90,90,90,90,
90,90,90,10,10,10,10,10,10,10,10,10,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,0,-2,-2,-2,
-2,-2,-2,-2,-2,-2,2,2,2,2,2,2,2,2,2,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1],[140,140,
140,140,140,140,140,140,140,12,12,12,12,12,12,12,12,12,5,5,5,5,5,5,5,5,5,-4,-4
,-4,-4,-4,-4,5,4,4,4,4,4,4,4,4,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-3,-3,-3,
-3,-3,-3,-3,-3,-3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,
1,1,1],[189,189,189,189,189,189,189,189,189,-3,-3,-3,-3,-3,-3,-3,-3,-3,27,27,
27,27,27,27,27,27,27,0,0,0,0,0,0,0,5,5,5,5,5,5,5,5,5,1,1,1,1,1,1,1,1,1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,3,3,3,3,3,3,3,3,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,-1,
-1,-1,-1,-1,-1,-1,-1,-1],[210,210,210,210,210,210,210,210,210,2,2,2,2,2,2,2,2,
2,21,21,21,21,21,21,21,21,21,3,3,3,3,3,3,3,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2
,-2,-2,-2,-2,-2,-2,0,0,0,0,0,0,0,0,0,5,5,5,5,5,5,5,5,5,-1,-1,-1,-1,-1,-1,-1,-1
,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1],[280,280,280,280,280,280,280
,280,280,-8,-8,-8,-8,-8,-8,-8,-8,-8,10,10,10,10,10,10,10,10,10,10,10,10,1,1,1,
1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,-2,-2,-2,-2,-2,-2,
-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,2*E(3)-E(3)^2,2*E(3)-E(3)^2,2*E(3)-E(3)^2,
-E(3)+2*E(3)^2,-E(3)+2*E(3)^2,-E(3)+2*E(3)^2,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0],
[GALOIS,[9,2]],[280,280,280,280,280,280,280,280,280,-8,-8,-8,-8,-8,-8,-8,-8,
-8,10,10,10,10,10,10,10,10,10,1,1,1,10,10,10,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
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-2,-2,-2,-2,-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,
1,1,1,2*E(3)-E(3)^2,2*E(3)-E(3)^2,2*E(3)-E(3)^2,-E(3)+2*E(3)^2,-E(3)+2*E(3)^2,
-E(3)+2*E(3)^2,0,0,0,0,0,0,0,0,0],
[GALOIS,[11,2]],[315,315,315,315,315,315,315,315,315,11,11,11,11,11,11,11,11,
11,-9,-9,-9,-9,-9,-9,-9,-9,-9,18,18,18,-9,-9,-9,0,-1,-1,-1,-1,-1,-1,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,-1,-1,2,2,2,
2,2,2,2,2,2,-1,-1,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1
,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,-1,-1],[315,315,
315,315,315,315,315,315,315,11,11,11,11,11,11,11,11,11,-9,-9,-9,-9,-9,-9,-9,-9
,-9,-9,-9,-9,18,18,18,0,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
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0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,-1,-1],[420,420,420,420,420,420,420,420,420,4
,4,4,4,4,4,4,4,4,-39,-39,-39,-39,-39,-39,-39,-39,-39,6,6,6,6,6,6,-3,4,4,4,4,4,
4,4,4,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,-2,-2,-2,-2,-2,
-2,-2,-2,-2,-2,-2,-2,-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
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1],[560,560,560,560,560
,560,560,560,560,-16,-16,-16,-16,-16,-16,-16,-16,-16,-34,-34,-34,-34,-34,-34,
-34,-34,-34,2,2,2,2,2,2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,
0,0,0,0],[640,640,640,640,640,640,640,640,640,0,0,0,0,0,0,0,0,0,-8,-8,-8,-8,-8
,-8,-8,-8,-8,-8,-8,-8,-8,-8,-8,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
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)+E(7)^2+E(7)^4,
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)+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,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,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)^6,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0
,0],
[GALOIS,[17,3]],[729,729,729,729,729,729,729,729,729,9,9,9,9,9,9,9,9,9,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,-3,-3,-3,-3,-3,-3,-3,-3,-3,1,1,1,1,1,1,1,1,1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1
,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0],[896,896,896,896,896,896,896,896,896,0,0,0,0,0,0,0,0,
0,32,32,32,32,32,32,32,32,32,-4,-4,-4,-4,-4,-4,-4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,
-1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0],[36,36,36,36*E(3),36*E(3),36*E(3),36*E(3)^2,
36*E(3)^2,36*E(3)^2,4,4,4,4*E(3),4*E(3),4*E(3),4*E(3)^2,4*E(3)^2,4*E(3)^2,9,9,
9,9*E(3),9*E(3),9*E(3),9*E(3)^2,9*E(3)^2,9*E(3)^2,0,0,0,0,0,0,0,4,4,4,4*E(3),
4*E(3),4*E(3),4*E(3)^2,4*E(3)^2,4*E(3)^2,0,0,0,0,0,0,0,0,0,1,1,1,E(3),E(3),
E(3),E(3)^2,E(3)^2,E(3)^2,1,1,1,E(3),E(3),E(3),E(3)^2,E(3)^2,E(3)^2,-2,-2,-2,
-2*E(3),-2*E(3),-2*E(3),-2*E(3)^2,-2*E(3)^2,-2*E(3)^2,-2,-2,-2,-2*E(3),-2*E(3)
,-2*E(3),-2*E(3)^2,-2*E(3)^2,-2*E(3)^2,1,1,1,E(3),E(3),E(3),E(3)^2,E(3)^2,
E(3)^2,1,1,1,E(3),E(3),E(3),E(3)^2,E(3)^2,E(3)^2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,1,1,1,E(3),E(3),E(3),E(3)^2,E(3)^2,E(3)^2],
[GALOIS,[21,2]],[45,45,45,45*E(3),45*E(3),45*E(3),45*E(3)^2,45*E(3)^2,
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E(7)^3+E(7)^5+E(7)^6,E(21)+E(21)^4+E(21)^16,E(21)+E(21)^4+E(21)^16,
E(21)+E(21)^4+E(21)^16,E(21)^2+E(21)^8+E(21)^11,E(21)^2+E(21)^8+E(21)^11,
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[GALOIS,[23,2]],
[GALOIS,[23,10]],
[GALOIS,[23,5]],[126,126,126,126*E(3),126*E(3),126*E(3),126*E(3)^2,126*E(3)^2
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[GALOIS,[27,2]],[189,189,189,189*E(3),189*E(3),189*E(3),189*E(3)^2,189*E(3)^2
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[GALOIS,[31,2]],[315,315,315,315*E(3),315*E(3),315*E(3),315*E(3)^2,315*E(3)^2
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[GALOIS,[33,2]],[315,315,315,315*E(3),315*E(3),315*E(3),315*E(3)^2,315*E(3)^2
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[GALOIS,[35,2]],[630,630,630,630*E(3),630*E(3),630*E(3),630*E(3)^2,630*E(3)^2
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[GALOIS,[37,2]],[720,720,720,720*E(3),720*E(3),720*E(3),720*E(3)^2,720*E(3)^2
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[GALOIS,[39,2]],[729,729,729,729*E(3),729*E(3),729*E(3),729*E(3)^2,729*E(3)^2
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[GALOIS,[41,2]],[756,756,756,756*E(3),756*E(3),756*E(3),756*E(3)^2,756*E(3)^2
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[GALOIS,[43,2]],[945,945,945,945*E(3),945*E(3),945*E(3),945*E(3)^2,945*E(3)^2
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[GALOIS,[45,2]],[15,15*E(3),15*E(3)^2,15,15*E(3),15*E(3)^2,15,15*E(3),
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[GALOIS,[47,2]],[21,21*E(3),21*E(3)^2,21,21*E(3),21*E(3)^2,21,21*E(3),
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[GALOIS,[49,2]],[105,105*E(3),105*E(3)^2,105,105*E(3),105*E(3)^2,105,105*E(3)
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[GALOIS,[51,2]],[105,105*E(3),105*E(3)^2,105,105*E(3),105*E(3)^2,105,105*E(3)
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15*E(3),15*E(3)^2,15,15*E(3),15*E(3)^2,15,15*E(3),15*E(3)^2,3,3*E(3),3*E(3)^2,
0,0,0,0,5,5*E(3),5*E(3)^2,5,5*E(3),5*E(3)^2,5,5*E(3),5*E(3)^2,1,E(3),E(3)^2,1,
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0,-1,-E(3),-E(3)^2,-1,-E(3),-E(3)^2,-1,-E(3),-E(3)^2],
[GALOIS,[53,2]],[105,105*E(3),105*E(3)^2,105,105*E(3),105*E(3)^2,105,105*E(3)
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12*E(3)^2,0,0,0,0,1,E(3),E(3)^2,1,E(3),E(3)^2,1,E(3),E(3)^2,1,E(3),E(3)^2,1,
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E(3)^2,1,E(3),E(3)^2,E(3)-E(3)^2,E(3)+2*E(3)^2,-2*E(3)-E(3)^2,-E(3)+E(3)^2,
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-2*E(3)^2,-2,-2*E(3),-2*E(3)^2],
[GALOIS,[55,2]],[210,210*E(3),210*E(3)^2,210,210*E(3),210*E(3)^2,210,210*E(3)
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3*E(3)^2,3,3*E(3),3*E(3)^2,3,3*E(3),3*E(3)^2,15,15*E(3),15*E(3)^2,0,0,0,0,-2,
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-E(3)+E(3)^2,-2*E(3)-E(3)^2,E(3)-E(3)^2,E(3)+2*E(3)^2,0,0,0,0,0,0,1,E(3),
E(3)^2,1,E(3),E(3)^2,1,E(3),E(3)^2],
[GALOIS,[57,2]],[315,315*E(3),315*E(3)^2,315,315*E(3),315*E(3)^2,315,315*E(3)
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9*E(3)^2,0,0,0,0,3,3*E(3),3*E(3)^2,3,3*E(3),3*E(3)^2,3,3*E(3),3*E(3)^2,-1,
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4*E(3)^2,4,4*E(3),4*E(3)^2,4,4*E(3),4*E(3)^2,1,E(3),E(3)^2,1,E(3),E(3)^2,1,
E(3),E(3)^2,-2,-2*E(3),-2*E(3)^2,-2,-2*E(3),-2*E(3)^2,-2,-2*E(3),-2*E(3)^2,0,0
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-E(3)^2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[59,2]],[336,336*E(3),336*E(3)^2,336,336*E(3),336*E(3)^2,336,336*E(3)
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-6*E(3),-6*E(3)^2,-6,-6*E(3),-6*E(3)^2,-6,-6*E(3),-6*E(3)^2,6,6*E(3),6*E(3)^2,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,E(3),E(3)^2,1,E(3),E(3)^2,1,E(3)
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0,0,0,0,0,0,0,0,0,0,0,0,0,0,-E(3)+E(3)^2,-E(3)-2*E(3)^2,2*E(3)+E(3)^2,
E(3)-E(3)^2,E(3)+2*E(3)^2,-2*E(3)-E(3)^2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[61,2]],[360,360*E(3),360*E(3)^2,360,360*E(3),360*E(3)^2,360,360*E(3)
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2*E(3),2*E(3)^2,2,2*E(3),2*E(3)^2,2,2*E(3),2*E(3)^2,-1,-E(3),-E(3)^2,-1,-E(3),
-E(3)^2,-1,-E(3),-E(3)^2,2,2*E(3),2*E(3)^2,2,2*E(3),2*E(3)^2,2,2*E(3),2*E(3)^2
,E(7)+E(7)^2+E(7)^4,E(21)^10+E(21)^13+E(21)^19,E(21)^5+E(21)^17+E(21)^20,
E(7)+E(7)^2+E(7)^4,E(21)^10+E(21)^13+E(21)^19,E(21)^5+E(21)^17+E(21)^20,
E(7)+E(7)^2+E(7)^4,E(21)^10+E(21)^13+E(21)^19,E(21)^5+E(21)^17+E(21)^20,
E(7)^3+E(7)^5+E(7)^6,E(21)+E(21)^4+E(21)^16,E(21)^2+E(21)^8+E(21)^11,
E(7)^3+E(7)^5+E(7)^6,E(21)+E(21)^4+E(21)^16,E(21)^2+E(21)^8+E(21)^11,
E(7)^3+E(7)^5+E(7)^6,E(21)+E(21)^4+E(21)^16,E(21)^2+E(21)^8+E(21)^11,0,0,0,0,0
,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],
[GALOIS,[63,2]],
[GALOIS,[63,10]],
[GALOIS,[63,5]],[384,384*E(3),384*E(3)^2,384,384*E(3),384*E(3)^2,384,384*E(3)
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24*E(3),24*E(3)^2,12,12*E(3),12*E(3)^2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
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0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-E(3),-E(3)^2,-1,-E(3),-E(3)^2,-1,-E(3),
-E(3)^2,-1,-E(3),-E(3)^2,-1,-E(3),-E(3)^2,-1,-E(3),-E(3)^2,0,0,0,0,0,0,0,0,0,
E(3)+2*E(3)^2,-2*E(3)-E(3)^2,E(3)-E(3)^2,2*E(3)+E(3)^2,-E(3)+E(3)^2,
-E(3)-2*E(3)^2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[67,2]],[420,420*E(3),420*E(3)^2,420,420*E(3),420*E(3)^2,420,420*E(3)
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33*E(3)^2,33,33*E(3),33*E(3)^2,33,33*E(3),33*E(3)^2,-6,-6*E(3),-6*E(3)^2,0,0,0
,0,4,4*E(3),4*E(3)^2,4,4*E(3),4*E(3)^2,4,4*E(3),4*E(3)^2,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,1,E(3),E(3)^2,1,E(3),E(3)^2,1,E(3),E(3)^2,-2,-2*E(3),-2*E(3)^2,
-2,-2*E(3),-2*E(3)^2,-2,-2*E(3),-2*E(3)^2,-2,-2*E(3),-2*E(3)^2,-2,-2*E(3),
-2*E(3)^2,-2,-2*E(3),-2*E(3)^2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,E(3)-E(3)^2,E(3)+2*E(3)^2,-2*E(3)-E(3)^2,-E(3)+E(3)^2,-E(3)-2*E(3)^2,
2*E(3)+E(3)^2,0,0,0,0,0,0,1,E(3),E(3)^2,1,E(3),E(3)^2,1,E(3),E(3)^2],
[GALOIS,[69,2]],[630,630*E(3),630*E(3)^2,630,630*E(3),630*E(3)^2,630,630*E(3)
,630*E(3)^2,6,6*E(3),6*E(3)^2,6,6*E(3),6*E(3)^2,6,6*E(3),6*E(3)^2,9,9*E(3),
9*E(3)^2,9,9*E(3),9*E(3)^2,9,9*E(3),9*E(3)^2,-9,-9*E(3),-9*E(3)^2,0,0,0,0,2,
2*E(3),2*E(3)^2,2,2*E(3),2*E(3)^2,2,2*E(3),2*E(3)^2,-2,-2*E(3),-2*E(3)^2,-2,
-2*E(3),-2*E(3)^2,-2,-2*E(3),-2*E(3)^2,0,0,0,0,0,0,0,0,0,-3,-3*E(3),-3*E(3)^2,
-3,-3*E(3),-3*E(3)^2,-3,-3*E(3),-3*E(3)^2,3,3*E(3),3*E(3)^2,3,3*E(3),3*E(3)^2,
3,3*E(3),3*E(3)^2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-E(3),-E(3)^2,-1,-E(3),-E(3)^2,-1,-E(3)
,-E(3)^2],
[GALOIS,[71,2]],[729,729*E(3),729*E(3)^2,729,729*E(3),729*E(3)^2,729,729*E(3)
,729*E(3)^2,9,9*E(3),9*E(3)^2,9,9*E(3),9*E(3)^2,9,9*E(3),9*E(3)^2,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,-3,-3*E(3),-3*E(3)^2,-3,-3*E(3),-3*E(3)^2,-3,-3*E(3),
-3*E(3)^2,1,E(3),E(3)^2,1,E(3),E(3)^2,1,E(3),E(3)^2,-1,-E(3),-E(3)^2,-1,-E(3),
-E(3)^2,-1,-E(3),-E(3)^2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,1,E(3),E(3)^2,1,E(3),E(3)^2,1,E(3),E(3)^2,1,E(3),E(3)^2,1,E(3),E(3)^2,1,E(3),
E(3)^2,-1,-E(3),-E(3)^2,-1,-E(3),-E(3)^2,-1,-E(3),-E(3)^2,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[73,2]],[756,756*E(3),756*E(3)^2,756,756*E(3),756*E(3)^2,756,756*E(3)
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-12*E(3)^2,27,27*E(3),27*E(3)^2,27,27*E(3),27*E(3)^2,27,27*E(3),27*E(3)^2,0,0,
0,0,0,0,0,-4,-4*E(3),-4*E(3)^2,-4,-4*E(3),-4*E(3)^2,-4,-4*E(3),-4*E(3)^2,0,0,0
,0,0,0,0,0,0,1,E(3),E(3)^2,1,E(3),E(3)^2,1,E(3),E(3)^2,3,3*E(3),3*E(3)^2,3,
3*E(3),3*E(3)^2,3,3*E(3),3*E(3)^2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
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,-E(3)^2,-1,-E(3),-E(3)^2,-1,-E(3),-E(3)^2],
[GALOIS,[75,2]],[945,945*E(3),945*E(3)^2,945,945*E(3),945*E(3)^2,945,945*E(3)
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-15*E(3)^2,-27,-27*E(3),-27*E(3)^2,-27,-27*E(3),-27*E(3)^2,-27,-27*E(3),
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E(3)^2,1,E(3),E(3)^2,1,E(3),E(3)^2,0,0,0,0,0,0,0,0,0,-3,-3*E(3),-3*E(3)^2,-3,
-3*E(3),-3*E(3)^2,-3,-3*E(3),-3*E(3)^2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
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,0,0,0,0,0,0,0,0,0,0,1,E(3),E(3)^2,1,E(3),E(3)^2,1,E(3),E(3)^2],
[GALOIS,[77,2]],[15,15*E(3),15*E(3)^2,15*E(3)^2,15,15*E(3),15*E(3),15*E(3)^2,
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6*E(3)^2,6,6*E(3),6*E(3),6*E(3)^2,6,0,0,0,3*E(3),3*E(3)^2,3,0,3,3*E(3),
3*E(3)^2,3*E(3)^2,3,3*E(3),3*E(3),3*E(3)^2,3,-1,-E(3),-E(3)^2,-E(3)^2,-1,-E(3)
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-E(3)^2,-E(3)^2,-1,-E(3),-E(3),-E(3)^2,-1,1,E(3),E(3)^2,E(3)^2,1,E(3),E(3),
E(3)^2,1,1,E(3),E(3)^2,E(3)^2,1,E(3),E(3),E(3)^2,1,1,E(3),E(3)^2,E(3)^2,1,E(3)
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E(3)+2*E(3)^2,-2*E(3)-E(3)^2,E(3)-E(3)^2,0,0,0,0,0,0,0,0,0],
[GALOIS,[79,2]],[21,21*E(3),21*E(3)^2,21*E(3)^2,21,21*E(3),21*E(3),21*E(3)^2,
21,5,5*E(3),5*E(3)^2,5*E(3)^2,5,5*E(3),5*E(3),5*E(3)^2,5,3,3*E(3),3*E(3)^2,
3*E(3)^2,3,3*E(3),3*E(3),3*E(3)^2,3,0,0,0,6*E(3),6*E(3)^2,6,0,1,E(3),E(3)^2,
E(3)^2,1,E(3),E(3),E(3)^2,1,1,E(3),E(3)^2,E(3)^2,1,E(3),E(3),E(3)^2,1,1,E(3),
E(3)^2,E(3)^2,1,E(3),E(3),E(3)^2,1,-1,-E(3),-E(3)^2,-E(3)^2,-1,-E(3),-E(3),
-E(3)^2,-1,2,2*E(3),2*E(3)^2,2*E(3)^2,2,2*E(3),2*E(3),2*E(3)^2,2,2,2*E(3),
2*E(3)^2,2*E(3)^2,2,2*E(3),2*E(3),2*E(3)^2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,-1,-E(3),-E(3)^2,-E(3)^2,-1,-E(3),-E(3),-E(3)^2,-1,0,0,0,0,0,0,E(3)-E(3)^2,
E(3)+2*E(3)^2,-2*E(3)-E(3)^2,2*E(3)+E(3)^2,-E(3)+E(3)^2,-E(3)-2*E(3)^2,1,E(3),
E(3)^2,E(3)^2,1,E(3),E(3),E(3)^2,1],
[GALOIS,[81,2]],[105,105*E(3),105*E(3)^2,105*E(3)^2,105,105*E(3),105*E(3),
105*E(3)^2,105,9,9*E(3),9*E(3)^2,9*E(3)^2,9,9*E(3),9*E(3),9*E(3)^2,9,15,
15*E(3),15*E(3)^2,15*E(3)^2,15,15*E(3),15*E(3),15*E(3)^2,15,0,0,0,3*E(3),
3*E(3)^2,3,0,1,E(3),E(3)^2,E(3)^2,1,E(3),E(3),E(3)^2,1,1,E(3),E(3)^2,E(3)^2,1,
E(3),E(3),E(3)^2,1,0,0,0,0,0,0,0,0,0,3,3*E(3),3*E(3)^2,3*E(3)^2,3,3*E(3),
3*E(3),3*E(3)^2,3,0,0,0,0,0,0,0,0,0,3,3*E(3),3*E(3)^2,3*E(3)^2,3,3*E(3),3*E(3)
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E(3),E(3)^2,1,0,0,0,0,0,0,-E(3)+E(3)^2,-E(3)-2*E(3)^2,2*E(3)+E(3)^2,
-2*E(3)-E(3)^2,E(3)-E(3)^2,E(3)+2*E(3)^2,1,E(3),E(3)^2,E(3)^2,1,E(3),E(3),
E(3)^2,1],
[GALOIS,[83,2]],[105,105*E(3),105*E(3)^2,105*E(3)^2,105,105*E(3),105*E(3),
105*E(3)^2,105,-7,-7*E(3),-7*E(3)^2,-7*E(3)^2,-7,-7*E(3),-7*E(3),-7*E(3)^2,-7,
15,15*E(3),15*E(3)^2,15*E(3)^2,15,15*E(3),15*E(3),15*E(3)^2,15,0,0,0,3*E(3),
3*E(3)^2,3,0,5,5*E(3),5*E(3)^2,5*E(3)^2,5,5*E(3),5*E(3),5*E(3)^2,5,1,E(3),
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2,-1,-E(3),-E(3)^2,-E(3)^2,-1,-E(3),-E(3),-E(3)^2,-1,0,0,0,0,0,0,0,0,0,0,0,0,0
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E(3)+2*E(3)^2,-1,-E(3),-E(3)^2,-E(3)^2,-1,-E(3),-E(3),-E(3)^2,-1],
[GALOIS,[85,2]],[105,105*E(3),105*E(3)^2,105*E(3)^2,105,105*E(3),105*E(3),
105*E(3)^2,105,9,9*E(3),9*E(3)^2,9*E(3)^2,9,9*E(3),9*E(3),9*E(3)^2,9,-12,
-12*E(3),-12*E(3)^2,-12*E(3)^2,-12,-12*E(3),-12*E(3),-12*E(3)^2,-12,0,0,0,
12*E(3),12*E(3)^2,12,0,1,E(3),E(3)^2,E(3)^2,1,E(3),E(3),E(3)^2,1,1,E(3),E(3)^2
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E(3)^2,1,E(3),E(3),E(3)^2,1,0,0,0,0,0,0,2*E(3)+E(3)^2,-E(3)+E(3)^2,
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-2*E(3)^2,-2,-2*E(3),-2*E(3),-2*E(3)^2,-2],
[GALOIS,[87,2]],[210,210*E(3),210*E(3)^2,210*E(3)^2,210,210*E(3),210*E(3),
210*E(3)^2,210,2,2*E(3),2*E(3)^2,2*E(3)^2,2,2*E(3),2*E(3),2*E(3)^2,2,3,3*E(3),
3*E(3)^2,3*E(3)^2,3,3*E(3),3*E(3),3*E(3)^2,3,0,0,0,15*E(3),15*E(3)^2,15,0,-2,
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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,E(3)+2*E(3)^2,
-2*E(3)-E(3)^2,E(3)-E(3)^2,-E(3)-2*E(3)^2,2*E(3)+E(3)^2,-E(3)+E(3)^2,1,E(3),
E(3)^2,E(3)^2,1,E(3),E(3),E(3)^2,1],
[GALOIS,[89,2]],[315,315*E(3),315*E(3)^2,315*E(3)^2,315,315*E(3),315*E(3),
315*E(3)^2,315,-5,-5*E(3),-5*E(3)^2,-5*E(3)^2,-5,-5*E(3),-5*E(3),-5*E(3)^2,-5,
-36,-36*E(3),-36*E(3)^2,-36*E(3)^2,-36,-36*E(3),-36*E(3),-36*E(3)^2,-36,0,0,0,
9*E(3),9*E(3)^2,9,0,3,3*E(3),3*E(3)^2,3*E(3)^2,3,3*E(3),3*E(3),3*E(3)^2,3,-1,
-E(3),-E(3)^2,-E(3)^2,-1,-E(3),-E(3),-E(3)^2,-1,0,0,0,0,0,0,0,0,0,4,4*E(3),
4*E(3)^2,4*E(3)^2,4,4*E(3),4*E(3),4*E(3)^2,4,-2,-2*E(3),-2*E(3)^2,-2*E(3)^2,-2
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0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-E(3),-E(3)^2,-E(3)^2,-1,-E(3),-E(3),-E(3)^2,
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[GALOIS,[91,2]],[336,336*E(3),336*E(3)^2,336*E(3)^2,336,336*E(3),336*E(3),
336*E(3)^2,336,16,16*E(3),16*E(3)^2,16*E(3)^2,16,16*E(3),16*E(3),16*E(3)^2,16,
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6*E(3)^2,6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,E(3),E(3)^2,E(3)^2,1,E(3),
E(3),E(3)^2,1,-2,-2*E(3),-2*E(3)^2,-2*E(3)^2,-2,-2*E(3),-2*E(3),-2*E(3)^2,-2,
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-2*E(3)^2,-2*E(3)^2,-2,-2*E(3),-2*E(3),-2*E(3)^2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2*E(3)-E(3)^2,E(3)-E(3)^2,
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[GALOIS,[93,2]],[360,360*E(3),360*E(3)^2,360*E(3)^2,360,360*E(3),360*E(3),
360*E(3)^2,360,8,8*E(3),8*E(3)^2,8*E(3)^2,8,8*E(3),8*E(3),8*E(3)^2,8,-18,
-18*E(3),-18*E(3)^2,-18*E(3)^2,-18,-18*E(3),-18*E(3),-18*E(3)^2,-18,0,0,0,
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2*E(3)^2,2,2*E(3),2*E(3),2*E(3)^2,2,-1,-E(3),-E(3)^2,-E(3)^2,-1,-E(3),-E(3),
-E(3)^2,-1,E(7)+E(7)^2+E(7)^4,E(21)^10+E(21)^13+E(21)^19,
E(21)^5+E(21)^17+E(21)^20,E(21)^5+E(21)^17+E(21)^20,E(7)+E(7)^2+E(7)^4,
E(21)^10+E(21)^13+E(21)^19,E(21)^10+E(21)^13+E(21)^19,
E(21)^5+E(21)^17+E(21)^20,E(7)+E(7)^2+E(7)^4,E(7)^3+E(7)^5+E(7)^6,
E(21)+E(21)^4+E(21)^16,E(21)^2+E(21)^8+E(21)^11,E(21)^2+E(21)^8+E(21)^11,
E(7)^3+E(7)^5+E(7)^6,E(21)+E(21)^4+E(21)^16,E(21)+E(21)^4+E(21)^16,
E(21)^2+E(21)^8+E(21)^11,E(7)^3+E(7)^5+E(7)^6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[95,2]],
[GALOIS,[95,10]],
[GALOIS,[95,5]],[384,384*E(3),384*E(3)^2,384*E(3)^2,384,384*E(3),384*E(3),
384*E(3)^2,384,0,0,0,0,0,0,0,0,0,24,24*E(3),24*E(3)^2,24*E(3)^2,24,24*E(3),
24*E(3),24*E(3)^2,24,0,0,0,12*E(3),12*E(3)^2,12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,-1,-E(3),-E(3)^2,-E(3)^2,-1,-E(3),-E(3),-E(3)^2,-1,0,0,0,0,0,0,0,0,0,0
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0,0,0,0,0,0,0,-E(3)-2*E(3)^2,2*E(3)+E(3)^2,-E(3)+E(3)^2,E(3)+2*E(3)^2,
-2*E(3)-E(3)^2,E(3)-E(3)^2,0,0,0,0,0,0,0,0,0],
[GALOIS,[99,2]],[420,420*E(3),420*E(3)^2,420*E(3)^2,420,420*E(3),420*E(3),
420*E(3)^2,420,4,4*E(3),4*E(3)^2,4*E(3)^2,4,4*E(3),4*E(3),4*E(3)^2,4,33,
33*E(3),33*E(3)^2,33*E(3)^2,33,33*E(3),33*E(3),33*E(3)^2,33,0,0,0,-6*E(3),
-6*E(3)^2,-6,0,4,4*E(3),4*E(3)^2,4*E(3)^2,4,4*E(3),4*E(3),4*E(3)^2,4,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,1,E(3),E(3)^2,E(3)^2,1,E(3),E(3),E(3)^2,1,-2,
-2*E(3),-2*E(3)^2,-2*E(3)^2,-2,-2*E(3),-2*E(3),-2*E(3)^2,-2,-2,-2*E(3),
-2*E(3)^2,-2*E(3)^2,-2,-2*E(3),-2*E(3),-2*E(3)^2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2*E(3)+E(3)^2,-E(3)+E(3)^2,
-E(3)-2*E(3)^2,E(3)-E(3)^2,E(3)+2*E(3)^2,-2*E(3)-E(3)^2,1,E(3),E(3)^2,E(3)^2,1
,E(3),E(3),E(3)^2,1],
[GALOIS,[101,2]],[630,630*E(3),630*E(3)^2,630*E(3)^2,630,630*E(3),630*E(3),
630*E(3)^2,630,6,6*E(3),6*E(3)^2,6*E(3)^2,6,6*E(3),6*E(3),6*E(3)^2,6,9,9*E(3),
9*E(3)^2,9*E(3)^2,9,9*E(3),9*E(3),9*E(3)^2,9,0,0,0,-9*E(3),-9*E(3)^2,-9,0,2,
2*E(3),2*E(3)^2,2*E(3)^2,2,2*E(3),2*E(3),2*E(3)^2,2,-2,-2*E(3),-2*E(3)^2,
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-E(3),-E(3),-E(3)^2,-1],
[GALOIS,[103,2]],[729,729*E(3),729*E(3)^2,729*E(3)^2,729,729*E(3),729*E(3),
729*E(3)^2,729,9,9*E(3),9*E(3)^2,9*E(3)^2,9,9*E(3),9*E(3),9*E(3)^2,9,0,0,0,0,0
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-E(3)^2,-1,-E(3),-E(3),-E(3)^2,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,1,E(3),E(3)^2,E(3)^2,1,E(3),E(3),E(3)^2,1,1,E(3),E(3)^2,E(3)^2,1,
E(3),E(3),E(3)^2,1,-1,-E(3),-E(3)^2,-E(3)^2,-1,-E(3),-E(3),-E(3)^2,-1,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[105,2]],[756,756*E(3),756*E(3)^2,756*E(3)^2,756,756*E(3),756*E(3),
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-12*E(3)^2,-12,27,27*E(3),27*E(3)^2,27*E(3)^2,27,27*E(3),27*E(3),27*E(3)^2,27,
0,0,0,0,0,0,0,-4,-4*E(3),-4*E(3)^2,-4*E(3)^2,-4,-4*E(3),-4*E(3),-4*E(3)^2,-4,0
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3*E(3)^2,3,3*E(3),3*E(3),3*E(3)^2,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
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-E(3),-E(3)^2,-E(3)^2,-1,-E(3),-E(3),-E(3)^2,-1],
[GALOIS,[107,2]],[945,945*E(3),945*E(3)^2,945*E(3)^2,945,945*E(3),945*E(3),
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0,0,0,0,0,0,0,0,0,0,0,0,1,E(3),E(3)^2,E(3)^2,1,E(3),E(3),E(3)^2,1],
[GALOIS,[109,2]],[36,36*E(3),36*E(3)^2,36*E(3),36*E(3)^2,36,36*E(3)^2,36,
36*E(3),4,4*E(3),4*E(3)^2,4*E(3),4*E(3)^2,4,4*E(3)^2,4,4*E(3),9,9*E(3),
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E(3)^2,1,E(3)^2,1,E(3),1,E(3),E(3)^2,E(3),E(3)^2,1,E(3)^2,1,E(3),-2,-2*E(3),
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0,0,0,0,0,0,1,E(3),E(3)^2,E(3),E(3)^2,1,E(3)^2,1,E(3)],
[GALOIS,[111,2]],[45,45*E(3),45*E(3)^2,45*E(3),45*E(3)^2,45,45*E(3)^2,45,
45*E(3),-3,-3*E(3),-3*E(3)^2,-3*E(3),-3*E(3)^2,-3,-3*E(3)^2,-3,-3*E(3),-9,
-9*E(3),-9*E(3)^2,-9*E(3),-9*E(3)^2,-9,-9*E(3)^2,-9,-9*E(3),0,0,0,0,0,0,0,1,
E(3),E(3)^2,E(3),E(3)^2,1,E(3)^2,1,E(3),1,E(3),E(3)^2,E(3),E(3)^2,1,E(3)^2,1,
E(3),0,0,0,0,0,0,0,0,0,3,3*E(3),3*E(3)^2,3*E(3),3*E(3)^2,3,3*E(3)^2,3,3*E(3),0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,E(7)+E(7)^2+E(7)^4,
E(21)^10+E(21)^13+E(21)^19,E(21)^5+E(21)^17+E(21)^20,
E(21)^10+E(21)^13+E(21)^19,E(21)^5+E(21)^17+E(21)^20,E(7)+E(7)^2+E(7)^4,
E(21)^5+E(21)^17+E(21)^20,E(7)+E(7)^2+E(7)^4,E(21)^10+E(21)^13+E(21)^19,
E(7)^3+E(7)^5+E(7)^6,E(21)+E(21)^4+E(21)^16,E(21)^2+E(21)^8+E(21)^11,
E(21)+E(21)^4+E(21)^16,E(21)^2+E(21)^8+E(21)^11,E(7)^3+E(7)^5+E(7)^6,
E(21)^2+E(21)^8+E(21)^11,E(7)^3+E(7)^5+E(7)^6,E(21)+E(21)^4+E(21)^16,-1,-E(3),
-E(3)^2,-E(3),-E(3)^2,-1,-E(3)^2,-1,-E(3),0,0,0,0,0,0,0,0,0,0,0,0,1,E(3),
E(3)^2,E(3),E(3)^2,1,E(3)^2,1,E(3)],
[GALOIS,[113,2]],
[GALOIS,[113,10]],
[GALOIS,[113,5]],[126,126*E(3),126*E(3)^2,126*E(3),126*E(3)^2,126,126*E(3)^2,
126,126*E(3),14,14*E(3),14*E(3)^2,14*E(3),14*E(3)^2,14,14*E(3)^2,14,14*E(3),-9
,-9*E(3),-9*E(3)^2,-9*E(3),-9*E(3)^2,-9,-9*E(3)^2,-9,-9*E(3),0,0,0,0,0,0,0,2,
2*E(3),2*E(3)^2,2*E(3),2*E(3)^2,2,2*E(3)^2,2,2*E(3),2,2*E(3),2*E(3)^2,2*E(3),
2*E(3)^2,2,2*E(3)^2,2,2*E(3),1,E(3),E(3)^2,E(3),E(3)^2,1,E(3)^2,1,E(3),-1,
-E(3),-E(3)^2,-E(3),-E(3)^2,-1,-E(3)^2,-1,-E(3),2,2*E(3),2*E(3)^2,2*E(3),
2*E(3)^2,2,2*E(3)^2,2,2*E(3),2,2*E(3),2*E(3)^2,2*E(3),2*E(3)^2,2,2*E(3)^2,2,
2*E(3),0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,-1,-E(3),-E(3)^2,-E(3),-E(3)^2,-1,-E(3)^2,-1,-E(3)],
[GALOIS,[117,2]],[189,189*E(3),189*E(3)^2,189*E(3),189*E(3)^2,189,189*E(3)^2,
189,189*E(3),-3,-3*E(3),-3*E(3)^2,-3*E(3),-3*E(3)^2,-3,-3*E(3)^2,-3,-3*E(3),27
,27*E(3),27*E(3)^2,27*E(3),27*E(3)^2,27,27*E(3)^2,27,27*E(3),0,0,0,0,0,0,0,5,
5*E(3),5*E(3)^2,5*E(3),5*E(3)^2,5,5*E(3)^2,5,5*E(3),1,E(3),E(3)^2,E(3),E(3)^2,
1,E(3)^2,1,E(3),-1,-E(3),-E(3)^2,-E(3),-E(3)^2,-1,-E(3)^2,-1,-E(3),3,3*E(3),
3*E(3)^2,3*E(3),3*E(3)^2,3,3*E(3)^2,3,3*E(3),0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,E(3),E(3)^2,E(3),E(3)^2,1,E(3)^2,1,
E(3),0,0,0,0,0,0,0,0,0,0,0,0,-1,-E(3),-E(3)^2,-E(3),-E(3)^2,-1,-E(3)^2,-1,
-E(3)],
[GALOIS,[119,2]],[315,315*E(3),315*E(3)^2,315*E(3),315*E(3)^2,315,315*E(3)^2,
315,315*E(3),11,11*E(3),11*E(3)^2,11*E(3),11*E(3)^2,11,11*E(3)^2,11,11*E(3),18
,18*E(3),18*E(3)^2,18*E(3),18*E(3)^2,18,18*E(3)^2,18,18*E(3),0,0,0,0,0,0,0,-1,
-E(3),-E(3)^2,-E(3),-E(3)^2,-1,-E(3)^2,-1,-E(3),-1,-E(3),-E(3)^2,-E(3),-E(3)^2
,-1,-E(3)^2,-1,-E(3),0,0,0,0,0,0,0,0,0,2,2*E(3),2*E(3)^2,2*E(3),2*E(3)^2,2,
2*E(3)^2,2,2*E(3),2,2*E(3),2*E(3)^2,2*E(3),2*E(3)^2,2,2*E(3)^2,2,2*E(3),2,
2*E(3),2*E(3)^2,2*E(3),2*E(3)^2,2,2*E(3)^2,2,2*E(3),0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,1,E(3),E(3)^2,E(3),E(3)^2,1,E(3)^2,1,E(3),0,0,0,0,0,0,0,0,0,0,0,0,2,
2*E(3),2*E(3)^2,2*E(3),2*E(3)^2,2,2*E(3)^2,2,2*E(3)],
[GALOIS,[121,2]],[315,315*E(3),315*E(3)^2,315*E(3),315*E(3)^2,315,315*E(3)^2,
315,315*E(3),-5,-5*E(3),-5*E(3)^2,-5*E(3),-5*E(3)^2,-5,-5*E(3)^2,-5,-5*E(3),18
,18*E(3),18*E(3)^2,18*E(3),18*E(3)^2,18,18*E(3)^2,18,18*E(3),0,0,0,0,0,0,0,3,
3*E(3),3*E(3)^2,3*E(3),3*E(3)^2,3,3*E(3)^2,3,3*E(3),-1,-E(3),-E(3)^2,-E(3),
-E(3)^2,-1,-E(3)^2,-1,-E(3),0,0,0,0,0,0,0,0,0,-2,-2*E(3),-2*E(3)^2,-2*E(3),
-2*E(3)^2,-2,-2*E(3)^2,-2,-2*E(3),-2,-2*E(3),-2*E(3)^2,-2*E(3),-2*E(3)^2,-2,
-2*E(3)^2,-2,-2*E(3),4,4*E(3),4*E(3)^2,4*E(3),4*E(3)^2,4,4*E(3)^2,4,4*E(3),0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-E(3),-E(3)^2,-E(3),-E(3)^2,-1,-E(3)^2,-1,
-E(3),0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[123,2]],[315,315*E(3),315*E(3)^2,315*E(3),315*E(3)^2,315,315*E(3)^2,
315,315*E(3),-5,-5*E(3),-5*E(3)^2,-5*E(3),-5*E(3)^2,-5,-5*E(3)^2,-5,-5*E(3),18
,18*E(3),18*E(3)^2,18*E(3),18*E(3)^2,18,18*E(3)^2,18,18*E(3),0,0,0,0,0,0,0,3,
3*E(3),3*E(3)^2,3*E(3),3*E(3)^2,3,3*E(3)^2,3,3*E(3),-1,-E(3),-E(3)^2,-E(3),
-E(3)^2,-1,-E(3)^2,-1,-E(3),0,0,0,0,0,0,0,0,0,-2,-2*E(3),-2*E(3)^2,-2*E(3),
-2*E(3)^2,-2,-2*E(3)^2,-2,-2*E(3),4,4*E(3),4*E(3)^2,4*E(3),4*E(3)^2,4,4*E(3)^2
,4,4*E(3),-2,-2*E(3),-2*E(3)^2,-2*E(3),-2*E(3)^2,-2,-2*E(3)^2,-2,-2*E(3),0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-E(3),-E(3)^2,-E(3),-E(3)^2,-1,-E(3)^2,-1,
-E(3),0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[125,2]],[630,630*E(3),630*E(3)^2,630*E(3),630*E(3)^2,630,630*E(3)^2,
630,630*E(3),6,6*E(3),6*E(3)^2,6*E(3),6*E(3)^2,6,6*E(3)^2,6,6*E(3),-45,
-45*E(3),-45*E(3)^2,-45*E(3),-45*E(3)^2,-45,-45*E(3)^2,-45,-45*E(3),0,0,0,0,0,
0,0,2,2*E(3),2*E(3)^2,2*E(3),2*E(3)^2,2,2*E(3)^2,2,2*E(3),-2,-2*E(3),-2*E(3)^2
,-2*E(3),-2*E(3)^2,-2,-2*E(3)^2,-2,-2*E(3),0,0,0,0,0,0,0,0,0,3,3*E(3),3*E(3)^2
,3*E(3),3*E(3)^2,3,3*E(3)^2,3,3*E(3),0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,
-E(3),-E(3)^2,-E(3),-E(3)^2,-1,-E(3)^2,-1,-E(3)],
[GALOIS,[127,2]],[720,720*E(3),720*E(3)^2,720*E(3),720*E(3)^2,720,720*E(3)^2,
720,720*E(3),16,16*E(3),16*E(3)^2,16*E(3),16*E(3)^2,16,16*E(3)^2,16,16*E(3),18
,18*E(3),18*E(3)^2,18*E(3),18*E(3)^2,18,18*E(3)^2,18,18*E(3),0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,-2*E(3),-2*E(3)^2,
-2*E(3),-2*E(3)^2,-2,-2*E(3)^2,-2,-2*E(3),-2,-2*E(3),-2*E(3)^2,-2*E(3),
-2*E(3)^2,-2,-2*E(3)^2,-2,-2*E(3),-2,-2*E(3),-2*E(3)^2,-2*E(3),-2*E(3)^2,-2,
-2*E(3)^2,-2,-2*E(3),-1,-E(3),-E(3)^2,-E(3),-E(3)^2,-1,-E(3)^2,-1,-E(3),-1,
-E(3),-E(3)^2,-E(3),-E(3)^2,-1,-E(3)^2,-1,-E(3),0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[129,2]],[729,729*E(3),729*E(3)^2,729*E(3),729*E(3)^2,729,729*E(3)^2,
729,729*E(3),9,9*E(3),9*E(3)^2,9*E(3),9*E(3)^2,9,9*E(3)^2,9,9*E(3),0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,-3,-3*E(3),-3*E(3)^2,-3*E(3),-3*E(3)^2,-3,-3*E(3)^2,-3,
-3*E(3),1,E(3),E(3)^2,E(3),E(3)^2,1,E(3)^2,1,E(3),-1,-E(3),-E(3)^2,-E(3),
-E(3)^2,-1,-E(3)^2,-1,-E(3),0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,1,E(3),E(3)^2,E(3),E(3)^2,1,E(3)^2,1,E(3),1,E(3),E(3)^2,E(3),E(3)^2,1,
E(3)^2,1,E(3),-1,-E(3),-E(3)^2,-E(3),-E(3)^2,-1,-E(3)^2,-1,-E(3),0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[131,2]],[756,756*E(3),756*E(3)^2,756*E(3),756*E(3)^2,756,756*E(3)^2,
756,756*E(3),-12,-12*E(3),-12*E(3)^2,-12*E(3),-12*E(3)^2,-12,-12*E(3)^2,-12,
-12*E(3),27,27*E(3),27*E(3)^2,27*E(3),27*E(3)^2,27,27*E(3)^2,27,27*E(3),0,0,0,
0,0,0,0,-4,-4*E(3),-4*E(3)^2,-4*E(3),-4*E(3)^2,-4,-4*E(3)^2,-4,-4*E(3),0,0,0,0
,0,0,0,0,0,1,E(3),E(3)^2,E(3),E(3)^2,1,E(3)^2,1,E(3),3,3*E(3),3*E(3)^2,3*E(3),
3*E(3)^2,3,3*E(3)^2,3,3*E(3),0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-E(3),
-E(3)^2,-E(3),-E(3)^2,-1,-E(3)^2,-1,-E(3)],
[GALOIS,[133,2]],[945,945*E(3),945*E(3)^2,945*E(3),945*E(3)^2,945,945*E(3)^2,
945,945*E(3),-15,-15*E(3),-15*E(3)^2,-15*E(3),-15*E(3)^2,-15,-15*E(3)^2,-15,
-15*E(3),-27,-27*E(3),-27*E(3)^2,-27*E(3),-27*E(3)^2,-27,-27*E(3)^2,-27,
-27*E(3),0,0,0,0,0,0,0,1,E(3),E(3)^2,E(3),E(3)^2,1,E(3)^2,1,E(3),1,E(3),E(3)^2
,E(3),E(3)^2,1,E(3)^2,1,E(3),0,0,0,0,0,0,0,0,0,-3,-3*E(3),-3*E(3)^2,-3*E(3),
-3*E(3)^2,-3,-3*E(3)^2,-3,-3*E(3),0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,E(3),E(3)^2,E(3),E(3)^2,1,E(3)^2,1,E(3),0,0,0,0,
0,0,0,0,0,0,0,0,1,E(3),E(3)^2,E(3),E(3)^2,1,E(3)^2,1,E(3)],
[GALOIS,[135,2]]],
[
( 89, 98)( 90, 99)( 91,100)( 92,101)( 93,102)( 94,103)( 95,104)( 96,105)
( 97,106)
,
(  4,  9)(  5,  7)(  6,  8)( 13, 18)( 14, 16)( 15, 17)( 22, 27)( 23, 25)
( 24, 26)( 28, 33)( 29, 31)( 30, 32)( 38, 43)( 39, 41)( 40, 42)( 47, 52)
( 48, 50)( 49, 51)( 56, 61)( 57, 59)( 58, 60)( 65, 70)( 66, 68)( 67, 69)
( 71, 80)( 72, 81)( 73, 82)( 74, 88)( 75, 86)( 76, 87)( 77, 84)( 78, 85)
( 79, 83)( 92, 97)( 93, 95)( 94, 96)(101,106)(102,104)(103,105)(110,115)
(111,113)(112,114)(116,125)(117,126)(118,127)(119,123)(120,124)(121,122)
(131,136)(132,134)(133,135)
,
(  2,  3)(  4,  5)(  7,  9)( 11, 12)( 13, 14)( 16, 18)( 20, 21)( 22, 23)
( 25, 27)( 28, 33)( 29, 32)( 30, 31)( 36, 37)( 38, 39)( 41, 43)( 45, 46)
( 47, 48)( 50, 52)( 54, 55)( 56, 57)( 59, 61)( 63, 64)( 65, 66)( 68, 70)
( 71, 80)( 72, 82)( 73, 81)( 74, 84)( 75, 83)( 76, 85)( 77, 88)( 78, 87)
( 79, 86)( 90, 91)( 92, 93)( 95, 97)( 99,100)(101,102)(104,106)(108,109)
(110,111)(113,115)(116,123)(117,122)(118,124)(119,125)(120,127)(121,126)
(129,130)(131,132)(134,136)
,
(  2,  6)(  3,  8)(  5,  9)( 11, 15)( 12, 17)( 14, 18)( 20, 24)( 21, 26)
( 23, 27)( 29, 30)( 36, 40)( 37, 42)( 39, 43)( 45, 49)( 46, 51)( 48, 52)
( 54, 58)( 55, 60)( 57, 61)( 63, 67)( 64, 69)( 66, 70)( 72, 76)( 73, 78)
( 75, 79)( 81, 85)( 82, 87)( 84, 88)( 90, 94)( 91, 96)( 93, 97)( 99,103)
(100,105)(102,106)(108,112)(109,114)(111,115)(116,119)(117,121)(118,120)
(129,133)(130,135)(132,136)
]);
ALF("3^2.U4(3)","3_1.U4(3)",[1,2,3,1,2,3,1,2,3,4,5,6,4,5,6,4,5,6,7,8,9,7,
8,9,7,8,9,10,11,12,13,13,13,14,15,16,17,15,16,17,15,16,17,18,19,20,18,19,
20,18,19,20,21,22,23,21,22,23,21,22,23,24,25,26,24,25,26,24,25,26,27,28,
29,27,28,29,27,28,29,30,31,32,30,31,32,30,31,32,33,34,35,33,34,35,33,34,
35,36,37,38,36,37,38,36,37,38,39,40,41,39,40,41,39,40,41,42,43,44,45,46,
47,48,48,48,49,49,49,50,51,52,50,51,52,50,51,52]);
ALF("3^2.U4(3)","3_2.U4(3)",[1,1,1,2,2,2,3,3,3,4,4,4,5,5,5,6,6,6,7,7,7,8,
8,8,9,9,9,10,10,10,11,11,11,12,13,13,13,14,14,14,15,15,15,16,16,16,17,17,
17,18,18,18,19,19,19,20,20,20,21,21,21,22,22,22,23,23,23,24,24,24,25,25,
25,26,26,26,27,27,27,28,28,28,29,29,29,30,30,30,31,31,31,32,32,32,33,33,
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]);
ALF("3^2.U4(3)","U4(3)",[1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,
3,3,3,4,4,4,5,5,5,6,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,
10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,
12,12,12,13,13,13,13,13,13,13,13,13,14,14,14,14,14,14,14,14,14,15,15,15,
15,15,15,15,15,15,16,16,16,17,17,17,18,18,18,19,19,19,20,20,20,20,20,20,
20,20,20]);
ALF("3^2.U4(3)","3^2.U4(3).2_3'",[1,2,3,5,6,4,6,4,5,7,8,9,11,12,10,12,10,
11,13,14,15,17,18,16,18,16,17,19,20,21,20,21,19,22,23,24,25,27,28,26,28,
26,27,29,30,31,33,34,32,34,32,33,35,36,37,39,40,38,40,38,39,41,42,43,45,
46,44,46,44,45,47,48,49,50,51,52,53,54,55,47,48,49,55,53,54,51,52,50,56,
57,58,60,61,59,64,62,63,56,57,58,63,64,62,61,59,60,65,66,67,69,70,68,70,
68,69,74,75,76,71,72,73,73,71,72,74,75,76,77,78,79,81,82,80,82,80,81],[
"fusion map is unique up to table autom."
]);
ALF("3^2.U4(3)","3^2.U4(3).(2^2)_{133}",[1,2,2,4,4,3,4,3,4,5,6,6,8,8,7,8,
7,8,9,10,10,12,12,11,12,11,12,13,14,14,14,14,13,15,16,17,17,19,19,18,19,
18,19,20,21,21,23,23,22,23,22,23,24,25,25,27,27,26,27,26,27,28,29,29,31,
31,30,31,30,31,32,33,33,34,35,36,34,36,35,32,33,33,35,34,36,35,36,34,37,
38,38,40,41,39,40,39,41,37,38,38,41,40,39,41,39,40,42,43,43,45,45,44,45,
44,45,46,48,47,46,47,48,48,46,47,46,48,47,49,50,50,52,52,51,52,51,52],[
"fusion map is unique up to table autom."
]);
ALF("3^2.U4(3)","3^2.U4(3).D8",[1,3,3,2,2,3,2,3,2,6,5,5,4,4,5,4,5,4,9,7,7,
8,8,7,8,7,8,11,10,10,10,10,11,12,15,13,13,14,14,13,14,13,14,17,18,18,16,
16,18,16,18,16,21,20,20,19,19,20,19,20,19,24,22,22,23,23,22,23,22,23,28,
25,25,26,27,25,26,25,27,28,25,25,27,26,25,27,25,26,31,29,29,30,30,29,30,
29,30,31,29,29,30,30,29,30,29,30,34,32,32,33,33,32,33,32,33,36,35,37,36,
37,35,35,36,37,36,35,37,40,39,39,38,38,39,38,39,38],[
"fusion map is unique"
]);

