Quelle  ctounit2.tbl   Sprache: unbekannt

#############################################################################
##
#W  ctounit2.tbl                GAP table library               Thomas Breuer
##
##  This file contains the ordinary character tables related to the unitary
##  groups $U_3(q)$, for $q$ in [ 3, 4, 5, 7, 8, 9 ] of the ATLAS.
##
#H  ctbllib history
#H  ---------------
#H  $Log: ctounit2.tbl,v $
#H  Revision 4.36  2012/06/20 14:45:33  gap
#H  added tables and fusions, as documented in ctbldiff.dat
#H      TB
#H
#H  Revision 4.35  2012/03/28 13:16:36  gap
#H  added a permutation (of the maximal subgroups) for the fusion to the
#H  table of marks of Sz(8).3, L2(11).2, HS.2, He.2, S4(5), U3(3), U4(2).2
#H      TB
#H
#H  Revision 4.34  2012/01/30 08:32:04  gap
#H  removed #H entries from the headers
#H      TB
#H
#H  Revision 4.33  2011/09/28 14:18:04  gap
#H  - removed revision entry and SET_TABLEFILENAME call,
#H  - added maxes entry for U3(3)
#H      TB
#H
#H  Revision 4.32  2010/09/15 08:08:25  gap
#H  adjusted the "tom:<n>" information in some fusions
#H      TB
#H
#H  Revision 4.31  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 4.30  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 4.29  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 4.28  2008/06/24 16:23:06  gap
#H  added several fusions and names
#H      TB
#H
#H  Revision 4.27  2006/06/07 07:54:27  gap
#H  unified ConstructMixed and ConstructMGA (for better programmatic access)
#H      TB
#H
#H  Revision 4.26  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 4.25  2003/06/20 15:03:13  gap
#H  added several fusions
#H      TB
#H
#H  Revision 4.24  2003/06/10 16:19:17  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 4.23  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 4.22  2003/01/24 15:57:41  gap
#H  replaced several fusions by ones that are compatible with Brauer tables
#H      TB
#H
#H  Revision 4.21  2003/01/21 16:25:33  gap
#H  further standardizations of `InfoText' strings,
#H  added and corrected `Maxes' infos,
#H  added some fusions
#H      TB
#H
#H  Revision 4.20  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 4.19  2003/01/13 17:17:04  gap
#H  typo
#H      TB
#H
#H  Revision 4.18  2003/01/03 10:11:06  gap
#H  added tables of U3(8).S3 and 3.U3(8).S3
#H      TB
#H
#H  Revision 4.17  2002/11/04 16:33:47  gap
#H  added fusions of maxes of U3(3).2,
#H  added fusion U3(3).2 -> Fi24' (this took me a whole afternoon ...)
#H      TB
#H
#H  Revision 4.16  2002/09/23 15:07:46  gap
#H  removed trailing blanks
#H      TB
#H
#H  Revision 4.15  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 4.14  2002/08/21 13:53:52  gap
#H  removed names of the form `c1m<n>', `c2m<n>', `c3m<n>'
#H      TB
#H
#H  Revision 4.13  2002/08/01 13:41:55  gap
#H  added 2-modular tables of L3(7).S3, 3.L3(7).S3, 3.U3(5).S3, U3(11).S3,
#H  and 3.U3(11).S3
#H      TB
#H
#H  Revision 4.12  2002/08/01 08:24:22  gap
#H  added tables of 3.L3(7).S3, L3(7).S3, 3.U3(5).S3, 3.U3(11).S3, U3(11).S3
#H      TB
#H
#H  Revision 4.11  2002/07/12 06:45:57  gap
#H  further tidying up: removed `irredinfo' stuff, rearranged constructions
#H      TB
#H
#H  Revision 4.10  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 4.9  2001/05/04 16:50:36  gap
#H  first revision for ctbllib
#H
#H
#H  tbl history (GAP 4)
#H  -------------------
#H  (Rev. 4.9 of ctbllib coincides with Rev. 4.8 of tbl in GAP 4)
#H  
#H  RCS file: /gap/CVS/GAP/4.0/tbl/ctounit2.tbl,v
#H  Working file: ctounit2.tbl
#H  head: 4.8
#H  branch:
#H  locks: strict
#H  access list:
#H  symbolic names:
#H   GAP4R2: 4.8.0.6
#H   GAP4R2PRE2: 4.8.0.4
#H   GAP4R2PRE1: 4.8.0.2
#H   GAP4R1: 4.5.0.2
#H  keyword substitution: kv
#H  total revisions: 9; selected revisions: 9
#H  description:
#H  ----------------------------
#H  revision 4.8
#H  date: 1999/10/22 13:24:48;  author: gap;  state: Exp;  lines: +5 -2
#H  added maxes of J2.2
#H  
#H      TB
#H  ----------------------------
#H  revision 4.7
#H  date: 1999/10/21 14:15:49;  author: gap;  state: Exp;  lines: +20 -2
#H  added many `tomidentifer' and `tomfusion' values, which yields a better
#H  interface between `tom' and `tbl';
#H  
#H  added maxes of McL.2,
#H  
#H  unified tables `J2.2M4', `2^(2+4):(3x3):2^2', `2^(2+4):(S3xS3)'.
#H  
#H      TB
#H  ----------------------------
#H  revision 4.6
#H  date: 1999/08/23 10:28:06;  author: gap;  state: Exp;  lines: +25 -72
#H  unified tables of U3(5).S3 and U3(5).3.2
#H  (one CAS table, one ATLAS conformal table)
#H  
#H      TB
#H  ----------------------------
#H  revision 4.5
#H  date: 1999/05/14 08:05:57;  author: gap;  state: Exp;  lines: +34 -3
#H  added the tables of some maxes of O8+(3)
#H  (yes, these tables are not relevant for the release of GAP 4,
#H  but Bob Guralnick had asked for them ...)
#H  
#H      TB
#H  ----------------------------
#H  revision 4.4
#H  date: 1998/10/28 15:05:52;  author: gap;  state: Exp;  lines: +6 -2
#H  added fusions from S12 and U3(8).6 into HN.2
#H  
#H      TB
#H  ----------------------------
#H  revision 4.3
#H  date: 1998/04/03 13:26:55;  author: gap;  state: Exp;  lines: +21 -3
#H  added tables of maxes of G2(3) and fusions into G2(3)
#H  
#H      TB
#H  ----------------------------
#H  revision 4.2
#H  date: 1997/11/25 15:46:05;  author: gap;  state: Exp;  lines: +14 -3
#H  first attempt to link the library of character tables and the
#H      library of tables of marks
#H          TB
#H  ----------------------------
#H  revision 4.1
#H  date: 1997/07/17 15:48:26;  author: fceller;  state: Exp;  lines: +2 -2
#H  for version 4
#H  ----------------------------
#H  revision 1.1
#H  date: 1996/10/21 16:02:07;  author: sam;  state: Exp;
#H  first proposal of the table library
#H  ==========================================================================
##

MOT("3.U3(5)",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7],\n",
"constructions: SU(3,5)"
],
[378000,378000,378000,720,720,720,36,24,24,24,750,750,750,75,75,75,75,75,75,
75,75,75,36,36,36,21,21,21,21,21,21,24,24,24,24,24,24,30,30,30],
[,[1,3,2,1,3,2,7,4,6,5,11,13,12,14,16,15,17,19,18,20,22,21,7,7,7,26,28,27,29,
31,30,8,10,9,8,10,9,11,13,12],[1,1,1,4,4,4,1,8,8,8,11,11,11,14,14,14,17,17,17,
20,20,20,4,4,4,29,29,29,26,26,26,32,32,32,35,35,35,38,38,38],,[1,3,2,4,6,5,7,
8,10,9,1,3,2,1,3,2,1,3,2,1,3,2,23,25,24,29,31,30,26,28,27,35,37,36,32,34,33,4,
6,5],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,1,2,
3,1,2,3,35,36,37,32,33,34,38,39,40]],
0,
[(32,35)(33,36)(34,37),(26,29)(27,30)(28,31),( 2, 3)( 5, 6)( 9,10)(12,13)
(15,16)(18,19)(21,22)(24,25)(27,28)(30,31)(33,34)(36,37)(39,40),(17,20)(18,21)
(19,22),(14,17)(15,18)(16,19)],
["ConstructProj",[["U3(5)",[]],,["3.U3(5)",[-1,-1,-1,-1,-1,-1,-1,-1,-1,17,17,
-13,-13]]]]);
ARC("3.U3(5)","maxes",["3.A7","3.U3(5)M2","3.U3(5)M3","3x5^(1+2)_+:8",
"3.A6.2_3","3.U3(5)M6","3.U3(5)M7","3x2S5"]);
ALF("3.U3(5)","U3(5)",[1,1,1,2,2,2,3,4,4,4,5,5,5,6,6,6,7,7,7,8,8,8,9,9,9,
10,10,10,11,11,11,12,12,12,13,13,13,14,14,14]);
ALF("3.U3(5)","3.U3(5).2",[1,2,2,3,4,4,5,6,7,7,8,9,9,10,11,11,12,13,14,12,
14,13,15,16,16,17,18,19,17,19,18,20,21,22,20,22,21,23,24,24],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);
ALF("3.U3(5)","3.U3(5).3",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,14,15,
16,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);
ALF("3.U3(5)","3.McL",[1,3,2,4,6,5,10,11,13,12,14,16,15,17,19,18,17,19,18,
17,19,18,23,25,24,26,28,27,29,31,30,32,34,33,32,34,33,37,39,38],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);

MOT("3.U3(5).2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[756000,378000,1440,720,72,48,24,1500,750,150,75,75,75,75,72,36,21,21,21,24,
24,24,60,30,240,240,12,8,10,12,20,20],
[,[1,2,1,2,5,3,4,8,9,10,11,12,14,13,5,5,17,19,18,6,7,7,8,9,1,3,5,6,10,15,23,
23],[1,1,3,3,1,6,6,8,8,10,10,12,12,12,3,3,17,17,17,20,20,20,23,23,25,26,25,28,
29,26,31,32],,[1,2,3,4,5,6,7,1,2,1,2,1,2,2,15,16,17,18,19,20,21,22,3,4,25,26,
27,28,25,30,26,26],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,1,2,2,20,22,21,23,
24,25,26,27,28,29,30,31,32]],
0,
[(31,32),(21,22),(21,22)(31,32),(18,19),(13,14),(13,14)(18,19)(21,22)],
["ConstructMGA","3.U3(5)","U3(5).2",
     [ [ 15, 16 ], [ 17, 18 ], [ 19, 20 ], [ 21, 24 ], [ 22, 23 ],
        [ 25, 26 ], [ 27, 28 ], [ 29, 30 ], [ 31, 32 ], [ 33, 36 ],
        [ 34, 35 ], [ 37, 40 ], [ 38, 39 ] ], ()]);
ALF("3.U3(5).2","U3(5).2",[1,1,2,2,3,4,4,5,5,6,6,7,7,7,8,8,9,9,9,10,10,10,
11,11,12,13,14,15,16,17,18,19]);
ALF("3.U3(5).2","3.U3(5).S3",[1,2,3,4,5,6,7,8,9,10,11,10,11,11,12,13,14,
15,16,17,18,19,20,21,53,54,55,56,57,58,59,60],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);
ALF("3.U3(5).2","G2(5)",[1,3,2,12,4,5,22,7,24,9,25,10,26,27,13,14,15,31,
32,16,34,33,18,38,2,6,14,16,20,23,30,30],[
"fusion map is unique up to table automorphisms,\n",
"compatible with Brauer tables"
]);
ALF("3.U3(5).2","3.McL.2",[1,2,3,4,7,8,9,10,11,12,13,12,13,13,16,17,18,19,
20,21,22,22,24,25,41,42,43,44,46,48,49,50],[
"fusion map is unique up to table aut."
]);
ALN("3.U3(5).2",["G2(5)N3A"]);

MOT("3.U3(5).3",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[1134000,1134000,1134000,2160,2160,2160,108,72,72,72,2250,2250,2250,75,75,75,
108,108,108,63,63,63,63,63,63,72,72,72,72,72,72,90,90,90,2160,2160,2160,2160,
2160,2160,63,63,2160,2160,2160,2160,2160,2160,108,108,108,108,108,108,72,72,
72,72,72,72,90,90,90,90,90,90,63,63,63,63,63,63,63,63,63,63,63,63,72,72,72,72,
72,72,72,72,72,72,72,72,90,90,90,90,90,90],
[,[1,3,2,1,3,2,7,4,6,5,11,13,12,14,16,15,7,7,7,20,22,21,23,25,24,8,10,9,8,10,
9,11,13,12,38,39,40,35,36,37,42,41,38,39,40,35,36,37,38,39,40,35,36,37,46,47,
48,43,44,45,64,65,66,61,62,63,71,72,70,68,69,67,77,78,76,74,75,73,58,59,60,55,
56,57,58,59,60,55,56,57,64,65,66,61,62,63],[1,1,1,4,4,4,1,8,8,8,11,11,11,14,
14,14,4,4,4,23,23,23,20,20,20,26,26,26,29,29,29,32,32,32,1,1,1,1,1,1,2,3,4,4,
4,4,4,4,4,4,4,4,4,4,8,8,8,8,8,8,11,11,11,11,11,11,24,24,24,25,25,25,21,21,21,
22,22,22,26,26,26,26,26,26,29,29,29,29,29,29,32,32,32,32,32,32],,[1,3,2,4,6,5,
7,8,10,9,1,3,2,1,3,2,17,19,18,23,25,24,20,22,21,29,31,30,26,28,27,4,6,5,38,39,
40,35,36,37,42,41,46,47,48,43,44,45,52,53,54,49,50,51,58,59,60,55,56,57,38,39,
40,35,36,37,76,77,78,73,74,75,70,71,72,67,68,69,88,89,90,85,86,87,82,83,84,79,
80,81,46,47,48,43,44,45],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,1,
2,3,1,2,3,29,30,31,26,27,28,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,
48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,41,41,41,42,42,42,41,
41,41,42,42,42,85,86,87,88,89,90,79,80,81,82,83,84,91,92,93,94,95,96]],
0,
[(26,29)(27,30)(28,31)(79,85)(80,86)(81,87)(82,88)(83,89)(84,90),(20,23)
(21,24)(22,25)(67,74,69,73,68,75)(70,77,72,76,71,78),( 2, 3)( 5, 6)( 9,10)
(12,13)(15,16)(18,19)(21,22)(24,25)(27,28)(30,31)(33,34)(35,38)(36,39)(37,40)
(41,42)(43,46)(44,47)(45,48)(49,52)(50,53)(51,54)(55,58)(56,59)(57,60)(61,64)
(62,65)(63,66)(67,72,68,70,69,71)(73,78,74,76,75,77)(79,82)(80,83)(81,84)
(85,88)(86,89)(87,90)(91,94)(92,95)(93,96),(67,69,68)(70,72,71)(73,75,74)
(76,78,77),(35,36,37)(38,39,40)(43,44,45)(46,47,48)(49,50,51)(52,53,54)
(55,56,57)(58,59,60)(61,62,63)(64,65,66)(79,80,81)(82,83,84)(85,86,87)
(88,89,90)(91,92,93)(94,95,96)],
["ConstructProj",[["U3(5).3",[]],,["3.U3(5).3",[-1,-1,-1,-1,-1,-1,-1,17,17,
-55,-55]]]]);
ALF("3.U3(5).3","U3(5).3",[1,1,1,2,2,2,3,4,4,4,5,5,5,6,6,6,7,7,7,8,8,8,9,
9,9,10,10,10,11,11,11,12,12,12,13,13,13,14,14,14,15,16,17,17,17,18,18,18,
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]);
ALF("3.U3(5).3","3.U3(5).S3",[1,2,2,3,4,4,5,6,7,7,8,9,9,10,11,11,12,13,13,
14,15,16,14,16,15,17,18,19,17,19,18,20,21,21,22,23,24,22,23,24,25,25,26,
27,28,26,27,28,29,30,31,29,30,31,32,33,34,32,33,34,35,36,37,35,36,37,38,
39,40,41,42,43,41,42,43,38,39,40,44,45,46,47,48,49,47,48,49,44,45,46,50,
51,52,50,51,52],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables"
]);

MOT("Isoclinic(3.U3(5).3,1)",
[
"1st isoclinic group of the 3.U3(5).3 given in the ATLAS"
],
0,
0,
0,
[(2,3)(5,6)(9,10)(12,13)(15,16)(18,19)(21,22)(24,25)(27,28)(30,31)(33,34)(35,
38,36,39,37,40)(41,42)(43,46,44,47,45,48)(49,52,50,53,51,54)(55,58,56,59,57,
60)(61,64,62,65,63,66)(67,70,68,71,69,72)(73,76,74,77,75,78)(79,82,80,83,81,
84)(85,88,86,89,87,90)(91,94,92,95,93,96),(67,68,69)(70,71,72)(73,74,75)(76,
77,78),(35,36,37)(38,39,40)(43,44,45)(46,47,48)(49,50,51)(52,53,54)(55,56,57)
(58,59,60)(61,62,63)(64,65,66)(79,80,81)(82,83,84)(85,86,87)(88,89,90)(91,92,
93)(94,95,96),(26,29)(27,30)(28,31)(79,85)(80,86)(81,87)(82,88)(83,89)(84,90),
(20,23)(21,24)(22,25)(67,73)(68,74)(69,75)(70,76)(71,77)(72,78)],
["ConstructIsoclinic",[["3.U3(5).3"]],rec(k:=1)]);
ALF("Isoclinic(3.U3(5).3,1)","U3(5).3",[1,1,1,2,2,2,3,4,4,4,5,5,5,6,6,6,7,
7,7,8,8,8,9,9,9,10,10,10,11,11,11,12,12,12,13,13,13,14,14,14,15,16,17,17,
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]);

MOT("Isoclinic(3.U3(5).3,2)",
[
"2nd isoclinic group of the 3.U3(5).3 given in the ATLAS"
],
0,
0,
0,
[(2,3)(5,6)(9,10)(12,13)(15,16)(18,19)(21,22)(24,25)(27,28)(30,31)(33,34)(35,
38,37,40,36,39)(41,42)(43,46,45,48,44,47)(49,52,51,54,50,53)(55,58,57,60,56,
59)(61,64,63,66,62,65)(67,70,69,72,68,71)(73,76,75,78,74,77)(79,82,81,84,80,
83)(85,88,87,90,86,89)(91,94,93,96,92,95),(67,68,69)(70,71,72)(73,74,75)(76,
77,78),(35,36,37)(38,39,40)(43,44,45)(46,47,48)(49,50,51)(52,53,54)(55,56,57)
(58,59,60)(61,62,63)(64,65,66)(79,80,81)(82,83,84)(85,86,87)(88,89,90)(91,92,
93)(94,95,96),(26,29)(27,30)(28,31)(79,85)(80,86)(81,87)(82,88)(83,89)(84,90),
(20,23)(21,24)(22,25)(67,73)(68,74)(69,75)(70,76)(71,77)(72,78)],
["ConstructIsoclinic",[["3.U3(5).3"]],rec(k:=2)]);
ALF("Isoclinic(3.U3(5).3,2)","U3(5).3",[1,1,1,2,2,2,3,4,4,4,5,5,5,6,6,6,7,
7,7,8,8,8,9,9,9,10,10,10,11,11,11,12,12,12,13,13,13,14,14,14,15,16,17,17,
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]);

MOT("3.U3(5).S3",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[2268000,1134000,4320,2160,216,144,72,4500,2250,150,75,216,108,63,63,63,72,72,
72,180,90,2160,2160,2160,63,2160,2160,2160,108,108,108,72,72,72,90,90,90,63,63
,63,63,63,63,72,72,72,72,72,72,90,90,90,240,240,12,8,10,12,20,20],
[,[1,2,1,2,5,3,4,8,9,10,11,5,5,14,16,15,6,7,7,8,9,22,23,24,25,22,23,24,22,23,
24,26,27,28,35,36,37,42,43,41,39,40,38,32,33,34,32,33,34,35,36,37,1,3,5,6,10,
12,20,20],[1,1,3,3,1,6,6,8,8,10,10,3,3,14,14,14,17,17,17,20,20,1,1,1,2,3,3,3,3
,3,3,6,6,6,8,8,8,16,16,16,15,15,15,17,17,17,17,17,17,20,20,20,53,54,53,56,57,
54,59,60],,[1,2,3,4,5,6,7,1,2,1,2,12,13,14,15,16,17,18,19,3,4,22,23,24,25,26,
27,28,29,30,31,32,33,34,22,23,24,38,39,40,41,42,43,44,45,46,47,48,49,26,27,28,
53,54,55,56,53,58,54,54],,[1,2,3,4,5,6,7,8,9,10,11,12,13,1,2,2,17,19,18,20,21,
22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,25,25,25,25,25,25,47,48,49,44,
45,46,50,51,52,53,54,55,56,57,58,59,60]],
0,
[(59,60),(38,39,40)(41,42,43),(15,16)(38,41)(39,42)(40,43),(22,23,24)(26,27,
28)(29,30,31)(32,33,34)(35,36,37)(44,45,46)(47,48,49)(50,51,52),(18,19)(44,
47)(45,48)(46,49)],
["ConstructGS3","3.U3(5).2","3.U3(5).3",[7,8,22],[[2,3],[5,6],[8,9],[12,13],
[15,16],[18,19],[21,22],[23,26],[25,27],[24,28],[29,32],[31,33],[30,34],[35,
38],[37,39],[36,40],[41,44],[43,45],[42,46],[49,52],[51,53],[50,54],[55,58],
[57,59],[56,60],[61,64],[63,65],[62,66],[67,70],[69,71],[68,72],[76,79],[78,
80],[77,81],[73,82],[75,83],[74,84],[88,91],[90,92],[89,93],[85,94],[87,95],
[86,96]],[[1,1],[4,3],[7,5],[11,10],[14,12],[17,14],[20,16]],(1,10,23,37,53,
12,26,40,50,5,6,9,20,33,48,2,11,24,39,51,7,14,27,42,60,22,34,47)(3,36,54,13,
25,38,49,4)(8,17,30,45,57,18,32,46,56,16,28,41,58,19,31,44,55,15,29,43,59,21,
35,52)]);
ALF("3.U3(5).S3","U3(5).3.2",[1,1,2,2,3,4,4,5,5,6,6,7,7,8,8,8,9,9,9,10,10,
11,11,11,12,13,13,13,14,14,14,15,15,15,16,16,16,17,17,17,18,18,18,19,19,
19,20,20,20,21,21,21,22,23,24,25,26,27,28,29]);

