Quelle  ctoholpl.tbl   Sprache: unbekannt

#############################################################################
##
#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,
24,24,24,24,24,16,16,16,16,14,14,14,14],
[,[1,1,1,1,1,1,1,1,5,3,7,1,3,2,2,2,17,17,17,17,17,17,17,17,8,12,13,10,29,29,
31,31],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,1,4,7,4,6,5,6,3,25,26,27,28,31,
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),(18,20)(21,23),( 8,12)(10,13)(15,16)(25,26)(27,28)],
["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",7,10]],[[1,2,2,3,3,5,5,5,6],[2,2,4,
2,4,2,4,5,3],["elab",9,1,(2,4,3,8,7,5,6),(2,3,5,8,4,6,9,7)]],[[1,2,3,4,4,6,7,
7],[3,3,3,4,5,2,2,3],["elab",8,6,(2,8)(3,5,7)]],[[1,2,3,5],[4,5,5,3],["elab",
4,12,(3,4)]],[[1,4],[5,2],[[1,1],[1,-1]]],[[1,4],[6,3],[[1,1],[1,-1]]]]]]);
ALF("P11/G3/L3/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/L3/V1/ext2",["2^7.L3(2)v2"]);

MOT("P11/G3/L3/V2/ext3",
[
"origin: Hanrath library,\n",
"structure is 3^7.L3(2)"
],
0,
0,
0,
0,
["ConstructPermuted",["P11/G3/L1/V2/ext3"],(),()]);
ALF("P11/G3/L3/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/L3/V2/ext3",["3^7.L3(2)v3"]);

MOT("P11/G3/L4/V2/ext2",
[
"origin: Hanrath library,\n",
"structure is 2^7.L3(2)"
],
[21504,1024,1024,768,768,3072,3072,3072,3072,21504,128,64,64,64,64,64,128,64,
128,128,24,24,24,24,24,24,24,24,32,32,32,32,32,32,32,32,14,14,14,14],
[,[1,1,1,1,1,1,1,1,1,1,2,9,6,10,10,9,2,6,2,2,23,23,23,23,23,23,23,23,11,19,19,
11,17,20,20,17,37,37,39,39],[1,2,3,4,5,6,7,8,9,10,11,12,13,15,14,16,17,18,19,
20,8,5,1,9,7,10,4,6,32,31,30,29,36,35,34,33,39,40,37,38],,,,[1,2,3,4,5,6,7,8,
9,10,11,12,13,15,14,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,
35,36,1,10,1,10]],
0,
[(37,39)(38,40),(29,32)(30,31)(33,36)(34,35),(14,15),(11,17)(12,16)(13,18)
(19,20)(29,33)(30,34)(31,35)(32,36),(11,19)(12,16)(17,20)(29,30)(31,32)(33,34)
(35,36),( 6, 9)( 7, 8)(12,13)(16,18)(19,20)(21,25)(24,28)(30,34)(31,35)],
["ConstructClifford",[[[1,2,3,4,5,6],[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],[1,3,2],[1,3,
2]],[["L3(2)"],["projectives","L3(2)","2.L3(2)"],["Symm(4)"],["projectives",
"Symm(4)","2.Symm(4)"],["Symm(4)"],["projectives","Symm(4)","2.Symm(4)"],
["D8"],["projectives","D8","2.D8"],["S3"],["S3"]],[[[1,2,3,4,5,6,7,8,9,10],[1,
1,1,1,1,1,1,1,1,1],["elab",10,5]],[[1,3,3,5,5,7,7,7,9,10],[2,2,4,2,4,2,4,5,3,
3],["elab",10,6]],[[1,2,3,4,5,6,9,10],[3,3,3,3,3,3,2,2],["elab",8,6,(2,5,3)(4,
7),(1,3,2)(6,7,8)]],[[1,2,3,4,5,6,7,8],[4,4,5,5,5,5,3,3],["elab",8,7]],[[1,2],
[5,5],[[1,1],[1,-1]]],[[1,2],[6,6],[[1,1],[1,-1]]]]]]);
ALF("P11/G3/L4/V2/ext2","L3(2)",[1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,
3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,5,5,6,6]);
ALN("P11/G3/L4/V2/ext2",["2^7.L3(2)v3"]);

MOT("P11/G3/L4/V2/ext3",
[
"origin: Hanrath library,\n",
"structure is 3^7.L3(2)"
],
0,
0,
0,
0,
["ConstructPermuted",["P11/G3/L1/V2/ext3"],(2,6,4,23,24,27,26,13,15,19,25)(3,
22,8,21,10,7)(5,16,14,12,11,9,17)(18,20)(28,30,35)(29,31,34,36,33,32)(37,58,
52)(38,45,50,54,62,63)(39,47,48,59,57,44)(40,55,46,43,61,49)(41,42,53,51,56,
60)(67,71)(68,70)(69,72),(2,3)(7,14,9,13,8,12)(10,16)(11,15)(21,22,23)(25,26)
(31,33)(35,36)(38,41)(39,43)(40,42)(44,56)(45,57)(46,58)(47,50,53)(48,51,54)
(49,52,55)(59,60)(65,66)(67,68,69)]);
ALF("P11/G3/L4/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/L4/V2/ext3",["3^7.L3(2)v4"]);

MOT("P11/G3/L4/V3/ext2",
[
"origin: Hanrath library,\n",
"structure is 2^7.L3(2)"
],
0,
0,
0,
0,
["ConstructPermuted",["P11/G3/L4/V2/ext2"],(21,23)(22,24)(25,27)(26,28)(29,33)
(30,34)(31,35)(32,36)(39,40),(9,10)(17,18)(20,21)(23,24)]);
ALF("P11/G3/L4/V3/ext2","L3(2)",[1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,
3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,5,5,6,6]);
ALN("P11/G3/L4/V3/ext2",["2^7.L3(2)v4"]);

MOT("P11/G4/L1/V1/ext2",
[
"origin: Hanrath library,\n",
"structure is 2^8.L3(2)"
],
[43008,1024,512,1536,768,2048,1792,128,32,64,32,128,64,64,12,12,12,12,16,16,
16,16,28,28,28,28,28,28,28,28],
[,[1,1,1,1,1,1,1,1,4,6,3,6,2,6,15,15,15,15,8,12,13,13,23,23,23,23,27,27,27,
27],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,1,5,4,5,19,20,22,21,27,28,29,30,23,26,
24,25],,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,22,21,1,7,7,7,1,
7,7,7]],
0,
[(21,22),(16,18),(10,14),(24,25,26)(28,29,30),(23,27)(24,28,26,30,25,29)],
["ConstructClifford",[[[1,2,3,4,5,6],[1,2,4,2,2],[1,5,5,6,
5,6,6],[1,3,2],[1,4,2,4],[1,3,3],[1,2]],[["L3(2)"],["D8"],["Cyclic",
7],["S3"],["Cyclic",4],["Cyclic",3],["Cyclic",2]],[[[1,2,3,4,5,6,7],[1,1,1,1,
1,1,1],["elab",7,11]],[[1,2,2,2,4,5,7],[2,2,4,5,3,3,2],["elab",7,5,
(2,7,4,5,6,3),(2,5,7,4,6)]],[[1,4,6,6],[3,2,2,3],["elab",4,12,(2,4)]],[[1,2,5,
5],[4,3,2,4],["elab",4,12]],[[1,3,3,3],[5,2,3,5],["elab",4,12,(2,3,4)]],[[1,3,
3,3],[6,4,6,7],["elab",4,12,(2,4)]]]]]);
ALF("P11/G4/L1/V1/ext2","L3(2)",[1,1,1,1,1,1,1,2,2,2,2,2,2,2,3,3,3,3,4,4,
4,4,5,5,5,5,6,6,6,6]);
ALN("P11/G4/L1/V1/ext2",["2^8.L3(2)"]);