MOT("3^2.U4(3).2_3'",
[
"2nd maximal subgroup of 3.Suz,\n",
"table constructed with GAP from the tables of 3.Suz and SuzM2,\n",
"tests: 1.o.r., pow[2,3,5,7]"
],
[58786560,58786560,58786560,29393280,29393280,29393280,20736,20736,20736,
10368,10368,10368,104976,104976,104976,52488,52488,52488,2916,2916,2916,162,
1728,1728,1728,864,864,864,288,288,288,144,144,144,90,90,90,45,45,45,1296,
1296,1296,648,648,648,324,324,324,324,324,324,324,324,324,63,63,63,63,63,63,
63,63,63,144,144,144,72,72,72,81,81,81,81,81,81,216,216,216,108,108,108,4320,
4320,4320,288,288,288,18,288,288,288,96,96,96,24,24,24,30,30,30,36,36,36,72,
72,72,72,72,72],
[,[1,3,2,4,6,5,1,3,2,4,6,5,13,15,14,16,18,17,19,21,20,22,7,9,8,10,12,11,7,9,8,
10,12,11,35,37,36,38,40,39,13,15,14,16,18,17,19,21,20,19,21,20,19,21,20,56,58,
57,62,64,63,59,61,60,23,25,24,26,28,27,74,76,75,71,73,72,41,43,42,44,46,45,1,
3,2,7,9,8,22,23,25,24,23,25,24,29,31,30,35,37,36,41,43,42,77,79,78,77,79,78],[
1,1,1,1,1,1,7,7,7,7,7,7,1,1,1,1,1,1,1,1,1,1,23,23,23,23,23,23,29,29,29,29,29,
29,35,35,35,35,35,35,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,56,56,56,56,56,56,56,56,56,
65,65,65,65,65,65,18,18,18,17,17,17,23,23,23,23,23,23,83,83,83,86,86,86,83,90,
90,90,93,93,93,96,96,96,99,99,99,86,86,86,90,90,90,90,90,90],,[1,3,2,4,6,5,7,
9,8,10,12,11,13,15,14,16,18,17,19,21,20,22,23,25,24,26,28,27,29,31,30,32,34,
33,1,3,2,4,6,5,41,43,42,44,46,45,47,49,48,53,55,54,50,52,51,56,58,57,59,61,60,
62,64,63,65,67,66,68,70,69,74,76,75,71,73,72,77,79,78,80,82,81,83,85,84,86,88,
87,89,90,92,91,93,95,94,96,98,97,83,85,84,102,104,103,105,107,106,108,110,
109],,[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,
53,54,55,1,2,3,4,5,6,4,5,6,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,
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]],
0,
[(59,62)(60,63)(61,64),(105,108)(106,109)(107,110),(  2,  3)(  5,  6)(  8,  9)
( 11, 12)( 14, 15)( 17, 18)( 20, 21)( 24, 25)( 27, 28)( 30, 31)( 33, 34)
( 36, 37)( 39, 40)( 42, 43)( 45, 46)( 48, 49)( 50, 53)( 51, 55)( 52, 54)
( 57, 58)( 60, 61)( 63, 64)( 66, 67)( 69, 70)( 71, 74)( 72, 76)( 73, 75)
( 78, 79)( 81, 82)( 84, 85)( 87, 88)( 91, 92)( 94, 95)( 97, 98)(100,101)
(103,104)(106,107)(109,110)],
["ConstructProj",[["3_2.U4(3).2_3'",[]],,["3^2.U4(3).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,-1,
-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1]]]]);
ALF("3^2.U4(3).2_3'","3_2.U4(3).2_3'",[1,1,1,2,2,2,3,3,3,4,4,4,5,5,5,6,6,
6,7,7,7,8,9,9,9,10,10,10,11,11,11,12,12,12,13,13,13,14,14,14,15,15,15,16,
16,16,17,17,17,18,18,18,19,19,19,20,20,20,21,21,21,22,22,22,23,23,23,24,
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]);
ALF("3^2.U4(3).2_3'","3.Suz",[1,2,3,10,11,12,4,5,6,35,36,37,10,11,12,13,
14,15,13,14,15,16,17,18,19,75,76,77,23,24,25,81,82,83,32,33,34,99,100,101,
35,36,37,44,45,46,44,45,46,38,39,40,41,42,43,48,49,50,111,112,113,114,115,
116,51,52,53,117,118,119,60,61,62,63,64,65,75,76,77,78,79,80,7,8,9,23,24,
25,47,51,52,53,51,52,53,57,58,59,69,70,71,81,82,83,117,118,119,117,118,
119],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
#ALF("3^2.U4(3).2_3'","3^2.U4(3).(2^2)_{133}",[1,3,3,2,4,4,5,7,7,6,8,8,9,
#11,11,10,12,12,13,14,14,15,16,18,18,17,19,19,20,22,22,21,23,23,24,26,26,
#25,27,27,28,30,30,29,31,31,32,36,36,34,35,33,34,33,35,37,39,39,38,40,41,
#38,41,40,42,44,44,43,45,45,46,47,48,46,48,47,49,51,51,50,52,52,71,72,72,
#73,74,74,75,76,77,77,78,79,79,80,81,81,82,83,83,84,85,85,86,87,88,86,88,
#87],[
#"fusion map is unique up to table autom.,\n",
#"representative compatible with factors"
#]);
#T ConstructMGA is too restrictive!!
ALF("3^2.U4(3).2_3'","3^2.U4(3).(2^2)_{133}",[1,2,2,3,4,4,5,6,6,7,8,8,9,
10,10,11,12,12,13,14,14,15,16,17,17,18,19,19,20,21,21,22,23,23,24,25,25,
26,27,27,28,29,29,30,31,31,32,33,33,34,35,36,34,36,35,37,38,38,39,40,41,
39,41,40,42,43,43,44,45,45,46,47,48,46,48,47,49,50,50,51,52,52,53,54,54,
55,56,56,57,58,59,59,60,61,61,62,63,63,64,65,65,66,67,67,68,69,70,68,70,
69],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("3^2.U4(3).2_3'","U4(3).2_3'",[1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,4,4,
4,5,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,9,9,9,9,9,10,10,10,10,10,10,10,
10,10,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,13,13,13,14,14,14,15,
15,15,15,15,15,16,16,16,17,17,17,18,19,19,19,20,20,20,21,21,21,22,22,22,
23,23,23,24,24,24,25,25,25]);
ARC("3^2.U4(3).2_3'","projectives",["(3^2x2).U4(3).2_3'",[[12,-12*E(3),
12*E(3)^2,6,-6*E(3),6*E(3)^2,-4,4*E(3),-4*E(3)^2,-2,2*E(3),-2*E(3)^2,-6,6*E(3)
,-6*E(3)^2,-3,3*E(3),-3*E(3)^2,3,-3*E(3),3*E(3)^2,0,4,-4*E(3),4*E(3)^2,2,
-2*E(3),2*E(3)^2,0,0,0,0,0,0,2,-2*E(3),2*E(3)^2,1,-E(3),E(3)^2,2,-2*E(3),
2*E(3)^2,1,-E(3),E(3)^2,-1,E(3),-E(3)^2,E(3)+3*E(3)^2,3*E(3)+2*E(3)^2,
2*E(3)-E(3)^2,-3*E(3)-E(3)^2,-E(3)+2*E(3)^2,2*E(3)+3*E(3)^2,-2,2*E(3),
-2*E(3)^2,-1,E(3),-E(3)^2,1,-E(3),E(3)^2,0,0,0,0,0,0,-E(3)+E(3)^2,
E(3)+2*E(3)^2,2*E(3)+E(3)^2,E(3)-E(3)^2,-E(3)-2*E(3)^2,-2*E(3)-E(3)^2,-2,
2*E(3),-2*E(3)^2,-1,E(3),-E(3)^2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0],
[GALOIS,[1,2]],[20,-20,20,-20,20,-20,4,-4,4,-4,4,-4,-7,7,-7,7,-7,7,2,-2,2,2,4
,-4,4,-4,4,-4,0,0,0,0,0,0,0,0,0,0,0,0,1,-1,1,-1,1,-1,-2,2,-2,2,-2,2,-2,2,-2,-1
,1,-1,1,-1,1,-1,1,-1,0,0,0,0,0,0,-1,1,-1,-1,1,-1,1,-1,1,-1,1,-1,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,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,-E(3)+E(3)^2],[70,-70,70,-70
,70,-70,-2,2,-2,2,-2,2,16,-16,16,-16,16,-16,7,-7,7,-2,2,-2,2,-2,2,-2,0,0,0,0,0
,0,0,0,0,0,0,0,4,-4,4,-4,4,-4,1,-1,1,-1,1,-1,1,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,1,-1,1,1,-1,1,2,-2,2,-2,2,-2,0,0,0,0,0,0,0,-2*E(8)+2*E(8)^3,
2*E(8)-2*E(8)^3,-2*E(8)+2*E(8)^3,0,0,0,-E(8)+E(8)^3,E(8)-E(8)^3,-E(8)+E(8)^3,0
,0,0,0,0,0,E(8)-E(8)^3,-E(8)+E(8)^3,E(8)-E(8)^3,E(8)-E(8)^3,-E(8)+E(8)^3,
E(8)-E(8)^3],[90,-90*E(3),90*E(3)^2,-90,90*E(3),-90*E(3)^2,2,-2*E(3),2*E(3)^2,
-2,2*E(3),-2*E(3)^2,-18,18*E(3),-18*E(3)^2,18,-18*E(3),18*E(3)^2,0,0,0,0,6,
-6*E(3),6*E(3)^2,-6,6*E(3),-6*E(3)^2,0,0,0,0,0,0,0,0,0,0,0,0,2,-2*E(3),
2*E(3)^2,-2,2*E(3),-2*E(3)^2,2,-2*E(3),2*E(3)^2,-2*E(3),2*E(3)^2,-2,2*E(3)^2,
-2,2*E(3),-1,E(3),-E(3)^2,1,-E(3),E(3)^2,-1,E(3),-E(3)^2,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2*E(8)+2*E(8)^3,2*E(24)^11-2*E(24)^17,
2*E(24)-2*E(24)^19,0,0,0,-E(8)+E(8)^3,E(24)^11-E(24)^17,E(24)-E(24)^19,0,0,0,0
,0,0,E(8)-E(8)^3,-E(24)^11+E(24)^17,-E(24)+E(24)^19,E(8)-E(8)^3,
-E(24)^11+E(24)^17,-E(24)+E(24)^19],
[GALOIS,[5,17]],[112,-112,112,-112,112,-112,-16,16,-16,16,-16,16,4,-4,4,-4,4,
-4,13,-13,13,4,0,0,0,0,0,0,0,0,0,0,0,0,2,-2,2,-2,2,-2,-4,4,-4,4,-4,4,-1,1,-1,1
,-1,1,-1,1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1,1,1,-1,1,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[120,-120,120,-120,120,-120,
-8,8,-8,8,-8,8,12,-12,12,-12,12,-12,-6,6,-6,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,4,-4,4,-4,4,-4,-2,2,-2,2,-2,2,-2,2,-2,1,-1,1,-1,1,-1,1,-1,1,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
,[140,-140,140,-140,140,-140,-4,4,-4,4,-4,4,-22,22,-22,22,-22,22,5,-5,5,-4,4,
-4,4,-4,4,-4,0,0,0,0,0,0,0,0,0,0,0,0,2,-2,2,-2,2,-2,-1,1,-1,1,-1,1,-1,1,-1,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,-2*E(3)+E(3)^2,2*E(3)-E(3)^2,-2*E(3)+E(3)^2,
E(3)-2*E(3)^2,-E(3)+2*E(3)^2,E(3)-2*E(3)^2,-2,2,-2,2,-2,2,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[9,2]],[168,-168*E(3),168*E(3)^2,84,-84*E(3),84*E(3)^2,8,-8*E(3),
8*E(3)^2,4,-4*E(3),4*E(3)^2,-30,30*E(3),-30*E(3)^2,-15,15*E(3),-15*E(3)^2,6,
-6*E(3),6*E(3)^2,0,8,-8*E(3),8*E(3)^2,4,-4*E(3),4*E(3)^2,0,0,0,0,0,0,-2,2*E(3)
,-2*E(3)^2,-1,E(3),-E(3)^2,2,-2*E(3),2*E(3)^2,1,-E(3),E(3)^2,-4,4*E(3),
-4*E(3)^2,-2*E(3),2*E(3)^2,-2,2*E(3)^2,-2,2*E(3),0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,-2*E(3)-E(3)^2,-E(3)+E(3)^2,E(3)+2*E(3)^2,-E(3)-2*E(3)^2,-2*E(3)-E(3)^2,
-E(3)+E(3)^2,2,-2*E(3),2*E(3)^2,1,-E(3),E(3)^2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[11,2]],[180,-180,180,90,-90,90,4,-4,4,2,-2,2,-36,36,-36,-18,18,-18,0
,0,0,0,12,-12,12,6,-6,6,0,0,0,0,0,0,0,0,0,0,0,0,4,-4,4,2,-2,2,4,-4,4,2,-2,2,-2
,2,-2,-2,2,-2,-1,1,-1,1,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[240,-240*E(3),240*E(3)^2,120,
-120*E(3),120*E(3)^2,-16,16*E(3),-16*E(3)^2,-8,8*E(3),-8*E(3)^2,-12,12*E(3),
-12*E(3)^2,-6,6*E(3),-6*E(3)^2,15,-15*E(3),15*E(3)^2,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,-4,4*E(3),-4*E(3)^2,-2,2*E(3),-2*E(3)^2,-1,E(3),-E(3)^2,
E(3)+3*E(3)^2,3*E(3)+2*E(3)^2,2*E(3)-E(3)^2,-3*E(3)-E(3)^2,-E(3)+2*E(3)^2,
2*E(3)+3*E(3)^2,2,-2*E(3),2*E(3)^2,1,-E(3),E(3)^2,-1,E(3),-E(3)^2,0,0,0,0,0,0,
E(3)+2*E(3)^2,2*E(3)+E(3)^2,E(3)-E(3)^2,2*E(3)+E(3)^2,E(3)-E(3)^2,
-E(3)-2*E(3)^2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0],
[GALOIS,[14,2]],[252,-252*E(3),252*E(3)^2,126,-126*E(3),126*E(3)^2,-20,
20*E(3),-20*E(3)^2,-10,10*E(3),-10*E(3)^2,36,-36*E(3),36*E(3)^2,18,-18*E(3),
18*E(3)^2,9,-9*E(3),9*E(3)^2,0,4,-4*E(3),4*E(3)^2,2,-2*E(3),2*E(3)^2,0,0,0,0,0
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0,0,0,0,0,0,0,E(5)-E(5)^2-E(5)^3+E(5)^4,-E(5)+E(5)^2+E(5)^3-E(5)^4,
E(5)-E(5)^2-E(5)^3+E(5)^4,0,0,0,0,0,0,0,0,0],[1008,-1008,1008,504,-504,504,-16
,16,-16,-8,8,-8,-72,72,-72,-36,36,-36,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,2,-2,
-1,1,-1,8,-8,8,4,-4,4,-4,4,-4,-2,2,-2,2,-2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[1008,-1008,1008,-1008,1008,-1008,-16,16,-16,16,-16,16,36,-36,36,-36,36,-36,9,
-9,9,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,2,-2,2,-2,2,-4,4,-4,4,-4,4,-1,1,-1,1,-1,1,-1
,1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[1080,-1080,1080,540,-540,540,24,-24,24
,12,-12,12,-54,54,-54,-27,27,-27,0,0,0,0,8,-8,8,4,-4,4,0,0,0,0,0,0,0,0,0,0,0,0
,-6,6,-6,-3,3,-3,0,0,0,0,0,0,0,0,0,2,-2,2,1,-1,1,-1,1,-1,0,0,0,0,0,0,0,0,0,0,0
,0,2,-2,2,1,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[
1260,-1260,1260,630,-630,630,-36,36,-36,-18,18,-18,72,-72,72,36,-36,36,0,0,0,0
,4,-4,4,2,-2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,4,-4,4,2,-2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0],[1260,-1260*E(3),1260*E(3)^2,-1260,1260*E(3),
-1260*E(3)^2,-4,4*E(3),-4*E(3)^2,4,-4*E(3),4*E(3)^2,-9,9*E(3),-9*E(3)^2,9,
-9*E(3),9*E(3)^2,0,0,0,0,-4,4*E(3),-4*E(3)^2,4,-4*E(3),4*E(3)^2,0,0,0,0,0,0,0,
0,0,0,0,0,-1,E(3),-E(3)^2,1,-E(3),E(3)^2,2,-2*E(3),2*E(3)^2,-2*E(3),2*E(3)^2,
-2,2*E(3)^2,-2,2*E(3),0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,E(3),
-E(3)^2,1,-E(3),E(3)^2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,E(3)-E(3)^2,
-E(3)-2*E(3)^2,-2*E(3)-E(3)^2,E(3)-E(3)^2,-E(3)-2*E(3)^2,-2*E(3)-E(3)^2,
-E(3)+E(3)^2,E(3)+2*E(3)^2,2*E(3)+E(3)^2],
[GALOIS,[59,2]],[1260,-1260*E(3),1260*E(3)^2,630,-630*E(3),630*E(3)^2,-36,
36*E(3),-36*E(3)^2,-18,18*E(3),-18*E(3)^2,18,-18*E(3),18*E(3)^2,9,-9*E(3),
9*E(3)^2,-9,9*E(3),-9*E(3)^2,0,4,-4*E(3),4*E(3)^2,2,-2*E(3),2*E(3)^2,0,0,0,0,0
,0,0,0,0,0,0,0,-6,6*E(3),-6*E(3)^2,-3,3*E(3),-3*E(3)^2,-3,3*E(3),-3*E(3)^2,3,
-3*E(3),3*E(3)^2,-3,3*E(3),-3*E(3)^2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,-2,2*E(3),-2*E(3)^2,-1,E(3),-E(3)^2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0],
[GALOIS,[61,2]],[1260,-1260*E(3),1260*E(3)^2,630,-630*E(3),630*E(3)^2,-4,
4*E(3),-4*E(3)^2,-2,2*E(3),-2*E(3)^2,18,-18*E(3),18*E(3)^2,9,-9*E(3),9*E(3)^2,
-9,9*E(3),-9*E(3)^2,0,-4,4*E(3),-4*E(3)^2,-2,2*E(3),-2*E(3)^2,0,0,0,0,0,0,0,0,
0,0,0,0,2,-2*E(3),2*E(3)^2,1,-E(3),E(3)^2,-1,E(3),-E(3)^2,E(3)+3*E(3)^2,
3*E(3)+2*E(3)^2,2*E(3)-E(3)^2,-3*E(3)-E(3)^2,-E(3)+2*E(3)^2,2*E(3)+3*E(3)^2,0,
0,0,0,0,0,0,0,0,0,0,0,2*E(12)^7-2*E(12)^11,-2*E(12)^7-4*E(12)^11,
-4*E(12)^7-2*E(12)^11,0,0,0,0,0,0,2,-2*E(3),2*E(3)^2,1,-E(3),E(3)^2,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[63,7]],
[GALOIS,[63,5]],
[GALOIS,[63,11]],[1280,-1280,1280,-1280,1280,-1280,0,0,0,0,0,0,-16,16,-16,16,
-16,16,-16,16,-16,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,-1,1,-1,1,-1,1,-1,1,-1,0,0,0,0,0,0,2,-2,2,2,-2,2,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[1440,-1440,1440,720,-720,720,
32,-32,32,16,-16,16,36,-36,36,18,-18,18,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,-4,4,-4,-2,2,-2,-4,4,-4,-2,2,-2,2,-2,2,-2,2,-2,-1,1,-1,1,-1,1,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0],[1680,-1680*E(3),1680*E(3)^2,840,-840*E(3),840*E(3)^2,16,-16*E(3),
16*E(3)^2,8,-8*E(3),8*E(3)^2,24,-24*E(3),24*E(3)^2,12,-12*E(3),12*E(3)^2,6,
-6*E(3),6*E(3)^2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-8,8*E(3),-8*E(3)^2,-4,
4*E(3),-4*E(3)^2,4,-4*E(3),4*E(3)^2,2*E(3),-2*E(3)^2,2,-2*E(3)^2,2,-2*E(3),0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,-2*E(3)-E(3)^2,-E(3)+E(3)^2,E(3)+2*E(3)^2,
-E(3)-2*E(3)^2,-2*E(3)-E(3)^2,-E(3)+E(3)^2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[69,2]],[1680,-1680*E(3),1680*E(3)^2,840,-840*E(3),840*E(3)^2,16,
-16*E(3),16*E(3)^2,8,-8*E(3),8*E(3)^2,-84,84*E(3),-84*E(3)^2,-42,42*E(3),
-42*E(3)^2,-3,3*E(3),-3*E(3)^2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,4,-4*E(3)
,4*E(3)^2,2,-2*E(3),2*E(3)^2,1,-E(3),E(3)^2,-E(3)-3*E(3)^2,-3*E(3)-2*E(3)^2,
-2*E(3)+E(3)^2,3*E(3)+E(3)^2,E(3)-2*E(3)^2,-2*E(3)-3*E(3)^2,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,E(3)+2*E(3)^2,2*E(3)+E(3)^2,E(3)-E(3)^2,2*E(3)+E(3)^2,E(3)-E(3)^2,
-E(3)-2*E(3)^2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0],
[GALOIS,[71,2]],[2520,-2520,2520,1260,-1260,1260,-8,8,-8,-4,4,-4,-18,18,-18,
-9,9,-9,0,0,0,0,-8,8,-8,-4,4,-4,0,0,0,0,0,0,0,0,0,0,0,0,-2,2,-2,-1,1,-1,4,-4,4
,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,-2,2,-2,-1,1,-1,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]],]);
ALN("3^2.U4(3).2_3'",["3.SuzN3C"]);

MOT("3^2.U4(3).(2^2)_{133}",
[
"3rd maximal subgroup of 3.Suz.2"
],
[117573120,58786560,58786560,29393280,41472,20736,20736,10368,209952,104976,
104976,52488,5832,2916,324,3456,1728,1728,864,576,288,288,144,180,90,90,45,
2592,1296,1296,648,648,324,324,324,324,126,63,63,63,63,288,144,144,72,81,81,
81,432,216,216,108,8640,4320,576,288,36,576,288,192,96,48,24,60,30,72,36,72,
72,72,8640,4320,576,288,36,576,288,192,96,48,24,60,30,72,36,72,72,72,24192,
2880,2304,256,432,36,36,32,20,144,36,14],
[,[1,2,3,4,1,2,3,4,9,10,11,12,13,14,15,5,6,7,8,5,6,7,8,24,25,26,27,9,10,11,12,
13,14,13,14,14,37,38,39,40,41,16,17,18,19,46,47,48,28,29,30,31,1,2,5,6,15,16,
17,16,17,20,21,24,25,28,29,49,50,50,1,3,5,7,15,16,18,16,18,20,22,24,26,28,30,
49,51,51,1,1,5,5,9,13,15,16,24,28,32,37],[1,1,1,1,5,5,5,5,1,1,1,1,1,1,1,16,16,
16,16,20,20,20,20,24,24,24,24,5,5,5,5,5,5,5,5,5,37,37,37,37,37,42,42,42,42,12,
12,12,16,16,16,16,53,53,55,55,53,58,58,60,60,62,62,64,64,55,55,58,58,58,71,71,
73,73,71,76,76,78,78,80,80,82,82,73,73,76,76,76,89,90,91,92,89,90,89,96,97,91,
91,100],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,1,2,3,4,
28,29,30,31,32,33,34,35,36,37,38,39,41,40,42,43,44,45,46,47,48,49,50,51,52,53,
54,55,56,57,58,59,60,61,62,63,53,54,66,67,68,70,69,71,72,73,74,75,76,77,78,79,
80,81,71,72,84,85,86,88,87,89,90,91,92,93,94,95,96,90,98,99,100],,[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,
33,34,35,36,1,2,3,4,4,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,
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,
86,87,88,89,90,91,92,93,94,95,96,97,98,99,89]],
0,
[(40,41),(87,88),(69,70),( 2, 3)( 6, 7)(10,11)(17,18)(21,22)(25,26)(29,30)(33,
36)(38,39)(43,44)(50,51)(53,71)(54,72)(55,73)(56,74)(57,75)(58,76)(59,77)(60,
78)(61,79)(62,80)(63,81)(64,82)(65,83)(66,84)(67,85)(68,86)(69,87)(70,88)],
["ConstructMGA","3^2.U4(3).2_3'","3_2.U4(3).(2^2)_{133}",
 [ [ 39, 41 ], [ 40, 42 ], [ 43, 44 ], [ 45, 47 ], [ 46, 48 ],
   [ 49, 51 ], [ 50, 52 ], [ 53, 55 ], [ 54, 56 ], [ 57, 59 ], [ 58, 60 ],
   [ 61, 62 ], [ 63, 65 ], [ 64, 66 ], [ 67, 69 ], [ 68, 70 ], [ 71, 73 ],
   [ 72, 74 ], [ 75, 77 ], [ 76, 78 ], [ 79, 80 ], [ 81, 82 ], [ 83, 84 ],
   [ 85, 86 ], [ 87, 88 ], [ 89, 90 ], [ 91, 92 ], [ 93, 94 ], [ 95, 98 ],
   [ 96, 97 ], [ 99, 100 ], [ 101, 102 ], [ 103, 104 ], [ 105, 106 ],
   [ 107, 108 ], [ 109, 110 ] ], ()]);
ALF("3^2.U4(3).(2^2)_{133}","3_2.U4(3).(2^2)_{133}",[1,1,2,2,3,3,4,4,5,5,6,6,
7,7,8,9,9,10,10,11,11,12,12,13,13,14,14,15,15,16,16,17,17,18,18,18,19,19,
20,20,20,21,21,22,22,23,23,23,24,24,25,25,56,56,57,57,58,59,59,60,60,61,
61,62,62,63,63,64,64,64,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,
42,43,44,45,46,47,48,49,50,51,52,53,54,55]);
ALF("3^2.U4(3).(2^2)_{133}","3.Suz.2",[1,2,7,8,3,4,24,25,7,8,9,10,9,10,11,
12,13,49,50,16,17,53,54,22,23,64,65,24,25,29,30,29,30,26,27,28,32,33,71,
72,73,34,35,74,75,40,41,42,49,50,51,52,5,6,16,17,31,34,35,34,35,38,39,45,
46,53,54,74,75,75,76,80,78,92,82,84,98,85,99,88,102,89,104,92,93,98,100,
100,76,77,78,78,80,81,82,87,91,92,93,95],[
"fusion map is unique up to table automorphisms"
]);
ALF("3^2.U4(3).(2^2)_{133}","U4(3).(2^2)_{133}",[1,1,1,1,2,2,2,2,3,3,3,3,
4,4,5,6,6,6,6,7,7,7,7,8,8,8,8,9,9,9,9,10,10,10,10,10,11,11,11,11,11,12,12,
12,12,13,13,13,14,14,14,14,36,36,37,37,38,39,39,40,40,41,41,42,42,43,43,
44,44,44,27,27,28,28,29,30,30,31,31,32,32,33,33,34,34,35,35,35,15,16,17,
18,19,20,21,22,23,24,25,26]);

