|
#############################################################################
##
#W ctoholpl.tbl GAP table library Thomas Breuer
##
## This file contains ordinary character tables from the microfiche in the
## book ``Perfect Groups'' by Derek Holt and Wilhelm Plesken,
## computed by Wilhelm Hanrath, encoded via Clifford matrices.
##
#H ctbllib history
#H ---------------
#H $Log: ctoholpl.tbl,v $
#H Revision 4.20 2012/04/23 16:16:07 gap
#H next step of consolidation:
#H
#H - removed a few unnecessary duplicate tables,
#H and changed some related fusions, names of maxes, table constructions
#H - make sure that duplicate tables arise only via `ConstructPermuted'
#H constructions
#H - added some relative names
#H - added fusions A11.2 -> A12.2, L2(11).2 -> A12.2, D8x2F4(2)'.2 -> B,
#H L2(41) -> M, (A5xA12):2 -> A17,
#H - added maxes of A12.2, L6(2), 2.M22.2
#H - added table of QD16.2,
#H - fixed the syntax of two `ALN' calls
#H TB
#H
#H Revision 4.19 2012/01/30 08:31:43 gap
#H removed #H entries from the headers
#H TB
#H
#H Revision 4.18 2011/09/28 14:32:11 gap
#H removed revision entry and SET_TABLEFILENAME call
#H TB
#H
#H Revision 4.17 2011/02/09 15:55:37 gap
#H P1/G2/L1/V1/ext2 is also 2aM20, P1/G2/L1/V2/ext2 is also 2cM20
#H (names used in AtlasRep)
#H TB
#H
#H Revision 4.16 2010/12/01 17:47:55 gap
#H renamed "Sym(4)" to "Symm(4)";
#H note that the table constructed with `CharacterTable( "Symmetric", 4 )'
#H gets the identifier `"Sym(4)"', and this table is sorted differently
#H TB
#H
#H Revision 4.15 2010/05/05 13:20:01 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 4.14 2009/04/22 12:39:01 gap
#H added missing maxes of He.2, ON.2, HN.2, Fi24, and B
#H TB
#H
#H Revision 4.13 2009/01/07 10:14:19 gap
#H added missing assignment to ALN at the end of the file
#H TB
#H
#H Revision 4.12 2006/12/06 16:52:00 gap
#H corrected the corrupted table of P41/G1/L1/V4/ext2;
#H for that, added a new Clifford matrix
#H TB
#H
#H Revision 4.11 2005/09/27 09:33:42 gap
#H corrected the known error in the table "P12/G1/L2/V1/ext2"
#H TB
#H
#H Revision 4.10 2003/07/22 15:02:57 gap
#H added fusion "P31/G1/L1/V1/ext2" -> "2^6:A8"
#H TB
#H
#H Revision 4.9 2003/06/20 15:02:55 gap
#H added several fusions
#H TB
#H
#H Revision 4.8 2003/05/15 17:38:02 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 4.7 2003/03/07 15:53:33 gap
#H added tables of `Isoclinic(2.A5.2)' and `L2(125)',
#H and many `tomidentifier' components (still several are missing)
#H TB
#H
#H Revision 4.6 2002/10/22 12:44:07 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 4.5 2002/07/15 15:19:03 gap
#H adjusted `ConstructClifford' calls to the new format
#H TB
#H
#H Revision 4.4 2001/05/04 16:47:26 gap
#H first revision for ctbllib
#H
#H
#H tbl history (GAP 4)
#H -------------------
#H (Rev. 4.4 of ctbllib coincides with Rev. 4.3 of tbl in GAP 4)
#H
#H RCS file: /gap/CVS/GAP/4.0/tbl/ctoholpl.tbl,v
#H Working file: ctoholpl.tbl
#H head: 4.3
#H branch:
#H locks: strict
#H access list:
#H symbolic names:
#H GAP4R2: 4.3.0.8
#H GAP4R2PRE2: 4.3.0.6
#H GAP4R2PRE1: 4.3.0.4
#H GAP4R1: 4.3.0.2
#H keyword substitution: kv
#H total revisions: 4; selected revisions: 4
#H description:
#H ----------------------------
#H revision 4.3
#H date: 1999/07/14 11:44:58; author: gap; state: Exp; lines: +10 -10
#H adjusted factor fusions (now used for constructing Brauer tables)
#H
#H TB
#H ----------------------------
#H revision 4.2
#H date: 1999/07/14 11:39:38; author: gap; state: Exp; lines: +4 -3
#H cosmetic changes for the release ...
#H
#H TB
#H ----------------------------
#H revision 4.1
#H date: 1997/07/17 15:39:21; author: fceller; state: Exp; lines: +2 -2
#H for version 4
#H ----------------------------
#H revision 1.1
#H date: 1996/10/21 15:59:23; author: sam; state: Exp;
#H first proposal of the table library
#H ==========================================================================
##
MOT("P1/G1/L1/V1/ext2",
[
"origin: Hanrath library,\n",
"structure is 2^4.A5"
],
[960,96,192,16,8,16,12,12,12,12,5,5],
[,[1,1,1,1,2,3,7,7,7,7,12,11],[1,2,3,4,5,6,1,3,3,2,12,11],,[1,2,3,4,5,6,7,9,8,
10,1,1]],
0,
[( 8, 9),(11,12)],
["ConstructClifford",[[[1,2,3,5,4],[1,2,3,3],[1,3,2]],[["A5"],["A4"],["S3"]],
[[[1,2,3],[1,1,1],["elab",3,5,,(2,3)]],[[1,2,3],[2,2,3],["elab",3,8,,(2,3)]],
[[1,2,2,3],[3,3,4,2],["elab",4,12,(3,4)]],[[1],[5]],[[1],[4]]]]]);
ARC("P1/G1/L1/V1/ext2","tomfusion",rec(name:="2^4:A5`",map:=[1,3,2,4,12,
10,5,16,16,15,14,14],text:=[
"fusion map is unique"
]));
ALF("P1/G1/L1/V1/ext2","A5",[1,1,1,2,2,2,3,3,3,3,5,4]);
ALF("P1/G1/L1/V1/ext2","U4(2)",[1,3,2,3,9,8,6,13,14,16,10,10],[
"fusion map is unique up to table autom."
]);
ALF("P1/G1/L1/V1/ext2","2^4:a6",[1,2,2,3,5,4,6,7,7,7,12,11],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("P1/G1/L1/V1/ext2","S4(5)",[1,3,2,3,7,6,4,15,15,16,12,13],[
"fusion map is unique up to table autom."
]);
ALF("P1/G1/L1/V1/ext2","mo62",[1,2,3,4,6,5,7,9,9,8,10,10],[
"fusion map is unique"
]);
ALN("P1/G1/L1/V1/ext2",["2^4.A5"]);
MOT("P1/G1/L1/V1/ext3",
[
"origin: Hanrath library,\n",
"structure is 3^4.A5"
],
[4860,243,486,486,162,972,972,36,36,36,18,18,18,27,27,27,27,27,27,27,27,27,5,
5],
[,[1,2,4,3,5,7,6,1,6,7,5,4,3,14,16,15,18,17,19,22,21,20,24,23],[1,1,1,1,1,1,1,
8,8,8,8,8,8,1,3,4,3,4,1,4,1,3,24,23],,[1,2,4,3,5,7,6,8,10,9,11,13,12,14,16,15,
18,17,19,22,21,20,1,1]],
0,
[(23,24),(17,22)(18,20)(19,21),(14,19)(15,17)(16,18),( 3, 4)( 6, 7)( 9,10)
(12,13)(15,16)(17,18)(20,22)],
["ConstructClifford",[[[1,2,3,5,4],[1,2,3,3],[1,2,3,3],[1,3,2],[1,3,2],[1,3,
3],[1,2]],[["A5"],["A4"],["A4"],["S3"],["S3"],["Cyclic",3],["Cyclic",2]],[[[1,
2,3,4,5,6,7],[1,1,1,1,1,1,1],["elab",7,8]],[[1,2,3,4,5,7],[2,2,2,3,3,2],
["elab",6,15]],[[1,2,2,3,3,4,5,6,6],[3,3,4,3,4,2,2,2,3],["elab",9,5]],[[1],
[5]],[[1],[4]]]]]);
ALF("P1/G1/L1/V1/ext3","A5",[1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,
5,4]);
ALN("P1/G1/L1/V1/ext3",["3^4.A5v1"]);
MOT("P1/G1/L1/V1/ext4",
[
"origin: Hanrath library,\n",
"structure is 4^4.A5"
],
[15360,768,1536,512,512,3072,512,256,3072,3072,768,1536,768,1536,64,32,32,32,
32,64,32,64,32,64,48,48,48,48,48,48,48,48,48,48,48,48,48,48,48,48,5,5],
[,[1,3,1,3,3,9,9,3,1,9,9,3,9,3,1,12,3,14,7,10,4,9,5,6,25,33,25,33,27,35,27,35,
25,33,25,33,27,35,27,35,42,41],[1,2,3,5,4,10,7,8,9,6,13,14,11,12,15,18,17,16,
19,24,23,22,21,20,1,11,9,13,6,14,13,2,9,10,3,6,10,2,11,12,42,41],,[1,2,3,4,5,
6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,39,33,31,36,30,28,38,
27,37,35,29,34,32,26,40,1,1]],
0,
[(41,42),(26,39)(27,33)(28,31)(29,36)(32,38)(34,37),( 4, 5)( 6,10)(11,13)
(12,14)(16,18)(20,24)(21,23)(26,28)(29,37)(30,40)(31,39)(32,38)(34,36)],
["ConstructClifford",[[[1,2,3,5,4],[1,2,3,3],[1,2,3,3],[1,2,3,3],[1,3,2],[1,3,
2],[1,3,2],[1,3,3],[1,3,3],[1,3,3],[1,2],[1,2],[1,2],[1]],[["A5"],["A4"],
["A4"],["A4"],["S3"],["S3"],["S3"],["Cyclic",3],["Cyclic",3],["Cyclic",3],
["Cyclic",2],["Cyclic",2],["Cyclic",2],["Cyclic",1]],[[[1,2,3,4,5,6,7,8,9,10,
11,12,13,14],[1,1,1,1,1,1,1,1,1,1,1,1,1,1],["elab",14,1]],[[1,2,3,4,5,6,7,11,
12,13],[2,2,2,2,3,3,3,2,2,2],["elab",10,4]],[[1,2,2,3,3,4,4,5,6,7,8,8,9,9,10,
10],[3,3,4,3,4,3,4,2,2,2,2,3,2,3,2,3],["elab",16,1]],[[1],[5]],[[1],[4]]]]]);
ALF("P1/G1/L1/V1/ext4","A5",[1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,
2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,5,4]);
ALN("P1/G1/L1/V1/ext4",["4^4.A5"]);
MOT("P1/G1/L1/V1/ext5",
[
"origin: Hanrath library,\n",
"structure is 5^4.A5"
],
[37500,1875,1875,1250,1250,1250,1250,1875,1250,625,625,1875,1875,1250,1875,
37500,1875,1250,1250,1875,1875,1250,37500,1250,1875,37500,37500,100,50,50,50,
50,50,100,50,50,50,100,50,50,100,100,75,75,75,75,75,75,75,75,75,75,75,75,75,
75,75,75,75,75,75,75,75,75,75,75,75,25,25,25,25,25,25,25,25,25,25],
[,[1,3,2,5,6,7,4,13,14,11,10,8,15,9,12,23,20,24,18,21,25,19,27,22,17,16,26,1,
19,18,22,24,9,23,7,4,14,27,5,6,16,26,43,49,55,61,67,66,47,48,54,60,59,65,46,
52,53,57,58,64,45,51,50,56,62,63,44,73,74,75,76,77,68,69,70,71,72],[1,3,2,7,4,
5,6,12,14,11,10,15,8,9,13,26,25,19,22,17,20,24,16,18,21,27,23,28,31,29,32,30,
37,41,40,35,33,34,36,39,42,38,1,17,20,25,21,8,20,12,27,3,13,26,21,2,8,12,15,2,
17,23,15,3,16,13,25,73,74,75,76,77,68,69,70,71,72],,[1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,43,
43,43,43,43,43,43,43,43,43,43,43,43,43,43,43,43,43,43,43,43,43,43,43,43,1,1,1,
1,1,1,1,1,1,1]],
0,
[(44,61)(45,49)(46,67)(47,55)(48,57)(50,58)(52,64)(53,66)(56,60)(59,63),
( 4, 6)( 5, 7)( 8,15)(12,13)(16,27)(17,21)(18,22)(19,24)(20,25)(23,26)(29,32)