MOT("P11/G4/L1/V1/ext3",
[
"origin: Hanrath library,\n",
"structure is 3^8.L3(2)"
],
[1102248,13122,19683,19683,13122,13122,39366,6561,6561,13122,39366,13122,6561,
6561,6561,6561,6561,6561,26244,13122,6561,26244,6561,6561,6561,6561,6561,6561,
6561,6561,6561,6561,13122,19683,6561,6561,6561,39366,6561,6561,19683,6561,
6561,45927,6561,13122,19683,6561,19683,45927,19683,6561,39366,19683,13122,
19683,39366,26244,26244,39366,26244,1102248,1102248,648,162,162,324,324,324,
162,162,162,162,162,324,162,162,162,162,324,162,162,648,162,324,324,162,324,
648,324,81,81,81,81,81,81,81,81,81,81,81,81,81,81,81,81,81,81,81,81,81,81,81,
81,81,81,81,36,36,36,36,36,36,36,36,36,63,63,63,63,63,63,63,63,63,63,63,63,63,
63,63,63,63,63],
[,[1,2,4,3,10,12,11,8,9,5,7,6,30,16,24,14,31,29,19,33,28,22,25,15,23,26,32,21,
18,13,17,27,20,34,42,48,45,53,52,40,49,35,43,50,37,46,51,36,41,44,47,39,38,56,
55,54,60,59,58,57,61,63,62,1,20,33,22,19,19,12,7,46,11,38,61,53,6,5,55,59,60,
57,62,2,22,19,10,58,63,22,91,114,107,102,95,115,110,103,99,117,101,94,98,109,
105,106,93,113,104,97,111,112,108,92,96,116,100,64,83,89,88,75,80,80,88,75,
127,129,128,135,134,133,131,130,132,136,138,137,144,143,142,140,139,141],[1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,64,64,64,64,64,64,64,64,64,64,64,
64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,1,49,41,41,34,11,49,7,34,41,1,
49,11,41,34,34,49,7,49,41,1,34,11,41,7,34,49,118,118,118,118,118,118,118,118,
118,136,136,136,136,136,136,136,136,136,127,127,127,127,127,127,127,127,
127],,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,
27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,
53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,
79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,
103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,125,
126,124,123,121,122,1,63,62,50,50,50,44,44,44,1,63,62,50,50,50,44,44,44]],
0,
[(121,125)(122,126)(123,124),( 92,107)( 93,114)( 94,110)( 95, 99)( 96,103)
( 97,102)( 98,115)(100,104)(101,111)(105,116)(106,112)(109,117),( 91,101,111)
( 92,102,109)( 93,100,110)( 94,104,114)( 95,105,112)( 96,103,113)( 97,107,117)
( 98,108,115)( 99,106,116),(  5,  6)( 10, 12)( 17, 35)( 19, 22)( 26, 40)
( 31, 42)( 36, 37)( 45, 48)( 46, 55)( 67, 86)( 68, 85)( 69, 90)( 70, 87)
( 72, 79)( 77, 78)( 92,109)( 93,100)( 95,112)( 96,103)( 98,115)( 99,106)
(101,111)(104,114)(107,117),(130,131,132)(133,135,134)(139,140,141)
(142,144,143),(127,136)(128,137)(129,138)(130,139,131,140,132,141)
(133,142,135,144,134,143),(  3,  4)(  5, 10)(  6, 12)(  7, 11)( 13, 30)
( 14, 16)( 15, 24)( 17, 31)( 18, 29)( 20, 33)( 21, 28)( 23, 25)( 27, 32)
( 35, 42)( 36, 48)( 37, 45)( 38, 53)( 39, 52)( 41, 49)( 44, 50)( 47, 51)
( 54, 56)( 57, 60)( 58, 59)( 62, 63)( 65, 66)( 68, 69)( 70, 77)( 71, 73)
( 74, 76)( 78, 87)( 80, 88)( 81, 82)( 83, 89)( 85, 90)( 92, 93)( 94, 97)
( 95, 99)( 96, 98)(100,109)(101,111)(102,110)(103,115)(104,117)(105,116)
(106,112)(107,114)(108,113)(119,120)(121,123)(124,125)(128,129)(130,133)
(131,135)(132,134)(137,138)(139,142)(140,144)(141,143)],
["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],[1,2,4,2,2],[1,2,4,2,2],[1,5,5,6,5,6,6],[1,5,5,6,5,6,
6],[1,3,2],[1,3,2],[1,4,2,4],[1,4,2,4],[1,4,2,4],[1,3,3],[1,3,3],[1,3,3],[1,3,
3],[1,3,3],[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],[1,2],[1,2],[1,2],[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]],[["L3(2)"],["7:3"],["7:3"],["A4"],["A4"],["D8"],["D8"],["Cyclic",
7],["Cyclic",7],["S3"],["S3"],["Cyclic",4],["Cyclic",4],["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",
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],["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,
23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,
49,50,51,52,53,54,55,56,57,58,59,60,61,62,63],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1],["elab",63,1]],[[1,4,5,6,6,6,7,7,7,10,11,12,13,14,23,24,25,
26,27,28,29,30,31,32,33,34,35],[2,2,2,2,4,5,2,4,5,3,3,3,3,3,2,2,2,2,2,2,2,2,2,
2,2,2,2],["elab",27,6]],[[1,2,2,3,3,4,4,5,5,10,11,15,15,16,16,17,17,18,18,19,
19,20,20,21,21,22,22],[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,( 2,18,10,13,21,26, 5)( 3, 4,23, 8, 6,16,20, 9, 7,14,25,11,12,
 24,15,22,27)(17,19)]],[[1,6,7,12,12,13,13,14,14],[4,3,3,2,4,2,4,2,4],["elab",
9,5,(2,3,8,4)(5,7,9)]],[[1,2,3,8,8,8,9,9,9],[5,2,2,2,3,5,2,3,5],["elab",9,5,
(2,5,7,6,9,3,4,8)]],[[1,2,3,8,8,8,9,9,9],[6,3,3,4,6,7,4,6,7],["elab",9,5,
(2,6,8)(3,4,9)(5,7)]]]]]);
ALF("P11/G4/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,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,
3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,
5,5,5,5,6,6,6,6,6,6,6,6,6]);
ALN("P11/G4/L1/V1/ext3",["3^8.L3(2)"]);

MOT("P12/G1/L2/V1/ext2",
[
"origin: Hanrath library,\n",
"structure is 2^8.2.L3(2),\n",
"characters sorted with permutation (59,60).\n",
"The table on the microfiche is incorrect:\n",
"A comparison with the table computed from the group showed that\n",
"in the 12 irreducible characters 72,73,75,76,78,79,81,82,84,85,87,88\n",
"(of degree 56), the values on the classes 51..64 had to be replaced\n",
"by their complex conjugates;\n",
"the structure constant for 12, 25, 51 was not integral."
],
[86016,1536,1024,6144,6144,6144,1536,86016,6144,86016,86016,86016,1536,86016,
1536,6144,6144,6144,1024,6144,86016,86016,96,96,96,96,96,96,96,96,96,96,96,96,
96,96,96,96,128,64,64,64,64,128,64,128,64,128,96,96,96,96,96,96,96,96,96,96,
96,96,96,96,96,96,56,56,56,56,56,56,56,56,32,32,32,32,32,32,32,32,56,56,56,56,
56,56,56,56],
[,[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,23,23,23,23,23,23,23,23,23,23,
23,23,23,23,23,23,12,18,19,16,19,14,17,21,20,22,23,23,23,23,23,23,23,23,23,23,
23,23,23,23,23,23,65,65,65,65,69,69,69,69,39,48,44,46,39,48,44,46,65,65,65,65,
69,69,69,69],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,1,8,2,
7,9,9,5,6,4,4,6,5,11,10,2,7,39,40,43,42,41,44,45,46,47,48,12,14,13,15,20,20,
18,17,16,16,17,18,21,22,13,15,69,70,71,72,65,66,67,68,77,78,79,80,73,74,75,76,
85,86,87,88,81,82,83,84],,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,
20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,43,42,41,44,45,
46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,1,10,11,8,1,10,11,8,
73,74,75,76,77,78,79,80,12,22,21,14,12,22,21,14]],
0,
[(73,77)(74,78)(75,79)(76,80),(65,69)(66,70)(67,71)(68,72)(81,85)(82,86)
(83,87)(84,88),(41,43),(25,37)(26,38)(27,28)(29,34)(30,33)(31,32)(51,63)
(52,64)(53,54)(55,60)(56,59)(57,58),( 4, 5)( 6, 9)( 8,10)(14,22)(16,18)(17,20)
(24,36)(26,38)(27,33)(28,30)(29,31)(32,34)(40,42)(44,48)(45,47)(50,62)(52,64)
(53,59)(54,56)(55,57)(58,60)(66,68)(70,72)(74,75)(78,79)(82,84)(86,88),(12,14)
(13,15)(17,18)(21,22)(39,44)(40,45)(46,48)(49,50)(51,52)(53,54)(55,56)(57,58)
(59,60)(61,62)(63,64)(65,69)(66,70)(67,71)(68,72)(73,75)(74,76)(77,79)(78,80)
(81,88)(82,87)(83,86)(84,85),(12,21)(14,22)(16,20)(17,18)(39,46)(40,45)(42,47)
(44,48)(49,61)(50,62)(51,63)(52,64)(53,57)(54,58)(55,59)(56,60)(65,69)(66,70)
(67,71)(68,72)(73,76)(74,75)(77,80)(78,79)(81,87)(82,88)(83,85)(84,86)],
["ConstructClifford",[[[1,2,4,3,5,9,8,7,11,6,10],[1,2,4,3,5,4,8,9],[1,2,4,3,5,
4,8,9],[1,2,6,10,7,11,3,5,3,5],[1,2,6,10,7,11,3,5,3,5],[1,2,6,10,7,11,3,5,3,
5],[1,2,4,8,9,4,4],[1,2,3,5,4,4],[1,5,3,2,3,5],[1,5,3,2,3,5],[1,5,3,2,3,
5]],[["2.L3(2)"],["2.Symm(4)"],["2.Symm(4)"],["2x7:3"],["2x7:3"],["2x7:3"],
["2.D8"],["2.S3"],["C6"],["C6"],["C6"]],[[[1,2,3,4,5,6,7,8,9,10,11],[1,1,1,1,
1,1,1,1,1,1,1],["elab",11,2]],[[1,2,3,4,5,6,7,8,9,10,11],[2,2,2,2,2,2,2,2,4,4,
4],["elab",11,2,,( 3, 8)( 4, 5, 7)(10,11)]],[[1,2,3,4,4,5,5,6,6,8,9,9,10,10,
11,11],[4,4,4,7,9,7,9,7,9,3,3,5,3,5,3,5],["elab",16,5]],[[1,2,2,3,3,7,7,7,8,
8],[3,3,6,3,6,3,6,7,5,6],["elab",10,1,( 2,10, 8, 5, 6, 4, 9, 7, 3),
( 2, 6, 5, 3, 8)( 4,10, 9, 7)]],[[1,2,3,4,4,5,5,6,6,8,9,9,10,10,11,11],[5,5,5,
8,10,8,10,8,10,4,2,6,2,6,2,6],["elab",16,5,(11,12)(13,14)(15,16)]],[[1,4,5,6],
[10,3,3,3],["elab",4,12,(2,3)]],[[1,4,5,6],[8,5,5,5],["elab",4,12,(2,3)]],[[1,
2,3,7],[7,7,7,4],["elab",4,12,(2,3,4)]],[[1,2,3,7],[6,8,8,5],["elab",4,12,(2,
3,4)]],[[1,4,5,6],[11,4,4,4],["elab",4,12,(2,3)]],[[1,4,5,6],[9,6,6,6],
["elab",4,12,(2,3)]]]]]);
ALF("P12/G1/L2/V1/ext2","2.L3(2)",[1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,
2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,3,3,3,3,3,3,3,3,3,3,5,5,5,5,5,5,5,5,
5,5,5,5,5,5,5,5,8,8,8,8,10,10,10,10,6,6,6,6,7,7,7,7,9,9,9,9,11,11,11,11]);
ALF("P12/G1/L2/V1/ext2","L3(2)",[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,
3,3,3,3,3,3,3,5,5,5,5,6,6,6,6,4,4,4,4,4,4,4,4,5,5,5,5,6,6,6,6]);
ALN("P12/G1/L2/V1/ext2",["2^8.2.L3(2)"]);