MOT("3^2.U4(3).D8",
[
"origin: ATLAS of finite groups,\n",
"table was constructed by Dixon's algorithm,\n",
"tests: 1.o.r., pow[2,3,5,7]"
],
[235146240,58786560,58786560,20736,20736,82944,104976,104976,419904,5832,
11664,648,1728,1728,6912,288,1152,288,90,90,360,1296,1296,5184,324,648,648,
1296,63,63,252,144,144,576,162,162,162,216,216,864,48384,5760,4608,512,864,72,
72,64,40,288,72,28,24192,384,80,192,64,432,48,36,20,24,28,28,155520,311040,
3456,6912,576,1152,576,288,3888,3888,3888,648,1296,324,648,144,36,48,96,30,60,
144,72,36,72,54,54,54,4320,8640,576,288,36,288,576,96,192,24,48,30,60,72,36,
72,72,72],
[,[1,2,3,2,3,1,7,8,9,10,11,12,5,4,6,4,6,5,19,20,21,7,8,9,10,11,10,11,29,30,31,
13,14,15,35,36,37,23,22,24,1,1,6,6,9,11,12,15,21,24,28,31,41,41,42,43,43,45,
45,47,49,50,52,52,2,1,2,1,4,6,6,4,8,9,8,11,11,10,11,11,12,14,15,19,21,24,23,
27,28,36,35,37,3,1,6,5,12,13,15,13,15,18,17,20,21,24,22,39,39,40],[1,1,1,6,6,
6,1,1,1,1,1,1,15,15,15,17,17,17,21,21,21,6,6,6,6,6,6,6,31,31,31,34,34,34,8,8,
8,15,15,15,41,42,43,44,41,42,41,48,49,43,43,52,53,54,55,56,57,53,54,53,61,56,
63,64,66,66,68,68,70,70,71,71,66,66,66,66,66,66,66,68,68,83,83,85,85,70,70,71,
71,73,73,73,94,94,95,95,94,99,99,101,101,103,103,105,105,95,95,99,99,99],,[1,
2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,2,3,1,22,23,24,25,26,27,28,29,30,
31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,42,50,51,52,53,54,55,56,
57,58,59,60,55,62,64,63,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,
83,65,66,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,93,94,106,
107,109,108,110],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,
23,24,25,26,27,28,3,2,1,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,
50,51,41,53,54,55,56,57,58,59,60,61,62,53,53,65,66,67,68,69,70,71,72,73,74,75,
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]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
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[TENSOR,[109,2]]],
[(108,109),(63,64)]);
ALF("3^2.U4(3).D8","Co1",[1,6,5,22,18,2,6,7,5,7,6,8,45,49,9,54,12,47,64,
62,16,22,23,18,23,20,21,22,74,75,27,80,82,29,35,36,37,48,49,45,3,4,12,12,
19,24,25,30,43,47,54,59,13,13,14,34,34,50,50,56,72,83,88,88,20,2,24,4,51,
10,11,53,23,18,21,22,20,23,22,24,26,84,30,92,41,46,55,52,53,69,68,70,19,3,
12,47,25,80,29,80,29,83,34,90,40,47,54,82,82,80],[
"fusion map is unique"
]);
ALF("3^2.U4(3).D8","U4(3).D8",[1,1,1,2,2,2,3,3,3,4,4,5,6,6,6,7,7,7,8,8,8,
9,9,9,10,10,10,10,11,11,11,12,12,12,13,13,13,14,14,14,15,16,17,18,19,20,
21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,39,40,40,41,41,
42,42,43,43,43,44,44,45,45,46,47,48,48,49,49,50,50,51,51,52,52,52,53,53,
54,54,55,56,56,57,57,58,58,59,59,60,60,61,61,61]);

MOT("3_1.U4(3)",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
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81,288,288,288,48,48,48,15,15,15,216,216,216,108,108,108,108,108,108,21,21,21,
21,21,21,24,24,24,81,81,81,81,81,81,27,27,36,36,36],
[,[1,3,2,1,3,2,7,9,8,10,12,11,13,14,4,6,5,4,6,5,21,23,22,7,9,8,10,12,11,13,13,
13,33,35,34,36,38,37,15,17,16,45,47,46,42,44,43,49,48,24,26,25],[1,1,1,4,4,4,
1,1,1,1,1,1,1,1,15,15,15,18,18,18,21,21,21,4,4,4,4,4,4,4,4,4,36,36,36,33,33,
33,39,39,39,9,9,9,8,8,8,7,7,15,15,15],,[1,3,2,4,6,5,7,9,8,10,12,11,13,14,15,
17,16,18,20,19,1,3,2,24,26,25,27,29,28,30,32,31,36,38,37,33,35,34,39,41,40,45,
47,46,42,44,43,49,48,50,52,51],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,
19,20,21,22,23,24,25,26,27,28,29,30,31,32,1,2,3,1,2,3,39,40,41,42,43,44,45,46,
47,48,49,50,51,52]],
0,
[(48,49),(33,36)(34,37)(35,38),( 2, 3)( 5, 6)( 8, 9)(11,12)(16,17)(19,20)
(22,23)(25,26)(28,29)(31,32)(34,35)(37,38)(40,41)(42,45)(43,47)(44,46)(48,49)
(51,52),( 2, 3)( 5, 6)( 8, 9)(11,12)(16,17)(19,20)(22,23)(25,26)(28,29)(31,32)
(34,35)(37,38)(40,41)(42,45)(43,47)(44,46)(51,52)],
["ConstructProj",[["U4(3)",[]],,["3_1.U4(3)",[-1,-1,-1,-1,-1,-1,-1,-1,-13,-13,
-1,-1,-1,-1,-1,-1]]]]);
ALF("3_1.U4(3)","U4(3)",[1,1,1,2,2,2,3,3,3,4,4,4,5,6,7,7,7,8,8,8,9,9,9,10,
10,10,11,11,11,12,12,12,13,13,13,14,14,14,15,15,15,16,16,16,17,17,17,18,
19,20,20,20]);
ALF("3_1.U4(3)","3_1.U4(3).2_1",[1,2,2,3,4,4,5,6,6,7,8,8,9,10,11,12,12,13,
14,14,15,16,16,17,18,18,19,20,20,21,22,22,23,24,24,25,26,26,27,28,28,29,
30,31,29,31,30,32,32,33,34,34],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("3_1.U4(3)","3_1.U4(3).2_2",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,
17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,33,34,35,36,37,
38,39,40,41,42,43,44,45,45,46,47,48],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("3_1.U4(3)","3_1.U4(3).2_2'",[1,2,2,3,4,4,5,6,6,7,8,8,9,10,11,12,12,
13,14,14,15,16,16,17,18,18,19,20,20,21,22,22,23,24,25,23,25,24,26,27,27,
28,29,30,28,30,29,31,32,33,34,34],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);

MOT("3_1.U4(3).2_1",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
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15,432,216,216,108,216,108,42,21,42,21,48,24,81,81,81,27,72,36,12096,1440,
1152,128,216,36,36,18,16,10,144,144,36,36,14,14],
[,[1,2,1,2,5,6,7,8,9,10,3,4,3,4,15,16,5,6,7,8,9,9,23,24,25,26,11,12,29,30,31,
32,17,18,1,1,3,3,5,7,9,10,11,15,17,17,19,21,23,25],[1,1,3,3,1,1,1,1,1,1,11,11,
13,13,15,15,3,3,3,3,3,3,25,25,23,23,27,27,6,6,6,5,11,11,35,36,37,38,35,36,36,
35,43,44,37,37,37,37,50,49],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,1,2,17,18,19,
20,21,22,25,26,23,24,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,36,45,
46,47,48,50,49],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,1,
2,1,2,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,46,45,47,48,35,
35]],
0,
[(45,46),(23,25)(24,26)(49,50)],
["ConstructMGA","3_1.U4(3)","U4(3).2_1",
     [ [ 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 ] ], ()]);
ALF("3_1.U4(3).2_1","U4(3).2_1",[1,1,2,2,3,3,4,4,5,6,7,7,8,8,9,9,10,10,11,
11,12,12,13,13,14,14,15,15,16,16,16,17,18,18,19,20,21,22,23,24,25,26,27,
28,29,30,31,32,33,34]);
ALF("3_1.U4(3).2_1","3_1.U4(3).(2^2)_{122}",[1,2,3,4,5,6,7,8,9,10,11,12,
13,14,15,16,17,18,19,20,21,22,23,24,23,24,25,26,27,28,29,30,31,32,61,62,
63,64,65,66,67,68,69,70,71,71,72,73,74,74],[
"fusion map is unique"
]);

MOT("3_1.U4(3).2_2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[19595520,19595520,19595520,6912,6912,6912,34992,34992,34992,5832,5832,5832,
1944,162,576,576,576,96,96,96,30,30,30,432,432,432,216,216,216,216,216,216,21,
21,21,48,48,48,162,162,162,162,162,162,27,72,72,72,155520,155520,155520,3456,
3456,3456,576,576,576,288,288,288,3888,3888,3888,3888,3888,3888,648,648,648,
324,324,324,72,18,48,48,48,30,30,30,72,72,72,36,36,36,54,54,54,54,54,54],
[,[1,3,2,1,3,2,7,9,8,10,12,11,13,14,4,6,5,4,6,5,21,23,22,7,9,8,10,12,11,13,13,
13,33,35,34,15,17,16,42,44,43,39,41,40,45,24,26,25,1,3,2,1,3,2,4,6,5,4,6,5,7,
9,8,7,9,8,13,13,13,10,12,11,13,14,15,17,16,21,23,22,24,26,25,27,29,28,42,44,
43,39,41,40],[1,1,1,4,4,4,1,1,1,1,1,1,1,1,15,15,15,18,18,18,21,21,21,4,4,4,4,
4,4,4,4,4,33,33,33,36,36,36,9,9,9,8,8,8,7,15,15,15,49,49,49,52,52,52,55,55,55,
58,58,58,49,49,49,49,49,49,49,49,49,49,49,49,52,52,75,75,75,78,78,78,55,55,55,
58,58,58,63,63,63,65,65,65],,[1,3,2,4,6,5,7,9,8,10,12,11,13,14,15,17,16,18,20,
19,1,3,2,24,26,25,27,29,28,30,32,31,33,35,34,36,38,37,42,44,43,39,41,40,45,46,
48,47,49,51,50,52,54,53,55,57,56,58,60,59,64,66,65,61,63,62,67,69,68,70,72,71,
73,74,75,77,76,49,51,50,81,83,82,84,86,85,90,92,91,87,89,88],,[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,
3,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,
61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,
87,88,89,90,91,92]],
0,
[( 2, 3)( 5, 6)( 8, 9)(11,12)(16,17)(19,20)(22,23)(25,26)(28,29)(31,32)(34,35)
(37,38)(39,42)(40,44)(41,43)(47,48)(50,51)(53,54)(56,57)(59,60)(61,64)(62,66)
(63,65)(68,69)(71,72)(76,77)(79,80)(82,83)(85,86)(87,90)(88,92)(89,91)],
["ConstructProj",[["U4(3).2_2",[]],,["3_1.U4(3).2_2",[-1,-1,-1,-1,-1,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1]]]]);
ALF("3_1.U4(3).2_2","U4(3).2_2",[1,1,1,2,2,2,3,3,3,4,4,4,5,6,7,7,7,8,8,8,
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,
18,18,18,19,19,19,20,20,20,21,21,21,22,22,22,23,23,23,24,24,24,25,25,25,
26,26,26,27,28,29,29,29,30,30,30,31,31,31,32,32,32,33,33,33,34,34,34]);
ALF("3_1.U4(3).2_2","3.U6(2)",[1,3,2,7,9,8,16,18,17,13,15,14,19,19,26,28,
27,38,40,39,41,43,42,53,55,54,56,58,57,62,64,63,66,68,67,72,74,73,82,81,
83,86,85,84,87,112,114,113,4,6,5,10,12,11,26,28,27,35,37,36,44,46,45,47,
49,48,59,61,60,50,52,51,65,65,72,74,73,88,90,89,112,114,113,121,123,122,
128,127,129,132,131,130],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("3_1.U4(3).2_2","3_1.U4(3).(2^2)_{122}",[1,2,2,3,4,4,5,6,6,7,8,8,9,10,
11,12,12,13,14,14,15,16,16,17,18,18,19,20,20,21,22,22,23,24,24,25,26,26,
27,28,29,27,29,28,30,31,32,32,33,34,34,35,36,36,37,38,38,39,40,40,41,42,
43,41,43,42,44,45,45,46,47,47,48,49,50,51,51,52,53,53,54,55,55,56,57,57,
58,59,60,58,60,59],[
"fusion map is unique"
]);

MOT("3_1.U4(3).2_2'",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]\n"
],
[19595520,9797760,6912,3456,34992,17496,5832,2916,1944,162,576,288,96,48,30,15
,432,216,216,108,216,108,21,21,21,48,24,81,81,81,54,54,72,36,51840,1152,192,96
,1296,1296,216,108,72,18,16,10,24,12,18,18],
[,[1,2,1,2,5,6,7,8,9,10,3,4,3,4,15,16,5,6,7,8,9,9,23,25,24,11,12,28,29,30,32,
31,17,18,1,1,3,3,5,5,7,9,7,10,11,15,17,21,32,31],[1,1,3,3,1,1,1,1,1,1,11,11,13
,13,15,15,3,3,3,3,3,3,23,23,23,26,26,6,6,6,5,5,11,11,35,36,37,38,35,35,35,35,
36,36,45,46,37,38,39,40],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,1,2,17,18,19,20,21
,22,23,24,25,26,27,28,29,30,32,31,33,34,35,36,37,38,40,39,41,42,43,44,45,35,47
,48,50,49],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,1,2,2,26
,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50]],
0,
[(24,25),(31,32)(39,40)(49,50)],
["ConstructMGA","3_1.U4(3)","U4(3).2_2'",
     [ [ 21, 22 ], [ 23, 24 ], [ 25, 26 ], [ 27, 28 ], [ 29, 30 ], [ 31, 32 ],
       [ 33, 34 ], [ 35, 36 ], [ 37, 40 ], [ 38, 39 ], [ 41, 42 ], [ 43, 44 ],
       [ 45, 46 ], [ 47, 48 ], [ 49, 50 ], [ 51, 52 ] ], ()]);
ALF("3_1.U4(3).2_2'","U4(3).2_2'",[1,1,2,2,3,3,4,4,5,6,7,7,8,8,9,9,10,10,
11,11,12,12,13,13,13,14,14,15,15,15,16,17,18,18,19,20,21,22,23,24,25,26,
27,28,29,30,31,32,33,34]);
ALF("3_1.U4(3).2_2'","3_1.U4(3).(2^2)_{122}",[1,2,3,4,5,6,7,8,9,10,11,12,
13,14,15,16,17,18,19,20,21,22,23,24,24,25,26,27,28,29,30,30,31,32,75,76,
77,78,79,79,80,81,82,83,84,85,86,87,88,88],[
"fusion map is unique"
]);

MOT("3_1.U4(3).(2^2)_{122}",
[
"constructed using `PossibleCharacterTablesOfTypeMGA'"
],
[39191040,19595520,13824,6912,69984,34992,11664,5832,3888,324,1152,576,192,96,
60,30,864,432,432,216,432,216,42,21,96,48,162,162,162,54,144,72,311040,155520,
6912,3456,1152,576,576,288,3888,3888,3888,1296,648,648,324,144,36,96,48,60,30,
144,72,72,36,54,54,54,24192,2880,2304,256,432,72,72,36,32,20,144,72,72,14,
103680,2304,384,192,1296,432,216,144,36,32,20,48,24,18],
[,[1,2,1,2,5,6,7,8,9,10,3,4,3,4,15,16,5,6,7,8,9,9,23,24,11,12,27,28,29,30,17,
18,1,2,1,2,3,4,3,4,5,6,6,9,9,7,8,9,10,11,12,15,16,17,18,19,20,27,28,29,1,1,3,3
,5,7,9,10,11,15,17,19,21,23,1,1,3,3,5,7,9,7,10,11,15,17,21,30],[1,1,3,3,1,1,1,
1,1,1,11,11,13,13,15,15,3,3,3,3,3,3,23,23,25,25,6,6,6,5,11,11,33,33,35,35,37,
37,39,39,33,33,33,33,33,33,33,35,35,50,50,52,52,37,37,39,39,43,43,43,61,62,63,
64,61,62,62,61,69,70,63,63,63,74,75,76,77,78,75,75,75,76,76,84,85,77,78,79],,[
1,2,3,4,5,6,7,8,9,10,11,12,13,14,1,2,17,18,19,20,21,22,23,24,25,26,27,28,29,30
,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,33,34,54,55,56
,57,58,59,60,61,62,63,64,65,66,67,68,69,62,71,72,73,74,75,76,77,78,79,80,81,82
,83,84,75,86,87,88],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22
,1,2,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,
49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,61,
75,76,77,78,79,80,81,82,83,84,85,86,87,88]],
0,
[],
["ConstructMGA","3_1.U4(3).2_2","U4(3).(2^2)_{122}",[[35,37],[36,38],[39,41],[
40,42],[43,45],[44,46],[47,49],[48,50],[51,53],[52,54],[55,57],[56,58],[59,61]
,[60,62],[63,65],[64,66],[67,68],[69,71],[70,72],[73,75],[74,76],[77,79],[78,
80],[81,83],[82,84],[85,87],[86,88],[89,91],[90,92]],()]);
ALF("3_1.U4(3).(2^2)_{122}","U4(3).(2^2)_{122}",[1,1,2,2,3,3,4,4,5,6,7,7,
8,8,9,9,10,10,11,11,12,12,13,13,14,14,15,15,15,16,17,17,32,32,33,33,34,34,
35,35,36,36,36,37,37,38,38,39,40,41,41,42,42,43,43,44,44,45,45,45,18, 19,
20,21,22,23,24,25,26,27,28,29,30,31,46,47,48,49,50,51,52,53,54,55,56, 57,
58,59]);

MOT("3_2.U4(3)",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]\n",
"3rd power map determined only up to matrix automorphisms (40,41), (42,43)"
],
[9797760,9797760,9797760,3456,3456,3456,17496,17496,17496,972,972,81,288,288,
288,48,48,48,15,15,15,216,216,216,108,108,108,108,108,108,21,21,21,21,21,21,
24,24,24,27,27,27,27,36,36,36],
[,[1,3,2,1,3,2,7,9,8,10,11,12,4,6,5,4,6,5,19,21,20,7,9,8,10,10,10,11,11,11,31,
33,32,34,36,35,13,15,14,41,40,43,42,22,24,23],[1,1,1,4,4,4,1,1,1,1,1,1,13,13,
13,16,16,16,19,19,19,4,4,4,4,4,4,4,4,4,34,34,34,31,31,31,37,37,37,9,8,9,8,13,
13,13],,[1,3,2,4,6,5,7,9,8,10,11,12,13,15,14,16,18,17,1,3,2,22,24,23,25,27,26,
28,30,29,34,36,35,31,33,32,37,39,38,41,40,43,42,44,46,45],,[1,2,3,4,5,6,7,8,9,
10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,1,2,3,1,2,3,37,
38,39,40,41,42,43,44,45,46]],
0,
[(31,34)(32,35)(33,36),( 2, 3)( 5, 6)( 8, 9)(14,15)(17,18)(20,21)(23,24)
(26,27)(29,30)(32,33)(35,36)(38,39)(40,41)(42,43)(45,46),(10,11)(25,28)(26,29)
(27,30)(40,42)(41,43)],
["ConstructProj",[["U4(3)",[]],,["3_2.U4(3)",[-1,-13,-13,-1,-1,-1,-1,-1,-1,-1,
-1,-1,-1]]]]);
ALF("3_2.U4(3)","U4(3)",[1,1,1,2,2,2,3,3,3,4,5,6,7,7,7,8,8,8,9,9,9,10,10,
10,11,11,11,12,12,12,13,13,13,14,14,14,15,15,15,16,17,18,19,20,20,20]);
ALF("3_2.U4(3)","3_2.U4(3).2_1",[1,2,2,3,4,4,5,6,6,7,8,9,10,11,11,12,13,
13,14,15,15,16,17,17,18,19,19,20,21,21,22,23,23,24,25,25,26,27,27,28,28,
29,29,30,31,31],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("3_2.U4(3)","3_2.U4(3).2_3",[1,2,3,4,5,6,7,8,9,10,10,11,12,13,14,15,
16,17,18,19,20,21,22,23,24,25,26,24,25,26,27,28,29,27,28,29,30,31,32,33,
34,33,34,35,36,37],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("3_2.U4(3)","3_2.U4(3).2_3'",[1,2,2,3,4,4,5,6,6,7,7,8,9,10,10,11,12,
12,13,14,14,15,16,16,17,18,19,17,19,18,20,21,22,20,22,21,23,24,24,25,26,
26,25,27,28,28],[
"fusion map determined up to table aut. by compatibility\n",
"with factors"
]);
ALF("3_2.U4(3)","3.McL",[1,3,2,4,6,5,7,9,8,10,10,10,11,13,12,11,13,12,17,
19,18,20,22,21,23,25,24,23,25,24,26,28,27,29,31,30,32,34,33,35,36,35,36,
46,48,47],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);

MOT("3_2.U4(3).2_1",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[19595520,9797760,6912,3456,34992,17496,1944,1944,162,576,288,96,48,30,15,432,
216,216,108,216,108,42,21,42,21,48,24,27,27,72,36,12096,1440,1152,128,216,36,
36,18,16,10,144,144,36,36,14,14],
[,[1,2,1,2,5,6,7,8,9,3,4,3,4,14,15,5,6,7,7,8,8,22,23,24,25,10,11,28,29,16,17,
1,1,3,3,5,7,8,9,10,14,16,16,18,20,22,24],[1,1,3,3,1,1,1,1,1,10,10,12,12,14,14,
3,3,3,3,3,3,24,24,22,22,26,26,6,6,10,10,32,33,34,35,32,33,33,32,40,41,34,34,
34,34,47,46],,[1,2,3,4,5,6,7,8,9,10,11,12,13,1,2,16,17,18,19,20,21,24,25,22,
23,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,33,42,43,44,45,47,46],,[1,2,3,
4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,1,2,1,2,26,27,28,29,30,31,32,
33,34,35,36,37,38,39,40,41,43,42,44,45,32,32]],
0,
[(42,43),(22,24)(23,25)(46,47),( 7, 8)(18,20)(19,21)(28,29)(37,38)(44,45)],
["ConstructMGA","3_2.U4(3)","U4(3).2_1",
     [ [ 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 ] ], ()]);
ALF("3_2.U4(3).2_1","U4(3).2_1",[1,1,2,2,3,3,4,5,6,7,7,8,8,9,9,10,10,11,
11,12,12,13,13,14,14,15,15,16,17,18,18,19,20,21,22,23,24,25,26,27,28,29,
30,31,32,33,34]);
ALF("3_2.U4(3).2_1","3_2.U4(3).(2^2)_{133}",[1,2,3,4,5,6,7,7,8,9,10,11,12,
13,14,15,16,17,18,17,18,19,20,19,20,21,22,23,23,24,25,44,45,46,47,48,49,
49,50,51,52,53,53,54,54,55,55]);

MOT("3_2.U4(3).2_3",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,5,7]\n",
"3rd power map determined only up to table automorphism (33,34)"
],
[19595520,19595520,19595520,6912,6912,6912,34992,34992,34992,972,162,576,576,
576,96,96,96,30,30,30,432,432,432,108,108,108,21,21,21,48,48,48,27,27,72,72,
72,4320,4320,4320,288,288,288,18,288,288,288,96,96,96,24,24,24,30,30,30,36,36,
36,72,72,72,72,72,72],
[,[1,3,2,1,3,2,7,9,8,10,11,4,6,5,4,6,5,18,20,19,7,9,8,10,10,10,27,29,28,12,14,
13,34,33,21,23,22,1,3,2,4,6,5,11,12,14,13,12,14,13,15,17,16,18,20,19,21,23,22,
35,37,36,35,37,36],[1,1,1,4,4,4,1,1,1,1,1,12,12,12,15,15,15,18,18,18,4,4,4,4,
4,4,27,27,27,30,30,30,9,8,12,12,12,38,38,38,41,41,41,38,45,45,45,48,48,48,51,
51,51,54,54,54,41,41,41,45,45,45,45,45,45],,[1,3,2,4,6,5,7,9,8,10,11,12,14,13,
15,17,16,1,3,2,21,23,22,24,26,25,27,29,28,30,32,31,34,33,35,37,36,38,40,39,41,
43,42,44,45,47,46,48,50,49,51,53,52,38,40,39,57,59,58,60,62,61,63,65,64],,[1,
2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,1,2,3,30,
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]],
0,
[(60,63)(61,64)(62,65),( 2, 3)( 5, 6)( 8, 9)(13,14)(16,17)(19,20)(22,23)
(25,26)(28,29)(31,32)(33,34)(36,37)(39,40)(42,43)(46,47)(49,50)(52,53)(55,56)
(58,59)(60,63)(61,65)(62,64),( 2, 3)( 5, 6)( 8, 9)(13,14)(16,17)(19,20)(22,23)
(25,26)(28,29)(31,32)(33,34)(36,37)(39,40)(42,43)(46,47)(49,50)(52,53)(55,56)
(58,59)(61,62)(64,65)],
["ConstructProj",[["U4(3).2_3",[]],,["3_2.U4(3).2_3",[-1,-1,-1,-1,-1,-1,-1,17,
-1,-1,-1]]]]);
ALF("3_2.U4(3).2_3","U4(3).2_3",[1,1,1,2,2,2,3,3,3,4,5,6,6,6,7,7,7,8,8,8,
9,9,9,10,10,10,11,11,11,12,12,12,13,14,15,15,15,16,16,16,17,17,17,18,19,
19,19,20,20,20,21,21,21,22,22,22,23,23,23,24,24,24,25,25,25]);
ALF("3_2.U4(3).2_3","3_2.U4(3).(2^2)_{133}",[1,2,2,3,4,4,5,6,6,7,8,9,10,
10,11,12,12,13,14,14,15,16,16,17,18,18,19,20,20,21,22,22,23,23,24,25,25,
26,27,27,28,29,29,30,31,32,32,33,34,34,35,36,36,37,38,38,39,40,40,41,42,
43,41,43,42],[
"fusion map is unique up to table autom.,\n",
"unique map that is compatible with Brauer tables"
]);

MOT("3_2.U4(3).2_3'",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[19595520,9797760,6912,3456,34992,17496,972,162,576,288,96,48,30,15,432,216,
108,108,108,21,21,21,48,24,27,27,72,36,1440,96,18,96,32,8,10,12,24,24],
[,[1,2,1,2,5,6,7,8,3,4,3,4,13,14,5,6,7,7,7,20,22,21,9,10,26,25,15,16,1,3,8,9,
9,11,13,15,27,27],[1,1,3,3,1,1,1,1,9,9,11,11,13,13,3,3,3,3,3,20,20,20,23,23,6,
6,9,9,29,30,29,32,33,34,35,30,32,32],,[1,2,3,4,5,6,7,8,9,10,11,12,1,2,15,16,
17,19,18,20,21,22,23,24,26,25,27,28,29,30,31,32,33,34,29,36,37,38],,[1,2,3,4,
5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,1,2,2,23,24,25,26,27,28,29,30,31,32,
33,34,35,36,37,38]],
0,
[(37,38),(21,22),(18,19),(25,26)],
["ConstructMGA","3_2.U4(3)","U4(3).2_3'",
     [ [ 21, 22 ], [ 23, 26 ], [ 24, 25 ], [ 27, 28 ], [ 29, 30 ],
        [ 31, 32 ], [ 33, 36 ], [ 34, 35 ], [ 37, 38 ], [ 39, 40 ],
        [ 41, 42 ], [ 43, 44 ], [ 45, 46 ] ], ()]);
ARC("3_2.U4(3).2_3'","projectives",["3^2.U4(3).2_3'",[[36,36,4,4,9,9,0,0,4,4,
0,0,1,1,1,1,-2,-2*E(3),-2*E(3)^2,1,1,1,0,0,0,0,1,1,-6,2,0,-2,-2,0,-1,-1,1,1],[
90,90,-6,-6,-18,-18,0,0,2,2,2,2,0,0,6,6,0,0,0,-1,-1,-1,-2,-2,0,0,2,2,0,0,0,0,
0,0,0,0,0,0],[126,126,14,14,-9,-9,0,0,2,2,2,2,1,1,-1,-1,2,2*E(3),2*E(3)^2,0,0,
0,0,0,0,0,-1,-1,6,2,0,4,0,0,1,-1,1,1],[189,189,-3,-3,27,27,0,0,5,5,1,1,-1,-1,
3,3,0,0,0,0,0,0,1,1,0,0,-1,-1,9,1,0,1,1,-1,-1,1,1,1],[315,315,11,11,18,18,0,0,
-1,-1,-1,-1,0,0,2,2,2,2*E(3),2*E(3)^2,0,0,0,1,1,0,0,2,2,-15,-3,0,3,-1,-1,0,0,
0,0],[630,630,6,6,-45,-45,0,0,2,2,-2,-2,0,0,3,3,0,0,0,0,0,0,0,0,0,0,-1,-1,0,4,
0,2,-2,0,0,1,-1,-1],[630,630,-10,-10,36,36,0,0,6,6,-2,-2,0,0,-4,-4,2,2*E(3),
2*E(3)^2,0,0,0,-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[720,720,16,16,18,18,0,0,0,
0,0,0,0,0,-2,-2,-2,-2*E(3),-2*E(3)^2,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
E(24)+E(24)^11-E(24)^17-E(24)^19,-E(24)-E(24)^11+E(24)^17+E(24)^19],[729,729,
9,9,0,0,0,0,-3,-3,1,1,-1,-1,0,0,0,0,0,1,1,1,-1,-1,0,0,0,0,-9,3,0,-3,1,-1,1,0,
0,0],[756,756,-12,-12,27,27,0,0,-4,-4,0,0,1,1,3,3,0,0,0,0,0,0,0,0,0,0,-1,-1,6,
-2,0,-2,-2,0,1,1,1,1],[945,945,-15,-15,-27,-27,0,0,1,1,1,1,0,0,-3,-3,0,0,0,0,
0,0,1,1,0,0,1,1,15,-1,0,-1,-1,-1,0,-1,-1,-1],[30,-15,-2,1,12,-6,3,0,6,-3,-2,1,
0,0,4,-2,1,E(3)+3*E(3)^2,3*E(3)+E(3)^2,2,-1,-1,2,-1,2*E(3)+E(3)^2,
E(3)+2*E(3)^2,0,0,0,0,0,0,0,0,0,0,0,0],[42,-21,10,-5,6,-3,6,0,2,-1,2,-1,2,-1,
-2,1,4,-2*E(3),-2*E(3)^2,0,0,0,-2,1,E(3)+2*E(3)^2,2*E(3)+E(3)^2,2,-1,0,0,0,0,
0,0,0,0,0,0],[210,-105,18,-9,30,-15,3,0,2,-1,2,-1,0,0,6,-3,3,3,3,0,0,0,2,-1,
-E(3)-2*E(3)^2,-2*E(3)-E(3)^2,2,-1,0,0,0,0,0,0,0,0,0,0],[210,-105,-14,7,30,
-15,3,0,10,-5,2,-1,0,0,-2,1,1,E(3)+3*E(3)^2,3*E(3)+E(3)^2,0,0,0,-2,1,
-E(3)-2*E(3)^2,-2*E(3)-E(3)^2,-2,1,0,0,0,0,0,0,0,0,0,0],[210,-105,18,-9,-24,
12,12,0,2,-1,2,-1,0,0,0,0,0,0,0,0,0,0,2,-1,-E(3)+E(3)^2,E(3)-E(3)^2,-4,2,0,0,
0,0,0,0,0,0,0,0],[420,-210,4,-2,6,-3,15,0,-4,2,-4,2,0,0,-2,1,1,E(3)+3*E(3)^2,
3*E(3)+E(3)^2,0,0,0,0,0,-2*E(3)-E(3)^2,-E(3)-2*E(3)^2,2,-1,0,0,0,0,0,0,0,0,0,
0],[630,-315,-10,5,-72,36,9,0,6,-3,-2,1,0,0,8,-4,-1,-E(3)-3*E(3)^2,
-3*E(3)-E(3)^2,0,0,0,-2,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[672,-336,32,-16,-12,6,
6,0,0,0,0,0,2,-1,-4,2,-4,2*E(3),2*E(3)^2,0,0,0,0,0,E(3)-E(3)^2,-E(3)+E(3)^2,0,
0,0,0,0,0,0,0,0,0,0,0],[720,-360,16,-8,-36,18,-9,0,0,0,0,0,0,0,4,-2,1,
E(3)+3*E(3)^2,3*E(3)+E(3)^2,-1,E(21)+E(21)^4+E(21)^5+E(21)^16+E(21)^17
 +E(21)^20,E(21)^2+E(21)^8+E(21)^10+E(21)^11+E(21)^13+E(21)^19,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0],
[GALOIS,[20,10]],[768,-384,0,0,48,-24,12,0,0,0,0,0,-2,1,0,0,0,0,0,-2,1,1,0,0,
2*E(3)+E(3)^2,E(3)+2*E(3)^2,0,0,0,0,0,0,0,0,0,0,0,0],[840,-420,8,-4,66,-33,-6,
0,8,-4,0,0,0,0,2,-1,-4,2*E(3),2*E(3)^2,0,0,0,0,0,-E(3)+E(3)^2,E(3)-E(3)^2,2,
-1,0,0,0,0,0,0,0,0,0,0],[1260,-630,12,-6,18,-9,-9,0,4,-2,-4,2,0,0,-6,3,3,3,3,
0,0,0,0,0,0,0,-2,1,0,0,0,0,0,0,0,0,0,0],[1458,-729,18,-9,0,0,0,0,-6,3,2,-1,-2,
1,0,0,0,0,0,2,-1,-1,-2,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[1512,-756,-24,12,54,
-27,0,0,-8,4,0,0,2,-1,6,-3,0,0,0,0,0,0,0,0,0,0,-2,1,0,0,0,0,0,0,0,0,0,0],[
1890,-945,-30,15,-54,27,0,0,2,-1,2,-1,0,0,-6,3,0,0,0,0,0,0,2,-1,0,0,2,-1,0,0,
0,0,0,0,0,0,0,0]],]);
ARC("3_2.U4(3).2_3'","CAS",[rec(name:="3.u4(3):2",
permclasses:=( 5,11, 7,13,24,10, 6,12, 8,14,25,15,17,19,21,27,22,28,23, 9)
(16,18,20,26),
permchars:=( 2,11, 5,21,25,10,15,22,19,18, 7, 3,12,16,24,20, 8,14,23, 9, 4)
( 6,13)(27,36,33,37,34,31,29)(28,38,35,32,30),
text:="test:= 1. o.r., sym 2 decompose correctly")]);
ALF("3_2.U4(3).2_3'","U4(3).2_3'",[1,1,2,2,3,3,4,5,6,6,7,7,8,8,9,9,10,10,
10,11,11,11,12,12,13,14,15,15,16,17,18,19,20,21,22,23,24,25]);
ALF("3_2.U4(3).2_3'","3_2.U4(3).(2^2)_{133}",[1,2,3,4,5,6,7,8,9,10,11,12,
13,14,15,16,17,18,18,19,20,20,21,22,23,23,24,25,56,57,58,59,60,61,62,63,
64,64],[
"fusion map is unique"
]);
ALF("3_2.U4(3).2_3'","3.McL.2",[1,2,3,4,5,6,7,7,8,9,8,9,12,13,14,15,16,17,
17,18,19,20,21,22,23,23,30,31,41,42,43,44,45,45,46,47,53,54],[
"fusion map is unique up to table automorphisms"
]);
ALF("3_2.U4(3).2_3'","Suz",[1,4,2,13,4,5,5,6,7,27,9,29,12,37,13,16,16,14,
15,18,41,42,19,43,22,23,27,28,3,9,17,19,19,21,25,29,43,43],[
"fusion map is unique up to table automorphisms"
]);
ALN("3_2.U4(3).2_3'",["3.u4(3):2","SuzN3A"]);