MOT("3.U3(8)",
[
"origin: ATLAS of finite groups, tests: 1.o.r.,\n",
"constructions: SU(3,8)"
],
[16547328,16547328,16547328,4608,4608,4608,4536,4536,4536,4536,4536,4536,81,
192,192,192,192,192,192,192,192,192,72,72,72,72,72,72,63,63,63,63,63,63,63,63,
63,81,81,81,81,81,81,81,81,81,57,57,57,57,57,57,57,57,57,57,57,57,57,57,57,57,
57,57,63,63,63,63,63,63,63,63,63,63,63,63,63,63,63,63,63,63],
[,[1,3,2,1,3,2,11,10,12,9,8,7,13,4,6,5,4,6,5,4,6,5,11,10,12,9,8,7,32,34,33,35,
37,36,29,31,30,41,43,42,44,46,45,38,40,39,56,58,57,53,55,54,62,64,63,59,61,60,
50,52,51,47,49,48,75,74,76,73,72,71,81,80,82,79,78,77,69,68,70,67,66,65],[1,1,
1,4,4,4,2,2,2,3,3,3,1,14,14,14,17,17,17,20,20,20,5,5,5,6,6,6,35,35,35,29,29,
29,32,32,32,13,13,13,13,13,13,13,13,13,56,56,56,53,53,53,62,62,62,59,59,59,50,
50,50,47,47,47,36,36,36,37,37,37,30,30,30,31,31,31,33,33,33,34,34,34],,,,[1,2,
3,4,5,6,9,7,8,11,12,10,13,14,15,16,17,18,19,20,21,22,25,23,24,27,28,26,1,2,3,
1,2,3,1,2,3,41,42,43,44,45,46,38,39,40,47,48,49,50,51,52,53,54,55,56,57,58,59,
60,61,62,63,64,9,7,8,11,12,10,9,7,8,11,12,10,9,7,8,11,12,10],,,,,,,,,,,,[1,2,
3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,32,33,
34,35,36,37,29,30,31,38,39,40,41,42,43,44,45,46,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,
1,2,3,71,72,73,74,75,76,77,78,79,80,81,82,65,66,67,68,69,70]],
0,
[(47,50)(48,51)(49,52)(53,56)(54,57)(55,58)(59,62)(60,63)(61,64),
(47,56,59,50,53,62)(48,57,60,51,54,63)(49,58,61,52,55,64),(47,59,53)(48,60,54)
(49,61,55)(50,62,56)(51,63,57)(52,64,58),(29,35,32)(30,36,33)(31,37,34)
(65,77,71)(66,78,72)(67,79,73)(68,80,74)(69,81,75)(70,82,76),(14,20)(15,21)
(16,22),(14,17)(15,18)(16,19),(17,20)(18,21)(19,22),( 2, 3)( 5, 6)
( 7,11, 8,10, 9,12)(15,16)(18,19)(21,22)(23,27,24,26,25,28)(30,31)(33,34)
(36,37)(38,41,44)(39,43,45,40,42,46)(48,49)(51,52)(54,55)(57,58)(60,61)(63,64)
(65,69,66,68,67,70)(71,75,72,74,73,76)(77,81,78,80,79,82)],
["ConstructProj",[["U3(8)",[]],,["3.U3(8)",[-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
-1,-55,-55,-55,-55,-55,-55,-55,-55,-55,-37,-37,-37,-37,-37,-37]]]]);
ARC("3.U3(8)","CAS",[rec(name:="u3q8a",
permchars:=( 3, 6,21,33, 4, 9,74,56,44,81,62,27,64,39,72,58,24,59,31,10,75,53,
 23,66,42,82,51,12,17,49,18,28,52,19,25,55,26,60,36,69,41,79,61,47,15,37,70,
 32, 5,20,40,73,67,34,11,14,43,77,57,35,68,48,16,30, 8,76,63,46,80,54,29, 7,
 22,45,78,65,38,71,50,13),
permclasses:=( 7,16,13,33,40,36,64,73,41,35,58,78,38,32,52,69,42,34,55,80,54,
 72,46,37,43,28,25,26,27,23,22,15,10,21,12,19,14)( 8,18,11,17)( 9,20)
(29,45,31,60,82,44,30,48,77,61,71,56,70,57,68,39)(47,67,62,81,63,65,50,79,49,
 66,53,75,59,74)(51,76),
text:=[
" test:= 1. o.r., sym 2 decompose correctly \n",
""])]);
ALF("3.U3(8)","U3(8)",[1,1,1,2,2,2,3,3,3,4,4,4,5,6,6,6,7,7,7,8,8,8,9,9,9,
10,10,10,11,11,11,12,12,12,13,13,13,14,14,14,15,15,15,16,16,16,17,17,17,
18,18,18,19,19,19,20,20,20,21,21,21,22,22,22,23,23,23,24,24,24,25,25,25,
26,26,26,27,27,27,28,28,28]);
ALF("3.U3(8)","3.U3(8).2",[1,2,2,3,4,4,5,6,7,5,7,6,8,9,10,10,11,12,13,11,
13,12,14,15,16,14,16,15,17,18,18,19,20,20,21,22,22,23,24,24,25,26,26,27,
28,28,29,30,31,29,31,30,32,33,34,32,34,33,35,36,37,35,37,36,38,39,40,38,
40,39,41,42,43,41,43,42,44,45,46,44,46,45],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);
ALF("3.U3(8)","3.U3(8).3_1",[1,2,3,4,5,6,7,7,7,8,8,8,9,10,11,12,13,14,15,
16,17,18,19,19,19,20,20,20,21,22,23,21,22,23,21,22,23,24,25,26,24,25,26,
24,25,26,27,28,29,30,31,32,27,28,29,30,31,32,27,28,29,30,31,32,33,34,35,
36,37,38,34,35,33,38,36,37,35,33,34,37,38,36],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);
ALF("3.U3(8)","3.U3(8).3_2",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,14,15,
16,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,
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],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);
ALF("3.U3(8)","3.U3(8).6",[1,2,2,3,4,4,5,5,5,5,5,5,6,7,8,8,9,10,11,9,11,
10,12,12,12,12,12,12,13,14,14,13,14,14,13,14,14,15,16,16,15,16,16,15,16,
16,17,18,19,17,19,18,17,18,19,17,19,18,17,18,19,17,19,18,20,21,22,20,22,
21,21,22,20,21,20,22,22,20,21,22,21,20],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);
ALN("3.U3(8)",["u3q8a"]);

MOT("3.U3(8).2",
[
"origin: ATLAS of finite groups, tests: 1.o.r."
],
[33094656,16547328,9216,4608,4536,4536,4536,162,384,192,192,192,192,72,72,72,
126,63,126,63,126,63,162,81,162,81,162,81,57,57,57,57,57,57,57,57,57,63,63,63,
63,63,63,63,63,63,1008,18,32,32,14,14,14,18,18,18],
[,[1,2,1,2,7,5,6,8,3,4,3,4,4,7,5,6,19,20,21,22,17,18,25,26,27,28,23,24,32,33,
34,35,36,37,29,30,31,43,41,42,46,44,45,40,38,39,1,8,9,9,19,21,17,25,27,23],[1,
1,3,3,2,2,2,1,9,9,11,11,11,4,4,4,21,21,17,17,19,19,8,8,8,8,8,8,32,32,32,35,35,
35,29,29,29,22,22,22,18,18,18,20,20,20,47,47,49,50,53,51,52,48,48,48],,,,[1,2,
3,4,7,5,6,8,9,10,11,12,13,16,14,15,1,2,1,2,1,2,25,26,27,28,23,24,29,30,31,32,
33,34,35,36,37,7,5,6,7,5,6,7,5,6,47,48,50,49,47,47,47,55,56,54],,,,,,,,,,,,[1,
2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,19,20,21,22,17,18,23,24,25,26,27,28,1,2,
2,1,2,2,1,2,2,41,42,43,44,45,46,38,39,40,47,48,49,50,52,53,51,54,55,56]],
0,
[(49,50),(30,31)(33,34)(36,37),(29,32,35)(30,34,36,31,33,37),(17,21,19)
(18,22,20)(38,44,41)(39,45,42)(40,46,43)(51,53,52),(12,13),( 5, 7, 6)(12,13)
(14,16,15)(23,25,27)(24,26,28)(30,31)(33,34)(36,37)(38,40,39)(41,43,42)
(44,46,45)(54,55,56),( 5, 7, 6)(14,16,15)(23,25,27)(24,26,28)(38,40,39)
(41,43,42)(44,46,45)(54,55,56)],
["ConstructMGA","3.U3(8)","U3(8).2",
     [ [ 29, 30 ], [ 31, 32 ], [ 33, 34 ], [ 35, 36 ], [ 37, 40 ],
        [ 38, 39 ], [ 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, 74 ], [ 72, 73 ], [ 75, 78 ], [ 76, 77 ],
        [ 79, 82 ], [ 80, 81 ] ], ()]);
ALF("3.U3(8).2","U3(8).2",[1,1,2,2,3,3,3,4,5,5,6,6,6,7,7,7,8,8,9,9,10,10,
11,11,12,12,13,13,14,14,14,15,15,15,16,16,16,17,17,17,18,18,18,19,19,19,
20,21,22,23,24,25,26,27,28,29]);
ALF("3.U3(8).2","3.U3(8).6",[1,2,3,4,5,5,5,6,7,8,9,10,11,12,12,12,13,14,
13,14,13,14,15,16,15,16,15,16,17,18,19,17,18,19,17,18,19,20,21,22,21,22,
20,22,20,21,23,24,25,26,27,27,27,28,28,28],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);
ALF("3.U3(8).2","3.U3(8).S3",[1,2,3,4,5,6,7,8,9,10,9,10,10,11,12,13,14,15,
16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,
40,41,42,43,117,118,119,120,121,122,123,124,125,126],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);

MOT("3.U3(8).3_1",
[
"origin: ATLAS of finite groups, tests: 1.o.r."
],
[49641984,49641984,49641984,13824,13824,13824,4536,4536,243,576,576,576,576,
576,576,576,576,576,72,72,63,63,63,81,81,81,57,57,57,57,57,57,63,63,63,63,63,
63,648,648,648,648,648,648,72,72,72,72,72,72,27,27,36,36,36,36,36,36,36,36,36,
36,36,36,36,36,36,36,36,36],
[,[1,3,2,1,3,2,8,7,9,4,6,5,4,6,5,4,6,5,8,7,21,23,22,24,26,25,30,32,31,27,29,
28,36,38,37,33,35,34,40,39,42,41,44,43,40,39,42,41,44,43,52,51,46,46,46,45,45,
45,48,48,48,47,47,47,50,50,50,49,49,49],[1,1,1,4,4,4,2,3,1,10,10,10,13,13,13,
16,16,16,5,6,21,21,21,9,9,9,30,30,30,27,27,27,22,22,22,23,23,23,1,1,2,3,3,2,4,
4,5,6,6,5,9,9,10,10,10,10,10,10,14,14,14,15,15,15,18,18,18,17,17,17],,,,[1,2,
3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,1,2,3,24,25,26,27,28,29,30,31,
32,7,7,7,8,8,8,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,61,
59,60,64,62,63,66,67,65,69,70,68],,,,,,,,,,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,
14,15,16,17,18,19,20,21,22,23,24,25,26,1,2,3,1,2,3,34,35,33,38,36,37,39,40,41,
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]],
0,
[(53,55,54)(56,58,57),(33,35,34)(36,37,38),(27,30)(28,31)(29,32),( 2, 3)
( 5, 6)( 7, 8)(11,12)(14,15)(17,18)(19,20)(22,23)(25,26)(28,29)(31,32)
(33,37,34,36,35,38)(39,40)(41,42)(43,44)(45,46)(47,48)(49,50)(51,52)(53,56)
(54,57)(55,58)(59,64,60,62,61,63)(65,69,67,68,66,70),(59,61,60)(62,64,63)
(65,66,67)(68,69,70),(65,67,66)(68,70,69),(13,16)(14,17)(15,18)(39,40)(41,44)
(42,43)(45,46)(47,50)(48,49)(51,52)(53,56)(54,58)(55,57)(59,68,60,70,61,69)
(62,65,63,67,64,66)],
["ConstructProj",[["U3(8).3_1",[]],,["3.U3(8).3_1",[-1,-1,-1,-1,-1,-1,-55,-55,
-55,-37,-37]]]]);
ALF("3.U3(8).3_1","U3(8).3_1",[1,1,1,2,2,2,3,4,5,6,6,6,7,7,7,8,8,8,9,10,
11,11,11,12,12,12,13,13,13,14,14,14,15,15,15,16,16,16,17,18,19,20,21,22,
23,24,25,26,27,28,29,30,31,31,31,32,32,32,33,33,33,34,34,34,35,35,35,36,
36,36]);
ALF("3.U3(8).3_1","3.U3(8).6",[1,2,2,3,4,4,5,5,6,7,8,8,9,10,11,9,11,10,12,
12,13,14,14,15,16,16,17,18,19,17,19,18,20,21,22,20,22,21,29,30,31,32,31,
32,33,34,35,36,35,36,37,38,39,40,40,41,42,42,43,44,45,46,47,48,43,45,44,
46,48,47],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);

MOT("3.U3(8).3_2",
[
"origin: ATLAS of finite groups, tests: 1.o.r."
],
[49641984,49641984,49641984,13824,13824,13824,13608,13608,13608,13608,13608,
13608,243,192,192,192,216,216,216,216,216,216,189,189,189,189,189,189,189,189,
189,243,243,243,243,243,243,243,243,243,171,171,171,171,171,171,171,171,171,
171,171,171,171,171,171,171,171,171,189,189,189,189,189,189,189,189,189,189,
189,189,189,189,189,189,189,189,171,171,13608,13608,13608,13608,13608,13608,
13608,13608,13608,13608,13608,13608,13608,13608,13608,13608,13608,13608,243,
243,243,243,243,243,243,243,243,243,243,243,243,243,243,243,243,243,216,216,
216,216,216,216,216,216,216,216,216,216,216,216,216,216,216,216,171,171,171,
171,171,171,171,171,171,171,171,171,171,171,171,171,171,171,171,171,171,171,
171,171,171,171,171,171,171,171,171,171,171,171,171,171,189,189,189,189,189,
189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,
189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,
189,189,189,189,189,189,189,189,189,189,189],
[,[1,3,2,1,3,2,11,10,12,9,8,7,13,4,6,5,11,10,12,9,8,7,26,28,27,29,31,30,23,25,
24,35,37,36,38,40,39,32,34,33,50,52,51,47,49,48,56,58,57,53,55,54,44,46,45,41,
43,42,69,68,70,67,66,65,75,74,76,73,72,71,63,62,64,61,60,59,78,77,90,88,89,87,
85,86,96,94,95,93,91,92,83,84,82,80,81,79,108,106,107,105,103,104,114,112,113,
111,109,110,101,102,100,98,99,97,90,88,89,87,85,86,96,94,95,93,91,92,83,84,82,
80,81,79,156,154,155,153,151,152,150,148,149,147,145,146,168,166,167,165,163,
164,162,160,161,159,157,158,143,144,142,140,141,139,137,138,136,134,135,133,
180,178,179,177,175,176,186,184,185,183,181,182,173,174,172,170,171,169,198,
196,197,195,193,194,204,202,203,201,199,200,191,192,190,188,189,187,216,214,
215,213,211,212,222,220,221,219,217,218,209,210,208,206,207,205],[1,1,1,4,4,4,
2,2,2,3,3,3,1,14,14,14,5,5,5,6,6,6,29,29,29,23,23,23,26,26,26,13,13,13,13,13,
13,13,13,13,50,50,50,47,47,47,56,56,56,53,53,53,44,44,44,41,41,41,30,30,30,31,
31,31,24,24,24,25,25,25,27,27,27,28,28,28,2,3,8,8,8,12,12,12,7,7,7,10,10,10,9,
9,9,11,11,11,8,8,8,12,12,12,7,7,7,10,10,10,9,9,9,11,11,11,18,18,18,22,22,22,
17,17,17,20,20,20,19,19,19,21,21,21,51,51,51,52,52,52,48,48,48,49,49,49,57,57,
57,58,58,58,54,54,54,55,55,55,45,45,45,46,46,46,42,42,42,43,43,43,72,72,72,76,
76,76,59,59,59,62,62,62,67,67,67,69,69,69,60,60,60,64,64,64,65,65,65,68,68,68,
73,73,73,75,75,75,66,66,66,70,70,70,71,71,71,74,74,74,61,61,61,63,63,63],,,,[
1,2,3,4,5,6,9,7,8,11,12,10,13,14,15,16,19,17,18,21,22,20,1,2,3,1,2,3,1,2,3,35,
36,37,38,39,40,32,33,34,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,
9,7,8,11,12,10,9,7,8,11,12,10,9,7,8,11,12,10,77,78,85,86,87,88,89,90,91,92,93,
94,95,96,81,79,80,84,82,83,103,104,105,106,107,108,109,110,111,112,113,114,99,
97,98,102,100,101,121,122,123,124,125,126,127,128,129,130,131,132,117,115,116,
120,118,119,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,
149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,
168,85,86,87,88,89,90,91,92,93,94,95,96,81,79,80,84,82,83,85,86,87,88,89,90,
91,92,93,94,95,96,81,79,80,84,82,83,85,86,87,88,89,90,91,92,93,94,95,96,81,79,
80,84,82,83],,,,,,,,,,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,
21,22,26,27,28,29,30,31,23,24,25,32,33,34,35,36,37,38,39,40,1,2,3,1,2,3,1,2,3,
1,2,3,1,2,3,1,2,3,65,66,67,68,69,70,71,72,73,74,75,76,59,60,61,62,63,64,77,78,
81,79,80,84,82,83,87,85,86,90,88,89,93,91,92,96,94,95,99,97,98,102,100,101,
105,103,104,108,106,107,111,109,110,114,112,113,117,115,116,120,118,119,123,
121,122,126,124,125,129,127,128,132,130,131,77,77,77,78,78,78,77,77,77,78,78,
78,77,77,77,78,78,78,77,77,77,78,78,78,77,77,77,78,78,78,77,77,77,78,78,78,
189,187,188,192,190,191,195,193,194,198,196,197,201,199,200,204,202,203,207,
205,206,210,208,209,213,211,212,216,214,215,219,217,218,222,220,221,171,169,
170,174,172,173,177,175,176,180,178,179,183,181,182,186,184,185]],
0,
[(133,135,134)(136,138,137)(139,141,140)(142,144,143)(145,147,146)
(148,150,149)(151,153,152)(154,156,155)(157,159,158)(160,162,161)(163,165,164)
(166,168,167),( 41, 50, 53, 44, 47, 56)( 42, 51, 54, 45, 48, 57)
( 43, 52, 55, 46, 49, 58)(133,151,157,141,147,165,134,152,158,139,145,163,135,
 153,159,140,146,164)(136,154,160,144,150,168,137,155,161,142,148,166,138,156,
 162,143,149,167),( 23, 29, 26)( 24, 30, 27)( 25, 31, 28)( 59, 71, 65)
( 60, 72, 66)( 61, 73, 67)( 62, 74, 68)( 63, 75, 69)( 64, 76, 70)(169,205,187)
(170,206,188)(171,207,189)(172,208,190)(173,209,191)(174,210,192)(175,211,193)
(176,212,194)(177,213,195)(178,214,196)(179,215,197)(180,216,198)(181,217,199)
(182,218,200)(183,219,201)(184,220,202)(185,221,203)(186,222,204),(  2,  3)
(  5,  6)(  7, 11,  8, 10,  9, 12)( 15, 16)( 17, 21, 18, 20, 19, 22)( 24, 25)
( 27, 28)( 30, 31)( 32, 35, 38)( 33, 37, 39, 34, 36, 40)( 42, 43)( 45, 46)
( 48, 49)( 51, 52)( 54, 55)( 57, 58)( 59, 63, 60, 62, 61, 64)( 65, 69, 66, 68,
 67, 70)( 71, 75, 72, 74, 73, 76)( 77, 78)( 79, 90, 92, 84, 86, 94, 80, 88,
  93, 82, 87, 95, 81, 89, 91, 83, 85, 96)( 97,108,110,102,104,112, 98,106,111,
 100,105,113, 99,107,109,101,103,114)(115,126,128,120,122,130,116,124,129,118,
 123,131,117,125,127,119,121,132)(133,138,134,136,135,137)(139,144,140,142,
 141,143)(145,150,146,148,147,149)(151,156,152,154,153,155)(157,162,158,160,
 159,161)(163,168,164,166,165,167)(169,216,200,174,212,202,170,214,201,172,
 213,203,171,215,199,173,211,204)(175,222,187,180,218,192,176,220,188,178,219,
 190,177,221,189,179,217,191)(181,209,193,186,205,198,182,210,194,184,206,196,
 183,208,195,185,207,197),(  7,  9,  8)( 10, 11, 12)( 17, 19, 18)( 20, 21, 22)
( 32, 35, 38)( 33, 36, 39)( 34, 37, 40)( 59, 61, 60)( 62, 63, 64)( 65, 67, 66)
( 68, 69, 70)( 71, 73, 72)( 74, 75, 76)( 79, 85, 91, 81, 87, 93, 80, 86, 92)
( 82, 88, 94, 84, 90, 96, 83, 89, 95)( 97,103,109, 99,105,111, 98,104,110)
(100,106,112,102,108,114,101,107,113)(115,121,127,117,123,129,116,122,128)
(118,124,130,120,126,132,119,125,131)(169,211,199,171,213,201,170,212,200)
(172,214,202,174,216,204,173,215,203)(175,217,189,177,219,188,176,218,187)
(178,220,192,180,222,191,179,221,190)(181,207,195,183,206,194,182,205,193)
(184,210,198,186,209,197,185,208,196),( 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)(169,170,171)(172,173,174)(175,176,177)
(178,179,180)(181,182,183)(184,185,186)(187,188,189)(190,191,192)(193,194,195)
(196,197,198)(199,200,201)(202,203,204)(205,206,207)(208,209,210)(211,212,213)
(214,215,216)(217,218,219)(220,221,222)],
["ConstructProj",[["U3(8).3_2",[]],,["3.U3(8).3_2",[-1,-1,-1,-1,-1,-1,-1,-1,
-1,-1,-55,-55,-55,-55,-55,-55,-55,-55,-55,-37,-37,-37,-37,-37,-37]]]]);
ALF("3.U3(8).3_2","U3(8).3_2",[1,1,1,2,2,2,3,3,3,4,4,4,5,6,6,6,7,7,7,8,8,
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,
17,17,18,18,18,19,19,19,20,20,20,21,21,21,22,22,22,23,23,23,24,24,24,25,
25,25,26,26,26,27,28,29,29,29,30,30,30,31,31,31,32,32,32,33,33,33,34,34,
34,35,35,35,36,36,36,37,37,37,38,38,38,39,39,39,40,40,40,41,41,41,42,42,
42,43,43,43,44,44,44,45,45,45,46,46,46,47,47,47,48,48,48,49,49,49,50,50,
50,51,51,51,52,52,52,53,53,53,54,54,54,55,55,55,56,56,56,57,57,57,58,58,
58,59,59,59,60,60,60,61,61,61,62,62,62,63,63,63,64,64,64,65,65,65,66,66,
66,67,67,67,68,68,68,69,69,69,70,70,70,71,71,71,72,72,72,73,73,73,74,74,
74,75,75,75,76,76,76]);
ALF("3.U3(8).3_2","3.U3(8).S3",[1,2,2,3,4,4,5,6,7,5,7,6,8,9,10,10,11,12,
13,11,13,12,14,15,15,16,17,17,18,19,19,20,21,21,22,23,23,24,25,25,26,27,
28,26,28,27,29,30,31,29,31,30,32,33,34,32,34,33,35,36,37,35,37,36,38,39,
40,38,40,39,41,42,43,41,43,42,44,44,45,46,47,45,46,47,48,49,50,48,49,50,
51,52,53,51,52,53,54,55,56,54,55,56,57,58,59,57,58,59,60,61,62,60,61,62,
63,64,65,63,64,65,66,67,68,66,67,68,69,70,71,69,70,71,72,73,74,75,76,77,
75,76,77,72,73,74,78,79,80,81,82,83,81,82,83,78,79,80,84,85,86,87,88,89,
87,88,89,84,85,86,90,91,92,90,91,92,93,94,95,93,94,95,96,97,98,96,97,98,
99,100,101,99,100,101,102,103,104,102,103,104,105,106,107,105,106,107,108,
109,110,108,109,110,111,112,113,111,112,113,114,115,116,114,115,116],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);