(30,31)(34,42)(35,39)(36,40)(38,41)(44,47)(45,46)(48,63)(49,67)(50,66)(51,65)
(52,64)(53,58)(54,62)(55,61)(56,60)(57,59),( 2, 3)( 4, 5, 6, 7)( 8,13,15,12)
( 9,14)(16,23,27,26)(17,20,21,25)(18,24,22,19)(29,30,32,31)(33,37)
(34,38,42,41)(35,36,39,40)(44,45,47,46)(48,53,63,58)(49,55,67,61)(50,57,66,59)
(51,54,65,62)(52,56,64,60),(69,72)(70,71)(74,77)(75,76),(68,69)(70,72)(73,74)
(75,77),(68,73)(69,75,72,76)(70,77,71,74),(10,11)(69,70,72,71)(74,75,77,76)],
["ConstructClifford",[[[1,2,3,5,4],[1,2,3,3],[1,2,3,3],[1,2,3,3],[1,2,3,3],[1,
3,2],[1,3,2],[1,3,2],[1,3,2],[1,4,5,5,4],[1,4,5,5,4],[1,3,3],[1,3,3],[1,3,3],
[1,3,3],[1,3,3],[1,3,3],[1,2],[1,2],[1,2],[1,2],[1,2],[1,2],[1],[1],[1],[
1]],[["A5"],["A4"],["A4"],["A4"],["A4"],["S3"],["S3"],["S3"],["S3"],["Cyclic",
5],["Cyclic",5],["Cyclic",3],["Cyclic",3],["Cyclic",3],["Cyclic",3],["Cyclic",
3],["Cyclic",3],["Cyclic",2],["Cyclic",2],["Cyclic",2],["Cyclic",2],["Cyclic",
2],["Cyclic",2],["Cyclic",1],["Cyclic",1],["Cyclic",1],["Cyclic",1]],[[[1,2,3,
4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27],[1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],["elab",27,1]],[[1,2,3,4,5,6,7,8,
9,18,19,20,21,22,23],[2,2,2,2,2,3,3,3,3,2,2,2,2,2,2],["elab",15,1]],[[1,2,2,3,
3,4,4,5,5,6,7,8,9,12,12,13,13,14,14,15,15,16,16,17,17],[3,3,4,3,4,3,4,3,4,2,2,
2,2,2,3,2,3,2,3,2,3,2,3,2,3],["elab",25,1]],[[1,10,10,11,11],[5,2,5,2,
5],["elab",5,16]],[[1,10,10,11,11],[4,3,4,3,4],["elab",5,16,(2,5,3,4)]]]]]);
ALF("P1/G1/L1/V1/ext5","A5",[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,
3,3,3,3,3,3,3,3,5,5,5,5,5,4,4,4,4,4]);
ALN("P1/G1/L1/V1/ext5",["5^4.A5"]);
MOT("P1/G1/L1/V1/ext6",
[
"origin: Hanrath library,\n",
"structure is 6^4.A5"
],
[77760,3888,3888,7776,2592,1296,7776,2592,1296,7776,3888,2592,2592,1296,1296,
1296,1296,1296,2592,1296,15552,3888,2592,15552,3888,1296,2592,2592,3888,1296,
3888,3888,1296,3888,15552,7776,2592,2592,1296,15552,3888,7776,15552,144,72,
144,72,144,72,72,72,72,72,72,72,72,72,72,144,144,144,72,72,72,108,108,108,108,
108,108,108,108,108,108,108,108,108,108,108,108,108,108,108,108,108,108,108,
108,108,108,108,108,108,108,108,108,108,108,108,108,5,5],
[,[1,3,3,1,7,3,10,10,3,7,7,19,19,19,19,3,7,10,19,3,1,10,19,35,35,19,35,7,40,
19,3,40,19,35,40,10,40,10,19,35,3,7,40,1,27,35,4,40,37,13,36,28,23,38,5,19,10,
7,21,43,24,8,12,42,65,67,69,65,67,69,93,89,91,93,89,91,79,81,77,79,81,77,65,
67,69,65,67,69,93,89,91,93,89,91,79,81,77,79,81,77,102,101],[1,4,1,4,4,4,1,4,
4,1,21,4,21,4,4,21,4,4,1,4,21,21,4,21,21,21,4,21,4,4,21,21,21,4,1,4,4,21,4,1,
21,4,21,44,47,44,47,44,47,59,47,59,47,59,47,44,44,44,59,59,59,47,47,47,1,11,7,
21,10,22,11,36,21,42,22,4,7,21,10,22,1,11,21,42,22,4,11,36,10,22,1,11,7,21,22,
4,11,36,21,42,102,101],,[1,2,3,4,8,9,10,5,6,7,22,23,13,14,15,16,18,17,19,20,
21,11,12,43,32,33,37,38,34,39,41,25,26,29,40,42,27,28,30,35,31,36,24,44,49,48,
47,46,45,50,64,54,63,52,62,56,58,57,59,61,60,55,53,51,65,85,69,83,67,87,90,74,
94,72,92,76,79,99,77,97,81,95,68,88,66,86,70,84,93,71,91,75,89,73,82,96,80,
100,78,98,1,1]],
0,
[(101,102),( 14, 15),( 66, 87)( 68, 83)( 70, 85)( 71, 82)( 72, 98)( 73, 78)
( 74,100)( 75, 80)( 76, 96)( 77, 93)( 79, 89)( 81, 91)( 90, 95)( 92, 97)
( 94, 99),( 65, 81, 91)( 66, 82, 92)( 67, 77, 93)( 68, 78, 94)( 69, 79, 89)
( 70, 80, 90)( 71, 87, 97)( 72, 88, 98)( 73, 83, 99)( 74, 84,100)( 75, 85, 95)
( 76, 86, 96),( 5, 8)( 6, 9)( 7, 10)( 11, 22)( 12, 23)( 17, 18)( 24, 43)
( 25, 32)( 26, 33)( 27, 37)( 28, 38)( 29, 34)( 30, 39)( 31, 41)( 35, 40)
( 36, 42)( 45, 49)( 46, 48)( 51, 64)( 52, 54)( 53, 63)( 55, 62)( 57, 58)
( 60, 61)( 66, 70)( 67, 69)( 71, 95)( 72,100)( 73, 99)( 74, 98)( 75, 97)
( 76, 96)( 77, 89)( 78, 94)( 79, 93)( 80, 92)( 81, 91)( 82, 90)( 84, 88)
( 85, 87)],
["ConstructClifford",[[[1,2,3,5,4],[1,2,3,3],[1,2,3,3],[1,2,3,3],[1,2,3,3],[1,
2,3,3],[1,3,2],[1,3,2],[1,3,2],[1,3,2],[1,3,2],[1,3,3],[1,3,3],[1,3,3],[1,3,
3],[1,3,3],[1,3,3],[1,3,3],[1,3,3],[1,3,3],[1,3,3],[1,2],[1,2],[1,2],[1,2],[1,
2],[1,2],[1,2],[1,2],[1,2],[1,2],[1],[1],[1],[1],[1],[1],[1],[1],[1],[1],[1],[
1]],[["A5"],["A4"],["A4"],["A4"],["A4"],["A4"],["S3"],["S3"],["S3"],["S3"],
["S3"],["Cyclic",3],["Cyclic",3],["Cyclic",3],["Cyclic",3],["Cyclic",
3],["Cyclic",3],["Cyclic",3],["Cyclic",3],["Cyclic",3],["Cyclic",3],["Cyclic",
2],["Cyclic",2],["Cyclic",2],["Cyclic",2],["Cyclic",2],["Cyclic",2],["Cyclic",
2],["Cyclic",2],["Cyclic",2],["Cyclic",2],["Cyclic",1],["Cyclic",1],["Cyclic",
1],["Cyclic",1],["Cyclic",1],["Cyclic",1],["Cyclic",1],["Cyclic",1],["Cyclic",
1],["Cyclic",1],["Cyclic",1],["Cyclic",1]],[[[1,2,3,4,5,6,7,8,9,10,11,12,13,
14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,
40,41,42,43],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1],["elab",43,1]],[[1,2,3,4,5,6,7,8,9,10,11,22,23,24,25,
26,27,28,29,30,31],[2,2,2,2,2,2,3,3,3,3,3,2,2,2,2,2,2,2,2,2,2],["elab",21,
1]],[[1,2,2,3,3,4,4,5,5,6,6,7,8,9,10,11,12,12,13,13,14,14,15,15,16,16,17,17,
18,18,19,19,20,20,21,21],[3,3,4,3,4,3,4,3,4,3,4,2,2,2,2,2,2,3,2,3,2,3,2,3,2,3,
2,3,2,3,2,3,2,3,2,3],["elab",36,1]],[[1],[5]],[[1],[4]]]]]);
ALF("P1/G1/L1/V1/ext6","A5",[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,
2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,
3,3,3,3,5,4]);
ALF("P1/G1/L1/V1/ext6","P1/G1/L1/V1/ext3",[1,2,2,1,3,2,4,4,2,3,3,5,5,5,5,
2,3,4,5,2,1,4,5,6,6,5,6,3,7,5,2,7,5,6,7,4,7,4,5,6,2,3,7,8,9,10,8,9,10,11,
12,13,11,12,13,11,13,12,8,10,9,12,11,13,14,15,16,14,15,16,17,18,19,17,18,
19,20,21,22,20,21,22,14,15,16,14,15,16,17,18,19,17,18,19,20,21,22,20,21,
22,23,24]);
ALF("P1/G1/L1/V1/ext6","P1/G1/L1/V1/ext2",[1,2,1,2,2,2,1,2,2,1,3,2,3,2,2,
3,2,2,1,2,3,3,2,3,3,3,2,3,2,2,3,3,3,2,1,2,2,3,2,1,3,2,3,4,5,4,5,4,5,6,5,6,
5,6,5,4,4,4,6,6,6,5,5,5,7,8,7,8,7,8,9,10,9,10,9,10,7,8,7,8,7,8,9,10,9,10,
9,10,7,8,7,8,7,8,9,10,9,10,9,10,11,12]);
ALN("P1/G1/L1/V1/ext6",["6^4.A5v1"]);
MOT("P1/G1/L1/V2/ext3",
[
"origin: Hanrath library,\n",
"structure is 3^4.A5"
],
[4860,243,486,486,162,972,972,36,36,36,18,18,18,27,27,27,27,27,27,27,27,27,5,
5],
[,[1,2,4,3,5,7,6,1,6,7,5,4,3,19,18,17,20,22,21,15,14,16,24,23],[1,1,1,1,1,1,1,
8,8,8,8,8,8,2,6,7,6,7,2,7,2,6,24,23],,[1,2,4,3,5,7,6,8,10,9,11,13,12,21,20,22,
16,15,14,17,19,18,1,1]],
0,
[(23,24),(14,19,21)(15,17,22)(16,18,20),( 3, 4)( 6, 7)( 9,10)(12,13)(15,16)
(17,18)(20,22)],
["ConstructClifford",[[[1,2,3,5,4],[1,2,3,3],[1,2,3,3],[1,3,2],[1,3,2],[1,3,
3],[1,2]],[["A5"],["A4"],["A4"],["S3"],["S3"],["Cyclic",3],["Cyclic",2]],[[[1,
2,3,4,5,6,7],[1,1,1,1,1,1,1],["elab",7,8]],[[1,2,3,4,5,7],[2,2,2,3,3,2],
["elab",6,15]],[[1,2,2,3,3,4,5,6,6],[3,3,4,3,4,2,2,2,3],["elab",9,6]],[[1],
[5]],[[1],[4]]]]]);
ALF("P1/G1/L1/V2/ext3","A5",[1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,
5,4]);
ALN("P1/G1/L1/V2/ext3",["3^4.A5v2"]);
MOT("P1/G1/L1/V2/ext6",
[
"origin: Hanrath library,\n",
"structure is 6^4.A5"
],
[77760,3888,3888,7776,2592,1296,7776,2592,1296,7776,3888,2592,2592,1296,1296,
1296,1296,1296,2592,1296,15552,3888,2592,15552,3888,1296,2592,2592,3888,1296,
3888,3888,1296,3888,15552,7776,2592,2592,1296,15552,3888,7776,15552,144,72,
144,72,144,72,72,72,72,72,72,72,72,72,72,144,144,144,72,72,72,108,108,108,108,
108,108,108,108,108,108,108,108,108,108,108,108,108,108,108,108,108,108,108,
108,108,108,108,108,108,108,108,108,108,108,108,108,5,5],
[,[1,3,3,1,7,3,10,10,3,7,7,19,19,19,19,3,7,10,19,3,1,10,19,35,35,19,35,7,40,
19,3,40,19,35,40,10,40,10,19,35,3,7,40,1,27,35,4,40,37,13,36,28,23,38,5,19,10,
7,21,43,24,8,12,42,76,72,74,76,72,74,98,100,96,98,100,96,84,86,88,84,86,88,76,
72,74,76,72,74,98,100,96,98,100,96,84,86,88,84,86,88,102,101],[1,4,1,4,4,4,1,
4,4,1,21,4,21,4,4,21,4,4,1,4,21,21,4,21,21,21,4,21,4,4,21,21,21,4,1,4,4,21,4,
1,21,4,21,44,47,44,47,44,47,59,47,59,47,59,47,44,44,44,59,59,59,47,47,47,2,25,
29,41,34,43,24,35,31,40,32,3,29,41,34,43,2,25,31,40,32,3,24,35,34,43,2,25,29,
41,32,3,24,35,31,40,102,101],,[1,2,3,4,8,9,10,5,6,7,22,23,13,14,15,16,18,17,
19,20,21,11,12,43,32,33,37,38,34,39,41,25,26,29,40,42,27,28,30,35,31,36,24,44,
49,48,47,46,45,50,64,54,63,52,62,56,58,57,59,61,60,55,53,51,81,95,79,99,77,97,
70,84,68,88,66,86,89,73,93,71,91,75,78,98,82,96,80,100,67,87,65,85,69,83,92,
76,90,74,94,72,1,1]],
0,
[(101,102),( 14, 15),( 65, 81, 91)( 66, 82, 92)( 67, 77, 93)( 68, 78, 94)
( 69, 79, 89)( 70, 80, 90)( 71, 87, 97)( 72, 88, 98)( 73, 83, 99)( 74, 84,100)
( 75, 85, 95)( 76, 86, 96),( 5, 8)( 6, 9)( 7, 10)( 11, 22)( 12, 23)
( 17, 18)( 24, 43)( 25, 32)( 26, 33)( 27, 37)( 28, 38)( 29, 34)( 30, 39)
( 31, 41)( 35, 40)( 36, 42)( 45, 49)( 46, 48)( 51, 64)( 52, 54)( 53, 63)