MOT("3_2.U4(3).(2^2)_{133}",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[39191040,19595520,13824,6912,69984,34992,1944,324,1152,576,192,96,60,30,864,
432,216,108,42,21,96,48,27,144,72,8640,4320,576,288,36,576,288,192,96,48,24,
60,30,72,36,72,72,72,24192,2880,2304,256,432,36,36,32,20,144,36,14,2880,192,
36,192,64,16,20,24,24],
[,[1,2,1,2,5,6,7,8,3,4,3,4,13,14,5,6,7,7,19,20,9,10,23,15,16,1,2,3,4,8,9,10,9,
10,11,12,13,14,15,16,24,25,25,1,1,3,3,5,7,8,9,13,15,17,19,1,3,8,9,9,11,13,15,
24],[1,1,3,3,1,1,1,1,9,9,11,11,13,13,3,3,3,3,19,19,21,21,6,9,9,26,26,28,28,26,
31,31,33,33,35,35,37,37,28,28,31,31,31,44,45,46,47,44,45,44,51,52,46,46,55,56,
57,56,59,60,61,62,57,59],,[1,2,3,4,5,6,7,8,9,10,11,12,1,2,15,16,17,18,19,20,
21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,26,27,39,40,41,43,42,44,45,46,
47,48,49,50,51,45,53,54,55,56,57,58,59,60,61,56,63,64],,[1,2,3,4,5,6,7,8,9,10,
11,12,13,14,15,16,17,18,1,2,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,
37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,44,56,57,58,59,60,61,62,
63,64]],
0,
[(42,43)],
["ConstructMGA","3_2.U4(3).2_3","U4(3).(2^2)_{133}",
[[26,28],[27,29],[30,31],[32,34],[33,35],[36,38],[37,39],[40,42],[41,43],[44,
45],[46,48],[47,49],[50,52],[51,53],[54,56],[55,57],[58,60],[59,61],[62,64],
[63,65]],()]);
ALF("3_2.U4(3).(2^2)_{133}","U4(3).(2^2)_{133}",[1,1,2,2,3,3,4,5,6,6,7,7,
8,8,9,9,10,10,11,11,12,12,13,14,14,27,27,28,28,29,30,30,31,31,32,32,33,33,
34,34,35,35,35,15,16,17,18,19,20,21,22,23,24,25,26,36,37,38,39,40,41,42,
43,44]);
ALF("3_2.U4(3).(2^2)_{133}","Suz.2",[1,4,2,13,4,5,5,6,7,25,9,27,12,33,13,
15,15,14,17,36,18,37,21,25,26,38,42,40,54,44,46,60,47,61,50,64,51,66,54,
55,60,62,62,38,39,40,40,42,43,44,49,53,54,55,57,3,9,16,18,18,20,23,27,37],[
"fusion map is unique"
]);
ALN("3_2.U4(3).(2^2)_{133}",["Suz.2N3A"]);

MOT("4.U4(3)",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7],\n",
"constructions: SU(4,3)"
],
[13063680,13063680,13063680,13063680,2304,2304,23328,23328,23328,23328,3888,
3888,3888,3888,3888,3888,3888,3888,324,324,324,324,384,384,384,384,16,20,20,
20,20,288,288,288,288,72,72,72,72,28,28,28,28,28,28,28,28,32,32,32,32,108,108,
108,108,108,108,108,108,108,108,108,108,108,108,108,108,48,48,48,48],
[,[1,3,1,3,1,3,7,9,7,9,11,13,11,13,15,17,15,17,19,21,19,21,5,5,5,5,6,28,30,28,
30,7,9,7,9,11,13,15,17,40,42,40,42,44,46,44,46,24,26,24,26,56,58,56,58,52,54,
52,54,64,66,64,66,60,62,60,62,32,34,32,34],[1,4,3,2,5,6,1,4,3,2,1,4,3,2,1,4,3,
2,1,4,3,2,23,26,25,24,27,28,31,30,29,5,6,5,6,5,6,5,6,44,47,46,45,40,43,42,41,
51,50,49,48,7,10,9,8,7,10,9,8,7,10,9,8,7,10,9,8,23,26,25,24],,[1,2,3,4,5,6,7,
8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,1,2,3,4,32,33,34,35,
36,37,38,39,44,45,46,47,40,41,42,43,48,49,50,51,56,57,58,59,52,53,54,55,64,65,
66,67,60,61,62,63,68,69,70,71],,[1,4,3,2,5,6,7,10,9,8,11,14,13,12,15,18,17,16,
19,22,21,20,23,26,25,24,27,28,31,30,29,32,35,34,33,36,37,38,39,1,4,3,2,1,4,3,
2,51,50,49,48,52,55,54,53,56,59,58,57,60,63,62,61,64,67,66,65,68,71,70,69]],
0,
[(52,56)(53,57)(54,58)(55,59)(60,64)(61,65)(62,66)(63,67),(40,44)(41,45)
(42,46)(43,47),( 2, 4)( 8,10)(12,14)(16,18)(20,22)(24,26)(29,31)(33,35)(41,43)
(45,47)(48,51)(49,50)(53,55)(57,59)(61,63)(65,67)(69,71),(60,64)(61,65)(62,66)
(63,67),(11,15)(12,16)(13,17)(14,18)(36,38)(37,39)(52,60)(53,61)(54,62)(55,63)
(56,64)(57,65)(58,66)(59,67)],
["ConstructProj",[["U4(3)",[]],["2.U4(3)",[]],,["4.U4(3)",[-1,-1,-1,7,7,7,7,
-1,-1,-1,-1,-1,15,15,-1,-1]]]]);
ALF("4.U4(3)","U4(3)",[1,1,1,1,2,2,3,3,3,3,4,4,4,4,5,5,5,5,6,6,6,6,7,7,7,
7,8,9,9,9,9,10,10,10,10,11,11,12,12,13,13,13,13,14,14,14,14,15,15,15,15,
16,16,16,16,17,17,17,17,18,18,18,18,19,19,19,19,20,20,20,20]);
ALF("4.U4(3)","2.U4(3)",[1,2,1,2,3,4,5,6,5,6,7,8,7,8,9,10,9,10,11,12,11,
12,13,14,13,14,15,16,17,16,17,18,19,18,19,20,21,22,23,24,25,24,25,26,27,
26,27,28,29,28,29,30,31,30,31,32,33,32,33,34,35,34,35,36,37,36,37,38,39,
38,39]);
ALF("4.U4(3)","4.U4(3).2_1",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,
19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,
43,44,45,46,47,48,49,50,51,52,53,54,55,52,53,54,55,56,57,58,59,56,57,58,
59,60,61,62,63],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);
ALF("4.U4(3)","4.U4(3).2_2",[1,2,3,2,4,5,6,7,8,7,9,10,11,10,12,13,14,13,
15,16,17,16,18,19,20,19,21,22,23,24,23,25,26,27,26,28,29,30,31,32,33,34,
35,32,35,34,33,36,37,37,36,38,39,40,39,41,42,43,42,44,45,46,47,44,47,46,
45,48,49,50,49],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);
ALF("4.U4(3)","4.U4(3).2_3",[1,2,3,2,4,5,6,7,8,7,9,10,11,12,9,12,11,10,13,
14,15,14,16,17,18,17,19,20,21,22,21,23,24,25,24,26,27,26,27,28,29,30,31,
28,31,30,29,32,33,33,32,34,35,36,37,38,39,40,41,34,37,36,35,38,41,40,39,
42,43,44,43],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);
ALF("4.U4(3)","4.U4(3).4",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,11,12,13,14,
15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,32,33,34,35,36,
37,38,39,40,41,42,43,44,45,46,47,48,49,46,47,48,49,46,47,48,49,46,47,48,
49,50,51,52,53],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);

MOT("4.U4(3).2_1",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[26127360,26127360,26127360,26127360,4608,4608,46656,46656,46656,46656,7776,
7776,7776,7776,7776,7776,7776,7776,648,648,648,648,768,768,768,768,32,40,40,
40,40,576,576,576,576,144,144,144,144,56,56,56,56,56,56,56,56,64,64,64,64,108,
108,108,108,108,108,108,108,96,96,96,96,48384,48384,48384,48384,2880,2880,
4608,4608,4608,4608,128,864,864,864,864,72,72,72,72,72,72,72,72,64,64,64,64,
40,40,40,40,576,576,576,576,576,576,576,576,144,144,144,144,144,144,144,144,
56,56,56,56,56,56,56,56],
[,[1,3,1,3,1,3,7,9,7,9,11,13,11,13,15,17,15,17,19,21,19,21,5,5,5,5,6,28,30,28,
30,7,9,7,9,11,13,15,17,40,42,40,42,44,46,44,46,24,26,24,26,52,54,52,54,56,58,
56,58,32,34,32,34,1,3,1,3,2,4,5,5,5,5,5,7,9,7,9,12,14,16,18,19,21,19,21,26,24,
26,24,29,31,29,31,32,34,32,34,34,32,34,32,36,36,36,36,38,38,38,38,40,42,40,42,
44,46,44,46],[1,4,3,2,5,6,1,4,3,2,1,4,3,2,1,4,3,2,1,4,3,2,23,26,25,24,27,28,
31,30,29,5,6,5,6,5,6,5,6,44,47,46,45,40,43,42,41,51,50,49,48,7,10,9,8,7,10,9,
8,23,26,25,24,64,67,66,65,69,68,73,72,71,70,74,64,67,66,65,69,68,69,68,64,67,
66,65,90,89,88,87,94,93,92,91,73,72,71,70,73,72,71,70,73,72,71,70,73,72,71,70,
115,118,117,116,111,114,113,112],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,
18,19,20,21,22,23,24,25,26,27,1,2,3,4,32,33,34,35,36,37,38,39,44,45,46,47,40,
41,42,43,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,
71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,68,69,68,69,95,96,
97,98,99,100,101,102,103,104,105,106,107,108,109,110,115,116,117,118,111,112,
113,114],,[1,4,3,2,5,6,7,10,9,8,11,14,13,12,15,18,17,16,19,22,21,20,23,26,25,
24,27,28,31,30,29,32,35,34,33,36,37,38,39,1,4,3,2,1,4,3,2,51,50,49,48,52,55,
54,53,56,59,58,57,60,63,62,61,64,67,66,65,69,68,73,72,71,70,74,75,78,77,76,80,
79,82,81,83,86,85,84,90,89,88,87,92,91,94,93,102,101,100,99,98,97,96,95,106,
105,104,103,110,109,108,107,64,67,66,65,64,67,66,65]],
0,
[(91,93)(92,94),( 40, 44)( 41, 45)( 42, 46)( 43, 47)(111,115)(112,116)
(113,117)(114,118),(  2,  4)(  8, 10)( 12, 14)( 16, 18)( 20, 22)( 24, 26)
( 29, 31)( 33, 35)( 41, 43)( 45, 47)( 48, 51)( 49, 50)( 53, 55)( 57, 59)
( 61, 63)( 65, 67)( 68, 69)( 70, 73)( 71, 72)( 76, 78)( 79, 80)( 81, 82)
( 84, 86)( 87, 90)( 88, 89)( 91, 92)( 93, 94)( 95,102)( 96,101)( 97,100)
( 98, 99)(103,106)(104,105)(107,110)(108,109)(112,114)(116,118),(  2,  4)
(  8, 10)( 12, 14)( 16, 18)( 20, 22)( 24, 26)( 29, 31)( 33, 35)( 41, 43)
( 45, 47)( 48, 51)( 49, 50)( 53, 55)( 57, 59)( 61, 63)( 65, 67)( 68, 69)
( 70, 73)( 71, 72)( 76, 78)( 79, 80)( 81, 82)( 84, 86)( 87, 90)( 88, 89)
( 91, 94)( 92, 93)( 95,102)( 96,101)( 97,100)( 98, 99)(103,106)(104,105)
(107,110)(108,109)(112,114)(116,118),( 11, 15)( 12, 16)( 13, 17)( 14, 18)
( 36, 38)( 37, 39)( 52, 56)( 53, 57)( 54, 58)( 55, 59)( 79, 81)( 80, 82)
(103,107)(104,108)(105,109)(106,110),(  2,  4)(  8, 10)( 12, 14)( 16, 18)
( 20, 22)( 24, 26)( 29, 31)( 33, 35)( 41, 43)( 45, 47)( 48, 51)( 49, 50)
( 53, 55)( 57, 59)( 61, 63)( 64, 66)( 68, 69)( 70, 71)( 72, 73)( 75, 77)
( 79, 80)( 81, 82)( 83, 85)( 87, 88)( 89, 90)( 91, 92)( 93, 94)( 95,100)
( 96, 99)( 97,102)( 98,101)(103,104)(105,106)(107,108)(109,110)(111,113)
(115,117)],
["ConstructProj",[["U4(3).2_1",[]],["2.U4(3).2_1",[]],,["4.U4(3).2_1",[-1,-1,
-1,-1,-1,-1,-1,-1,-1,-1,15,15,-1,31]]]]);
ALF("4.U4(3).2_1","U4(3).2_1",[1,1,1,1,2,2,3,3,3,3,4,4,4,4,5,5,5,5,6,6,6,
6,7,7,7,7,8,9,9,9,9,10,10,10,10,11,11,12,12,13,13,13,13,14,14,14,14,15,15,
15,15,16,16,16,16,17,17,17,17,18,18,18,18,19,19,19,19,20,20,21,21,21,21,
22,23,23,23,23,24,24,25,25,26,26,26,26,27,27,27,27,28,28,28,28,29,29,29,
29,30,30,30,30,31,31,31,31,32,32,32,32,33,33,33,33,34,34,34,34]);
ALF("4.U4(3).2_1","2.U4(3).2_1",[1,2,1,2,3,4,5,6,5,6,7,8,7,8,9,10,9,10,11,
12,11,12,13,14,13,14,15,16,17,16,17,18,19,18,19,20,21,22,23,24,25,24,25,
26,27,26,27,28,29,28,29,30,31,30,31,32,33,32,33,34,35,34,35,36,37,36,37,
38,39,40,41,40,41,42,43,44,43,44,45,46,47,48,49,50,49,50,51,52,51,52,53,
54,53,54,55,56,55,56,57,58,57,58,59,60,59,60,61,62,61,62,63,64,63,64,65,
66,65,66]);
ALF("4.U4(3).2_1","4.U4(3).4",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,11,12,13,
14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,32,33,34,35,
36,37,38,39,40,41,42,43,44,45,46,47,48,49,46,47,48,49,50,51,52,53,54,55,
56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,69,70,71,72,73,74,75,76,77,
78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,91,92,93,94,95,96,97,
98,99,100,101,102],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);

MOT("4.U4(3).2_2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[26127360,13063680,26127360,4608,4608,46656,23328,46656,7776,3888,7776,7776,
3888,7776,648,324,648,768,384,768,32,40,20,40,576,288,576,144,144,144,144,28,
28,28,28,32,32,216,108,216,216,108,216,108,108,108,108,96,48,96,103680,103680,
1152,192,192,192,2592,2592,2592,2592,432,432,216,216,144,144,36,36,16,20,20,
48,48,24,24,36,36,36,36],
[,[1,3,1,1,3,6,8,6,9,11,9,12,14,12,15,17,15,4,4,4,5,22,24,22,6,8,6,9,11,12,14,
32,34,32,34,19,19,41,43,41,38,40,38,44,46,44,46,25,27,25,3,3,1,4,5,5,8,8,8,8,
14,14,11,11,12,12,15,15,18,24,24,27,27,29,29,43,43,40,40],[1,2,3,4,5,1,2,3,1,
2,3,1,2,3,1,2,3,18,19,20,21,22,23,24,4,5,4,4,5,4,5,32,33,34,35,36,37,6,7,8,6,
7,8,6,7,8,7,18,19,20,51,52,53,54,55,56,51,52,51,52,51,52,51,52,53,53,53,53,69,
70,71,54,54,55,56,57,58,59,60],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,
19,20,21,1,2,3,25,26,27,28,29,30,31,32,35,34,33,36,37,41,42,43,38,39,40,44,47,
46,45,48,49,50,51,52,53,54,55,56,59,60,57,58,61,62,63,64,65,66,67,68,69,51,52,
73,72,74,75,78,79,76,77],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,
21,22,23,24,25,26,27,28,29,30,31,1,2,3,2,36,37,38,39,40,41,42,43,44,47,46,45,
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]],
0,
[(67,68),(45,47),(38,41)(39,42)(40,43)(45,47)(57,59)(58,60)(72,73)(76,78)
(77,79),(33,35),(33,35)(45,47),(38,41)(39,42)(40,43)(57,59)(58,60)(72,73)
(76,78)(77,79),(51,52)(55,56)(57,58)(59,60)(61,62)(63,64)(65,66)(70,71)(72,73)
(74,75)(76,77)(78,79)],
["ConstructMGA","4.U4(3)","2.U4(3).2_2",
     [ [ 40, 41 ], [ 42, 43 ], [ 44, 45 ], [ 46, 47 ], [ 48, 49 ],
        [ 50, 53 ], [ 51, 52 ], [ 54, 55 ], [ 56, 57 ], [ 58, 59 ],
        [ 60, 61 ], [ 62, 63 ], [ 64, 67 ], [ 65, 66 ], [ 68, 69 ],
        [ 70, 71 ] ], ()]);
ALF("4.U4(3).2_2","U4(3).2_2",[1,1,1,2,2,3,3,3,4,4,4,5,5,5,6,6,6,7,7,7,8,
9,9,9,10,10,10,11,11,12,12,13,13,13,13,14,14,15,15,15,16,16,16,17,17,17,
17,18,18,18,19,19,20,21,22,22,23,23,24,24,25,25,26,26,27,27,28,28,29,30,
30,31,31,32,32,33,33,34,34]);
ALF("4.U4(3).2_2","2.U4(3).2_2",[1,2,1,3,4,5,6,5,7,8,7,9,10,9,11,12,11,13,
14,13,15,16,17,16,18,19,18,20,21,22,23,24,25,24,25,26,26,27,28,27,29,30,
29,31,32,31,32,33,34,33,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,
51,52,53,54,55,56,57,58,59,60,61,62,63]);
ALF("4.U4(3).2_2","2.O7(3)",[1,3,2,5,4,6,27,7,8,28,9,10,29,11,16,38,17,21,
23,22,24,25,61,26,34,30,33,36,35,37,32,47,79,48,78,50,51,52,83,53,52,82,
53,54,84,55,85,64,68,65,3,4,5,23,20,24,27,30,27,30,29,32,28,35,31,37,43,
44,49,61,60,68,68,67,73,82,86,83,86],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);

MOT("Isoclinic(4.U4(3).2_2)",
[
"isoclinic group of the 4.U4(3).2_2 given in the ATLAS"
],
0,
0,
0,
[(67,68),(51,52)(55,56)(57,58)(59,60)(61,62)(63,64)(65,66)(70,71)(72,73)(74,
75)(76,77)(78,79),(45,47),(38,41)(39,42)(40,43)(57,59)(58,60)(72,73)(76,78)
(77,79),(33,35)],
["ConstructIsoclinic",[["4.U4(3).2_2"]]]);
ALF("Isoclinic(4.U4(3).2_2)","2.U4(3).2_2",[1,2,1,3,4,5,6,5,7,8,7,9,10,9,
11,12,11,13,14,13,15,16,17,16,18,19,18,20,21,22,23,24,25,24,25,26,26,27,
28,27,29,30,29,31,32,31,32,33,34,33,35,36,37,38,39,40,41,42,43,44,45,46,
47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63]);

MOT("4.U4(3).2_3",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[26127360,13063680,26127360,4608,4608,46656,23328,46656,3888,3888,3888,3888,
648,324,648,768,384,768,32,40,20,40,576,288,576,72,72,28,28,28,28,32,32,108,
108,108,108,108,108,108,108,96,48,96,1440,96,36,36,192,192,32,16,16,20,20,24,
24,48,48,48,48],
[,[1,3,1,1,3,6,8,6,9,11,9,11,13,15,13,4,4,4,5,20,22,20,6,8,6,9,11,28,30,28,30,
17,17,38,40,38,40,34,36,34,36,23,25,23,1,4,13,13,18,18,16,19,19,20,20,25,25,
44,44,44,44],[1,2,3,4,5,1,2,3,1,2,3,2,1,2,3,16,17,18,19,20,21,22,4,5,4,4,5,28,
29,30,31,32,33,6,7,8,7,6,7,8,7,16,17,18,45,46,45,45,50,49,51,53,52,55,54,46,
46,50,49,50,49],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,1,2,3,23,24,
25,26,27,28,31,30,29,32,33,38,39,40,41,34,35,36,37,42,43,44,45,46,47,48,50,49,
51,53,52,45,45,57,56,59,58,61,60],,[1,2,3,4,5,6,7,8,9,12,11,10,13,14,15,16,17,
18,19,20,21,22,23,24,25,26,27,1,2,3,2,32,33,34,37,36,35,38,41,40,39,42,43,44,
45,46,47,48,49,50,51,52,53,55,54,56,57,58,59,60,61]],
0,
[(56,57)(58,60)(59,61),(54,55),(49,50)(52,53)(58,61)(59,60),(47,48),(34,38)
(35,39)(36,40)(37,41)(56,57)(58,60)(59,61),(29,31),(10,12)(29,31)(35,37)
(39,41),(10,12)(29,31)(35,37)(39,41)(49,50)(52,53)(58,61)(59,60),(34,38)
(35,39)(36,40)(37,41),(10,12)(35,37)(39,41)],
["ConstructMGA","4.U4(3)","2.U4(3).2_3",
     [ [ 40, 41 ], [ 42, 43 ], [ 44, 45 ], [ 46, 51 ], [ 47, 50 ],
        [ 48, 53 ], [ 49, 52 ], [ 54, 55 ], [ 56, 59 ], [ 57, 58 ],
        [ 60, 61 ], [ 62, 63 ], [ 64, 67 ], [ 65, 66 ], [ 68, 69 ],
        [ 70, 71 ] ], ()]);
ALF("4.U4(3).2_3","U4(3).2_3",[1,1,1,2,2,3,3,3,4,4,4,4,5,5,5,6,6,6,7,8,8,
8,9,9,9,10,10,11,11,11,11,12,12,13,13,13,13,14,14,14,14,15,15,15,16,17,18,
18,19,19,20,21,21,22,22,23,23,24,24,25,25]);
ALF("4.U4(3).2_3","2.U4(3).2_3",[1,2,1,3,4,5,6,5,7,8,7,8,9,10,9,11,12,11,
13,14,15,14,16,17,16,18,19,20,21,20,21,22,22,23,24,23,24,25,26,25,26,27,
28,27,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45]);

MOT("Isoclinic(4.U4(3).2_3)",
[
"isoclinic group of the 4.U4(3).2_3 given in the ATLAS"
],
0,
0,
0,
[(56,57)(58,60)(59,61),(54,55),(49,50)(52,53)(56,57)(58,59)(60,61),(47,48),
(34,38)(35,39)(36,40)(37,41),(29,31),(10,12)(35,37)(39,41)],
["ConstructIsoclinic",[["4.U4(3).2_3"]]]);
ALF("Isoclinic(4.U4(3).2_3)","2.U4(3).2_3",[1,2,1,3,4,5,6,5,7,8,7,8,9,10,
9,11,12,11,13,14,15,14,16,17,16,18,19,20,21,20,21,22,22,23,24,23,24,25,26,
25,26,27,28,27,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45]);

MOT("4.U4(3).4",
[
"origin: ATLAS of finite groups, test: 1.o.r., pow[2,3,5,7],\n",
"constructions: GU(4,3)"
],
[52254720,52254720,52254720,52254720,9216,9216,93312,93312,93312,93312,7776,
7776,7776,7776,1296,1296,1296,1296,1536,1536,1536,1536,64,80,80,80,80,1152,
1152,1152,1152,144,144,112,112,112,112,112,112,112,112,128,128,128,128,108,
108,108,108,192,192,192,192,96768,96768,96768,96768,5760,5760,9216,9216,9216,
9216,256,1728,1728,1728,1728,72,72,144,144,144,144,128,128,128,128,80,80,80,
80,1152,1152,1152,1152,1152,1152,1152,1152,144,144,144,144,112,112,112,112,
112,112,112,112,96768,96768,96768,96768,96768,96768,96768,96768,1536,1536,
1536,1536,1536,1536,1536,1536,80,80,768,768,768,768,768,768,768,768,128,128,
128,128,1728,1728,1728,1728,1728,1728,1728,1728,192,192,192,192,192,192,192,
192,144,144,144,144,144,144,144,144,80,80,80,80,80,80,80,80,96,96,96,96,96,96,
96,96,112,112,112,112,112,112,112,112,112,112,112,112,112,112,112,112],
[,[1,3,1,3,1,3,7,9,7,9,11,13,11,13,15,17,15,17,5,5,5,5,6,24,26,24,26,7,9,7,9,
11,13,34,36,34,36,38,40,38,40,20,22,20,22,46,48,46,48,28,30,28,30,1,3,1,3,2,4,
5,5,5,5,5,7,9,7,9,12,14,15,17,15,17,22,20,22,20,25,27,25,27,28,30,28,30,30,28,
30,28,32,32,32,32,34,36,34,36,38,40,38,40,54,56,54,56,54,56,54,56,54,56,54,56,
54,56,54,56,58,59,60,62,60,62,63,61,63,61,63,61,60,62,65,67,65,67,65,67,65,67,
65,67,65,67,65,67,65,67,71,73,71,73,71,73,71,73,81,79,81,79,80,82,80,82,83,85,
83,85,90,88,90,88,95,97,95,97,95,97,95,97,99,101,99,101,99,101,99,101],[1,4,3,
2,5,6,1,4,3,2,1,4,3,2,1,4,3,2,19,22,21,20,23,24,27,26,25,5,6,5,6,5,6,38,41,40,
39,34,37,36,35,45,44,43,42,7,10,9,8,19,22,21,20,54,57,56,55,59,58,63,62,61,60,
64,54,57,56,55,59,58,54,57,56,55,78,77,76,75,82,81,80,79,63,62,61,60,63,62,61,
60,63,62,61,60,99,102,101,100,95,98,97,96,107,108,109,110,103,104,105,106,115,
116,117,118,111,112,113,114,120,119,125,126,127,128,121,122,123,124,131,132,
129,130,107,108,109,110,103,104,105,106,115,116,117,118,111,112,113,114,107,
108,109,110,103,104,105,106,163,164,161,162,159,160,157,158,125,126,127,128,
121,122,123,124,185,186,187,188,181,182,183,184,177,178,179,180,173,174,175,
176],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,1,2,3,4,28,
29,30,31,32,33,38,39,40,41,34,35,36,37,42,43,44,45,46,47,48,49,50,51,52,53,54,
55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,58,59,
58,59,83,84,85,86,87,88,89,90,91,92,93,94,99,100,101,102,95,96,97,98,103,104,
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,
143,144,145,146,147,148,149,150,151,152,153,154,155,156,119,119,119,119,120,
120,120,120,165,166,167,168,169,170,171,172,181,182,183,184,185,186,187,188,
173,174,175,176,177,178,179,180],,[1,4,3,2,5,6,7,10,9,8,11,14,13,12,15,18,17,
16,19,22,21,20,23,24,27,26,25,28,31,30,29,32,33,1,4,3,2,1,4,3,2,45,44,43,42,
46,49,48,47,50,53,52,51,54,57,56,55,59,58,63,62,61,60,64,65,68,67,66,70,69,71,
74,73,72,78,77,76,75,80,79,82,81,90,89,88,87,86,85,84,83,94,93,92,91,54,57,56,
55,54,57,56,55,107,108,109,110,103,104,105,106,115,116,117,118,111,112,113,
114,120,119,125,126,127,128,121,122,123,124,131,132,129,130,137,138,139,140,
133,134,135,136,145,146,147,148,141,142,143,144,153,154,155,156,149,150,151,
152,164,161,162,163,160,157,158,159,169,170,171,172,165,166,167,168,107,108,
109,110,103,104,105,106,107,108,109,110,103,104,105,106]],
0,
[(157,159)(158,160)(161,163)(162,164),( 79, 81)( 80, 82)(157,158,159,160)
(161,162,163,164),( 34, 38)( 35, 39)( 36, 40)( 37, 41)( 95, 99)( 96,100)
( 97,101)( 98,102)(173,181)(174,182)(175,183)(176,184)(177,185)(178,186)
(179,187)(180,188),(  2,  4)(  8, 10)( 12, 14)( 16, 18)( 20, 22)( 25, 27)
( 29, 31)( 35, 37)( 39, 41)( 42, 45)( 43, 44)( 47, 49)( 51, 53)( 55, 57)
( 58, 59)( 60, 63)( 61, 62)( 66, 68)( 69, 70)( 72, 74)( 75, 78)( 76, 77)
( 79, 82)( 80, 81)( 83, 90)( 84, 89)( 85, 88)( 86, 87)( 91, 94)( 92, 93)
( 96, 98)(100,102)(103,107)(104,108)(105,109)(106,110)(111,115)(112,116)
(113,117)(114,118)(119,120)(121,125)(122,126)(123,127)(124,128)(129,131)
(130,132)(133,137)(134,138)(135,139)(136,140)(141,145)(142,146)(143,147)
(144,148)(149,153)(150,154)(151,155)(152,156)(157,161)(158,162)(159,163)
(160,164)(165,169)(166,170)(167,171)(168,172)(173,177)(174,178)(175,179)
(176,180)(181,185)(182,186)(183,187)(184,188),(103,105)(104,106)(107,109)
(108,110)(111,113)(112,114)(115,117)(116,118)(121,123)(122,124)(125,127)
(126,128)(133,135)(134,136)(137,139)(138,140)(141,143)(142,144)(145,147)
(146,148)(149,151)(150,152)(153,155)(154,156)(165,167)(166,168)(169,171)
(170,172)(173,175)(174,176)(177,179)(178,180)(181,183)(182,184)(185,187)
(186,188),( 54, 56)( 55, 57)( 60, 62)( 61, 63)( 65, 67)( 66, 68)( 71, 73)
( 72, 74)( 75, 77)( 76, 78)( 83, 85)( 84, 86)( 87, 89)( 88, 90)( 91, 93)
( 92, 94)( 95, 97)( 96, 98)( 99,101)(100,102)(103,104,105,106)(107,108,109,110
 )(111,112,113,114)(115,116,117,118)(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)(165,166,167,168)
(169,170,171,172)(173,174,175,176)(177,178,179,180)(181,182,183,184)
(185,186,187,188)],
["ConstructProj",[["U4(3).4",[]],["2.U4(3).4",[]],,["4.U4(3).4",[-1,-1,-1,-1,
-1,-1,-1,-1,15,15,-1,31]]]]);
ALF("4.U4(3).4","2.U4(3).4",[1,2,1,2,3,4,5,6,5,6,7,8,7,8,9,10,9,10,11,12,
11,12,13,14,15,14,15,16,17,16,17,18,19,20,21,20,21,22,23,22,23,24,25,24,
25,26,27,26,27,28,29,28,29,30,31,30,31,32,33,34,35,34,35,36,37,38,37,38,
39,40,41,42,41,42,43,44,43,44,45,46,45,46,47,48,47,48,49,50,49,50,51,52,
51,52,53,54,53,54,55,56,55,56,57,58,57,58,59,60,59,60,61,62,61,62,63,64,
63,64,65,66,67,68,67,68,69,70,69,70,71,72,73,74,75,76,75,76,77,78,77,78,
79,80,79,80,81,82,81,82,83,84,83,84,85,86,85,86,87,88,87,88,89,90,89,90,
91,92,91,92,93,94,93,94,95,96,95,96,97,98,97,98,99,100,99,100,101,102,101,
102]);
ALF("4.U4(3).4","U4(3).4",[1,1,1,1,2,2,3,3,3,3,4,4,4,4,5,5,5,5,6,6,6,6,7,
8,8,8,8,9,9,9,9,10,10,11,11,11,11,12,12,12,12,13,13,13,13,14,14,14,14,15,
15,15,15,16,16,16,16,17,17,18,18,18,18,19,20,20,20,20,21,21,22,22,22,22,
23,23,23,23,24,24,24,24,25,25,25,25,26,26,26,26,27,27,27,27,28,28,28,28,
29,29,29,29,30,30,30,30,31,31,31,31,32,32,32,32,33,33,33,33,34,35,36,36,
36,36,37,37,37,37,38,38,39,39,40,40,40,40,41,41,41,41,42,42,42,42,43,43,
43,43,44,44,44,44,45,45,45,45,46,46,46,46,47,47,47,47,48,48,48,48,49,49,
49,49,50,50,50,50,51,51,51,51,52,52,52,52,53,53,53,53]);
ALF("4.U4(3).4","U5(3)",[1,8,2,9,3,15,4,47,20,46,5,52,23,53,6,57,24,58,12,
17,18,16,42,19,85,45,86,22,64,21,63,25,71,28,107,80,106,29,105,81,108,35,
41,40,34,43,115,84,116,54,66,69,65,2,13,3,14,32,33,10,16,17,11,18,20,55,
22,56,100,99,24,72,26,73,39,40,41,38,117,119,120,118,50,65,61,48,49,62,66,
51,60,74,75,59,80,112,78,109,81,110,79,111,8,11,13,12,9,10,14,12,15,17,14,
18,15,16,13,18,82,83,31,38,37,35,30,39,36,34,36,41,37,40,47,51,55,54,46,
50,56,54,63,61,56,69,64,62,55,69,57,68,72,70,58,67,73,70,144,143,146,139,
142,140,141,145,89,96,94,91,90,95,93,92,107,101,112,113,106,104,109,113,
105,103,110,114,108,102,111,114],[
"fusion map is unique up to table aut."
]);
ALN("4.U4(3).4",["U5(3)M2"]);

MOT("6_1.U4(3)",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[19595520,19595520,19595520,19595520,19595520,19595520,6912,6912,6912,6912,
6912,6912,34992,34992,34992,34992,34992,34992,5832,5832,5832,5832,5832,5832,
1944,1944,162,162,576,576,576,576,576,576,48,48,48,30,30,30,30,30,30,432,432,
432,432,432,432,216,216,216,216,216,216,216,216,216,216,216,216,42,42,42,42,
42,42,42,42,42,42,42,42,48,48,48,48,48,48,162,162,162,162,162,162,162,162,162,
162,162,162,54,54,54,54,72,72,72,72,72,72],
[,[1,3,5,1,3,5,1,3,5,1,3,5,13,15,17,13,15,17,19,21,23,19,21,23,25,25,27,27,7,
9,11,7,9,11,10,12,8,38,40,42,38,40,42,13,15,17,13,15,17,19,21,23,19,21,23,25,
25,25,25,25,25,62,64,66,62,64,66,68,70,72,68,70,72,32,34,30,32,34,30,86,88,90,
86,88,90,80,82,84,80,82,84,94,94,92,92,44,46,48,44,46,48],[1,4,1,4,1,4,7,10,7,
10,7,10,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,29,32,29,32,29,32,35,35,35,38,41,38,
41,38,41,7,10,7,10,7,10,7,10,7,10,7,10,7,10,7,10,7,10,68,71,68,71,68,71,62,65,
62,65,62,65,77,74,77,74,77,74,15,18,15,18,15,18,17,14,17,14,17,14,13,16,13,16,
29,32,29,32,29,32],,[1,6,5,4,3,2,7,12,11,10,9,8,13,18,17,16,15,14,19,24,23,22,
21,20,25,26,27,28,29,34,33,32,31,30,35,37,36,1,6,5,4,3,2,44,49,48,47,46,45,50,
55,54,53,52,51,56,61,60,59,58,57,68,73,72,71,70,69,62,67,66,65,64,63,74,79,78,
77,76,75,86,91,90,89,88,87,80,85,84,83,82,81,94,95,92,93,96,101,100,99,98,
97],,[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,
54,55,56,57,58,59,60,61,1,2,3,4,5,6,1,2,3,4,5,6,77,78,79,74,75,76,80,81,82,83,
84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101]],
0,
[(92,94)(93,95),(74,77)(75,78)(76,79),(62,68)(63,69)(64,70)(65,71)(66,72)
(67,73),(  2,  6)(  3,  5)(  8, 12)(  9, 11)( 14, 18)( 15, 17)( 20, 24)
( 21, 23)( 30, 34)( 31, 33)( 36, 37)( 39, 43)( 40, 42)( 45, 49)( 46, 48)
( 51, 55)( 52, 54)( 57, 61)( 58, 60)( 63, 67)( 64, 66)( 69, 73)( 70, 72)
( 75, 79)( 76, 78)( 80, 86)( 81, 91)( 82, 90)( 83, 89)( 84, 88)( 85, 87)
( 92, 94)( 93, 95)( 97,101)( 98,100),(  2,  6)(  3,  5)(  8, 12)(  9, 11)
( 14, 18)( 15, 17)( 20, 24)( 21, 23)( 30, 34)( 31, 33)( 36, 37)( 39, 43)
( 40, 42)( 45, 49)( 46, 48)( 51, 55)( 52, 54)( 57, 61)( 58, 60)( 63, 67)
( 64, 66)( 69, 73)( 70, 72)( 75, 79)( 76, 78)( 80, 86)( 81, 91)( 82, 90)
( 83, 89)( 84, 88)( 85, 87)( 97,101)( 98,100)],
["ConstructProj",[["U4(3)",[]],["2.U4(3)",[]],["3_1.U4(3)",[-1,-1,-1,-1,-1,-1,
-1,-1,-13,-13,-1,-1,-1,-1,-1,-1]],,,["6_1.U4(3)",[-1,-1,-1,-1,-1,-13,-13,-1,
-1,-1,-1,-7,-7,-1,-1]]]]);
ALF("6_1.U4(3)","U4(3)",[1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,
5,5,6,6,7,7,7,7,7,7,8,8,8,9,9,9,9,9,9,10,10,10,10,10,10,11,11,11,11,11,11,
12,12,12,12,12,12,13,13,13,13,13,13,14,14,14,14,14,14,15,15,15,15,15,15,
16,16,16,16,16,16,17,17,17,17,17,17,18,18,19,19,20,20,20,20,20,20]);
ALF("6_1.U4(3)","2.U4(3)",[1,2,1,2,1,2,3,4,3,4,3,4,5,6,5,6,5,6,7,8,7,8,7,
8,9,10,11,12,13,14,13,14,13,14,15,15,15,16,17,16,17,16,17,18,19,18,19,18,
19,20,21,20,21,20,21,22,23,22,23,22,23,24,25,24,25,24,25,26,27,26,27,26,
27,28,29,28,29,28,29,30,31,30,31,30,31,32,33,32,33,32,33,34,35,36,37,38,
39,38,39,38,39]);
ALF("6_1.U4(3)","3_1.U4(3)",[1,2,3,1,2,3,4,5,6,4,5,6,7,8,9,7,8,9,10,11,12,
10,11,12,13,13,14,14,15,16,17,15,16,17,18,19,20,21,22,23,21,22,23,24,25,
26,24,25,26,27,28,29,27,28,29,30,31,32,30,31,32,33,34,35,33,34,35,36,37,
38,36,37,38,39,40,41,39,40,41,42,43,44,42,43,44,45,46,47,45,46,47,48,48,
49,49,50,51,52,50,51,52]);
ALF("6_1.U4(3)","6_1.U4(3).2_1",[1,2,3,4,3,2,5,6,7,8,7,6,9,10,11,12,11,10,
13,14,15,16,15,14,17,18,19,20,21,22,23,24,23,22,25,26,26,27,28,29,30,29,
28,31,32,33,34,33,32,35,36,37,38,37,36,39,40,41,42,41,40,43,44,45,46,45,
44,47,48,49,50,49,48,51,52,53,54,53,52,55,56,57,58,59,60,55,60,59,58,57,
56,61,62,61,62,63,64,65,66,65,64],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);
ALF("6_1.U4(3)","6_1.U4(3).2_2",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,
17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,
41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,
65,66,67,62,63,64,65,66,67,68,69,70,68,69,70,71,72,73,74,75,76,77,78,79,
80,81,82,83,84,83,84,85,86,87,88,89,90],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("6_1.U4(3)","6_1.U4(3).2_2'",[1,2,3,4,3,2,5,6,7,8,7,6,9,10,11,12,11,
10,13,14,15,16,15,14,17,18,19,20,21,22,23,24,23,22,25,26,26,27,28,29,30,
29,28,31,32,33,34,33,32,35,36,37,38,37,36,39,40,41,42,41,40,43,44,45,46,
47,48,43,48,47,46,45,44,49,50,50,49,51,51,52,53,54,55,56,57,52,57,56,55,
54,53,58,59,60,61,62,63,64,65,64,63]);