MOT("Isoclinic(3.U3(8).3_2,1)",
[
"1st isoclinic group of the 3.U3(8).3_2 given in the ATLAS"
],
0,
0,
0,
[(41,47,53)(42,48,54)(43,49,55)(44,50,56)(45,51,57)(46,52,58)(133,145,157,135,
147,159,134,146,158)(136,148,160,138,150,162,137,149,161)(139,151,163,141,153,
165,140,152,164)(142,154,166,144,156,168,143,155,167),(7,8,9)(10,12,11)(17,18,
19)(20,22,21)(32,38,35)(33,39,36)(34,40,37)(59,60,61)(62,64,63)(65,66,67)(68,
70,69)(71,72,73)(74,76,75)(79,91,87,80,92,85,81,93,86)(82,94,90,83,95,88,84,
96,89)(97,109,105,98,110,103,99,111,104)(100,112,108,101,113,106,102,114,107)
(115,127,123,116,128,121,117,129,122)(118,130,126,119,131,124,120,132,125)
(169,199,213,170,200,211,171,201,212)(172,202,216,173,203,214,174,204,215)
(175,189,219,176,187,217,177,188,218)(178,192,222,179,190,220,180,191,221)
(181,195,206,182,193,207,183,194,205)(184,198,209,185,196,210,186,197,208),(2,
3)(5,6)(7,10)(8,12)(9,11)(15,16)(17,20)(18,22)(19,21)(24,25)(27,28)(30,31)(33,
34)(36,37)(39,40)(42,43)(45,46)(48,49)(51,52)(54,55)(57,58)(59,62)(60,64)(61,
63)(65,68)(66,70)(67,69)(71,74)(72,76)(73,75)(77,78)(79,82,80,83,81,84)(85,88,
86,89,87,90)(91,94,92,95,93,96)(97,100,98,101,99,102)(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)(133,136,134,137,135,138)(139,142,140,143,141,144)
(145,148,146,149,147,150)(151,154,152,155,153,156)(157,160,158,161,159,162)
(163,166,164,167,165,168)(169,172,170,173,171,174)(175,178,176,179,177,180)
(181,184,182,185,183,186)(187,190,188,191,189,192)(193,196,194,197,195,198)
(199,202,200,203,201,204)(205,208,206,209,207,210)(211,214,212,215,213,216)
(217,220,218,221,219,222),(23,26,29)(24,27,30)(25,28,31)(59,65,71)(60,66,72)
(61,67,73)(62,68,74)(63,69,75)(64,70,76)(169,187,205)(170,188,206)(171,189,
207)(172,190,208)(173,191,209)(174,192,210)(175,193,211)(176,194,212)(177,195,
213)(178,196,214)(179,197,215)(180,198,216)(181,199,217)(182,200,218)(183,201,
219)(184,202,220)(185,203,221)(186,204,222),(41,44)(42,45)(43,46)(47,50)(48,
51)(49,52)(53,56)(54,57)(55,58)(133,139)(134,140)(135,141)(136,142)(137,143)
(138,144)(145,151)(146,152)(147,153)(148,154)(149,155)(150,156)(157,163)(158,
164)(159,165)(160,166)(161,167)(162,168)],
["ConstructIsoclinic",[["3.U3(8).3_2"]],rec(k:=1)]);
ALF("Isoclinic(3.U3(8).3_2,1)","U3(8).3_2",[1,1,1,2,2,2,3,3,3,4,4,4,5,6,6,
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,
16,16,16,17,17,17,18,18,18,19,19,19,20,20,20,21,21,21,22,22,22,23,23,23,
24,24,24,25,25,25,26,26,26,27,28,29,29,29,30,30,30,31,31,31,32,32,32,33,
33,33,34,34,34,35,35,35,36,36,36,37,37,37,38,38,38,39,39,39,40,40,40,41,
41,41,42,42,42,43,43,43,44,44,44,45,45,45,46,46,46,47,47,47,48,48,48,49,
49,49,50,50,50,51,51,51,52,52,52,53,53,53,54,54,54,55,55,55,56,56,56,57,
57,57,58,58,58,59,59,59,60,60,60,61,61,61,62,62,62,63,63,63,64,64,64,65,
65,65,66,66,66,67,67,67,68,68,68,69,69,69,70,70,70,71,71,71,72,72,72,73,
73,73,74,74,74,75,75,75,76,76,76]);

MOT("Isoclinic(3.U3(8).3_2,2)",
[
"2nd isoclinic group of the 3.U3(8).3_2 given in the ATLAS"
],
0,
0,
0,
[(41,47,53)(42,48,54)(43,49,55)(44,50,56)(45,51,57)(46,52,58)(133,145,157,135,
147,159,134,146,158)(136,148,160,138,150,162,137,149,161)(139,151,163,141,153,
165,140,152,164)(142,154,166,144,156,168,143,155,167),(7,8,9)(10,12,11)(17,18,
19)(20,22,21)(32,38,35)(33,39,36)(34,40,37)(59,60,61)(62,64,63)(65,66,67)(68,
70,69)(71,72,73)(74,76,75)(79,91,87,80,92,85,81,93,86)(82,94,90,83,95,88,84,
96,89)(97,109,105,98,110,103,99,111,104)(100,112,108,101,113,106,102,114,107)
(115,127,123,116,128,121,117,129,122)(118,130,126,119,131,124,120,132,125)
(169,199,213,170,200,211,171,201,212)(172,202,216,173,203,214,174,204,215)
(175,189,219,176,187,217,177,188,218)(178,192,222,179,190,220,180,191,221)
(181,195,206,182,193,207,183,194,205)(184,198,209,185,196,210,186,197,208),(2,
3)(5,6)(7,10)(8,12)(9,11)(15,16)(17,20)(18,22)(19,21)(24,25)(27,28)(30,31)(33,
34)(36,37)(39,40)(42,43)(45,46)(48,49)(51,52)(54,55)(57,58)(59,62)(60,64)(61,
63)(65,68)(66,70)(67,69)(71,74)(72,76)(73,75)(77,78)(79,82,81,84,80,83)(85,88,
87,90,86,89)(91,94,93,96,92,95)(97,100,99,102,98,101)(103,106,105,108,104,107)
(109,112,111,114,110,113)(115,118,117,120,116,119)(121,124,123,126,122,125)
(127,130,129,132,128,131)(133,136,135,138,134,137)(139,142,141,144,140,143)
(145,148,147,150,146,149)(151,154,153,156,152,155)(157,160,159,162,158,161)
(163,166,165,168,164,167)(169,172,171,174,170,173)(175,178,177,180,176,179)
(181,184,183,186,182,185)(187,190,189,192,188,191)(193,196,195,198,194,197)
(199,202,201,204,200,203)(205,208,207,210,206,209)(211,214,213,216,212,215)
(217,220,219,222,218,221),(23,26,29)(24,27,30)(25,28,31)(59,65,71)(60,66,72)
(61,67,73)(62,68,74)(63,69,75)(64,70,76)(169,187,205)(170,188,206)(171,189,
207)(172,190,208)(173,191,209)(174,192,210)(175,193,211)(176,194,212)(177,195,
213)(178,196,214)(179,197,215)(180,198,216)(181,199,217)(182,200,218)(183,201,
219)(184,202,220)(185,203,221)(186,204,222),(41,44)(42,45)(43,46)(47,50)(48,
51)(49,52)(53,56)(54,57)(55,58)(133,139)(134,140)(135,141)(136,142)(137,143)
(138,144)(145,151)(146,152)(147,153)(148,154)(149,155)(150,156)(157,163)(158,
164)(159,165)(160,166)(161,167)(162,168)],
["ConstructIsoclinic",[["3.U3(8).3_2"]],rec(k:=2)]);
ALF("Isoclinic(3.U3(8).3_2,2)","U3(8).3_2",[1,1,1,2,2,2,3,3,3,4,4,4,5,6,6,
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,
16,16,16,17,17,17,18,18,18,19,19,19,20,20,20,21,21,21,22,22,22,23,23,23,
24,24,24,25,25,25,26,26,26,27,28,29,29,29,30,30,30,31,31,31,32,32,32,33,
33,33,34,34,34,35,35,35,36,36,36,37,37,37,38,38,38,39,39,39,40,40,40,41,
41,41,42,42,42,43,43,43,44,44,44,45,45,45,46,46,46,47,47,47,48,48,48,49,
49,49,50,50,50,51,51,51,52,52,52,53,53,53,54,54,54,55,55,55,56,56,56,57,
57,57,58,58,58,59,59,59,60,60,60,61,61,61,62,62,62,63,63,63,64,64,64,65,
65,65,66,66,66,67,67,67,68,68,68,69,69,69,70,70,70,71,71,71,72,72,72,73,
73,73,74,74,74,75,75,75,76,76,76]);

MOT("3.U3(8).6",
[
"origin: ATLAS of finite groups, tests: 1.o.r., tests: 1.o.r."
],
[99283968,49641984,27648,13824,4536,486,1152,576,576,576,576,72,126,63,162,81,
57,57,57,63,63,63,3024,54,96,96,14,18,1296,1296,648,648,144,144,72,72,54,54,
72,36,72,36,36,36,36,36,36,36,36,36,18,18,24,24,24,24],
[,[1,2,1,2,5,6,3,4,3,4,4,5,13,14,15,16,17,18,19,20,21,22,1,6,7,7,13,15,30,29,
32,31,30,29,32,31,38,37,34,34,33,33,36,36,36,35,35,35,30,29,38,37,41,39,41,
39],[1,1,3,3,2,1,7,7,9,9,9,4,13,13,6,6,17,17,17,14,14,14,23,23,25,26,27,24,1,
1,2,2,3,3,4,4,6,6,7,7,7,7,10,10,10,11,11,11,23,23,24,24,25,25,26,26],,,,[1,2,
3,4,5,6,7,8,9,10,11,12,1,2,15,16,17,18,19,5,5,5,23,24,26,25,23,28,29,30,31,32,
33,34,35,36,37,38,39,40,41,42,45,43,44,48,46,47,49,50,51,52,55,56,53,
54],,,,,,,,,,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,1,2,2,21,22,20,23,24,
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]],
0,
[(25,26)(53,55)(54,56),(20,22,21),(18,19),(10,11)(18,19)(20,22,21)(29,30)
(31,32)(33,34)(35,36)(37,38)(39,41)(40,42)(43,48,44,46,45,47)(49,50)(51,52)
(53,54)(55,56),(10,11)(29,30)(31,32)(33,34)(35,36)(37,38)(39,41)(40,42)
(43,48,44,46,45,47)(49,50)(51,52)(53,54)(55,56),(43,45,44)(46,48,47)],
["ConstructMGA","3.U3(8).3_1","U3(8).6",[[37,38],[39,42],[40,43],[41,44],[45,
54],[46,55],[47,56],[48,51],[50,53],[49,52],[57,58],[59,60],[61,62],[63,64],
[65,66],[67,70],[68,69]],()]);
ALF("3.U3(8).6","U3(8).6",[1,1,2,2,3,4,5,5,6,6,6,7,8,8,9,9,10,10,10,11,11,
11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,28,29,29,30,30,30,
31,31,31,32,33,34,35,36,37,38,39]);

MOT("3.U3(8).S3",
[
"origin: ATLAS of finite groups"
],
[99283968,49641984,27648,13824,13608,13608,13608,486,384,192,216,216,216,378,
189,378,189,378,189,486,243,486,243,486,243,171,171,171,171,171,171,171,171,
171,189,189,189,189,189,189,189,189,189,171,13608,13608,13608,13608,13608,
13608,13608,13608,13608,243,243,243,243,243,243,243,243,243,216,216,216,216,
216,216,216,216,216,171,171,171,171,171,171,171,171,171,171,171,171,171,171,
171,171,171,171,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,
189,189,189,189,189,189,189,189,189,189,189,189,1008,18,32,32,14,14,14,18,18,
18],
[,[1,2,1,2,7,5,6,8,3,4,7,5,6,16,17,18,19,14,15,22,23,24,25,20,21,29,30,31,32,
33,34,26,27,28,40,38,39,43,41,42,37,35,36,44,50,48,49,53,51,52,46,47,45,59,57,
58,62,60,61,55,56,54,50,48,49,53,51,52,46,47,45,80,78,79,83,81,82,86,84,85,89,
87,88,73,74,72,76,77,75,95,93,94,98,96,97,91,92,90,104,102,103,107,105,106,100
,101,99,113,111,112,116,114,115,109,110,108,1,8,9,9,16,18,14,22,24,20],[1,1,3,
3,2,2,2,1,9,9,4,4,4,18,18,14,14,16,16,8,8,8,8,8,8,29,29,29,32,32,32,26,26,26,
19,19,19,15,15,15,17,17,17,2,6,6,6,5,5,5,7,7,7,6,6,6,5,5,5,7,7,7,12,12,12,11,
11,11,13,13,13,31,31,31,30,30,30,34,34,34,33,33,33,28,28,28,27,27,27,42,42,42,
35,35,35,40,40,40,36,36,36,38,38,38,43,43,43,39,39,39,41,41,41,37,37,37,117,
117,119,120,123,121,122,118,118,118],,,,[1,2,3,4,7,5,6,8,9,10,13,11,12,1,2,1,2
,1,2,22,23,24,25,20,21,26,27,28,29,30,31,32,33,34,7,5,6,7,5,6,7,5,6,44,48,49,
50,51,52,53,47,45,46,57,58,59,60,61,62,56,54,55,66,67,68,69,70,71,65,63,64,72,
73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,48,49,50,51,52,53,47,45,46,
48,49,50,51,52,53,47,45,46,48,49,50,51,52,53,47,45,46,117,118,120,119,117,117,
117,125,126,124],,,,,,,,,,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,16,17,18,19,14,15,
20,21,22,23,24,25,1,2,2,1,2,2,1,2,2,38,39,40,41,42,43,35,36,37,44,47,45,46,50,
48,49,53,51,52,56,54,55,59,57,58,62,60,61,65,63,64,68,66,67,71,69,70,44,44,44,
44,44,44,44,44,44,44,44,44,44,44,44,44,44,44,101,99,100,104,102,103,107,105,
106,110,108,109,113,111,112,116,114,115,92,90,91,95,93,94,98,96,97,117,118,119
,120,122,123,121,124,125,126]],
0,
[(119,120),( 72, 73, 74)( 75, 76, 77)( 78, 79, 80)( 81, 82, 83)( 84, 85, 86)
( 87, 88, 89),( 27, 28)( 30, 31)( 33, 34)( 72, 75)( 73, 76)( 74, 77)( 78, 81)
( 79, 82)( 80, 83)( 84, 87)( 85, 88)( 86, 89),( 26, 29, 32)( 27, 30, 33)( 28,
 31, 34)( 72, 78, 84, 74, 80, 86, 73, 79, 85)( 75, 81, 87, 77, 83, 89, 76, 82,
 88),( 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)( 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),( 14, 16, 18)( 15, 17, 19)( 35, 38, 41)( 36, 39, 42)( 37, 40, 43)
( 90, 99,108)( 91,100,109)( 92,101,110)( 93,102,111)( 94,103,112)( 95,104,113)
( 96,105,114)( 97,106,115)( 98,107,116)(121,122,123),(  5,  6,  7)( 11, 12,
 13)( 20, 24, 22)( 21, 25, 23)( 35, 36, 37)( 38, 39, 40)( 41, 42, 43)( 45, 51,
 50, 46, 52, 48, 47, 53, 49)( 54, 60, 59, 55, 61, 57, 56, 62, 58)( 63, 69, 68,
 64, 70, 66, 65, 71, 67)( 90,105,113, 91,106,111, 92,107,112)( 93,101,116, 94,
 99,114, 95,100,115)( 96,104,109, 97,102,110, 98,103,108)(124,126,125)],
["ConstructGS3","3.U3(8).2","3.U3(8).3_2",[6,7,33],[[2,3],[5,6],[7,10],[9,11],
[8,12],[15,16],[18,19],[21,22],[23,26],[25,27],[24,28],[30,31],[33,34],[36,
37],[39,40],[41,44],[43,45],[42,46],[47,50],[49,51],[48,52],[53,56],[55,57],
[54,58],[59,62],[61,63],[60,64],[65,68],[67,69],[66,70],[71,74],[73,75],[72,
76],[77,80],[79,81],[78,82],[83,86],[85,87],[84,88],[89,92],[91,93],[90,94],
[97,100],[99,101],[98,102],[103,106],[105,107],[104,108],[109,112],[111,113],
[110,114],[115,118],[117,119],[116,120],[121,124],[123,125],[122,126],[127,
130],[129,131],[128,132],[133,136],[135,137],[134,138],[139,142],[141,143],
[140,144],[145,148],[147,149],[146,150],[151,154],[153,155],[152,156],[157,
160],[159,161],[158,162],[163,166],[165,167],[164,168],[169,172],[171,173],
[170,174],[175,178],[177,179],[176,180],[181,184],[183,185],[182,186],[190,
193],[192,194],[191,195],[187,196],[189,197],[188,198],[202,205],[204,206],
[203,207],[199,208],[201,209],[200,210],[214,217],[216,218],[215,219],[211,
220],[213,221],[212,222]],[[1,1],[4,3],[14,9],[17,11],[20,13],[29,16],[32,18],
[35,20],[38,22]],(1,10,17,32,50,69,86,105,125,33,49,67,85,103,124,31,48,65,84,
101,117,18,35,53,72,89,108,122,28,45,61,79,97,118,19,36,52,70,88,106,121,27,
43,60,77,96,110,2,11,20,38,56,75,92,114,13,23,41,59,78,95,111,4,3,63,80,99,
119,24,40,57,74,93,113,12,21,37,54,71,90,107,123,30,46,64,82,100,115,15,26,44,
62,81,98,120,25,42,58,76,94,109)(5,6,7,9,14,22,39,55,73,91,112)(16,29,47,66,
83,102,116)(34,51,68,87,104,126)]);
ALF("3.U3(8).S3","U3(8).S3",[1,1,2,2,3,3,3,4,5,5,6,6,6,7,7,8,8,9,9,10,10,
11,11,12,12,13,13,13,14,14,14,15,15,15,16,16,16,17,17,17,18,18,18,19,20,
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,
45,46,47,48,49,50,51,52,53]);

MOT("Isoclinic(3.U3(8)x3)",
[
"central product of 3.U3(8).2_3 with a cyclic group of order 9,\n",
"subgroup of 9.U3(8).3_3"
],
0,
0,
0,
[(139,148)(140,149)(141,150)(142,151)(143,152)(144,153)(145,154)(146,155)(147,
156)(157,166)(158,167)(159,168)(160,169)(161,170)(162,171)(163,172)(164,173)(
165,174)(175,184)(176,185)(177,186)(178,187)(179,188)(180,189)(181,190)(182,
191)(183,192),(139,157,175)(140,158,176)(141,159,177)(142,160,178)(143,161,179
)(144,162,180)(145,163,181)(146,164,182)(147,165,183)(148,166,184)(149,167,185
)(150,168,186)(151,169,187)(152,170,188)(153,171,189)(154,172,190)(155,173,191
)(156,174,192),(49,58)(50,59)(51,60)(52,61)(53,62)(54,63)(55,64)(56,65)(57,66)
,(40,49)(41,50)(42,51)(43,52)(44,53)(45,54)(46,55)(47,56)(48,57),(85,94,103)(
86,95,104)(87,96,105)(88,97,106)(89,98,107)(90,99,108)(91,100,109)(92,101,110)
(93,102,111)(193,211,229)(194,212,230)(195,213,231)(196,214,232)(197,215,233)(
198,216,234)(199,217,235)(200,218,236)(201,219,237)(202,220,238)(203,221,239)(
204,222,240)(205,223,241)(206,224,242)(207,225,243)(208,226,244)(209,227,245)(
210,228,246),(19,22,25)(20,23,26)(21,24,27)(28,34,31)(29,35,32)(30,36,33)(67,
70,73)(68,71,74)(69,72,75)(76,82,79)(77,83,80)(78,84,81)(112,130,121)(113,131,
122)(114,132,123)(115,133,124)(116,134,125)(117,135,126)(118,136,127)(119,137,
128)(120,138,129)(193,196,199)(194,197,200)(195,198,201)(202,208,205)(203,209,
206)(204,210,207)(211,214,217)(212,215,218)(213,216,219)(220,226,223)(221,227,
224)(222,228,225)(229,232,235)(230,233,236)(231,234,237)(238,244,241)(239,245,
242)(240,246,243),(2,3,5,9,8,6)(4,7)(11,12,14,18,17,15)(13,16)(19,28)(20,30,23
,36,26,33)(21,32,27,35,24,29)(22,34)(25,31)(38,39)(41,42,44,48,47,45)(43,46)(
50,51,53,57,56,54)(52,55)(59,60,62,66,65,63)(61,64)(67,76)(68,78,71,84,74,81)(
69,80,75,83,72,77)(70,82)(73,79)(86,87,89,93,92,90)(88,91)(95,96,98,102,101,99
)(97,100)(104,105,107,111,110,108)(106,109)(113,114,116,120,119,117)(115,118)(
122,123,125,129,128,126)(124,127)(131,132,134,138,137,135)(133,136)(140,141,
143,147,146,144)(142,145)(149,150,152,156,155,153)(151,154)(158,159,161,165,
164,162)(160,163)(167,168,170,174,173,171)(169,172)(176,177,179,183,182,180)(
178,181)(185,186,188,192,191,189)(187,190)(193,202)(194,204,197,210,200,207)(
195,206,201,209,198,203)(196,208)(199,205)(211,220)(212,222,215,228,218,225)(
213,224,219,227,216,221)(214,226)(217,223)(229,238)(230,240,233,246,236,243)(
231,242,237,245,234,239)(232,244)(235,241)],
["ConstructIsoclinic",[["3.U3(8)"],["Cyclic",3]],rec(k:=1)]);
ALF("Isoclinic(3.U3(8)x3)","9.U3(8).3_3",[1,2,3,4,2,3,5,2,3,6,7,8,9,7,8,
10,7,8,11,12,13,11,12,14,11,12,15,16,17,18,16,19,18,16,20,18,21,22,23,24,
25,26,27,28,29,30,31,32,24,31,29,27,25,32,30,28,26,24,28,32,27,31,26,30,
25,29,33,34,35,33,34,36,33,34,37,38,39,40,38,41,40,38,42,40,43,44,45,46,
47,48,49,50,51,43,47,51,46,50,45,49,44,48,43,50,48,46,44,51,49,47,45,52,
53,54,55,56,57,58,59,60,52,56,60,55,59,54,58,53,57,52,59,57,55,53,60,58,
56,54,70,71,72,73,74,75,76,77,78,61,62,63,64,65,66,67,68,69,70,74,78,73,
77,72,76,71,75,61,65,69,64,68,63,67,62,66,70,77,75,73,71,78,76,74,72,61,
68,66,64,62,69,67,65,63,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,
95,96,82,86,81,85,80,84,79,83,87,94,89,93,88,92,96,91,95,90,85,83,81,79,
86,84,82,80,87,91,89,96,94,92,90,88,95,93]);

MOT("Isoclinic(U3(8).3_3x3)",
[
"subdirect product of U3(8).3_3 with a cyclic group of order 9,\n",
"factor group of 9.U3(8).3_3"
],
0,
0,
0,
[(43,49,55)(44,50,56)(45,51,57)(46,52,58)(47,53,59)(48,54,60)(67,73,79)(68,74,
80)(69,75,81)(70,76,82)(71,77,83)(72,78,84),(31,34)(32,35)(33,36),(43,44,45)(
46,48,47)(49,50,51)(52,54,53)(55,56,57)(58,60,59)(61,62,63)(64,66,65)(67,68,69
)(70,72,71)(73,74,75)(76,78,77)(79,80,81)(82,84,83),(2,3)(5,6)(7,10)(8,12)(9,
11)(14,15)(17,18)(19,22)(20,24)(21,23)(26,27)(29,30)(32,33)(35,36)(37,40)(38,
42)(39,41)(43,46,44,48,45,47)(49,52,50,54,51,53)(55,58,56,60,57,59)(61,64,62,
66,63,65)(67,70,68,72,69,71)(73,76,74,78,75,77)(79,82,80,84,81,83)],
["ConstructIsoclinic",[["U3(8).3_3"],["Cyclic",3]],rec(k:=1)]);
ALF("Isoclinic(U3(8).3_3x3)","U3(8).3_3",[1,1,1,2,2,2,3,3,3,4,4,4,5,5,
5,6,6,6,7,7,7,8,8,8,9,9,9,10,10,10,11,11,11,12,12,12,13,13,13,14,14,14,15,
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]);

