|
#############################################################################
##
#W ctoorth2.tbl GAP table library Thomas Breuer
##
## This file contains the ordinary character tables related to the
## orthogonal groups $O_8^+(2)$ and $O_8^+(3)$.
##
#H ctbllib history
#H ---------------
#H $Log: ctoorth2.tbl,v $
#H Revision 4.33 2012/01/30 08:31:59 gap
#H removed #H entries from the headers
#H TB
#H
#H Revision 4.32 2011/09/28 12:55:44 gap
#H - removed revision entry and SET_TABLEFILENAME call,
#H - renamed (6x2.U4(2)):2 and (6xU4(2)):2 to 2x(3x2.U4(2)):2 and
#H 2x(3xU4(2)):2, respectively (and changed the constructions accordingly)
#H - renamed 2.(3^(1+2)+:2S4), 2^2.(7:3xS3), and 2^2.(L2(7)x2)
#H to 2x3^(1+2)_+:2S4, 7:3xS4, and D8xL3(2), respectively
#H (and changed the construction accordingly)
#H - added tables of 2^{3+6}:(L3(2)x3), 2^{1+8}_+:(S3xA5),
#H - added maxes entry for O8-(2)
#H TB
#H
#H Revision 4.31 2010/12/01 17:45:29 gap
#H added text to the ambiguous fusion O8+(3).2_1 -> O8+(3).D8
#H TB
#H
#H Revision 4.30 2010/05/05 13:20:08 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 4.29 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 4.28 2009/04/22 12:39:07 gap
#H added missing maxes of He.2, ON.2, HN.2, Fi24, and B
#H TB
#H
#H Revision 4.27 2009/03/31 16:34:48 gap
#H added tables of 2.O8+(3), 2^2.O8+(3) (contributed by Max), 2^2.O8+(3).3
#H TB
#H
#H Revision 4.26 2008/06/24 16:23:06 gap
#H added several fusions and names
#H TB
#H
#H Revision 4.25 2006/06/07 07:54:27 gap
#H unified ConstructMixed and ConstructMGA (for better programmatic access)
#H TB
#H
#H Revision 4.24 2005/08/10 14:39:55 gap
#H corrected InfoText values of GV4 constructed tables
#H TB
#H
#H Revision 4.23 2004/08/31 12:33:33 gap
#H added tables of 4.L2(25).2_3,
#H L2(49).2^2,
#H L2(81).2^2,
#H L2(81).(2x4),
#H 3.L3(4).3.2_2,
#H L3(9).2^2,
#H L4(4).2^2,
#H 2x2^3:L3(2)x2,
#H (2xA6).2^2,
#H 2xL2(11).2,
#H S3xTh,
#H 41:40,
#H 7^(1+4):(3x2.S7),
#H 7xL2(8),
#H (7xL2(8)).3,
#H O7(3)N3A,
#H O8+(3).2_1',
#H O8+(3).2_1'',
#H O8+(3).2_2',
#H O8+(3).(2^2)_{122},
#H S4(9),
#H S4(9).2_i,
#H 2.U4(3).2_2',
#H 2.U4(3).(2^2)_{133},
#H 2.U4(3).D8,
#H 3.U6(2).S3,
#H added fusions 3.A6.2_i -> 3.A6.2^2,
#H L2(49).2_i -> L2(49).2^2,
#H L3(9).2_i -> L3(9).2^2,
#H L4(4).2_i -> L4(4).2^2,
#H G2(3) -> O7(3),
#H L2(17) -> S8(2),
#H 2.L3(4).2_2 -> 2.M22.2
#H 3.L3(4).2_2 -> 3.L3(4).3.2_2
#H 3.L3(4).3 -> 3.L3(4).3.2_2
#H 2^5:S6 -> 2.M22.2
#H O8+(3) -> O8+(3).2_1',
#H O8+(3) -> O8+(3).2_1'',
#H O8+(3) -> O8+(3).2_2',
#H O8+(3) -> O8+(3).(2^2)_{122},
#H O8+(3).2_1 -> O8+(3).(2^2)_{122},
#H O8+(3).2_2 -> O8+(3).(2^2)_{122},
#H 2.U4(3) -> 2.U4(3).2_2',
#H 2.U4(3).2_1 -> 2.U4(3).(2^2)_{133},
#H 2.U4(3).2_2 -> O7(3),
#H 2.U4(3).2_2' -> U4(3).2_2,
#H 2.U4(3).2_3 -> 2.U4(3).(2^2)_{133},
#H 2.U4(3).2_3' -> 2.U4(3).(2^2)_{133},
#H 2.U4(3).4 -> 2.U4(3).D8,
#H 3.U6(2).2 -> 3.U6(2).S3,
#H 3.U6(2).3 -> 3.U6(2).S3,
#H replaced table of psl(3,4):d12 by L3(4).D12,
#H changed table of O8+(3).S4 to a construction table,
#H changed encoding of the table of 12.A6.2_3,
#H added maxes of Sz(8), Sz(8).3,
#H TB
#H
#H Revision 4.22 2003/09/23 16:30:45 gap
#H added fusions O8+(3).2_1 -> O8+(3).D8, O8+(3).2_2 -> O8+(3).D8
#H (needed for `AtlasClassNames( "O8+(3).D8" )')
#H TB
#H
#H Revision 4.21 2003/06/20 15:03:10 gap
#H added several fusions
#H TB
#H
#H Revision 4.20 2003/05/15 17:38:20 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 4.19 2003/04/23 08:00:57 gap
#H added table of O8+(3).D8
#H TB
#H
#H Revision 4.18 2003/01/24 15:57:35 gap
#H replaced several fusions by ones that are compatible with Brauer tables
#H TB
#H
#H Revision 4.17 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 4.16 2002/10/22 12:44:13 gap
#H added 215 factor fusions for cases <tbl> -> <tbl> / O_{<p>}(<tbl>)
#H (they make it possible to construct <p>-modular Brauer tables
#H for tables of the type [p^n].<fact> where the <p>-modular Brauer table
#H of <fact> is in the library)
#H TB
#H
#H Revision 4.15 2002/09/30 13:19:49 gap
#H added tables of 2^2.O8+(2).2, 2^2.O8+(2).3, 2^2.O8+(2).3.2
#H TB
#H
#H Revision 4.14 2002/09/18 15:22:01 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 4.13 2002/07/12 06:45:57 gap
#H further tidying up: removed `irredinfo' stuff, rearranged constructions
#H TB
#H
#H Revision 4.12 2002/07/08 16:06:56 gap
#H changed `construction' component from function (call) to list of function
#H name and arguments
#H TB
#H
#H Revision 4.11 2001/05/04 16:49:31 gap
#H first revision for ctbllib
#H
#H
#H tbl history (GAP 4)
#H -------------------
#H (Rev. 4.11 of ctbllib coincides with Rev. 4.10 of tbl in GAP 4)
#H
#H RCS file: /gap/CVS/GAP/4.0/tbl/ctoorth2.tbl,v
#H Working file: ctoorth2.tbl
#H head: 4.10
#H branch:
#H locks: strict
#H access list:
#H symbolic names:
#H GAP4R2: 4.7.0.6
#H GAP4R2PRE2: 4.7.0.4
#H GAP4R2PRE1: 4.7.0.2
#H GAP4R1: 4.5.0.2
#H keyword substitution: kv
#H total revisions: 11; selected revisions: 11
#H description:
#H ----------------------------
#H revision 4.10
#H date: 2001/03/02 18:30:17; author: gap; state: Exp; lines: +28 -2
#H for G = O8+(3),
#H added fusions of G.2_1, G.2_2, G.3 into G.S4,
#H and fusion of G.2_1 into G.A4
#H
#H TB
#H ----------------------------
#H revision 4.9
#H date: 2001/01/10 16:35:28; author: gap; state: Exp; lines: +5 -5
#H typo in the version I had committed a few seconds ago ...