MOT("6_1.U4(3).2_1",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[39191040,19595520,19595520,39191040,13824,6912,6912,13824,69984,34992,34992,
69984,11664,5832,5832,11664,3888,3888,324,324,1152,576,576,1152,96,48,60,30,
30,60,864,432,432,864,432,216,216,432,432,216,216,432,84,42,42,84,84,42,42,84,
96,48,48,96,162,162,162,162,162,162,54,54,144,72,72,144,24192,24192,2880,2880,
2304,2304,128,432,432,72,72,72,72,36,36,32,32,20,20,288,288,288,288,72,72,72,
72,28,28,28,28],
[,[1,3,3,1,1,3,3,1,9,11,11,9,13,15,15,13,17,17,19,19,5,7,7,5,8,6,27,29,29,27,
9,11,11,9,13,15,15,13,17,17,17,17,43,45,45,43,47,49,49,47,24,22,22,24,55,59,
57,55,59,57,61,61,31,33,33,31,1,1,4,4,5,5,5,9,9,16,16,18,18,19,19,24,24,30,30,
31,31,31,31,35,35,39,39,43,43,47,47],[1,4,1,4,5,8,5,8,1,4,1,4,1,4,1,4,1,4,1,4,
21,24,21,24,25,25,27,30,27,30,5,8,5,8,5,8,5,8,5,8,5,8,47,50,47,50,43,46,43,46,
54,51,54,51,11,10,11,10,11,10,9,12,21,24,21,24,67,68,70,69,72,71,73,67,68,70,
69,70,69,67,68,83,82,85,84,72,71,72,71,72,71,72,71,96,97,94,95],,[1,2,3,4,5,6,
7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,1,2,3,4,31,32,33,34,
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,
61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,69,70,86,
87,88,89,90,91,92,93,96,97,94,95],,[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,
2,3,4,1,2,3,4,54,53,52,51,55,56,57,58,59,60,61,62,63,64,65,66,67,68,70,69,72,
71,73,74,75,77,76,79,78,80,81,83,82,85,84,89,88,87,86,91,90,93,92,67,68,67,
68]],
0,
[(51,54)(52,53)(69,70)(71,72)(76,77)(78,79)(82,83)(84,85)(86,89)(87,88)(90,91)
(92,93),(43,47)(44,48)(45,49)(46,50)(94,96)(95,97),(67,68)(69,70)(71,72)
(74,75)(76,77)(78,79)(80,81)(82,83)(84,85)(86,87)(88,89)(90,91)(92,93)(94,95)
(96,97)],
["ConstructMGA","6_1.U4(3)","2.U4(3).2_1",
     [ [ 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 ] ], ()]);
ALF("6_1.U4(3).2_1","U4(3).2_1",[1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4,5,5,6,6,
7,7,7,7,8,8,9,9,9,9,10,10,10,10,11,11,11,11,12,12,12,12,13,13,13,13,14,14,
14,14,15,15,15,15,16,16,16,16,16,16,17,17,18,18,18,18,19,19,20,20,21,21,
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]);
ALF("6_1.U4(3).2_1","2.U4(3).2_1",[1,2,1,2,3,4,3,4,5,6,5,6,7,8,7,8,9,10,
11,12,13,14,13,14,15,15,16,17,16,17,18,19,18,19,20,21,20,21,22,23,22,23,
24,25,24,25,26,27,26,27,28,29,28,29,30,31,30,31,30,31,32,33,34,35,34,35,
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]);
ALF("6_1.U4(3).2_1","3_1.U4(3).2_1",[1,2,2,1,3,4,4,3,5,6,6,5,7,8,8,7,9,9,
10,10,11,12,12,11,13,14,15,16,16,15,17,18,18,17,19,20,20,19,21,22,22,21,
23,24,24,23,25,26,26,25,27,28,28,27,29,30,31,29,30,31,32,32,33,34,34,33,
35,35,36,36,37,37,38,39,39,40,40,41,41,42,42,43,43,44,44,45,45,46,46,47,
47,48,48,49,49,50,50]);

MOT("Isoclinic(6_1.U4(3).2_1)",
[
"isoclinic group of the 6_1.U4(3).2_1 given in the ATLAS"
],
0,
0,
0,
[(67,68)(69,70)(71,72)(74,75)(76,77)(78,79)(80,81)(82,83)(84,85)(86,87)(88,89)
(90,91)(92,93)(94,95)(96,97),(51,54)(52,53)(69,70)(71,72)(76,77)(78,79)(82,83)
(84,85)(86,89)(87,88)(90,91)(92,93),(43,47)(44,48)(45,49)(46,50)(94,96)(95,97)
],
["ConstructIsoclinic",[["6_1.U4(3).2_1"]]]);
ALF("Isoclinic(6_1.U4(3).2_1)","3_1.U4(3).2_1",[1,2,2,1,3,4,4,3,5,6,6,5,7,
8,8,7,9,9,10,10,11,12,12,11,13,14,15,16,16,15,17,18,18,17,19,20,20,19,21,
22,22,21,23,24,24,23,25,26,26,25,27,28,28,27,29,30,31,29,30,31,32,32,33,
34,34,33,35,35,36,36,37,37,38,39,39,40,40,41,41,42,42,43,43,44,44,45,45,
46,46,47,47,48,48,49,49,50,50]);

MOT("6_1.U4(3).2_2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[39191040,39191040,39191040,39191040,39191040,39191040,13824,13824,13824,
13824,13824,13824,69984,69984,69984,69984,69984,69984,11664,11664,11664,11664,
11664,11664,3888,3888,324,324,1152,1152,1152,1152,1152,1152,96,96,96,60,60,60,
60,60,60,864,864,864,864,864,864,432,432,432,432,432,432,432,432,432,432,432,
432,42,42,42,42,42,42,48,48,48,324,324,324,324,324,324,324,324,324,324,324,
324,54,54,144,144,144,144,144,144,311040,311040,311040,311040,311040,311040,
3456,3456,3456,576,576,576,576,576,576,576,576,576,7776,7776,7776,7776,7776,
7776,7776,7776,7776,7776,7776,7776,1296,1296,1296,1296,1296,1296,648,648,648,
648,648,648,144,144,36,36,48,48,48,60,60,60,60,60,60,144,144,144,144,144,144,
72,72,72,72,72,72,108,108,108,108,108,108,108,108,108,108,108,108],
[,[1,3,5,1,3,5,1,3,5,1,3,5,13,15,17,13,15,17,19,21,23,19,21,23,25,25,27,27,7,
9,11,7,9,11,10,12,8,38,40,42,38,40,42,13,15,17,13,15,17,19,21,23,19,21,23,25,
25,25,25,25,25,62,64,66,62,64,66,32,34,30,77,79,81,77,79,81,71,73,75,71,73,75,
83,83,44,46,48,44,46,48,1,3,5,1,3,5,1,3,5,7,9,11,10,12,8,10,12,8,13,15,17,13,
15,17,13,15,17,13,15,17,25,25,25,25,25,25,19,21,23,19,21,23,25,25,27,27,29,31,
33,38,40,42,38,40,42,44,46,48,44,46,48,53,55,51,53,55,51,77,79,81,77,79,81,71,
73,75,71,73,75],[1,4,1,4,1,4,7,10,7,10,7,10,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,
29,32,29,32,29,32,35,35,35,38,41,38,41,38,41,7,10,7,10,7,10,7,10,7,10,7,10,7,
10,7,10,7,10,62,65,62,65,62,65,68,68,68,15,18,15,18,15,18,17,14,17,14,17,14,
13,16,29,32,29,32,29,32,91,94,91,94,91,94,97,97,97,100,100,100,103,106,103,
106,103,106,91,94,91,94,91,94,91,94,91,94,91,94,91,94,91,94,91,94,91,94,91,94,
91,94,97,97,97,97,137,137,137,140,143,140,143,140,143,100,100,100,100,100,100,
103,106,103,106,103,106,111,114,111,114,111,114,119,116,119,116,119,116],,[1,
6,5,4,3,2,7,12,11,10,9,8,13,18,17,16,15,14,19,24,23,22,21,20,25,26,27,28,29,
34,33,32,31,30,35,37,36,1,6,5,4,3,2,44,49,48,47,46,45,50,55,54,53,52,51,56,61,
60,59,58,57,62,67,66,65,64,63,68,70,69,77,82,81,80,79,78,71,76,75,74,73,72,83,
84,85,90,89,88,87,86,91,96,95,94,93,92,97,99,98,100,102,101,103,108,107,106,
105,104,115,120,119,118,117,116,109,114,113,112,111,110,121,126,125,124,123,
122,127,132,131,130,129,128,133,134,135,136,137,139,138,91,96,95,94,93,92,149,
148,147,146,151,150,152,157,156,155,154,153,164,169,168,167,166,165,158,163,
162,161,160,159],,[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,
49,50,51,52,53,54,55,56,57,58,59,60,61,1,2,3,4,5,6,68,69,70,71,72,73,74,75,76,
77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,
102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,
121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,
140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,
159,160,161,162,163,164,165,166,167,168,169]],
0,
[(135,136),(  2,  6)(  3,  5)(  8, 12)(  9, 11)( 14, 18)( 15, 17)( 20, 24)
( 21, 23)( 30, 34)( 31, 33)( 36, 37)( 39, 43)( 40, 42)( 45, 49)( 46, 48)
( 51, 55)( 52, 54)( 57, 61)( 58, 60)( 63, 67)( 64, 66)( 69, 70)( 71, 77)
( 72, 82)( 73, 81)( 74, 80)( 75, 79)( 76, 78)( 86, 90)( 87, 89)( 92, 96)
( 93, 95)( 98, 99)(101,102)(104,108)(105,107)(109,115)(110,120)(111,119)
(112,118)(113,117)(114,116)(122,126)(123,125)(128,132)(129,131)(138,139)
(141,145)(142,144)(146,149)(147,148)(150,151)(153,157)(154,156)(158,164)
(159,169)(160,168)(161,167)(162,166)(163,165),( 91, 94)( 92, 95)( 93, 96)
(103,106)(104,107)(105,108)(109,112)(110,113)(111,114)(115,118)(116,119)
(117,120)(121,124)(122,125)(123,126)(127,130)(128,131)(129,132)(133,134)
(140,143)(141,144)(142,145)(146,149)(147,150)(148,151)(152,155)(153,156)
(154,157)(158,161)(159,162)(160,163)(164,167)(165,168)(166,169)],
["ConstructProj",[["U4(3).2_2",[]],["2.U4(3).2_2",[]],["3_1.U4(3).2_2",[-1,-1,
-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1]],,,["6_1.U4(3).2_2",[-1,-1,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,-1]]]]);
ALF("6_1.U4(3).2_2","U4(3).2_2",[1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,4,4,
4,4,4,4,5,5,6,6,7,7,7,7,7,7,8,8,8,9,9,9,9,9,9,10,10,10,10,10,10,11,11,11,
11,11,11,12,12,12,12,12,12,13,13,13,13,13,13,14,14,14,15,15,15,15,15,15,
16,16,16,16,16,16,17,17,18,18,18,18,18,18,19,19,19,19,19,19,20,20,20,21,
21,21,22,22,22,22,22,22,23,23,23,23,23,23,24,24,24,24,24,24,25,25,25,25,
25,25,26,26,26,26,26,26,27,27,28,28,29,29,29,30,30,30,30,30,30,31,31,31,
31,31,31,32,32,32,32,32,32,33,33,33,33,33,33,34,34,34,34,34,34]);
ALF("6_1.U4(3).2_2","2.U4(3).2_2",[1,2,1,2,1,2,3,4,3,4,3,4,5,6,5,6,5,6,7,
8,7,8,7,8,9,10,11,12,13,14,13,14,13,14,15,15,15,16,17,16,17,16,17,18,19,
18,19,18,19,20,21,20,21,20,21,22,23,22,23,22,23,24,25,24,25,24,25,26,26,
26,27,28,27,28,27,28,29,30,29,30,29,30,31,32,33,34,33,34,33,34,35,36,35,
36,35,36,37,37,37,38,38,38,39,40,39,40,39,40,41,42,41,42,41,42,43,44,43,
44,43,44,45,46,45,46,45,46,47,48,47,48,47,48,49,50,51,52,53,53,53,54,55,
54,55,54,55,56,57,56,57,56,57,58,59,58,59,58,59,60,61,60,61,60,61,62,63,
62,63,62,63]);
ALF("6_1.U4(3).2_2","3_1.U4(3).2_2",[1,2,3,1,2,3,4,5,6,4,5,6,7,8,9,7,8,9,
10,11,12,10,11,12,13,13,14,14,15,16,17,15,16,17,18,19,20,21,22,23,21,22,
23,24,25,26,24,25,26,27,28,29,27,28,29,30,31,32,30,31,32,33,34,35,33,34,
35,36,37,38,39,40,41,39,40,41,42,43,44,42,43,44,45,45,46,47,48,46,47,48,
49,50,51,49,50,51,52,53,54,55,56,57,58,59,60,58,59,60,61,62,63,61,62,63,
64,65,66,64,65,66,67,68,69,67,68,69,70,71,72,70,71,72,73,73,74,74,75,76,
77,78,79,80,78,79,80,81,82,83,81,82,83,84,85,86,84,85,86,87,88,89,87,88,
89,90,91,92,90,91,92]);
ALF("6_1.U4(3).2_2","3.U6(2)M5",[1,2,3,1,2,3,4,5,6,4,5,6,7,8,9,7,8,9,10,
11,12,10,11,12,13,13,14,14,15,16,17,15,16,17,18,19,20,21,22,23,21,22,23,
24,25,26,24,25,26,27,28,29,27,28,29,30,31,32,30,31,32,33,34,35,33,34,35,
36,37,38,39,40,41,39,40,41,42,43,44,42,43,44,45,45,46,47,48,46,47,48,49,
50,51,49,50,51,52,53,54,55,56,57,58,59,60,58,59,60,61,62,63,61,62,63,64,
65,66,64,65,66,67,68,69,67,68,69,70,71,72,70,71,72,73,73,74,74,75,76,77,
78,79,80,78,79,80,81,82,83,81,82,83,84,85,86,84,85,86,87,88,89,87,88,89,
90,91,92,90,91,92]);
ALF("6_1.U4(3).2_2","6.U6(2)",[1,6,5,4,3,2,16,15,14,13,18,17,28,33,32,31,
30,29,22,27,26,25,24,23,34,35,34,35,48,50,49,48,50,49,60,62,61,63,68,67,
66,65,64,90,89,88,87,92,91,96,95,94,93,98,97,108,107,106,105,110,109,113,
118,117,116,115,114,128,130,129,138,137,136,135,134,139,142,141,140,145,
144,143,146,147,190,192,191,190,192,191,7,12,11,10,9,8,19,21,20,48,50,49,
54,59,58,57,56,55,69,74,73,72,71,70,75,80,79,78,77,76,99,104,103,102,101,
100,81,86,85,84,83,82,112,111,112,111,128,130,129,148,153,152,151,150,149,
190,192,191,190,192,191,196,201,200,199,198,197,212,211,210,209,208,213,
216,215,214,219,218,217],[
"fusion map is unique up to table autom.,\n",
"representative compatible with relevant factors"
]);
ALF("6_1.U4(3).2_2","3.O7(3)",[1,5,3,4,2,6,10,8,12,7,11,9,13,38,13,37,13,
39,14,41,16,40,15,42,17,43,20,59,25,29,27,28,26,30,31,32,33,34,84,36,83,
35,85,51,45,51,44,51,46,55,53,57,52,56,54,58,49,58,48,58,50,65,109,67,108,
66,110,71,72,73,75,119,74,118,76,117,76,114,75,116,74,115,77,120,87,95,87,
94,87,96,4,8,6,7,5,9,10,11,12,28,29,30,22,32,24,31,23,33,39,46,38,45,37,
44,38,44,37,46,39,45,43,49,43,48,43,50,40,53,42,52,41,54,47,58,62,63,68,
69,70,83,81,85,80,84,82,95,94,94,96,96,95,91,100,93,99,92,101,115,123,114,
122,116,121,119,121,118,123,117,122],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);

MOT("Isoclinic(6_1.U4(3).2_2)",
[
"isoclinic group of the 6_1.U4(3).2_2 given in the ATLAS"
],
0,
0,
0,
[(135,136),(91,94)(92,95)(93,96)(103,106)(104,107)(105,108)(109,112)(110,113)
(111,114)(115,118)(116,119)(117,120)(121,124)(122,125)(123,126)(127,130)(128,
131)(129,132)(133,134)(140,143)(141,144)(142,145)(146,149)(147,150)(148,151)
(152,155)(153,156)(154,157)(158,161)(159,162)(160,163)(164,167)(165,168)(166,
169),(2,6)(3,5)(8,12)(9,11)(14,18)(15,17)(20,24)(21,23)(30,34)(31,33)(36,37)
(39,43)(40,42)(45,49)(46,48)(51,55)(52,54)(57,61)(58,60)(63,67)(64,66)(69,70)
(71,77)(72,82)(73,81)(74,80)(75,79)(76,78)(86,90)(87,89)(92,96)(93,95)(98,99)
(101,102)(104,108)(105,107)(109,115)(110,120)(111,119)(112,118)(113,117)(114,
116)(122,126)(123,125)(128,132)(129,131)(138,139)(141,145)(142,144)(146,149)
(147,148)(150,151)(153,157)(154,156)(158,164)(159,169)(160,168)(161,167)(162,
166)(163,165)],
["ConstructIsoclinic",[["6_1.U4(3).2_2"]]]);
ALF("Isoclinic(6_1.U4(3).2_2)","U4(3).2_2",[1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,
3,3,3,4,4,4,4,4,4,5,5,6,6,7,7,7,7,7,7,8,8,8,9,9,9,9,9,9,10,10,10,10,10,10,
11,11,11,11,11,11,12,12,12,12,12,12,13,13,13,13,13,13,14,14,14,15,15,15,
15,15,15,16,16,16,16,16,16,17,17,18,18,18,18,18,18,19,19,19,19,19,19,20,
20,20,21,21,21,22,22,22,22,22,22,23,23,23,23,23,23,24,24,24,24,24,24,25,
25,25,25,25,25,26,26,26,26,26,26,27,27,28,28,29,29,29,30,30,30,30,30,30,
31,31,31,31,31,31,32,32,32,32,32,32,33,33,33,33,33,33,34,34,34,34,34,34]);

MOT("6_1.U4(3).2_2'",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[39191040,19595520,19595520,39191040,13824,6912,6912,13824,69984,34992,34992,
69984,11664,5832,5832,11664,3888,3888,324,324,1152,576,576,1152,96,48,60,30,30
,60,864,432,432,864,432,216,216,432,432,216,216,432,42,42,42,42,42,42,48,48,48
,162,162,162,162,162,162,108,108,108,108,144,72,72,144,103680,103680,1152,192,
192,192,2592,2592,2592,2592,432,432,216,216,144,144,36,36,16,20,20,48,48,24,24
,36,36,36,36],
[,[1,3,3,1,1,3,3,1,9,11,11,9,13,15,15,13,17,17,19,19,5,7,7,5,8,6,27,29,29,27,9
,11,11,9,13,15,15,13,17,17,17,17,43,45,47,43,45,47,24,22,22,52,56,54,52,56,54,
60,60,58,58,31,33,33,31,1,1,1,5,8,8,9,9,9,9,13,13,17,17,13,13,19,19,21,27,27,
31,31,42,42,60,60,58,58],[1,4,1,4,5,8,5,8,1,4,1,4,1,4,1,4,1,4,1,4,21,24,21,24,
25,25,27,30,27,30,5,8,5,8,5,8,5,8,5,8,5,8,43,46,43,46,43,46,49,49,49,11,10,11,
10,11,10,9,12,9,12,21,24,21,24,66,67,68,69,70,71,66,67,66,67,66,67,66,67,68,68
,68,68,84,85,86,69,69,70,71,72,73,74,75],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15
,16,17,18,19,20,21,22,23,24,25,26,1,2,3,4,31,32,33,34,35,36,37,38,39,40,41,42,
43,44,45,46,47,48,49,51,50,52,53,54,55,56,57,60,61,58,59,62,63,64,65,66,67,68,
69,70,71,74,75,72,73,76,77,78,79,80,81,82,83,84,66,67,88,87,89,90,93,94,91,92]
,,[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,
29,30,31,32,33,34,35,36,37,38,39,40,41,42,1,2,3,4,3,2,49,51,50,52,53,54,55,56,
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]],
0,
[(82,83),(50,51),
(58,60)(59,61)(66,67)(70,71)(72,75)(73,74)(76,77)(78,79)(80,81)(85,86)(89,90)
(91,94)(92,93)
,(58,60)(59,61)(72,74)(73,75)(87,88)(91,93)(92,94),
(44,48)(45,47)(58,60)(59,61)(66,67)(70,71)(72,75)(73,74)(76,77)(78,79)(80,81)
(85,86)(89,90)(91,94)(92,93)
],
["ConstructMGA","6_1.U4(3)","2.U4(3).2_2'",[[40,41],[42,43],[44,45],[46,47],[
48,49],[50,51],[52,53],[54,55],[56,59],[57,58],[60,61],[62,63],[64,65],[66,67]
,[68,69],[70,71],[72,73],[74,75],[76,77],[78,79],[80,81],[82,85],[83,84],[86,
87],[88,89],[90,91],[92,93],[94,97],[95,96],[98,99],[100,101]],()]);
ALF("6_1.U4(3).2_2'","U4(3).2_2'",[1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4,5,5,6,
6,7,7,7,7,8,8,9,9,9,9,10,10,10,10,11,11,11,11,12,12,12,12,13,13,13,13,13,
13,14,14,14,15,15,15,15,15,15,16,16,17,17,18,18,18,18,19,19,20,21,22,22,
23,23,24,24,25,25,26,26,27,27,28,28,29,30,30,31,31,32,32,33,33,34,34]);
ALF("6_1.U4(3).2_2'","2.U4(3).2_2'",[1,2,1,2,3,4,3,4,5,6,5,6,7,8,7,8,9,10,
11,12,13,14,13,14,15,15,16,17,16,17,18,19,18,19,20,21,20,21,22,23,22,23,
24,25,24,25,24,25,26,26,26,27,28,27,28,27,28,29,30,31,32,33,34,33,34,35,
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]);
ALF("6_1.U4(3).2_2'","3_1.U4(3).2_2'",[1,2,2,1,3,4,4,3,5,6,6,5,7,8,8,7,9,
9,10,10,11,12,12,11,13,14,15,16,16,15,17,18,18,17,19,20,20,19,21,22,22,21,
23,24,25,23,24,25,26,27,27,28,29,30,28,29,30,31,31,32,32,33,34,34,33,35,
35,36,37,38,38,39,39,40,40,41,41,42,42,43,43,44,44,45,46,46,47,47,48,48,
49,49,50,50]);

MOT("Isoclinic(6_1.U4(3).2_2')",
[
"isoclinic group of the 6_1.U4(3).2_2' given in the ATLAS"
],
0,
0,
0,
[(82,83),(66,67)(70,71)(72,73)(74,75)(76,77)(78,79)(80,81)(85,86)(87,88)(89,
90)(91,92)(93,94),(58,60)(59,61)(72,74)(73,75)(87,88)(91,93)(92,94),(50,51),
(44,48)(45,47)],
["ConstructIsoclinic",[["6_1.U4(3).2_2'"]]]);
ALF("Isoclinic(6_1.U4(3).2_2')","3_1.U4(3).2_2'",[1,2,2,1,3,4,4,3,5,6,6,5,
7,8,8,7,9,9,10,10,11,12,12,11,13,14,15,16,16,15,17,18,18,17,19,20,20,19,
21,22,22,21,23,24,25,23,24,25,26,27,27,28,29,30,28,29,30,31,31,32,32,33,
34,34,33,35,35,36,37,38,38,39,39,40,40,41,41,42,42,43,43,44,44,45,46,46,
47,47,48,48,49,49,50,50]);

MOT("6_2.U4(3)",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]\n",
"3rd power map determined only up to matrix automorphisms (80,82)(81,83)\n",
"and (76,78)(77,79)"
],
[19595520,19595520,19595520,19595520,19595520,19595520,6912,6912,6912,6912,
6912,6912,34992,34992,34992,34992,34992,34992,1944,1944,1944,1944,162,162,576,
576,576,576,576,576,48,48,48,30,30,30,30,30,30,432,432,432,432,432,432,216,
216,216,216,216,216,216,216,216,216,216,216,42,42,42,42,42,42,42,42,42,42,42,
42,48,48,48,48,48,48,54,54,54,54,54,54,54,54,72,72,72,72,72,72],
[,[1,3,5,1,3,5,1,3,5,1,3,5,13,15,17,13,15,17,19,19,21,21,23,23,7,9,11,7,9,11,
10,12,8,34,36,38,34,36,38,13,15,17,13,15,17,19,19,19,19,19,19,21,21,21,21,21,
21,58,60,62,58,60,62,64,66,68,64,66,68,28,30,26,28,30,26,78,78,76,76,82,82,80,
80,40,42,44,40,42,44],[1,4,1,4,1,4,7,10,7,10,7,10,1,4,1,4,1,4,1,4,1,4,1,4,25,
28,25,28,25,28,31,31,31,34,37,34,37,34,37,7,10,7,10,7,10,7,10,7,10,7,10,7,10,
7,10,7,10,64,67,64,67,64,67,58,61,58,61,58,61,73,70,73,70,73,70,15,18,17,14,
15,18,17,14,25,28,25,28,25,28],,[1,6,5,4,3,2,7,12,11,10,9,8,13,18,17,16,15,14,
19,20,21,22,23,24,25,30,29,28,27,26,31,33,32,1,6,5,4,3,2,40,45,44,43,42,41,46,
51,50,49,48,47,52,57,56,55,54,53,64,69,68,67,66,65,58,63,62,61,60,59,70,75,74,
73,72,71,78,79,76,77,82,83,80,81,84,89,88,87,86,85],,[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,
38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,1,2,3,4,5,6,1,2,3,
4,5,6,73,74,75,70,71,72,76,77,78,79,80,81,82,83,84,85,86,87,88,89]],
0,
[(70,73)(71,74)(72,75),(58,64)(59,65)(60,66)(61,67)(62,68)(63,69),( 2, 6)
( 3, 5)( 8,12)( 9,11)(14,18)(15,17)(26,30)(27,29)(32,33)(35,39)(36,38)(41,45)
(42,44)(47,51)(48,50)(53,57)(54,56)(59,63)(60,62)(65,69)(66,68)(71,75)(72,74)
(76,78)(77,79)(80,82)(81,83)(85,89)(86,88),(19,21)(20,22)(46,52)(47,53)(48,54)
(49,55)(50,56)(51,57)(76,80)(77,81)(78,82)(79,83)],
["ConstructProj",[["U4(3)",[]],["2.U4(3)",[]],["3_2.U4(3)",[-1,-13,-13,-1,-1,
-1,-1,-1,-1,-1,-1,-1,-1]],,,["6_2.U4(3)",[-1,-1,-1,-7,-7,-13,-13,-1,-1,-1,-1,
-1]]]]);
ALF("6_2.U4(3)","U4(3)",[1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,4,4,5,5,6,6,
7,7,7,7,7,7,8,8,8,9,9,9,9,9,9,10,10,10,10,10,10,11,11,11,11,11,11,12,12,
12,12,12,12,13,13,13,13,13,13,14,14,14,14,14,14,15,15,15,15,15,15,16,16,
17,17,18,18,19,19,20,20,20,20,20,20]);
ALF("6_2.U4(3)","2.U4(3)",[1,2,1,2,1,2,3,4,3,4,3,4,5,6,5,6,5,6,7,8,9,10,
11,12,13,14,13,14,13,14,15,15,15,16,17,16,17,16,17,18,19,18,19,18,19,20,
21,20,21,20,21,22,23,22,23,22,23,24,25,24,25,24,25,26,27,26,27,26,27,28,
29,28,29,28,29,30,31,32,33,34,35,36,37,38,39,38,39,38,39]);
ALF("6_2.U4(3)","3_2.U4(3)",[1,2,3,1,2,3,4,5,6,4,5,6,7,8,9,7,8,9,10,10,11,
11,12,12,13,14,15,13,14,15,16,17,18,19,20,21,19,20,21,22,23,24,22,23,24,
25,26,27,25,26,27,28,29,30,28,29,30,31,32,33,31,32,33,34,35,36,34,35,36,
37,38,39,37,38,39,40,40,41,41,42,42,43,43,44,45,46,44,45,46]);
ALF("6_2.U4(3)","6_2.U4(3).2_1",[1,2,3,4,3,2,5,6,7,8,7,6,9,10,11,12,11,10,
13,14,15,16,17,18,19,20,21,22,21,20,23,24,24,25,26,27,28,27,26,29,30,31,
32,31,30,33,34,35,36,35,34,37,38,39,40,39,38,41,42,43,44,43,42,45,46,47,
48,47,46,49,50,51,52,51,50,53,54,53,54,55,56,55,56,57,58,59,60,59,58],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);
ALF("6_2.U4(3)","6_2.U4(3).2_3",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,
17,18,19,20,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,
39,40,41,42,43,44,45,46,47,48,49,44,45,46,47,48,49,50,51,52,53,54,55,50,
51,52,53,54,55,56,57,58,56,57,58,59,60,61,62,59,60,61,62,63,64,65,66,67,
68],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("6_2.U4(3)","6_2.U4(3).2_3'",[1,2,3,4,3,2,5,6,7,8,7,6,9,10,11,12,11,10,
13,14,13,14,15,16,17,18,19,20,19,18,21,22,22,23,24,25,26,25,24,27,28,29,30,
29,28,31,32,33,34,35,36,31,36,35,34,33,32,37,38,39,40,41,42,37,42,41,40,39,
38,43,44,44,43,45,45,46,47,48,49,48,49,46,47,50,51,52,53,52,51],[
"fusion map determined up to table aut. by compatibility\n",
"with factors"
]);

MOT("6_2.U4(3).2_1",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[39191040,19595520,19595520,39191040,13824,6912,6912,13824,69984,34992,34992,
69984,3888,3888,3888,3888,324,324,1152,576,576,1152,96,48,60,30,30,60,864,432,
432,864,432,216,216,432,432,216,216,432,84,42,42,84,84,42,42,84,96,48,48,96,
54,54,54,54,144,72,72,144,24192,24192,2880,2880,2304,2304,128,432,432,72,72,
72,72,36,36,32,32,20,20,288,288,288,288,72,72,72,72,28,28,28,28],
[,[1,3,3,1,1,3,3,1,9,11,11,9,13,13,15,15,17,17,5,7,7,5,8,6,25,27,27,25,9,11,
11,9,13,13,13,13,15,15,15,15,41,43,43,41,45,47,47,45,22,20,20,22,53,53,55,55,
29,31,31,29,1,1,4,4,5,5,5,9,9,14,14,16,16,17,17,22,22,28,28,29,29,29,29,33,33,
37,37,41,41,45,45],[1,4,1,4,5,8,5,8,1,4,1,4,1,4,1,4,1,4,19,22,19,22,23,23,25,
28,25,28,5,8,5,8,5,8,5,8,5,8,5,8,45,48,45,48,41,44,41,44,52,49,52,49,11,10,11,
10,19,22,19,22,61,62,64,63,66,65,67,61,62,64,63,64,63,61,62,77,76,79,78,66,65,
66,65,66,65,66,65,90,91,88,89],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,
19,20,21,22,23,24,1,2,3,4,29,30,31,32,33,34,35,36,37,38,39,40,45,46,47,48,41,
42,43,44,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,
72,73,74,75,76,77,63,64,80,81,82,83,84,85,86,87,90,91,88,89],,[1,2,3,4,5,6,7,
8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,
34,35,36,37,38,39,40,1,2,3,4,1,2,3,4,52,51,50,49,53,54,55,56,57,58,59,60,61,
62,64,63,66,65,67,68,69,71,70,73,72,74,75,77,76,79,78,83,82,81,80,85,84,87,86,
61,62,61,62]],
0,
[(49,52)(50,51)(63,64)(65,66)(70,71)(72,73)(76,77)(78,79)(80,83)(81,82)(84,85)
(86,87),(41,45)(42,46)(43,47)(44,48)(88,90)(89,91),(61,62)(63,64)(65,66)
(68,69)(70,71)(72,73)(74,75)(76,77)(78,79)(80,81)(82,83)(84,85)(86,87)(88,89)
(90,91),(13,15)(14,16)(33,37)(34,38)(35,39)(36,40)(53,55)(54,56)(70,72)(71,73)
(84,86)(85,87)],
["ConstructMGA","6_2.U4(3)","2.U4(3).2_1",
     [ [ 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 ] ], ()]);
ALF("6_2.U4(3).2_1","U4(3).2_1",[1,1,1,1,2,2,2,2,3,3,3,3,4,4,5,5,6,6,7,7,
7,7,8,8,9,9,9,9,10,10,10,10,11,11,11,11,12,12,12,12,13,13,13,13,14,14,14,
14,15,15,15,15,16,16,17,17,18,18,18,18,19,19,20,20,21,21,22,23,23,24,24,
25,25,26,26,27,27,28,28,29,29,30,30,31,31,32,32,33,33,34,34]);
ALF("6_2.U4(3).2_1","2.U4(3).2_1",[1,2,1,2,3,4,3,4,5,6,5,6,7,8,9,10,11,12,
13,14,13,14,15,15,16,17,16,17,18,19,18,19,20,21,20,21,22,23,22,23,24,25,
24,25,26,27,26,27,28,29,28,29,30,31,32,33,34,35,34,35,36,37,38,39,40,41,
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]);
ALF("6_2.U4(3).2_1","3_2.U4(3).2_1",[1,2,2,1,3,4,4,3,5,6,6,5,7,7,8,8,9,9,
10,11,11,10,12,13,14,15,15,14,16,17,17,16,18,19,19,18,20,21,21,20,22,23,
23,22,24,25,25,24,26,27,27,26,28,28,29,29,30,31,31,30,32,32,33,33,34,34,
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]);

MOT("Isoclinic(6_2.U4(3).2_1)",
[
"isoclinic group of the 6_2.U4(3).2_1 given in the ATLAS"
],
0,
0,
0,
[(61,62)(63,64)(65,66)(68,69)(70,71)(72,73)(74,75)(76,77)(78,79)(80,81)(82,83)
(84,85)(86,87)(88,89)(90,91),(49,52)(50,51)(63,64)(65,66)(70,71)(72,73)(76,77)
(78,79)(80,83)(81,82)(84,85)(86,87),(41,45)(42,46)(43,47)(44,48)(88,90)(89,91)
,(13,15)(14,16)(33,37)(34,38)(35,39)(36,40)(53,55)(54,56)(70,72)(71,73)(84,86)
(85,87)],
["ConstructIsoclinic",[["6_2.U4(3).2_1"]]]);
ALF("Isoclinic(6_2.U4(3).2_1)","3_2.U4(3).2_1",[1,2,2,1,3,4,4,3,5,6,6,5,7,
7,8,8,9,9,10,11,11,10,12,13,14,15,15,14,16,17,17,16,18,19,19,18,20,21,21,
20,22,23,23,22,24,25,25,24,26,27,27,26,28,28,29,29,30,31,31,30,32,32,33,
33,34,34,35,36,36,37,37,38,38,39,39,40,40,41,41,42,42,43,43,44,44,45,45,
46,46,47,47]);

MOT("6_2.U4(3).2_3",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]\n",
"3rd power map determined only up to table automorphism (59,61)(60,62)"
],
[39191040,39191040,39191040,39191040,39191040,39191040,13824,13824,13824,
13824,13824,13824,69984,69984,69984,69984,69984,69984,1944,1944,324,324,1152,
1152,1152,1152,1152,1152,96,96,96,60,60,60,60,60,60,864,864,864,864,864,864,
216,216,216,216,216,216,42,42,42,42,42,42,48,48,48,54,54,54,54,144,144,144,
144,144,144,4320,4320,4320,288,288,288,36,36,576,576,576,576,576,576,96,96,96,
48,48,48,48,48,48,60,60,60,60,60,60,72,72,72,72,72,72,144,144,144,144,144,144,
144,144,144,144,144,144],
[,[1,3,5,1,3,5,1,3,5,1,3,5,13,15,17,13,15,17,19,19,21,21,7,9,11,7,9,11,10,12,
8,32,34,36,32,34,36,13,15,17,13,15,17,19,19,19,19,19,19,50,52,54,50,52,54,26,
28,24,61,61,59,59,38,40,42,38,40,42,1,3,5,7,9,11,21,21,23,25,27,23,25,27,23,
25,27,29,31,30,29,31,30,32,34,36,32,34,36,38,40,42,38,40,42,63,65,67,63,65,67,
63,65,67,63,65,67],[1,4,1,4,1,4,7,10,7,10,7,10,1,4,1,4,1,4,1,4,1,4,23,26,23,
26,23,26,29,29,29,32,35,32,35,32,35,7,10,7,10,7,10,7,10,7,10,7,10,50,53,50,53,
50,53,56,56,56,15,18,17,14,23,26,23,26,23,26,69,69,69,72,72,72,69,69,80,77,80,
77,80,77,83,83,83,89,86,89,86,89,86,95,92,95,92,95,92,72,72,72,72,72,72,80,77,
80,77,80,77,80,77,80,77,80,77],,[1,6,5,4,3,2,7,12,11,10,9,8,13,18,17,16,15,14,
19,20,21,22,23,28,27,26,25,24,29,31,30,1,6,5,4,3,2,38,43,42,41,40,39,44,49,48,
47,46,45,50,55,54,53,52,51,56,58,57,61,62,59,60,63,68,67,66,65,64,69,71,70,72,
74,73,75,76,80,79,78,77,82,81,83,85,84,89,88,87,86,91,90,69,71,70,69,71,70,
101,100,99,98,103,102,107,106,105,104,109,108,113,112,111,110,115,114],,[1,2,
3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,
31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,1,2,3,4,5,6,56,57,58,
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,
85,86,87,88,89,90,91,95,96,97,92,93,94,98,99,100,101,102,103,104,105,106,107,
108,109,110,111,112,113,114,115]],
0,
[(92,95)(93,96)(94,97),( 77, 80)( 78, 81)( 79, 82)( 86, 89)( 87, 90)( 88, 91)
(104,113)(105,114)(106,115)(107,110)(108,111)(109,112),(75,76),(  2,  6)
(  3,  5)(  8, 12)(  9, 11)( 14, 18)( 15, 17)( 24, 28)( 25, 27)( 30, 31)
( 33, 37)( 34, 36)( 39, 43)( 40, 42)( 45, 49)( 46, 48)( 51, 55)( 52, 54)
( 57, 58)( 59, 61)( 60, 62)( 64, 68)( 65, 67)( 70, 71)( 73, 74)( 78, 82)
( 79, 81)( 84, 85)( 87, 91)( 88, 90)( 93, 97)( 94, 96)( 98,101)( 99,100)
(102,103)(104,110)(105,115)(106,114)(107,113)(108,112)(109,111),( 77, 80)
( 78, 81)( 79, 82)( 86, 89)( 87, 90)( 88, 91)( 98,101)( 99,102)(100,103)
(104,107)(105,108)(106,109)(110,113)(111,114)(112,115)],
["ConstructProj",[["U4(3).2_3",[]],["2.U4(3).2_3",[]],["3_2.U4(3).2_3",[-1,-1,
-1,-1,-1,-1,-1,17,-1,-1,-1]],,,["6_2.U4(3).2_3",[17,-1,-1,-1,11,-1,17,17,
-1]]]]);
ALF("6_2.U4(3).2_3","U4(3).2_3",[1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,4,4,
5,5,6,6,6,6,6,6,7,7,7,8,8,8,8,8,8,9,9,9,9,9,9,10,10,10,10,10,10,11,11,11,
11,11,11,12,12,12,13,13,14,14,15,15,15,15,15,15,16,16,16,17,17,17,18,18,
19,19,19,19,19,19,20,20,20,21,21,21,21,21,21,22,22,22,22,22,22,23,23,23,
23,23,23,24,24,24,24,24,24,25,25,25,25,25,25]);
ALF("6_2.U4(3).2_3","2.U4(3).2_3",[1,2,1,2,1,2,3,4,3,4,3,4,5,6,5,6,5,6,7,
8,9,10,11,12,11,12,11,12,13,13,13,14,15,14,15,14,15,16,17,16,17,16,17,18,
19,18,19,18,19,20,21,20,21,20,21,22,22,22,23,24,25,26,27,28,27,28,27,28,
29,29,29,30,30,30,31,32,33,34,33,34,33,34,35,35,35,36,37,36,37,36,37,38,
39,38,39,38,39,40,41,40,41,40,41,42,43,42,43,42,43,44,45,44,45,44,45]);
ALF("6_2.U4(3).2_3","3_2.U4(3).2_3",[1,2,3,1,2,3,4,5,6,4,5,6,7,8,9,7,8,9,
10,10,11,11,12,13,14,12,13,14,15,16,17,18,19,20,18,19,20,21,22,23,21,22,
23,24,25,26,24,25,26,27,28,29,27,28,29,30,31,32,33,33,34,34,35,36,37,35,
36,37,38,39,40,41,42,43,44,44,45,46,47,45,46,47,48,49,50,51,52,53,51,52,
53,54,55,56,54,55,56,57,58,59,57,58,59,60,61,62,60,61,62,63,64,65,63,64,
65]);