( 55, 62)( 57, 58)( 60, 61)( 66, 85)( 67, 69)( 68, 83)( 70, 87)( 71, 90)
( 72, 74)( 73, 94)( 75, 92)( 77, 79)( 78, 99)( 80, 97)( 82, 95)( 84, 88)
( 89, 93)( 98,100)],
["ConstructClifford",[[[1,2,3,5,4],[1,2,3,3],[1,2,3,3],[1,2,3,3],[1,2,3,3],[1,
2,3,3],[1,3,2],[1,3,2],[1,3,2],[1,3,2],[1,3,2],[1,3,3],[1,3,3],[1,3,3],[1,3,
3],[1,3,3],[1,3,3],[1,3,3],[1,3,3],[1,3,3],[1,3,3],[1,2],[1,2],[1,2],[1,2],[1,
2],[1,2],[1,2],[1,2],[1,2],[1,2],[1],[1],[1],[1],[1],[1],[1],[1],[1],[1],[1],[
1]],[["A5"],["A4"],["A4"],["A4"],["A4"],["A4"],["S3"],["S3"],["S3"],["S3"],
["S3"],["Cyclic",3],["Cyclic",3],["Cyclic",3],["Cyclic",3],["Cyclic",
3],["Cyclic",3],["Cyclic",3],["Cyclic",3],["Cyclic",3],["Cyclic",3],["Cyclic",
2],["Cyclic",2],["Cyclic",2],["Cyclic",2],["Cyclic",2],["Cyclic",2],["Cyclic",
2],["Cyclic",2],["Cyclic",2],["Cyclic",2],["Cyclic",1],["Cyclic",1],["Cyclic",
1],["Cyclic",1],["Cyclic",1],["Cyclic",1],["Cyclic",1],["Cyclic",1],["Cyclic",
1],["Cyclic",1],["Cyclic",1],["Cyclic",1]],[[[1,2,3,4,5,6,7,8,9,10,11,12,13,
14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,
40,41,42,43],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1],["elab",43,1]],[[1,2,3,4,5,6,7,8,9,10,11,22,23,24,25,
26,27,28,29,30,31],[2,2,2,2,2,2,3,3,3,3,3,2,2,2,2,2,2,2,2,2,2],["elab",21,
1]],[[1,2,2,3,3,4,4,5,5,6,6,7,8,9,10,11,12,12,13,13,14,14,15,15,16,16,17,17,
18,18,19,19,20,20,21,21],[3,3,4,3,4,3,4,3,4,3,4,2,2,2,2,2,2,3,2,3,2,3,2,3,2,3,
2,3,2,3,2,3,2,3,2,3],["elab",36,2]],[[1],[5]],[[1],[4]]]]]);
ALF("P1/G1/L1/V2/ext6","A5",[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,
2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,
3,3,3,3,5,4]);
ALF("P1/G1/L1/V2/ext6","P1/G1/L1/V2/ext3",[1,2,2,1,3,2,4,4,2,3,3,5,5,5,5,
2,3,4,5,2,1,4,5,6,6,5,6,3,7,5,2,7,5,6,7,4,7,4,5,6,2,3,7,8,9,10,8,9,10,11,
12,13,11,12,13,11,13,12,8,10,9,12,11,13,14,15,16,14,15,16,17,18,19,17,18,
19,20,21,22,20,21,22,14,15,16,14,15,16,17,18,19,17,18,19,20,21,22,20,21,
22,23,24]);
ALF("P1/G1/L1/V2/ext6","P1/G1/L1/V1/ext2",[1,2,1,2,2,2,1,2,2,1,3,2,3,2,2,
3,2,2,1,2,3,3,2,3,3,3,2,3,2,2,3,3,3,2,1,2,2,3,2,1,3,2,3,4,5,4,5,4,5,6,5,6,
5,6,5,4,4,4,6,6,6,5,5,5,10,8,10,8,10,8,9,7,9,7,9,7,10,8,10,8,10,8,9,7,9,7,
9,7,10,8,10,8,10,8,9,7,9,7,9,7,11,12]);
ALN("P1/G1/L1/V2/ext6",["6^4.A5v2"]);
MOT("P1/G2/L1/V1/ext2",
[
"origin: Hanrath library,\n",
"structure is 2^5.A5"
],
[1920,128,128,1920,32,32,16,16,32,32,6,6,10,10,10,10],
[,[1,1,1,1,1,3,2,2,3,1,11,11,15,15,13,13],[1,2,3,4,5,6,7,8,9,10,1,4,15,16,13,
14],,[1,2,3,4,5,6,7,8,9,10,11,12,1,4,1,4]],
0,
[( 7, 8),( 5,10)( 6, 9),(13,15)(14,16)],
["ConstructClifford",[[[1,2,3,5,4],[1,4,5,2],[1,3,2],[1,2,2,2]],[["A5"],
["Dihedral",10],["S3"],["V4"]],[[[1,2,3,4],[1,1,1,1],["elab",4,18]],[[1,2,3,4,
4,4],[2,4,3,2,3,4],["elab",6,16]],[[1,3],[3,2],[[1,1],[1,-1]]],[[1,2],[5,2],
[[1,1],[1,-1]]],[[1,2],[4,3],[[1,1],[1,-1]]]]]]);
ALF("P1/G2/L1/V1/ext2","A5",[1,1,1,1,2,2,2,2,2,2,3,3,5,5,4,4]);
ALF("P1/G2/L1/V1/ext2","2.L3(4)",[1,4,3,2,3,7,9,10,8,4,5,6,11,12,13,14],[
"fusion map is unique up to table automorphisms"
]);
ALN("P1/G2/L1/V1/ext2",["2^5.A5v1","2aM20"]);
MOT("P1/G2/L1/V1/ext3",
[
"origin: Hanrath library,\n",
"structure is 3^5.A5"
],
[14580,486,1458,1458,1458,972,243,1458,972,486,486,14580,1458,1458,14580,108,
54,54,108,54,54,108,54,54,54,108,54,108,54,108,108,108,108,27,27,27,27,27,27,
27,27,27,15,15,15,15,15,15],
[,[1,2,4,3,8,9,7,5,6,11,10,15,14,13,12,1,10,11,9,8,3,6,4,5,13,9,14,6,2,12,6,
15,9,34,36,35,37,39,38,40,42,41,46,48,47,43,45,44],[1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,1,14,13,1,14,13,1,
14,13,46,46,46,43,43,43],,[1,2,4,3,8,9,7,5,6,11,10,15,14,13,12,16,18,17,22,24,
23,19,21,20,27,31,25,33,29,32,26,30,28,34,36,35,37,39,38,40,42,41,1,15,12,1,
15,12]],
0,
[(43,46)(44,47)(45,48),(37,40)(38,41)(39,42),(34,37)(35,38)(36,39),( 3, 4)
( 5, 8)( 6, 9)(10,11)(12,15)(13,14)(17,18)(19,22)(20,24)(21,23)(25,27)(26,31)
(28,33)(30,32)(35,36)(38,39)(41,42)(44,45)(47,48),( 3, 5)( 4, 8)( 6, 9)(13,14)
(19,22)(20,23)(21,24)(25,27)(26,28)(31,33)(35,36)(38,39)(41,42)],
["ConstructClifford",[[[1,2,3,5,4],[1,2,3,3],[1,2,3,3],[1,4,5,2],[1,4,5,2],[1,
3,2],[1,3,2],[1,2,2,2],[1,2,2,2],[1,3,3],[1,2],[1,2],[1,2],[1,2],[1,2]],
[["A5"],["A4"],["A4"],["Dihedral",10],["Dihedral",10],["S3"],["S3"],["V4"],
["V4"],["Cyclic",3],["Cyclic",2],["Cyclic",2],["Cyclic",2],["Cyclic",2],
["Cyclic",2]],[[[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],[1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1],["elab",15,2]],[[1,2,3,4,5,6,7,8,8,8,9,9,9,11,12,13,14,15],[2,2,2,4,
4,3,3,2,3,4,2,3,4,2,2,2,2,2],["elab",18,1]],[[1,2,2,3,3,6,7,10,10],[3,3,4,3,4,
2,2,2,3],["elab",9,5,(2,5,6)(3,7,4)]],[[1,4,5],[5,2,2],["elab",3,1]],[[1,4,5],
[4,3,3],["elab",3,1]]]]]);
ALF("P1/G2/L1/V1/ext3","A5",[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,
2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,5,5,5,4,4,4]);
ALN("P1/G2/L1/V1/ext3",["3^5.A5"]);
MOT("P1/G2/L1/V1/ext4",
[
"origin: Hanrath library,\n",
"structure is 4^5.A5"
],
[61440,2048,4096,2048,2048,2048,4096,4096,1024,1024,2048,2048,4096,2048,1024,
4096,4096,1024,1024,2048,2048,1024,1024,2048,2048,10240,4096,6144,4096,1024,
6144,4096,2048,10240,61440,4096,256,256,256,256,128,128,128,128,128,128,128,
128,128,128,128,128,256,256,256,256,128,128,128,128,128,128,128,128,256,256,
256,256,128,128,128,128,256,256,256,256,12,12,12,12,20,20,20,20,20,20,20,20],
[,[1,3,1,3,3,3,13,13,3,13,3,3,1,3,3,13,13,13,13,3,3,13,13,3,3,35,13,35,13,13,
35,13,3,35,1,13,1,27,13,36,20,25,14,4,3,32,3,29,24,5,6,21,16,13,8,13,21,24,5,
6,17,3,7,35,13,36,1,27,14,4,20,25,8,13,16,13,77,79,77,79,85,87,85,87,81,83,81,
83],[1,2,3,5,4,14,17,16,15,10,11,12,13,6,9,8,7,22,23,24,25,18,19,20,21,34,36,
31,32,30,28,29,33,26,35,27,37,40,39,38,49,52,51,50,45,48,47,46,41,44,43,42,73,
76,75,74,72,71,70,69,63,62,61,64,65,68,67,66,60,59,58,57,53,56,55,54,1,28,35,
31,85,88,87,86,81,84,83,82],,[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,
72,73,74,75,76,77,78,79,80,1,34,35,26,1,34,35,26]],
0,
[(81,85)(82,86)(83,87)(84,88),(37,67)(38,68)(39,65)(40,66)(41,71)(42,72)
(43,69)(44,70)(49,58)(50,59)(51,60)(52,57)(53,75)(54,76)(55,73)(56,74),( 4, 5)
( 6,14)( 7,17)( 8,16)( 9,15)(18,22)(19,23)(20,24)(21,25)(26,34)(27,36)(28,31)
(29,32)(38,40)(41,49)(42,52)(43,51)(44,50)(46,48)(53,73)(54,76)(55,75)(56,74)
(57,72)(58,71)(59,70)(60,69)(61,63)(66,68)(78,80)(82,84)(86,88),( 4, 6)( 5,14)
( 8,16)( 9,15)(11,12)(18,19)(20,21)(22,23)(24,25)(28,31)(29,32)(41,57)(42,58)
(43,59)(44,60)(45,47)(46,48)(49,72)(50,69)(51,70)(52,71)(53,73)(54,74)(55,75)
(56,76)(78,80)],
["ConstructClifford",[[[1,2,3,5,4],[1,4,5,2],[1,4,5,2],[1,4,5,2],[1,3,2],[1,3,
2],[1,3,2],[1,2,2,2],[1,2,2,2],[1,2,2,2],[1,2,2,2],[1,2,2,2],[1,2],[1,2],[1,
2],[1,2],[1,2],[1,2],[1,2],[1,2],[1,2],[1,2],[1,2],[1,2],[1,2],[1,2],[1,2],[1,
2],[1,2],[1,2],[1],[1],[1],[1],[1],[1]],[["A5"],["Dihedral",10],["Dihedral",
10],["Dihedral",10],["S3"],["S3"],["S3"],["V4"],["V4"],["V4"],["V4"],["V4"],
["Cyclic",2],["Cyclic",2],["Cyclic",2],["Cyclic",2],["Cyclic",2],["Cyclic",2],
["Cyclic",2],["Cyclic",2],["Cyclic",2],["Cyclic",2],["Cyclic",2],["Cyclic",2],
["Cyclic",2],["Cyclic",2],["Cyclic",2],["Cyclic",2],["Cyclic",2],["Cyclic",2],
["Cyclic",1],["Cyclic",1],["Cyclic",1],["Cyclic",1],["Cyclic",1],["Cyclic",
1]],[[[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,
27,28,29,30,31,32,33,34,35,36],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1],["elab",36,3]],[[1,2,3,4,5,6,7,8,8,8,9,9,9,10,10,
10,11,11,11,12,12,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30],
[2,4,4,4,3,3,3,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,
2,2],["elab",40,1]],[[1,5,6,7],[3,2,2,2],["elab",4,19]],[[1,2,3,4],[5,2,2,2],
["elab",4,19]],[[1,2,3,4],[4,3,3,3],["elab",4,19]]]]]);
ALF("P1/G2/L1/V1/ext4","A5",[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,
2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,5,5,5,5,4,4,4,4]);
ALN("P1/G2/L1/V1/ext4",["4^5.A5v1"]);
MOT("P1/G2/L1/V2/ext2",
[
"origin: Hanrath library,\n",
"structure is 2^5.A5"
],
[1920,128,128,1920,16,16,32,32,32,32,6,6,10,10,10,10],
[,[1,1,1,1,2,4,3,3,3,3,11,11,15,15,13,13],[1,2,3,4,5,6,10,9,8,7,1,4,15,16,13,
14],,[1,2,3,4,5,6,7,8,9,10,11,12,1,4,1,4]],
0,
[( 7, 8)( 9,10),( 7, 9)( 8,10),(13,15)(14,16)],
["ConstructClifford",[[[1,2,3,5,4],[1,4,5,2],[1,3,2],[1,2,2,2]],[["A5"],
["Dihedral",10],["S3"],["V4"]],[[[1,2,3,4],[1,1,1,1],["elab",4,18]],[[1,2,3,4,
4,4],[2,4,3,2,3,4],["elab",6,17]],[[1,3],[3,2],[[1,1],[1,-1]]],[[1,2],[5,2],