#H
#H TB
#H ----------------------------
#H revision 4.8
#H date: 2001/01/10 16:33:07; author: gap; state: Exp; lines: +6 -2
#H added fusion of the table of O8+(2) into the table of marks
#H (nontrivial to find it)
#H
#H TB
#H ----------------------------
#H revision 4.7
#H date: 1999/10/21 14:15:48; author: gap; state: Exp; lines: +5 -8
#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: 1999/07/28 14:25:50; author: gap; state: Exp; lines: +5 -5
#H fixed a ``too long line''
#H
#H TB
#H ----------------------------
#H revision 4.5
#H date: 1999/07/12 14:53:29; author: gap; state: Exp; lines: +4 -4
#H fixed CAS components of a few tables
#H (now more restrictive than in GAP 3)
#H
#H TB
#H ----------------------------
#H revision 4.4
#H date: 1999/05/31 15:14:25; author: gap; state: Exp; lines: +7 -2
#H added `maxes' entry for O8+(3)
#H
#H TB
#H ----------------------------
#H revision 4.3
#H date: 1999/05/14 08:05:56; author: gap; state: Exp; lines: +59 -2
#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 4.2
#H date: 1998/12/07 13:11:52; author: gap; state: Exp; lines: +9 -3
#H added new table of S8(2)M3, added some fusions into S8(2)
#H
#H TB
#H ----------------------------
#H revision 4.1
#H date: 1997/07/17 15:46:15; author: fceller; state: Exp; lines: +2 -2
#H for version 4
#H ----------------------------
#H revision 1.1
#H date: 1996/10/21 16:01:17; author: sam; state: Exp;
#H first proposal of the table library
#H ==========================================================================
##
MOT("2.O8+(2)",
[
"origin: ATLAS of finite groups, tests: 1.o.r."
],
[348364800,348364800,110592,92160,92160,46080,46080,3072,155520,155520,155520,
155520,155520,155520,3888,3888,1296,1296,9216,9216,512,384,384,192,192,64,600,
600,600,600,600,600,3456,3456,1728,1728,576,576,288,288,432,432,216,216,216,
144,144,72,72,24,14,14,32,64,64,54,54,54,54,54,54,40,40,20,20,288,288,288,288,
288,288,72,72,48,48,24,24,30,30,30,30,30,30],
[,[1,1,1,1,1,2,2,1,9,9,11,11,13,13,15,15,17,17,3,3,3,4,4,6,7,8,27,27,29,29,31,
31,9,9,11,13,9,9,12,14,15,15,17,17,17,17,17,18,18,17,51,51,19,21,21,56,56,58,
58,60,60,27,27,30,32,33,33,35,35,36,36,41,41,37,37,39,40,78,78,80,80,82,82],[
1,2,3,4,5,6,7,8,1,2,1,2,1,2,1,2,1,2,19,20,21,22,23,24,25,26,27,28,29,30,31,32,
3,3,3,3,4,5,6,7,3,3,3,3,3,4,5,6,7,8,51,52,53,54,55,15,16,15,16,15,16,62,63,64,
65,19,20,19,20,19,20,19,20,22,23,24,25,27,28,29,30,31,32],,[1,2,3,4,5,6,7,8,9,
10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,1,2,1,2,1,2,33,34,35,36,37,
38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,4,5,6,
7,66,67,68,69,70,71,72,73,74,75,76,77,9,10,11,12,13,14],,[1,2,3,4,5,6,7,8,9,
10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,
36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,1,2,53,54,55,56,57,58,59,60,61,
62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83]],
0,
[( 6, 7)(11,13)(12,14)(24,25)(29,31)(30,32)(35,36)(39,40)(44,45)(48,49)(58,60)
(59,61)(64,65)(68,70)(69,71)(76,77)(80,82)(81,83)],
["ConstructProj",[["O8+(2)",[]],["2.O8+(2)",[]]]]);
ARC("2.O8+(2)","maxes",["2xS6(2)","2.S6(2)","2.O8+(2)M3","P31/G1/L1/V1/ext2",
"2^(1+6)_+.A8","2.O8+(2)M6","2xA9","2.A9","2.O8+(2)M9","2x(3xU4(2)):2",
"(3x2.U4(2)):2","2.O8+(2)M12","2.2^(1+8)_+:(S3xS3xS3)","(2x3^4:2^3).S4",
"(A5xA5).(2x4)","2.(A5xA5).2^2","2.O8+(2)M17"]);
ALF("2.O8+(2)","O8+(2)",[1,1,2,3,3,4,5,6,7,7,8,8,9,9,10,10,11,11,12,12,13,
14,14,15,16,17,18,18,19,19,20,20,21,21,22,23,24,24,25,26,27,27,28,29,30,
31,31,32,33,34,35,35,36,37,37,38,38,39,39,40,40,41,41,42,43,44,44,45,45,
46,46,47,47,48,48,49,50,51,51,52,52,53,53]);
ALF("2.O8+(2)","2.O8+(2).2",[1,2,3,4,5,6,6,7,8,9,10,11,10,11,12,13,14,15,
16,17,18,19,20,21,21,22,23,24,25,26,25,26,27,28,29,29,30,31,32,32,33,34,
35,36,36,37,38,39,39,40,41,42,43,44,45,46,47,48,49,48,49,50,51,52,52,53,
54,55,56,55,56,57,58,59,60,61,61,62,63,64,65,64,65]);
MOT("2.O8+(2).2",
[
"origin: ATLAS of finite groups, tests: 1.o.r."