MOT("Isoclinic(6_2.U4(3).2_3)",
[
"isoclinic group of the 6_2.U4(3).2_3 given in the ATLAS"
],
0,
0,
0,
[(98,101)(99,102)(100,103)(104,110)(105,111)(106,112)(107,113)(108,114)(109,
115),(92,95)(93,96)(94,97),(77,80)(78,81)(79,82)(86,89)(87,90)(88,91)(104,113)
(105,114)(106,115)(107,110)(108,111)(109,112),(75,76),(2,6)(3,5)(8,12)(9,11)
(14,18)(15,17)(24,28)(25,27)(30,31)(33,37)(34,36)(39,43)(40,42)(45,49)(46,48)
(51,55)(52,54)(57,58)(59,61)(60,62)(64,68)(65,67)(70,71)(73,74)(78,82)(79,81)
(84,85)(87,91)(88,90)(93,97)(94,96)(98,101)(99,100)(102,103)(104,110)(105,115)
(106,114)(107,113)(108,112)(109,111)],
["ConstructIsoclinic",[["6_2.U4(3).2_3"]]]);
ALF("Isoclinic(6_2.U4(3).2_3)","U4(3).2_3",[1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,
3,3,3,4,4,5,5,6,6,6,6,6,6,7,7,7,8,8,8,8,8,8,9,9,9,9,9,9,10,10,10,10,10,10,
11,11,11,11,11,11,12,12,12,13,13,14,14,15,15,15,15,15,15,16,16,16,17,17,
17,18,18,19,19,19,19,19,19,20,20,20,21,21,21,21,21,21,22,22,22,22,22,22,
23,23,23,23,23,23,24,24,24,24,24,24,25,25,25,25,25,25]);

MOT("6_2.U4(3).2_3'",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[39191040,19595520,19595520,39191040,13824,6912,6912,13824,69984,34992,34992,
69984,1944,1944,324,324,1152,576,576,1152,96,48,60,30,30,60,864,432,432,864,
216,216,216,216,216,216,42,42,42,42,42,42,48,48,48,54,54,54,54,144,72,72,144,
1440,96,36,36,192,192,32,16,16,20,20,24,24,48,48,48,48],
[,[1,3,3,1,1,3,3,1,9,11,11,9,13,13,15,15,5,7,7,5,8,6,23,25,25,23,9,11,11,9,
13,13,13,13,13,13,37,39,41,37,39,41,20,18,18,48,48,46,46,27,29,29,27,1,5,15,
15,17,17,17,21,21,23,23,27,27,50,50,50,50],[1,4,1,4,5,8,5,8,1,4,1,4,1,4,1,4,
17,20,17,20,21,21,23,26,23,26,5,8,5,8,5,8,5,8,5,8,37,40,37,40,37,40,43,43,43,
11,10,11,10,17,20,17,20,54,55,54,54,59,58,60,62,61,64,63,55,55,59,58,59,58],,
[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,
30,31,36,35,34,33,32,37,38,39,40,41,42,43,45,44,48,49,46,47,50,51,52,53,54,
55,56,57,59,58,60,62,61,54,54,66,65,68,67,70,69],,[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,
2,3,4,3,2,43,45,44,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,64,63,
65,66,67,68,69,70]],
0,
[(65,66)(67,69)(68,70),(63,64),(58,59)(61,62)(67,70)(68,69),(56,57),(44,45),
(38,42)(39,41),(32,36)(33,35),(46,48)(47,49)],
["ConstructMGA","6_2.U4(3)","2.U4(3).2_3'",
     [ [ 40, 41 ], [ 42, 45 ], [ 43, 44 ], [ 46, 47 ], [ 48, 49 ],
        [ 50, 51 ], [ 52, 55 ], [ 53, 54 ], [ 56, 57 ], [ 58, 59 ],
        [ 60, 61 ], [ 62, 63 ], [ 64, 65 ], [ 66, 67 ], [ 68, 71 ],
        [ 69, 70 ], [ 72, 75 ], [ 73, 74 ], [ 76, 79 ], [ 77, 78 ],
        [ 80, 81 ], [ 82, 83 ], [ 84, 85 ], [ 86, 87 ], [ 88, 89 ] ], ()]);
ALF("6_2.U4(3).2_3'","U4(3).2_3'",[1,1,1,1,2,2,2,2,3,3,3,3,4,4,5,5,6,6,6,
6,7,7,8,8,8,8,9,9,9,9,10,10,10,10,10,10,11,11,11,11,11,11,12,12,12,13,13,
14,14,15,15,15,15,16,17,18,18,19,19,20,21,21,22,22,23,23,24,24,25,25]);
ALF("6_2.U4(3).2_3'","2.U4(3).2_3'",[1,2,1,2,3,4,3,4,5,6,5,6,7,8,9,10,11,12,
11,12,13,13,14,15,14,15,16,17,16,17,18,19,18,19,18,19,20,21,20,21,20,21,22,
22,22,23,24,25,26,27,28,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,
44,45]);
ALF("6_2.U4(3).2_3'","3_2.U4(3).2_3'",[1,2,2,1,3,4,4,3,5,6,6,5,7,7,8,8,9,
10,10,9,11,12,13,14,14,13,15,16,16,15,17,18,19,17,18,19,20,21,22,20,21,22,
23,24,24,25,25,26,26,27,28,28,27,29,30,31,31,32,32,33,34,34,35,35,36,36,
37,37,38,38]);

MOT("Isoclinic(6_2.U4(3).2_3')",
[
"2nd maximal subgroup of 2.Suz,\n",
"isoclinic group of the 6_2.U4(3).2_3' given in the ATLAS"
],
0,
0,
0,
[(65,66)(67,69)(68,70),(63,64),(58,59)(61,62)(67,70)(68,69),(56,57),(44,45),
(38,42)(39,41),(32,36)(33,35),(46,48)(47,49)],
["ConstructIsoclinic",[["6_2.U4(3).2_3'"]]]);
ALF("Isoclinic(6_2.U4(3).2_3')","2.Suz",[1,7,6,2,3,22,21,4,6,9,8,7,8,9,10,
11,13,45,46,12,15,49,19,64,63,20,21,28,27,22,27,24,25,28,23,26,30,72,73,
31,71,74,32,75,76,36,37,38,39,46,47,48,45,5,15,29,29,32,32,32,35,35,42,42,
49,49,75,76,76,75],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("Isoclinic(6_2.U4(3).2_3')","3_2.U4(3).2_3'",[1,2,2,1,3,4,4,3,5,6,6,5,
7,7,8,8,9,10,10,9,11,12,13,14,14,13,15,16,16,15,17,18,19,17,18,19,20,21,
22,20,21,22,23,24,24,25,25,26,26,27,28,28,27,29,30,31,31,32,32,33,34,34,
35,35,36,36,37,37,38,38]);
ALN("Isoclinic(6_2.U4(3).2_3')",["6_2.U4(3).2_3'*","2.SuzN3A"]);

MOT("U4(3)",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[3265920,1152,5832,972,972,81,96,16,5,72,36,36,7,7,8,27,27,27,27,12],
[,[1,1,3,4,5,6,2,2,9,3,4,5,13,14,7,17,16,19,18,10],[1,2,1,1,1,1,7,8,9,2,2,2,
14,13,15,3,3,3,3,7],,[1,2,3,4,5,6,7,8,1,10,11,12,14,13,15,17,16,19,18,20],,[1,
2,3,4,5,6,7,8,9,10,11,12,1,1,15,16,17,18,19,20]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[21,5,-6,3,3,3,1,1,1,2,-1,-1,0,0,
-1,0,0,0,0,-2],[35,3,8,8,-1,-1,3,-1,0,0,0,3,0,0,-1,2,2,-1,-1,0],[35,3,8,-1,8,
-1,3,-1,0,0,3,0,0,0,-1,-1,-1,2,2,0],[90,10,9,9,9,0,-2,2,0,1,1,1,-1,-1,0,0,0,0,
0,1],[140,12,5,-4,-4,5,4,0,0,-3,0,0,0,0,0,-1,-1,-1,-1,1],[189,-3,27,0,0,0,5,1,
-1,3,0,0,0,0,1,0,0,0,0,-1],[210,2,21,3,3,3,-2,-2,0,5,-1,-1,0,0,0,0,0,0,0,1],[
280,-8,10,10,1,1,0,0,0,-2,-2,1,0,0,0,2*E(3)-E(3)^2,-E(3)+2*E(3)^2,1,1,0],
[GALOIS,[9,2]],[280,-8,10,1,10,1,0,0,0,-2,1,-2,0,0,0,1,1,2*E(3)-E(3)^2,
-E(3)+2*E(3)^2,0],
[GALOIS,[11,2]],[315,11,-9,18,-9,0,-1,-1,0,-1,2,-1,0,0,1,0,0,0,0,-1],[315,11,
-9,-9,18,0,-1,-1,0,-1,-1,2,0,0,1,0,0,0,0,-1],[420,4,-39,6,6,-3,4,0,0,1,-2,-2,
0,0,0,0,0,0,0,1],[560,-16,-34,2,2,2,0,0,0,2,2,2,0,0,0,-1,-1,-1,-1,0],[640,0,
-8,-8,-8,1,0,0,0,0,0,0,E(7)+E(7)^2+E(7)^4,E(7)^3+E(7)^5+E(7)^6,0,1,1,1,1,0],
[GALOIS,[17,3]],[729,9,0,0,0,0,-3,1,-1,0,0,0,1,1,-1,0,0,0,0,0],[896,0,32,-4,
-4,-4,0,0,1,0,0,0,0,0,0,-1,-1,-1,-1,0]],
[(16,17)(18,19),(13,14),(18,19),( 4, 5)(11,12)(16,18)(17,19)]);
ARC("U4(3)","CAS",[rec(name:="u4q3",
permchars:=( 9,12,10,11),
permclasses:=(16,18,17,19),
text:=[
"names:u4q3; psu4[3]\n",
"2a3(3)    (lie-not.)\n",
"order: 2^7.3^6.5.7 = 3,265,920\n",
"number of classes: 20\n",
"source:wright, donald\n",
"the irreducible characters of the simple group\n",
"of m. suzuki of order 448,345,497,600\n",
"j.algebra 29\n",
"(1974),303-323\n",
"test: 1. o.r., sym 2 decompose correctly\n",
"comments: - \n",
""])]);
ARC("U4(3)","projectives",["2.U4(3)",[[20,4,-7,2,2,2,4,0,0,1,-2,-2,-1,-1,0,-1,
-1,-1,-1,1],[56,-8,2,11,2,2,0,0,1,-2,1,-2,0,0,0,2,2,-1,-1,0],[56,-8,2,2,11,2,
0,0,1,-2,-2,1,0,0,0,-1,-1,2,2,0],[70,-2,16,7,7,-2,2,0,0,4,1,1,0,0,0,1,1,1,1,
2],[70,-2,-11,7,-2,-2,2,0,0,1,1,-2,0,0,0,2*E(3)-E(3)^2,-E(3)+2*E(3)^2,1,1,-1],
[GALOIS,[5,2]],[70,-2,-11,-2,7,-2,2,0,0,1,-2,1,0,0,0,1,1,2*E(3)-E(3)^2,
-E(3)+2*E(3)^2,-1],
[GALOIS,[7,2]],[120,-8,12,-6,-6,3,0,0,0,4,-2,-2,1,1,0,0,0,0,0,0],[210,10,21,3,
3,3,2,0,0,1,1,1,0,0,2*E(4),0,0,0,0,-1],
[GALOIS,[10,3]],[504,-8,18,18,-9,0,0,0,-1,-2,-2,1,0,0,0,0,0,0,0,0],[504,-8,18,
-9,18,0,0,0,-1,-2,1,-2,0,0,0,0,0,0,0,0],[540,12,-27,0,0,0,4,0,0,-3,0,0,1,1,0,
0,0,0,0,1],[560,-16,-34,2,2,2,0,0,0,2,2,2,0,0,0,-1,-1,-1,-1,0],[630,14,-18,9,
9,0,-6,0,0,2,-1,-1,0,0,0,0,0,0,0,0],[640,0,-8,-8,-8,1,0,0,0,0,0,0,
E(7)+E(7)^2+E(7)^4,E(7)^3+E(7)^5+E(7)^6,0,1,1,1,1,0],
[GALOIS,[17,3]],[896,0,32,-4,-4,-4,0,0,1,0,0,0,0,0,0,-1,-1,-1,-1,
0]],"4.U4(3)",[[20,0,-7,2,2,2,2,0,0,-3,0,0,-1,-1,-1-E(4),-1,-1,-1,-1,-1],[120,
0,12,-6,-6,3,4,0,0,0,0,0,1,1,0,0,0,0,0,-2],[140,0,5,-4,-4,5,-2,0,0,-3,0,0,0,0,
1+E(4),-1,-1,-1,-1,1],[224,0,8,8,-10,-1,0,0,-1,0,0,0,0,0,0,-2*E(3)+E(3)^2,
E(3)-2*E(3)^2,-1,-1,0],
[GALOIS,[4,2]],[224,0,8,-10,8,-1,0,0,-1,0,0,0,0,0,0,-1,-1,-2*E(3)+E(3)^2,
E(3)-2*E(3)^2,0],
[GALOIS,[6,2]],[280,0,37,10,10,1,4,0,0,-3,0,0,0,0,0,1,1,1,1,1],[280,0,-17,10,
-8,1,4,0,0,3,0,0,0,0,0,-2,-2,1,1,1],[280,0,-17,-8,10,1,4,0,0,3,0,0,0,0,0,1,1,
-2,-2,1],[420,0,-39,6,6,-3,2,0,0,-3,0,0,0,0,1+E(4),0,0,0,0,-1],[540,0,-27,0,0,
0,-2,0,0,-3,0,0,1,1,-1-E(4),0,0,0,0,1],[640,0,-8,-8,-8,1,0,0,0,0,0,0,
E(7)+E(7)^2+E(7)^4,E(7)^3+E(7)^5+E(7)^6,0,1,1,1,1,0],
[GALOIS,[13,3]],[840,0,3,12,12,3,-4,0,0,3,0,0,0,0,0,0,0,0,0,-1],[896,0,32,-4,
-4,-4,0,0,1,0,0,0,0,0,0,-1,-1,-1,-1,0]],"3_1.U4(3)",[[15,-1,6,3,0,0,3,-1,0,2,
-1,2,1,1,1,E(3)+2*E(3)^2,2*E(3)+E(3)^2,0,0,0],[21,5,3,6,0,0,1,1,1,-1,2,2,0,0,
-1,2*E(3)+E(3)^2,E(3)+2*E(3)^2,0,0,1],[105,9,15,3,0,0,1,1,0,3,3,0,0,0,1,
-2*E(3)-E(3)^2,-E(3)-2*E(3)^2,0,0,1],[105,-7,15,3,0,0,5,1,0,-1,-1,2,0,0,-1,
-2*E(3)-E(3)^2,-E(3)-2*E(3)^2,0,0,-1],[105,9,-12,12,0,0,1,1,0,0,0,0,0,0,1,
E(3)-E(3)^2,-E(3)+E(3)^2,0,0,-2],[210,2,3,15,0,0,-2,-2,0,-1,-1,2,0,0,0,
-E(3)-2*E(3)^2,-2*E(3)-E(3)^2,0,0,1],[315,-5,-36,9,0,0,3,-1,0,4,1,-2,0,0,-1,0,
0,0,0,0],[336,16,-6,6,0,0,0,0,1,-2,-2,-2,0,0,0,-E(3)+E(3)^2,E(3)-E(3)^2,0,0,
0],[360,8,-18,-9,0,0,0,0,0,2,-1,2,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]],[384,0,24,12,0,0,0,0,-1,0,0,0,-1,-1,0,E(3)+2*E(3)^2,
2*E(3)+E(3)^2,0,0,0],[420,4,33,-6,0,0,4,0,0,1,-2,-2,0,0,0,E(3)-E(3)^2,
-E(3)+E(3)^2,0,0,1],[630,6,9,-9,0,0,2,-2,0,-3,3,0,0,0,0,0,0,0,0,-1],[729,9,0,
0,0,0,-3,1,-1,0,0,0,1,1,-1,0,0,0,0,0],[756,-12,27,0,0,0,-4,0,1,3,0,0,0,0,0,0,
0,0,0,-1],[945,-15,-27,0,0,0,1,1,0,-3,0,0,0,0,1,0,0,0,0,1]],"3_2.U4(3)",[[36,
4,9,0,0,0,4,0,1,1,-2,-2,1,1,0,0,0,0,0,1],[45,-3,-9,0,0,0,1,1,0,3,0,0,
E(7)+E(7)^2+E(7)^4,E(7)^3+E(7)^5+E(7)^6,-1,0,0,0,0,1],
[GALOIS,[2,3]],[126,14,-9,0,0,0,2,2,1,-1,2,2,0,0,0,0,0,0,0,-1],[189,-3,27,0,0,
0,5,1,-1,3,0,0,0,0,1,0,0,0,0,-1],[315,11,18,0,0,0,-1,-1,0,2,2,2,0,0,1,0,0,0,0,
2],[315,-5,18,0,0,0,3,-1,0,-2,-2,4,0,0,-1,0,0,0,0,0],[315,-5,18,0,0,0,3,-1,0,
-2,4,-2,0,0,-1,0,0,0,0,0],[630,6,-45,0,0,0,2,-2,0,3,0,0,0,0,0,0,0,0,0,-1],[
720,16,18,0,0,0,0,0,0,-2,-2,-2,-1,-1,0,0,0,0,0,0],[729,9,0,0,0,0,-3,1,-1,0,0,
0,1,1,-1,0,0,0,0,0],[756,-12,27,0,0,0,-4,0,1,3,0,0,0,0,0,0,0,0,0,-1],[945,-15,
-27,0,0,0,1,1,0,-3,0,0,0,0,1,0,0,0,0,1]],"6_1.U4(3)",[[6,-2,-3,3,0,0,2,0,1,1,
1,-2,-1,-1,0,E(3)-E(3)^2,-E(3)+E(3)^2,0,0,-1],[84,4,-15,6,0,0,4,0,-1,1,-2,-2,
0,0,0,-E(3)-2*E(3)^2,-2*E(3)-E(3)^2,0,0,1],[120,-8,-6,15,0,0,0,0,0,-2,1,-2,1,
1,0,2*E(3)+E(3)^2,E(3)+2*E(3)^2,0,0,0],[126,-10,18,9,0,0,2,0,1,2,-1,2,0,0,0,0,
0,0,0,2],[210,-6,-24,-3,0,0,6,0,0,0,3,0,0,0,0,-E(3)+E(3)^2,E(3)-E(3)^2,0,0,
0],[270,6,27,0,0,0,2,0,0,3,0,0,-E(7)-E(7)^2-E(7)^4,-E(7)^3-E(7)^5-E(7)^6,0,0,
0,0,0,-1],
[GALOIS,[6,3]],[336,16,-6,6,0,0,0,0,1,-2,-2,-2,0,0,0,-E(3)+E(3)^2,E(3)-E(3)^2,
0,0,0],[384,0,24,12,0,0,0,0,-1,0,0,0,-1,-1,0,E(3)+2*E(3)^2,2*E(3)+E(3)^2,0,0,
0],[420,-12,-21,12,0,0,-4,0,0,3,0,0,0,0,0,-2*E(3)-E(3)^2,-E(3)-2*E(3)^2,0,0,
-1],[630,-18,9,-9,0,0,2,0,0,-3,-3,0,0,0,0,0,0,0,0,-1],[630,-2,9,-9,0,0,-2,0,0,
1,1,-2,0,0,2*E(4),0,0,0,0,1],
[GALOIS,[12,3]],[840,8,12,6,0,0,0,0,0,-4,2,2,0,0,0,-E(3)-2*E(3)^2,
-2*E(3)-E(3)^2,0,0,0],[840,8,-42,-3,0,0,0,0,0,2,-1,2,0,0,0,2*E(3)+E(3)^2,
E(3)+2*E(3)^2,0,0,0]],"6_2.U4(3)",[[90,2,-18,0,0,0,6,0,0,2,2,2,-1,-1,0,0,0,0,
0,0],[126,-10,-9,0,0,0,2,0,1,-1,-4,2,0,0,0,0,0,0,0,-1],[126,-10,-9,0,0,0,2,0,
1,-1,2,-4,0,0,0,0,0,0,0,-1],[126,6,-9,0,0,0,-2,0,1,3,0,0,0,0,2*E(4),0,0,0,0,
1],
[GALOIS,[4,3]],[270,6,27,0,0,0,2,0,0,3,0,0,-E(7)-E(7)^2-E(7)^4,
-E(7)^3-E(7)^5-E(7)^6,0,0,0,0,0,-1],
[GALOIS,[6,3]],[504,-8,-36,0,0,0,0,0,-1,4,-2,-2,0,0,0,0,0,0,0,0],[540,12,-27,
0,0,0,4,0,0,-3,0,0,1,1,0,0,0,0,0,1],[630,-18,36,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,
0,2],[720,16,18,0,0,0,0,0,0,-2,-2,-2,-1,-1,0,0,0,0,0,0],[1260,-4,-9,0,0,0,-4,
0,0,-1,2,2,0,0,0,0,0,0,0,-1]],"12_1.U4(3)",[[84,0,-15,6,0,0,2,0,-1,-3,0,0,0,0,
-1-E(4),-E(3)-2*E(3)^2,-2*E(3)-E(3)^2,0,0,-1],[120,0,21,6,0,0,4,0,0,-3,0,0,1,
1,0,-E(3)+E(3)^2,E(3)-E(3)^2,0,0,1],[216,0,-27,0,0,0,4,0,1,-3,0,0,-1,-1,0,0,0,
0,0,1],[384,0,24,12,0,0,0,0,-1,0,0,0,-1,-1,0,E(3)+2*E(3)^2,2*E(3)+E(3)^2,0,0,
0],[420,0,-21,12,0,0,2,0,0,3,0,0,0,0,1+E(4),-2*E(3)-E(3)^2,-E(3)-2*E(3)^2,0,0,
-1],[420,0,33,-6,0,0,2,0,0,-3,0,0,0,0,1+E(4),E(3)-E(3)^2,-E(3)+E(3)^2,0,0,
-1],[480,0,-24,6,0,0,0,0,0,0,0,0,-E(7)-E(7)^2-E(7)^4,-E(7)^3-E(7)^5-E(7)^6,0,
2*E(3)+E(3)^2,E(3)+2*E(3)^2,0,0,0],
[GALOIS,[7,10]],[504,0,-9,-18,0,0,4,0,-1,3,0,0,0,0,0,0,0,0,0,1],[756,0,27,0,0,
0,2,0,1,3,0,0,0,0,-1-E(4),0,0,0,0,-1],[840,0,-15,-12,0,0,-4,0,0,-3,0,0,0,0,0,
-E(3)+E(3)^2,E(3)-E(3)^2,0,0,-1],[840,0,12,6,0,0,-4,0,0,0,0,0,0,0,0,
-E(3)-2*E(3)^2,-2*E(3)-E(3)^2,0,0,2]],"12_2.U4(3)",[[36,0,9,0,0,0,2,0,1,-3,0,
0,1,1,1+E(4),0,0,0,0,-1],[216,0,-27,0,0,0,4,0,1,-3,0,0,-1,-1,0,0,0,0,0,1],[
360,0,9,0,0,0,-4,0,0,-3,0,0,E(7)+E(7)^2+E(7)^4,E(7)^3+E(7)^5+E(7)^6,0,0,0,0,0,
-1],
[GALOIS,[3,3]],[504,0,-36,0,0,0,4,0,-1,0,0,0,0,0,0,0,0,0,0,-2],[504,0,45,0,0,
0,4,0,-1,-3,0,0,0,0,0,0,0,0,0,1],[540,0,-27,0,0,0,-2,0,0,-3,0,0,1,1,-1-E(4),0,
0,0,0,1],[756,0,27,0,0,0,2,0,1,3,0,0,0,0,-1-E(4),0,0,0,0,-1],[1260,0,-9,0,0,0,
-2,0,0,3,0,0,0,0,1+E(4),0,0,0,0,1]],]);
ARC("U4(3)","isSimple",true);
ARC("U4(3)","extInfo",["(3^2x4)","D8"]);
ARC("U4(3)","tomfusion",rec(name:="U4(3)",map:=[1,2,3,5,6,4,10,11,12,13,
14,15,19,19,28,38,38,39,39,52],text:=[
"fusion map is unique up to table autom."
],perm:=(8,9)));
ALF("U4(3)","U4(3).2_1",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,16,17,17,
18]);
ALF("U4(3)","U4(3).2_2",[1,2,3,4,5,6,7,8,9,10,11,12,13,13,14,15,16,17,17,
18]);
ALF("U4(3)","U4(3).2_2'",[1,2,3,4,5,6,7,8,9,10,11,12,13,13,14,15,15,16,17,
18]);
ALF("U4(3)","U4(3).2_3",[1,2,3,4,4,5,6,7,8,9,10,10,11,11,12,13,14,13,14,
15]);
ALF("U4(3)","U4(3).2_3'",[1,2,3,4,4,5,6,7,8,9,10,10,11,11,12,13,14,14,13,
15]);
ALF("U4(3)","U4(3).4",[1,2,3,4,4,5,6,7,8,9,10,10,11,12,13,14,14,14,14,15]);
ALF("U4(3)","Co3",[1,2,4,5,5,5,8,8,10,11,13,13,16,16,19,21,21,21,21,27],[
"fusion map is unique, equal to that on the CAS table"
]);
ALF("U4(3)","Fi22",[1,3,6,5,7,7,9,13,14,17,18,23,26,26,28,31,31,32,32,38],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("U4(3)","McL",[1,2,3,4,4,4,5,5,7,8,9,9,10,11,12,13,14,13,14,18],[
"fusion map is unique up to table automorphisms,\n",
"compatible with 3_2.U4(3) -> 3.McL"
]);
ARC("U4(3)","maxes",["3^4:A6","U4(2)","U4(3)M3","L3(4)","L3(4)",
"3^(1+4)_+.2S4","U3(3)","2^4:a6","U4(3)M9","A7","A7","U4(3)M12","U4(3)M12",
"2(A4xA4).2^2","A6.2_3","A6.2_3"]);
ALN("U4(3)",["c3u1","f22u1","u4q3"]);

MOT("U4(3).(2^2)_{122}",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[13063680,4608,23328,3888,3888,324,384,64,20,288,144,144,14,32,54,54,48,24192,
2880,2304,256,432,72,72,36,32,20,144,72,72,14,103680,2304,384,192,1296,432,
216,144,36,32,20,48,24,18,103680,2304,384,192,1296,432,216,144,36,32,20,48,24,
18],
[,[1,1,3,4,5,6,2,2,9,3,4,5,13,7,15,16,10,1,1,2,2,3,4,5,6,7,9,10,11,12,13,1,1,
2,2,3,5,4,5,6,7,9,10,11,15,1,1,2,2,3,4,5,4,6,7,9,10,12,16],[1,2,1,1,1,1,7,8,9,
2,2,2,13,14,3,3,7,18,19,20,21,18,19,19,18,26,27,20,20,20,31,32,33,34,35,32,32,
32,33,33,41,42,34,35,36,46,47,48,49,46,46,46,47,47,55,56,48,49,50],,[1,2,3,4,
5,6,7,8,1,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,19,28,29,30,31,
32,33,34,35,36,37,38,39,40,41,32,43,44,45,46,47,48,49,50,51,52,53,54,55,46,57,
58,59],,[1,2,3,4,5,6,7,8,9,10,11,12,1,14,15,16,17,18,19,20,21,22,23,24,25,26,
27,28,29,30,18,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,
53,54,55,56,57,58,59]],
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1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],
[TENSOR,[2,3]],[21,5,-6,3,3,3,1,1,1,2,-1,-1,0,-1,0,0,-2,-7,1,5,-3,2,1,1,-1,-1,
1,2,-1,-1,0,9,1,-3,1,0,-3,3,1,1,-1,-1,0,1,0,9,1,-3,1,0,-3,3,1,1,-1,-1,0,1,0],
[TENSOR,[5,2]],
[TENSOR,[5,3]],
[TENSOR,[5,4]],[35,3,8,8,-1,-1,3,-1,0,0,0,3,0,-1,2,-1,0,7,-5,-1,-1,-2,-2,1,1,
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-1,1],
[TENSOR,[9,2]],
[TENSOR,[9,3]],
[TENSOR,[9,4]],[35,3,8,-1,8,-1,3,-1,0,0,3,0,0,-1,-1,2,0,7,-5,-1,-1,-2,1,-2,1,
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2,0,0],
[TENSOR,[13,2]],
[TENSOR,[13,3]],
[TENSOR,[13,4]],[90,10,9,9,9,0,-2,2,0,1,1,1,-1,0,0,0,1,6,10,10,2,-3,1,1,0,0,0,
1,1,1,-1,30,6,2,2,3,3,3,3,0,0,0,-1,-1,0,30,6,2,2,3,3,3,3,0,0,0,-1,-1,0],
[TENSOR,[17,2]],
[TENSOR,[17,3]],
[TENSOR,[17,4]],[140,12,5,-4,-4,5,4,0,0,-3,0,0,0,0,-1,-1,1,28,0,4,4,1,0,0,1,0,
0,1,-2,-2,0,20,4,4,0,-7,2,2,-2,1,0,0,1,0,-1,20,4,4,0,-7,2,2,-2,1,0,0,1,0,-1],
[TENSOR,[21,2]],
[TENSOR,[21,3]],
[TENSOR,[21,4]],[189,-3,27,0,0,0,5,1,-1,3,0,0,0,1,0,0,-1,21,9,-3,-3,3,0,0,0,1,
-1,3,0,0,0,9,9,1,-3,9,0,0,0,0,1,-1,1,0,0,9,9,1,-3,9,0,0,0,0,1,-1,1,0,0],
[TENSOR,[25,2]],
[TENSOR,[25,3]],
[TENSOR,[25,4]],[210,2,21,3,3,3,-2,-2,0,5,-1,-1,0,0,0,0,1,14,-10,10,2,5,-1,-1,
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-1,1,0],
[TENSOR,[29,2]],
[TENSOR,[29,3]],
[TENSOR,[29,4]],[560,-16,20,20,2,2,0,0,0,-4,-4,2,0,0,-1,2,0,0,0,0,0,0,0,0,0,0,
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[TENSOR,[33,2]],[560,-16,20,2,20,2,0,0,0,-4,2,-4,0,0,2,-1,0,0,0,0,0,0,0,0,0,0,
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[TENSOR,[35,2]],[315,11,-9,18,-9,0,-1,-1,0,-1,2,-1,0,1,0,0,-1,-21,-5,7,-1,-3,
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0,1,-1,0],
[TENSOR,[37,2]],
[TENSOR,[37,3]],
[TENSOR,[37,4]],[315,11,-9,-9,18,0,-1,-1,0,-1,-1,2,0,1,0,0,-1,-21,-5,7,-1,-3,
1,-2,0,1,0,1,1,-2,0,15,-9,-5,-1,-3,0,3,0,0,1,0,1,-1,0,75,3,-1,3,3,-3,0,-3,0,1,
0,-1,0,0],
[TENSOR,[41,2]],
[TENSOR,[41,3]],
[TENSOR,[41,4]],[420,4,-39,6,6,-3,4,0,0,1,-2,-2,0,0,0,0,1,28,0,12,-4,1,0,0,1,
0,0,-3,0,0,0,60,-4,4,0,-3,-6,0,2,-1,0,0,1,0,0,60,-4,4,0,-3,-6,0,2,-1,0,0,1,0,
0],
[TENSOR,[45,2]],
[TENSOR,[45,3]],
[TENSOR,[45,4]],[1120,-32,-68,4,4,4,0,0,0,4,4,4,0,0,-2,-2,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[1280,0,
-16,-16,-16,2,0,0,0,0,0,0,-1,0,2,2,0,-64,0,0,0,8,0,0,2,0,0,0,0,0,-1,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[50,3]],[729,9,0,0,0,0,-3,1,-1,0,0,0,1,-1,0,0,0,-27,9,9,1,0,0,0,0,-1,
-1,0,0,0,1,81,9,-3,-3,0,0,0,0,0,-1,1,0,0,0,81,9,-3,-3,0,0,0,0,0,-1,1,0,0,0],
[TENSOR,[52,2]],
[TENSOR,[52,3]],
[TENSOR,[52,4]],[896,0,32,-4,-4,-4,0,0,1,0,0,0,0,0,-1,-1,0,0,16,0,0,0,-2,-2,0,
0,1,0,0,0,0,64,0,0,0,-8,4,-2,0,0,0,-1,0,0,1,64,0,0,0,-8,4,-2,0,0,0,-1,0,0,1],
[TENSOR,[56,2]],
[TENSOR,[56,3]],
[TENSOR,[56,4]]],
[( 4, 5)(11,12)(15,16)(23,24)(29,30)(32,46)(33,47)(34,48)(35,49)(36,50)(37,51)
(38,52)(39,53)(40,54)(41,55)(42,56)(43,57)(44,58)(45,59)]);
ALF("U4(3).(2^2)_{122}","U4(3).D8",[1,2,3,4,4,5,6,7,8,9,10,10,11,12,13,13,
14,15,16,17,18,19,20,20,21,22,23,24,25,25,26,39,40,41,42,43,44,45,46,47,
48,49,50,51,52,39,40,41,42,43,44,45,46,47,48,49,50,51,52]);
ALF("U4(3).(2^2)_{122}","U6(2).2",[1,3,6,5,7,7,10,13,14,17,18,20,22,24,26,
27,33,38,39,40,41,44,45,47,46,50,53,55,54,57,59,2,4,10,12,15,19,16,21,21,
24,28,33,35,37,38,39,40,42,44,43,46,45,47,51,52,55,58,62],[
"fusion map is unique up to table aut."
]);

MOT("U4(3).(2^2)_{133}",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7],\n",
"computed from the tables of U4(3), U4(3).2_1, U4(3).2_3, U4(3).2_3'"
],
[13063680,4608,23328,1944,324,384,64,20,288,72,14,32,27,48,24192,2880,2304,
256,432,36,36,32,20,144,36,14,2880,192,36,192,64,16,20,24,24,2880,192,36,192,
64,16,20,24,24],
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44]],
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[TENSOR,[5,2]],
[TENSOR,[5,3]],
[TENSOR,[5,4]],[70,6,16,7,-2,6,-2,0,0,3,0,-2,1,0,14,-10,-2,-2,-4,-1,2,-2,0,4,
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[TENSOR,[9,3]],[90,10,9,9,0,-2,2,0,1,1,-1,0,0,1,6,10,10,2,-3,1,0,0,0,1,1,-1,0,
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[TENSOR,[11,2]],
[TENSOR,[11,3]],
[TENSOR,[11,4]],[140,12,5,-4,5,4,0,0,-3,0,0,0,-1,1,28,0,4,4,1,0,1,0,0,1,-2,0,
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[TENSOR,[15,2]],
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[TENSOR,[15,4]],[189,-3,27,0,0,5,1,-1,3,0,0,1,0,-1,21,9,-3,-3,3,0,0,1,-1,3,0,
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[TENSOR,[35,3]],[729,9,0,0,0,-3,1,-1,0,0,1,-1,0,0,-27,9,9,1,0,0,0,-1,-1,0,0,1,
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[TENSOR,[37,2]],
[TENSOR,[37,3]],
[TENSOR,[37,4]],[896,0,32,-4,-4,0,0,1,0,0,0,0,-1,0,0,16,0,0,0,-2,0,0,1,0,0,0,
16,0,-2,0,0,0,1,0,0,16,0,-2,0,0,0,1,0,0],
[TENSOR,[41,2]],
[TENSOR,[41,3]],
[TENSOR,[41,4]]],
[(27,36)(28,37)(29,38)(30,39)(31,40)(32,41)(33,42)(34,43)(35,44)]);
ARC("U4(3).(2^2)_{133}","maxes",["U4(3).2_1","U4(3).2_3","U4(3).2_3'",
"3^4:(M10x2)","L3(4).2^2","U4(3).(2^2)_{133}M6","3^(1+4)+.2^(1+4)-.S3",
"2xU3(3).2","2(A4xA4).4.2^2","2xa6.2^2","U4(3).(2^2)_{133}M11",
"U4(3).(2^2)_{133}M12","(4^2x2)(2xS4)"]);
ARC("U4(3).(2^2)_{133}","tomfusion",rec(name:="U4(3).2^2_133",map:=[1,6,7,
9,8,14,15,25,30,31,43,88,115,124,2,5,10,13,26,32,29,89,120,123,125,156,3,
12,27,84,86,90,122,126,406,4,11,28,85,87,91,121,127,407],text:=[
"fusion map is unique up to table autom."
],perm:=(10,12,11)));
ARC("U4(3).(2^2)_{133}","CAS",[rec(name:="u4q3:2^2",
permclasses:=(),
permchars:=(2,3)(6,7)(12,13)(16,17)(20,21)(24,25)(31,32)(38,39)(42,43),
text:=[
"origin: CAS library,\n",
"maximal subgroup of Co3,\n",
"Source: Atlas [Atlas-table character X.16 extends to both types of u4q3:2\n",
"involved, but does not extend to u4q3:2^2 !!].\n",
"Test: 1.OR, JAMES, JAMES,n=3,\n",
"and restricted characters decompose properly.\n"])]);
ALF("U4(3).(2^2)_{133}","U4(3).D8",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,
16,17,18,19,20,21,22,23,24,25,26,53,54,55,56,57,58,59,60,61,53,54,55,56,
57,58,59,60,61]);
ALF("U4(3).(2^2)_{133}","Co3",[1,2,4,5,5,8,8,10,11,13,16,19,21,27,2,3,7,8,
12,14,13,19,23,26,28,29,3,7,14,17,18,18,23,26,40,3,8,14,18,17,19,23,27,41],[
"fusion map is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);