MOT("9.U3(8).3_3",
[
"origin: ATLAS of finite groups,",
"constructed using `PossibleCharacterTablesOfTypeMGA'"
],
[148925952,49641984,49641984,148925952,148925952,41472,13824,13824,41472,41472
,13608,13608,40824,40824,40824,13608,40824,13608,40824,40824,729,729,729,576,
576,576,576,576,576,576,576,576,216,216,648,648,648,216,648,216,648,648,189,
189,189,189,189,189,189,189,189,243,243,243,243,243,243,243,243,243,171,171,
171,171,171,171,171,171,171,171,171,171,171,171,171,171,171,171,189,189,189,
189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,162,162,162,162,
162,162,162,162,162,162,162,162,162,162,162,162,162,162,27,27,27,27,27,27,54,
54,54,54,54,54,54,54,54,54,54,54,54,54,54,54,54,54],
[,[1,3,2,5,4,1,3,2,5,4,16,18,20,19,17,11,15,12,14,13,21,23,22,6,8,7,10,8,7,9,8
,7,16,18,20,19,17,11,15,12,14,13,43,51,50,49,48,47,46,45,44,52,60,59,58,57,56,
55,54,53,70,78,77,76,75,74,73,72,71,61,69,68,67,66,65,64,63,62,88,96,95,94,93,
92,91,90,89,79,87,86,85,84,83,82,81,80,106,108,107,104,103,105,112,114,113,110
,109,111,100,102,101,98,97,99,118,120,119,116,115,117,106,108,107,104,103,105,
112,114,113,110,109,111,100,102,101,98,97,99],[1,4,5,1,1,6,9,10,6,6,4,5,1,1,1,
5,1,4,1,1,1,4,5,24,27,30,24,27,30,24,27,30,9,10,6,6,6,10,6,9,6,6,43,46,49,43,
46,49,43,46,49,21,21,21,21,21,21,21,21,21,70,73,76,70,73,76,70,73,76,61,64,67,
61,64,67,61,64,67,46,49,43,46,49,43,46,49,43,49,43,46,49,43,46,49,43,46,17,19,
20,13,14,15,19,20,17,15,13,14,20,17,19,14,15,13,22,22,22,23,23,23,39,41,42,35,
36,37,41,42,39,37,35,36,42,39,41,36,37,35],,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,
14,15,16,17,18,19,20,21,22,23,24,31,29,27,25,32,30,28,26,33,34,35,36,37,38,39,
40,41,42,1,2,3,4,2,3,5,2,3,52,53,54,55,56,57,58,59,60,61,68,66,64,62,69,67,65,
63,70,77,75,73,71,78,76,74,72,11,12,13,11,12,14,11,12,15,16,17,18,16,19,18,16,
20,18,105,103,104,107,108,106,111,109,110,113,114,112,99,97,98,101,102,100,117
,115,116,119,120,118,129,127,128,131,132,130,135,133,134,137,138,136,123,121,
122,125,126,124],,,,,,,,,,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,
20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,47,51,
46,50,45,49,44,48,52,53,54,55,56,57,58,59,60,1,2,3,4,2,3,5,2,3,1,2,3,4,2,3,5,2
,3,82,86,81,85,80,84,79,83,87,94,89,93,88,92,96,91,95,90,97,98,99,100,101,102,
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]],
0,
[(62,65,68)(63,69,66)(71,74,77)(72,78,75),(61,70)(62,71)(63,72)(64,73)(65,74)(
66,75)(67,76)(68,77)(69,78),(44,47,50)(45,51,48)(79,82,85)(80,86,83)(88,94,91)
(90,93,96),(25,28,31)(26,32,29),(97,105,110)(98,103,111)(99,104,109)(100,107,
114)(101,108,112)(102,106,113)(115,117,116)(118,119,120)(121,129,134)(122,127,
135)(123,128,133)(124,131,138)(125,132,136)(126,130,137),(13,14,15)(17,20,19)(
35,36,37)(39,42,41)(53,59,56)(54,57,60)(79,82,85)(80,83,86)(81,84,87)(88,94,91
)(89,95,92)(90,96,93)(97,104,111)(98,105,109)(99,103,110)(100,108,113)(101,106
,114)(102,107,112)(115,116,117)(118,120,119)(121,128,135)(122,129,133)(123,127
,134)(124,132,137)(125,130,138)(126,131,136),(2,3)(4,5)(7,8)(9,10)(11,16)(12,
18)(13,17,14,20,15,19)(22,23)(25,26,28,32,31,29)(27,30)(33,38)(34,40)(35,39,36
,42,37,41)(44,45,47,51,50,48)(46,49)(53,57,59,60,56,54)(55,58)(62,63,65,69,68,
66)(64,67)(71,72,74,78,77,75)(73,76)(79,94,85,88,82,91)(80,96)(81,89,84,95,87,
92)(83,93)(86,90)(97,108,109,102,103,114)(98,107,110,101,104,113)(99,106,111,
100,105,112)(115,120)(116,119)(117,118)(121,132,133,126,127,138)(122,131,134,
125,128,137)(123,130,135,124,129,136)],
["ConstructMGA","Isoclinic(3.U3(8)x3)","Isoclinic(U3(8).3_3x3)",[[85,92..99],[
86,93,97],[87,91,98],[88,96,101],[89,94,102],[90,95..100],[103,111,116],[104,
109,117],[105,110..115],[106,113..120],[107,114,118],[108,112,119],[121,128..
135],[122,129,133],[123,127,134],[124,132,137],[125,130,138],[126,131..136],[
139,146..153],[140,147,151],[141,145,152],[142,150,155],[143,148,156],[144,149
..154],[157,164..171],[158,165,169],[159,163,170],[160,168,173],[161,166,174],
[162,167..172],[175,182..189],[176,183,187],[177,181,188],[178,186,191],[179,
184,192],[180,185..190],[193,200..207],[194,201,205],[195,199,206],[196,204,
209],[197,202,210],[198,203..208],[211,224..237],[212,225,235],[213,223,236],[
214,228,239],[215,226,240],[216,227..238],[217,230..243],[218,231,241],[219,
229,242],[220,234,245],[221,232,246],[222,233..244]],()]);
ALF("9.U3(8).3_3","Isoclinic(U3(8).3_3x3)",[1,2,3,1,1,4,5,6,4,4,10,11,12,
12,12,7,8,9,8,8,13,14,15,16,17,18,16,17,18,16,17,18,22,23,24,24,24,19,20,
21,20,20,25,26,27,25,26,27,25,26,27,28,29,30,28,29,30,28,29,30,31,32,33,
31,32,33,31,32,33,34,35,36,34,35,36,34,35,36,40,41,42,40,41,42,40,41,42,
37,38,39,37,38,39,37,38,39,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,
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]);
ALF("9.U3(8).3_3","U3(8).3_3",[1,1,1,1,1,2,2,2,2,2,4,4,4,4,4,3,3,3,3,3,5,
5,5,6,6,6,6,6,6,6,6,6,8,8,8,8,8,7,7,7,7,7,9,9,9,9,9,9,9,9,9,10,10,10,10,
10,10,10,10,10,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,14,
14,14,14,14,14,14,14,14,13,13,13,13,13,13,13,13,13,15,15,15,16,16,16,17,
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]);

MOT("HSM3",
[
"3rd maximal subgroup of HS,\n",
"differs from HSM2 only by fusion map"
],
0,
0,
0,
0,
["ConstructPermuted",["U3(5).2"]]);
ALF("HSM3","HS",[1,2,4,7,8,9,10,12,13,16,17,3,5,11,15,18,21,24,23],[
"fusion U3(5).2 -> HS mapped under HS.2"
]);

MOT("U3(3)",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,7]"
],
[6048,96,108,9,96,96,16,12,7,7,8,8,12,12],
[,[1,1,3,4,2,2,2,3,9,10,5,6,8,8],[1,2,1,1,6,5,7,2,10,9,12,11,6,5],,,,[1,2,3,4,
6,5,7,8,1,1,12,11,14,13]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1],[6,-2,-3,0,-2,-2,2,1,-1,-1,0,0,1,1],[7,-1,-2,1,
3,3,-1,2,0,0,-1,-1,0,0],[7,3,-2,1,-1-2*E(4),-1+2*E(4),1,0,0,0,E(4),-E(4),
-1+E(4),-1-E(4)],
[GALOIS,[4,3]],[14,-2,5,-1,2,2,2,1,0,0,0,0,-1,-1],[21,5,3,0,1,1,1,-1,0,0,-1,
-1,1,1],[21,1,3,0,-3+2*E(4),-3-2*E(4),-1,1,0,0,E(4),-E(4),-E(4),E(4)],
[GALOIS,[8,3]],[27,3,0,0,3,3,-1,0,-1,-1,1,1,0,0],[28,-4,1,1,4*E(4),-4*E(4),0,
-1,0,0,0,0,E(4),-E(4)],
[GALOIS,[11,3]],[32,0,-4,-1,0,0,0,0,-E(7)-E(7)^2-E(7)^4,-E(7)^3-E(7)^5-E(7)^6,
0,0,0,0],
[GALOIS,[13,3]]],
[( 9,10),( 5, 6)(11,12)(13,14)]);
ARC("U3(3)","CAS",[rec(name:="u3q3",
permchars:=(),
permclasses:=(),
text:=[
"names:u3q3; psu3[3], su3(3)\n",
"2a2(3)     (lie-not.)\n",
"order: 2^5.3^3.7 = 6,048\n",
"number of classes: 14\n",
"source:mckay, john\n",
"the non-abelian simple groups g,\n",
"ord(g)<10^6 - character tables\n",
"comm.algebra 7\n",
"(1979),1407-1445\n",
"maximal subgroup     index\n",
"4^2:s3               63\n",
"test: 1. o.r., sym 2 decompose correctly\n",
"Maximal subgroup of sporadic Janko group j4. Fusion determined using a\n",
"subgroup of type 3^1+2:8 in C(2A) = j4m4, therefore an element of order\n",
"12 and one of order 8 have the same 3rd , resp. 2nd, power.\n",
""])]);
ARC("U3(3)","isSimple",true);
ARC("U3(3)","extInfo",["","2"]);
ARC("U3(3)","tomfusion",rec(name:="U3(3)",map:=[1,2,3,4,6,6,7,8,10,10,14,
14,17,17],text:=[
"fusion map is unique"
],perm:=(3,4)));
ARC("U3(3)","maxes",["3^(1+2):8","L3(2)","4.s4","4^2:s3"]);
ALF("U3(3)","U3(3).2",[1,2,3,4,5,5,6,7,8,8,9,9,10,10]);
ALF("U3(3)","U4(3)",[1,2,3,6,7,7,7,10,13,14,15,15,20,20],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("U3(3)","J2",[1,2,4,5,6,6,6,11,13,13,14,14,19,19],[
"fusion map is unique, equal to that on the CAS table"
]);
ALF("U3(3)","J4",[1,2,4,4,5,5,6,10,12,13,14,14,21,21],[
"fusion determined using that U3(3) contains 8A elements,\n",
"the representative is equal to that on the CAS table"
]);
ALF("U3(3)","L3(9)",[1,2,3,4,5,6,7,10,11,12,17,18,25,26],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables"
]);
ALF("U3(3)","2^6:u3(3)",[1,3,6,7,9,11,13,16,17,18,19,21,23,24],[
"fusion map is unique up to table automorphisms"
]);
ALF("U3(3)","P49/G1/L1/V1/ext3",[1,8,12,17,32,36,40,43,46,49,52,55,58,61],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables"
]);
ALN("U3(3)",["G2(2)'","u3q3"]);

MOT("U3(3).2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,7],\n",
"constructions: Aut(U3(3))"
],
[12096,192,216,18,96,32,24,7,8,12,48,48,6,8,12,12],
[,[1,1,3,4,2,2,3,8,5,7,1,2,4,6,7,7],[1,2,1,1,5,6,2,8,9,5,11,12,11,14,12,
12],,,,[1,2,3,4,5,6,7,1,9,10,11,12,13,14,15,16]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1],[6,
-2,-3,0,-2,2,1,-1,0,1,0,0,0,0,E(3)-E(3)^2,-E(3)+E(3)^2],
[TENSOR,[3,2]],[7,-1,-2,1,3,-1,2,0,-1,0,1,-3,1,-1,0,0],
[TENSOR,[5,2]],[14,6,-4,2,-2,2,0,0,0,-2,0,0,0,0,0,0],[14,-2,5,-1,2,2,1,0,0,-1,
2,-2,-1,0,1,1],
[TENSOR,[8,2]],[21,5,3,0,1,1,-1,0,-1,1,3,-1,0,1,-1,-1],
[TENSOR,[10,2]],[42,2,6,0,-6,-2,2,0,0,0,0,0,0,0,0,0],[27,3,0,0,3,-1,0,-1,1,0,
3,3,0,-1,0,0],
[TENSOR,[13,2]],[56,-8,2,2,0,0,-2,0,0,0,0,0,0,0,0,0],[64,0,-8,-2,0,0,0,1,0,0,
0,0,0,0,0,0]],
[(15,16)]);
ARC("U3(3).2","CAS",[rec(name:="u3q3a",
permchars:=(),
permclasses:=(),
text:=[
" maximal subgroup of g2f4 \n",
"    test:= 1. o.r., sym 2 decompose correctly \n",
""]),rec(name:="u332",
permchars:=( 2, 8,13, 4,16, 7, 9, 6)( 3,15, 5,11)(12,14),
permclasses:=( 2, 7,11, 4, 3,13)( 5, 6, 8)( 9,15)(10,14,16),
text:="")]);
ARC("U3(3).2","tomfusion",rec(name:="U3(3).2",map:=[1,2,4,5,6,9,12,17,27,
34,3,8,16,28,36,36],text:=[
"fusion map is unique"
],perm:=(4,5)));
ARC("U3(3).2","maxes",["U3(3)","3^(1+2):SD16","L3(2).2","2^(1+4).S3",
"4^2:D12"]);
ALF("U3(3).2","S6(2)",[1,3,7,8,9,12,17,22,23,29,5,9,21,24,29,29],[
"fusion map is unique, equal to that on the CAS table"
]);
ALF("U3(3).2","G2(3)",[1,2,4,7,9,8,11,14,16,21,2,9,13,15,21,21],[
"fusion map is unique up to table automorphisms"
],"tom:432");
ALF("U3(3).2","J2.2",[1,2,4,5,6,6,9,11,12,15,17,18,20,22,23,23],[
"fusion map is unique"
]);
ALF("U3(3).2","3D4(2)",[1,2,5,4,7,6,9,14,16,20,3,7,10,15,20,20],[
"fusion map is unique"
]);
ALF("U3(3).2","G2(4)",[1,2,4,5,6,6,13,15,16,22,3,7,14,16,23,24],[
"fusion map is unique up to table automorphisms"
]);
ALF("U3(3).2","G2(5)",[1,2,3,4,5,6,12,15,16,22,2,5,14,17,22,22],[
"fusion map is unique"
]);
ALF("U3(3).2","F3+",[1,3,7,8,11,11,22,25,28,50,3,11,23,28,50,50],[
"fusion map determined by the ATLAS description of the U3(3) classes\n",
"and the compatibility of the fusions from U3(3).2N3A into F3+ through\n",
"U3(3).2 or the maxes of F3+ that contain F3+N3D"
]);
ALF("U3(3).2","U4(3).2_3",[1,2,3,5,6,6,9,11,12,15,16,17,18,20,23,23],[
"fusion map is unique"
]);
ALN("U3(3).2",["u3q3a","u332","G2(2)"]);

MOT("G2(3)M2",
[
"2nd maximal subgroup of G2(3),\n",
"differs from G2(3)M1 only by fusion map"
],
0,
0,
0,
0,
["ConstructPermuted",["U3(3).2"]]);
ALF("G2(3)M2","G2(3)",[1,2,3,7,8,9,10,14,15,20,2,8,13,16,20,20],[
"fusion U3(3).2 -> G2(3) mapped under G2(3).2"
]);

MOT("U3(4)",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,13]"
],
[62400,320,15,16,300,300,300,300,25,25,20,20,20,20,13,13,13,13,15,15,15,15],
[,[1,1,3,2,7,8,6,5,10,9,7,8,6,5,17,18,16,15,21,22,20,19],[1,2,1,4,8,7,5,6,10,
9,14,13,11,12,15,16,17,18,8,7,5,6],,[1,2,3,4,1,1,1,1,1,1,2,2,2,2,17,18,16,15,
3,3,3,3],,,,,,,,[1,2,3,4,8,7,5,6,10,9,14,13,11,12,1,1,1,1,22,21,19,20]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[12,-4,0,0,-3,-3,-3,-3,2,2,1,1,
1,1,-1,-1,-1,-1,0,0,0,0],[13,-3,1,1,E(5)-3*E(5)^2,-3*E(5)^3+E(5)^4,
E(5)^2-3*E(5)^4,-3*E(5)+E(5)^3,-E(5)-E(5)^4,-E(5)^2-E(5)^3,E(5)+E(5)^2,
E(5)^3+E(5)^4,E(5)^2+E(5)^4,E(5)+E(5)^3,0,0,0,0,E(5),E(5)^4,E(5)^2,E(5)^3],
[GALOIS,[3,4]],
[GALOIS,[3,3]],
[GALOIS,[3,2]],[39,7,0,-1,-3*E(5)-3*E(5)^4,-3*E(5)-3*E(5)^4,-3*E(5)^2-3*E(5)^3
 ,-3*E(5)^2-3*E(5)^3,-2*E(5)-E(5)^2-E(5)^3-2*E(5)^4,-E(5)-2*E(5)^2-2*E(5)^3
 -E(5)^4,E(5)+E(5)^4,E(5)+E(5)^4,E(5)^2+E(5)^3,E(5)^2+E(5)^3,0,0,0,0,0,0,0,0],
[GALOIS,[7,2]],[52,4,1,0,4*E(5)+3*E(5)^2,3*E(5)^3+4*E(5)^4,4*E(5)^2+3*E(5)^4,
3*E(5)+4*E(5)^3,E(5)+E(5)^4,E(5)^2+E(5)^3,-E(5)^2,-E(5)^3,-E(5)^4,-E(5),0,0,0,
0,E(5),E(5)^4,E(5)^2,E(5)^3],
[GALOIS,[9,4]],
[GALOIS,[9,3]],
[GALOIS,[9,2]],[64,0,1,0,4,4,4,4,-1,-1,0,0,0,0,-1,-1,-1,-1,1,1,1,1],[65,1,-1,
1,5,5,5,5,0,0,1,1,1,1,0,0,0,0,-1,-1,-1,-1],[65,1,-1,1,5*E(5),5*E(5)^4,
5*E(5)^2,5*E(5)^3,0,0,E(5),E(5)^4,E(5)^2,E(5)^3,0,0,0,0,-E(5),-E(5)^4,-E(5)^2,
-E(5)^3],
[GALOIS,[15,4]],
[GALOIS,[15,3]],
[GALOIS,[15,2]],[75,-5,0,-1,0,0,0,0,0,0,0,0,0,0,-E(13)-E(13)^3-E(13)^9,
-E(13)^4-E(13)^10-E(13)^12,-E(13)^2-E(13)^5-E(13)^6,-E(13)^7-E(13)^8-E(13)^11,
0,0,0,0],
[GALOIS,[19,4]],
[GALOIS,[19,7]],
[GALOIS,[19,2]]],
[(15,16)(17,18),(15,17,16,18),(15,18,16,17),( 5, 7, 6, 8)( 9,10)(11,13,12,14)
(19,21,20,22)]);
ARC("U3(4)","CAS",[rec(name:="u3q4",
permchars:=( 4, 5)(10,11)(16,17)(19,20,22),
permclasses:=( 6, 7)(12,13)(16,17)(20,21),
text:=[
"names:=u3q4; psu3[4]\n",
"              2a2(4)     (lie-not.)\n",
"   order: 2^6.3.5^2.13 = 62,400\n",
"   number of classes: 22\n",
"   source:mckay, john\n",
"         the non-abelian simple groups g,\n",
"         ord(g)<10^6 - character tables\n",
"         comm.algebra 7\n",
"         (1979),1407-1445\n",
"   test: 1.o.r., sym 2 decompose correctly\n",
"   comments: - \n",
""])]);
ARC("U3(4)","isSimple",true);
ARC("U3(4)","extInfo",["","4"]);
ARC("U3(4)","maxes",["2^(2+4):15","5xA5","5^2:S3","13:3"]);
ARC("U3(4)","tomfusion",rec(name:="U3(4)",map:=[1,2,3,5,6,6,6,6,7,7,10,10,
10,10,13,13,13,13,14,14,14,14],text:=[
"fusion map is unique"
]));
ALF("U3(4)","U3(4).2",[1,2,3,4,5,5,6,6,7,8,9,9,10,10,11,11,12,12,13,13,14,
14],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables"
]);
ALF("U3(4)","U3(4).4",[1,2,3,4,5,5,5,5,6,6,7,7,7,7,8,8,8,8,9,9,9,9]);
ALN("U3(4)",["u3q4"]);

MOT("U3(4).2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,13]"
],
[124800,640,30,32,300,300,50,50,20,20,13,13,15,15,120,6,16,16,10,10],
[,[1,1,3,2,6,5,8,7,6,5,12,11,14,13,1,3,4,4,8,7],[1,2,1,4,6,5,8,7,10,9,11,12,6,
5,15,15,18,17,20,19],,[1,2,3,4,1,1,1,1,2,2,12,11,3,3,15,16,17,18,15,
15],,,,,,,,[1,2,3,4,6,5,8,7,10,9,1,1,14,13,15,16,17,18,20,19]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,
-1,-1,-1,-1],[12,-4,0,0,-3,-3,2,2,1,1,-1,-1,0,0,0,0,2*E(4),-2*E(4),0,0],
[TENSOR,[3,2]],[26,-6,2,2,E(5)-3*E(5)^2-3*E(5)^3+E(5)^4,-3*E(5)+E(5)^2+E(5)^3
 -3*E(5)^4,-2*E(5)-2*E(5)^4,-2*E(5)^2-2*E(5)^3,-1,-1,0,0,E(5)+E(5)^4,
E(5)^2+E(5)^3,0,0,0,0,0,0],
[GALOIS,[5,2]],[39,7,0,-1,-3*E(5)-3*E(5)^4,-3*E(5)^2-3*E(5)^3,
-2*E(5)-E(5)^2-E(5)^3-2*E(5)^4,-E(5)-2*E(5)^2-2*E(5)^3-E(5)^4,E(5)+E(5)^4,
E(5)^2+E(5)^3,0,0,0,0,3,0,-1,-1,-E(5)^2-E(5)^3,-E(5)-E(5)^4],
[TENSOR,[7,2]],
[GALOIS,[7,2]],
[TENSOR,[9,2]],[104,8,2,0,4*E(5)+3*E(5)^2+3*E(5)^3+4*E(5)^4,
3*E(5)+4*E(5)^2+4*E(5)^3+3*E(5)^4,2*E(5)+2*E(5)^4,2*E(5)^2+2*E(5)^3,
-E(5)^2-E(5)^3,-E(5)-E(5)^4,0,0,E(5)+E(5)^4,E(5)^2+E(5)^3,0,0,0,0,0,0],
[GALOIS,[11,2]],[64,0,1,0,4,4,-1,-1,0,0,-1,-1,1,1,4,1,0,0,-1,-1],
[TENSOR,[13,2]],[65,1,-1,1,5,5,0,0,1,1,0,0,-1,-1,5,-1,1,1,0,0],
[TENSOR,[15,2]],[130,2,-2,2,5*E(5)+5*E(5)^4,5*E(5)^2+5*E(5)^3,0,0,E(5)+E(5)^4,
E(5)^2+E(5)^3,0,0,-E(5)-E(5)^4,-E(5)^2-E(5)^3,0,0,0,0,0,0],
[GALOIS,[17,2]],[150,-10,0,-2,0,0,0,0,0,0,-E(13)-E(13)^3-E(13)^4-E(13)^9
 -E(13)^10-E(13)^12,-E(13)^2-E(13)^5-E(13)^6-E(13)^7-E(13)^8-E(13)^11,0,0,0,0,
0,0,0,0],
[GALOIS,[19,2]]],
[(17,18),(11,12),( 5, 6)( 7, 8)( 9,10)(13,14)(19,20)]);
ARC("U3(4).2","CAS",[rec(name:="u3q4a",
permchars:=(3,4),
permclasses:=(),
text:=[
"u3q4\n",
"  test: 1. o.r., sym 2 decompose correctly \n",
""])]);
ARC("U3(4).2","maxes",["U3(4)","2^(2+4):(3xD10)","a5xd10","5^2:D12","13:6"]);
ARC("U3(4).2","tomfusion",rec(name:="U3(4).2",map:=[1,3,4,6,8,8,9,9,21,21,
26,26,27,27,2,10,16,16,18,18],text:=[
"fusion map is unique"
]));
ALF("U3(4).2","U3(4).4",[1,2,3,4,5,5,6,6,7,7,8,8,9,9,10,11,12,13,14,14]);
ALF("U3(4).2","G2(4)",[1,2,5,8,11,12,9,10,18,19,25,26,29,30,3,14,17,17,20,
21],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables",
"the representative is equal to the fusion map on the CAS table"
]);
ALN("U3(4).2",["u3q4a","U3(4).4M1"]);