],
[696729600,696729600,221184,184320,184320,46080,6144,311040,311040,155520,
155520,7776,7776,2592,2592,18432,18432,1024,768,768,192,128,1200,1200,600,600,
6912,6912,1728,1152,1152,288,864,864,432,216,288,288,72,48,28,28,64,128,128,
108,108,54,54,80,80,20,576,576,288,288,144,144,96,96,24,60,60,30,30,5806080,
5806080,18432,18432,15360,15360,4608,1536,1536,768,256,8640,8640,2592,2592,
576,576,432,432,288,288,144,144,384,384,64,16,120,120,576,576,192,192,72,24,
48,48,28,28,36,36,40,40,48,48,60,60],
[,[1,1,1,1,1,2,1,8,8,10,10,12,12,14,14,3,3,3,4,4,6,7,23,23,25,25,8,8,10,8,8,
11,12,12,14,14,14,14,15,14,41,41,16,18,18,46,46,48,48,23,23,26,27,27,29,29,33,
33,30,30,32,62,62,64,64,1,1,1,1,4,4,4,3,3,5,4,8,8,12,12,8,8,14,14,12,12,14,14,
16,16,18,22,23,23,30,30,30,30,37,38,33,33,41,41,46,46,50,50,53,53,62,62],[1,2,
3,4,5,6,7,1,2,1,2,1,2,1,2,16,17,18,19,20,21,22,23,24,25,26,3,3,3,4,5,6,3,3,3,
3,4,5,6,7,41,42,43,44,45,12,13,12,13,50,51,52,16,17,16,17,16,17,19,20,21,23,
24,25,26,66,67,68,69,70,71,72,73,74,75,76,66,67,66,67,68,69,66,67,68,69,68,69,
89,90,91,92,93,94,72,72,70,71,72,75,73,74,103,104,79,80,107,108,89,90,93,
94],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,1,2,1,2,27,28,
29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,4,5,6,53,54,55,
56,57,58,59,60,61,8,9,10,11,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,
82,83,84,85,86,87,88,89,90,91,92,66,67,95,96,97,98,99,100,101,102,103,104,105,
106,70,71,109,110,77,78],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,
21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,1,2,43,44,45,46,
47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,
73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,
99,100,101,102,66,67,105,106,107,108,109,110,111,112]],
0,
[( 66, 67)( 68, 69)( 70, 71)( 73, 74)( 77, 78)( 79, 80)( 81, 82)( 83, 84)
( 85, 86)( 87, 88)( 89, 90)( 93, 94)( 95, 96)( 97, 98)(101,102)(103,104)
(105,106)(107,108)(109,110)(111,112)],
["ConstructProj",[["O8+(2).2",[]],["2.O8+(2).2",[]]]]);
ALF("2.O8+(2).2","O8+(2).2",[1,1,2,3,3,4,5,6,6,7,7,8,8,9,9,10,10,11,12,12,
13,14,15,15,16,16,17,17,18,19,19,20,21,21,22,23,24,24,25,26,27,27,28,29,
29,30,30,31,31,32,32,33,34,34,35,35,36,36,37,37,38,39,39,40,40,41,41,42,
42,43,43,44,45,45,46,47,48,48,49,49,50,50,51,51,52,52,53,53,54,54,55,56,
57,57,58,58,59,59,60,61,62,62,63,63,64,64,65,65,66,66,67,67]);
ALN("2.O8+(2).2",["w(e8)"]);
MOT("Isoclinic(2.O8+(2).2)",
[
"isoclinic group of the 2.O8+(2).2 given in the ATLAS"
],
0,
0,
0,
[(66,67)(68,69)(70,71)(73,74)(77,78)(79,80)(81,82)(83,84)(85,86)(87,88)(89,90)
(93,94)(95,96)(97,98)(101,102)(103,104)(105,106)(107,108)(109,110)(111,112)],
["ConstructIsoclinic",[["2.O8+(2).2"]]]);
ALF("Isoclinic(2.O8+(2).2)","O8+(2).2",[1,1,2,3,3,4,5,6,6,7,7,8,8,9,9,10,
10,11,12,12,13,14,15,15,16,16,17,17,18,19,19,20,21,21,22,23,24,24,25,26,
27,27,28,29,29,30,30,31,31,32,32,33,34,34,35,35,36,36,37,37,38,39,39,40,
40,41,41,42,42,43,43,44,45,45,46,47,48,48,49,49,50,50,51,51,52,52,53,53,
54,54,55,56,57,57,58,58,59,59,60,61,62,62,63,63,64,64,65,65,66,66,67,67]);
MOT("2^2.O8+(2)",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[696729600,696729600,696729600,696729600,110592,92160,92160,92160,92160,92160,
92160,3072,311040,311040,311040,311040,311040,311040,311040,311040,311040,
311040,311040,311040,7776,7776,7776,7776,2592,2592,2592,2592,18432,18432,
18432,18432,512,384,384,384,384,384,384,64,1200,1200,1200,1200,1200,1200,1200,
1200,1200,1200,1200,1200,3456,3456,3456,3456,3456,3456,576,576,576,576,576,
576,864,864,864,864,216,216,216,144,144,144,144,144,144,24,28,28,28,28,32,128,
128,128,128,108,108,108,108,108,108,108,108,108,108,108,108,40,40,40,40,40,40,
576,576,576,576,576,576,576,576,576,576,576,576,144,144,144,144,48,48,48,48,
48,48,60,60,60,60,60,60,60,60,60,60,60,60],
[,[1,1,1,1,1,2,2,3,3,4,4,1,13,13,13,13,17,17,17,17,21,21,21,21,25,25,25,25,29,
29,29,29,5,5,5,5,5,6,6,8,8,10,10,12,45,45,45,45,49,49,49,49,53,53,53,53,13,13,
17,17,21,21,14,14,19,19,24,24,25,25,25,25,29,29,29,30,30,31,31,32,32,29,83,83,
83,83,33,37,37,37,37,92,92,92,92,96,96,96,96,100,100,100,100,46,46,51,51,56,
56,57,57,57,57,59,59,59,59,61,61,61,61,69,69,69,69,63,63,65,65,67,67,132,132,
132,132,136,136,136,136,140,140,140,140],[1,2,3,4,5,6,7,8,9,10,11,12,1,2,3,4,
1,2,3,4,1,2,3,4,1,2,3,4,1,2,3,4,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,
48,49,50,51,52,53,54,55,56,5,5,5,5,5,5,6,7,8,9,10,11,5,5,5,5,5,5,5,6,7,8,9,10,
11,12,83,84,85,86,87,88,89,90,91,25,26,27,28,25,26,27,28,25,26,27,28,104,105,
106,107,108,109,33,34,35,36,33,34,35,36,33,34,35,36,33,34,35,36,38,39,40,41,
42,43,45,46,47,48,49,50,51,52,53,54,55,56],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,
15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,
41,42,43,44,1,2,3,4,1,2,3,4,1,2,3,4,57,58,59,60,61,62,63,64,65,66,67,68,69,70,
71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,
97,98,99,100,101,102,103,6,7,8,9,10,11,110,111,112,113,114,115,116,117,118,
119,120,121,122,123,124,125,126,127,128,129,130,131,13,14,15,16,17,18,19,20,
21,22,23,24],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,
