|
#############################################################################
##
#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"]);
--> --------------------
--> maximum size reached
--> --------------------
[ Dauer der Verarbeitung: 0.30 Sekunden
(vorverarbeitet)
]
|