MOT("U3(4).4",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,13],\n",
"constructions: Aut(U3(4))"
],
[249600,1280,60,64,300,50,20,13,15,240,12,32,32,10,24,24,12,12,16,16,16,16],
[,[1,1,3,2,5,6,5,8,9,1,3,4,4,6,10,10,11,11,12,13,12,13],[1,2,1,4,5,6,7,8,5,10,
10,13,12,14,16,15,16,15,20,19,22,21],,[1,2,3,4,1,1,2,8,3,10,11,12,13,10,15,16,
17,18,19,20,21,22],,,,,,,,[1,2,3,4,5,6,7,1,9,10,11,12,13,14,15,16,17,18,19,20,
21,22]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,
-1,E(4),-E(4),E(4),-E(4),E(4),-E(4),E(4),-E(4)],
[TENSOR,[2,2]],
[TENSOR,[2,3]],[12,-4,0,0,-3,2,1,-1,0,0,0,2*E(4),-2*E(4),0,0,0,0,0,1-E(4),
1+E(4),-1+E(4),-1-E(4)],
[TENSOR,[5,2]],
[TENSOR,[5,3]],
[TENSOR,[5,4]],[52,-12,4,4,2,2,-2,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0],[78,14,0,-2,
3,3,-1,0,0,6,0,-2,-2,1,0,0,0,0,0,0,0,0],
[TENSOR,[10,2]],[208,16,4,0,-7,-2,1,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0],[64,0,1,0,
4,-1,0,-1,1,4,1,0,0,-1,2,2,-1,-1,0,0,0,0],
[TENSOR,[13,2]],
[TENSOR,[13,3]],
[TENSOR,[13,4]],[65,1,-1,1,5,0,1,0,-1,5,-1,1,1,0,1,1,1,1,-1,-1,-1,-1],
[TENSOR,[17,2]],
[TENSOR,[17,3]],
[TENSOR,[17,4]],[260,4,-4,4,-5,0,-1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0],[300,-20,0,
-4,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0]],
[(12,13)(15,16)(17,18)(19,20)(21,22),(19,21)(20,22)]);
ALF("U3(4).4","G2(4).2",[1,2,5,8,10,9,16,21,23,3,12,15,15,17,27,27,34,34,
36,37,36,37],[
"fusion map is unique up to table autom."
]);
ALF("U3(4).4","M",[1,3,6,9,12,12,33,46,53,3,18,25,25,33,10,10,44,44,55,55,
56,56],[
"fusion map determined up to table automorphisms by the facts that\n",
"the subgroup contains elements from the classes 13B, 15D, 16B, 16C,\n",
"and that all elements of order 10 are in class 10E"
]);

MOT("U3(5)",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[126000,240,36,8,250,25,25,25,12,7,7,8,8,10],
[,[1,1,3,2,5,6,7,8,3,10,11,4,4,5],[1,2,1,4,5,6,7,8,2,11,10,12,13,14],,[1,2,3,
4,1,1,1,1,9,11,10,13,12,2],,[1,2,3,4,5,6,7,8,9,1,1,13,12,14]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1],[20,-4,2,0,-5,0,0,0,2,-1,-1,0,0,1],[21,5,3,1,
-4,1,1,1,-1,0,0,-1,-1,0],[28,4,1,0,3,3,-2,-2,1,0,0,0,0,-1],[28,4,1,0,3,-2,3,
-2,1,0,0,0,0,-1],[28,4,1,0,3,-2,-2,3,1,0,0,0,0,-1],[84,-4,3,0,9,-1,-1,-1,-1,0,
0,0,0,1],[105,1,-3,1,5,0,0,0,1,0,0,-1,-1,1],[125,5,-1,1,0,0,0,0,-1,-1,-1,1,1,
0],[126,6,0,-2,1,1,1,1,0,0,0,0,0,1],[126,-6,0,0,1,1,1,1,0,0,0,E(8)+E(8)^3,
-E(8)-E(8)^3,-1],
[GALOIS,[11,5]],[144,0,0,0,-6,-1,-1,-1,0,-E(7)-E(7)^2-E(7)^4,
-E(7)^3-E(7)^5-E(7)^6,0,0,0],
[GALOIS,[13,3]]],
[(12,13),(10,11),(7,8),(6,7)]);
ARC("U3(5)","CAS",[rec(name:="u3q5",
permchars:=(),
permclasses:=(),
text:=[
"names:=u3q5; psu3[5]\n",
"                 2a2(5)     (lie-not.)\n",
"      order: 2^4.3^2.5^3.7 = 126,000\n",
"      number of classes: 14\n",
"      source:mckay, john\n",
"            the non-abelian simple groups g,\n",
"            ord(g)<10^6 - character tables\n",
"            comm.algebra 7\n",
"            (1979),1407-1445\n",
"      test: 1.o.r., sym 2 decompose correctly\n",
"      comments: - \n",
""])]);
ARC("U3(5)","projectives",["3.U3(5)",[[21,-3,0,1,-4,1,1,1,0,0,0,1,1,2],[21,5,
0,1,-4,1,1,1,2,0,0,-1,-1,0],[48,0,0,0,-2,3,-2,-2,0,-1,-1,0,0,0],[48,0,0,0,-2,
-2,3,-2,0,-1,-1,0,0,0],[48,0,0,0,-2,-2,-2,3,0,-1,-1,0,0,0],[84,-4,0,0,9,-1,-1,
-1,2,0,0,0,0,1],[105,9,0,1,5,0,0,0,0,0,0,1,1,-1],[105,1,0,1,5,0,0,0,-2,0,0,-1,
-1,1],[126,6,0,-2,1,1,1,1,0,0,0,0,0,1],[126,-6,0,0,1,1,1,1,0,0,0,E(8)+E(8)^3,
-E(8)-E(8)^3,-1],
[GALOIS,[10,5]],[144,0,0,0,-6,-1,-1,-1,0,-E(7)-E(7)^2-E(7)^4,
-E(7)^3-E(7)^5-E(7)^6,0,0,0],
[GALOIS,[12,3]]],]);
ARC("U3(5)","isSimple",true);
ARC("U3(5)","extInfo",["3","3.2"]);
ARC("U3(5)","maxes",["A7","U3(5)M2","U3(5)M3","5^(1+2)+:8","A6.2_3","U3(5)M6",
"U3(5)M7","2.A5.2"]);
ARC("U3(5)","tomfusion",rec(name:="U3(5)",map:=[1,2,3,4,9,7,6,8,11,12,12,
14,14,20],text:=[
"fusion map is unique up to table autom., compatible with `Maxes'"
]));
ALF("U3(5)","U3(5).2",[1,2,3,4,5,6,7,7,8,9,9,10,10,11]);
ALF("U3(5)","U3(5).3",[1,2,3,4,5,6,6,6,7,8,9,10,11,12],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables"
]);
ALF("U3(5)","U3(5).3.2",[1,2,3,4,5,6,6,6,7,8,8,9,9,10],[
"fusion map is unique"
]);
ALF("U3(5)","McL",[1,2,4,5,6,7,7,7,9,10,11,12,12,15],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALN("U3(5)",["u3q5"]);

MOT("U3(5).2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[252000,480,72,16,500,50,25,24,7,8,20,240,240,12,8,10,12,20,20],
[,[1,1,3,2,5,6,7,3,9,4,5,1,2,3,4,6,8,11,11],[1,2,1,4,5,6,7,2,9,10,11,12,13,12,
15,16,13,18,19],,[1,2,3,4,1,1,1,8,9,10,2,12,13,14,15,12,17,13,13],,[1,2,3,4,5,
6,7,8,1,10,11,12,13,14,15,16,17,18,19]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,
-1,-1,-1,-1],[20,-4,2,0,-5,0,0,2,-1,0,1,0,0,0,0,0,0,E(20)+E(20)^9-E(20)^13
 -E(20)^17,-E(20)-E(20)^9+E(20)^13+E(20)^17],
[TENSOR,[3,2]],[21,5,3,1,-4,1,1,-1,0,-1,0,1,5,1,-1,1,-1,0,0],
[TENSOR,[5,2]],[28,4,1,0,3,3,-2,1,0,0,-1,4,4,1,0,-1,1,-1,-1],
[TENSOR,[7,2]],[56,8,2,0,6,-4,1,2,0,0,-2,0,0,0,0,0,0,0,0],[84,-4,3,0,9,-1,-1,
-1,0,0,1,4,-4,1,0,-1,-1,1,1],
[TENSOR,[10,2]],[105,1,-3,1,5,0,0,1,0,-1,1,5,1,-1,-1,0,1,1,1],
[TENSOR,[12,2]],[125,5,-1,1,0,0,0,-1,-1,1,0,5,5,-1,1,0,-1,0,0],
[TENSOR,[14,2]],[126,6,0,-2,1,1,1,0,0,0,1,6,-6,0,0,1,0,-1,-1],
[TENSOR,[16,2]],[252,-12,0,0,2,2,2,0,0,0,-2,0,0,0,0,0,0,0,0],[288,0,0,0,-12,
-2,-2,0,1,0,0,0,0,0,0,0,0,0,0]],
[(18,19)]);
ARC("U3(5).2","CAS",[rec(name:="u3q5:2",
permchars:=(16,17),
permclasses:=(),
text:=[
"names:u3q5d; psu3[5].z2, psiu3(5)\n",
"order: 2^5.3^2.5^3.7 = 252,000\n",
"number of classes: 19\n",
"source:magliveras, s.s.\n",
"the subgroup structure of the higman-sims\n",
"simple group\n",
"univ. of birmingham (1970)\n",
"test: 1. o.r., sym 2,3 and restricted characters decompose correctly\n",
"comments: -\n",
""])]);
ARC("U3(5).2","maxes",["U3(5)","A7.2","5^(1+2):(8.2)","A6.2^2","2S5.2",
"L3(2).2"]);
ARC("U3(5).2","tomfusion",rec(name:="U3(5).2",map:=[1,2,4,6,10,12,11,16,
18,25,33,3,5,17,26,34,45,61,61],text:=[
"fusion map is unique"
]));
ALF("U3(5).2","U3(5).3.2",[1,2,3,4,5,6,6,7,8,9,10,22,23,24,25,26,27,28,29],[
"fusion is unique up to table automorphisms"
]);
ALF("U3(5).2","Co3",[1,2,5,8,9,10,10,13,16,17,22,3,7,14,19,23,28,33,34],[
"fusion determined by fusion of U3(5).S3 in Co3,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("U3(5).2","HS",[1,2,4,7,8,9,10,12,13,15,17,3,5,11,16,18,21,23,24],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
],"tom:587");
ALF("U3(5).2","Ru",[1,2,4,8,9,9,10,11,12,15,16,2,5,11,15,16,18,27,27],[
"fusion map is unique, equal to that on the CAS table"
]);
ALF("U3(5).2","McL.2",[1,2,4,5,6,7,7,9,10,11,13,20,21,22,23,25,27,28,29],[
"fusion is unique up to table automorphisms"
]);
ALN("U3(5).2",["c4u2","u3q5:2"]);

MOT("U3(5).3",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7],\n",
"constructions: PGU(3,5)"
],
[378000,720,108,24,750,25,36,21,21,24,24,30,720,720,63,63,720,720,36,36,24,24,
30,30,21,21,21,21,24,24,24,24,30,30],
[,[1,1,3,2,5,6,3,8,9,4,4,5,14,13,16,15,14,13,14,13,18,17,24,23,26,25,28,27,22,
21,22,21,24,23],[1,2,1,4,5,6,2,9,8,10,11,12,1,1,1,1,2,2,2,2,4,4,5,5,9,9,8,8,
10,10,11,11,12,12],,[1,2,3,4,1,1,7,9,8,11,10,2,14,13,16,15,18,17,20,19,22,21,
14,13,28,27,26,25,32,31,30,29,18,17],,[1,2,3,4,5,6,7,1,1,11,10,12,13,14,15,16,
17,18,19,20,21,22,23,24,15,16,15,16,31,32,29,30,33,34]],
[[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,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,E(3),E(3)^2,E(3),E(3)^2],
[TENSOR,[2,2]],[20,-4,2,0,-5,0,2,-1,-1,0,0,1,-4,-4,-1,-1,-4,-4,2,2,0,0,1,1,-1,
-1,-1,-1,0,0,0,0,1,1],
[TENSOR,[4,2]],
[TENSOR,[4,3]],[21,5,3,1,-4,1,-1,0,0,-1,-1,0,-3,-3,0,0,5,5,-1,-1,1,1,2,2,0,0,
0,0,-1,-1,-1,-1,0,0],
[TENSOR,[7,2]],
[TENSOR,[7,3]],[84,12,3,0,9,-1,3,0,0,0,0,-3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0],[84,-4,3,0,9,-1,-1,0,0,0,0,1,0,0,0,0,8,8,2,2,0,0,0,0,0,0,0,0,0,0,0,
0,-2,-2],
[TENSOR,[11,2]],
[TENSOR,[11,3]],[105,1,-3,1,5,0,1,0,0,-1,-1,1,9,9,0,0,1,1,1,1,1,1,-1,-1,0,0,0,
0,-1,-1,-1,-1,1,1],
[TENSOR,[14,2]],
[TENSOR,[14,3]],[125,5,-1,1,0,0,-1,-1,-1,1,1,0,5,5,-1,-1,5,5,-1,-1,1,1,0,0,-1,
-1,-1,-1,1,1,1,1,0,0],
[TENSOR,[17,2]],
[TENSOR,[17,3]],[126,6,0,-2,1,1,0,0,0,0,0,1,6,6,0,0,6,6,0,0,-2,-2,1,1,0,0,0,0,
0,0,0,0,1,1],
[TENSOR,[20,2]],
[TENSOR,[20,3]],[126,-6,0,0,1,1,0,0,0,E(8)+E(8)^3,-E(8)-E(8)^3,-1,6,6,0,0,-6,
-6,0,0,0,0,1,1,0,0,0,0,E(8)+E(8)^3,E(8)+E(8)^3,-E(8)-E(8)^3,-E(8)-E(8)^3,-1,
-1],
[TENSOR,[23,2]],
[TENSOR,[23,3]],
[GALOIS,[23,5]],
[TENSOR,[26,2]],
[TENSOR,[26,3]],[144,0,0,0,-6,-1,0,-E(7)-E(7)^2-E(7)^4,-E(7)^3-E(7)^5-E(7)^6,
0,0,0,0,0,-3,-3,0,0,0,0,0,0,0,0,-E(7)-E(7)^2-E(7)^4,-E(7)-E(7)^2-E(7)^4,
-E(7)^3-E(7)^5-E(7)^6,-E(7)^3-E(7)^5-E(7)^6,0,0,0,0,0,0],
[TENSOR,[29,2]],
[TENSOR,[29,3]],
[GALOIS,[29,3]],
[TENSOR,[32,2]],
[TENSOR,[32,3]]],
[(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)
(33,34),(10,11)(29,31)(30,32),( 8, 9)(25,27)(26,28)]);
ARC("U3(5).3","CAS",[rec(name:="u3q5.3",
permchars:=(),
permclasses:=(),
text:=[
"u3q5                , test:= 1. o.r., sym 2 decompose correctly\n",
"errors in 2nd power map and 5th power map corrected \n",
""])]);
ARC("U3(5).3","projectives",["3.U3(5).3",[[21,-3,0,1,-4,1,0,0,0,1,1,2,
-E(3)-5*E(3)^2,-5*E(3)-E(3)^2,0,0,-E(3)-5*E(3)^2,-5*E(3)-E(3)^2,-E(3)+E(3)^2,
E(3)-E(3)^2,1,1,-E(3),-E(3)^2,0,0,0,0,1,1,1,1,-E(3),-E(3)^2],[21,5,0,1,-4,1,2,
0,0,-1,-1,0,-E(3)-5*E(3)^2,-5*E(3)-E(3)^2,0,0,-E(3)+3*E(3)^2,3*E(3)-E(3)^2,-1,
-1,1,1,-E(3),-E(3)^2,0,0,0,0,-1,-1,-1,-1,-E(3)-2*E(3)^2,-2*E(3)-E(3)^2],[144,
0,0,0,-6,-1,0,-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],[84,-4,
0,0,9,-1,2,0,0,0,0,1,-4*E(3)+4*E(3)^2,4*E(3)-4*E(3)^2,0,0,-4,-4,2*E(3)^2,
2*E(3),0,0,E(3)-E(3)^2,-E(3)+E(3)^2,0,0,0,0,0,0,0,0,1,1],[105,9,0,1,5,0,0,0,0,
1,1,-1,-5*E(3)-E(3)^2,-E(3)-5*E(3)^2,0,0,-5*E(3)-E(3)^2,-E(3)-5*E(3)^2,
E(3)-E(3)^2,-E(3)+E(3)^2,1,1,-E(3)^2,-E(3),0,0,0,0,1,1,1,1,-E(3)^2,-E(3)],[
105,1,0,1,5,0,-2,0,0,-1,-1,1,-5*E(3)-E(3)^2,-E(3)-5*E(3)^2,0,0,
-5*E(3)-9*E(3)^2,-9*E(3)-5*E(3)^2,1,1,1,1,-E(3)^2,-E(3),0,0,0,0,-1,-1,-1,-1,
E(3)^2,E(3)],[126,6,0,-2,1,1,0,0,0,0,0,1,6,6,0,0,6,6,0,0,-2,-2,1,1,0,0,0,0,0,
0,0,0,1,1],[126,-6,0,0,1,1,0,0,0,E(8)+E(8)^3,-E(8)-E(8)^3,-1,6,6,0,0,-6,-6,0,
0,0,0,1,1,0,0,0,0,E(8)+E(8)^3,E(8)+E(8)^3,-E(8)-E(8)^3,-E(8)-E(8)^3,-1,-1],
[GALOIS,[8,5]],[144,0,0,0,-6,-1,0,-E(7)-E(7)^2-E(7)^4,-E(7)^3-E(7)^5-E(7)^6,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,-E(63)+E(63)^4+E(63)^46-E(63)^58,-E(63)^8-E(63)^23
 +E(63)^32+E(63)^53,E(63)^10+E(63)^31-E(63)^40-E(63)^55,-E(63)^5+E(63)^17
 +E(63)^59-E(63)^62,0,0,0,0,0,0],
[GALOIS,[10,40]]],]);
ARC("U3(5).3","maxes",["U3(5)","5^(1+2)+:24","3x2S5","3^2:2A4","6^2:S3",
"7:3x3"]);
ARC("U3(5).3","tomfusion",rec(name:="U3(5).3",map:=[1,2,5,7,8,9,12,14,14,
16,16,21,3,3,4,4,10,10,11,11,29,29,30,30,40,40,40,40,45,45,45,45,50,50],
text:=[
"fusion map is unique"
]));
ALF("U3(5).3","U3(5).3.2",[1,2,3,4,5,6,7,8,8,9,9,10,11,11,12,12,13,13,14,
14,15,15,16,16,17,18,18,17,19,20,20,19,21,21],[
"fusion map is unique up to table autom.,\n",
"unique map that is compatible with Brauer tables"
]);

ALN("U3(5).3",["u3q5.3"]);

MOT("U3(5).3.2",
[
"origin: ATLAS of finite groups,\n",
"maximal subgroup of Co3,\n",
"tests: 1.o.r., pow[2,3,5,7],\n",
"constructions: Aut(U3(5))"
],
[756000,1440,216,48,1500,50,72,21,24,60,720,63,720,36,24,30,21,21,24,24,30,
240,240,12,8,10,12,20,20],
[,[1,1,3,2,5,6,3,8,4,5,11,12,11,11,13,16,18,17,15,15,16,1,2,3,4,6,7,10,10],[1,
2,1,4,5,6,2,8,9,10,1,1,2,2,4,5,8,8,9,9,10,22,23,22,25,26,23,28,29],,[1,2,3,4,
1,1,7,8,9,2,11,12,13,14,15,11,17,18,19,20,13,22,23,24,25,22,27,23,23],,[1,2,3,
4,5,6,7,1,9,10,11,12,13,14,15,16,12,12,20,19,21,22,23,24,25,26,27,28,29]],
0,
[(28,29),(19,20),(19,20)(28,29),(17,18),(17,18)(19,20)],
["ConstructGS3","U3(5).2","U3(5).3",[7,8],[[2,3],[5,6],[8,9],[12,13],[15,16],
[18,19],[21,22],[23,26],[25,27],[24,28],[29,32],[31,33],[30,34]],[[1,1],[4,3],
[7,5],[11,10],[14,12],[17,14],[20,16]],
( 1,10,24,15,28,21, 8,20, 7,17, 2,11,26,18, 4, 6,14,29,22,12,25,16)
( 5, 9,23,13,27,19)]);
ARC("U3(5).3.2","CAS",[rec(name:="u3q5:s3",
permclasses:=(11,19,27,16,24,13,21,29,18,26,15,23,12,20,28,17,25,14,22),
permchars:=(),
text:=[
"Maximal subgroup of sporadic Conway group c3.\n",
"Source: Atlas.\n",
"Test: JAMES, JAMES,n=3,\n",
"and restricted characters decompose properly.\n",
""])]);
ARC("U3(5).3.2","maxes",["U3(5).3","U3(5).2","5^(1+2):(24:2)","(3x2S5).2",
"6^2:D12","3^2.2.S4","(7:3x3):2"]);
ARC("U3(5).3.2","tomfusion",rec(name:="U3(5).S3",map:=[1,2,6,8,12,13,15,24,30,
37,4,5,14,17,58,61,85,85,106,106,110,3,7,16,31,38,59,82,82],text:=[
"fusion map is unique"
]));
ALF("U3(5).3.2","Co3",[1,2,5,8,9,10,13,16,17,22,4,6,11,12,27,30,35,35,40,40,
42,3,7,14,19,23,28,33,34],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALN("U3(5).3.2",["U3(5).S3","U3(5):S3","u3q5:s3"]);