25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,
51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,
77,78,79,80,81,82,1,2,3,4,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,
103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,
122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,
141,142,143]],
0,
[( 3, 4)( 8, 10)( 9, 11)( 15, 16)( 17, 21)( 18, 22)( 19, 24)( 20, 23)
( 27, 28)( 31, 32)( 35, 36)( 40, 42)( 41, 43)( 47, 48)( 49, 53)( 50, 54)
( 51, 56)( 52, 55)( 59, 61)( 60, 62)( 65, 67)( 66, 68)( 71, 72)( 74, 75)
( 78, 80)( 79, 81)( 85, 86)( 90, 91)( 94, 95)( 96,100)( 97,101)( 98,103)
( 99,102)(106,108)(107,109)(112,113)(114,118)(115,119)(116,121)(117,120)
(124,125)(128,130)(129,131)(134,135)(136,140)(137,141)(138,143)(139,142),
( 2, 3)( 6, 8)( 7, 9)( 13, 17)( 14, 19)( 15, 18)( 16, 20)( 22, 23)
( 26, 27)( 30, 31)( 34, 35)( 38, 40)( 39, 41)( 45, 49)( 46, 51)( 47, 50)
( 48, 52)( 54, 55)( 57, 59)( 58, 60)( 63, 65)( 64, 66)( 70, 71)( 73, 74)
( 76, 78)( 77, 79)( 84, 85)( 89, 90)( 92, 96)( 93, 98)( 94, 97)( 95, 99)
(101,102)(104,106)(105,107)(110,114)(111,116)(112,115)(113,117)(119,120)
(123,124)(126,128)(127,129)(132,136)(133,138)(134,137)(135,139)(141,142)],
["ConstructV4G","2.O8+(2)",( 2, 3, 4)( 6, 8, 10)
( 7, 9, 11)( 13, 17, 21)( 14, 19, 24)( 15, 20, 22)( 16, 18, 23)( 26, 27,
28)( 30, 31, 32)( 34, 35, 36)( 38, 40, 42)( 39, 41, 43)( 45, 49, 53)( 46,
51, 56)( 47, 52, 54)( 48, 50, 55)( 57, 59, 61)( 58, 60, 62)( 63, 65, 67)
( 64, 66, 68)( 70, 71, 72)( 73, 74, 75)( 76, 78, 80)( 77, 79, 81)( 84, 85,
86)( 89, 90, 91)( 92, 96,100)( 93, 98,103)( 94, 99,101)( 95, 97,102)(104,
106,108)(105,107,109)(110,114,118)(111,116,121)(112,117,119)(113,115,120)
(123,124,125)(126,128,130)(127,129,131)(132,136,140)(133,138,143)(134,139,
141)(135,137,142)]);
ARC("2^2.O8+(2)","maxes",["2x2.S6(2)","2^2.O8+(2)M2","2^2.O8+(2)M3",
"(2x2^(1+6)_+).A8","2^2.O8+(2)M5","2^2.O8+(2)M6","2x2.A9","2^2.O8+(2)M8",
"2^2.O8+(2)M9","2x(3x2.U4(2)):2","2^2.O8+(2)M11","2^2.O8+(2)M12",
"2^2.(2^(1+8)_+:(S3xS3xS3))","(2^2x3^4).2^3.S4","(2x2.(A5xA5)):2^2",
"2^2.O8+(2)M16","2^2.O8+(2)M17"]);
ALF("2^2.O8+(2)","O8+(2)",[1,1,1,1,2,3,3,4,4,5,5,6,7,7,7,7,8,8,8,8,9,9,9,
9,10,10,10,10,11,11,11,11,12,12,12,12,13,14,14,15,15,16,16,17,18,18,18,18,
19,19,19,19,20,20,20,20,21,21,22,22,23,23,24,24,25,25,26,26,27,27,27,27,
28,29,30,31,31,32,32,33,33,34,35,35,35,35,36,37,37,37,37,38,38,38,38,39,
39,39,39,40,40,40,40,41,41,42,42,43,43,44,44,44,44,45,45,45,45,46,46,46,
46,47,47,47,47,48,48,49,49,50,50,51,51,51,51,52,52,52,52,53,53,53,53]);
ALF("2^2.O8+(2)","2.O8+(2)",[1,1,2,2,3,4,5,6,6,7,7,8,9,9,10,10,11,11,12,
12,13,13,14,14,15,15,16,16,17,17,18,18,19,19,20,20,21,22,23,24,24,25,25,
26,27,27,28,28,29,29,30,30,31,31,32,32,33,34,35,35,36,36,37,38,39,39,40,
40,41,41,42,42,43,44,45,46,47,48,48,49,49,50,51,51,52,52,53,54,54,55,55,
56,56,57,57,58,58,59,59,60,60,61,61,62,63,64,64,65,65,66,66,67,67,68,68,
69,69,70,70,71,71,72,72,73,73,74,75,76,76,77,77,78,78,79,79,80,80,81,81,
82,82,83,83]);
ALF("2^2.O8+(2)","2^2.O8+(2).2",[1,2,3,3,4,5,6,7,8,7,8,9,10,11,12,12,13,
14,15,16,13,14,16,15,17,18,19,19,20,21,22,22,23,24,25,25,26,27,28,29,30,
29,30,31,32,33,34,34,35,36,37,38,35,36,38,37,39,40,41,42,41,42,43,44,45,
46,45,46,47,48,49,49,50,51,51,52,53,54,55,54,55,56,57,58,59,59,60,61,62,
63,63,64,65,66,66,67,68,69,70,67,68,70,69,71,72,73,74,73,74,75,76,77,77,
78,79,80,81,78,79,81,80,82,83,84,84,85,86,87,88,87,88,89,90,91,91,92,93,
94,95,92,93,95,94],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("2^2.O8+(2)","2^2.O8+(2).3",[1,2,2,2,3,4,5,4,5,4,5,6,7,8,9,10,7,10,8,
9,7,9,10,8,11,12,12,12,13,14,14,14,15,16,16,16,17,18,19,18,19,18,19,20,21,
22,23,24,21,24,22,23,21,23,24,22,25,26,25,26,25,26,27,28,27,28,27,28,29,
30,30,30,31,31,31,32,33,32,33,32,33,34,35,36,36,36,37,38,39,39,39,40,41,
42,43,40,43,41,42,40,42,43,41,44,45,44,45,44,45,46,47,48,49,46,49,47,48,
46,48,49,47,50,51,51,51,52,53,52,53,52,53,54,55,56,57,54,57,55,56,54,56,
57,55]);
MOT("2^2.O8+(2).2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[1393459200,1393459200,696729600,221184,184320,184320,92160,92160,6144,622080,
622080,311040,311040,311040,311040,311040,15552,15552,7776,5184,5184,2592,
36864,36864,18432,1024,768,768,384,384,128,2400,2400,1200,1200,1200,1200,1200,
6912,6912,3456,3456,1152,1152,576,576,1728,1728,864,432,216,288,288,144,144,48
,56,56,28,64,256,256,128,216,216,108,108,108,108,108,80,80,40,40,1152,1152,576
,576,576,576,576,288,288,144,96,96,48,48,120,120,60,60,60,60,60,5806080,
5806080,18432,18432,15360,15360,4608,1536,1536,768,256,8640,8640,2592,2592,576
,576,432,432,288,288,144,144,384,384,64,16,120,120,576,576,192,192,72,24,48,48
,28,28,36,36,40,40,48,48,60,60],
[,[1,1,1,1,2,2,3,3,1,10,10,10,13,13,13,13,17,17,17,20,20,20,4,4,4,4,5,5,7,7,9,
32,32,32,35,35,35,35,10,10,13,13,11,11,15,15,17,17,17,20,20,21,21,22,22,20,57,
57,57,23,26,26,26,64,64,64,67,67,67,67,33,33,37,37,39,39,39,41,41,41,41,47,47,
47,43,43,45,45,89,89,89,92,92,92,92,1,2,2,1,5,5,5,4,4,6,5,10,11,17,18,11,10,20
,21,18,17,21,20,24,23,26,31,32,33,43,43,43,43,52,53,47,48,57,58,64,65,71,71,76