[[1,1],[1,-1]]],[[1,2],[4,3],[[1,1],[1,-1]]]]]]);
ALF("P1/G2/L1/V2/ext2","A5",[1,1,1,1,2,2,2,2,2,2,3,3,5,5,4,4]);
ALN("P1/G2/L1/V2/ext2",["2^5.A5v2","2cM20"]);
MOT("P1/G2/L1/V2/ext4",
[
"origin: Hanrath library,\n",
"structure is 4^5.A5"
],
[61440,2048,4096,2048,2048,2048,4096,4096,1024,1024,2048,2048,4096,2048,1024,
4096,4096,1024,1024,2048,2048,1024,1024,2048,2048,10240,4096,6144,4096,1024,
6144,4096,2048,10240,61440,4096,128,128,128,128,256,256,256,256,128,128,128,
128,128,128,128,128,128,128,128,128,256,256,256,256,128,128,128,128,128,128,
128,128,256,256,256,256,256,256,256,256,12,12,12,12,20,20,20,20,20,20,20,20],
[,[1,3,1,3,3,3,13,13,3,13,3,3,1,3,3,13,13,13,13,3,3,13,13,3,3,35,13,35,13,13,
35,13,3,35,1,13,2,26,33,34,27,36,16,16,12,31,11,28,29,17,7,29,7,32,32,17,27,
36,8,8,34,2,26,33,11,28,12,31,16,16,27,36,8,8,27,36,77,79,77,79,85,87,85,87,
81,83,81,83],[1,2,3,5,4,14,17,16,15,10,11,12,13,6,9,8,7,22,23,24,25,18,19,20,
21,34,36,31,32,30,28,29,33,26,35,27,62,61,64,63,58,57,60,59,45,48,47,46,54,53,
56,55,50,49,52,51,42,41,44,43,38,37,40,39,65,68,67,66,74,73,76,75,70,69,72,71,
1,28,35,31,85,88,87,86,81,84,83,82],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,
17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,62,63,64,61,71,72,
69,70,67,68,65,66,49,50,51,52,53,54,55,56,75,76,73,74,40,37,38,39,47,48,45,46,
43,44,41,42,59,60,57,58,77,78,79,80,1,34,35,26,1,34,35,26]],
0,
[(81,85)(82,86)(83,87)(84,88),(37,62)(38,63)(39,64)(40,61)(41,71)(42,72)
(43,69)(44,70)(45,67)(46,68)(47,65)(48,66)(57,75)(58,76)(59,73)(60,74),( 4, 5)
( 6,14)( 7,17)( 8,16)( 9,15)(18,22)(19,23)(20,24)(21,25)(26,34)(27,36)(28,31)
(29,32)(38,40)(41,76)(42,75)(43,74)(44,73)(45,67)(46,66)(47,65)(48,68)(49,54)
(50,53)(51,56)(52,55)(57,72)(58,71)(59,70)(60,69)(61,63)(78,80)(82,84)(86,88),
( 4, 6)( 5,14)( 8,16)( 9,15)(11,12)(18,19)(20,21)(22,23)(24,25)(28,31)(29,32)
(41,57)(42,58)(43,59)(44,60)(45,65)(46,66)(47,67)(48,68)(49,55)(50,56)(51,53)
(52,54)(69,73)(70,74)(71,75)(72,76)(78,80)],
["ConstructClifford",[[[1,2,3,5,4],[1,4,5,2],[1,4,5,2],[1,4,5,2],[1,3,2],[1,3,
2],[1,3,2],[1,2,2,2],[1,2,2,2],[1,2,2,2],[1,2,2,2],[1,2,2,2],[1,2],[1,2],[1,
2],[1,2],[1,2],[1,2],[1,2],[1,2],[1,2],[1,2],[1,2],[1,2],[1,2],[1,2],[1,2],[1,
2],[1,2],[1,2],[1],[1],[1],[1],[1],[1]],[["A5"],["Dihedral",10],["Dihedral",
10],["Dihedral",10],["S3"],["S3"],["S3"],["V4"],["V4"],["V4"],["V4"],["V4"],
["Cyclic",2],["Cyclic",2],["Cyclic",2],["Cyclic",2],["Cyclic",2],["Cyclic",2],
["Cyclic",2],["Cyclic",2],["Cyclic",2],["Cyclic",2],["Cyclic",2],["Cyclic",2],
["Cyclic",2],["Cyclic",2],["Cyclic",2],["Cyclic",2],["Cyclic",2],["Cyclic",2],
["Cyclic",1],["Cyclic",1],["Cyclic",1],["Cyclic",1],["Cyclic",1],["Cyclic",
1]],[[[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,
27,28,29,30,31,32,33,34,35,36],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1],["elab",36,3]],[[1,2,3,4,5,6,7,8,8,8,9,9,9,10,10,
10,11,11,11,12,12,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30],
[2,4,4,4,3,3,3,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,
2,2],["elab",40,2]],[[1,5,6,7],[3,2,2,2],["elab",4,19]],[[1,2,3,4],[5,2,2,2],
["elab",4,19]],[[1,2,3,4],[4,3,3,3],["elab",4,19]]]]]);
ALF("P1/G2/L1/V2/ext4","A5",[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,
2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,5,5,5,5,4,4,4,4]);
ALN("P1/G2/L1/V2/ext4",["4^5.A5v2"]);
MOT("P1/G2/L2/V2/ext2",
[
"origin: Hanrath library,\n",
"structure is 2^5.A5"
],
[1920,192,128,320,16,16,16,16,6,6,10,10,10,10],
[,[1,1,1,1,2,4,4,2,9,9,13,13,11,11],[1,2,3,4,8,7,6,5,1,2,13,14,11,12],,[1,2,3,
4,5,6,7,8,9,10,1,4,1,4]],
0,
[(11,13)(12,14),( 6, 7),(5,8)],
["ConstructClifford",[[[1,2,3,5,4],[1,2,3,5,4],[1,2,2,2],[1,2,2,2]],[["A5"],
["projectives","A5","2.A5"],["V4"],["projectives","V4","Q8"]],[[[1,2,3,4],[1,
1,1,1],["elab",4,20]],[[1,3,3,3],[2,2,3,4],["elab",4,21]],[[1,2],[3,3],[[1,1],
[1,-1]]],[[1,2],[5,5],[[1,1],[1,-1]]],[[1,2],[4,4],[[1,1],[1,-1]]]]]]);
ALF("P1/G2/L2/V2/ext2","A5",[1,1,1,1,2,2,2,2,3,3,5,5,4,4]);
ALN("P1/G2/L2/V2/ext2",["2^5.A5v3"]);
MOT("P1/G2/L2/V2/ext4",
[
"origin: Hanrath library,\n",
"structure is 4^5.A5"
],
[61440,6144,6144,6144,4096,2048,2048,4096,2048,4096,1024,1024,2048,1024,2048,
2048,2048,2048,1024,2048,2048,1024,10240,2048,2048,2048,1024,2048,2048,2048,
4096,2048,2048,4096,10240,10240,128,128,128,128,128,128,128,128,128,128,128,
128,128,128,128,128,128,128,128,128,128,128,128,128,128,128,128,128,128,128,
128,128,12,12,12,12,20,20,20,20,20,20,20,20],
[,[1,3,1,3,8,3,8,1,3,8,3,8,23,8,23,3,8,23,3,8,3,8,1,3,23,3,8,8,23,8,8,23,8,8,
23,23,9,29,16,15,16,15,9,29,2,25,21,35,21,35,2,25,36,24,18,4,18,4,36,24,13,26,
32,6,32,6,13,26,69,71,69,71,77,79,77,79,73,75,73,75],[1,4,3,2,10,9,7,8,6,5,19,
12,15,14,13,26,20,25,11,17,24,22,23,21,18,16,27,33,32,30,34,29,28,31,36,35,66,
65,68,67,62,61,64,63,58,57,60,59,54,53,56,55,50,49,52,51,46,45,48,47,42,41,44,
43,38,37,40,39,1,2,3,4,77,80,79,78,73,76,75,74],,[1,2,3,4,5,6,7,8,9,10,11,12,
13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,43,44,
41,42,39,40,37,38,51,52,49,50,47,48,45,46,59,60,57,58,55,56,53,54,67,68,65,66,
63,64,61,62,69,70,71,72,1,36,23,35,1,36,23,35]],
0,
[(73,77)(74,78)(75,79)(76,80),(13,15)(14,22)(16,21)(17,28)(18,29)(20,33)
(24,26)(25,32)(31,34)(35,36)(38,57)(39,49)(40,61)(41,47)(42,67)(44,55)(46,65)
(48,53)(50,59)(52,63)(54,68)(60,62)(74,76)(78,80),(37,43)(38,44)(39,41)(40,42)
(45,51)(46,52)(47,49)(48,50)(53,59)(54,60)(55,57)(56,58)(61,67)(62,68)(63,65)
(64,66),( 2, 4)( 5,10)( 6, 9)(11,19)(14,22)(16,24)(17,33)(18,32)(20,28)(21,26)
(25,29)(37,64)(38,52)(39,60)(41,54)(43,66)(44,46)(45,56)(47,68)(49,62)(51,58)
(55,65)(57,63)(70,72)],
["ConstructClifford",[[[1,2,3,5,4],[1,2,3,5,4],[1,4,5,2],[1,4,5,2],[1,3,2],[1,
3,2],[1,2,2,2],[1,2,2,2],[1,2,2,2],[1,2,2,2],[1,2,2,2],[1,2,2,2],[1,2,2,2],[1,
2,2,2],[1,2,2,2],[1,2,2,2],[1,2],[1,2],[1,2],[1,2],[1,2],[1,2],[1,2],[1,2],[1,
2],[1,2],[1,2],[1,2],[1],[1],[1],[1],[1],[1],[1],[1]],[["A5"],["projectives",
"A5","2.A5"],["Dihedral",10],["Dihedral",10],["S3"],["S3"],["V4"],["V4"],
["V4"],["V4"],["V4"],["projectives","V4","Q8"],["projectives","V4","Q8"],
["projectives","V4","Q8"],["projectives","V4","Q8"],["projectives","V4","Q8"],
["Cyclic",2],["Cyclic",2],["Cyclic",2],["Cyclic",2],["Cyclic",2],["Cyclic",2],
["Cyclic",2],["Cyclic",2],["Cyclic",2],["Cyclic",2],["Cyclic",2],["Cyclic",2],
["Cyclic",1],["Cyclic",1],["Cyclic",1],["Cyclic",1],["Cyclic",1],["Cyclic",1],
["Cyclic",1],["Cyclic",1]],[[[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,
20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36],[1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],["elab",36,4]],[[1,3,4,5,6,7,
7,7,8,8,8,9,9,9,10,10,10,11,11,11,17,18,19,20,21,22,23,24,25,26,27,28],[2,4,4,
3,3,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,2,2,2,2,2,2,2,2,2,2,2],["elab",32,1]],[[1,
2,5,6],[3,3,2,2],["elab",4,19,(2,4,3)]],[[1,2,3,4],[5,5,2,2],["elab",4,19,
(2,3)]],[[1,2,3,4],[4,4,3,3],["elab",4,19,(2,3)]]]]]);
ALF("P1/G2/L2/V2/ext4","A5",[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,
2,2,2,2,2,2,2,2,2,3,3,3,3,5,5,5,5,4,4,4,4]);
ALN("P1/G2/L2/V2/ext4",["4^5.A5v3"]);
MOT("P1/G3/L2/V1/ext2",
[
"origin: Hanrath library,\n",
"structure is 2^6.A5"
],
[3840,256,256,256,256,3840,3840,3840,64,32,32,32,32,64,32,32,64,64,12,12,12,
12,20,20,20,20,20,20,20,20],
[,[1,1,1,1,1,1,1,1,1,2,4,3,2,1,3,4,1,1,19,19,19,19,27,27,27,27,23,23,23,23],[
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,1,7,8,6,27,28,29,30,23,24,25,
26],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,1,6,8,7,1,6,8,
7]],
0,
[(23,27)(24,28)(25,29)(26,30),( 9,14)(10,13)(12,15)(17,18),( 9,17)(11,16)
(12,15)(14,18),( 3, 4)( 7, 8)(11,12)(14,18)(15,16)(20,21)(25,26)(29,30),
( 2, 3)( 6, 7)(10,15)(12,13)(17,18)(20,22)(24,26)(28,30)],
["ConstructClifford",[[[1,2,3,5,4],[1,4,5,2],[1,4,5,2],[1,4,5,2],[1,3,2],[1,3,
2],[1,3,2],[1,2,2,2]],[["A5"],["Dihedral",10],["Dihedral",10],["Dihedral",10],
["S3"],["S3"],["S3"],["V4"]],[[[1,2,3,4,5,6,7,8],[1,1,1,1,1,1,1,1],["elab",8,
5]],[[1,2,3,4,5,6,7,8,8,8],[2,4,4,4,3,3,3,2,3,4],["elab",10,1,(2,3,9,4,7,5,8,
6,10),(2,6,5)(3,9,7)(4,10,8)]],[[1,5,6,7],[3,2,2,2],["elab",4,12,(2,3,4)]],
[[1,2,3,4],[5,2,2,2],["elab",4,12,(2,3,4)]],[[1,2,3,4],[4,3,3,3],["elab",4,12,
(2,3,4)]]]]]);
ARC("P1/G3/L2/V1/ext2","tomfusion",rec(name:="2^2.(2^4:A5)",map:=[1,5,6,8,
7,4,2,3,9,64,105,83,57,11,104,106,12,10,13,113,110,112,108,393,391,395,
108,393,391,395],text:=[
"fusion map is unique up to table autom."