MOT("U3(7)",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,7,43]"
],
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64,48,48,56,48,48,48,48,48,48,48,48,56,56,43,43,43,43,43,43,43,43,43,43,43,43,
43,43,48,48,48,48,48,48,48,48,56,56,56,56],
[,[1,1,3,2,2,2,3,8,9,4,5,4,5,4,5,6,6,6,6,7,7,8,10,11,12,13,20,21,20,21,22,22,
36,35,38,37,40,39,42,41,44,43,46,45,34,33,27,28,29,30,27,28,29,30,31,32,31,
32],[1,2,1,5,4,6,2,8,9,13,12,11,10,15,14,17,16,18,19,5,4,22,26,25,24,23,13,12,
11,10,32,31,46,45,34,33,36,35,38,37,40,39,42,41,44,43,26,25,24,23,26,25,24,23,
58,57,56,55],,,,[1,2,3,5,4,6,7,1,1,11,10,13,12,15,14,16,17,19,18,21,20,2,24,
23,26,25,28,27,30,29,5,4,34,33,36,35,38,37,40,39,42,41,44,43,46,45,48,47,50,
49,52,51,54,53,11,10,13,12],,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,[1,2,3,5,4,6,7,
8,9,13,12,11,10,15,14,17,16,18,19,21,20,22,26,25,24,23,30,29,28,27,32,31,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,50,49,52,51,54,53,48,47,58,57,56,55]],
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1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[42,-6,0,-6,-6,2,0,-7,0,-6,-6,-6,-6,
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-1,0,0,0,0,0,0,0,0,1,1,1,1],[43,-5,1,-5,-5,3,1,-6,1,7,7,7,7,-1,-1,-1,-1,-1,-1,
1,1,2,-1,-1,-1,-1,1,1,1,1,2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,
-1,-1,0,0,0,0],[43,-5,1,7,7,-1,1,-6,1,-1+6*E(4),-1-6*E(4),-1+6*E(4),-1-6*E(4),
-1-2*E(4),-1+2*E(4),1,1,1,1,1,1,2,E(4),-E(4),E(4),-E(4),-1,-1,-1,-1,0,0,0,0,0,
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-1+E(4),-1-E(4),-1+E(4)],
[GALOIS,[4,3]],[43,7,1,-1+6*E(4),-1-6*E(4),1,1,-6,1,E(8)^2-6*E(8)^3,
6*E(8)-E(8)^2,E(8)^2+6*E(8)^3,-6*E(8)-E(8)^2,-E(4),E(4),1-E(8)+E(8)^3,
1+E(8)-E(8)^3,-1+E(8)+E(8)^3,-1-E(8)-E(8)^3,-1,-1,0,E(8),-E(8)^3,-E(8),E(8)^3,
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E(8)^2-E(8)^3,E(8)-E(8)^2],
[GALOIS,[6,7]],
[GALOIS,[6,5]],
[GALOIS,[6,3]],[258,18,0,-6,-6,2,0,13,-1,6,6,6,6,-2,-2,2,2,2,2,0,0,-3,0,0,0,0,
0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,-1],[258,-6,
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[GALOIS,[15,5]],[301,13,1,13,13,-3,1,7,0,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,
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-E(4)],
[GALOIS,[18,3]],[301,1,1,-7-6*E(4),-7+6*E(4),-1,1,7,0,7*E(8)^2+6*E(8)^3,
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-E(8),E(8)^3,E(8),-E(8)^3,-E(8),E(8)^3,-E(8)^3,E(8),E(8)^3,-E(8)],
[GALOIS,[20,7]],
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[GALOIS,[27,3]],[344,8,-1,-8,-8,0,-1,1,1,8*E(4),-8*E(4),8*E(4),-8*E(4),0,0,0,
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0,0,0,0,0,0,0,0,0,0,0,0,E(8),-E(8)^3,-E(8),E(8)^3,E(8),-E(8)^3,-E(8),E(8)^3,
E(4),-E(4),E(4),-E(4)],
[GALOIS,[29,7]],
[GALOIS,[29,5]],
[GALOIS,[29,3]],[344,-8,2,8*E(4),-8*E(4),0,-2,1,1,8*E(8),-8*E(8)^3,-8*E(8),
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-E(8),E(8)^3],
[GALOIS,[33,7]],
[GALOIS,[33,5]],
[GALOIS,[33,3]],[344,-8,-1,-8*E(4),8*E(4),0,1,1,1,8*E(8)^3,-8*E(8),-8*E(8)^3,
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-E(48)^5+E(48)^37,E(48)^19-E(48)^35,E(8)^3,-E(8),-E(8)^3,E(8)],
[GALOIS,[37,7]],
[GALOIS,[37,29]],
[GALOIS,[37,11]],
[GALOIS,[37,17]],
[GALOIS,[37,23]],
[GALOIS,[37,5]],
[GALOIS,[37,35]],[384,0,0,0,0,0,0,-8,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
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-E(43)^19-E(43)^28-E(43)^39,-E(43)^13-E(43)^35-E(43)^38,-E(43)^5-E(43)^8
 -E(43)^30,-E(43)^10-E(43)^16-E(43)^17,-E(43)^26-E(43)^27-E(43)^33,
-E(43)^9-E(43)^11-E(43)^23,-E(43)^20-E(43)^32-E(43)^34,-E(43)^21-E(43)^25
 -E(43)^40,-E(43)^3-E(43)^18-E(43)^22,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[45,7]],
[GALOIS,[45,21]],
[GALOIS,[45,3]],
[GALOIS,[45,9]],
[GALOIS,[45,20]],
[GALOIS,[45,10]],
[GALOIS,[45,26]],
[GALOIS,[45,13]],
[GALOIS,[45,5]],
[GALOIS,[45,4]],
[GALOIS,[45,19]],
[GALOIS,[45,14]],
[GALOIS,[45,2]]],
[(47,51)(48,52)(49,53)(50,54),(33,46,43,42,39,38,35,34,45,44,41,40,37,36),
(10,12)(11,13)(16,17)(18,19)(23,25)(24,26)(27,29)(28,30)(47,53,51,49)
(48,54,52,50)(55,57)(56,58),( 4, 5)(10,11)(12,13)(14,15)(18,19)(20,21)(23,24)
(25,26)(27,28)(29,30)(31,32)(47,52)(48,51)(49,54)(50,53)(55,56)(57,58),( 4, 5)
(10,13)(11,12)(14,15)(16,17)(20,21)(23,26)(24,25)(27,30)(28,29)(31,32)
(47,50,51,54)(48,49,52,53)(55,58)(56,57),(33,34)(35,36)(37,38)(39,40)(41,42)
(43,44)(45,46),(33,45,43,41,39,37,35)(34,46,44,42,40,38,36)]);
ARC("U3(7)","isSimple",true);
ARC("U3(7)","extInfo",["","2"]);
ARC("U3(7)","maxes",["7^(1+2):48","2(L2(7)x4).2","8^2:S3","L3(2).2","43:3"]);
ARC("U3(7)","tomfusion",rec(name:="U3(7)",map:=[1,2,3,4,4,5,7,9,10,11,11,11,
11,14,14,13,13,12,12,19,19,22,31,31,31,31,38,38,38,38,40,40,49,49,49,49,49,49,
49,49,49,49,49,49,49,49,55,55,55,55,55,55,55,55,58,58,58,58],text:=[
"fusion map is unique"
]));
ALF("U3(7)","U3(7).2",[1,2,3,4,4,5,6,7,8,9,9,10,10,11,11,12,13,14,14,15,
15,16,17,17,18,18,19,19,20,20,21,21,22,22,23,23,24,24,25,25,26,26,27,27,
28,28,29,29,30,30,31,31,32,32,33,33,34,34],[
"fusion map is unique up to table autom.,\n",
"unique map that is compatible with Brauer tables"
]);

MOT("U3(7).2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,7,43],\n",
"constructions: Aut(U3(7))"
],
[11327232,5376,96,2688,128,96,5488,98,2688,2688,64,128,128,64,48,112,48,48,48,
48,56,43,43,43,43,43,43,43,48,48,48,48,56,56,672,672,12,16,12,14,16,16,28,28],
[,[1,1,3,2,2,3,7,8,4,4,4,5,5,5,6,7,9,10,15,15,16,23,24,25,26,27,28,22,19,20,
19,20,21,21,1,2,3,5,6,8,12,13,16,16],[1,2,1,4,5,2,7,8,10,9,11,13,12,14,4,16,
18,17,10,9,21,28,22,23,24,25,26,27,18,17,18,17,34,33,35,36,35,38,36,40,42,41,
44,43],,,,[1,2,3,4,5,6,1,1,9,10,11,12,13,14,15,2,17,18,19,20,4,22,23,24,25,26,
27,28,29,30,31,32,9,10,35,36,37,38,39,35,41,42,36,
36],,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,[1,2,3,4,5,6,7,8,10,9,11,13,12,14,15,
16,18,17,20,19,21,1,1,1,1,1,1,1,30,31,32,29,34,33,35,36,37,38,39,40,42,41,43,
44]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[42,-6,0,-6,2,0,-7,0,-6,-6,2,2,2,2,0,1,0,0,
0,0,1,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,1,1,0,0,0,0,0,0,0,0,E(7)+E(7)^2-E(7)^3
 +E(7)^4-E(7)^5-E(7)^6,-E(7)-E(7)^2+E(7)^3-E(7)^4+E(7)^5+E(7)^6],
[TENSOR,[3,2]],[43,-5,1,-5,3,1,-6,1,7,7,-1,-1,-1,-1,1,2,-1,-1,1,1,2,0,0,0,0,0,
0,0,-1,-1,-1,-1,0,0,-1,7,-1,-1,1,-1,1,1,0,0],
[TENSOR,[5,2]],[86,-10,2,14,-2,2,-12,2,-2,-2,-2,2,2,2,2,4,0,0,-2,-2,0,0,0,0,0,
0,0,0,0,0,0,0,-2,-2,0,0,0,0,0,0,0,0,0,0],[86,14,2,-2,2,2,-12,2,
6*E(8)-6*E(8)^3,-6*E(8)+6*E(8)^3,0,2-2*E(8)+2*E(8)^3,2+2*E(8)-2*E(8)^3,-2,-2,
0,E(8)-E(8)^3,-E(8)+E(8)^3,0,0,-2,0,0,0,0,0,0,0,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)^3,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[8,3]],[258,18,0,-6,2,0,13,-1,6,6,-2,2,2,2,0,-3,0,0,0,0,1,0,0,0,0,0,0,
0,0,0,0,0,-1,-1,6,6,0,2,0,-1,0,0,-1,-1],
[TENSOR,[10,2]],[258,-6,0,6,2,0,13,-1,6+6*E(8)-6*E(8)^3,6-6*E(8)+6*E(8)^3,2,
2*E(8)-2*E(8)^3,-2*E(8)+2*E(8)^3,0,0,1,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,
-1-E(8)+E(8)^3,-1+E(8)-E(8)^3,6,-6,0,0,0,-1,E(8)-E(8)^3,-E(8)+E(8)^3,1,1],
[TENSOR,[12,2]],
[GALOIS,[12,3]],
[TENSOR,[14,2]],[516,-12,0,-12,-4,0,26,-2,0,0,0,4,4,-4,0,2,0,0,0,0,2,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[516,-12,0,12,4,0,26,-2,-12,-12,-4,0,0,
0,0,2,0,0,0,0,-2,0,0,0,0,0,0,0,0,0,0,0,2,2,0,0,0,0,0,0,0,0,0,0],[301,13,1,13,
-3,1,7,0,1,1,1,1,1,1,1,-1,-1,-1,1,1,-1,0,0,0,0,0,0,0,-1,-1,-1,-1,1,1,7,-1,1,
-1,-1,0,1,1,-1,-1],
[TENSOR,[18,2]],[602,26,2,2,2,2,14,0,-14,-14,2,-2,-2,-2,2,-2,0,0,-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],[602,2,2,-14,-2,2,14,0,
-6*E(8)+6*E(8)^3,6*E(8)-6*E(8)^3,0,-2+2*E(8)-2*E(8)^3,-2-2*E(8)+2*E(8)^3,2,-2,
2,E(8)-E(8)^3,-E(8)+E(8)^3,0,0,0,0,0,0,0,0,0,0,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)^3,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[21,3]],[343,7,1,7,-1,1,0,0,7,7,-1,-1,-1,-1,1,0,1,1,1,1,0,-1,-1,-1,-1,
-1,-1,-1,1,1,1,1,0,0,7,7,1,-1,1,0,-1,-1,0,0],
[TENSOR,[23,2]],[344,8,-1,8,0,-1,1,1,8,8,0,0,0,0,-1,1,-2,-2,-1,-1,1,0,0,0,0,0,
0,0,1,1,1,1,1,1,8,-8,-1,0,1,1,0,0,-1,-1],
[TENSOR,[25,2]],[344,8,-1,8,0,-1,1,1,8,8,0,0,0,0,-1,1,2,2,-1,-1,1,0,0,0,0,0,0,
0,-1,-1,-1,-1,1,1,8,8,-1,0,-1,1,0,0,1,1],
[TENSOR,[27,2]],[688,16,-2,16,0,-2,2,2,-16,-16,0,0,0,0,-2,2,0,0,2,2,2,0,0,0,0,
0,0,0,0,0,0,0,-2,-2,0,0,0,0,0,0,0,0,0,0],[688,16,-2,-16,0,-2,2,2,0,0,0,0,0,0,
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-E(8)+E(8)^3,E(8)-E(8)^3,-E(8)+E(8)^3,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[30,3]],[688,-16,4,0,0,-4,2,2,8*E(8)-8*E(8)^3,-8*E(8)+8*E(8)^3,0,0,0,
0,0,-2,0,0,2*E(8)-2*E(8)^3,-2*E(8)+2*E(8)^3,0,0,0,0,0,0,0,0,0,0,0,0,
E(8)-E(8)^3,-E(8)+E(8)^3,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[32,3]],[688,-16,-2,0,0,2,2,2,-8*E(8)+8*E(8)^3,8*E(8)-8*E(8)^3,0,0,0,
0,0,-2,0,0,E(8)-E(8)^3,-E(8)+E(8)^3,0,0,0,0,0,0,0,0,-E(48)^25-E(48)^31
 +E(48)^41+E(48)^47,E(48)^5-E(48)^19+E(48)^35-E(48)^37,E(48)^25+E(48)^31
 -E(48)^41-E(48)^47,-E(48)^5+E(48)^19-E(48)^35+E(48)^37,-E(8)+E(8)^3,
E(8)-E(8)^3,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[34,11]],
[GALOIS,[34,17]],
[GALOIS,[34,5]],[768,0,0,0,0,0,-16,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,
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 -E(43)^29-E(43)^31-E(43)^41,-E(43)^4-E(43)^15-E(43)^19-E(43)^24-E(43)^28
 -E(43)^39,-E(43)^5-E(43)^8-E(43)^13-E(43)^30-E(43)^35-E(43)^38,
-E(43)^10-E(43)^16-E(43)^17-E(43)^26-E(43)^27-E(43)^33,-E(43)^9-E(43)^11
 -E(43)^20-E(43)^23-E(43)^32-E(43)^34,-E(43)^3-E(43)^18-E(43)^21-E(43)^22
 -E(43)^25-E(43)^40,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[38,3]],
[GALOIS,[38,9]],
[GALOIS,[38,10]],
[GALOIS,[38,5]],
[GALOIS,[38,4]],
[GALOIS,[38,2]]],
[(43,44),(29,31)(30,32),(22,28,27,26,25,24,23),( 9,10)(12,13)(17,18)(19,20)
(29,30,31,32)(33,34)(41,42)]);

MOT("U3(8)",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,7,19]"
],
[5515776,1536,1512,1512,81,64,64,64,24,24,21,21,21,27,27,27,19,19,19,19,19,19,
21,21,21,21,21,21],
[,[1,1,4,3,5,2,2,2,4,3,12,13,11,15,16,14,20,19,22,21,18,17,26,25,28,27,24,
23],[1,2,1,1,1,6,7,8,2,2,13,11,12,5,5,5,20,19,22,21,18,17,13,13,11,11,12,
12],,,,[1,2,3,4,5,6,7,8,9,10,1,1,1,15,16,14,17,18,19,20,21,22,3,4,3,4,3,
4],,,,,,,,,,,,[1,2,3,4,5,6,7,8,9,10,12,13,11,14,15,16,1,1,1,1,1,1,25,26,27,28,
23,24]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[56,-8,-7,-7,2,0,0,
0,1,1,0,0,0,2,2,2,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0],[57,-7,-6*E(3),-6*E(3)^2,3,1,
1,1,2*E(3),2*E(3)^2,1,1,1,0,0,0,0,0,0,0,0,0,E(3),E(3)^2,E(3),E(3)^2,E(3),
E(3)^2],
[GALOIS,[3,2]],[133,5,7,7,-2,5,-3,-3,-1,-1,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,
0],[133,5,7,7,-2,-3,5,-3,-1,-1,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0],[133,5,7,
7,-2,-3,-3,5,-1,-1,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0],[399,15,0,0,3,-1,-1,
-1,0,0,0,0,0,-2*E(9)^2-E(9)^4-E(9)^5-2*E(9)^7,E(9)^2-E(9)^4-E(9)^5+E(9)^7,
E(9)^2+2*E(9)^4+2*E(9)^5+E(9)^7,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[8,4]],
[GALOIS,[8,2]],[456,8,15*E(3),15*E(3)^2,-3,0,0,0,-E(3),-E(3)^2,1,1,1,0,0,0,0,
0,0,0,0,0,E(3),E(3)^2,E(3),E(3)^2,E(3),E(3)^2],
[GALOIS,[11,2]],[512,0,8,8,-1,0,0,0,0,0,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,
1,1,1,1],[513,1,9,9,0,1,1,1,1,1,E(7)+E(7)^6,E(7)^2+E(7)^5,E(7)^3+E(7)^4,0,0,0,
0,0,0,0,0,0,E(7)+E(7)^6,E(7)+E(7)^6,E(7)^2+E(7)^5,E(7)^2+E(7)^5,E(7)^3+E(7)^4,
E(7)^3+E(7)^4],
[GALOIS,[14,3]],
[GALOIS,[14,2]],[513,1,9*E(3),9*E(3)^2,0,1,1,1,E(3),E(3)^2,E(7)+E(7)^6,
E(7)^2+E(7)^5,E(7)^3+E(7)^4,0,0,0,0,0,0,0,0,0,E(21)^4+E(21)^10,
E(21)^11+E(21)^17,E(21)+E(21)^13,E(21)^8+E(21)^20,E(21)^16+E(21)^19,
E(21)^2+E(21)^5],
[GALOIS,[17,8]],
[GALOIS,[17,4]],
[GALOIS,[17,11]],
[GALOIS,[17,16]],
[GALOIS,[17,2]],[567,-9,0,0,0,-1,-1,-1,0,0,0,0,0,0,0,0,-E(19)-E(19)^7-E(19)^11
 ,-E(19)^8-E(19)^12-E(19)^18,-E(19)^5-E(19)^16-E(19)^17,-E(19)^2-E(19)^3
 -E(19)^14,-E(19)^4-E(19)^6-E(19)^9,-E(19)^10-E(19)^13-E(19)^15,0,0,0,0,0,0],
[GALOIS,[23,8]],
[GALOIS,[23,4]],
[GALOIS,[23,10]],
[GALOIS,[23,5]],
[GALOIS,[23,2]]],
[(17,18)(19,20)(21,22),(17,20,21,18,19,22),(17,21,19)(18,22,20),(14,16,15),
(11,13,12)(23,27,25)(24,28,26),(6,8),(6,7),(7,8),( 3, 4)( 9,10)(14,15,16)
(23,24)(25,26)(27,28),( 3, 4)( 9,10)(23,24)(25,26)(27,28)]);
ARC("U3(8)","CAS",[rec(name:="u3q8",
permchars:=( 3, 4, 5, 8,11, 6, 9,12, 7,10,13)(14,16,18,21)(15,20)(19,22)
(24,27,26,28),
permclasses:=( 3, 6)( 4, 7)( 5,10, 9, 8)(11,18,27,17,23,14)(12,20,24,19,26,15,
 13,16)(21,25,22,28),
text:=[
"names:= u3q8; psu 3[8]\n",
" order: 2^9.3^4.7.19 = 5,515,776\n",
" number of classes: 28\n",
" source:generated by cas-system\n",
" test: 1. o.r., sym 2 decompose correctly\n",
" comments: - \n",
""])]);
ARC("U3(8)","projectives",["3.U3(8)",[[57,-7,-8*E(9)^4-E(9)^7,-E(9)^2-8*E(9)^5
 ,0,1,1,1,-E(9)^7,-E(9)^2,1,1,1,-E(9)^2-E(9)^3-E(9)^4-E(9)^5-E(9)^6-E(9)^7,
E(9)^2-E(9)^3-E(9)^6+E(9)^7,-E(9)^3+E(9)^4+E(9)^5-E(9)^6,0,0,0,0,0,0,
-E(9)^4-E(9)^7,-E(9)^2-E(9)^5,-E(9)^4-E(9)^7,-E(9)^2-E(9)^5,-E(9)^4-E(9)^7,
-E(9)^2-E(9)^5],
[GALOIS,[1,4]],
[GALOIS,[1,7]],[189,-3,0,0,0,5,-3,-3,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,0,0,0,
0,0,0],[189,-3,0,0,0,-3,5,-3,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0],[
189,-3,0,0,0,-3,-3,5,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0],[399,15,
7*E(9)^4-7*E(9)^7,-7*E(9)^2+7*E(9)^5,0,-1,-1,-1,-E(9)^4+E(9)^7,E(9)^2-E(9)^5,
0,0,0,-E(9)^2-E(9)^3-E(9)^4-E(9)^5-E(9)^6-E(9)^7,E(9)^2-E(9)^3-E(9)^6+E(9)^7,
-E(9)^3+E(9)^4+E(9)^5-E(9)^6,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[7,4]],
[GALOIS,[7,7]],[456,8,-E(9)^4-8*E(9)^7,-8*E(9)^2-E(9)^5,0,0,0,0,-E(9)^4,
-E(9)^5,1,1,1,E(9)^2+E(9)^3+E(9)^4+E(9)^5+E(9)^6+E(9)^7,-E(9)^2+E(9)^3+E(9)^6
 -E(9)^7,E(9)^3-E(9)^4-E(9)^5+E(9)^6,0,0,0,0,0,0,-E(9)^4-E(9)^7,
-E(9)^2-E(9)^5,-E(9)^4-E(9)^7,-E(9)^2-E(9)^5,-E(9)^4-E(9)^7,-E(9)^2-E(9)^5],
[GALOIS,[10,4]],
[GALOIS,[10,7]],[513,1,-9*E(9)^4-9*E(9)^7,-9*E(9)^2-9*E(9)^5,0,1,1,1,
-E(9)^4-E(9)^7,-E(9)^2-E(9)^5,E(7)+E(7)^6,E(7)^2+E(7)^5,E(7)^3+E(7)^4,0,0,0,0,
0,0,0,0,0,-E(63)^19-E(63)^37-E(63)^40-E(63)^58,-E(63)^5-E(63)^23-E(63)^26
 -E(63)^44,-E(63)^4-E(63)^10-E(63)^31-E(63)^46,-E(63)^17-E(63)^32-E(63)^53
 -E(63)^59,-E(63)-E(63)^13-E(63)^22-E(63)^55,-E(63)^8-E(63)^41-E(63)^50
 -E(63)^62],
[GALOIS,[13,4]],
[GALOIS,[13,16]],
[GALOIS,[13,10]],
[GALOIS,[13,40]],
[GALOIS,[13,34]],
[GALOIS,[13,19]],
[GALOIS,[13,13]],
[GALOIS,[13,25]],[567,-9,0,0,0,-1,-1,-1,0,0,0,0,0,0,0,0,
-E(19)-E(19)^7-E(19)^11,-E(19)^8-E(19)^12-E(19)^18,-E(19)^5-E(19)^16-E(19)^17,
-E(19)^2-E(19)^3-E(19)^14,-E(19)^4-E(19)^6-E(19)^9,-E(19)^10-E(19)^13-E(19)^15
 ,0,0,0,0,0,0],
[GALOIS,[22,8]],
[GALOIS,[22,4]],
[GALOIS,[22,10]],
[GALOIS,[22,5]],
[GALOIS,[22,2]]],]);
ARC("U3(8)","isSimple",true);
ARC("U3(8)","extInfo",["3","(S3x3)"]);
ARC("U3(8)","maxes",["2^(3+6):21","3xL2(8)","3^2:2A4","U3(8)M4","U3(8)M5",
"(9x3).S3","19:3"]);
ARC("U3(8)","tomfusion",rec(name:="U3(8)",map:=[1,2,3,3,4,8,7,6,9,9,11,11,
11,29,29,29,61,61,61,61,61,61,62,62,62,62,62,62],text:=[
"fusion map is unique up to table autom."
]));
ALF("U3(8)","U3(8).2",[1,2,3,3,4,5,6,6,7,7,8,9,10,11,12,13,14,14,15,15,16,
16,17,17,18,18,19,19],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables"
]);
ALF("U3(8)","U3(8).3_1",[1,2,3,4,5,6,7,8,9,10,11,11,11,12,12,12,13,14,13,
14,13,14,15,16,15,16,15,16],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables"
]);
ALF("U3(8)","U3(8).3_2",[1,2,3,4,5,6,6,6,7,8,9,10,11,12,13,14,15,16,17,18,
19,20,21,22,23,24,25,26],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables"
]);
ALF("U3(8)","U3(8).3_3",[1,2,3,4,5,6,6,6,7,8,9,9,9,10,10,10,11,12,11,12,
11,12,13,14,13,14,13,14],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables"
]);
ALF("U3(8)","U3(8).6",[1,2,3,3,4,5,6,6,7,7,8,8,8,9,9,9,10,10,10,10,10,10,
11,11,11,11,11,11]);
ALF("U3(8)","U3(8).3^2",[1,2,3,4,5,6,6,6,7,8,9,9,9,10,10,10,11,12,11,12,
11,12,13,14,13,14,13,14],[
"fusion map is unique up to table autom."
]);
ALN("U3(8)",["u3q8"]);