,75,89,90],[1,2,3,4,5,6,7,8,9,1,2,3,1,2,3,3,1,2,3,1,2,3,23,24,25,26,27,28,29,
30,31,32,33,34,35,36,37,38,4,4,4,4,5,6,7,8,4,4,4,4,4,5,6,7,8,9,57,58,59,60,61,
62,63,17,18,19,17,18,19,19,71,72,73,74,23,24,25,23,24,25,25,23,24,25,27,28,29,
30,32,33,34,35,36,37,38,96,97,98,99,100,101,102,103,104,105,106,96,97,96,97,98
,99,96,97,98,99,98,99,119,120,121,122,123,124,102,102,100,101,102,105,103,104,
133,134,109,110,137,138,119,120,123,124],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15
,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,1,2,3,1,2,3,3,39,40,41,42,43,
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,
70,5,6,7,8,75,76,77,78,79,80,81,82,83,84,85,86,87,88,10,11,12,13,14,15,16,96,
97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,
117,118,119,120,121,122,96,97,125,126,127,128,129,130,131,132,133,134,135,136,
100,101,139,140,107,108],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,
21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,
47,48,49,50,51,52,53,54,55,56,1,2,3,60,61,62,63,64,65,66,67,68,69,70,71,72,73,
74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,
100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,
119,120,121,122,123,124,125,126,127,128,129,130,131,132,96,97,135,136,137,138,
139,140,141,142]],
0,
[],
["ConstructMGA","2^2.O8+(2)","2.O8+(2).2",[[84,114],[85,115],[86,116],[87,
117],[88,119],[89,118],[90,120],[91,121],[92,122],[93,124],[94,123],[95,125],
[96,126],[97,128],[98,127],[99,129],[100,130],[101,131],[102,132],[103,133],
[104,135],[105,134],[106,136],[107,137],[108,139],[109,138],[110,140],[111,
141],[112,142],[113,143]],()]);
ALF("2^2.O8+(2).2","2.O8+(2).2",[1,1,2,3,4,5,6,6,7,8,8,9,10,10,11,11,12,
12,13,14,14,15,16,16,17,18,19,20,21,21,22,23,23,24,25,25,26,26,27,28,29,
29,30,31,32,32,33,33,34,35,36,37,38,39,39,40,41,41,42,43,44,44,45,46,46,
47,48,48,49,49,50,51,52,52,53,53,54,55,55,56,56,57,57,58,59,60,61,61,62,
62,63,64,64,65,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,
84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,
106,107,108,109,110,111,112]);
ALF("2^2.O8+(2).2","2^2.O8+(2).3.2",[1,2,2,3,4,5,4,5,6,7,8,9,7,9,8,9,10,
11,11,12,13,13,14,15,15,16,17,18,17,18,19,20,21,22,20,22,21,22,23,24,23,
24,25,26,25,26,27,28,28,29,29,30,31,30,31,32,33,34,34,35,36,37,37,38,39,
40,38,40,39,40,41,42,41,42,43,44,45,43,45,44,45,46,47,47,48,49,48,49,50,
51,52,50,52,51,52,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,
85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,
107,108,109,110,111,112,113]);
ALF("2^2.O8+(2).2","O8+(2).2",[1,1,1,2,3,3,4,4,5,6,6,6,7,7,7,7,8,8,8,9,9,
9,10,10,10,11,12,12,13,13,14,15,15,15,16,16,16,16,17,17,18,18,19,19,20,20,
21,21,21,22,23,24,24,25,25,26,27,27,27,28,29,29,29,30,30,30,31,31,31,31,
32,32,33,33,34,34,34,35,35,35,35,36,36,36,37,37,38,38,39,39,39,40,40,40,
40,41,41,42,42,43,43,44,45,45,46,47,48,48,49,49,50,50,51,51,52,52,53,53,
54,54,55,56,57,57,58,58,59,59,60,61,62,62,63,63,64,64,65,65,66,66,67,67]);
MOT("2^2.O8+(2).3",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[2090188800,696729600,331776,92160,92160,9216,311040,311040,311040,311040,
23328,7776,7776,2592,55296,18432,1536,384,384,192,1200,1200,1200,1200,3456,
3456,576,576,2592,864,216,144,144,72,84,28,96,384,128,108,108,108,108,40,40,
576,576,576,576,432,144,48,48,60,60,60,60,36288,36288,648,648,576,576,144,144,
72,72,54,54,288,288,144,144,96,96,12,12,18,18,21,21,24,24,24,24],
[,[1,1,1,2,2,1,7,7,7,7,11,11,13,13,3,3,3,4,4,6,21,21,21,21,7,7,8,8,11,11,13,14
,14,13,35,35,15,17,17,40,40,40,40,22,22,25,25,25,25,29,29,27,27,54,54,54,54,59
,58,61,60,59,58,59,58,61,60,69,68,63,62,63,62,63,62,67,66,69,68,81,80,71,70,75
,74],[1,2,3,4,5,6,1,2,2,2,1,2,1,2,15,16,17,18,19,20,21,22,23,24,3,3,4,5,3,3,3,
4,5,6,35,36,37,38,39,11,12,12,12,44,45,15,16,16,16,15,16,18,19,21,22,23,24,1,1
,1,1,3,3,6,6,6,6,11,11,15,15,15,15,17,17,20,20,29,29,35,35,37,37,38,38],,[1,2,
3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,1,2,2,2,25,26,27,28,29,30,31,32
,33,34,35,36,37,38,39,40,41,42,43,4,5,46,47,48,49,50,51,52,53,7,8,9,10,59,58,
61,60,63,62,65,64,67,66,69,68,71,70,73,72,75,74,77,76,79,78,81,80,83,82,85,84]
,,[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,
29,30,31,32,33,34,1,2,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55
,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,58,59
,82,83,84,85]],
0,
[(58,59)(60,61)(62,63)(64,65)(66,67)(68,69)(70,71)(72,73)(74,75)(76,77)(78,79)
(80,81)(82,83)(84,85),(9,10)(23,24)(42,43)(48,49)(56,57)(58,59)(60,61)(62,63)
(64,65)(66,67)(68,69)(70,71)(72,73)(74,75)(76,77)(78,79)(80,81)(82,83)(84,85)
],
["ConstructMGA","2^2.O8+(2)","O8+(2).3",[[54,84,114],[55,85,115],[56,86,
116],[57,87,117],[58,88,118],[59,89,119],[60,90,120],[61,91,121],[62,92,122],
[63,93,123],[64,94,124],[65,95,125],[66,96,126],[67,97,127],[68,98,128],[69,
99,129],[70,100,130],[71,101,131],[72,102,132],[73,103,133],[74,104,134],[75,
105,135],[76,106,136],[77,107,137],[78,108,138],[79,109,139],[80,110,140],[81,
111,141],[82,112,142],[83,113,143]],()]);