]));
ALF("P1/G3/L2/V1/ext2","A5",[1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,3,3,3,3,
5,5,5,5,4,4,4,4]);
ALF("P1/G3/L2/V1/ext2","2^2.L3(4)",[1,6,7,8,5,2,3,4,5,14,17,15,13,8,16,18,
6,7,9,11,12,10,19,20,22,21,23,24,26,25],[
"fusion map is unique up to table autom."
]);
ALN("P1/G3/L2/V1/ext2",["2^6.A5"]);
MOT("P1/G3/L2/V1/ext3",
[
"origin: Hanrath library,\n",
"structure is 3^6.A5"
],
[43740,1458,729,1458,1458,729,2187,729,729,729,1458,729,729,729,3645,2187,
3645,2187,2187,3645,3645,36,18,18,18,18,27,27,27,27,27,27,27,27,27,45,45,45,
45,45,45,45,45,45,45,45,45,45,45,45,45,45,45],
[,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,1,11,5,2,4,27,28,29,
30,31,32,33,34,35,45,47,46,51,53,52,48,50,49,36,37,38,39,40,41,42,43,44],[1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,22,22,22,22,22,1,19,19,7,18,16,7,16,18,
45,45,45,45,45,45,45,45,45,36,36,36,36,36,36,36,36,36],,[1,2,3,4,5,6,7,8,9,10,
11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,1,
20,20,15,21,17,15,17,21,1,20,20,15,21,17,15,17,21]],
0,
[(28,29)(30,33)(31,35)(32,34),(37,38)(39,42)(40,44)(41,43)(46,47)(48,51)
(49,53)(50,52),(36,45)(37,46,38,47)(39,48,42,51)(40,49,44,53)(41,50,43,52),
( 3, 6)( 4, 5)( 9,12)(10,14)(15,17)(18,19)(20,21)(24,26)(28,31)(29,35)(30,33)
(37,40,38,44)(39,43,42,41)(46,49,47,53)(48,52,51,50),( 2, 4,11, 5)
( 3, 6,14,10)( 7,19,16,18)( 8, 9,13,12)(15,20,21,17)(23,24,25,26)
(28,32,35,33,29,34,31,30)(37,40,41,42,38,44,43,39)(46,49,50,51,47,53,52,48)],
["ConstructClifford",[[[1,2,3,5,4],[1,4,5,5,4],[1,4,5,5,4],[1,4,5,5,4],[1,4,5,
5,4],[1,3,3],[1,3,3],[1,3,3],[1,3,3],[1,2],[1,2],[1,2],[1,2],[1],[1],[1],[1],
[1],[1],[1],[1]],[["A5"],["Cyclic",5],["Cyclic",5],["Cyclic",5],["Cyclic",5],
["Cyclic",3],["Cyclic",3],["Cyclic",3],["Cyclic",3],["Cyclic",2],["Cyclic",2],
["Cyclic",2],["Cyclic",2],["Cyclic",1],["Cyclic",1],["Cyclic",1],["Cyclic",1],
["Cyclic",1],["Cyclic",1],["Cyclic",1],["Cyclic",1]],[[[1,2,3,4,5,6,7,8,9,10,
11,12,13,14,15,16,17,18,19,20,21],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],
["elab",21,2]],[[1,10,11,12,13],[2,2,2,2,2],["elab",5,17]],[[1,6,6,7,7,8,8,9,
9],[3,2,3,2,3,2,3,2,3],["elab",9,5,(2,9,4,8,5,3)(6,7)]],[[1,2,2,3,3,4,4,5,5],
[5,2,5,2,5,2,5,2,5],["elab",9,5,(2,8,7,5,3)(4,9,6)]],[[1,2,2,3,3,4,4,5,5],[4,
3,4,3,4,3,4,3,4],["elab",9,5,(2,8,7,5,3)(4,9,6)]]]]]);
ALF("P1/G3/L2/V1/ext3","A5",[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,
2,2,2,2,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,5,4,4,4,4,4,4,4,4,4]);
ALN("P1/G3/L2/V1/ext3",["3^6.A5"]);
MOT("P11/G1/L1/V1/ext2",
[
"origin: Hanrath library,\n",
"structure is 2^6.L3(2)"
],
[10752,512,384,1536,1536,128,64,32,64,64,128,64,128,128,12,12,12,12,16,16,16,
16,7,7],
[,[1,1,1,1,1,1,5,2,4,4,1,5,1,1,15,15,15,15,6,14,13,11,23,24],[1,2,3,4,5,6,7,8,
9,10,11,12,13,14,1,5,4,3,19,20,21,22,24,23],,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,
14,15,16,17,18,19,20,21,22,1,1]],
0,
[(23,24),( 6,11)( 9,10)(13,14)(19,22)(20,21),( 6,13)( 7,12)(11,14)(19,21)
(20,22),( 4, 5)( 7,10)( 9,12)(11,13)(16,17)(21,22)],
["ConstructClifford",[[[1,2,3,4,5,6],[1,2,3,2,4],[1,2,3,2,4],[1,2,4,2,2],[1,3,
2]],[["L3(2)"],["Symm(4)"],["Symm(4)"],["D8"],["S3"]],[[[1,2,3,4,5],[1,1,1,1,
1],["elab",5,8,(2,4),(2,4)(3,5)]],[[1,2,2,3,3,4,4,4,5],[2,2,4,2,4,2,4,5,3],
["elab",9,1,(2,6,4,8,5),(2,6,7,4,9,3,8,5)]],[[1,2,3,5],[3,3,3,2],["elab",4,12,
(3,4)]],[[1,2,3,4],[4,5,5,3],["elab",4,12,(2,4,3)]],[[1],[5]],[[1],[6]]]]]);
ALF("P11/G1/L1/V1/ext2","L3(2)",[1,1,1,1,1,2,2,2,2,2,2,2,2,2,3,3,3,3,4,4,
4,4,5,6]);
ALN("P11/G1/L1/V1/ext2",["2^6.L3(2)v1"]);
MOT("P11/G1/L1/V1/ext3",
[
"origin: Hanrath library,\n",
"structure is 3^6.L3(2)"
],
[122472,2916,2187,729,2187,2916,729,2187,2916,2187,2916,72,36,36,36,36,27,27,
27,27,27,27,27,27,27,36,36,36,36,36,36,36,36,36,7,7],
[,[1,2,3,4,5,6,7,8,9,10,11,1,11,2,6,9,17,18,19,20,21,22,23,24,25,12,14,14,15,
13,16,15,16,13,35,36],[1,1,1,1,1,1,1,1,1,1,1,12,12,12,12,12,1,10,10,8,5,3,8,3,
5,26,26,26,26,26,26,26,26,26,36,35],,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,
16,17,18,19,20,21,22,23,24,25,26,28,27,32,34,33,29,31,30,1,1]],
0,
[(35,36),(27,28)(29,32)(30,34)(31,33),( 6, 9)(15,16)(29,33)(30,34)(31,32),
(18,19)(20,23)(21,25)(22,24),( 8,10)(18,20)(19,23)(22,24),( 3, 5)(20,23)
(21,24)(22,25),( 2, 6)( 3, 8)( 4, 7)( 5,10)( 9,11)(13,16)(14,15)(18,21,19,25)
(20,24,23,22)(27,29,28,32)(30,31,34,33)],
["ConstructClifford",[[[1,2,3,4,5,6],[1,4,2,4],[1,4,2,4],[1,4,2,4],[1,4,2,4],
[1,3,3],[1,3,3],[1,3,3],[1,3,3],[1],[1]],[["L3(2)"],["Cyclic",4],["Cyclic",4],
["Cyclic",4],["Cyclic",4],["Cyclic",3],["Cyclic",3],["Cyclic",3],["Cyclic",3],
["Cyclic",1],["Cyclic",1]],[[[1,2,3,4,5,6,7,8,9,10,11],[1,1,1,1,1,1,1,1,1,1,
1],["elab",11,1]],[[1,2,3,4,5],[2,3,3,3,3],["elab",5,17,(2,5,4)]],[[1,6,6,7,7,
8,8,9,9],[3,2,3,2,3,2,3,2,3],["elab",9,5,(2,3,8,6,4)(5,9,7)]],[[1,2,2,3,3,4,4,
5,5],[4,2,4,2,4,2,4,2,4],["elab",9,5,(2,7,5,9,3,8)(4,6)]],[[1],[5]],[[1],
[6]]]]]);
ALF("P11/G1/L1/V1/ext3","L3(2)",[1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,3,3,3,3,
3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,6]);
ALN("P11/G1/L1/V1/ext3",["3^6.L3(2)v1"]);
MOT("P11/G1/L1/V1/ext4",
[
"origin: Hanrath library,\n",
"structure is 4^6.L3(2)"
],
[688128,16384,32768,12288,4096,4096,4096,24576,4096,8192,4096,16384,8192,4096,
4096,4096,4096,4096,12288,16384,4096,12288,4096,4096,8192,4096,49152,49152,
98304,12288,98304,4096,4096,16384,16384,4096,8192,4096,8192,16384,16384,16384,
512,512,512,512,128,128,512,512,512,512,128,128,128,128,128,128,128,128,512,
512,512,512,128,128,512,512,512,512,48,48,48,48,48,48,48,48,48,48,48,48,48,48,
48,48,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,7,7],
[,[1,3,1,8,3,8,3,1,3,3,8,29,3,8,3,8,29,3,29,31,8,31,8,31,3,3,29,31,1,8,1,8,8,
29,31,8,29,8,31,29,3,31,1,1,1,1,34,34,29,29,29,29,2,2,35,35,41,41,20,20,3,3,3,
3,12,12,31,31,31,31,71,73,71,73,79,81,79,81,71,73,71,73,79,81,79,81,43,62,43,
62,51,70,51,70,43,62,43,62,51,70,51,70,103,104],[1,2,3,4,5,6,7,8,9,10,11,12,
13,23,15,16,17,18,19,20,21,22,14,24,25,26,27,28,29,30,31,33,32,34,35,36,37,38,
39,40,41,42,43,44,45,46,47,48,49,50,51,52,54,53,55,56,58,57,59,60,61,62,63,64,
65,66,67,68,69,70,1,22,31,22,19,30,27,4,29,28,8,28,19,4,27,30,87,88,89,90,91,
92,93,94,95,96,97,98,99,100,101,102,104,103],,,,[1,2,3,4,5,6,7,8,9,10,11,12,
13,23,15,16,17,18,19,20,21,22,14,24,25,26,27,28,29,30,31,33,32,34,35,36,37,38,
39,40,41,42,43,44,45,46,47,48,49,50,51,52,54,53,55,56,58,57,59,60,61,62,63,64,
65,66,67,68,69,70,71,74,73,72,83,86,85,84,79,82,81,80,75,78,77,76,87,88,89,90,
91,92,93,94,95,96,97,98,99,100,101,102,1,1]],
0,
[(103,104),( 72, 74)( 75, 83)( 76, 86)( 77, 85)( 78, 84)( 80, 82),( 53, 54)
( 57, 58),( 32, 33),( 14, 23),( 88, 90)( 91, 99)( 92,102)( 93,101)( 94,100)
( 96, 98),( 87, 89)( 91,101)( 92,100)( 93, 99)( 94,102)( 95, 97),( 87, 95)
( 88, 96)( 89, 97)( 90, 98)( 91, 99)( 92,100)( 93,101)( 94,102),( 5, 7)
( 12, 20)( 13, 25)( 15, 26)( 16, 21)( 17, 24)( 19, 22)( 27, 28)( 29, 31)
( 34, 35)( 36, 38)( 37, 39)( 40, 42)( 45, 46)( 47, 55)( 48, 56)( 49, 67)
( 50, 68)( 51, 70)( 52, 69)( 57, 58)( 59, 65)( 60, 66)( 63, 64)( 72, 75)
( 73, 79)( 74, 83)( 77, 80)( 78, 84)( 82, 85)( 91,100)( 92,101)( 93,102)
( 94, 99)( 95, 97)( 96, 98),( 2, 41)( 4, 30)( 6, 11)( 9, 18)( 14, 32)
( 16, 36)( 21, 38)( 23, 33)( 53, 57)( 54, 58)( 75, 83)( 76, 84)( 77, 85)
( 78, 86)( 88, 96)( 90, 98)( 91, 99)( 93,101)],