MOT("P12/G1/L2/V1/ext3",
[
"origin: Hanrath library,\n",
"structure is 3^8.2.L3(2)"
],
[2204496,19683,6561,6561,6561,19683,19683,6561,19683,19683,19683,6561,19683,
6561,6561,6561,6561,19683,6561,6561,19683,19683,6561,6561,19683,6561,19683,
137781,19683,19683,137781,19683,19683,137781,137781,336,486,243,243,243,243,
243,243,243,243,243,243,243,243,243,243,243,243,243,243,243,243,243,243,243,
243,243,243,243,243,243,243,243,243,243,243,243,243,243,243,243,243,8,6,126,
63,63,63,63,126,63,63,63,63,8,8,14,14],
[,[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,
29,30,31,32,33,34,35,1,37,57,76,44,68,56,52,40,49,64,71,60,45,72,77,43,67,75,
66,42,38,59,58,48,63,69,61,46,74,55,53,41,62,73,47,50,70,65,54,39,51,36,37,80,
81,82,83,84,85,86,87,88,89,78,78,80,85],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,36,1,11,11,21,21,11,21,21,11,21,21,1,11,11,
11,21,21,1,11,11,11,21,21,1,11,11,11,21,21,11,21,21,11,21,21,11,21,21,1,11,11,
78,36,85,85,85,85,85,80,80,80,80,80,91,90,93,92],,,,[1,2,3,4,5,6,7,8,9,10,11,
12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,
38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,
64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,1,28,34,35,31,1,28,34,35,31,
90,91,36,36]],
0,
[(90,91),(80,85)(81,86)(82,87)(83,88)(84,89)(92,93),(15,16),(38,57)(39,76)
(40,44)(41,68)(42,56)(43,52)(45,49)(46,64)(47,71)(48,60)(50,72)(51,77)(53,67)
(54,75)(55,66)(58,59)(61,63)(62,69)(65,74)(70,73),( 6,10)( 7, 9)(12,23)(13,32)
(14,19)(27,33)(28,31)(29,30)(39,51)(40,52)(41,53)(43,44)(45,69)(46,70)(47,71)
(48,60)(49,62)(50,61)(58,59)(63,72)(64,73)(65,74)(67,68)(76,77)(81,84)(86,89),
( 2, 6)( 3,14)( 4, 8)( 5,12)( 7,13)( 9,27)(10,18)(11,21)(17,24)(19,20)(22,25)
(23,26)(28,35)(29,32)(30,33)(31,34)(38,58)(39,71)(40,50)(41,63)(42,46)(43,62)
(44,72)(45,67)(47,76)(48,54)(49,53)(51,65)(52,69)(55,70)(56,64)(57,59)(60,75)
(61,68)(66,73)(74,77)(81,83)(82,84)(86,88)(87,89)],
["ConstructClifford",[[[1,2,4,3,5,9,8,7,11,6,10],[1,6,7,3,
3],[1,6,7,3,3],[1,6,7,3,3],[1,6,7,3,3],[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],[1,3,3],[1,3,3],[1,3,3],[1,3,3],[1,3,3],[1,
3,3],[1,3,3],[1],[1],[1],[1],[1],[1],[1],[1],[1],[1],[1],[1],[1],[
1]],[["2.L3(2)"],["7:3"],["7:3"],["7:3"],["7:3"],["Cyclic",3],["Cyclic",
3],["Cyclic",3],["Cyclic",3],["Cyclic",3],["Cyclic",3],["Cyclic",3],["Cyclic",
3],["Cyclic",3],["Cyclic",3],["Cyclic",3],["Cyclic",3],["Cyclic",3],["Cyclic",
3],["Cyclic",3],["Cyclic",3],["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],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1],["elab",35,1]],[[1],[2]],[[1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,9,10,10,11,11,
12,12,13,13,14,14,15,15,16,16,17,17,18,18,19,19,20,20,21,21],[4,4,5,4,5,4,5,4,
5,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3],["elab",41,
1]],[[1],[3]],[[1],[5]],[[1,2,3,4,5],[10,2,2,2,2],["elab",5,17,(2,4)]],[[1,2,
3,4,5],[8,3,3,3,3],["elab",5,17,(2,4)]],[[1],[7]],[[1],[6]],[[1],[11]],[[1],[
9]]]]]);
ALF("P12/G1/L2/V1/ext3","2.L3(2)",[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,
4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,3,5,8,8,8,8,8,10,10,10,10,10,6,
7,9,11]);
ALN("P12/G1/L2/V1/ext3",["3^8.2.L3(2)"]);

MOT("P13/G1/L2/V1/ext2",
[
"origin: Hanrath library,\n",
"structure is 2^7.2^3:sl(3,2),\n",
"characters sorted with permutation (45,47,49,46)(48,51,52,50)"
],
[172032,4096,3072,24576,24576,12288,172032,12288,1024,3072,4096,2048,1024,
1024,2048,3072,4096,12288,1024,512,128,256,1024,512,512,256,256,1024,1024,512,
512,256,256,128,256,512,256,512,512,256,128,128,256,128,256,256,128,256,256,
256,256,48,48,24,24,48,48,24,24,24,24,64,32,64,32,64,64,32,32,32,32,14,14,14,
14],
[,[1,1,1,1,1,1,1,1,7,7,1,1,1,7,1,7,1,1,1,5,2,2,1,5,5,1,2,1,1,5,1,7,2,2,2,4,5,
1,4,8,15,15,18,15,8,18,15,18,8,18,8,52,52,52,52,52,52,52,52,56,56,19,25,28,30,
19,28,31,39,38,36,72,72,74,74],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,
19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,
45,46,47,48,49,50,51,1,5,3,6,7,4,8,18,16,10,62,63,64,65,66,67,68,69,70,71,74,
75,72,73],,,,[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,
51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,1,7,1,7]],
0,
[(72,74)(73,75),(19,28)(22,27)(23,29)(25,30)(31,38)(33,35)(36,39)(40,49)
(41,42)(43,48)(44,47)(45,51)(46,50)(62,67)(63,65)(64,66)(68,70)(69,71),( 8,18)
( 9,14)(10,16)(11,17)(31,38)(33,35)(36,39)(40,46)(41,47)(42,44)(43,45)(48,51)
(49,50)(58,59)(60,61)(68,70)(69,71)],
["ConstructClifford",[[[1,2,3,4,5,8,9,6,7,11,10],[1,2,2,3,
4,5,6,7,3,5,5,4,8,9],[1,2,2,3,4,5,6,7,3,4,9,8,5],[1,3,6,8,11,10],[1,2,2,3,4,3,
4,2,5,5,3,5,8,4,5,9],[1,2,6,3,5,2,2,7,4,5],[1,3,6,3,
8]],[["2^3:sl(3,2)"],["2^3.S4v1"],["2^3.S4v2"],["L3(2)"],["2^3.D8"],["2^3.S3"]
,["Symm(4)"]],[[[1,2,3,4,5,6,7],[1,1,1,1,1,1,1],["elab",7,10,(2,3),(3,4)]],
[[1,2,2,3,3,5,5,5,6,6,6],[2,2,3,2,3,2,3,8,2,6,7],["elab",11,3]],[[1,2,2,3,3,4,
5,5,5,6,7,7],[3,4,9,4,9,2,4,6,11,4,2,4],["elab",12,2]],[[1,2,2,3,3,5,5,5,6],
[4,5,12,5,10,5,7,14,9],["elab",9,7,(2,4,6)(3,5),(1,5,9)(2,4,6,3)(7,8)]],[[1,2,
2,2,3,3,5,5,5,5,6,6],[5,6,10,11,6,13,9,10,12,15,5,10],["elab",12,3]],[[1,2,3,
4,6,7],[8,7,7,3,3,3],["elab",6,16,(2,6,3,4,5),(5,6)]],[[1,2,3,6],[9,8,8,8],
["elab",4,12,(2,3)]],[[1,2,3,4,5,7],[6,13,12,4,13,5],["elab",6,18]],[[1,2,3,
5],[7,14,11,16],["elab",4,22,(3,4),(2,3)]],[[1,4],[11,6],[[1,1],[1,-1]]],[[1,
4],[10,5],[[1,1],[1,-1]]]]]]);
ALF("P13/G1/L2/V1/ext2","2^3:sl(3,2)",[1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,
2,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,8,8,8,
8,8,8,9,9,9,9,6,6,6,6,6,6,7,7,7,7,11,11,10,10]);
ALF("P13/G1/L2/V1/ext2","L3(2)",[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,
2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,
3,3,3,3,4,4,4,4,4,4,4,4,4,4,6,6,5,5]);
ALN("P13/G1/L2/V1/ext2",["2^7.2^3:sl(3,2)v1"]);