ALF("2^2.O8+(2).3","O8+(2).3",[1,1,2,3,3,4,5,5,5,5,6,6,7,7,8,8,9,10,10,11,
12,12,12,12,13,13,14,14,15,15,16,17,17,18,19,19,20,21,21,22,22,22,22,23,
23,24,24,24,24,25,25,26,26,27,27,27,27,28,29,30,31,32,33,34,35,36,37,38,
39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55]);
ALF("2^2.O8+(2).3","2^2.O8+(2).3.2",[1,2,3,4,5,6,7,8,9,9,10,11,12,13,14,
15,16,17,18,19,20,21,22,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,
38,39,40,40,41,42,43,44,45,45,46,47,48,49,50,51,52,52,53,53,54,54,55,55,
56,56,57,57,58,58,59,59,60,60,61,61,62,62,63,63,64,64,65,65,66,66]);
MOT("2^2.O8+(2).3.2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[4180377600,1393459200,663552,184320,184320,18432,622080,622080,311040,46656,
15552,15552,5184,110592,36864,3072,768,768,384,2400,2400,1200,6912,6912,1152,
1152,5184,1728,432,288,288,144,168,56,192,768,256,216,216,108,80,80,1152,1152,
576,864,288,96,96,120,120,60,36288,648,576,144,72,54,288,144,96,12,18,21,24,24
,5806080,5806080,18432,18432,15360,15360,4608,1536,1536,768,256,8640,8640,2592
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MOT("O8+(2)",
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40,40,8,-30,-30,-30,15,-3,-8,-8,0,0,0,0,0,0,0,-6,-6,-6,-2,-2,-2,3,3,3,3,1,1,1,
-1,0,0,0,0,0,0,0,0,0,-2,-2,-2,1,0,0,0,0,0,0],[6075,27,-45,-45,-45,-21,0,0,0,0,
0,-9,-1,3,3,3,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,1,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0]],
[( 4, 5)( 8, 9)(15,16)(19,20)(22,23)(25,26)(29,30)(32,33)(39,40)(42,43)(45,46)
(49,50)(52,53),( 3, 4)( 7, 8)(14,15)(18,19)(21,22)(24,25)(28,29)(31,32)(38,39)
(41,42)(44,45)(48,49)(51,52)]);
ARC("O8+(2)","CAS",[rec(name:="o8p2",
permchars:=(),
permclasses:=(),
text:=[
" test:= 1. o.r., sym 2 decompose correctly \n",
""])]);
ARC("O8+(2)","projectives",["2.O8+(2)",[[8,0,4,0,0,0,5,-4,-4,-1,2,4,0,2,0,0,0,
3,-2,-2,-3,0,0,1,0,0,3,0,0,0,-2,0,0,0,1,0,2,2,-1,-1,-1,0,0,1,-2,-2,1,-1,0,0,0,
1,1],[56,0,-4,0,0,0,11,-16,-16,2,2,12,0,-2,0,0,0,1,-4,-4,3,0,0,-1,0,0,6,0,0,0,
2,0,0,0,0,0,2,-1,-1,-1,1,0,0,3,0,0,0,1,0,0,1,-1,-1],[112,0,24,0,0,0,31,4,4,4,
4,8,0,4,0,0,0,7,2,2,-9,0,0,3,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,-1,0,0,-1,2,2,2,
1,0,0,1,-1,-1],[160,0,16,0,0,0,34,-20,-20,-2,-2,16,0,0,0,0,0,5,0,0,-6,0,0,-2,
0,0,6,0,0,0,-2,0,0,0,-1,0,0,1,1,1,1,0,0,-2,-2,-2,-2,0,0,0,-1,0,0],[224,0,-16,
0,0,0,14,-40,-4,-1,2,16,0,0,0,0,0,-1,-6,4,6,0,0,2,0,0,3,0,0,0,2,0,0,0,0,0,0,
-1,-1,2,-1,0,0,-2,4,-2,1,0,0,0,-1,0,1],[224,0,-16,0,0,0,14,-4,-40,-1,2,16,0,0,
0,0,0,-1,4,-6,6,0,0,2,0,0,3,0,0,0,2,0,0,0,0,0,0,-1,2,-1,-1,0,0,-2,-2,4,1,0,0,
0,-1,1,0],[400,0,40,0,0,0,25,-20,-20,4,10,-8,0,4,0,0,0,0,0,0,9,0,0,1,0,0,0,0,
0,0,-2,0,0,0,1,0,0,-2,1,1,0,0,0,1,-2,-2,-2,1,0,0,0,0,0],[448,0,32,0,0,0,16,16,
16,16,-2,0,0,0,0,0,0,-2,-2,-2,0,0,0,8,0,0,0,0,0,0,2,0,0,0,0,0,0,1,1,1,2,0,0,0,
0,0,0,0,0,0,1,1,1],[560,0,56,0,0,0,74,20,20,-7,2,8,0,4,0,0,0,5,0,0,-6,0,0,2,0,
0,-3,0,0,0,2,0,0,0,0,0,0,-1,-1,-1,1,0,0,2,2,2,-1,-2,0,0,-1,0,0],[672,0,16,0,0,
0,-30,-84,24,-3,6,16,0,0,0,0,0,-3,-8,2,-6,0,0,-2,0,0,-3,0,0,0,-2,0,0,0,0,0,0,
0,0,0,1,0,0,-2,-2,4,1,0,0,0,0,1,-1],[672,0,16,0,0,0,-30,24,-84,-3,6,16,0,0,0,
0,0,-3,2,-8,-6,0,0,-2,0,0,-3,0,0,0,-2,0,0,0,0,0,0,0,0,0,1,0,0,-2,4,-2,1,0,0,0,
0,-1,1],[840,0,4,0,0,0,21,-60,-60,3,-6,20,0,2,0,0,0,-5,0,0,-3,0,0,1,0,0,3,0,0,
0,-2,0,0,0,0,0,-2,0,0,0,-1,0,0,5,2,2,-1,-1,0,0,1,0,0],[1008,0,24,0,0,0,90,36,
36,9,0,8,0,-4,0,0,0,3,-2,-2,-6,0,0,-6,0,0,-3,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,
2,2,2,-1,2,0,0,0,1,1],[1008,0,24,0,0,0,-45,36,-72,9,0,8,0,-4,0,0,0,3,-2,-2,3,
0,0,3,0,0,-3,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,-1,2,-4,-1,-1,0,0,0,1,-2],[1008,
0,24,0,0,0,-45,-72,36,9,0,8,0,-4,0,0,0,3,-2,-2,3,0,0,3,0,0,-3,0,0,0,0,0,0,0,0,
0,0,0,0,0,-1,0,0,-1,-4,2,-1,-1,0,0,0,-2,1],[1296,0,-24,0,0,0,81,0,0,0,0,24,0,
-4,0,0,0,1,6,6,9,0,0,-3,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,-3,0,0,0,-1,0,0,
1,0,0],[1400,0,60,0,0,0,-25,20,20,-13,8,-4,0,-2,0,0,0,0,0,0,15,0,0,3,0,0,3,0,
0,0,0,0,0,0,0,0,-2,2,-1,-1,0,0,0,-1,2,2,-1,1,0,0,0,0,0],[1400,0,60,0,0,0,95,
-40,-40,-4,-4,-4,0,-2,0,0,0,0,0,0,-9,0,0,3,0,0,0,0,0,0,0,0,0,0,0,0,-2,-1,-1,
-1,0,0,0,-1,-4,-4,2,1,0,0,0,0,0],[2400,0,-80,0,0,0,60,60,60,-3,6,16,0,0,0,0,0,
0,0,0,12,0,0,4,0,0,-3,0,0,0,-2,0,0,0,-1,0,0,0,0,0,0,0,0,4,-2,-2,1,0,0,0,0,0,
0],[2800,0,-40,0,0,0,55,-80,-80,-8,10,-24,0,-4,0,0,0,0,0,0,-9,0,0,-1,0,0,0,0,
0,0,2,0,0,0,0,0,0,1,1,1,0,0,0,3,0,0,0,-1,0,0,0,0,0],[2800,0,-40,0,0,0,-5,40,
-140,1,-2,8,0,4,0,0,0,0,0,0,3,0,0,-1,0,0,-3,0,0,0,2,0,0,0,0,0,0,1,-2,1,0,0,0,
-1,-4,2,-1,1,0,0,0,0,0],[2800,0,-40,0,0,0,-5,-140,40,1,-2,8,0,4,0,0,0,0,0,0,3,
0,0,-1,0,0,-3,0,0,0,2,0,0,0,0,0,0,1,1,-2,0,0,0,-1,2,-4,-1,1,0,0,0,0,0],[3240,
0,84,0,0,0,81,0,0,0,0,-12,0,2,0,0,0,-5,0,0,9,0,0,-3,0,0,0,0,0,0,0,0,0,0,-1,0,
2,0,0,0,-1,0,0,-3,0,0,0,-1,0,0,1,0,0],[3360,0,16,0,0,0,-6,-60,-60,12,-6,-16,0,
0,0,0,0,5,0,0,18,0,0,-2,0,0,0,0,0,0,-2,0,0,0,0,0,0,0,0,0,1,0,0,2,2,2,2,0,0,0,
-1,0,0],[3584,0,0,0,0,0,-64,80,-64,-16,-4,0,0,0,0,0,0,4,-6,4,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,-1,2,-1,0,0,0,0,0,0,0,0,0,0,1,0,1],[3584,0,0,0,0,0,-64,-64,