["ConstructClifford",[[[1,2,3,4,5,6],[1,2,3,2,4],[1,2,3,2,4],[1,2,3,3],[1,2,3,
3],[1,2,4,2,2],[1,3,2],[1,4,2,4],[1,4,2,4],[1,4,2,4],[1,4,2,4],[1,4,2,4],[1,4,
2,4],[1,2,2,2],[1,2,2,2],[1,3,3],[1,3,3],[1,3,3],[1,3,3],[1,2],[1,2],[1,2],[1,
2],[1,2],[1],[1],[1],[1],[1],[1],[1],[1],[1],[1],[1],[1],[1],[1],[1],[1],[1],[
1]],[["L3(2)"],["Symm(4)"],["Symm(4)"],["A4"],["A4"],["D8"],["S3"],["Cyclic",
4],["Cyclic",4],["Cyclic",4],["Cyclic",4],["Cyclic",4],["Cyclic",
4],["V4"],["V4"],["Cyclic",3],["Cyclic",3],["Cyclic",3],["Cyclic",
3],["Cyclic",2],["Cyclic",2],["Cyclic",2],["Cyclic",2],["Cyclic",2],["Cyclic",
1],["Cyclic",1],["Cyclic",1],["Cyclic",1],["Cyclic",1],["Cyclic",1],["Cyclic",
1],["Cyclic",1],["Cyclic",1],["Cyclic",1],["Cyclic",1],["Cyclic",1],["Cyclic",
1],["Cyclic",1],["Cyclic",1],["Cyclic",1],["Cyclic",1],["Cyclic",1]],[[[1,2,3,
4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,
32,33,34,35,36,37,38,39,40,41,42],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],["elab",42,1]],[[1,2,2,3,3,4,5,6,6,
6,7,8,9,10,11,12,13,14,14,14,15,15,15,20,21,22,23,24],[2,2,4,2,4,2,2,2,4,5,3,
3,3,3,3,3,3,2,3,4,2,3,4,2,2,2,2,2],["elab",28,1]],[[1,2,3,4,4,5,5,7,16,16,17,
17,18,18,19,19],[3,3,3,3,4,3,4,2,2,3,2,3,2,3,2,3],["elab",16,1,( 2, 4)
( 3,13,15,11, 7,14,16, 6, 5)( 8, 9)]],[[1,2,3,6,8,8,9,9,10,10,11,11,12,12,13,
13],[4,5,5,3,2,4,2,4,2,4,2,4,2,4,2,4],["elab",16,1,( 2,16, 9)( 3,13,11,10, 8,
7,14,12, 6,15, 5)]],[[1],[5]],[[1],[6]]]]]);
ALF("P11/G1/L1/V1/ext4","L3(2)",[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,
2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,
4,4,4,4,4,4,4,4,5,6]);
ALN("P11/G1/L1/V1/ext4",["4^6.L3(2)v1"]);
MOT("P11/G1/L1/V2/ext2",
[
"origin: Hanrath library,\n",
"structure is 2^6.L3(2)"
],
[10752,512,384,1536,1536,64,32,64,128,128,64,128,64,128,12,12,12,12,16,16,16,
16,7,7],
[,[1,1,1,1,1,1,5,2,4,4,1,4,2,4,15,15,15,15,9,14,12,10,23,24],[1,2,3,4,5,6,7,8,
9,10,11,12,13,14,1,5,4,3,19,20,21,22,24,23],,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,
14,15,16,17,18,19,20,21,22,1,1]],
0,
[(23,24),(8,13)(9,12)(10,14)(19,21)(20,22),(6,11)(9,10)(12,14)(19,22)(20,21)],
["ConstructClifford",[[[1,2,3,4,5,6],[1,2,3,2,4],[1,2,3,2,4],[1,2,4,2,2],[1,3,
2]],[["L3(2)"],["Symm(4)"],["Symm(4)"],["D8"],["S3"]],[[[1,2,3,4,5],[1,1,1,1,
1],["elab",5,8,(2,4),(2,4)(3,5)]],[[1,2,2,3,3,4,4,4,5],[2,2,4,2,4,2,4,5,3],
["elab",9,7]],[[1,2,3,5],[3,3,3,2],["elab",4,12,(3,4)]],[[1,2,3,4],[4,5,5,3],
["elab",4,22]],[[1],[5]],[[1],[6]]]]]);
ALF("P11/G1/L1/V2/ext2","L3(2)",[1,1,1,1,1,2,2,2,2,2,2,2,2,2,3,3,3,3,4,4,
4,4,5,6]);
ALN("P11/G1/L1/V2/ext2",["2^6.L3(2)v2"]);
MOT("P11/G1/L1/V2/ext4",
[
"origin: Hanrath library,\n",
"structure is 4^6.L3(2)"
],
[688128,16384,32768,12288,4096,4096,4096,24576,4096,8192,4096,16384,8192,4096,
4096,4096,4096,4096,12288,16384,4096,12288,4096,4096,8192,4096,49152,49152,
98304,12288,98304,4096,4096,16384,16384,4096,8192,4096,8192,16384,16384,16384,
256,256,256,256,256,256,256,256,128,128,128,128,128,128,128,128,256,256,256,
256,256,256,256,256,48,48,48,48,48,48,48,48,48,48,48,48,48,48,48,48,64,64,64,
64,64,64,64,64,64,64,64,64,64,64,64,64,7,7],
[,[1,3,1,8,3,8,3,1,3,3,8,29,3,8,3,8,29,3,29,31,8,31,8,31,3,3,29,31,1,8,1,8,8,
29,31,8,29,8,31,29,3,31,1,1,34,34,34,34,29,29,2,2,35,35,41,41,20,20,3,3,12,12,
12,12,31,31,67,69,67,69,75,77,75,77,67,69,67,69,75,77,75,77,63,48,63,48,61,46,
61,46,63,48,63,48,61,46,61,46,99,100],[1,2,3,4,5,6,7,8,9,10,11,12,13,23,15,16,
17,18,19,20,21,22,14,24,25,26,27,28,29,30,31,33,32,34,35,36,37,38,39,40,41,42,
43,44,45,46,47,48,49,50,51,52,54,53,55,56,58,57,59,60,61,62,63,64,65,66,1,22,
31,22,19,30,27,4,29,28,8,28,19,4,27,30,91,92,93,94,95,96,97,98,83,84,85,86,87,
88,89,90,100,99],,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,23,15,16,17,18,19,20,21,22,
14,24,25,26,27,28,29,30,31,33,32,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,
49,50,51,52,54,53,55,56,58,57,59,60,61,62,63,64,65,66,67,70,69,68,79,82,81,80,
75,78,77,76,71,74,73,72,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,1,1]],
0,
[( 99,100),( 83, 85)( 84, 86)( 87, 89)( 88, 90)( 91, 93)( 92, 94)( 95, 97)
( 96, 98),( 68, 70)( 71, 79)( 72, 82)( 73, 81)( 74, 80)( 76, 78),( 53, 54)
( 57, 58),( 32, 33),( 14, 23),( 83, 91)( 84, 92)( 85, 93)( 86, 94)( 87, 95)
( 88, 96)( 89, 97)( 90, 98),( 45, 47)( 46, 48)( 51, 52)( 55, 56)( 61, 63)
( 62, 64)( 83, 87)( 84, 90)( 85, 89)( 86, 88)( 91, 95)( 92, 98)( 93, 97)
( 94, 96),( 2, 41)( 4, 30)( 6, 11)( 9, 18)( 14, 32)( 16, 36)( 21, 38)
( 23, 33)( 51, 55)( 52, 56)( 71, 79)( 72, 80)( 73, 81)( 74, 82)( 84, 94)
( 86, 92)( 88, 98)( 90, 96)],
["ConstructClifford",[[[1,2,3,4,5,6],[1,2,3,2,4],[1,2,3,2,4],[1,2,3,3],[1,2,3,
3],[1,2,4,2,2],[1,3,2],[1,4,2,4],[1,4,2,4],[1,4,2,4],[1,4,2,4],[1,4,2,4],[1,4,
2,4],[1,2,2,2],[1,2,2,2],[1,3,3],[1,3,3],[1,3,3],[1,3,3],[1,2],[1,2],[1,2],[1,
2],[1,2],[1],[1],[1],[1],[1],[1],[1],[1],[1],[1],[1],[1],[1],[1],[1],[1],[1],[
1]],[["L3(2)"],["Symm(4)"],["Symm(4)"],["projectives","a4","2.L2(3)"],["A4"],
["D8"],["S3"],["Cyclic",4],["Cyclic",4],["Cyclic",4],["Cyclic",4],["Cyclic",
4],["Cyclic",4],["projectives","V4","Q8"],["V4"],["Cyclic",3],["Cyclic",
3],["Cyclic",3],["Cyclic",3],["Cyclic",2],["Cyclic",2],["Cyclic",2],["Cyclic",
2],["Cyclic",2],["Cyclic",1],["Cyclic",1],["Cyclic",1],["Cyclic",1],["Cyclic",
1],["Cyclic",1],["Cyclic",1],["Cyclic",1],["Cyclic",1],["Cyclic",1],["Cyclic",
1],["Cyclic",1],["Cyclic",1],["Cyclic",1],["Cyclic",1],["Cyclic",1],["Cyclic",
1],["Cyclic",1]],[[[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,
23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42],[1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],["elab",
42,1]],[[1,2,2,3,3,5,6,6,6,7,8,9,10,11,12,13,15,15,15,20,21,22,23,24],[2,2,4,
2,4,2,2,4,5,3,3,3,3,3,3,3,2,3,4,2,2,2,2,2],["elab",24,1]],[[1,2,3,4,4,5,5,7,
16,16,17,17,18,18,19,19],[3,3,3,3,4,3,4,2,2,3,2,3,2,3,2,3],["elab",16,1,
( 2, 4)( 3,13,15,11, 7,14,16, 6, 5)( 8, 9)]],[[1,2,3,6,8,8,9,9,10,10,11,11,12,
12,13,13],[4,5,5,3,2,4,2,4,2,4,2,4,2,4,2,4],["elab",16,2]],[[1],[5]],[[1],[
6]]]]]);
ALF("P11/G1/L1/V2/ext4","L3(2)",[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,
2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,
4,4,4,4,5,6]);
ALN("P11/G1/L1/V2/ext4",["4^6.L3(2)v2"]);
MOT("P11/G1/L1/V3/ext2",
[
"origin: Hanrath library,\n",
"structure is 2^6.L3(2)"
],
[10752,512,384,1536,1536,128,64,32,64,64,128,64,128,128,12,12,12,12,16,16,16,
16,7,7],
[,[1,1,1,1,1,2,4,1,5,5,2,4,2,2,15,15,15,15,11,13,14,6,23,24],[1,2,3,4,5,6,7,8,
9,10,11,12,13,14,1,5,4,3,19,20,21,22,24,23],,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,
14,15,16,17,18,19,20,21,22,1,1]],
0,
[(23,24),( 6,11)( 9,10)(13,14)(19,22)(20,21),( 6,13)( 7,12)(11,14)(19,21)
(20,22),( 4, 5)( 7,10)( 9,12)(11,13)(16,17)(19,20)],
["ConstructClifford",[[[1,2,3,4,5,6],[1,2,3,2,4],[1,2,3,2,4],[1,2,4,2,2],[1,3,
2]],[["L3(2)"],["Symm(4)"],["Symm(4)"],["D8"],["S3"]],[[[1,2,3,4,5],[1,1,1,1,
1],["elab",5,8,(2,4),(2,4)(3,5)]],[[1,2,2,3,3,4,4,4,5],[2,2,4,2,4,2,4,5,3],
["elab",9,8]],[[1,2,3,5],[3,3,3,2],["elab",4,12,(3,4)]],[[1,2,3,4],[4,5,5,3],
["elab",4,12,(2,4,3)]],[[1],[5]],[[1],[6]]]]]);
ALF("P11/G1/L1/V3/ext2","L3(2)",[1,1,1,1,1,2,2,2,2,2,2,2,2,2,3,3,3,3,4,4,
4,4,5,6]);
ALN("P11/G1/L1/V3/ext2",["2^6.L3(2)v3"]);
MOT("P11/G1/L1/V3/ext4",
[
"origin: Hanrath library,\n",
"structure is 4^6.L3(2)"
],
[688128,16384,32768,12288,4096,4096,4096,24576,4096,8192,4096,16384,8192,4096,