MOT("P13/G1/L2/V1/ext3",
[
"origin: Hanrath library,\n",
"structure is 3^7.2^3:sl(3,2),\n",
"characters sorted with permutation (82,83)(95,97)(100,102)"
],
[2939328,34992,13122,13122,13122,104976,104976,17496,52488,8748,17496,52488,
52488,8748,52488,52488,52488,367416,367416,209952,5184,1296,1296,432,864,7776,
972,972,972,1944,486,972,486,1944,486,3888,1944,972,972,1944,972,3888,972,
1944,1944,972,1944,1944,972,1944,972,3888,1944,972,972,1944,972,1944,1944,
3888,972,1944,1944,7776,3888,3888,7776,864,216,216,108,216,216,432,48,24,162,
81,81,81,81,81,81,81,162,81,81,81,81,162,81,18,18,18,216,216,216,108,108,108,
108,108,108,108,108,108,216,216,216,216,216,216,24,12,21,21,21,21,21,21],
[,[1,2,3,5,4,7,6,11,9,10,8,12,15,14,13,17,16,19,18,20,1,7,6,2,20,1,10,10,8,18,
4,11,5,19,3,7,13,13,9,8,16,6,17,11,15,15,16,2,11,2,14,2,6,14,12,2,8,17,7,7,14,
20,12,20,2,6,20,1,6,7,10,2,9,20,21,25,77,79,78,83,81,84,80,82,90,86,91,88,89,
85,87,77,90,85,26,36,42,58,40,37,47,45,44,63,34,30,36,64,65,42,65,67,68,73,
115,117,116,118,120,119],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,21,21,21,21,
21,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,
26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,68,68,68,68,68,68,68,75,75,
1,13,15,6,3,13,7,15,6,3,15,3,1,7,13,21,22,23,95,95,95,95,95,95,95,95,95,95,95,
95,95,95,95,95,95,95,113,113,118,118,118,115,115,115],,,,[1,2,3,4,5,6,7,8,9,
10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,
36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,
62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,
88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,
110,111,112,113,114,1,18,19,1,18,19]],
0,
[(115,118)(116,119)(117,120),(  4,  5)(  6,  7)(  8, 11)( 13, 15)( 16, 17)
( 18, 19)( 22, 23)( 27, 28)( 29, 32)( 30, 34)( 31, 33)( 36, 42)( 37, 45)
( 38, 46)( 40, 44)( 41, 43)( 47, 58)( 48, 56)( 49, 57)( 51, 54)( 53, 59)
( 60, 66)( 64, 67)( 69, 70)( 78, 79)( 80, 83)( 82, 84)( 85, 90)( 87, 91)
( 93, 94)( 96, 97)( 98,101)( 99,103)(100,102)(105,106)(107,110)(108,112)
(109,111)(116,117)(119,120)],
["ConstructClifford",[[[1,2,3,4,5,8,9,6,7,11,10],[1,3,6,8,
11,10],[1,3,6,8,11,10],[1,2,3,3,4,6,3,5,8,8],[1,2,3,3,6,7,3,4,8,8],[1,2,3,3,6,
7,3,4,8,8],[1,3,6,3,8],[1,3,6,3,8],[1,3,6,3,8],[1,3,6,3,8],[1,4,6,3,9],[1,3,6,
3,8],[1,3,2,3,8,8,3,3,3,4],[1,3,8,3,3],[1,3,8,3,3],[1,6,3],[1,6,3],[1,6,3],[1,
4,3,3],[1,3,3,
3]],[["2^3:sl(3,2)"],["L3(2)"],["L3(2)"],["2^2:S4"],["2xSymm(4)"],
["2xSymm(4)"],["Symm(4)"],["Symm(4)"],["Symm(4)"],["Symm(4)"],["Symm(4)"],
["Symm(4)"],["D8x2"],
["D8"],["D8"],["S3"],["S3"],["S3"],["V4"],["V4"]],[[[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",
20,3]],[[1,4,5,6,13],[2,2,2,2,3],["elab",5,5,(3,4),(2,4,5,3)]],[[1,2,3,4,4,4,
5,5,5,6,6,6,7,7,8,8,9,9,10,10,11,12,12,13,13,13,13,13,14,14,14,15,15,15,16,17,
18,19,19,20,20,20],[3,2,2,3,4,7,3,4,7,3,4,7,2,4,2,4,2,4,2,4,4,2,4,2,4,7,8,9,2,
4,5,2,4,5,3,3,3,3,4,2,3,4],["elab",42,2]],[[1,4,5,6,11,13,19],[4,5,8,8,2,10,
2],["elab",7,12]],[[1,4],[5,8],[[1,1],[2,-1]]],[[1,2,3,4,5,6,7,8,9,10,11,12,
16,17,18],[8,3,3,6,5,5,3,3,3,3,3,3,2,2,2],["elab",15,3]],[[1,5,6],[9,6,6],
["elab",3,1]],[[1,2,3,4,4,5,5,6,6,7,8,9,10,12,13,13,14,15],[6,4,4,9,10,9,10,9,
10,5,5,5,5,5,5,6,3,3],["elab",18,1,( 2, 9, 4)( 3, 7,10, 6,11,15,13, 8,16,12,
 5),( 2, 4)( 3, 7)( 6, 8)(10,11,14)(13,15)(16,18,17)]],[[1,11],[7,5],[[1,1],
[2,-1]]],[[1,2,3],[11,6,6],["elab",3,1,(2,3)]],[[1,2,3],[10,5,5],["elab",3,1,
(2,3)]]]]]);
ALF("P13/G1/L2/V1/ext3","2^3:sl(3,2)",[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,
3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,5,5,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,
9,9,9,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,11,11,11,10,10,10]);
ALN("P13/G1/L2/V1/ext3",["3^7.2^3:sl(3,2)"]);

MOT("P13/G1/L6/V1/ext2",
[
"origin: Hanrath library,\n",
"structure is 2^7.2^3:sl(3,2),\n",
"characters sorted with permutation (45,46)(50,51)"
],
[172032,6144,3072,12288,6144,172032,3072,256,3072,3072,3072,1024,128,128,512,
256,256,512,1024,1024,1024,512,64,256,512,256,512,512,64,64,64,64,48,48,24,24,
48,48,24,24,24,24,64,64,64,64,32,32,32,32,32,32,14,14,14,14],
[,[1,1,1,1,1,1,1,4,6,1,6,1,2,2,4,4,1,1,4,1,4,1,3,4,1,4,6,6,7,9,11,10,33,33,33,
33,33,33,33,34,33,34,12,12,15,15,19,18,22,25,28,27,53,53,55,55],[1,2,3,4,5,6,
7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,1,
6,3,4,2,5,7,11,10,9,43,44,45,46,47,48,49,50,51,52,55,56,53,54],,,,[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,
33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,1,6,1,6]],
0,
[(53,55)(54,56),( 7,10)( 9,11)(22,25)(24,26)(27,28)(29,32)(30,31)(39,41)
(40,42)(49,50)(51,52)],
["ConstructClifford",[[[1,2,3,4,5,8,9,6,7,11,10],[1,2,2,3,4,5,6,7,3,5,5,4,8,
9],[1,3,6,8,11,10],[1,2,3,3,6,7,3,4,8,8],[1,2,4,4,6,7,3,4,9,9],[1,3,6,3,
8]],[["2^3:sl(3,2)"],["2^3.S4v1"],["L3(2)"],["2xSymm(4)"],["2xSymm(4)"],
["Symm(4)"]],
[[[1,2,3,4,5,6],[1,1,1,1,1,1],["elab",6,19]],[[1,2,2,4,5],[2,2,3,2,2],["elab",
5,14,(2,4,5,3),(2,3,4,5)]],[[1,2,2,3,4,4,4,5,6,6],[3,4,9,2,3,4,7,7,2,4],
["elab",10,8]],[[1,2,2,4,5,5,5],[4,5,12,8,3,4,8],["elab",7,7,(2,7,5,4,3),
(2,4,7)(3,6,5)]],[[1,2,2,2],[5,6,10,11],["elab",4,12,(2,4)]],[[1,2,3,4,5,6],
[8,7,3,5,5,3],["elab",6,16,(2,3,6,4,5),(2,5,6)]],[[1,2,4,5],[9,8,6,6],["elab",
4,12,(3,4)]],[[1,2,3,4,4,6],[6,13,4,9,10,5],["elab",6,16,(2,6,4,5),(2,3,5,4,6)
]],[[1,2,5,5],[7,14,9,10],["elab",4,12,(2,3)]],[[1,3],[11,6],[[1,1],[1,-1]]],
[[1,3],[10,5],[[1,1],[1,-1]]]]]]);
ALF("P13/G1/L6/V1/ext2","2^3:sl(3,2)",[1,1,1,1,1,1,2,2,2,2,2,3,3,3,3,3,3,
3,3,3,3,4,4,4,4,4,4,4,5,5,5,5,8,8,8,8,8,8,9,9,9,9,6,6,6,6,6,6,7,7,7,7,11,
11,10,10]);
ALF("P13/G1/L6/V1/ext2","L3(2)",[1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,
2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,6,6,5,5]);
ALN("P13/G1/L6/V1/ext2",["2^7.2^3:sl(3,2)v2"]);

MOT("P2/G1/L1/V1/ext2",
[
"origin: Hanrath library,\n",
"structure is 2^8.2.A5"
],
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512,1536,1536,3072,1536,6144,1024,1024,6144,3072,1024,3072,6144,96,96,96,96,
96,96,96,96,96,96,96,96,96,96,96,96,64,64,64,64,64,64,64,64,64,64,64,64,64,64,
64,64,10,10,96,96,96,96,96,96,96,96,96,96,96,96,96,96,96,96,10,10],
[,[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,29,29,29,29,29,29,
29,29,29,29,29,29,29,29,29,29,15,24,26,25,27,23,22,22,19,19,23,27,26,25,28,21,
62,61,29,29,29,29,29,29,29,29,29,29,29,29,29,29,29,29,62,61],[1,2,3,4,5,6,7,8,
9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,1,14,7,7,8,8,11,12,
9,3,5,13,5,13,3,9,45,46,57,58,56,55,52,51,54,53,50,49,47,48,59,60,62,61,15,24,
17,27,18,20,20,28,21,18,28,21,17,25,19,24,80,79],,[1,2,3,4,5,6,7,8,9,10,11,12,
13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,32,31,34,33,35,36,44,43,
41,42,39,40,38,37,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,1,1,63,78,
75,66,72,69,68,73,74,67,70,71,65,76,77,64,15,15]],
0,
[(61,62)(79,80),(47,57)(48,58)(49,56)(50,55)(51,52)(53,54),(31,32)(33,34)
(37,44)(38,43)(39,41)(40,42)(64,78)(65,75)(67,72)(68,69)(70,73)(71,74),( 4,10)
( 5, 8)( 7,13)(11,14)(17,18)(19,25)(22,26)(24,28)(30,35)(31,40)(32,42)(33,39)
(34,41)(37,44)(46,59)(47,51)(48,53)(50,55)(52,57)(54,58)(64,70)(65,67)(71,74)
(72,75)(73,78)(76,77),( 3, 5)( 6,10)( 9,13)(11,12)(17,20)(19,27)(21,24)(22,23)
(33,34)(35,36)(37,40)(38,39)(41,43)(42,44)(46,60)(48,58)(49,53)(50,52)(51,55)
(54,56)(64,74)(65,68)(66,77)(67,72)(69,75)(71,78)],
["ConstructClifford",[[[1,2,4,3,7,6,9,5,8],[1,2,4,3,7,3,7],[
1,2,4,3,7,3,7],[1,2,4,3,7,3,7],[1,2,3,7,4,4],[1,2,3,7,4,4],[1,2,3,7,4,4],[1,7,
3,2,3,7],[1,7,3,2,3,7],[1,7,3,2,3,7],[1,4,2,4],[1,4,2,4],[1,4,2,4],[1,
2]],[["2.A5"],["2.L2(3)"],["2.L2(3)"],["2.L2(3)"],["2.S3"],["2.S3"],["2.S3"],[
"C6"],["C6"],["C6"],["C4"],["C4"],["C4"],["Cyclic",2]],[[[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",14,2]],[[1,2,3,4,5,6,7,
8,9,10,11,12,13,14],[2,2,2,2,2,2,2,4,4,4,3,3,3,2],["elab",14,2,( 2, 3, 4)
( 5, 6, 7)( 8,10, 9)(11,12,13),( 4, 9,10,12, 5)( 6, 8)(13,14)]],[[1,2,2,3,3,4,
4,5,6,7,8,8,9,9,10,10],[4,4,6,4,6,4,6,3,3,3,3,5,3,5,3,5],["elab",16,5,
( 2,13, 5,10, 3, 8, 4)( 9,16)(12,15,14)]],[[1,2,3,4,5,5,6,6,7,7,11,11,12,12,
13,13],[3,3,3,3,5,6,5,6,5,6,2,4,2,4,2,4],["elab",16,5,( 2, 5, 4, 6, 8,10)
( 3,13,12,16,14, 7, 9,11,15)]],[[1],[8]],[[1],[6]],[[1,2,2,3,3,4,4,5,6,7,8,8,
9,9,10,10],[5,5,7,5,7,5,7,4,4,4,2,6,2,6,2,6],["elab",16,5,( 2,14, 9,12,16,11,
 15, 7,13)( 4, 5, 6,10, 8)]],[[1],[9]],[[1],[7]]]]]);
ALF("P2/G1/L1/V1/ext2","2.A5",[1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,
2,2,2,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,3,3,3,3,3,3,3,3,3,3,3,3,3,3,
3,3,6,8,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,7,9]);
ALF("P2/G1/L1/V1/ext2","A5",[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,
2,4,5,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,5]);
ALN("P2/G1/L1/V1/ext2",["2^8.2.A5v1"]);