80,-16,-4,0,0,0,0,0,0,4,4,-6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,2,0,0,0,
0,0,0,0,0,0,0,1,1,0],[4096,0,0,0,0,0,64,64,64,-8,-8,0,0,0,0,0,0,-4,-4,-4,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0,-1,-1,-1],[4200,0,20,
0,0,0,-75,60,60,15,6,4,0,2,0,0,0,0,0,0,-3,0,0,-7,0,0,3,0,0,0,2,0,0,0,0,0,-2,0,
0,0,0,0,0,1,-2,-2,1,-1,0,0,0,0,0],[4536,0,60,0,0,0,-81,0,0,0,0,12,0,-2,0,0,0,
-4,6,6,-9,0,0,3,0,0,0,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,3,0,0,0,1,0,0,-1,0,0],[
5600,0,-80,0,0,0,20,20,20,11,2,-16,0,0,0,0,0,0,0,0,-12,0,0,4,0,0,3,0,0,0,-2,0,
0,0,0,0,0,-1,-1,-1,0,0,0,-4,2,2,-1,0,0,0,0,0,0]],]);
ARC("O8+(2)","isSimple",true);
ARC("O8+(2)","extInfo",["2^2","3.2"]);
ARC("O8+(2)","tomfusion",rec(name:="O8+(2)",map:=[1,2,3,4,5,6,8,7,9,10,11,
43,44,46,45,47,48,49,50,51,68,69,67,71,70,72,76,74,73,75,79,78,77,80,81,
291,290,301,302,303,312,311,310,329,330,331,332,334,333,335,409,410,411],
text:=[
"fusion map is unique up to table automorphisms, hard to determine"
],
perm:=(1,3,2)(4,5)(7,9,8)));
ARC("O8+(2)","maxes",["S6(2)","O8+(2)M2","O8+(2)M3","2^6:A8","O8+(2)M5",
"O8+(2)M6","A9","O8+(2)M8","O8+(2)M9","(3xU4(2)):2","O8+(2)M11","O8+(2)M12",
"2^(1+8)_+:(S3xS3xS3)","3^4:2^3.S4(a)","(A5xA5):2^2","O8+(2)M16",
"O8+(2)M17"]);
ALF("O8+(2)","O8+(2).2",[1,2,3,4,4,5,6,7,7,8,9,10,11,12,13,13,14,15,16,16,
17,18,18,19,20,20,21,22,23,23,24,25,25,26,27,28,29,30,31,31,32,33,33,34,
35,35,36,37,38,38,39,40,40],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("O8+(2)","O8+(2).3",[1,2,3,3,3,4,5,5,5,6,7,8,9,10,10,10,11,12,12,12,
13,13,13,14,14,14,15,16,16,16,17,17,17,18,19,20,21,22,22,22,23,23,23,24,
24,24,25,26,26,26,27,27,27],[
"fusion map is unique, equal to that on the CAS table"
]);
ALF("O8+(2)","O8+(3)",[1,5,2,3,4,5,7,8,12,16,17,19,23,20,21,22,23,24,25,26,
37,38,42,31,32,36,49,52,51,50,43,44,45,53,55,56,57,71,71,71,72,73,74,78,79,
83,88,89,90,94,100,101,105],[
"fusion map is unique up to table automorphisms,\n",
"the representative is the one mentioned in the ATLAS"
]);
ALF("O8+(2)","2^8:O8+(2)",[1,4,8,13,15,17,21,24,25,26,28,31,34,39,45,47,
49,52,55,56,57,60,61,62,67,68,69,71,74,76,78,81,83,85,88,92,95,98,100,101,
102,105,106,107,109,110,111,113,117,118,119,123,124],[
"fusion map is unique up to table automorphisms"
]);
ALN("O8+(2)",["o8p2","O8+(2).2M1","O8+(2).3M1"]);
MOT("O8+(3)M11",
[
"11th maximal subgroup of O8+(3),\n",
"differs from O8+(2) only by fusion map"
],
0,
0,
0,
0,
["ConstructPermuted",["O8+(2)"]]);
ALF("O8+(3)M11","O8+(3)",[1,5,2,3,4,5,7,11,9,15,17,19,23,20,21,22,23,24,25,
26,37,41,39,31,35,33,48,53,50,51,43,44,45,52,55,56,57,70,70,70,72,73,74,78,
82,80,87,89,93,91,100,104,102],[
"fusion O8+(2) -> O8+(3) mapped under O8+(3).2_1"
]);
MOT("O8+(3)M12",
[
"12th maximal subgroup of O8+(3),\n",
"differs from O8+(2) only by fusion map"
],
0,
0,
0,
0,
["ConstructPermuted",["O8+(2)"]]);
ALF("O8+(3)M12","O8+(3)",[1,5,2,3,4,5,10,8,9,14,17,19,23,20,21,22,23,24,25,
26,40,38,39,34,32,33,47,50,53,52,43,44,45,51,55,56,57,69,69,69,72,73,74,81,
79,80,86,92,90,91,103,101,102],[
"fusion O8+(2) -> O8+(3) mapped under O8+(3).2_1'"
]);
MOT("O8+(3)M13",
[
"13th maximal subgroup of O8+(3),\n",
"differs from O8+(2) only by fusion map"
],
0,
0,
0,
0,
["ConstructPermuted",["O8+(2)"]]);
ALF("O8+(3)M13","O8+(3)",[1,5,2,3,4,5,10,11,12,13,17,19,23,20,21,22,23,24,
25,26,40,41,42,34,35,36,46,51,52,53,43,44,45,50,55,56,57,68,68,68,72,73,74,
81,82,83,85,92,93,94,103,104,105],[
"fusion map is unique up to table automorphisms,\n",
"equal to the map from O8+(2), mapped under an outer autom.;\n",
"compatible with the ATLAS"
]);
MOT("O8+(2).2",
[
"origin: ATLAS of finite groups, tests: 1.o.r."
],
[348364800,221184,92160,46080,6144,155520,77760,3888,1296,9216,1024,384,192,
128,600,300,3456,1728,576,288,432,432,216,144,72,48,14,64,64,54,27,40,20,288,
144,72,48,24,30,15,2903040,9216,7680,4608,768,768,256,4320,1296,288,216,144,
72,192,64,16,60,288,96,72,24,24,14,18,20,24,30],
[,[1,1,1,1,1,6,7,8,9,2,2,3,4,5,15,16,6,7,6,7,8,9,9,9,9,9,27,10,11,30,31,15,16,
17,18,21,19,20,39,40,1,1,3,3,2,3,3,6,8,6,9,8,9,10,11,14,15,19,19,24,24,21,27,
30,32,34,39],[1,2,3,4,5,1,1,1,1,10,11,12,13,14,15,16,2,2,3,4,2,2,2,3,4,5,27,
28,29,8,8,32,33,10,10,10,12,13,15,16,41,42,43,44,45,46,47,41,41,42,41,42,42,
54,55,56,57,44,43,44,46,45,63,49,65,54,57],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,
1,1,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,3,4,34,35,36,37,38,6,7,41,42,
43,44,45,46,47,48,49,50,51,52,53,54,55,56,41,58,59,60,61,62,63,64,43,66,48],,[
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,1,28,29,
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,
56,57,58,59,60,61,62,41,64,65,66,67]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[28,-4,4,4,
-4,10,10,1,1,8,0,0,0,0,3,3,2,2,-2,-2,5,-1,-1,1,1,-1,0,-2,2,1,1,-1,-1,2,2,-1,0,
0,0,0,14,-2,6,-2,2,2,-2,2,5,-2,-1,1,1,0,0,0,-1,4,0,1,-1,-1,0,-1,1,0,2],
[TENSOR,[3,2]],[35,3,11,-5,3,14,5,-1,2,7,-1,3,-1,-1,5,0,6,-3,2,1,3,0,0,2,-2,0,
0,1,1,2,-1,1,0,-2,1,1,0,-1,-1,0,21,5,9,1,1,-3,1,6,3,2,0,-1,2,3,-1,-1,1,4,0,-2,
0,1,0,0,-1,0,1],