4096,4096,4096,4096,12288,16384,4096,12288,4096,4096,8192,4096,49152,49152,
98304,12288,98304,4096,4096,16384,16384,4096,8192,4096,8192,16384,16384,16384,
256,256,256,256,128,128,256,256,256,256,128,128,128,128,128,128,128,128,128,
128,48,48,48,48,48,48,48,48,48,48,48,48,48,48,48,48,64,64,64,64,64,64,64,64,
64,64,64,64,64,64,64,64,7,7],
[,[1,3,1,8,3,8,3,1,3,3,8,29,3,8,3,8,29,3,29,31,8,31,8,31,3,3,29,31,1,8,1,8,8,
29,31,8,29,8,31,29,3,31,2,2,2,2,35,35,41,41,41,41,20,20,3,12,12,31,1,34,34,29,
63,65,63,65,71,73,71,73,63,65,63,65,71,73,71,73,46,45,46,45,50,49,50,49,46,45,
46,45,50,49,50,49,95,96],[1,2,3,4,5,6,7,8,9,10,11,12,13,23,15,16,17,18,19,20,
21,22,14,24,25,26,27,28,29,30,31,33,32,34,35,36,37,38,39,40,41,42,43,44,45,46,
47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,1,22,31,22,19,30,27,4,29,28,8,
28,19,4,27,30,81,82,79,80,85,86,83,84,89,90,87,88,93,94,91,92,96,95],,,,[1,2,
3,4,5,6,7,8,9,10,11,12,13,23,15,16,17,18,19,20,21,22,14,24,25,26,27,28,29,30,
31,33,32,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,
57,58,59,60,61,62,63,66,65,64,75,78,77,76,71,74,73,72,67,70,69,68,79,80,81,82,
83,84,85,86,87,88,89,90,91,92,93,94,1,1]],
0,
[(95,96),(64,66)(67,75)(68,78)(69,77)(70,76)(72,74),(32,33),(14,23),(79,81)
(80,82)(83,85)(84,86)(87,89)(88,90)(91,93)(92,94),(79,87)(80,88)(81,89)(82,90)
(83,91)(84,92)(85,93)(86,94),(43,44)(45,46)(47,48)(49,50)(51,52)(53,54)(56,57)
(60,61)(79,80)(81,82)(83,92)(84,91)(85,94)(86,93)(87,88)(89,90),( 5, 7)(12,20)
(13,25)(15,26)(16,21)(17,24)(19,22)(27,28)(29,31)(34,35)(36,38)(37,39)(40,42)
(45,46)(47,60)(48,61)(51,52)(53,56)(54,57)(58,62)(64,67)(65,71)(66,75)(69,72)
(70,76)(74,77)(79,80)(81,82)(84,86)(87,90)(88,89)(91,93),( 2,41)( 4,30)( 6,11)
( 9,18)(14,32)(16,36)(21,38)(23,33)(43,51)(44,52)(45,49)(46,50)(56,57)(60,61)
(67,75)(68,76)(69,77)(70,78)(79,83)(80,92)(81,85)(82,94)(84,88)(86,90)(87,91)
(89,93)],
["ConstructClifford",[[[1,2,3,4,5,6],[1,2,3,2,4],[1,2,3,2,4],[1,2,3,3],[1,2,3,
3],[1,2,4,2,2],[1,3,2],[1,4,2,4],[1,4,2,4],[1,4,2,4],[1,4,2,4],[1,4,2,4],[1,4,
2,4],[1,2,2,2],[1,2,2,2],[1,3,3],[1,3,3],[1,3,3],[1,3,3],[1,2],[1,2],[1,2],[1,
2],[1,2],[1],[1],[1],[1],[1],[1],[1],[1],[1],[1],[1],[1],[1],[1],[1],[1],[1],[
1]],[["L3(2)"],["Symm(4)"],["Symm(4)"],["projectives","a4","2.L2(3)"],
["projectives","a4","2.L2(3)"],["D8"],["S3"],["Cyclic",4],["Cyclic",4],
["Cyclic",4],["Cyclic",4],["Cyclic",4],["Cyclic",
4],["projectives","V4","Q8"],["projectives","V4","Q8"],["Cyclic",3],["Cyclic",
3],["Cyclic",3],["Cyclic",3],["Cyclic",2],["Cyclic",2],["Cyclic",2],["Cyclic",
2],["Cyclic",2],["Cyclic",1],["Cyclic",1],["Cyclic",1],["Cyclic",1],["Cyclic",
1],["Cyclic",1],["Cyclic",1],["Cyclic",1],["Cyclic",1],["Cyclic",1],["Cyclic",
1],["Cyclic",1],["Cyclic",1],["Cyclic",1],["Cyclic",1],["Cyclic",1],["Cyclic",
1],["Cyclic",1]],[[[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,
23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42],[1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],["elab",
42,1]],[[1,2,2,3,3,6,6,6,7,8,9,10,11,12,13,20,21,22,23,24],[2,2,4,2,4,2,4,5,3,
3,3,3,3,3,3,2,2,2,2,2],["elab",20,1]],[[1,2,3,4,4,5,5,7,16,16,17,17,18,18,19,
19],[3,3,3,3,4,3,4,2,2,3,2,3,2,3,2,3],["elab",16,3]],[[1,2,3,6,8,8,9,9,10,10,
11,11,12,12,13,13],[4,5,5,3,2,4,2,4,2,4,2,4,2,4,2,4],["elab",16,4]],[[1],[
5]],[[1],[6]]]]]);
ALF("P11/G1/L1/V3/ext4","L3(2)",[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,
2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,
5,6]);
ALN("P11/G1/L1/V3/ext4",["4^6.L3(2)v3"]);
MOT("P11/G2/L1/V1/ext2",
[
"origin: Hanrath library,\n",
"structure is 2^6.L3(2)"
],
[10752,512,1536,384,1536,128,64,128,64,32,64,64,128,128,12,12,12,12,16,16,16,
16,7,7],
[,[1,1,1,1,1,1,2,1,2,2,1,3,3,3,15,15,15,15,6,8,14,13,23,24],[1,2,3,4,5,6,7,8,
9,10,11,12,13,14,1,5,4,3,19,20,21,22,24,23],,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,
14,15,16,17,18,19,20,21,22,1,1]],
0,
[(23,24),( 6, 8)( 7, 9)(13,14)(19,20)(21,22)],
["ConstructClifford",[[[1,2,3,4,5,6],[1,2,3,2,4],[1,2,3,2,4],[1,2,4,2,2],[1,3,
2]],[["L3(2)"],["Symm(4)"],["Symm(4)"],["D8"],["S3"]],[[[1,2,3,4,5],[1,1,1,1,
1],["elab",5,18]],[[1,2,2,3,3,4,4,4,5],[2,2,4,2,4,2,4,5,3],["elab",9,1,(2,4,8,
5)(3,7),(2,3,8,4,9,5,6,7)]],[[1,2,3,5],[3,3,3,2],["elab",4,12,(2,3)]],[[1,2,3,
4],[4,5,5,3],["elab",4,12,(3,4)]],[[1],[5]],[[1],[6]]]]]);
ALF("P11/G2/L1/V1/ext2","L3(2)",[1,1,1,1,1,2,2,2,2,2,2,2,2,2,3,3,3,3,4,4,
4,4,5,6]);
ALN("P11/G2/L1/V1/ext2",["2^6.L3(2)v4"]);
MOT("P11/G2/L1/V1/ext3",
[
"origin: Hanrath library,\n",
"structure is 3^6.L3(2)"
],
[122472,2916,4374,4374,2916,17496,1458,1458,1458,5832,17496,5832,1458,17496,
1458,4374,4374,17496,5832,5832,648,324,324,162,162,324,162,324,162,324,648,
324,162,324,162,648,324,324,648,324,324,162,162,324,324,648,324,162,648,324,
648,324,324,324,648,648,27,27,27,27,27,27,27,27,27,36,36,36,36,36,36,36,36,36,
7,7],
[,[1,2,4,3,5,11,8,7,13,12,6,10,9,18,15,17,16,14,20,19,1,20,19,4,13,14,3,18,9,
5,6,19,8,10,7,11,12,20,18,12,6,15,17,2,5,10,2,16,20,2,14,11,10,5,19,12,57,59,
58,63,65,64,60,62,61,21,55,49,39,31,56,51,46,36,75,76],[1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,
21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,1,14,18,6,17,4,11,3,16,66,66,
66,66,66,66,66,66,66,76,75],,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,
19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,
45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,
71,72,73,74,1,1]],
0,
[(75,76),( 3, 4)( 6,11)( 7, 8)( 9,13)(10,12)(14,18)(16,17)(19,20)(22,23)
(24,27)(25,29)(26,28)(31,36)(32,38)(33,35)(34,37)(39,51)(40,53)(41,52)(43,48)
(44,47)(45,54)(46,56)(49,55)(58,59)(60,63)(61,65)(62,64)(67,68)(69,72)(70,74)
(71,73),( 2, 5)( 3,16, 4,17)( 6,14,11,18)( 7, 9, 8,13)(10,19,12,20)
(22,34,23,37)(24,43,27,48)(25,35,29,33)(26,52,28,41)(30,50)(31,51,36,39)
(32,40,38,53)(44,54,47,45)(46,55,56,49)(58,63,59,60)(61,64,65,62)(67,71,68,73)
(69,70,72,74)],
["ConstructClifford",[[[1,2,3,4,5,6],[1,2,3,2,4],[1,2,3,2,4],[1,2,3,2,4],[1,2,
3,2,4],[1,2,4,2,2],[1,2,4,2,2],[1,2,4,2,2],[1,2,4,2,2],[1,3,2],[1,3,2],[1,3,
2],[1,3,2],[1,2,2,2],[1,2,2,2],[1,2],[1,2],[1,2],[1,2],[1,2]],[["L3(2)"],
["Symm(4)"],["Symm(4)"],["Symm(4)"],["Symm(4)"],["D8"],["D8"],["D8"],["D8"],
["S3"],["S3"],["S3"],["S3"],["V4"],["V4"],["Cyclic",2],["Cyclic",2],["Cyclic",
2],["Cyclic",2],["Cyclic",2]],[[[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,
19,20],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],["elab",20,2]],[[1,2,2,3,3,4,
4,5,5,6,6,6,7,7,7,8,8,8,9,9,9,10,11,12,13,14,14,14,15,15,15,16,17,18,19,20],
[2,2,4,2,4,2,4,2,4,2,4,5,2,4,5,2,4,5,2,4,5,3,3,3,3,2,3,4,2,3,4,2,2,2,2,2],
["elab",36,5]],[[1,2,3,4,5,10,11,12,13],[3,3,3,3,3,2,2,2,2],["elab",9,5,(2,4,
5,7)(3,6)(8,9)]],[[1,2,3,4,5,6,7,8,9],[4,5,5,5,5,3,3,3,3],["elab",9,5,(2,3,4)
(6,7)]],[[1],[5]],[[1],[6]]]]]);
ALF("P11/G2/L1/V1/ext3","L3(2)",[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,
3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,6]);
ALN("P11/G2/L1/V1/ext3",["3^6.L3(2)v2"]);
MOT("P11/G2/L1/V2/ext2",
[
"origin: Hanrath library,\n",
"structure is 2^6.L3(2)"
],
[10752,512,1536,384,1536,64,128,64,128,64,32,64,128,128,12,12,12,12,16,16,16,
16,7,7],
[,[1,1,1,1,1,3,5,3,5,5,3,2,2,2,15,15,15,15,9,7,13,14,23,24],[1,2,3,4,5,8,9,6,
7,10,11,12,14,13,1,5,4,3,20,19,22,21,24,23],,,,[1,2,3,4,5,8,9,6,7,10,11,12,14,
13,15,16,17,18,20,19,22,21,1,1]],
0,