MOT("U3(8).2",
[
"origin: ATLAS of finite groups, tests: 1.o.r.,\n",
"constructions: PSU(3,8) extended by transpose-inverse"
],
[11031552,3072,1512,162,128,64,24,42,42,42,54,54,54,19,19,19,21,21,21,1008,18,
32,32,14,14,14,18,18,18],
[,[1,1,3,4,2,2,3,9,10,8,12,13,11,15,16,14,18,19,17,1,4,5,5,9,10,8,12,13,11],[
1,2,1,1,5,6,2,10,8,9,4,4,4,15,16,14,10,8,9,20,20,22,23,26,24,25,21,21,21],,,,[
1,2,3,4,5,6,7,1,1,1,12,13,11,14,15,16,3,3,3,20,21,23,22,20,20,20,28,29,
27],,,,,,,,,,,,[1,2,3,4,5,6,7,9,10,8,11,12,13,1,1,1,18,19,17,20,21,22,23,25,
26,24,27,28,29]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[56,-8,-7,2,0,0,1,0,0,0,
2,2,2,-1,-1,-1,0,0,0,0,0,2*E(8)+2*E(8)^3,-2*E(8)-2*E(8)^3,0,0,0,0,0,0],
[TENSOR,[3,2]],[114,-14,6,6,2,2,-2,2,2,2,0,0,0,0,0,0,-1,-1,-1,0,0,0,0,0,0,0,0,
0,0],[133,5,7,-2,5,-3,-1,0,0,0,1,1,1,0,0,0,0,0,0,7,-2,-1,-1,0,0,0,1,1,1],
[TENSOR,[6,2]],[266,10,14,-4,-6,2,-2,0,0,0,2,2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0],[399,15,0,3,-1,-1,0,0,0,0,-2*E(9)^2-E(9)^4-E(9)^5-2*E(9)^7,
E(9)^2-E(9)^4-E(9)^5+E(9)^7,E(9)^2+2*E(9)^4+2*E(9)^5+E(9)^7,0,0,0,0,0,0,7,1,
-1,-1,0,0,0,-E(9)^4-E(9)^5,E(9)^2+E(9)^4+E(9)^5+E(9)^7,-E(9)^2-E(9)^7],
[TENSOR,[9,2]],
[GALOIS,[9,4]],
[TENSOR,[11,2]],
[GALOIS,[9,2]],
[TENSOR,[13,2]],[912,16,-15,-6,0,0,1,2,2,2,0,0,0,0,0,0,-1,-1,-1,0,0,0,0,0,0,0,
0,0,0],[512,0,8,-1,0,0,0,1,1,1,-1,-1,-1,-1,-1,-1,1,1,1,8,-1,0,0,1,1,1,-1,-1,
-1],
[TENSOR,[16,2]],[513,1,9,0,1,1,1,E(7)+E(7)^6,E(7)^2+E(7)^5,E(7)^3+E(7)^4,0,0,
0,0,0,0,E(7)+E(7)^6,E(7)^2+E(7)^5,E(7)^3+E(7)^4,9,0,1,1,E(7)+E(7)^6,
E(7)^2+E(7)^5,E(7)^3+E(7)^4,0,0,0],
[TENSOR,[18,2]],
[GALOIS,[18,3]],
[TENSOR,[20,2]],
[GALOIS,[18,2]],
[TENSOR,[22,2]],[1026,2,-9,0,2,2,-1,2*E(7)+2*E(7)^6,2*E(7)^2+2*E(7)^5,
2*E(7)^3+2*E(7)^4,0,0,0,0,0,0,-E(7)-E(7)^6,-E(7)^2-E(7)^5,-E(7)^3-E(7)^4,0,0,
0,0,0,0,0,0,0,0],
[GALOIS,[24,3]],
[GALOIS,[24,2]],[1134,-18,0,0,-2,-2,0,0,0,0,0,0,0,-E(19)-E(19)^7-E(19)^8
 -E(19)^11-E(19)^12-E(19)^18,-E(19)^2-E(19)^3-E(19)^5-E(19)^14-E(19)^16
 -E(19)^17,-E(19)^4-E(19)^6-E(19)^9-E(19)^10-E(19)^13-E(19)^15,0,0,0,0,0,0,0,
0,0,0,0,0,0],
[GALOIS,[27,4]],
[GALOIS,[27,2]]],
[(22,23),(14,15,16),(14,16,15),(11,12,13)(27,28,29),(11,13,12)(27,29,28),
( 8,10, 9)(17,19,18)(24,26,25)]);
ALF("U3(8).2","U3(8).6",[1,2,3,4,5,6,7,8,8,8,9,9,9,10,10,10,11,11,11,12,
13,14,15,16,16,16,17,17,17]);
ALF("U3(8).2","U3(8).S3",[1,2,3,4,5,5,6,7,8,9,10,11,12,13,14,15,16,17,18,
44,45,46,47,48,49,50,51,52,53],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables"
]);

MOT("U3(8).3_1",
[
"origin: ATLAS of finite groups, tests: 1.o.r.,\n",
"constructions: PSigmaU(3,8)"
],
[16547328,4608,4536,4536,243,192,192,192,72,72,21,27,19,19,21,21,648,648,648,
648,648,648,72,72,72,72,72,72,27,27,12,12,12,12,12,12],
[,[1,1,4,3,5,2,2,2,4,3,11,12,14,13,16,15,18,17,20,19,22,21,18,17,20,19,22,21,
30,29,24,23,26,25,28,27],[1,2,1,1,1,6,7,8,2,2,11,5,14,13,11,11,1,1,1,1,1,1,2,
2,2,2,2,2,5,5,6,6,7,7,8,8],,,,[1,2,3,4,5,6,7,8,9,10,1,12,13,14,3,4,17,18,19,
20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36],,,,,,,,,,,,[1,2,3,4,5,6,7,
8,9,10,11,12,1,1,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,
35,36]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,E(3),E(3)^2,E(3),E(3)^2,E(3),E(3)^2,E(3),E(3)^2,
E(3),E(3)^2,E(3),E(3)^2,E(3),E(3)^2,E(3),E(3)^2,E(3),E(3)^2,E(3),E(3)^2],
[TENSOR,[2,2]],[56,-8,-7,-7,2,0,0,0,1,1,0,2,-1,-1,0,0,2,2,2,2,2,2,-2,-2,-2,-2,
-2,-2,2,2,0,0,0,0,0,0],
[TENSOR,[4,2]],
[TENSOR,[4,3]],[57,-7,-6*E(3),-6*E(3)^2,3,1,1,1,2*E(3),2*E(3)^2,1,0,0,0,E(3),
E(3)^2,3,3,3*E(3),3*E(3)^2,3*E(3)^2,3*E(3),-1,-1,-E(3),-E(3)^2,-E(3)^2,-E(3),
0,0,1,1,E(3),E(3)^2,E(3)^2,E(3)],
[TENSOR,[7,2]],
[TENSOR,[7,3]],
[GALOIS,[7,2]],
[TENSOR,[10,2]],
[TENSOR,[10,3]],[133,5,7,7,-2,5,-3,-3,-1,-1,0,1,0,0,0,0,7,7,-2,-2,-2,-2,-1,-1,
2,2,2,2,1,1,-1,-1,0,0,0,0],
[TENSOR,[13,2]],
[TENSOR,[13,3]],[133,5,7,7,-2,-3,5,-3,-1,-1,0,1,0,0,0,0,-2,-2,7,7,-2,-2,2,2,
-1,-1,2,2,1,1,0,0,-1,-1,0,0],
[TENSOR,[16,2]],
[TENSOR,[16,3]],[133,5,7,7,-2,-3,-3,5,-1,-1,0,1,0,0,0,0,-2,-2,-2,-2,7,7,2,2,2,
2,-1,-1,1,1,0,0,0,0,-1,-1],
[TENSOR,[19,2]],
[TENSOR,[19,3]],[1197,45,0,0,9,-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],[456,8,15*E(3),15*E(3)^2,-3,0,0,0,-E(3),-E(3)^2,1,0,0,0,
E(3),E(3)^2,6,6,6*E(3),6*E(3)^2,6*E(3)^2,6*E(3),2,2,2*E(3),2*E(3)^2,2*E(3)^2,
2*E(3),0,0,0,0,0,0,0,0],
[TENSOR,[23,2]],
[TENSOR,[23,3]],
[GALOIS,[23,2]],
[TENSOR,[26,2]],
[TENSOR,[26,3]],[512,0,8,8,-1,0,0,0,0,0,1,-1,-1,-1,1,1,8,8,8,8,8,8,0,0,0,0,0,
0,-1,-1,0,0,0,0,0,0],
[TENSOR,[29,2]],
[TENSOR,[29,3]],[1539,3,27,27,0,3,3,3,3,3,-1,0,0,0,-1,-1,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0],[1539,3,27*E(3),27*E(3)^2,0,3,3,3,3*E(3),3*E(3)^2,-1,0,0,
0,-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],
[GALOIS,[33,2]],[1701,-27,0,0,0,-3,-3,-3,0,0,0,0,-E(19)-E(19)^4-E(19)^5
 -E(19)^6-E(19)^7-E(19)^9-E(19)^11-E(19)^16-E(19)^17,-E(19)^2-E(19)^3-E(19)^8
 -E(19)^10-E(19)^12-E(19)^13-E(19)^14-E(19)^15-E(19)^18,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[35,2]]],
[(13,14),( 3, 4)( 9,10)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)
(29,30)(31,32)(33,34)(35,36),( 7, 8)(17,18)(19,22)(20,21)(23,24)(25,28)(26,27)
(29,30)(31,32)(33,36)(34,35),( 6, 7, 8)(17,19,21)(18,20,22)(23,25,27)
(24,26,28)(31,33,35)(32,34,36)]);
ARC("U3(8).3_1","projectives",["3.U3(8).3_1",[[171,-21,0,0,0,3,3,3,0,0,3,3,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[189,-3,0,0,0,5,-3,-3,0,0,0,0,
-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,2,0,0,0,0],[189,-3,0,0,0,-3,5,-3,0,0,
0,0,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2*E(9)^4-2*E(9)^7,
-2*E(9)^2-2*E(9)^5,0,0],[189,-3,0,0,0,-3,-3,5,0,0,0,0,-1,-1,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,-2*E(9)^2-2*E(9)^5,-2*E(9)^4-2*E(9)^7],[1197,45,0,0,0,
-3,-3,-3,0,0,0,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[1368,24,0,
0,0,0,0,0,0,0,3,-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],[1539,3,0,
0,0,3,3,3,0,0,-1,0,0,0,E(63)+E(63)^4-E(63)^19+E(63)^31-E(63)^37-E(63)^40
 +E(63)^55-E(63)^58,-E(63)^5+E(63)^8-E(63)^23-E(63)^26+E(63)^32-E(63)^44
 +E(63)^59+E(63)^62,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[7,10]],
[GALOIS,[7,13]],[1701,-27,0,0,0,-3,-3,-3,0,0,0,0,-E(19)-E(19)^4-E(19)^5
 -E(19)^6-E(19)^7-E(19)^9-E(19)^11-E(19)^16-E(19)^17,-E(19)^2-E(19)^3-E(19)^8
 -E(19)^10-E(19)^12-E(19)^13-E(19)^14-E(19)^15-E(19)^18,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[10,2]]],]);
ALF("U3(8).3_1","U3(8).6",[1,2,3,3,4,5,6,6,7,7,8,9,10,10,11,11,18,19,20,
21,20,21,22,23,24,25,24,25,26,27,28,29,30,31,30,31]);
ALF("U3(8).3_1","U3(8).3^2",[1,2,3,4,5,6,6,6,7,8,9,10,11,12,13,14,15,16,
15,16,15,16,17,18,17,18,17,18,19,20,21,22,21,22,21,22],[
"fusion map is unique up to table autom."
]);
ALF("U3(8).3_1","HN",[1,3,4,4,5,6,8,8,15,15,17,20,37,38,44,44,4,4,5,5,5,5,
15,15,16,16,16,16,20,20,31,31,32,32,32,32],[
"fusion map is unique up to table automorphisms"
]);
ALF("U3(8).3_1","2E6(2)",[1,4,5,5,7,19,21,21,29,29,34,52,103,104,108,108,
6,6,7,7,7,7,31,31,32,32,32,32,52,52,74,74,81,82,81,82],[
"fusion map determined by the extension in 2E6(2).2"
]);
ALN("U3(8).3_1",["2E6(2)M15"]);

MOT("U3(8).3_2",
[
"origin: ATLAS of finite groups, tests: 1.o.r.,\n",
"constructions: PGU(3,8)"
],
[16547328,4608,4536,4536,243,64,72,72,63,63,63,81,81,81,57,57,57,57,57,57,63,
63,63,63,63,63,171,171,4536,4536,4536,4536,4536,4536,81,81,81,81,81,81,72,72,
72,72,72,72,57,57,57,57,57,57,57,57,57,57,57,57,63,63,63,63,63,63,63,63,63,63,
63,63,63,63,63,63,63,63],
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 -E(27)^19,-E(27)^8-E(27)^17-E(27)^20,-E(27)^16,-E(27)^11,E(27)^13+E(27)^22,
E(27)^5+E(27)^14,E(27)^10+E(27)^19,E(27)^8+E(27)^17,0,0,0,0,0,0,0,0,0,0,0,0,
-E(27)^13-E(27)^22,-E(27)^5-E(27)^14,-E(27)^10-E(27)^19,-E(27)^8-E(27)^17,
E(27)^7,E(27)^20,-E(27)^13-E(27)^22,-E(27)^5-E(27)^14,-E(27)^10-E(27)^19,
-E(27)^8-E(27)^17,E(27)^7,E(27)^20,-E(27)^13-E(27)^22,-E(27)^5-E(27)^14,
-E(27)^10-E(27)^19,-E(27)^8-E(27)^17,E(27)^7,E(27)^20],
[GALOIS,[8,4]],
[GALOIS,[8,7]],[513,1,-9*E(9)^4-9*E(9)^7,-9*E(9)^2-9*E(9)^5,0,1,
-E(9)^4-E(9)^7,-E(9)^2-E(9)^5,E(7)+E(7)^6,E(7)^2+E(7)^5,E(7)^3+E(7)^4,0,0,0,0,
0,0,0,0,0,-E(63)^19-E(63)^37-E(63)^40-E(63)^58,-E(63)^5-E(63)^23-E(63)^26
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 -E(63)^59,-E(63)-E(63)^13-E(63)^22-E(63)^55,-E(63)^8-E(63)^41-E(63)^50
 -E(63)^62,0,0,-9*E(27)^13-9*E(27)^22,-9*E(27)^5-9*E(27)^14,
-9*E(27)^10-9*E(27)^19,-9*E(27)^8-9*E(27)^17,9*E(27)^7,9*E(27)^20,0,0,0,0,0,0,
-E(27)^13-E(27)^22,-E(27)^5-E(27)^14,-E(27)^10-E(27)^19,-E(27)^8-E(27)^17,
E(27)^7,E(27)^20,0,0,0,0,0,0,0,0,0,0,0,0,-E(189)^64-E(189)^118-E(189)^127
 -E(189)^181,-E(189)^8-E(189)^62-E(189)^71-E(189)^125,-E(189)^16-E(189)^79
 -E(189)^124-E(189)^187,-E(189)^2-E(189)^65-E(189)^110-E(189)^173,
E(189)^130+E(189)^157,E(189)^32+E(189)^59,-E(189)^19-E(189)^37-E(189)^100
 -E(189)^145,-E(189)^44-E(189)^89-E(189)^152-E(189)^170,-E(189)^25-E(189)^52
 -E(189)^151-E(189)^178,-E(189)^11-E(189)^38-E(189)^137-E(189)^164,
E(189)^22+E(189)^76,E(189)^113+E(189)^167,-E(189)^10-E(189)^46-E(189)^73
 -E(189)^172,-E(189)^17-E(189)^116-E(189)^143-E(189)^179,-E(189)^43-E(189)^97
 -E(189)^106-E(189)^160,-E(189)^29-E(189)^83-E(189)^92-E(189)^146,
E(189)^103+E(189)^184,E(189)^5+E(189)^86],
[GALOIS,[11,4]],
[GALOIS,[11,16]],
[GALOIS,[11,109]],
[GALOIS,[11,58]],
[GALOIS,[11,43]],
[GALOIS,[11,82]],
[GALOIS,[11,85]],
[GALOIS,[11,151]],[567,-9,0,0,0,-1,0,0,0,0,0,0,0,0,-E(19)-E(19)^7-E(19)^11,
-E(19)^8-E(19)^12-E(19)^18,-E(19)^5-E(19)^16-E(19)^17,-E(19)^2-E(19)^3
 -E(19)^14,-E(19)^4-E(19)^6-E(19)^9,-E(19)^10-E(19)^13-E(19)^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,-E(171)^4-E(171)^25+E(171)^85+E(171)^142
 ,-E(171)^23+E(171)^47-E(171)^101+E(171)^104,E(171)^67-E(171)^70+E(171)^124
 -E(171)^148,E(171)^29+E(171)^86-E(171)^146-E(171)^167,-E(171)^7-E(171)^49
 +E(171)^58+E(171)^115,E(171)^20-E(171)^68+E(171)^77-E(171)^83,
-E(171)^88+E(171)^94-E(171)^103+E(171)^151,E(171)^56+E(171)^113-E(171)^122
 -E(171)^164,-E(171)^43+E(171)^112-E(171)^130+E(171)^169,E(171)^74-E(171)^119
 +E(171)^131-E(171)^149,-E(171)^22+E(171)^40-E(171)^52+E(171)^97,
E(171)^2-E(171)^41+E(171)^59-E(171)^128,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[20,37]],
[GALOIS,[20,4]],
[GALOIS,[20,10]],
[GALOIS,[20,43]],
[GALOIS,[20,22]]],]);
ALF("U3(8).3_2","U3(8).S3",[1,2,3,3,4,5,6,6,7,8,9,10,11,12,13,13,14,14,15,
15,16,16,17,17,18,18,19,19,20,20,21,21,22,22,23,23,24,24,25,25,26,26,27,
27,28,28,29,30,30,29,31,32,32,31,33,34,34,33,35,35,36,36,37,37,38,38,39,
39,40,40,41,41,42,42,43,43],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables"
]);
ALF("U3(8).3_2","U3(8).3^2",[1,2,3,4,5,6,7,8,9,9,9,10,10,10,11,12,11,12,
11,12,13,14,13,14,13,14,23,24,25,26,25,26,25,26,27,28,27,28,27,28,29,30,
29,30,29,30,31,32,33,34,31,32,33,34,31,32,33,34,35,36,35,36,35,36,37,38,
37,38,37,38,39,40,39,40,39,40],[
"fusion map is unique up to table autom."
]);

MOT("U3(8).3_3",
[
"origin: ATLAS of finite groups, tests: 1.o.r."
],
[16547328,4608,4536,4536,243,64,72,72,21,27,19,19,21,21,54,54,54,54,54,54,9,9,
18,18,18,18,18,18],
[,[1,1,4,3,5,2,4,3,9,10,12,11,14,13,18,17,20,19,16,15,22,21,18,17,20,19,16,
15],[1,2,1,1,1,6,2,2,9,5,12,11,9,9,3,4,3,4,3,4,5,5,7,8,7,8,7,8],,,,[1,2,3,4,5,
6,7,8,1,10,11,12,3,4,17,18,19,20,15,16,21,22,25,26,27,28,23,24],,,,,,,,,,,,[1,
2,3,4,5,6,7,8,9,10,1,1,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,
1,1,1,1,1,E(3),E(3)^2,E(3),E(3)^2,E(3),E(3)^2,E(3),E(3)^2,E(3),E(3)^2,E(3),
E(3)^2,E(3),E(3)^2],
[TENSOR,[2,2]],[56,-8,-7,-7,2,0,1,1,0,2,-1,-1,0,0,-1,-1,-1,-1,-1,-1,-1,-1,1,1,
1,1,1,1],
[TENSOR,[4,2]],
[TENSOR,[4,3]],[57,-7,-6*E(3),-6*E(3)^2,3,1,2*E(3),2*E(3)^2,1,0,0,0,E(3),
E(3)^2,E(9)^4-E(9)^7,-E(9)^2+E(9)^5,-2*E(9)^4-E(9)^7,-E(9)^2-2*E(9)^5,
E(9)^4+2*E(9)^7,2*E(9)^2+E(9)^5,0,0,E(9)^4+E(9)^7,E(9)^2+E(9)^5,-E(9)^7,
-E(9)^2,-E(9)^4,-E(9)^5],
[TENSOR,[7,2]],
[TENSOR,[7,3]],
[GALOIS,[7,8]],
[TENSOR,[10,2]],
[TENSOR,[10,3]],[399,15,21,21,-6,-1,-3,-3,0,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0],[1197,45,0,0,9,-3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[456,8,
15*E(3),15*E(3)^2,-3,0,-E(3),-E(3)^2,1,0,0,0,E(3),E(3)^2,-E(9)^4+E(9)^7,
E(9)^2-E(9)^5,2*E(9)^4+E(9)^7,E(9)^2+2*E(9)^5,-E(9)^4-2*E(9)^7,
-2*E(9)^2-E(9)^5,0,0,E(9)^4+E(9)^7,E(9)^2+E(9)^5,-E(9)^7,-E(9)^2,-E(9)^4,
-E(9)^5],
[TENSOR,[15,2]],
[TENSOR,[15,3]],
[GALOIS,[15,8]],
[TENSOR,[18,2]],
[TENSOR,[18,3]],[512,0,8,8,-1,0,0,0,1,-1,-1,-1,1,1,2,2,2,2,2,2,-1,-1,0,0,0,0,
0,0],
[TENSOR,[21,2]],
[TENSOR,[21,3]],[1539,3,27,27,0,3,3,3,-1,0,0,0,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,
0,0],[1539,3,27*E(3),27*E(3)^2,0,3,3*E(3),3*E(3)^2,-1,0,0,0,-E(3),-E(3)^2,0,0,
0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[25,2]],[1701,-27,0,0,0,-3,0,0,0,0,-E(19)-E(19)^4-E(19)^5-E(19)^6
 -E(19)^7-E(19)^9-E(19)^11-E(19)^16-E(19)^17,-E(19)^2-E(19)^3-E(19)^8-E(19)^10
 -E(19)^12-E(19)^13-E(19)^14-E(19)^15-E(19)^18,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0],
[GALOIS,[27,2]]],
[(11,12),( 3, 4)( 7, 8)(13,14)(15,18,19,16,17,20)(21,22)(23,26,27,24,25,28),
(15,17,19)(16,18,20)(23,25,27)(24,26,28)]);
ALF("U3(8).3_3","U3(8).3^2",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,41,42,41,42,
41,42,43,44,45,46,45,46,45,46],[
"fusion map is unique up to table autom."
]);