[TENSOR,[5,2]],[70,6,-10,6,6,10,19,-2,4,14,-2,-2,2,-2,0,5,-6,3,2,3,6,0,0,-4,0,
0,0,2,2,-2,1,0,1,2,-1,2,-2,-1,0,-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],[50,18,10,10,2,5,5,-4,5,-2,6,2,2,2,0,0,-3,-3,1,1,0,3,3,1,1,-1,1,
0,0,-1,-1,0,0,1,1,-2,-1,-1,0,0,20,4,0,8,0,4,0,5,2,1,-1,-2,1,-2,2,0,0,-1,3,-1,
1,0,-1,-1,0,1,0],
[TENSOR,[8,2]],[84,20,20,4,4,21,-6,3,3,4,4,4,0,0,4,-1,5,2,5,-2,-1,5,-1,-1,1,1,
0,0,0,0,0,0,-1,1,-2,1,1,0,1,-1,42,10,10,10,2,2,2,9,-3,1,3,1,1,2,2,0,2,1,1,1,
-1,-1,0,0,0,-1,-1],
[TENSOR,[10,2]],[168,40,8,24,8,-12,15,6,6,8,8,0,4,0,-2,3,4,7,-4,3,-2,-2,4,2,0,
2,0,0,0,0,0,-2,-1,-4,-1,2,0,1,-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],[175,-17,15,15,-1,-5,-5,13,4,-1,-1,-1,-1,3,0,0,-5,-5,3,3,1,-2,-2,
0,0,2,0,-1,-1,1,1,0,0,-1,-1,-1,-1,-1,0,0,35,3,-5,-5,-5,3,3,5,-1,-3,2,3,0,-1,
-1,1,0,1,1,-2,0,1,0,-1,0,-1,0],
[TENSOR,[13,2]],[210,-14,26,10,2,39,-15,-6,3,6,-2,2,-2,2,5,0,7,1,-1,1,-2,-5,1,
-1,1,-1,0,0,0,0,0,1,0,3,-3,0,-1,1,-1,0,84,4,16,-8,0,4,0,9,-6,1,-3,-2,1,2,-2,0,
-1,1,1,1,1,0,0,0,1,-1,-1],
[TENSOR,[15,2]],[420,-28,20,36,4,-30,24,-12,6,12,-4,-4,0,4,0,5,2,8,2,0,-4,2,
-4,2,0,-2,0,0,0,0,0,0,1,-6,0,0,2,0,0,-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],[300,12,20,20,12,30,30,3,-6,8,0,0,0,0,0,0,6,6,2,2,3,0,0,2,2,
0,-1,2,-2,0,0,0,0,2,2,-1,0,0,0,0,90,10,10,2,-2,6,2,0,9,4,0,1,-2,0,0,0,0,2,-2,
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[]);
ARC("O8+(2).2","CAS",[rec(name:="o8p2b",
permchars:=( 7, 9, 8)(17,21,20,19,18)(26,36,33,31,41,38,35,32,30,29,28,27)
(34,44,40,37)(39,47,55,51,48,45,42,52,49,46,43)(50,62,58,54)(53,63,59,65,61,57
)(56,64,60),
permclasses:=(),
text:=[
" test:= 1. o.r., sym 2 decompose correctly \n",
""])]);
ARC("O8+(2).2","projectives",["2.O8+(2).2",[[8,0,4,0,0,5,-4,-1,2,4,0,2,0,0,3,
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ALF("O8+(2).2","Fi22",[1,3,3,3,4,5,5,6,7,9,9,13,13,12,14,14,18,18,18,18,
17,23,23,23,23,22,26,28,27,32,32,35,35,39,39,38,46,46,52,52,2,4,10,10,11,
10,13,15,16,20,19,21,24,27,28,30,34,41,41,47,47,45,51,57,59,64,65],[
"fusion map is unique, equal to that on the CAS table"
]);
ALF("O8+(2).2","O8+(2).3.2",[1,2,3,3,4,5,5,6,7,8,9,10,10,11,12,12,13,13,
14,14,15,16,16,17,17,18,19,20,21,22,22,23,23,24,24,25,26,26,27,27,42,43,
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],[
"fusion map is unique, equal to that on the CAS table"
]);
ALF("O8+(2).2","S8(2)",[1,3,4,5,7,8,9,11,10,14,15,19,21,23,24,25,27,30,28,
36,35,29,34,37,38,41,42,45,46,49,50,53,54,55,59,63,62,67,69,71,2,6,13,12,
18,17,20,26,31,32,33,40,39,43,44,48,51,56,57,60,65,66,68,74,76,78,80],[
"fusion map is unique"
]);
ALF("O8+(2).2","2^8:O8+(2):2",[1,4,8,13,15,19,22,23,25,28,32,37,42,44,47,
50,51,54,55,60,61,63,66,68,71,73,76,80,83,85,87,88,91,92,94,95,98,101,102,
105,106,110,116,120,125,128,132,136,140,142,146,150,152,156,159,163,165,
169,172,176,178,180,182,184,186,189,190],[
"fusion map is unique"
]);
ALN("O8+(2).2",["f22u4","o8p2b"]);
MOT("O8+(2).3",
[
"origin: ATLAS of finite groups, tests: 1.o.r."
],
[522547200,331776,46080,9216,77760,5832,1944,13824,1536,192,192,300,1728,288,
648,216,72,72,21,96,96,27,20,144,108,24,15,36288,36288,648,648,576,576,144,
144,72,72,54,54,288,288,144,144,96,96,12,12,18,18,21,21,24,24,24,24],
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29,28,29,28,31,30,39,38,33,32,33,32,33,32,37,36,39,38,51,50,41,40,45,44],[1,2,
3,4,1,1,1,8,9,10,11,12,2,3,2,2,3,4,19,20,21,6,23,8,8,10,12,1,1,1,1,2,2,4,4,4,
4,6,6,8,8,8,8,9,9,11,11,15,15,19,19,20,20,21,21],,[1,2,3,4,5,6,7,8,9,10,11,1,
13,14,15,16,17,18,19,20,21,22,3,24,25,26,5,29,28,31,30,33,32,35,34,37,36,39,
38,41,40,43,42,45,44,47,46,49,48,51,50,53,52,55,54],,[1,2,3,4,5,6,7,8,9,10,11,
12,13,14,15,16,17,18,1,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,
38,39,40,41,42,43,44,45,46,47,48,49,28,29,52,53,54,55]],
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1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
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E(3)^2,E(3),E(3)^2,E(3),E(3)^2],
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[TENSOR,[44,2]],
[TENSOR,[44,3]],[4096,0,0,0,64,-8,-8,0,0,0,0,-4,0,0,0,0,0,0,1,0,0,1,0,0,0,0,
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[TENSOR,[47,2]],
[TENSOR,[47,3]],[4200,-24,40,8,-30,15,-3,-8,-8,0,0,0,-6,-2,3,3,1,-1,0,0,0,0,0,
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[TENSOR,[50,2]],
[TENSOR,[50,3]],[6075,27,-45,-21,0,0,0,-9,-1,3,3,0,0,0,0,0,0,0,-1,1,1,0,0,0,0,
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[TENSOR,[53,2]],
[TENSOR,[53,3]]],
[(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)]);
ARC("O8+(2).3","CAS",[rec(name:="o8p2d",
permchars:=(),
permclasses:=(),
text:=[
" test:= 1. o.r., sym 2 decompose correctly \n",
""])]);
ALF("O8+(2).3","O8+(2).3.2",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,
19,20,21,22,23,24,25,26,27,28,28,29,29,30,30,31,31,32,32,33,33,34,34,35,
35,36,36,37,37,38,38,39,39,40,40,41,41]);
--> --------------------
--> maximum size reached
--> --------------------
[ Dauer der Verarbeitung: 0.20 Sekunden
(vorverarbeitet)
]
|