MOT("U4(3).2_1",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7],\n",
"constructions: PSO(-1,6,3)"
],
[6531840,2304,11664,1944,1944,162,192,32,10,144,72,72,14,14,16,27,27,24,12096,
1440,1152,128,216,36,36,18,16,10,144,144,36,36,14,14],
[,[1,1,3,4,5,6,2,2,9,3,4,5,13,14,7,16,17,10,1,1,2,2,3,4,5,6,7,9,10,10,11,12,
13,14],[1,2,1,1,1,1,7,8,9,2,2,2,14,13,15,3,3,7,19,20,21,22,19,20,20,19,27,28,
21,21,21,21,34,33],,[1,2,3,4,5,6,7,8,1,10,11,12,14,13,15,16,17,18,19,20,21,22,
23,24,25,26,27,20,29,30,31,32,34,33],,[1,2,3,4,5,6,7,8,9,10,11,12,1,1,15,16,
17,18,19,20,21,22,23,24,25,26,27,28,30,29,31,32,19,19]],
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[TENSOR,[3,2]],[35,3,8,8,-1,-1,3,-1,0,0,0,3,0,0,-1,2,-1,0,7,-5,-1,-1,-2,-2,1,
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[TENSOR,[9,2]],[140,12,5,-4,-4,5,4,0,0,-3,0,0,0,0,0,-1,-1,1,28,0,4,4,1,0,0,1,
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[TENSOR,[13,2]],[210,2,21,3,3,3,-2,-2,0,5,-1,-1,0,0,0,0,0,1,14,-10,10,2,5,-1,
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[TENSOR,[21,2]],[420,4,-39,6,6,-3,4,0,0,1,-2,-2,0,0,0,0,0,1,28,0,12,-4,1,0,0,
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[TENSOR,[25,2]],[640,0,-8,-8,-8,1,0,0,0,0,0,0,E(7)+E(7)^2+E(7)^4,
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[TENSOR,[27,2]],
[GALOIS,[27,3]],
[TENSOR,[29,2]],[729,9,0,0,0,0,-3,1,-1,0,0,0,1,1,-1,0,0,0,-27,9,9,1,0,0,0,0,
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[TENSOR,[33,2]]],
[(29,30),(13,14)(33,34),( 4, 5)(11,12)(16,17)(24,25)(31,32)]);
ARC("U4(3).2_1","projectives",["2.U4(3).2_1",[[20,4,-7,2,2,2,4,0,0,1,-2,-2,-1,
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0,0,0,0,0,0,0,0,0,0,0,0,0],[140,-4,-22,-4,14,-4,4,0,0,2,-4,2,0,0,0,2,-1,-2,0,
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[GALOIS,[8,3]],[504,-8,18,18,-9,0,0,0,-1,-2,-2,1,0,0,0,0,0,0,0,-4*E(4),
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E(4),-2*E(4),-2*E(4),E(4),-2*E(4),0,0],[540,12,-27,0,0,0,4,0,0,-3,0,0,1,1,0,0,
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0,2*E(4),2*E(4),-E(4),-E(4),0,0],[640,0,-8,-8,-8,1,0,0,0,0,0,0,
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[GALOIS,[15,3]],[896,0,32,-4,-4,-4,0,0,1,0,0,0,0,0,0,-1,-1,0,0,16*E(4),0,0,0,
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0,0,0,0,0,0,0,0,0],[448,0,16,-20,16,-2,0,0,-2,0,0,0,0,0,0,-2,1,0,0,0,0,0,0,0,
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0,0],[280,0,-17,-8,10,1,4,0,0,3,0,0,0,0,0,1,-2,1,28,0,4+4*E(4),0,1,0,0,1,0,0,
1-2*E(4),-2+E(4),-2-2*E(4),1+E(4),0,0],[420,0,-39,6,6,-3,2,0,0,-3,0,0,0,0,
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-1-E(4),0,0],[540,0,-27,0,0,0,-2,0,0,-3,0,0,1,1,-1-E(4),0,0,1,6,0,6+6*E(4),0,
-3,0,0,0,-1-E(4),0,-3,-3*E(4),0,0,-1,-1],[640,0,-8,-8,-8,1,0,0,0,0,0,0,
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[GALOIS,[11,3]],[840,0,3,12,12,3,-4,0,0,3,0,0,0,0,0,0,0,-1,-28,0,12+12*E(4),0,
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ARC("U4(3).2_1","maxes",["U4(3)","3^4:(2xA6)","U4(2).2","U4(3).2_1M4",
"L3(4).2_2","L3(4).2_2","3^(1+4)+.4S4","2xU3(3)","2^4.s6","U4(3).2_1M10",
"4(A4xA4).4","A6.2^2","A6.2^2"]);
ARC("U4(3).2_1","tomfusion",rec(name:="U4(3).2_1",map:=[1,3,5,7,8,6,11,12,
20,32,34,33,37,37,68,79,78,91,2,4,9,10,30,36,35,31,67,80,88,88,90,89,112,
112],text:=[
"fusion map is unique up to table autom."
],perm:=(3,4)));
ALF("U4(3).2_1","U4(3).4",[1,2,3,4,4,5,6,7,8,9,10,10,11,12,13,14,14,15,16,
17,18,19,20,21,21,22,23,24,25,26,27,27,28,29]);
ALF("U4(3).2_1","U4(3).(2^2)_{122}",[1,2,3,4,5,6,7,8,9,10,11,12,13,13,14,
15,16,17,18,19,20,21,22,23,24,25,26,27,28,28,29,30,31,31]);
ALF("U4(3).2_1","U4(3).(2^2)_{133}",[1,2,3,4,4,5,6,7,8,9,10,10,11,11,12,
13,13,14,15,16,17,18,19,20,20,21,22,23,24,24,25,25,26,26]);
ALF("U4(3).2_1","U4(3).D8",[1,2,3,4,4,5,6,7,8,9,10,10,11,11,12,13,13,14,
15,16,17,18,19,20,20,21,22,23,24,24,25,25,26,26],[
"fusion map is unique"
]);

MOT("U4(3).2_2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7],\n",
"constructions: PSU(4,3) extended by transpose-inverse"
],
[6531840,2304,11664,1944,1944,162,192,32,10,144,72,72,7,16,54,54,27,24,51840,
1152,192,96,1296,1296,216,108,72,18,16,10,24,12,18,18],
[,[1,1,3,4,5,6,2,2,9,3,4,5,13,7,16,15,17,10,1,1,2,2,3,3,5,4,5,6,7,9,10,11,16,
15],[1,2,1,1,1,1,7,8,9,2,2,2,13,14,3,3,3,7,19,20,21,22,19,19,19,19,20,20,29,
30,21,22,23,24],,[1,2,3,4,5,6,7,8,1,10,11,12,13,14,16,15,17,18,19,20,21,22,24,
23,25,26,27,28,29,19,31,32,34,33],,[1,2,3,4,5,6,7,8,9,10,11,12,1,14,15,16,17,
18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34]],
[[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],[21,5,-6,3,3,3,1,1,1,2,-1,-1,0,-1,0,0,0,-2,9,1,-3,1,0,0,-3,3,1,1,-1,-1,0,
1,0,0],
[TENSOR,[3,2]],[35,3,8,8,-1,-1,3,-1,0,0,0,3,0,-1,2,2,-1,0,15,-1,-1,3,6,6,3,0,
-1,-1,-1,0,2,0,0,0],
[TENSOR,[5,2]],[35,3,8,-1,8,-1,3,-1,0,0,3,0,0,-1,-1,-1,2,0,-5,-5,3,-1,4,4,-2,
1,-2,1,-1,0,0,-1,1,1],
[TENSOR,[7,2]],[90,10,9,9,9,0,-2,2,0,1,1,1,-1,0,0,0,0,1,30,6,2,2,3,3,3,3,3,0,
0,0,-1,-1,0,0],
[TENSOR,[9,2]],[140,12,5,-4,-4,5,4,0,0,-3,0,0,0,0,-1,-1,-1,1,20,4,4,0,-7,-7,2,
2,-2,1,0,0,1,0,-1,-1],
[TENSOR,[11,2]],[189,-3,27,0,0,0,5,1,-1,3,0,0,0,1,0,0,0,-1,9,9,1,-3,9,9,0,0,0,
0,1,-1,1,0,0,0],
[TENSOR,[13,2]],[210,2,21,3,3,3,-2,-2,0,5,-1,-1,0,0,0,0,0,1,30,-10,2,-2,3,3,3,
3,-1,-1,0,0,-1,1,0,0],
[TENSOR,[15,2]],[280,-8,10,10,1,1,0,0,0,-2,-2,1,0,0,2*E(3)-E(3)^2,
-E(3)+2*E(3)^2,1,0,40,-8,0,0,2*E(3)-10*E(3)^2,-10*E(3)+2*E(3)^2,1,-2,1,1,0,0,
0,0,E(3)^2,E(3)],
[TENSOR,[17,2]],
[GALOIS,[17,2]],
[TENSOR,[19,2]],[560,-16,20,2,20,2,0,0,0,-4,2,-4,0,0,2,2,-1,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0],[315,11,-9,18,-9,0,-1,-1,0,-1,2,-1,0,1,0,0,0,-1,75,3,-1,3,3,
3,-3,0,-3,0,1,0,-1,0,0,0],
[TENSOR,[22,2]],[315,11,-9,-9,18,0,-1,-1,0,-1,-1,2,0,1,0,0,0,-1,15,-9,-5,-1,
-3,-3,0,3,0,0,1,0,1,-1,0,0],
[TENSOR,[24,2]],[420,4,-39,6,6,-3,4,0,0,1,-2,-2,0,0,0,0,0,1,60,-4,4,0,-3,-3,
-6,0,2,-1,0,0,1,0,0,0],
[TENSOR,[26,2]],[560,-16,-34,2,2,2,0,0,0,2,2,2,0,0,-1,-1,-1,0,0,0,0,0,
-6*E(3)+6*E(3)^2,6*E(3)-6*E(3)^2,0,0,0,0,0,0,0,0,-E(3)+E(3)^2,E(3)-E(3)^2],
[TENSOR,[28,2]],[1280,0,-16,-16,-16,2,0,0,0,0,0,0,-1,0,2,2,2,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0],[729,9,0,0,0,0,-3,1,-1,0,0,0,1,-1,0,0,0,0,81,9,-3,-3,0,0,0,
0,0,0,-1,1,0,0,0,0],
[TENSOR,[31,2]],[896,0,32,-4,-4,-4,0,0,1,0,0,0,0,0,-1,-1,-1,0,64,0,0,0,-8,-8,
4,-2,0,0,0,-1,0,0,1,1],
[TENSOR,[33,2]]],
[(15,16)(23,24)(33,34)]);
ARC("U4(3).2_2","CAS",[rec(name:="u4q3b",
permchars:=( 7, 8)(21,27,26,25,24,23,22)(28,29)(30,34,33,32,31),
permclasses:=(23,24)(33,34),
text:=[
"names:=u4q3b; u4q3.z2, psu4[3].z2\n",
"    order: 2^8.3^6.5.7 = 6,531,840\n",
"    number of classes: 34\n",
"    source:todd, j.a.\n",
"           the characters of a collineation group in\n",
"           five dimensions\n",
"           proc.roy.soc.london 200\n",
"           (1949), 320-336\n",
"    test: 1. o.r., sym 2 decompose correctly\n",
"    comments:extension of psu4(3) with an\n",
"             outer automorphism of order 2\n",
"             blown up using cas-system\n",
""])]);
ARC("U4(3).2_2","projectives",["2.U4(3).2_2",[[20,4,-7,2,2,2,4,0,0,1,-2,-2,-1,
0,-1,-1,-1,1,0,0,0,0,3*E(3)-3*E(3)^2,-3*E(3)+3*E(3)^2,0,0,0,0,0,0,E(3)-E(3)^2,
0,-E(3)+E(3)^2,E(3)-E(3)^2],[56,-8,2,11,2,2,0,0,1,-2,1,-2,0,0,2,2,-1,0,24,0,0,
4,6,6,0,3,0,0,0,-1,0,1,0,0],[56,-8,2,2,11,2,0,0,1,-2,-2,1,0,0,-1,-1,2,0,16,0,
0,0,-2,-2,1,4,3,0,0,1,0,0,1,1],[70,-2,16,7,7,-2,2,0,0,4,1,1,0,0,1,1,1,2,20,0,
0,2,2,2,5,-1,3,0,0,0,0,-1,-1,-1],[70,-2,-11,7,-2,-2,2,0,0,1,1,-2,0,0,
2*E(3)-E(3)^2,-E(3)+2*E(3)^2,1,-1,20,0,0,2,E(3)-5*E(3)^2,-5*E(3)+E(3)^2,-4,-1,
0,0,0,0,E(3)-E(3)^2,-1,-E(3)^2,-E(3)],
[GALOIS,[5,2]],[140,-4,-22,-4,14,-4,4,0,0,2,-4,2,0,0,2,2,-1,-2,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0],[120,-8,12,-6,-6,3,0,0,0,4,-2,-2,1,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,3,0,0,0,0,0,0],[420,20,42,6,6,6,4,0,0,2,2,2,0,0,0,0,0,-2,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0],[504,-8,18,18,-9,0,0,0,-1,-2,-2,1,0,0,0,0,0,0,96,0,0,0,6,6,3,
0,-3,0,0,1,0,0,0,0],[504,-8,18,-9,18,0,0,0,-1,-2,1,-2,0,0,0,0,0,0,24,0,0,-4,6,
6,0,3,0,0,0,-1,0,-1,0,0],[540,12,-27,0,0,0,4,0,0,-3,0,0,1,0,0,0,0,1,0,0,0,0,
9*E(3)-9*E(3)^2,-9*E(3)+9*E(3)^2,0,0,0,0,0,0,-E(3)+E(3)^2,0,0,0],[560,-16,-34,
2,2,2,0,0,0,2,2,2,0,0,-1,-1,-1,0,80,0,0,0,-10,-10,-4,2,0,0,0,0,0,0,-1,-1],[
630,14,-18,9,9,0,-6,0,0,2,-1,-1,0,0,0,0,0,0,60,0,0,-2,6,6,-3,-3,3,0,0,0,0,1,0,
0],[1280,0,-16,-16,-16,2,0,0,0,0,0,0,-1,0,2,2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0],[896,0,32,-4,-4,-4,0,0,1,0,0,0,0,0,-1,-1,-1,0,64,0,0,0,-8,-8,4,-2,0,0,0,
-1,0,0,1,1]],"3_1.U4(3).2_2",[[15,-1,6,3,0,0,3,-1,0,2,-1,2,1,1,E(3)+2*E(3)^2,
2*E(3)+E(3)^2,0,0,5,-3,1,1,-4*E(3),-4*E(3)^2,2,-1,0,0,-1,0,-2,1,-E(3),
-E(3)^2],[21,5,3,6,0,0,1,1,1,-1,2,2,0,-1,2*E(3)+E(3)^2,E(3)+2*E(3)^2,0,1,11,3,
-1,3,-E(3)+3*E(3)^2,3*E(3)-E(3)^2,2,2,0,0,1,1,-1,0,-E(3)^2,-E(3)],[105,9,15,3,
0,0,1,1,0,3,3,0,0,1,-2*E(3)-E(3)^2,-E(3)-2*E(3)^2,0,1,25,9,1,1,E(3)-3*E(3)^2,
-3*E(3)+E(3)^2,4,1,0,0,1,0,1,1,E(3)^2,E(3)],[105,-7,15,3,0,0,5,1,0,-1,-1,2,0,
-1,-2*E(3)-E(3)^2,-E(3)-2*E(3)^2,0,-1,5,-3,1,1,11*E(3)+3*E(3)^2,
3*E(3)+11*E(3)^2,2,-1,0,0,-1,0,1,1,-E(3)^2,-E(3)],[105,9,-12,12,0,0,1,1,0,0,0,
0,0,1,E(3)-E(3)^2,-E(3)+E(3)^2,0,-2,35,3,3,3,2*E(3)+6*E(3)^2,6*E(3)+2*E(3)^2,
-4,2,0,0,-1,0,0,0,-1,-1],[210,2,3,15,0,0,-2,-2,0,-1,-1,2,0,0,-E(3)-2*E(3)^2,
-2*E(3)-E(3)^2,0,1,50,-6,-2,2,5*E(3)+9*E(3)^2,9*E(3)+5*E(3)^2,2,-1,0,0,0,0,1,
-1,-E(3),-E(3)^2],[315,-5,-36,9,0,0,3,-1,0,4,1,-2,0,-1,0,0,0,0,45,-3,-3,1,0,0,
-6,-3,0,0,1,0,0,1,0,0],[336,16,-6,6,0,0,0,0,1,-2,-2,-2,0,0,-E(3)+E(3)^2,
E(3)-E(3)^2,0,0,64,0,0,0,-2*E(3)-6*E(3)^2,-6*E(3)-2*E(3)^2,-2,4,0,0,0,-1,0,0,
1,1],[720,16,-36,-18,0,0,0,0,0,4,-2,4,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0],[384,0,24,12,0,0,0,0,-1,0,0,0,-1,0,E(3)+2*E(3)^2,2*E(3)+E(3)^2,0,0,64,
0,0,0,-8*E(3),-8*E(3)^2,4,-2,0,0,0,-1,0,0,E(3),E(3)^2],[420,4,33,-6,0,0,4,0,0,
1,-2,-2,0,0,E(3)-E(3)^2,-E(3)+E(3)^2,0,1,20,-12,-4,0,5*E(3)-3*E(3)^2,
-3*E(3)+5*E(3)^2,2,2,0,0,0,0,-1,0,-1,-1],[630,6,9,-9,0,0,2,-2,0,-3,3,0,0,0,0,
0,0,-1,30,6,2,2,3*E(3)-9*E(3)^2,-9*E(3)+3*E(3)^2,0,-3,0,0,0,0,-1,-1,0,0],[729,
9,0,0,0,0,-3,1,-1,0,0,0,1,-1,0,0,0,0,81,9,-3,-3,0,0,0,0,0,0,-1,1,0,0,0,0],[
756,-12,27,0,0,0,-4,0,1,3,0,0,0,0,0,0,0,-1,36,-12,4,0,9,9,0,0,0,0,0,1,1,0,0,
0],[945,-15,-27,0,0,0,1,1,0,-3,0,0,0,1,0,0,0,1,45,-3,5,-3,-9,-9,0,0,0,0,1,0,
-1,0,0,0]],"6_1.U4(3).2_2",[[6,-2,-3,3,0,0,2,0,1,1,1,-2,-1,0,E(3)-E(3)^2,
-E(3)+E(3)^2,0,-1,4,0,0,2,E(3)+3*E(3)^2,3*E(3)+E(3)^2,-2,1,0,0,0,-1,
E(3)-E(3)^2,-1,1,1],[84,4,-15,6,0,0,4,0,-1,1,-2,-2,0,0,-E(3)-2*E(3)^2,
-2*E(3)-E(3)^2,0,1,16,0,0,0,7*E(3)+9*E(3)^2,9*E(3)+7*E(3)^2,-2,-2,0,0,0,1,
E(3)-E(3)^2,0,E(3),E(3)^2],[120,-8,-6,15,0,0,0,0,0,-2,1,-2,1,0,2*E(3)+E(3)^2,
E(3)+2*E(3)^2,0,0,40,0,0,4,-2*E(3)+6*E(3)^2,6*E(3)-2*E(3)^2,-2,1,0,0,0,0,0,1,
E(3)^2,E(3)],[126,-10,18,9,0,0,2,0,1,2,-1,2,0,0,0,0,0,2,36,0,0,2,0,0,6,3,0,0,
0,1,0,-1,0,0],[210,-6,-24,-3,0,0,6,0,0,0,3,0,0,0,-E(3)+E(3)^2,E(3)-E(3)^2,0,0,
20,0,0,2,-4*E(3)-12*E(3)^2,-12*E(3)-4*E(3)^2,-4,-1,0,0,0,0,0,-1,-1,-1],[540,
12,54,0,0,0,4,0,0,6,0,0,1,0,0,0,0,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[336,16,
-6,6,0,0,0,0,1,-2,-2,-2,0,0,-E(3)+E(3)^2,E(3)-E(3)^2,0,0,16,0,0,0,
-14*E(3)-6*E(3)^2,-6*E(3)-14*E(3)^2,-2,-2,0,0,0,1,0,0,1,1],[384,0,24,12,0,0,0,
0,-1,0,0,0,-1,0,E(3)+2*E(3)^2,2*E(3)+E(3)^2,0,0,64,0,0,0,-8*E(3),-8*E(3)^2,4,
-2,0,0,0,-1,0,0,E(3),E(3)^2],[420,-12,-21,12,0,0,-4,0,0,3,0,0,0,0,
-2*E(3)-E(3)^2,-E(3)-2*E(3)^2,0,-1,80,0,0,0,5*E(3)+3*E(3)^2,3*E(3)+5*E(3)^2,
-4,2,0,0,0,0,-E(3)+E(3)^2,0,-E(3)^2,-E(3)],[630,-18,9,-9,0,0,2,0,0,-3,-3,0,0,
0,0,0,0,-1,60,0,0,-2,-3*E(3)-9*E(3)^2,-9*E(3)-3*E(3)^2,0,3,0,0,0,0,
E(3)-E(3)^2,1,0,0],[1260,-4,18,-18,0,0,-4,0,0,2,2,-4,0,0,0,0,0,2,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0],[840,8,12,6,0,0,0,0,0,-4,2,2,0,0,-E(3)-2*E(3)^2,
-2*E(3)-E(3)^2,0,0,80,0,0,0,8*E(3),8*E(3)^2,2,-4,0,0,0,0,0,0,-E(3),-E(3)^2],[
840,8,-42,-3,0,0,0,0,0,2,-1,2,0,0,2*E(3)+E(3)^2,E(3)+2*E(3)^2,0,0,40,0,0,-4,
-2*E(3)+6*E(3)^2,6*E(3)-2*E(3)^2,-2,1,0,0,0,0,0,-1,E(3)^2,E(3)]],]);
ALF("U4(3).2_2","Fi22",[1,3,6,5,7,7,9,13,14,17,18,23,26,28,31,31,32,38,2,
4,9,10,16,16,19,15,24,22,27,34,38,41,56,55],[
"determined by the factorization through S3xU4(3).2_2,\n",
"with natural embedding into this group,\n",
"the fusion on the CAS table is wrong"
]);
ALF("U4(3).2_2","U4(3).(2^2)_{122}",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,
15,16,17,32,33,34,35,36,36,37,38,39,40,41,42,43,44,45,45]);
ALF("U4(3).2_2","U4(3).D8",[1,2,3,4,4,5,6,7,8,9,10,10,11,12,13,13,13,14,
39,40,41,42,43,43,44,45,46,47,48,49,50,51,52,52],[
"fusion map is unique"
]);
ALF("U4(3).2_2","U6(2)",[1,3,6,5,7,7,10,14,15,19,20,22,24,26,29,30,31,40,
2,4,10,13,16,17,21,18,23,23,26,32,40,43,45,46],[
"fusion map is unique up to table automorphisms"
]);
ALN("U4(3).2_2",["f22u2","u4q3b"]);

MOT("U4(3).2_2'",
0,
0,
0,
0,
[(16,17)(23,24)(33,34)],
["ConstructPermuted",["U4(3).2_2"],
( 4, 5)(11,12)(15,16,17),( 5, 7)( 6, 8)(17,18,19,20,21)(22,24)(23,25)]);
ALF("U4(3).2_2'","U4(3).(2^2)_{122}",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,
16,17,46,47,48,49,50,50,51,52,53,54,55,56,57,58,59,59]);

MOT("U4(3).2_3",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[6531840,2304,11664,972,162,192,32,10,144,36,7,16,27,27,24,1440,96,18,96,32,8,
10,12,24,24],
[,[1,1,3,4,5,2,2,8,3,4,11,6,14,13,9,1,2,5,6,6,7,8,9,15,15],[1,2,1,1,1,6,7,8,2,
2,11,12,3,3,6,16,17,16,19,20,21,22,17,19,19],,[1,2,3,4,5,6,7,1,9,10,11,12,14,
13,15,16,17,18,19,20,21,16,23,24,25],,[1,2,3,4,5,6,7,8,9,10,1,12,13,14,15,16,
17,18,19,20,21,22,23,24,25]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[21,5,-6,3,3,1,1,1,2,-1,0,-1,0,0,-2,1,-3,
1,3,-1,-1,1,0,0,0],
[TENSOR,[3,2]],[70,6,16,7,-2,6,-2,0,0,3,0,-2,1,1,0,0,0,0,0,0,0,0,0,0,0],[90,
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ARC("U4(3).2_3","projectives",["2.U4(3).2_3",[[20,4,-7,2,2,4,0,0,1,-2,-1,0,-1,
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ARC("U4(3).2_3","maxes",["U4(3)","3^4:m10","L3(4).2_3","L3(4).2_1",
"3^(1+4):4S4","U3(3).2","2(A4xA4).4.2","M10x2","A6.2^2","U4(3).2_3M10",
"(4^2x2)S4"]);
ARC("U4(3).2_3","tomfusion",rec(name:="U4(3).2_3",map:=[1,2,4,6,5,10,12,13,18,
19,21,30,49,49,60,3,11,20,28,29,31,50,61,127,127],text:=[
"fusion map is unique"
]));
ALF("U4(3).2_3","U4(3).(2^2)_{133}",[1,2,3,4,5,6,7,8,9,10,11,12,13,13,14,
27,28,29,30,31,32,33,34,35,35],[
"fusion map is unique up to table autom."
],"tom:1787");
ALF("U4(3).2_3","U4(3).D8",[1,2,3,4,5,6,7,8,9,10,11,12,13,13,14,53,54,55,
56,57,58,59,60,61,61],[
"fusion map is unique"
]);
ALF("U4(3).2_3","McL.2",[1,2,3,4,4,5,5,7,8,9,10,11,12,12,16,20,21,22,23,24,24,
25,26,32,33],[
"fusion map is unique up to table automorphisms"
]);

MOT("U4(3).2_3'",
0,
0,
0,
0,
0,
["ConstructPermuted",["U4(3).2_3"],(),()]);
ALF("U4(3).2_3'","U4(3).(2^2)_{133}",[1,2,3,4,5,6,7,8,9,10,11,12,13,13,14,
36,37,38,39,40,41,42,43,44,44],[
"fusion U4(3).2_3 -> U4(3).(2^2)_{133} mapped under U4(3).D8"
]);

MOT("U4(3).4",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7],\n",
"constructions: PGU(4,3)"
],
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432,432,48,48,36,36,20,20,24,24,28,28,28,28],
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[TENSOR,[2,2]],
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ALF("U4(3).4","U4(3).D8",[1,2,3,4,5,6,7,8,9,10,11,11,12,13,14,15,16,17,18,
19,20,21,22,23,24,24,25,26,26,27,27,28,28,29,29,30,30,31,31,32,32,33,33,
34,34,35,35,36,36,37,38,38,37],[
"fusion map is unique up to table autom.,\n",
"unique map that is compatible with Brauer tables"
]);

MOT("U4(3).D8",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7],\n",
"constructions: Aut(U4(3)), PGU(4,3) extended by transpose-inverse"
],
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[TENSOR,[57,3]],
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[(37,38)]);
ARC("U4(3).D8","CAS",[rec(name:="u4q3.d8",
permclasses:=(),
permchars:=(),
text:=[
"Maximal subgroup of sporadic Conway group c2.\n",
"Source: Atlas tables (autom.gp. of u4q3)\n",
"Test: 1.OR, JAMES, JAMES,n=3,\n",
"and restricted characters decompose properly"])]);
ALF("U4(3).D8","Co2",[1,3,5,6,6,9,11,15,16,20,22,27,29,35,2,4,9,8,17,21,
19,24,32,35,37,42,7,10,13,24,27,34,38,36,52,56,57,57,2,4,9,12,17,18,19,21,
21,27,31,35,41,50,4,11,21,24,27,28,32,40,56],[
"fusion map is unique, equal to that on the CAS table"
]);
ALN("U4(3).D8",["u4q3.d8"]);