MOT("P2/G1/L1/V1/ext3",
[
"origin: Hanrath library,\n",
"structure is 3^8.2.A5"
],
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6561,6561,19683,19683,6561,6561,6561,6561,19683,6561,6561,19683,19683,6561,
6561,6561,6561,6561,6561,6561,6561,6561,6561,6561,6561,6561,6561,6561,19683,
6561,6561,6561,6561,6561,6561,6561,6561,19683,19683,19683,6561,19683,19683,
6561,6561,19683,6561,6561,19683,6561,6561,19683,19683,19683,19683,120,486,243,
243,243,243,243,243,243,243,243,243,243,243,243,243,243,243,243,243,243,243,
243,243,243,243,243,243,243,243,243,243,243,243,243,243,243,243,243,243,243,
243,4,10,10,6,10,10],
[,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,
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,
55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,1,71,95,82,110,89,79,107,92,76,
86,104,73,101,98,108,80,91,102,75,97,87,78,103,96,72,94,90,84,109,111,83,88,
93,81,106,105,77,85,99,74,100,70,114,113,71,114,113],[1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,70,1,54,53,53,54,54,53,53,54,54,1,53,54,
53,53,54,53,1,54,54,53,53,54,53,54,53,54,53,53,54,54,1,54,1,54,54,53,53,53,53,
54,112,114,113,70,117,116],,[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,
95,82,110,89,79,107,92,76,86,104,73,101,98,108,80,91,102,75,97,87,78,103,96,
72,94,90,84,109,111,83,88,93,81,106,105,77,85,99,74,100,112,1,1,115,70,70]],
0,
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( 78, 92)( 80, 86)( 81,104)( 83,101)( 84, 98)( 85,108)( 87, 91)( 88,102)
( 90, 97)( 93,103)( 94, 96)( 99,109)(100,111)(105,106),(  4,  5)(  7, 48)
(  8, 11)(  9, 50)( 10, 33)( 12, 55)( 13, 23)( 14, 21)( 16, 51)( 17, 26)
( 19, 36)( 20, 32)( 22, 29)( 24, 40)( 25, 44)( 27, 52)( 28, 41)( 30, 34)
( 31, 42)( 37, 49)( 45, 59)( 46, 65)( 56, 63)( 60, 66)( 61, 62)( 68, 69)
( 72, 83)( 74, 77)( 75, 80)( 76, 79)( 85, 96)( 86, 89)( 87,109)( 88,102)
( 90,106)( 91, 99)( 93,103)( 94,108)( 95,101)( 97,105)(100,111)(107,110),
(  4, 28)(  5, 41)(  6, 18)(  7, 30)(  8, 11)(  9, 50)( 10, 33)( 12, 46)
( 13, 60)( 14, 42)( 16, 61)( 17, 63)( 19, 44)( 21, 31)( 22, 29)( 23, 66)
( 24, 40)( 25, 36)( 26, 56)( 34, 48)( 37, 49)( 38, 64)( 39, 47)( 43, 57)
( 51, 62)( 55, 65)( 73, 98)( 74, 99)( 75, 97)( 76, 93)( 77, 91)( 78, 92)
( 79,103)( 80,105)( 81,104)( 82, 84)( 85,108)( 86,106)( 87,107)( 89, 90)
( 94, 96)(109,110),(  3,  6)(  7, 29)(  8, 31)( 10, 41)( 11, 42)( 12, 65)
( 13, 23)( 15, 47)( 17, 68)( 19, 40)( 20, 32)( 22, 48)( 24, 36)( 26, 69)
( 27, 60)( 28, 33)( 37, 61)( 38, 58)( 43, 67)( 45, 59)( 46, 55)( 49, 62)
( 52, 66)( 56, 63)( 72,105)( 73, 78)( 74, 94)( 75, 86)( 76,111)( 77,108)
( 79,100)( 80, 89)( 82, 92)( 83, 97)( 85,107)( 87,109)( 90,101)( 91, 99)
( 95,106)( 96,110),(  2, 38, 45, 58)(  3, 43, 26, 52)(  4, 12)(  5, 46)
(  6, 60, 68, 67)(  7, 25, 34, 40)(  8, 61, 14, 51)(  9, 41, 65, 10)( 11, 62)
( 13, 69, 57, 17)( 15, 35, 47, 20)( 16, 21, 49, 42)( 18, 66, 56, 27)( 19, 29)
( 22, 36, 30, 44)( 23, 63)( 24, 48)( 28, 55, 33, 50)( 31, 37)( 32, 39)
( 53, 54)( 59, 64)( 72, 78, 76, 77)( 73, 97, 94,100)( 74, 89, 85, 93)
( 75,108,103,110)( 79,107, 95, 92)( 80, 99, 86,109)( 81, 88,104,102)
( 82, 90, 96,111)( 83, 98,105, 91)( 84,106, 87,101)],
["ConstructClifford",[[[1,2,4,3,7,6,9,5,8],[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],[1,3,3],[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],[1],[
1],[1],[1],[1],[1],[1],[1],[1],[1],[1],[1],[1],[1],[1],[1],[1],[1],[1],[1],[
1],[1],[1],[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.A5"],["Cyclic",3],["Cyclic",3],["Cyclic",
3],["Cyclic",3],["Cyclic",3],["Cyclic",3],["Cyclic",3],["Cyclic",3],["Cyclic",
3],["Cyclic",3],["Cyclic",3],["Cyclic",3],["Cyclic",3],["Cyclic",3],["Cyclic",
3],["Cyclic",3],["Cyclic",3],["Cyclic",3],["Cyclic",3],["Cyclic",3],["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],["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],["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,
32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,
58,59,60,61,62,63,64,65,66,67,68,69],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1],["elab",69,1]],[[1],[2]],[[1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,
9,9,10,10,11,11,12,12,13,13,14,14,15,15,16,16,17,17,18,18,19,19,20,20,21,21],[
4,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,
2,3],["elab",41,1,( 2,25,18,33)( 3, 7,32,24, 8,15)( 4,13,17,28,29,11,12, 6,36,
 30,22,38,16,20,39,34,23,19)( 5,41,40,10,21,27, 9,37,26,31,14,35)]],[[1],[
3]],[[1],[8]],[[1],[6]],[[1],[5]],[[1],[9]],[[1],[7]]]]]);
ALF("P2/G1/L1/V1/ext3","2.A5",[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,
4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,3,6,8,5,7,9]);
ALN("P2/G1/L1/V1/ext3",["3^8.2.A5v1"]);

MOT("P2/G2/L1/V1/ext2",
[
"origin: Hanrath library,\n",
"structure is 2^8.2.A5"
],
[30720,512,512,512,2048,2048,2048,2048,2048,30720,512,512,2048,2048,512,2048,
2048,2048,6,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,10,10,6,10,10],
[,[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,19,10,13,16,17,14,16,18,16,13,13,18,14,
18,17,17,14,37,36,19,37,36],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,1,
20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,37,36,10,40,39],,[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,
34,35,1,1,38,10,10]],
0,
[(36,37)(39,40),( 3, 4)(12,15),( 2, 3)(11,12),(21,28,29)(22,25,27)(23,33,34)
(24,35,31)(26,30,32),( 8, 9)(13,14)(21,24)(22,27)(28,31)(29,35)(30,32)(33,34),
( 7, 8)(14,17)(22,25)(23,24)(28,29)(30,32)(31,33)(34,35),( 6, 7)(17,18)(22,27)
(23,26)(28,29)(30,34)(31,35)(32,33),( 5, 6)(16,18)(22,32)(23,33)(24,31)(25,30)
(26,27)(28,29),( 7, 9)(13,17)(21,34)(22,27)(23,29)(24,31)(26,32)(28,33)],
["ConstructClifford",[[[1,2,4,3,7,6,9,5,8],[1,2,4,4,4],[1,2,
4,4,4],[1,2,4,4,4],[1,2,4,4,4],[1,2,4,4,4],[1,2],[1,2],[1,
2]],[["2.A5"],["Q8"],["Q8"],["Q8"],["Q8"],["Q8"],["Cyclic",2],["Cyclic",
2],["Cyclic",2]],[[[1,2,3,4,5,6,7,8,9],[1,1,1,1,1,1,1,1,1],["elab",9,12]],[[1,
2,3,4,5,6,7,8,9],[2,2,2,2,2,2,2,2,2],["elab",9,12,(2,4,6,3,5),(4,6,5)]],[[1],[
4]],[[1,2,2,2,3,3,3,4,4,4,5,5,5,6,6,6],[3,3,4,5,3,4,5,3,4,5,3,4,5,3,4,
5],["elab",16,5,( 2, 8, 6,11, 4,10,13, 3,15, 5, 9,14,12,16)]],[[1],[8]],[[1],[
6]],[[1],[5]],[[1],[9]],[[1],[7]]]]]);
ALF("P2/G2/L1/V1/ext2","2.A5",[1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,4,3,3,
3,3,3,3,3,3,3,3,3,3,3,3,3,3,6,8,5,7,9]);
ALF("P2/G2/L1/V1/ext2","A5",[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,3,2,2,2,
2,2,2,2,2,2,2,2,2,2,2,2,2,4,5,3,4,5]);
ALN("P2/G2/L1/V1/ext2",["2^8.2.A5v2"]);