[(23,24),( 6, 8)( 7, 9)(13,14)(19,20)(21,22)],
["ConstructClifford",[[[1,2,3,4,5,6],[1,2,3,2,4],[1,2,3,2,4],[1,2,4,2,2],[1,3,
2]],[["L3(2)"],["Symm(4)"],["Symm(4)"],["D8"],["S3"]],[[[1,2,3,4,5],[1,1,1,1,
1],["elab",5,18]],[[1,2,2,3,3,4,4,4,5],[2,2,4,2,4,2,4,5,3],["elab",9,9]],[[1,
2,3,5],[3,3,3,2],["elab",4,12,(2,3)]],[[1,2,3,4],[4,5,5,3],["elab",4,21,,(1,3,
2)]],[[1],[5]],[[1],[6]]]]]);
ALF("P11/G2/L1/V2/ext2","L3(2)",[1,1,1,1,1,2,2,2,2,2,2,2,2,2,3,3,3,3,4,4,
4,4,5,6]);
ALN("P11/G2/L1/V2/ext2",["2^6.L3(2)v5"]);
MOT("P11/G3/L1/V1/ext2",
[
"origin: Hanrath library,\n",
"structure is 2^7.L3(2)"
],
[21504,768,1536,512,1536,768,21504,128,128,64,64,64,32,128,128,64,24,24,24,24,
24,24,24,24,16,16,16,16,14,14,14,14],
[,[1,1,1,1,1,1,1,1,7,3,3,5,4,1,7,5,17,17,17,17,17,17,17,17,8,9,15,14,29,29,31,
31],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,1,7,2,6,5,5,3,3,25,26,27,28,31,32,
29,30],,,,[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,
26,27,28,1,7,1,7]],
0,
[(29,31)(30,32),(21,22)(23,24),( 8,14)( 9,15)(10,11)(12,16)(25,28)(26,27),
( 3, 5)( 9,15)(10,12)(11,16)(21,23)(22,24)(26,27)],
["ConstructClifford",[[[1,2,3,4,5,6],[1,2,3,2,4],[1,2,3,2,4],[1,5,6,3,3],[1,2,
4,2,2],[1,3,2],[1,3,3]],[["L3(2)"],["Symm(4)"],["Symm(4)"],["7:3"],["D8"],
["S3"],["Cyclic",3]],[[[1,2,3,4,5,6,7],[1,1,1,1,1,1,1],["elab",7,9]],[[1,2,2,
3,3,5,5,5,6],[2,2,4,2,4,2,4,5,3],["elab",9,1,(2,6)(3,8)(4,7,5),(3,8,4,7)(6,9)
]],[[1,2,3,4,4,6,7,7],[3,3,3,4,5,2,2,3],["elab",8,6]],[[1,2,3,5],[4,5,5,3],
["elab",4,12,(2,3,4)]],[[1,4],[5,2],[[1,1],[1,-1]]],[[1,4],[6,3],[[1,1],[1,-1]
]]]]]);
ALF("P11/G3/L1/V1/ext2","L3(2)",[1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,3,3,3,3,
3,3,3,3,4,4,4,4,5,5,6,6]);
ALN("P11/G3/L1/V1/ext2",["2^7.L3(2)v1"]);
MOT("P11/G3/L1/V1/ext3",
[
"origin: Hanrath library,\n",
"structure is 3^7.L3(2)"
],
[367416,6561,6561,6561,4374,2187,4374,4374,2187,6561,6561,6561,2187,6561,
13122,2187,2187,2187,6561,13122,2187,2187,45927,26244,8748,26244,45927,216,54,
54,54,54,54,108,108,108,81,81,81,81,81,81,81,81,81,81,81,81,81,81,81,81,81,81,
81,81,81,81,81,81,81,81,81,12,12,12,21,21,21,21,21,21],
[,[1,2,4,3,5,6,7,8,13,14,12,11,9,10,20,16,17,18,19,15,22,21,27,24,25,26,23,1,
15,20,8,5,7,24,25,26,37,51,62,53,55,42,60,44,46,45,47,58,49,63,38,56,40,54,41,
52,57,48,59,43,61,39,50,28,35,35,67,69,68,70,72,71],[1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,28,28,28,28,28,28,28,28,28,1,15,20,4,3,19,3,19,
4,3,19,4,1,15,20,4,3,19,4,3,19,3,19,4,1,15,20,64,64,64,70,70,70,67,67,67],,,,[
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,
56,57,58,59,60,61,62,63,64,66,65,1,27,23,1,27,23]],
0,
[(67,70)(68,71)(69,72),(65,66),(38,62)(39,51)(40,60)(41,46)(42,44)(43,53)
(45,55)(47,57)(48,52)(49,61)(54,59)(56,58),(37,49)(39,63)(40,45)(41,58)(42,47)
(43,56)(44,54)(46,53)(48,55)(50,62)(52,60)(57,59),( 5, 8)(10,12)(11,14)(16,18)
(24,26)(31,32)(34,36)(40,45)(41,43)(42,44)(46,53)(47,54)(48,52)(55,60)(56,58)
(57,59),( 3, 4)( 9,13)(10,14)(11,12)(15,20)(21,22)(23,27)(29,30)(38,39)(40,43)
(41,45)(42,44)(46,55)(47,57)(48,56)(49,61)(50,63)(51,62)(52,58)(53,60)(54,59)
(68,69)(71,72)],
["ConstructClifford",[[[1,2,3,4,5,6],[1,5,6,3,3],[1,5,6,3,
3],[1,2,3,3],[1,2,3,3],[1,3,2],[1,3,2],[1,4,2,4],[1,3,3],[1,3,3],[1,3,3],[1,3,
3],[1,3,3],[1,3,3],[1,3,3],[1,3,3],[1,2],[1,2],[1,2],[1],[1],[1],[1],[1],[1],[
1],[1]],[["L3(2)"],["7:3"],["7:3"],["A4"],["A4"],["S3"],["S3"],["Cyclic",
4],["Cyclic",3],["Cyclic",3],["Cyclic",3],["Cyclic",3],["Cyclic",3],["Cyclic",
3],["Cyclic",3],["Cyclic",3],["Cyclic",2],["Cyclic",2],["Cyclic",2],["Cyclic",
1],["Cyclic",1],["Cyclic",1],["Cyclic",1],["Cyclic",1],["Cyclic",1],["Cyclic",
1],["Cyclic",1]],[[[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,
23,24,25,26,27],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1],["elab",27,2]],[[1,4,5,6,7,8,17,18,19],[2,2,2,3,3,3,2,2,2],["elab",9,
10]],[[1,2,2,3,3,4,4,5,5,6,7,9,9,10,10,11,11,12,12,13,13,14,14,15,15,16,16],[
3,4,5,4,5,3,4,3,4,2,2,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3],["elab",27,3]],[[1,8,
8],[4,2,4],["elab",3,1,(2,3)]],[[1,2,3],[5,2,2],["elab",3,1]],[[1,2,3],[6,3,
3],["elab",3,1]]]]]);
ALF("P11/G3/L1/V1/ext3","L3(2)",[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,
3,3,3,3,3,3,4,4,4,5,5,5,6,6,6]);
ALN("P11/G3/L1/V1/ext3",["3^7.L3(2)v1"]);
MOT("P11/G3/L1/V2/ext3",
[
"origin: Hanrath library,\n",
"structure is 3^7.L3(2)"
],
[367416,6561,6561,6561,4374,2187,4374,4374,2187,6561,6561,6561,2187,6561,
13122,2187,2187,2187,6561,13122,2187,2187,45927,26244,8748,26244,45927,54,54,
216,54,54,54,108,108,108,81,81,81,81,81,81,81,81,81,81,81,81,81,81,81,81,81,
81,81,81,81,81,81,81,81,81,81,12,12,12,21,21,21,21,21,21],
[,[1,2,4,3,5,6,7,8,13,14,12,11,9,10,20,16,17,18,19,15,22,21,27,24,25,26,23,15,
20,1,5,7,8,24,25,26,62,37,51,42,53,55,46,60,44,58,45,47,38,49,63,54,56,40,57,
41,52,43,48,59,50,61,39,35,35,30,67,69,68,70,72,71],[1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,30,30,30,30,30,30,30,30,30,23,27,2,12,26,11,24,
14,10,24,14,10,23,27,2,12,26,11,12,26,11,24,14,10,23,27,2,66,66,66,70,70,70,
67,67,67],,[1,2,4,3,5,6,7,8,13,14,12,11,9,10,20,16,17,18,19,15,22,21,27,24,25,
26,23,29,28,30,31,32,33,34,35,36,38,49,63,54,56,40,58,45,47,43,48,59,50,61,39,
57,41,52,42,53,55,46,60,44,62,37,51,65,64,66,70,72,71,67,69,68],,[1,2,3,4,5,6,
7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,
34,35,36,49,50,51,52,53,54,46,47,48,58,59,60,61,62,63,55,56,57,40,41,42,43,44,
45,37,38,39,65,64,66,1,27,23,1,27,23]],
0,
[(67,70)(68,71)(69,72),(64,65),( 5, 8)(10,12)(11,14)(16,18)(24,26)(31,33)
(34,36)(40,45)(41,43)(42,44)(46,53)(47,54)(48,52)(55,60)(56,58)(57,59),( 3, 4)
( 9,13)(10,14)(11,12)(15,20)(21,22)(23,27)(28,29)(37,38,49,50,61,62)(39,63,51)
(40,54,52,57,55,42)(41,56,53)(43,58,46)(44,45,47,48,59,60)(68,69)(71,72),
(37,61,49)(38,62,50)(39,63,51)(40,55,52)(41,56,53)(42,57,54)(43,58,46)
(44,59,47)(45,60,48)],
["ConstructClifford",[[[1,2,3,4,5,6],[1,5,6,3,3],[1,5,6,3,
3],[1,2,3,3],[1,2,3,3],[1,3,2],[1,3,2],[1,4,2,4],[1,3,3],[1,3,3],[1,3,3],[1,3,
3],[1,3,3],[1,3,3],[1,3,3],[1,3,3],[1,2],[1,2],[1,2],[1],[1],[1],[1],[1],[1],[
1],[1]],[["L3(2)"],["7:3"],["7:3"],["A4"],["A4"],["S3"],["S3"],["Cyclic",
4],["Cyclic",3],["Cyclic",3],["Cyclic",3],["Cyclic",3],["Cyclic",3],["Cyclic",
3],["Cyclic",3],["Cyclic",3],["Cyclic",2],["Cyclic",2],["Cyclic",2],["Cyclic",
1],["Cyclic",1],["Cyclic",1],["Cyclic",1],["Cyclic",1],["Cyclic",1],["Cyclic",
1],["Cyclic",1]],[[[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,
23,24,25,26,27],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1],["elab",27,2]],[[1,4,5,6,7,8,17,18,19],[2,2,2,3,3,3,2,2,2],["elab",9,10,
(2,6,3)(7,8,9),(1,3,2)(7,8,9)]],[[1,2,2,3,3,4,4,5,5,6,7,9,9,10,10,11,11,12,12,
13,13,14,14,15,15,16,16],[3,4,5,4,5,3,4,3,4,2,2,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,
3],["elab",27,4]],[[1,8,8],[4,2,4],["elab",3,1,(2,3),(1,3,2)]],[[1,2,3],[5,2,
2],["elab",3,1]],[[1,2,3],[6,3,3],["elab",3,1]]]]]);
ALF("P11/G3/L1/V2/ext3","L3(2)",[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,
3,3,3,3,3,3,4,4,4,5,5,5,6,6,6]);
ALN("P11/G3/L1/V2/ext3",["3^7.L3(2)v2"]);
MOT("P11/G3/L3/V1/ext2",
[
"origin: Hanrath library,\n",
"structure is 2^7.L3(2)"
],
[21504,512,3072,384,3072,1536,21504,128,64,128,64,128,128,32,64,64,24,24,24,
--> --------------------
--> maximum size reached
--> --------------------
[ Dauer der Verarbeitung: 0.20 Sekunden
(vorverarbeitet)
]
|