MOT("(3^2x2).U4(3)",
[
"constructed using `CharacterTableOfCommonCentralExtension'"
],
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1296,1296,1296,1296,1296,1296,1296,1296,1296,1296,648,648,648,648,648,648,648,
648,648,648,648,648,648,648,648,648,648,648,648,648,648,648,648,648,648,648,
648,648,648,648,648,648,648,648,648,648,126,126,126,126,126,126,126,126,126,
126,126,126,126,126,126,126,126,126,126,126,126,126,126,126,126,126,126,126,
126,126,126,126,126,126,126,126,144,144,144,144,144,144,144,144,144,144,144,
144,144,144,144,144,144,144,162,162,162,162,162,162,162,162,162,162,162,162,
162,162,162,162,162,162,162,162,162,162,162,162,216,216,216,216,216,216,216,
216,216,216,216,216,216,216,216,216,216,216],
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59,55,57,59,65,61,63,65,61,63,67,67,19,21,23,19,21,23,31,33,35,31,33,35,28,30,
26,28,30,26,22,24,20,34,36,32,25,27,29,96,98,100,96,98,100,108,110,112,108,110
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48,44,55,57,59,55,57,59,55,57,59,55,57,59,55,57,59,55,57,59,63,65,61,63,65,61,
61,63,65,61,63,65,65,61,63,65,61,63,168,170,172,168,170,172,180,182,184,180,
182,184,177,179,175,177,179,175,186,188,190,186,188,190,198,200,202,198,200,
202,195,197,193,195,197,193,72,74,70,72,74,70,84,86,82,84,86,82,75,77,79,75,77
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238,234,236,238,234,236,114,116,118,114,116,118,126,128,130,126,128,130,123,
125,121,123,125,121],[1,4,1,4,1,4,4,1,4,1,4,1,1,4,1,4,1,4,19,22,19,22,19,22,22
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1,4,1,4,1,4,1,4,1,4,69,72,69,72,69,72,72,69,72,69,72,69,69,72,69,72,69,72,87,
87,87,87,87,87,87,87,87,96,99,96,99,96,99,99,96,99,96,99,96,96,99,96,99,96,99,
19,22,19,22,19,22,22,19,22,19,22,19,19,22,19,22,19,22,19,22,19,22,19,22,22,19,
22,19,22,19,19,22,19,22,19,22,19,22,19,22,19,22,22,19,22,19,22,19,19,22,19,22,
19,22,186,189,186,189,186,189,189,186,189,186,189,186,186,189,186,189,186,189,
168,171,168,171,168,171,171,168,171,168,171,168,168,171,168,171,168,171,207,
204,207,204,207,204,204,207,204,207,204,207,207,204,207,204,207,204,51,54,51,
54,51,54,44,47,44,47,44,47,49,52,49,52,49,52,46,43,46,43,46,43,69,72,69,72,69,
72,72,69,72,69,72,69,69,72,69,72,69,72],,[1,6,5,4,3,2,16,15,14,13,18,17,10,9,8
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38,52,51,50,49,54,53,46,45,44,43,48,47,55,60,59,58,57,56,65,64,63,62,61,66,67,
68,69,74,73,72,71,70,84,83,82,81,86,85,78,77,76,75,80,79,87,89,88,93,95,94,90,
92,91,1,6,5,4,3,2,16,15,14,13,18,17,10,9,8,7,12,11,114,119,118,117,116,115,129
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145,144,149,148,141,140,139,138,143,142,150,155,154,153,152,151,165,164,163,
162,167,166,159,158,157,156,161,160,186,191,190,189,188,187,201,200,199,198,
203,202,195,194,193,192,197,196,168,173,172,171,170,169,183,182,181,180,185,
184,177,176,175,174,179,178,204,209,208,207,206,205,219,218,217,216,221,220,
213,212,211,210,215,214,228,233,232,231,230,229,222,227,226,225,224,223,244,
243,242,241,240,245,238,237,236,235,234,239,246,251,250,249,248,247,261,260,
259,258,263,262,255,254,253,252,257,256],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15
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134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,
153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,1,2,3,4,5,6,7,8,9,
10,11,12,13,14,15,16,17,18,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,207,
208,209,204,205,206,213,214,215,210,211,212,219,220,221,216,217,218,222,223,
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]],
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1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[21,21,21,21,21,
21,21,21,21,21,21,21,21,21,21,21,21,21,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,-6,
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35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,3,3,3,3,3,3,3,3,3,3,3,3,3,3
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-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[35,35,35,35,35,35,35,35,35,35,35,
35,35,35,35,35,35,35,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,8,8,8,8,8,8,8,8,8,8,8
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0,0,0,0,0,0],[90,90,90,90,90,90,90,90,90,90,90,90,90,90,90,90,90,90,10,10,10,
10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9
,9,9,9,9,9,9,9,9,9,9,9,9,9,0,0,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2
,-2,-2,2,2,2,2,2,2,2,2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1
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,1,1,1],[140,140,140,140,140,140,140,140,140,140,140,140,140,140,140,140,140,
140,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,5,5,5,5,5,5,5,5,5,5,
5,5,5,5,5,5,5,5,-4,-4,-4,-4,-4,-4,-4,-4,-4,-4,-4,-4,5,5,4,4,4,4,4,4,4,4,4,4,4,
4,4,4,4,4,4,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-3,-3,-3,
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,1,1,1,1,1,1,1,1,1,1],[189,189,189,189,189,189,189,189,189,189,189,189,189,189
,189,189,189,189,-3,-3,-3,-3,-3,-3,-3,-3,-3,-3,-3,-3,-3,-3,-3,-3,-3,-3,27,27,
27,27,27,27,27,27,27,27,27,27,27,27,27,27,27,27,0,0,0,0,0,0,0,0,0,0,0,0,0,0,5,
5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1
,-1,-1,-1,-1,-1,-1,-1,-1,-1,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,-1
,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[210,210,210,210,210,210,210,210,210,210,
210,210,210,210,210,210,210,210,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,21,21,21,
21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,3,3,3,3,3,3,3,3,3,3,3,3,3,3,-2,-2
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0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[280,280,280,280,
280,280,280,280,280,280,280,280,280,280,280,280,280,280,-8,-8,-8,-8,-8,-8,-8,
-8,-8,-8,-8,-8,-8,-8,-8,-8,-8,-8,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,
10,10,10,10,10,10,10,10,10,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
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2*E(3)-E(3)^2,2*E(3)-E(3)^2,2*E(3)-E(3)^2,2*E(3)-E(3)^2,2*E(3)-E(3)^2,
2*E(3)-E(3)^2,-E(3)+2*E(3)^2,-E(3)+2*E(3)^2,-E(3)+2*E(3)^2,-E(3)+2*E(3)^2,
-E(3)+2*E(3)^2,-E(3)+2*E(3)^2,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0],
[GALOIS,[9,2]],[280,280,280,280,280,280,280,280,280,280,280,280,280,280,280,
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10,10,10,10,10,10,10,10,10,10,10,10,10,10,1,1,1,1,1,1,10,10,10,10,10,10,1,1,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
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,3*E(3),3*E(3)^2,3,3*E(3),3*E(3)^2,3,3*E(3),3*E(3)^2,3,3*E(3),3*E(3)^2,3,
3*E(3),3*E(3)^2,3,3*E(3),3*E(3)^2,3,3*E(3),3*E(3)^2,3,3*E(3),3*E(3)^2,3,3*E(3)
,3*E(3)^2,3,3*E(3),3*E(3)^2,3,3*E(3),3*E(3)^2,3,3*E(3),3*E(3)^2,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,1,E(3),E(3)^2,1,E(3),E(3)^2,1,E(3),E(3)^2,1,E(3),E(3)^2,1,E(3)
,E(3)^2,1,E(3),E(3)^2,-2*E(3)-E(3)^2,E(3)-E(3)^2,E(3)+2*E(3)^2,-2*E(3)-E(3)^2,
E(3)-E(3)^2,E(3)+2*E(3)^2,-E(3)-2*E(3)^2,2*E(3)+E(3)^2,-E(3)+E(3)^2,
-E(3)-2*E(3)^2,2*E(3)+E(3)^2,-E(3)+E(3)^2,0,0,0,0,0,0,0,0,0,0,0,0,1,E(3),
E(3)^2,1,E(3),E(3)^2,1,E(3),E(3)^2,1,E(3),E(3)^2,1,E(3),E(3)^2,1,E(3),E(3)^2],
[GALOIS,[94,2]],[105,105*E(3),105*E(3)^2,105,105*E(3),105*E(3)^2,105,105*E(3)
,105*E(3)^2,105,105*E(3),105*E(3)^2,105,105*E(3),105*E(3)^2,105,105*E(3),
105*E(3)^2,-7,-7*E(3),-7*E(3)^2,-7,-7*E(3),-7*E(3)^2,-7,-7*E(3),-7*E(3)^2,-7,
-7*E(3),-7*E(3)^2,-7,-7*E(3),-7*E(3)^2,-7,-7*E(3),-7*E(3)^2,15,15*E(3),
15*E(3)^2,15,15*E(3),15*E(3)^2,15,15*E(3),15*E(3)^2,15,15*E(3),15*E(3)^2,15,
15*E(3),15*E(3)^2,15,15*E(3),15*E(3)^2,3,3*E(3),3*E(3)^2,3,3*E(3),3*E(3)^2,0,0
,0,0,0,0,0,0,5,5*E(3),5*E(3)^2,5,5*E(3),5*E(3)^2,5,5*E(3),5*E(3)^2,5,5*E(3),
5*E(3)^2,5,5*E(3),5*E(3)^2,5,5*E(3),5*E(3)^2,1,E(3),E(3)^2,1,E(3),E(3)^2,1,
E(3),E(3)^2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-E(3),-E(3)^2,-1,-E(3),
-E(3)^2,-1,-E(3),-E(3)^2,-1,-E(3),-E(3)^2,-1,-E(3),-E(3)^2,-1,-E(3),-E(3)^2,-1
,-E(3),-E(3)^2,-1,-E(3),-E(3)^2,-1,-E(3),-E(3)^2,-1,-E(3),-E(3)^2,-1,-E(3),
-E(3)^2,-1,-E(3),-E(3)^2,2,2*E(3),2*E(3)^2,2,2*E(3),2*E(3)^2,2,2*E(3),2*E(3)^2
,2,2*E(3),2*E(3)^2,2,2*E(3),2*E(3)^2,2,2*E(3),2*E(3)^2,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-E(3),-E(3)^2,-1,-E(3),
-E(3)^2,-1,-E(3),-E(3)^2,-1,-E(3),-E(3)^2,-1,-E(3),-E(3)^2,-1,-E(3),-E(3)^2,
-2*E(3)-E(3)^2,E(3)-E(3)^2,E(3)+2*E(3)^2,-2*E(3)-E(3)^2,E(3)-E(3)^2,
E(3)+2*E(3)^2,-E(3)-2*E(3)^2,2*E(3)+E(3)^2,-E(3)+E(3)^2,-E(3)-2*E(3)^2,
2*E(3)+E(3)^2,-E(3)+E(3)^2,0,0,0,0,0,0,0,0,0,0,0,0,-1,-E(3),-E(3)^2,-1,-E(3),
-E(3)^2,-1,-E(3),-E(3)^2,-1,-E(3),-E(3)^2,-1,-E(3),-E(3)^2,-1,-E(3),-E(3)^2],
[GALOIS,[96,2]],[105,105*E(3),105*E(3)^2,105,105*E(3),105*E(3)^2,105,105*E(3)
,105*E(3)^2,105,105*E(3),105*E(3)^2,105,105*E(3),105*E(3)^2,105,105*E(3),
105*E(3)^2,9,9*E(3),9*E(3)^2,9,9*E(3),9*E(3)^2,9,9*E(3),9*E(3)^2,9,9*E(3),
9*E(3)^2,9,9*E(3),9*E(3)^2,9,9*E(3),9*E(3)^2,-12,-12*E(3),-12*E(3)^2,-12,
-12*E(3),-12*E(3)^2,-12,-12*E(3),-12*E(3)^2,-12,-12*E(3),-12*E(3)^2,-12,
-12*E(3),-12*E(3)^2,-12,-12*E(3),-12*E(3)^2,12,12*E(3),12*E(3)^2,12,12*E(3),
12*E(3)^2,0,0,0,0,0,0,0,0,1,E(3),E(3)^2,1,E(3),E(3)^2,1,E(3),E(3)^2,1,E(3),
E(3)^2,1,E(3),E(3)^2,1,E(3),E(3)^2,1,E(3),E(3)^2,1,E(3),E(3)^2,1,E(3),E(3)^2,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,E(3),E(3)^2,1,
E(3),E(3)^2,1,E(3),E(3)^2,1,E(3),E(3)^2,1,E(3),E(3)^2,1,E(3),E(3)^2,
E(3)-E(3)^2,E(3)+2*E(3)^2,-2*E(3)-E(3)^2,E(3)-E(3)^2,E(3)+2*E(3)^2,
-2*E(3)-E(3)^2,-E(3)+E(3)^2,-E(3)-2*E(3)^2,2*E(3)+E(3)^2,-E(3)+E(3)^2,
-E(3)-2*E(3)^2,2*E(3)+E(3)^2,0,0,0,0,0,0,0,0,0,0,0,0,-2,-2*E(3),-2*E(3)^2,-2,
-2*E(3),-2*E(3)^2,-2,-2*E(3),-2*E(3)^2,-2,-2*E(3),-2*E(3)^2,-2,-2*E(3),
-2*E(3)^2,-2,-2*E(3),-2*E(3)^2],
[GALOIS,[98,2]],[210,210*E(3),210*E(3)^2,210,210*E(3),210*E(3)^2,210,210*E(3)
,210*E(3)^2,210,210*E(3),210*E(3)^2,210,210*E(3),210*E(3)^2,210,210*E(3),
210*E(3)^2,2,2*E(3),2*E(3)^2,2,2*E(3),2*E(3)^2,2,2*E(3),2*E(3)^2,2,2*E(3),
2*E(3)^2,2,2*E(3),2*E(3)^2,2,2*E(3),2*E(3)^2,3,3*E(3),3*E(3)^2,3,3*E(3),
3*E(3)^2,3,3*E(3),3*E(3)^2,3,3*E(3),3*E(3)^2,3,3*E(3),3*E(3)^2,3,3*E(3),
3*E(3)^2,15,15*E(3),15*E(3)^2,15,15*E(3),15*E(3)^2,0,0,0,0,0,0,0,0,-2,-2*E(3),
-2*E(3)^2,-2,-2*E(3),-2*E(3)^2,-2,-2*E(3),-2*E(3)^2,-2,-2*E(3),-2*E(3)^2,-2,
-2*E(3),-2*E(3)^2,-2,-2*E(3),-2*E(3)^2,-2,-2*E(3),-2*E(3)^2,-2,-2*E(3),
-2*E(3)^2,-2,-2*E(3),-2*E(3)^2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-E(3),
-E(3)^2,-1,-E(3),-E(3)^2,-1,-E(3),-E(3)^2,-1,-E(3),-E(3)^2,-1,-E(3),-E(3)^2,-1
,-E(3),-E(3)^2,-1,-E(3),-E(3)^2,-1,-E(3),-E(3)^2,-1,-E(3),-E(3)^2,-1,-E(3),
-E(3)^2,-1,-E(3),-E(3)^2,-1,-E(3),-E(3)^2,2,2*E(3),2*E(3)^2,2,2*E(3),2*E(3)^2,
2,2*E(3),2*E(3)^2,2,2*E(3),2*E(3)^2,2,2*E(3),2*E(3)^2,2,2*E(3),2*E(3)^2,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,-E(3)-2*E(3)^2,2*E(3)+E(3)^2,-E(3)+E(3)^2,
-E(3)-2*E(3)^2,2*E(3)+E(3)^2,-E(3)+E(3)^2,-2*E(3)-E(3)^2,E(3)-E(3)^2,
E(3)+2*E(3)^2,-2*E(3)-E(3)^2,E(3)-E(3)^2,E(3)+2*E(3)^2,0,0,0,0,0,0,0,0,0,0,0,0
,1,E(3),E(3)^2,1,E(3),E(3)^2,1,E(3),E(3)^2,1,E(3),E(3)^2,1,E(3),E(3)^2,1,E(3),
E(3)^2],
[GALOIS,[100,2]],[315,315*E(3),315*E(3)^2,315,315*E(3),315*E(3)^2,315,
315*E(3),315*E(3)^2,315,315*E(3),315*E(3)^2,315,315*E(3),315*E(3)^2,315,
315*E(3),315*E(3)^2,-5,-5*E(3),-5*E(3)^2,-5,-5*E(3),-5*E(3)^2,-5,-5*E(3),
-5*E(3)^2,-5,-5*E(3),-5*E(3)^2,-5,-5*E(3),-5*E(3)^2,-5,-5*E(3),-5*E(3)^2,-36,
-36*E(3),-36*E(3)^2,-36,-36*E(3),-36*E(3)^2,-36,-36*E(3),-36*E(3)^2,-36,
-36*E(3),-36*E(3)^2,-36,-36*E(3),-36*E(3)^2,-36,-36*E(3),-36*E(3)^2,9,9*E(3),
9*E(3)^2,9,9*E(3),9*E(3)^2,0,0,0,0,0,0,0,0,3,3*E(3),3*E(3)^2,3,3*E(3),3*E(3)^2
,3,3*E(3),3*E(3)^2,3,3*E(3),3*E(3)^2,3,3*E(3),3*E(3)^2,3,3*E(3),3*E(3)^2,-1,
-E(3),-E(3)^2,-1,-E(3),-E(3)^2,-1,-E(3),-E(3)^2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,4,4*E(3),4*E(3)^2,4,4*E(3),4*E(3)^2,4,4*E(3),4*E(3)^2,4,4*E(3),4*E(3)^2,
4,4*E(3),4*E(3)^2,4,4*E(3),4*E(3)^2,1,E(3),E(3)^2,1,E(3),E(3)^2,1,E(3),E(3)^2,
1,E(3),E(3)^2,1,E(3),E(3)^2,1,E(3),E(3)^2,-2,-2*E(3),-2*E(3)^2,-2,-2*E(3),
-2*E(3)^2,-2,-2*E(3),-2*E(3)^2,-2,-2*E(3),-2*E(3)^2,-2,-2*E(3),-2*E(3)^2,-2,
-2*E(3),-2*E(3)^2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,-1,-E(3),-E(3)^2,-1,-E(3),-E(3)^2,-1,-E(3),-E(3)^2,-1,-E(3),
-E(3)^2,-1,-E(3),-E(3)^2,-1,-E(3),-E(3)^2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[102,2]],[336,336*E(3),336*E(3)^2,336,336*E(3),336*E(3)^2,336,
336*E(3),336*E(3)^2,336,336*E(3),336*E(3)^2,336,336*E(3),336*E(3)^2,336,
336*E(3),336*E(3)^2,16,16*E(3),16*E(3)^2,16,16*E(3),16*E(3)^2,16,16*E(3),
16*E(3)^2,16,16*E(3),16*E(3)^2,16,16*E(3),16*E(3)^2,16,16*E(3),16*E(3)^2,-6,
-6*E(3),-6*E(3)^2,-6,-6*E(3),-6*E(3)^2,-6,-6*E(3),-6*E(3)^2,-6,-6*E(3),
-6*E(3)^2,-6,-6*E(3),-6*E(3)^2,-6,-6*E(3),-6*E(3)^2,6,6*E(3),6*E(3)^2,6,6*E(3)
,6*E(3)^2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,1,E(3),E(3)^2,1,E(3),E(3)^2,1,E(3),E(3)^2,1,E(3),E(3)^2,1,E(3),E(3)^2,1,E(3)
,E(3)^2,-2,-2*E(3),-2*E(3)^2,-2,-2*E(3),-2*E(3)^2,-2,-2*E(3),-2*E(3)^2,-2,
-2*E(3),-2*E(3)^2,-2,-2*E(3),-2*E(3)^2,-2,-2*E(3),-2*E(3)^2,-2,-2*E(3),
-2*E(3)^2,-2,-2*E(3),-2*E(3)^2,-2,-2*E(3),-2*E(3)^2,-2,-2*E(3),-2*E(3)^2,-2,
-2*E(3),-2*E(3)^2,-2,-2*E(3),-2*E(3)^2,-2,-2*E(3),-2*E(3)^2,-2,-2*E(3),
-2*E(3)^2,-2,-2*E(3),-2*E(3)^2,-2,-2*E(3),-2*E(3)^2,-2,-2*E(3),-2*E(3)^2,-2,
-2*E(3),-2*E(3)^2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-E(3)+E(3)^2,-E(3)-2*E(3)^2,
2*E(3)+E(3)^2,-E(3)+E(3)^2,-E(3)-2*E(3)^2,2*E(3)+E(3)^2,E(3)-E(3)^2,
E(3)+2*E(3)^2,-2*E(3)-E(3)^2,E(3)-E(3)^2,E(3)+2*E(3)^2,-2*E(3)-E(3)^2,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[104,2]],[360,360*E(3),360*E(3)^2,360,360*E(3),360*E(3)^2,360,
360*E(3),360*E(3)^2,360,360*E(3),360*E(3)^2,360,360*E(3),360*E(3)^2,360,
360*E(3),360*E(3)^2,8,8*E(3),8*E(3)^2,8,8*E(3),8*E(3)^2,8,8*E(3),8*E(3)^2,8,
8*E(3),8*E(3)^2,8,8*E(3),8*E(3)^2,8,8*E(3),8*E(3)^2,-18,-18*E(3),-18*E(3)^2,
-18,-18*E(3),-18*E(3)^2,-18,-18*E(3),-18*E(3)^2,-18,-18*E(3),-18*E(3)^2,-18,
-18*E(3),-18*E(3)^2,-18,-18*E(3),-18*E(3)^2,-9,-9*E(3),-9*E(3)^2,-9,-9*E(3),
-9*E(3)^2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,2*E(3),2*E(3)^2,2,2*E(3),2*E(3)^2,2,
2*E(3),2*E(3)^2,2,2*E(3),2*E(3)^2,2,2*E(3),2*E(3)^2,2,2*E(3),2*E(3)^2,-1,-E(3)
,-E(3)^2,-1,-E(3),-E(3)^2,-1,-E(3),-E(3)^2,-1,-E(3),-E(3)^2,-1,-E(3),-E(3)^2,
-1,-E(3),-E(3)^2,2,2*E(3),2*E(3)^2,2,2*E(3),2*E(3)^2,2,2*E(3),2*E(3)^2,2,
2*E(3),2*E(3)^2,2,2*E(3),2*E(3)^2,2,2*E(3),2*E(3)^2,E(7)+E(7)^2+E(7)^4,
E(21)^10+E(21)^13+E(21)^19,E(21)^5+E(21)^17+E(21)^20,E(7)+E(7)^2+E(7)^4,
E(21)^10+E(21)^13+E(21)^19,E(21)^5+E(21)^17+E(21)^20,E(7)+E(7)^2+E(7)^4,
E(21)^10+E(21)^13+E(21)^19,E(21)^5+E(21)^17+E(21)^20,E(7)+E(7)^2+E(7)^4,
E(21)^10+E(21)^13+E(21)^19,E(21)^5+E(21)^17+E(21)^20,E(7)+E(7)^2+E(7)^4,
E(21)^10+E(21)^13+E(21)^19,E(21)^5+E(21)^17+E(21)^20,E(7)+E(7)^2+E(7)^4,
E(21)^10+E(21)^13+E(21)^19,E(21)^5+E(21)^17+E(21)^20,E(7)^3+E(7)^5+E(7)^6,
E(21)+E(21)^4+E(21)^16,E(21)^2+E(21)^8+E(21)^11,E(7)^3+E(7)^5+E(7)^6,
E(21)+E(21)^4+E(21)^16,E(21)^2+E(21)^8+E(21)^11,E(7)^3+E(7)^5+E(7)^6,
E(21)+E(21)^4+E(21)^16,E(21)^2+E(21)^8+E(21)^11,E(7)^3+E(7)^5+E(7)^6,
E(21)+E(21)^4+E(21)^16,E(21)^2+E(21)^8+E(21)^11,E(7)^3+E(7)^5+E(7)^6,
E(21)+E(21)^4+E(21)^16,E(21)^2+E(21)^8+E(21)^11,E(7)^3+E(7)^5+E(7)^6,
E(21)+E(21)^4+E(21)^16,E(21)^2+E(21)^8+E(21)^11,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0],
[GALOIS,[106,2]],
[GALOIS,[106,10]],
[GALOIS,[106,5]],[384,384*E(3),384*E(3)^2,384,384*E(3),384*E(3)^2,384,
384*E(3),384*E(3)^2,384,384*E(3),384*E(3)^2,384,384*E(3),384*E(3)^2,384,
384*E(3),384*E(3)^2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,24,24*E(3),24*E(3)^2,
24,24*E(3),24*E(3)^2,24,24*E(3),24*E(3)^2,24,24*E(3),24*E(3)^2,24,24*E(3),
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[GALOIS,[110,2]],[420,420*E(3),420*E(3)^2,420,420*E(3),420*E(3)^2,420,
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0,0,0,0,0,0,E(3)-E(3)^2,E(3)+2*E(3)^2,-2*E(3)-E(3)^2,E(3)-E(3)^2,E(3)+2*E(3)^2
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[GALOIS,[112,2]],[630,630*E(3),630*E(3)^2,630,630*E(3),630*E(3)^2,630,
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[GALOIS,[114,2]],[729,729*E(3),729*E(3)^2,729,729*E(3),729*E(3)^2,729,
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[GALOIS,[116,2]],[756,756*E(3),756*E(3)^2,756,756*E(3),756*E(3)^2,756,
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-E(3)^2,-1,-E(3),-E(3)^2,-1,-E(3),-E(3)^2,-1,-E(3),-E(3)^2,-1,-E(3),-E(3)^2],
[GALOIS,[118,2]],[945,945*E(3),945*E(3)^2,945,945*E(3),945*E(3)^2,945,
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E(3)^2],
[GALOIS,[120,2]],[15,15*E(3),15*E(3)^2,15,15*E(3),15*E(3)^2,15*E(3)^2,15,
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E(3)+2*E(3)^2,-2*E(3)-E(3)^2,E(3)-E(3)^2,E(3)+2*E(3)^2,-2*E(3)-E(3)^2,
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[GALOIS,[122,2]],[21,21*E(3),21*E(3)^2,21,21*E(3),21*E(3)^2,21*E(3)^2,21,
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5*E(3),5*E(3)^2,5,5*E(3),5*E(3)^2,5*E(3)^2,5,5*E(3),5*E(3)^2,5,5*E(3),5*E(3),
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2*E(3)^2,2*E(3)^2,2,2*E(3),2*E(3)^2,2,2*E(3),2*E(3),2*E(3)^2,2,2*E(3),2*E(3)^2
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[GALOIS,[124,2]],[105,105*E(3),105*E(3)^2,105,105*E(3),105*E(3)^2,105*E(3)^2,
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[GALOIS,[126,2]],[105,105*E(3),105*E(3)^2,105,105*E(3),105*E(3)^2,105*E(3)^2,
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[GALOIS,[128,2]],[105,105*E(3),105*E(3)^2,105,105*E(3),105*E(3)^2,105*E(3)^2,
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[GALOIS,[130,2]],[210,210*E(3),210*E(3)^2,210,210*E(3),210*E(3)^2,210*E(3)^2,
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[GALOIS,[132,2]],[315,315*E(3),315*E(3)^2,315,315*E(3),315*E(3)^2,315*E(3)^2,
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,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[136,2]],[360,360*E(3),360*E(3)^2,360,360*E(3),360*E(3)^2,360*E(3)^2,
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E(21)^10+E(21)^13+E(21)^19,E(21)^5+E(21)^17+E(21)^20,E(7)+E(7)^2+E(7)^4,
E(21)^10+E(21)^13+E(21)^19,E(21)^5+E(21)^17+E(21)^20,E(21)^5+E(21)^17+E(21)^20
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E(7)+E(7)^2+E(7)^4,E(21)^10+E(21)^13+E(21)^19,E(21)^10+E(21)^13+E(21)^19,
E(21)^5+E(21)^17+E(21)^20,E(7)+E(7)^2+E(7)^4,E(21)^10+E(21)^13+E(21)^19,
E(21)^5+E(21)^17+E(21)^20,E(7)+E(7)^2+E(7)^4,E(7)^3+E(7)^5+E(7)^6,
E(21)+E(21)^4+E(21)^16,E(21)^2+E(21)^8+E(21)^11,E(7)^3+E(7)^5+E(7)^6,
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3*E(3)^2,3,3*E(3),0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,E(7)+E(7)^2+E(7)^4,E(21)^10+E(21)^13+E(21)^19,
E(21)^5+E(21)^17+E(21)^20,E(7)+E(7)^2+E(7)^4,E(21)^10+E(21)^13+E(21)^19,
E(21)^5+E(21)^17+E(21)^20,E(21)^10+E(21)^13+E(21)^19,E(21)^5+E(21)^17+E(21)^20
,E(7)+E(7)^2+E(7)^4,E(21)^10+E(21)^13+E(21)^19,E(21)^5+E(21)^17+E(21)^20,
E(7)+E(7)^2+E(7)^4,E(21)^5+E(21)^17+E(21)^20,E(7)+E(7)^2+E(7)^4,
E(21)^10+E(21)^13+E(21)^19,E(21)^5+E(21)^17+E(21)^20,E(7)+E(7)^2+E(7)^4,
E(21)^10+E(21)^13+E(21)^19,E(7)^3+E(7)^5+E(7)^6,E(21)+E(21)^4+E(21)^16,
E(21)^2+E(21)^8+E(21)^11,E(7)^3+E(7)^5+E(7)^6,E(21)+E(21)^4+E(21)^16,
E(21)^2+E(21)^8+E(21)^11,E(21)+E(21)^4+E(21)^16,E(21)^2+E(21)^8+E(21)^11,
E(7)^3+E(7)^5+E(7)^6,E(21)+E(21)^4+E(21)^16,E(21)^2+E(21)^8+E(21)^11,
E(7)^3+E(7)^5+E(7)^6,E(21)^2+E(21)^8+E(21)^11,E(7)^3+E(7)^5+E(7)^6,
E(21)+E(21)^4+E(21)^16,E(21)^2+E(21)^8+E(21)^11,E(7)^3+E(7)^5+E(7)^6,
E(21)+E(21)^4+E(21)^16,-1,-E(3),-E(3)^2,-1,-E(3),-E(3)^2,-E(3),-E(3)^2,-1,
-E(3),-E(3)^2,-1,-E(3)^2,-1,-E(3),-E(3)^2,-1,-E(3),0,0,0,0,0,0,0,0,0,0,0,0,0,0
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E(3)^2,1,E(3),E(3)^2,1,E(3)],
[GALOIS,[156,2]],
[GALOIS,[156,10]],
[GALOIS,[156,5]],[126,126*E(3),126*E(3)^2,126,126*E(3),126*E(3)^2,126*E(3),
126*E(3)^2,126,126*E(3),126*E(3)^2,126,126*E(3)^2,126,126*E(3),126*E(3)^2,126,
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14*E(3),14*E(3)^2,14,14*E(3)^2,14,14*E(3),14*E(3)^2,14,14*E(3),-9,-9*E(3),
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1,E(3),-1,-E(3),-E(3)^2,-1,-E(3),-E(3)^2,-E(3),-E(3)^2,-1,-E(3),-E(3)^2,-1,
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-E(3),-E(3)^2,-1,-E(3)^2,-1,-E(3),-E(3)^2,-1,-E(3)],
[GALOIS,[160,2]],[189,189*E(3),189*E(3)^2,189,189*E(3),189*E(3)^2,189*E(3),
189*E(3)^2,189,189*E(3),189*E(3)^2,189,189*E(3)^2,189,189*E(3),189*E(3)^2,189,
189*E(3),-3,-3*E(3),-3*E(3)^2,-3,-3*E(3),-3*E(3)^2,-3*E(3),-3*E(3)^2,-3,
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5*E(3),5*E(3)^2,5,5*E(3),1,E(3),E(3)^2,E(3),E(3)^2,1,E(3)^2,1,E(3),-1,-E(3),
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-1,-E(3)^2,-1,-E(3),-E(3)^2,-1,-E(3)],
[GALOIS,[162,2]],[315,315*E(3),315*E(3)^2,315,315*E(3),315*E(3)^2,315*E(3),
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315*E(3),11,11*E(3),11*E(3)^2,11,11*E(3),11*E(3)^2,11*E(3),11*E(3)^2,11,
11*E(3),11*E(3)^2,11,11*E(3)^2,11,11*E(3),11*E(3)^2,11,11*E(3),18,18*E(3),
18*E(3)^2,18,18*E(3),18*E(3)^2,18*E(3),18*E(3)^2,18,18*E(3),18*E(3)^2,18,
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2*E(3),2*E(3)^2,2*E(3),2*E(3)^2,2,2*E(3),2*E(3)^2,2,2*E(3)^2,2,2*E(3),2*E(3)^2
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2*E(3),2*E(3)^2,2,2*E(3)^2,2,2*E(3),2*E(3)^2,2,2*E(3)],
[GALOIS,[164,2]],[315,315*E(3),315*E(3)^2,315,315*E(3),315*E(3)^2,315*E(3),
315*E(3)^2,315,315*E(3),315*E(3)^2,315,315*E(3)^2,315,315*E(3),315*E(3)^2,315,
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-5*E(3),-5*E(3)^2,-5,-5*E(3)^2,-5,-5*E(3),-5*E(3)^2,-5,-5*E(3),18,18*E(3),
18*E(3)^2,18,18*E(3),18*E(3)^2,18*E(3),18*E(3)^2,18,18*E(3),18*E(3)^2,18,
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3*E(3),3*E(3)^2,3,3*E(3),-1,-E(3),-E(3)^2,-E(3),-E(3)^2,-1,-E(3)^2,-1,-E(3),0,
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-2*E(3),-2*E(3)^2,-2,-2*E(3),-2*E(3)^2,-2,-2*E(3)^2,-2,-2*E(3),-2*E(3)^2,-2,
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4*E(3),4*E(3)^2,4*E(3),4*E(3)^2,4,4*E(3),4*E(3)^2,4,4*E(3)^2,4,4*E(3),4*E(3)^2
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0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[166,2]],[315,315*E(3),315*E(3)^2,315,315*E(3),315*E(3)^2,315*E(3),
315*E(3)^2,315,315*E(3),315*E(3)^2,315,315*E(3)^2,315,315*E(3),315*E(3)^2,315,
315*E(3),-5,-5*E(3),-5*E(3)^2,-5,-5*E(3),-5*E(3)^2,-5*E(3),-5*E(3)^2,-5,
-5*E(3),-5*E(3)^2,-5,-5*E(3)^2,-5,-5*E(3),-5*E(3)^2,-5,-5*E(3),18,18*E(3),
18*E(3)^2,18,18*E(3),18*E(3)^2,18*E(3),18*E(3)^2,18,18*E(3),18*E(3)^2,18,
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3*E(3),3*E(3)^2,3,3*E(3),-1,-E(3),-E(3)^2,-E(3),-E(3)^2,-1,-E(3)^2,-1,-E(3),0,
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4,4*E(3)^2,4,4*E(3),4*E(3)^2,4,4*E(3),-2,-2*E(3),-2*E(3)^2,-2,-2*E(3),
-2*E(3)^2,-2*E(3),-2*E(3)^2,-2,-2*E(3),-2*E(3)^2,-2,-2*E(3)^2,-2,-2*E(3),
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[GALOIS,[168,2]],[630,630*E(3),630*E(3)^2,630,630*E(3),630*E(3)^2,630*E(3),
630*E(3)^2,630,630*E(3),630*E(3)^2,630,630*E(3)^2,630,630*E(3),630*E(3)^2,630,
630*E(3),6,6*E(3),6*E(3)^2,6,6*E(3),6*E(3)^2,6*E(3),6*E(3)^2,6,6*E(3),6*E(3)^2
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-1,-E(3),-E(3)^2,-1,-E(3)],
[GALOIS,[170,2]],[720,720*E(3),720*E(3)^2,720,720*E(3),720*E(3)^2,720*E(3),
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16*E(3),16*E(3)^2,16,16*E(3)^2,16,16*E(3),16*E(3)^2,16,16*E(3),18,18*E(3),
18*E(3)^2,18,18*E(3),18*E(3)^2,18*E(3),18*E(3)^2,18,18*E(3),18*E(3)^2,18,
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[GALOIS,[176,2]],[945,945*E(3),945*E(3)^2,945,945*E(3),945*E(3)^2,945*E(3),
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[GALOIS,[186,2]],[84,-84*E(3)^2,84*E(3),-84,84*E(3)^2,-84*E(3),-84,84*E(3)^2,
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,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-E(3)+E(3)^2,-2*E(3)-E(3)^2,
-E(3)-2*E(3)^2,E(3)-E(3)^2,2*E(3)+E(3)^2,E(3)+2*E(3)^2,E(3)+2*E(3)^2,
-E(3)+E(3)^2,-2*E(3)-E(3)^2,-E(3)-2*E(3)^2,E(3)-E(3)^2,2*E(3)+E(3)^2,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[204,2]],[120,-120*E(3)^2,120*E(3),-120,120*E(3)^2,-120*E(3),
-120*E(3),120,-120*E(3)^2,120*E(3),-120,120*E(3)^2,120*E(3)^2,-120*E(3),120,
-120*E(3)^2,120*E(3),-120,-8,8*E(3)^2,-8*E(3),8,-8*E(3)^2,8*E(3),8*E(3),-8,
8*E(3)^2,-8*E(3),8,-8*E(3)^2,-8*E(3)^2,8*E(3),-8,8*E(3)^2,-8*E(3),8,-6,
6*E(3)^2,-6*E(3),6,-6*E(3)^2,6*E(3),6*E(3),-6,6*E(3)^2,-6*E(3),6,-6*E(3)^2,
-6*E(3)^2,6*E(3),-6,6*E(3)^2,-6*E(3),6,0,0,0,0,0,0,15*E(3)^2,-15*E(3),15,
-15*E(3)^2,15*E(3),-15,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,2*E(3)^2,-2*E(3),2,-2*E(3)^2,2*E(3),
2*E(3),-2,2*E(3)^2,-2*E(3),2,-2*E(3)^2,-2*E(3)^2,2*E(3),-2,2*E(3)^2,-2*E(3),2,
-2,2*E(3)^2,-2*E(3),2,-2*E(3)^2,2*E(3),2*E(3),-2,2*E(3)^2,-2*E(3),2,-2*E(3)^2,
-2*E(3)^2,2*E(3),-2,2*E(3)^2,-2*E(3),2,1,-E(3)^2,E(3),-1,E(3)^2,-E(3),-E(3),1,
-E(3)^2,E(3),-1,E(3)^2,E(3)^2,-E(3),1,-E(3)^2,E(3),-1,1,-E(3)^2,E(3),-1,E(3)^2
,-E(3),-E(3),1,-E(3)^2,E(3),-1,E(3)^2,E(3)^2,-E(3),1,-E(3)^2,E(3),-1,1,-E(3)^2
,E(3),-1,E(3)^2,-E(3),-E(3),1,-E(3)^2,E(3),-1,E(3)^2,E(3)^2,-E(3),1,-E(3)^2,
E(3),-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
-E(3)+E(3)^2,-2*E(3)-E(3)^2,-E(3)-2*E(3)^2,E(3)-E(3)^2,2*E(3)+E(3)^2,
E(3)+2*E(3)^2,E(3)+2*E(3)^2,-E(3)+E(3)^2,-2*E(3)-E(3)^2,-E(3)-2*E(3)^2,
E(3)-E(3)^2,2*E(3)+E(3)^2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[206,2]],[270,-270*E(3)^2,270*E(3),-270,270*E(3)^2,-270*E(3),
-270*E(3),270,-270*E(3)^2,270*E(3),-270,270*E(3)^2,270*E(3)^2,-270*E(3),270,
-270*E(3)^2,270*E(3),-270,6,-6*E(3)^2,6*E(3),-6,6*E(3)^2,-6*E(3),-6*E(3),6,
-6*E(3)^2,6*E(3),-6,6*E(3)^2,6*E(3)^2,-6*E(3),6,-6*E(3)^2,6*E(3),-6,27,
-27*E(3)^2,27*E(3),-27,27*E(3)^2,-27*E(3),-27*E(3),27,-27*E(3)^2,27*E(3),-27,
27*E(3)^2,27*E(3)^2,-27*E(3),27,-27*E(3)^2,27*E(3),-27,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,2,-2*E(3)^2,2*E(3),-2,2*E(3)^2,-2*E(3),-2*E(3),2,-2*E(3)^2,2*E(3),-2,
2*E(3)^2,2*E(3)^2,-2*E(3),2,-2*E(3)^2,2*E(3),-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,3,-3*E(3)^2,3*E(3),-3,3*E(3)^2,-3*E(3),-3*E(3),3,
-3*E(3)^2,3*E(3),-3,3*E(3)^2,3*E(3)^2,-3*E(3),3,-3*E(3)^2,3*E(3),-3,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
-E(7)^3-E(7)^5-E(7)^6,E(21)^2+E(21)^8+E(21)^11,-E(21)-E(21)^4-E(21)^16,
E(7)^3+E(7)^5+E(7)^6,-E(21)^2-E(21)^8-E(21)^11,E(21)+E(21)^4+E(21)^16,
E(21)+E(21)^4+E(21)^16,-E(7)^3-E(7)^5-E(7)^6,E(21)^2+E(21)^8+E(21)^11,
-E(21)-E(21)^4-E(21)^16,E(7)^3+E(7)^5+E(7)^6,-E(21)^2-E(21)^8-E(21)^11,
-E(21)^2-E(21)^8-E(21)^11,E(21)+E(21)^4+E(21)^16,-E(7)^3-E(7)^5-E(7)^6,
E(21)^2+E(21)^8+E(21)^11,-E(21)-E(21)^4-E(21)^16,E(7)^3+E(7)^5+E(7)^6,
-E(7)-E(7)^2-E(7)^4,E(21)^5+E(21)^17+E(21)^20,-E(21)^10-E(21)^13-E(21)^19,
E(7)+E(7)^2+E(7)^4,-E(21)^5-E(21)^17-E(21)^20,E(21)^10+E(21)^13+E(21)^19,
E(21)^10+E(21)^13+E(21)^19,-E(7)-E(7)^2-E(7)^4,E(21)^5+E(21)^17+E(21)^20,
-E(21)^10-E(21)^13-E(21)^19,E(7)+E(7)^2+E(7)^4,-E(21)^5-E(21)^17-E(21)^20,
-E(21)^5-E(21)^17-E(21)^20,E(21)^10+E(21)^13+E(21)^19,-E(7)-E(7)^2-E(7)^4,
E(21)^5+E(21)^17+E(21)^20,-E(21)^10-E(21)^13-E(21)^19,E(7)+E(7)^2+E(7)^4,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,-1,E(3)^2,-E(3),1,-E(3)^2,E(3),E(3),-1,E(3)^2,-E(3),1,-E(3)^2,-E(3)^2,E(3),-1
,E(3)^2,-E(3),1],
[GALOIS,[208,2]],
[GALOIS,[208,10]],
[GALOIS,[208,5]],[6,-6*E(3)^2,6*E(3),-6,6*E(3)^2,-6*E(3),-6*E(3),6,-6*E(3)^2,
6*E(3),-6,6*E(3)^2,6*E(3)^2,-6*E(3),6,-6*E(3)^2,6*E(3),-6,-2,2*E(3)^2,-2*E(3),
2,-2*E(3)^2,2*E(3),2*E(3),-2,2*E(3)^2,-2*E(3),2,-2*E(3)^2,-2*E(3)^2,2*E(3),-2,
2*E(3)^2,-2*E(3),2,-3,3*E(3)^2,-3*E(3),3,-3*E(3)^2,3*E(3),3*E(3),-3,3*E(3)^2,
-3*E(3),3,-3*E(3)^2,-3*E(3)^2,3*E(3),-3,3*E(3)^2,-3*E(3),3,0,0,0,0,0,0,
3*E(3)^2,-3*E(3),3,-3*E(3)^2,3*E(3),-3,0,0,2,-2*E(3)^2,2*E(3),-2,2*E(3)^2,
-2*E(3),-2*E(3),2,-2*E(3)^2,2*E(3),-2,2*E(3)^2,2*E(3)^2,-2*E(3),2,-2*E(3)^2,
2*E(3),-2,0,0,0,0,0,0,0,0,0,1,-E(3)^2,E(3),-1,E(3)^2,-E(3),-E(3),1,-E(3)^2,
E(3),-1,E(3)^2,E(3)^2,-E(3),1,-E(3)^2,E(3),-1,1,-E(3)^2,E(3),-1,E(3)^2,-E(3),
-E(3),1,-E(3)^2,E(3),-1,E(3)^2,E(3)^2,-E(3),1,-E(3)^2,E(3),-1,-2,2*E(3)^2,
-2*E(3),2,-2*E(3)^2,2*E(3),2*E(3),-2,2*E(3)^2,-2*E(3),2,-2*E(3)^2,-2*E(3)^2,
2*E(3),-2,2*E(3)^2,-2*E(3),2,1,-E(3)^2,E(3),-1,E(3)^2,-E(3),-E(3),1,-E(3)^2,
E(3),-1,E(3)^2,E(3)^2,-E(3),1,-E(3)^2,E(3),-1,-1,E(3)^2,-E(3),1,-E(3)^2,E(3),
E(3),-1,E(3)^2,-E(3),1,-E(3)^2,-E(3)^2,E(3),-1,E(3)^2,-E(3),1,-1,E(3)^2,-E(3),
1,-E(3)^2,E(3),E(3),-1,E(3)^2,-E(3),1,-E(3)^2,-E(3)^2,E(3),-1,E(3)^2,-E(3),1,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,E(3)+2*E(3)^2,
-E(3)+E(3)^2,-2*E(3)-E(3)^2,-E(3)-2*E(3)^2,E(3)-E(3)^2,2*E(3)+E(3)^2,
-E(3)+E(3)^2,-2*E(3)-E(3)^2,-E(3)-2*E(3)^2,E(3)-E(3)^2,2*E(3)+E(3)^2,
E(3)+2*E(3)^2,-1,E(3)^2,-E(3),1,-E(3)^2,E(3),E(3),-1,E(3)^2,-E(3),1,-E(3)^2,
-E(3)^2,E(3),-1,E(3)^2,-E(3),1],
[GALOIS,[212,2]],[126,-126*E(3)^2,126*E(3),-126,126*E(3)^2,-126*E(3),-126,
126*E(3)^2,-126*E(3),126,-126*E(3)^2,126*E(3),126,-126*E(3)^2,126*E(3),-126,
126*E(3)^2,-126*E(3),-10,10*E(3)^2,-10*E(3),10,-10*E(3)^2,10*E(3),10,
-10*E(3)^2,10*E(3),-10,10*E(3)^2,-10*E(3),-10,10*E(3)^2,-10*E(3),10,-10*E(3)^2
,10*E(3),18,-18*E(3)^2,18*E(3),-18,18*E(3)^2,-18*E(3),-18,18*E(3)^2,-18*E(3),
18,-18*E(3)^2,18*E(3),18,-18*E(3)^2,18*E(3),-18,18*E(3)^2,-18*E(3),9,-9*E(3)^2
,9*E(3),-9,9*E(3)^2,-9*E(3),0,0,0,0,0,0,0,0,2,-2*E(3)^2,2*E(3),-2,2*E(3)^2,
-2*E(3),-2,2*E(3)^2,-2*E(3),2,-2*E(3)^2,2*E(3),2,-2*E(3)^2,2*E(3),-2,2*E(3)^2,
-2*E(3),0,0,0,0,0,0,0,0,0,1,-E(3)^2,E(3),-1,E(3)^2,-E(3),-1,E(3)^2,-E(3),1,
-E(3)^2,E(3),1,-E(3)^2,E(3),-1,E(3)^2,-E(3),2,-2*E(3)^2,2*E(3),-2,2*E(3)^2,
-2*E(3),-2,2*E(3)^2,-2*E(3),2,-2*E(3)^2,2*E(3),2,-2*E(3)^2,2*E(3),-2,2*E(3)^2,
-2*E(3),-1,E(3)^2,-E(3),1,-E(3)^2,E(3),1,-E(3)^2,E(3),-1,E(3)^2,-E(3),-1,
E(3)^2,-E(3),1,-E(3)^2,E(3),2,-2*E(3)^2,2*E(3),-2,2*E(3)^2,-2*E(3),-2,2*E(3)^2
,-2*E(3),2,-2*E(3)^2,2*E(3),2,-2*E(3)^2,2*E(3),-2,2*E(3)^2,-2*E(3),0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,-2*E(3)^2
,2*E(3),-2,2*E(3)^2,-2*E(3),-2,2*E(3)^2,-2*E(3),2,-2*E(3)^2,2*E(3),2,-2*E(3)^2
,2*E(3),-2,2*E(3)^2,-2*E(3)],
[GALOIS,[214,2]],[630,-630*E(3)^2,630*E(3),-630,630*E(3)^2,-630*E(3),-630,
630*E(3)^2,-630*E(3),630,-630*E(3)^2,630*E(3),630,-630*E(3)^2,630*E(3),-630,
630*E(3)^2,-630*E(3),-18,18*E(3)^2,-18*E(3),18,-18*E(3)^2,18*E(3),18,
--> --------------------

--> maximum size reached

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