MOT("U3(8).6",
[
"origin: ATLAS of finite groups, tests: 1.o.r.,\n",
"constructions: PSigmaU(3,8) extended by transpose-inverse"
],
[33094656,9216,4536,486,384,192,72,42,54,19,21,3024,54,96,96,14,18,1296,1296,
648,648,144,144,72,72,54,54,24,24,12,12,36,36,18,18,24,24,24,24],
[,[1,1,3,4,2,2,3,8,9,10,11,1,4,5,5,8,9,19,18,21,20,19,18,21,20,27,26,23,22,25,
24,19,18,27,26,29,28,29,28],[1,2,1,1,5,6,2,8,4,10,8,12,12,14,15,16,13,1,1,1,1,
2,2,2,2,4,4,5,5,6,6,12,12,13,13,14,14,15,15],,,,[1,2,3,4,5,6,7,1,9,10,3,12,13,
15,14,12,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,38,39,36,
37],,,,,,,,,,,,[1,2,3,4,5,6,7,8,9,1,11,12,13,14,15,16,17,18,19,20,21,22,23,24,
25,26,27,28,29,30,31,32,33,34,35,36,37,38,39]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1],[1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,E(3),E(3)^2,E(3),E(3)^2,E(3),
E(3)^2,E(3),E(3)^2,E(3),E(3)^2,E(3),E(3)^2,E(3),E(3)^2,-E(3),-E(3)^2,-E(3),
-E(3)^2,-E(3),-E(3)^2,-E(3),-E(3)^2],
[TENSOR,[2,2]],
[TENSOR,[2,3]],
[TENSOR,[2,4]],
[TENSOR,[2,5]],[56,-8,-7,2,0,0,1,0,2,-1,0,0,0,2*E(8)+2*E(8)^3,-2*E(8)-2*E(8)^3
 ,0,0,2,2,2,2,-2,-2,-2,-2,2,2,0,0,0,0,0,0,0,0,-E(8)-E(8)^3,-E(8)-E(8)^3,
E(8)+E(8)^3,E(8)+E(8)^3],
[TENSOR,[7,2]],
[TENSOR,[7,3]],
[TENSOR,[7,4]],
[TENSOR,[7,5]],
[TENSOR,[7,6]],[114,-14,6,6,2,2,-2,2,0,0,-1,0,0,0,0,0,0,6,6,-3,-3,-2,-2,1,1,0,
0,2,2,-1,-1,0,0,0,0,0,0,0,0],
[TENSOR,[13,2]],
[TENSOR,[13,3]],[133,5,7,-2,5,-3,-1,0,1,0,0,7,-2,-1,-1,0,1,7,7,-2,-2,-1,-1,2,
2,1,1,-1,-1,0,0,1,1,1,1,-1,-1,-1,-1],
[TENSOR,[16,2]],
[TENSOR,[16,3]],
[TENSOR,[16,4]],
[TENSOR,[16,5]],
[TENSOR,[16,6]],[266,10,14,-4,-6,2,-2,0,2,0,0,0,0,0,0,0,0,-4,-4,5,5,4,4,1,1,2,
2,0,0,-1,-1,0,0,0,0,0,0,0,0],
[TENSOR,[22,2]],
[TENSOR,[22,3]],[1197,45,0,9,-3,-3,0,0,0,0,0,21,3,-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],
[TENSOR,[25,2]],[912,16,-15,-6,0,0,1,2,0,0,-1,0,0,0,0,0,0,12,12,-6,-6,4,4,-2,
-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[27,2]],
[TENSOR,[27,3]],[512,0,8,-1,0,0,0,1,-1,-1,1,8,-1,0,0,1,-1,8,8,8,8,0,0,0,0,-1,
-1,0,0,0,0,2,2,-1,-1,0,0,0,0],
[TENSOR,[30,2]],
[TENSOR,[30,3]],
[TENSOR,[30,4]],
[TENSOR,[30,5]],
[TENSOR,[30,6]],[1539,3,27,0,3,3,3,-1,0,0,-1,27,0,3,3,-1,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[36,2]],[3078,6,-27,0,6,6,-3,-2,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0],[3402,-54,0,0,-6,-6,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]],
[(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)
(38,39),(14,15)(36,38)(37,39)]);
ALF("U3(8).6","U3(8).(S3x3)",[1,2,3,4,5,5,6,7,8,9,10,34,35,36,37,38,39,11,
12,11,12,13,14,13,14,15,16,17,18,17,18,40,41,42,43,44,45,46,47],[
"fusion map is unique up to table automorphisms"
]);
ALF("U3(8).6","Th",[1,2,3,4,6,7,10,12,17,29,31,2,11,13,13,24,28,3,3,5,5,
10,10,9,9,17,17,19,20,22,22,10,10,28,28,33,32,33,32],[
"fusion is unique up to table automorphisms"
]);
ALF("U3(8).6","HN.2",[1,3,4,5,6,8,14,16,19,33,38,45,51,53,53,60,61,4,4,5,
5,14,14,15,15,19,19,28,28,29,29,50,50,61,61,67,67,67,67],[
"fusion map is unique"
]);
ALF("U3(8).6","2E6(2).2",[1,4,5,7,17,19,27,32,47,88,92,107,119,131,131,
149,157,6,6,7,7,29,29,30,30,47,47,65,65,70,71,118,118,157,157,171,171,171,
171],[
"fusion map is unique up to table automorphisms"
]);
ALN("U3(8).6",["2E6(2).2M13"]);

MOT("U3(8).S3",
[
"origin: ATLAS of finite groups, tests: 1.o.r.,\n",
"constructions: PGU(3,8) extended by transpose-inverse"
],
[33094656,9216,4536,486,128,72,126,126,126,162,162,162,57,57,57,63,63,63,171,
4536,4536,4536,81,81,81,72,72,72,57,57,57,57,57,57,63,63,63,63,63,63,63,63,63,
1008,18,32,32,14,14,14,18,18,18],
[,[1,1,3,4,2,3,8,9,7,11,12,10,14,15,13,17,18,16,19,21,22,20,24,25,23,21,22,20,
31,32,33,34,29,30,36,37,35,39,40,38,42,43,41,1,4,5,5,8,9,7,11,12,10],[1,2,1,1,
5,2,9,7,8,4,4,4,14,15,13,9,7,8,1,3,3,3,3,3,3,6,6,6,14,14,15,15,13,13,18,16,17,
16,17,18,17,18,16,44,44,46,47,50,48,49,45,45,45],,,,[1,2,3,4,5,6,1,1,1,11,12,
10,13,14,15,3,3,3,19,21,22,20,24,25,23,27,28,26,29,30,31,32,33,34,21,22,20,21,
22,20,21,22,20,44,45,47,46,44,44,44,52,53,51],,,,,,,,,,,,[1,2,3,4,5,6,8,9,7,10
,11,12,1,1,1,17,18,16,19,20,21,22,23,24,25,26,27,28,19,19,19,19,19,19,38,39,40
,41,42,43,35,36,37,44,45,46,47,49,50,48,51,52,53]],
0,
[(46,47),(29,30)(31,32)(33,34),(13,14,15)(29,31,33)(30,32,34),(10,11,12)(20,
21,22)(23,24,25)(26,27,28)(35,42,40)(36,43,38)(37,41,39)(51,52,53),( 7, 8, 9)
(16,17,18)(35,38,41)(36,39,42)(37,40,43)(48,49,50)],
["ConstructGS3","U3(8).2","U3(8).3_2",[6,7],[[2,3],[5,6],[7,10],[9,11],[8,12],
[15,16],[18,19],[21,22],[23,26],[25,27],[24,28],[30,31],[33,34],[36,37],[39,
40],[41,44],[43,45],[42,46],[47,50],[49,51],[48,52],[53,56],[55,57],[54,58],
[59,62],[61,63],[60,64],[65,68],[67,69],[66,70],[71,74],[73,75],[72,76]],[[1,
1],[4,3],[14,9],[17,11],[20,13],[29,16],[32,18],[35,20],[38,22]],(1,10,20,37,
2,11,21,39,5,7,8,14,26,43,16,32,49,28,47,25,44,18,36)(4,6,9,17,35,52,33,51,31,
50,30,48,27,45,19,38)(12,23,40)(13,22,41)(15,29,46,24,42)(34,53)]);

MOT("U3(8).3^2",
[
"origin: Dixon's Algorithm,\n",
"constructions: PGammaU(3,8)"
],
[49641984,13824,13608,13608,729,192,216,216,63,81,57,57,63,63,648,648,72,72,81
,81,12,12,513,513,4536,4536,81,81,72,72,57,57,57,57,63,63,63,63,63,63,54,54,27
,27,18,18,54,54,27,27,18,18],
[,[1,1,4,3,5,2,4,3,9,10,12,11,14,13,16,15,16,15,20,19,18,17,24,23,26,25,28,27,
26,25,34,33,32,31,36,35,38,37,40,39,42,41,44,43,42,41,48,47,50,49,48,47],[1,2,
1,1,1,6,2,2,9,5,12,11,9,9,1,1,2,2,5,5,6,6,1,1,3,4,3,4,7,8,12,12,11,11,13,14,13
,14,13,14,3,4,5,5,7,8,3,4,5,5,7,8],,,,[1,2,3,4,5,6,7,8,1,10,11,12,3,4,15,16,17
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[TENSOR,[50,3]],
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[(11,12)(31,33)(32,34),(35,39,37)(36,40,38),
(15,16)(17,18)(19,20)(21,22)(41,47)(42,48)(43,49)(44,50)(45,51)(46,52),
( 3, 4)( 7, 8)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)
(31,32)(33,34)(35,40,37,36,39,38)(41,42)(43,44)(45,46)(47,48)(49,50)(51,52)
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ALF("U3(8).3^2","U3(8).(S3x3)",[1,2,3,3,4,5,6,6,7,8,9,9,10,10,11,12,13,14,
15,16,17,18,19,19,20,20,21,21,22,22,23,24,24,23,25,25,26,26,27,27,28,29,
30,31,32,33,29,28,31,30,33,32],[
"fusion map is unique up to table automorphisms"
]);

MOT("U3(8).(S3x3)",
[
"origin: ATLAS of finite groups, tests: 1.o.r.,\n",
"constructions: Aut(U3(8))"
],
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24,513,4536,81,72,57,57,63,63,63,54,54,27,27,18,18,3024,54,96,96,14,18,36,36,
18,18,24,24,24,24],
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0,
[(25,26,27),(23,24),(11,12)(13,14)(15,16)(17,18)(28,29)(30,31)(32,33)(40,41)(
42,43)(44,45)(46,47),(36,37)(44,46)(45,47)],
["ConstructGS3","U3(8).6","U3(8).3^2",[13,16,17,18,19,20,21,27],[[2,3],[5,6],[
8,9],[11,12],[14,15],[17,18],[25,26],[30,31],[33,34],[36,37],[39,40],[41,44],[
43,45],[42,46],[47,50],[49,51],[48,52]],[[1,1],[4,2],[7,3],[10,7],[13,8],[16,9
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10,6,23,45,37,17,35,14,18,38,26)(2,20,42,33,11,9,3,22,43,34,13,15,28,4,24,47,
40,30,7,25,46,39,27)]);

MOT("U3(9)",
[
"origin: ATLAS of finite groups, tests: 1.o.r."
],
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73,73,73,73,73,73,73,73,73,73,73,80,80,80,80,80,80,80,80,80,80,80,80,80,80,80,
80],
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45,51,52,50,49,47,48,46,45],[1,2,1,1,5,9,8,6,7,11,10,2,14,13,18,17,15,16,20,
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ARC("U3(9)","isSimple",true);
ARC("U3(9)","extInfo",["","4"]);
ARC("U3(9)","maxes",["3^(2+4):80","5xIsoclinic(2.A6.2_2)","A6.2_2","10^2:S3",
"73:3"]);
ARC("U3(9)","tomfusion",rec(name:="U3(9)",map:=[1,2,3,4,6,7,7,7,7,8,8,9,12,12,
21,21,21,21,22,22,24,24,24,24,23,23,23,23,28,28,28,28,30,30,30,30,42,42,42,42,
52,52,52,52,58,58,58,58,58,58,58,58,74,74,74,74,74,74,74,74,74,74,74,74,74,74,
74,74,74,74,74,74,74,74,74,74,77,77,77,77,77,77,77,77,77,77,77,77,77,77,77,
77],text:=[
"fusion map is unique"
]));
ALF("U3(9)","U3(9).2",[1,2,3,4,5,6,6,7,7,8,9,10,11,12,13,13,14,14,15,16,
17,17,18,18,19,19,20,20,21,21,22,22,23,23,24,24,25,25,26,26,27,27,28,28,
29,29,30,30,31,31,32,32,33,33,34,34,35,35,36,36,37,37,38,38,39,39,40,40,
41,41,42,42,43,43,44,44,45,45,46,46,47,47,48,48,49,49,50,50,51,51,52,52],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables"
]);
ALF("U3(9)","U3(9).4",[1,2,3,4,5,6,6,6,6,7,7,8,9,9,10,10,10,10,11,11,12,
12,12,12,13,13,13,13,14,14,14,14,15,15,15,15,16,16,16,16,17,17,17,17,18,
18,18,18,19,19,19,19,20,20,20,20,21,21,21,21,22,22,22,22,23,23,23,23,24,
24,24,24,25,25,25,25,26,26,26,26,27,27,27,27,28,28,28,28,29,29,29,29],[
"fusion map is unique up to table autom.,\n",
"unique map that is compatible with Brauer tables"
]);

MOT("U3(9).2",
[
"origin: ATLAS of finite groups, tests: 1.o.r."
],
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73,73,73,73,80,80,80,80,80,80,80,80,1440,1440,18,16,20,20,36,36,16,16,20,20],
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(46,48,50,52)(59,60)(61,62),( 6, 7)( 8, 9)(13,14)(15,16)(17,18)(19,20)(21,22)
(25,26)(27,28)(29,32)(30,31)(45,52,49,48)(46,51,50,47)(57,58)(63,64),(33,34)
(35,36)(37,38)(39,40)(41,42)(43,44)]);
ALF("U3(9).2","U3(9).4",[1,2,3,4,5,6,6,7,7,8,9,9,10,10,11,11,12,12,13,13,
14,14,15,15,16,16,17,17,18,18,19,19,20,20,21,21,22,22,23,23,24,24,25,25,
26,26,27,27,28,28,29,29,30,31,32,33,34,34,35,36,37,37,38,38],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables"
]);

MOT("U3(9).4",
[
"origin: ATLAS of finite groups, tests: 1.o.r.,\n",
"constructions: Aut(U3(9))"
],
[170294400,28800,29160,324,320,7200,200,360,160,7200,200,100,100,90,80,80,90,
80,80,73,73,73,73,73,73,80,80,80,80,2880,2880,36,32,20,72,72,16,20,96,96,96,
96,12,12,16,16,24,24,24,24],
[,[1,1,3,4,2,6,7,3,5,6,7,6,7,14,9,10,14,16,16,24,25,20,21,22,23,19,18,19,18,1,
2,4,5,7,8,8,9,11,30,30,31,31,32,32,33,33,35,36,35,36],[1,2,1,1,5,6,7,2,9,10,
11,12,13,6,15,16,10,18,19,20,21,22,23,24,25,26,27,28,29,30,31,30,33,34,31,31,
37,38,40,39,42,41,40,39,46,45,42,41,42,41],,[1,2,3,4,5,1,1,8,9,2,2,2,2,3,15,5,
8,9,9,25,20,21,22,23,24,15,15,15,15,30,31,32,33,30,35,36,37,31,39,40,41,42,43,
44,45,46,47,48,49,
50],,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,[1,2,3,
4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,18,1,1,1,1,1,1,29,26,27,28,30,31,32,33,
34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,E(4),-E(4),E(4),-E(4),E(4),-E(4),E(4),-E(4),
E(4),-E(4),E(4),-E(4)],
[TENSOR,[2,2]],
[TENSOR,[2,3]],[72,-8,-9,0,0,-8,2,1,0,-8,2,2,2,1,0,0,1,0,0,-1,-1,-1,-1,-1,-1,
0,0,0,0,0,0,0,0,0,-3*E(4),3*E(4),0,0,0,0,0,0,0,0,0,0,E(24)-E(24)^17,
E(24)^11-E(24)^19,-E(24)+E(24)^17,-E(24)^11+E(24)^19],
[TENSOR,[5,2]],
[TENSOR,[5,3]],
[TENSOR,[5,4]],[73,9,-8,1,1,-7,3,0,1,9,-1,-1,-1,2,-1,1,0,1,1,0,0,0,0,0,0,-1,
-1,-1,-1,1,9,1,1,1,0,0,-1,-1,-1,-1,3,3,-1,-1,1,1,0,0,0,0],
[TENSOR,[9,2]],
[TENSOR,[9,3]],
[TENSOR,[9,4]],[292,-28,-32,4,4,7,2,8,4,7,2,-3,2,-2,4,-1,-2,-1,-1,0,0,0,0,0,0,
-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[292,36,-32,4,4,7,2,0,
4,-9,6,1,-4,-2,-4,-1,0,-1,-1,0,0,0,0,0,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0],[1168,-16,34,-2,0,8,3,2,0,24,-1,4,-1,-1,0,0,-3,0,0,0,0,0,0,0,0,
0,0,0,0,16,-16,-2,0,1,2,2,0,-1,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[15,2]],[1168,48,34,-2,0,8,3,-6,0,8,3,-2,3,-1,0,0,-1,0,0,0,0,0,0,0,0,
0,0,0,0,16,16,-2,0,1,-2,-2,0,1,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[17,2]],[2336,-32,68,-4,0,16,6,4,0,-32,-2,-2,-2,-2,0,0,4,0,0,0,0,0,0,
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],[2336,-32,68,-4,0,-24,
-4,4,0,8,8,-2,-2,3,0,0,-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,
0,0,0,0,0,0,0],[657,1,9,0,1,17,-3,1,1,1,1,1,1,-1,-1,1,1,1,1,0,0,0,0,0,0,-1,-1,
-1,-1,9,1,0,1,-1,1,1,-1,1,3,3,-1,-1,0,0,1,1,-1,-1,-1,-1],
[TENSOR,[21,2]],
[TENSOR,[21,3]],
[TENSOR,[21,4]],[2628,68,36,0,4,-17,-2,-4,4,-17,-2,3,-2,1,4,-1,1,-1,-1,0,0,0,
0,0,0,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[2628,4,36,0,4,
-17,-2,4,4,-1,-6,-1,4,1,-4,-1,-1,-1,-1,0,0,0,0,0,0,1,1,1,1,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0],[729,9,0,0,1,9,-1,0,1,9,-1,-1,-1,0,1,1,0,1,1,-1,-1,
-1,-1,-1,-1,1,1,1,1,9,9,0,1,-1,0,0,1,-1,3,3,3,3,0,0,-1,-1,0,0,0,0],
[TENSOR,[27,2]],
[TENSOR,[27,3]],
[TENSOR,[27,4]],[730,10,1,1,2,10,0,1,-2,10,0,0,0,1,0,2,1,-2,-2,0,0,0,0,0,0,0,
0,0,0,10,10,1,-2,0,1,1,0,0,2,2,-2,-2,-1,-1,0,0,1,1,1,1],
[TENSOR,[31,2]],
[TENSOR,[31,3]],
[TENSOR,[31,4]],[1460,20,2,2,-4,20,0,2,0,20,0,0,0,2,0,-4,2,0,0,0,0,0,0,0,0,0,
0,0,0,20,-20,2,0,0,-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[35,2]],[2920,40,4,4,8,-10,0,4,-8,-10,0,0,0,-1,0,-2,-1,2,2,0,0,0,0,0,
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],[2920,-40,4,4,0,40,0,-4,
0,-40,0,0,0,4,0,0,-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],[2920,40,4,4,-8,-10,0,4,0,-10,0,0,0,-1,0,2,-1,0,0,0,0,0,0,0,0,
-E(40)^7+E(40)^13-E(40)^21-E(40)^23-E(40)^29+E(40)^31+E(40)^37+E(40)^39,
E(40)^7-E(40)^13+E(40)^21+E(40)^23+E(40)^29-E(40)^31-E(40)^37-E(40)^39,
-E(40)^7+E(40)^13-E(40)^21-E(40)^23-E(40)^29+E(40)^31+E(40)^37+E(40)^39,
E(40)^7-E(40)^13+E(40)^21+E(40)^23+E(40)^29-E(40)^31-E(40)^37-E(40)^39,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[39,7]],[2920,-40,4,4,0,-10,0,-4,0,10,0,0,0,-1,0,0,1,-E(40)^7+E(40)^13
 -E(40)^21-E(40)^23-E(40)^29+E(40)^31+E(40)^37+E(40)^39,E(40)^7-E(40)^13
 +E(40)^21+E(40)^23+E(40)^29-E(40)^31-E(40)^37-E(40)^39,0,0,0,0,0,0,
-E(80)^19+E(80)^21-E(80)^47+E(80)^51-E(80)^57+E(80)^63-E(80)^69+E(80)^73,
E(80)^3+E(80)^9-E(80)^31-E(80)^37-E(80)^41+E(80)^53-E(80)^67+E(80)^79,
E(80)^19-E(80)^21+E(80)^47-E(80)^51+E(80)^57-E(80)^63+E(80)^69-E(80)^73,
-E(80)^3-E(80)^9+E(80)^31+E(80)^37+E(80)^41-E(80)^53+E(80)^67-E(80)^79,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[41,7]],
[GALOIS,[41,13]],
[GALOIS,[41,11]],[3200,0,-40,-4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
-E(73)-E(73)^3-E(73)^8-E(73)^9-E(73)^24-E(73)^27-E(73)^46-E(73)^49-E(73)^64
 -E(73)^65-E(73)^70-E(73)^72,-E(73)^13-E(73)^14-E(73)^20-E(73)^29-E(73)^31
 -E(73)^34-E(73)^39-E(73)^42-E(73)^44-E(73)^53-E(73)^59-E(73)^60,
-E(73)^4-E(73)^12-E(73)^23-E(73)^32-E(73)^35-E(73)^36-E(73)^37-E(73)^38
 -E(73)^41-E(73)^50-E(73)^61-E(73)^69,-E(73)^7-E(73)^10-E(73)^17-E(73)^21
 -E(73)^22-E(73)^30-E(73)^43-E(73)^51-E(73)^52-E(73)^56-E(73)^63-E(73)^66,
-E(73)^2-E(73)^6-E(73)^16-E(73)^18-E(73)^19-E(73)^25-E(73)^48-E(73)^54
 -E(73)^55-E(73)^57-E(73)^67-E(73)^71,-E(73)^5-E(73)^11-E(73)^15-E(73)^26
 -E(73)^28-E(73)^33-E(73)^40-E(73)^45-E(73)^47-E(73)^58-E(73)^62-E(73)^68,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[45,5]],
[GALOIS,[45,2]],
[GALOIS,[45,7]],
[GALOIS,[45,4]],
[GALOIS,[45,13]]],
[(47,49)(48,50),(35,36)(39,40)(41,42)(43,44)(45,46)(47,48)(49,50),(26,28)
(27,29),(26,28)(27,29)(35,36)(39,40)(41,42)(43,44)(45,46)(47,48)(49,50),
(20,25,24,23,22,21),(18,19)(26,27,28,29),(18,19)(26,27,28,29)(35,36)(39,40)
(41,42)(43,44)(45,46)(47,50)(48,49),(18,19)(26,29,28,27)]);

LIBTABLE.LOADSTATUS.ctounit2:="userloaded";

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