MOT("P2/G2/L1/V1/ext3",
[
"origin: Hanrath library,\n",
"structure is 3^8.2.A5"
],
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6561,6561,6561,6561,6561,6561,6561,6561,19683,6561,6561,6561,19683,6561,6561,
6561,6561,19683,6561,19683,6561,6561,6561,6561,6561,6561,6561,6561,19683,6561,
6561,19683,19683,6561,6561,19683,6561,6561,6561,19683,19683,19683,19683,6561,
6561,6561,19683,6561,6561,19683,19683,19683,19683,19683,19683,120,486,243,243,
243,243,243,243,243,243,243,243,243,243,243,243,243,243,243,243,243,243,243,
243,243,243,243,243,243,243,243,243,243,243,243,243,243,243,243,243,243,243,4,
10,10,6,10,10],
[,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,
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,
55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,1,71,83,101,108,85,87,100,107,
106,102,86,84,72,82,75,81,76,99,103,92,94,90,110,91,98,105,111,95,88,77,73,80,
89,109,96,79,78,74,104,93,97,70,114,113,71,114,113],[1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,70,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,112,114,113,70,117,116],,[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,
58,59,60,61,62,63,64,65,66,67,68,69,70,71,83,101,108,85,87,100,107,106,102,86,
84,72,82,75,81,76,99,103,92,94,90,110,91,98,105,111,95,88,77,73,80,89,109,96,
79,78,74,104,93,97,112,1,1,115,70,70]],
0,
[(113,114)(116,117),( 72, 83)( 73,101)( 74,108)( 75, 85)( 76, 87)( 77,100)
( 78,107)( 79,106)( 80,102)( 81, 86)( 82, 84)( 88, 99)( 89,103)( 90, 92)
( 91, 94)( 93,110)( 95, 98)( 96,105)( 97,111)(104,109),(  6, 61)(  7, 40)
(  9, 60)( 10, 44)( 12, 19)( 13, 31)( 14, 30)( 15, 24)( 17, 26)( 20, 21)
( 22, 28)( 23, 57)( 27, 68)( 32, 50)( 35, 63)( 37, 41)( 39, 49)( 42, 48)
( 43, 55)( 45, 53)( 46, 47)( 51, 58)( 56, 69)( 64, 66)( 72, 76)( 73,103)
( 74, 94)( 75, 85)( 77, 78)( 79,104)( 80, 95)( 81, 86)( 82,105)( 83, 87)
( 84, 96)( 88,110)( 89,101)( 90, 92)( 91,108)( 93, 99)( 97,111)( 98,102)
(100,107)(106,109),(  5, 15, 42, 48, 24)(  6, 65, 61, 68, 27)(  7, 13, 31, 40,
 8)(  9, 39, 18, 49, 60)( 10, 14, 30, 44, 11)( 12, 59, 19, 35, 63)
( 17, 26, 41, 36, 37)( 20, 21, 28, 62, 22)( 23, 57, 32, 54, 50)
( 29, 58, 45, 53, 51)( 34, 46, 43, 55, 47)( 56, 69, 64, 67, 66)
( 72, 95,102, 87, 90)( 73, 89, 96, 75, 82)( 74,110, 99, 91,111)
( 76, 92, 83, 98, 80)( 77,107,106, 81,104)( 78, 79, 86,109,100)
( 84,101,103,105, 85)( 88, 94, 97,108, 93),(  4,  5)(  6, 56)(  7, 13)
( 10, 14)( 12, 63)( 15, 24)( 18, 52)( 19, 35)( 22, 28)( 23, 57)( 25, 62)
( 27, 68)( 30, 44)( 31, 40)( 32, 43)( 33, 36)( 34, 54)( 37, 41)( 39, 49)
( 45, 58)( 50, 55)( 51, 53)( 61, 69)( 65, 67)( 72, 78)( 73, 89)( 74,108)
( 75, 97)( 76, 77)( 79,106)( 80, 98)( 81, 90)( 82, 99)( 83,107)( 84, 88)
( 85,111)( 86, 92)( 87,100)( 91, 94)( 93,105)( 95,102)( 96,110)(101,103)
(104,109),(  3, 16)(  4, 20,  5, 21)(  6, 61, 69, 56)(  7, 51, 31, 45)
(  8, 29)(  9, 33, 60, 36)( 10, 44, 30, 14)( 12, 63, 35, 19)( 13, 58, 40, 53)
( 15, 22)( 17, 18, 26, 52)( 23, 57)( 24, 28)( 25, 42, 62, 48)( 27, 68)
( 32, 50, 55, 43)( 34, 47, 54, 46)( 37, 49)( 39, 41)( 64, 65, 66, 67)
( 72, 78, 77, 76)( 73, 89,101,103)( 74, 97, 91, 85)( 75,108,111, 94)
( 79, 90,109, 86)( 80, 98,102, 95)( 81,106, 92,104)( 82, 88, 93, 96)
( 83,107,100, 87)( 84, 99,110,105),(  2,  3)(  6, 43, 61, 55)(  7, 30, 40, 14)
(  8, 11)(  9, 39, 60, 49)( 10, 31, 44, 13)( 12, 45, 19, 53)( 15, 48, 24, 42)
( 16, 38)( 17, 22, 26, 28)( 20, 37, 21, 41)( 23, 66, 57, 64)( 25, 33)
( 27, 47, 68, 46)( 29, 59)( 32, 56, 50, 69)( 34, 65)( 35, 58, 63, 51)( 36, 62)
( 54, 67)( 72, 88, 76,110)( 73,104,103, 79)( 74,102, 94, 98)( 75, 81, 85, 86)
( 77, 84, 78, 96)( 80, 91, 95,108)( 82,107,105,100)( 83, 99, 87, 93)
( 89,106,101,109)( 90, 97, 92,111),(  2,  4, 10, 18, 59, 48, 30, 60)
(  3, 25,  7, 36, 29, 21, 31, 17)(  5, 11,  9, 63, 42, 38, 52, 19)
(  6, 54, 68, 66, 69, 64, 57, 34)(  8, 26, 53, 20, 16, 33, 58, 62)
( 12, 24, 14, 49)( 13, 37, 51, 28)( 15, 44, 39, 35)( 22, 40, 41, 45)
( 23, 46, 55, 47, 27, 67, 32, 65)( 43, 61, 56, 50)( 72, 77, 84, 93, 83,100,
  82,110)( 73,108, 99, 94,102, 81, 96, 92)( 74, 88, 91, 80, 86,105, 90,101)
( 75, 98,104,107,106, 89,111, 76)( 78, 79,103, 97, 87, 85, 95,109)],
["ConstructClifford",[[[1,2,4,3,7,6,9,5,8],[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],[1,3,3],[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],[1],[
1],[1],[1],[1],[1],[1],[1],[1],[1],[1],[1],[1],[1],[1],[1],[1],[1],[1],[1],[
1],[1],[1],[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.A5"],["Cyclic",3],["Cyclic",3],["Cyclic",
3],["Cyclic",3],["Cyclic",3],["Cyclic",3],["Cyclic",3],["Cyclic",3],["Cyclic",
3],["Cyclic",3],["Cyclic",3],["Cyclic",3],["Cyclic",3],["Cyclic",3],["Cyclic",
3],["Cyclic",3],["Cyclic",3],["Cyclic",3],["Cyclic",3],["Cyclic",3],["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],["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],["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,
32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,
58,59,60,61,62,63,64,65,66,67,68,69],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1],["elab",69,2]],[[1],[2]],[[1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,
9,9,10,10,11,11,12,12,13,13,14,14,15,15,16,16,17,17,18,18,19,19,20,20,21,21],[
4,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,
2,3],["elab",41,1,( 2,23,11, 9,27, 7,28,40,12,13,36,37,32,26,10,15,17,21,19,
  5,24,33,14,22,16,39, 4,20,29,18,38,25, 3, 6,31, 8,35,30,34,41)]],[[1],[
3]],[[1],[8]],[[1],[6]],[[1],[5]],[[1],[9]],[[1],[7]]]]]);
ALF("P2/G2/L1/V1/ext3","2.A5",[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,
4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,3,6,8,5,7,9]);
ALN("P2/G2/L1/V1/ext3",["3^8.2.A5v2"]);

MOT("P2/G2/L1/V2/ext2",
[
"origin: Hanrath library,\n",
"structure is 2^8.2.A5"
],
[30720,512,512,512,2048,2048,2048,2048,2048,1024,1024,512,1024,1024,1024,1024,
3072,5120,6,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,10,10,6,10,10],
[,[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,19,10,14,13,11,11,13,14,10,16,17,15,18,
18,15,17,16,37,36,19,37,36],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,1,
27,26,25,24,23,22,21,20,35,34,33,32,31,30,29,28,37,36,17,40,39],,[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,
34,35,1,1,38,18,18]],
0,
[(36,37)(39,40),( 6, 8)( 7, 9)(11,14)(15,16)(21,23)(24,26)(28,33)(29,34)
(30,35)(31,32),(20,27)(21,26)(22,25)(23,24)(28,35)(29,34)(30,33)(31,32),
( 6, 7)( 8, 9)(10,13)(15,16)(20,22)(21,26)(23,24)(25,27)(28,33)(30,35),( 3, 4)
( 8, 9)(10,15)(13,16)(20,30)(22,35)(23,24)(25,28)(27,33)(29,34),( 2, 3)( 7, 8)
(10,14)(11,13)(20,21)(22,24)(23,25)(26,27)(30,33)(31,32)],
["ConstructClifford",[[[1,2,4,3,7,6,9,5,8],[1,2,4,4,4],[1,2,
4,4,4],[1,2,4,4,4],[1,2,4,4,4],[1,2,4,4,4],[1,2],[1,2],[1,
2]],[["2.A5"],["Q8"],["Q8"],["Q8"],["Q8"],["Q8"],["Cyclic",2],["Cyclic",
2],["Cyclic",2]],[[[1,2,3,4,5,6,7,8,9],[1,1,1,1,1,1,1,1,1],["elab",9,12]],[[1,
2,3,4,5,6,7,8,9],[2,2,2,2,2,2,2,2,2],["elab",9,13]],[[1],[4]],[[1,2,2,2,3,3,3,
4,4,4,5,5,5,6,6,6],[3,3,4,5,3,4,5,3,4,5,3,4,5,3,4,5],["elab",16,6]],[[1],[
8]],[[1],[6]],[[1],[5]],[[1],[9]],[[1],[7]]]]]);
ALF("P2/G2/L1/V2/ext2","2.A5",[1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,4,3,3,
3,3,3,3,3,3,3,3,3,3,3,3,3,3,6,8,5,7,9]);
ALF("P2/G2/L1/V2/ext2","A5",[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,3,2,2,2,
2,2,2,2,2,2,2,2,2,2,2,2,2,4,5,3,4,5]);
ALN("P2/G2/L1/V2/ext2",["2^8.2.A5v3"]);

MOT("P21/G1/L1/V1/ext2",
[
"origin: Hanrath library,\n",
"structure is 2^5.A6"
],
[11520,768,768,11520,64,64,64,64,16,72,72,24,24,18,18,16,16,16,16,10,10,10,
10],
[,[1,1,1,1,1,3,3,1,2,10,10,10,10,14,14,5,6,6,5,22,22,20,20],[1,2,3,4,5,6,7,8,
9,1,4,2,3,1,4,16,18,17,19,22,23,20,21],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,
16,17,18,19,1,4,1,4]],
0,
[(17,18),(16,19),(20,22)(21,23)],
["ConstructClifford",[[[1,2,3,4,5,7,6],[1,2,3,7,6],[1,3,4,
2,5,5],[1,2,3,2,5]],[["A6"],["A5"],["3^2:4"],["Symm(4)"]],[[[1,2,3,4],[1,1,1,
1],["elab",4,18]],[[1,2,3,4,4],[2,2,4,2,4],["elab",5,19]],[[1,2,3,4],[3,3,2,
3],["elab",4,23]],[[1,3],[4,3],[[1,1],[1,-1]]],[[1,3,3,4],[5,5,6,5],["elab",4,
12,(3,4)]],[[1,2],[7,5],[[1,1],[1,-1]]],[[1,2],[6,4],[[1,1],[1,-1]]]]]]);
ALF("P21/G1/L1/V1/ext2","A6",[1,1,1,1,2,2,2,2,2,3,3,3,3,4,4,5,5,5,5,7,7,6,
6]);
ALN("P21/G1/L1/V1/ext2",["2^5.A6"]);

MOT("P21/G1/L1/V1/ext3",
[
"origin: Hanrath library,\n",
"structure is 3^5.A6"
],
[87480,2916,4374,4374,972,2916,2916,87480,4374,87480,216,108,108,54,54,108,54,
108,108,216,108,216,243,81,81,81,81,81,81,81,243,81,243,81,27,27,81,81,12,12,
12,15,15,15,15,15,15],
[,[1,2,4,3,5,7,6,10,9,8,1,5,5,3,4,2,9,7,5,10,6,8,23,25,24,28,27,26,29,32,33,
30,31,34,36,35,37,38,11,20,22,45,47,46,42,44,43],[1,1,1,1,1,1,1,1,1,1,11,11,
11,11,11,11,11,11,11,11,11,11,1,3,4,4,1,3,1,4,1,3,1,1,9,9,1,1,39,39,39,45,45,
45,42,42,42],,[1,2,4,3,5,7,6,10,9,8,11,13,12,15,14,16,17,21,19,22,18,20,23,25,
24,28,27,26,29,32,33,30,31,34,36,35,37,38,39,41,40,1,10,8,1,10,8]],
0,
[(37,38),(35,36),(34,37),(27,29),(42,45)(43,46)(44,47),( 3, 4)( 6, 7)( 8,10)
(12,13)(14,15)(18,21)(20,22)(24,25)(26,28)(30,32)(31,33)(40,41)(43,44)
(46,47)],
["ConstructClifford",[[[1,2,3,4,5,7,6],[1,2,3,7,6],[1,2,3,
7,6],[1,2,3,2,5],[1,2,3,2,5],[1,3,3,4,4,2],[1,2,3,3],[1,2,4,4],[1,3,2],[1,3,
2]],[["A6"],["A5"],["A5"],["Symm(4)"],["Symm(4)"],["3^2:2"],["A4"],["A4"],
["S3"],["S3"]],[[[1,2,3,4,5,6,7,8,9,10],[1,1,1,1,1,1,1,1,1,1],["elab",10,9]],
[[1,2,3,4,4,5,5,6,7,8,9,10],[2,2,2,2,4,2,4,6,2,2,3,3],["elab",12,4]],[[1,2,3,
4,5,6,6,7,7,9,10],[3,3,3,3,3,2,3,3,4,2,2],["elab",11,4]],[[1,6,6,8,8],[4,4,5,
3,4],["elab",5,20]],[[1,4,5],[5,5,5],["elab",3,1]],[[1,2,3],[7,5,5],["elab",3,
1]],[[1,2,3],[6,4,4],["elab",3,1]]]]]);
ALF("P21/G1/L1/V1/ext3","A6",[1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,
3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,5,5,5,7,7,7,6,6,6]);
ALN("P21/G1/L1/V1/ext3",["3^5.A6v1"]);

MOT("P21/G1/L1/V1/ext4",
[
"origin: Hanrath library,\n",
"structure is 4^5.A6"
],
[368640,12288,24576,6144,6144,24576,4096,2048,24576,24576,3072,6144,3072,6144,
61440,24576,18432,4096,12288,61440,368640,24576,512,512,512,512,256,256,256,
256,512,512,512,512,128,128,128,128,128,128,128,128,128,128,256,256,256,256,
576,576,576,576,192,192,192,192,192,192,192,192,192,192,192,192,192,192,192,
192,192,192,192,192,36,36,36,36,32,32,32,32,32,32,32,32,20,20,20,20,20,20,20,
20],
[,[1,3,1,3,3,9,9,3,1,9,9,3,9,3,21,9,21,9,3,21,1,9,1,16,9,22,6,21,10,3,9,22,1,
16,5,4,12,14,4,12,14,5,3,18,7,9,7,9,49,51,49,51,57,59,57,59,49,51,49,51,57,59,
57,59,59,57,59,57,57,59,57,59,73,75,73,75,23,23,32,32,25,25,34,34,89,91,89,91,
85,87,85,87],[1,2,3,5,4,10,7,8,9,6,13,14,11,12,20,22,17,18,19,15,21,16,23,26,
25,24,29,28,27,30,31,34,33,32,39,42,41,40,35,38,37,36,43,44,45,48,47,46,1,17,
21,17,14,22,4,6,3,15,9,20,12,10,5,16,11,19,13,2,2,11,19,13,1,17,21,17,77,78,
84,83,81,82,80,79,89,92,91,90,85,88,87,86],,[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,
41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,70,71,
72,69,68,65,66,67,73,74,75,76,77,78,79,80,81,82,83,84,1,20,21,15,1,20,21,15]],
0,
[(85,89)(86,90)(87,91)(88,92),(79,80)(83,84),(77,78)(81,82),(74,76),(65,70)
(66,71)(67,72)(68,69),( 4, 5)( 6,10)(11,13)(12,14)(15,20)(16,22)(24,26)(27,29)
(32,34)(35,39)(36,42)(37,41)(38,40)(46,48)(50,52)(53,61)(54,64)(55,63)(56,62)
(58,60)(65,67)(70,72)(79,83)(80,84)(86,88)(90,92)],
["ConstructClifford",[[[1,2,3,4,5,7,6],[1,2,3,7,6],[1,2,3,
7,6],[1,2,3,7,6],[1,3,4,2,5,5],[1,2,3,2,5],[1,2,3,2,5],[1,2,3,2,5],[1,3,3,4,4,
2],[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,
2],[1,5,2,5],[1,2,2,2],[1,3,3],[1,
2]],[["A6"],["A5"],["A5"],["A5"],["3^2:4"],["Symm(4)"],["Symm(4)"],
["Symm(4)"],["3^2:2"],["A4"],["A4"],["A4"],["S3"],["S3"],["S3"],["S3"],["S3"],
["S3"],["C4"],["V4"],["Cyclic",3],["Cyclic",2]],[[[1,2,3,4,5,6,7,8,9,10,11,12,
13,14,15,16,17,18,19,20,21,22],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],
["elab",22,1]],[[1,2,3,4,5,6,6,7,7,8,8,9,10,11,12,13,14,15,16,17,18,19,20,20,
20,22],[2,2,2,2,4,2,4,2,4,2,4,6,2,2,2,3,3,3,3,3,3,3,2,3,4,2],["elab",26,1]],
[[1,2,3,4,5,6,7,8,9,9,10,10,11,11,12,12,13,14,15,16,17,18,21,21],[3,3,3,3,2,3,
3,3,2,3,3,4,3,4,3,4,2,2,2,2,2,2,2,3],["elab",24,2]],[[1,5,9,9],[4,3,4,5],
["elab",4,19,(2,4,3)]],[[1,5,5,6,7,8,19,19],[5,5,6,5,5,5,2,4],["elab",8,9]],
[[1,2,3,4],[7,5,5,5],["elab",4,19]],[[1,2,3,4],[6,4,4,4],["elab",4,19]]]]]);
ALF("P21/G1/L1/V1/ext4","A6",[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,
3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,5,5,5,5,5,5,5,5,7,7,7,7,6,6,6,6]);
ALN("P21/G1/L1/V1/ext4",["4^5.A6"]);

MOT("P21/G1/L3/V2/ext3",
[
"origin: Hanrath library,\n",
"structure is 3^5.A6"
],
[87480,5832,5832,2916,1458,1458,2916,4374,14580,14580,216,108,108,54,54,108,
108,54,108,108,216,216,81,81,81,81,81,81,81,81,81,27,27,27,12,12,12,15,15,15,
15,15,15],
[,[1,3,2,4,6,5,7,8,10,9,1,3,2,8,6,9,10,5,7,4,3,2,27,31,23,24,28,29,30,25,26,
32,34,33,11,22,21,41,42,43,38,39,40],[1,1,1,1,1,1,1,1,1,1,11,11,11,11,11,11,
11,11,11,11,11,11,7,7,7,7,7,7,7,7,7,1,8,8,35,35,35,41,41,41,38,38,38],,[1,3,2,
4,6,5,7,8,10,9,11,13,12,14,18,17,16,15,19,20,22,21,25,26,30,31,23,27,28,29,24,
32,34,33,35,37,36,1,10,9,1,9,10]],
0,
[(38,41)(39,43)(40,42),(33,34),(23,28,30)(24,26,31)(25,27,29),( 2, 3)( 5, 6)
( 9,10)(12,13)(15,18)(16,17)(21,22)(23,25,30,29,28,27)(24,26,31)(36,37)(39,40)
(42,43)],
["ConstructClifford",[[[1,2,3,4,5,7,6],[1,2,3,4,5,6,7],[1,2,3,4,5,6,7],[1,3,3,
4,4,2],[1,3,3,4,4,2],[1,3,3,4,4,2],[1,2,3,3],[1,2,3,3],[1,2,3,3],[1,2,2,
2]],[["A6"],["projectives","A6","3.A6"],["projectives","A6","3.A6"],["3^2:2"],
["projectives","3^2:2","3^(1+2)_+:2"],["projectives","3^2:2","3^(1+2)_+:2"],
["A4"],["A4"],["A4"],["V4"]],[[[1,2,3,4,5,6,7,8,9,10],[1,1,1,1,1,1,1,1,1,
1],["elab",10,10]],[[1,2,3,4,5,6,7,8,9,10,10,10],[2,2,2,6,6,6,2,2,2,2,3,
4],["elab",12,5]],[[1,4,4,7,7,8,8,9,9],[3,2,3,3,4,3,4,3,4],["elab",9,14]],[[1,
4,4],[4,4,5],["elab",3,1]],[[1,2,3],[5,5,5],["elab",3,1]],[[1,2,3],[7,6,
6],["elab",3,1]],[[1,2,3],[6,7,7],["elab",3,1,(2,3)]]]]]);
ALF("P21/G1/L3/V2/ext3","A6",[1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,
3,3,3,3,3,3,3,3,3,4,4,4,5,5,5,7,7,7,6,6,6]);
ALN("P21/G1/L3/V2/ext3",["3^5.A6v2"]);

MOT("P21/G2/L1/V1/ext2",
[
"origin: Hanrath library,\n",
"structure is 2^9.A6"
],
[184320,4096,12288,1024,12288,1024,12288,12288,4096,184320,256,256,64,64,64,
64,64,64,256,256,256,256,256,256,72,72,24,24,72,72,24,24,32,32,32,32,32,32,32,
32,10,10,10,10],
[,[1,1,1,1,1,1,1,1,1,1,1,9,2,8,2,7,4,4,1,9,5,3,5,3,25,25,25,25,29,29,29,29,11,
20,23,22,22,23,20,11,43,43,41,41],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,
18,19,20,21,22,23,24,1,10,7,3,1,10,8,5,33,34,38,37,36,35,39,40,43,44,41,42],,[
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,
30,31,32,33,34,35,36,37,38,39,40,1,10,1,10]],
0,
[(41,43)(42,44),(35,38)(36,37),(33,40)(34,39),( 3, 5)( 7, 8)(13,15)(14,16)
(21,24)(22,23)(25,29)(26,30)(27,31)(28,32)(35,36)(37,38)],
["ConstructClifford",[[[1,2,3,4,5,7,6],[1,3,4,2,5,5],[1,2,
3,2,5],[1,2,4,2,5],[1,6,7,2],[1,2,5,2,2],[1,3,2],[1,4,2],[1,5,2,5],[1,
2]],[["A6"],["3^2:4"],["Symm(4)"],["Symm(4)"],["Dihedral",
10],["D8"],["S3"],["S3"],["C4"],["Cyclic",2]],[[[1,2,3,4,5,6,7,8,9,10],[1,1,1,
1,1,1,1,1,1,1],["elab",10,11]],[[1,2,3,3,4,4,5,6,6,6,7,8,9,10],[2,4,2,4,2,4,4,
2,4,5,3,3,3,2],["elab",14,3]],[[1,2,3,7],[3,2,3,2],["elab",4,23,(2,4,3)]],[[1,
2,4,8],[4,3,3,2],["elab",4,23,(2,4,3)]],[[1,2,2,3,4,6,9,9],[5,5,6,5,5,3,2,
4],["elab",8,6,(2,6,8,4)(3,7)]],[[1,5],[7,2],[[1,1],[1,-1]]],[[1,5],[6,3],[[1,
1],[1,-1]]]]]]);
ALF("P21/G2/L1/V1/ext2","A6",[1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,
2,2,3,3,3,3,4,4,4,4,5,5,5,5,5,5,5,5,7,7,6,6]);
ALN("P21/G2/L1/V1/ext2",["2^9.A6v1"]);

MOT("P21/G2/L1/V2/ext2",
[
"origin: Hanrath library,\n",
"structure is 2^9.A6"
],
0,
0,
0,
0,
["ConstructPermuted",["P21/G2/L1/V1/ext2"],(11,21)(12,22)(15,16)(17,18)(19,23)
(20,24)(25,27)(26,28)(33,35)(34,36)(37,39)(38,40)(41,42)(43,44),(8,10,9,11)
(24,25)(33,34)(36,37)(39,42,40,41)]);
ALF("P21/G2/L1/V2/ext2","A6",[1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,
2,2,3,3,3,3,4,4,4,4,5,5,5,5,5,5,5,5,7,7,6,6]);
ALN("P21/G2/L1/V2/ext2",["2^9.A6v2"]);

MOT("P21/G2/L1/V3/ext2",
[
"origin: Hanrath library,\n",
"structure is 2^9.A6"
],
[184320,4096,12288,1024,12288,1024,12288,12288,4096,184320,128,128,64,64,128,
128,128,128,128,128,128,128,128,128,24,24,72,72,72,72,24,24,32,32,32,32,32,32,
32,32,10,10,10,10],
[,[1,1,1,1,1,1,1,1,1,1,9,3,6,6,7,8,5,9,9,3,5,9,2,10,27,27,27,27,29,29,29,29,
16,15,24,23,23,24,15,16,43,43,41,41],[1,2,3,4,5,6,7,8,9,10,19,20,14,13,15,16,
21,22,11,12,17,18,23,24,7,3,1,10,1,10,8,5,33,34,38,37,36,35,39,40,43,44,41,
42],,[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,
28,29,30,31,32,40,39,38,37,36,35,34,33,1,10,1,10]],
0,
[(41,43)(42,44),(33,40)(34,39)(35,38)(36,37),(13,14),(11,19)(12,20)(17,21)
(18,22)(35,38)(36,37),( 3, 5)( 7, 8)(11,18)(12,17)(15,16)(19,22)(20,21)(25,31)
(26,32)(27,29)(28,30)(33,34)(39,40)],
["ConstructClifford",[[[1,2,3,4,5,7,6],[1,3,4,2,5,5],[1,2,
3,2,5],[1,2,4,2,5],[1,6,7,2],[1,2,5,2,2],[1,3,2],[1,4,2],[1,5,2,5],[1,
2]],[["A6"],["3^2:4"],["Symm(4)"],["Symm(4)"],["Dihedral",
10],["D8"],["S3"],["S3"],["C4"],["Cyclic",2]],[[[1,2,3,4,5,6,7,8,9,10],[1,1,1,
1,1,1,1,1,1,1],["elab",10,11]],[[1,2,3,3,4,4,5,6,6,6,7,8,9,10],[2,4,2,4,2,4,4,
2,4,5,3,3,3,2],["elab",14,4]],[[1,2,3,7],[3,2,3,2],["elab",4,23,(2,4,3),(1,3)
(2,4)]],[[1,2,4,8],[4,3,3,2],["elab",4,23,(2,4,3)]],[[1,2,2,3,4,6,9,9],[5,5,6,
5,5,3,2,4],["elab",8,11]],[[1,5],[7,2],[[1,1],[1,-1]]],[[1,5],[6,3],[[1,1],[1,
-1]]]]]]);
ALF("P21/G2/L1/V3/ext2","A6",[1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,
2,2,3,3,3,3,4,4,4,4,5,5,5,5,5,5,5,5,7,7,6,6]);
ALN("P21/G2/L1/V3/ext2",["2^9.A6v3"]);

MOT("P21/G2/L2/V1/ext2",
[
"origin: Hanrath library,\n",
"structure is 2^9.A6"
],
[184320,4096,2048,1024,12288,3072,2048,30720,18432,12288,256,64,256,64,256,
256,256,256,256,256,64,128,64,128,128,128,72,24,24,72,72,24,24,72,32,32,32,32,
32,32,32,32,10,10,10,10],
[,[1,1,1,1,1,1,1,1,1,1,1,6,2,6,10,5,5,10,2,1,3,5,3,2,5,2,27,27,27,27,31,31,31,
31,11,16,15,13,13,15,16,11,45,45,43,43],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,
16,17,18,19,20,21,22,23,24,25,26,1,5,8,9,1,10,6,9,35,36,40,39,38,37,41,42,45,
46,43,44],,[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,
26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,1,8,1,8]],
0,
[(43,45)(44,46),(37,40)(38,39),(35,42)(36,41),(21,23)],
["ConstructClifford",[[[1,2,3,4,5,7,6],[1,2,4,7,6],[1,3,4,
2,5,5],[1,2,3,2,5],[1,2,4,2,5],[1,2,5,2,2],[1,3,2],[1,5,2,5],[1,2,2,2],[1,
2]],[["A6"],["A5"],["3^2:4"],["Symm(4)"],["Symm(4)"],["D8"],["S3"],["C4"],
["V4"],["Cyclic",2]],[[[1,2,3,4,5,6,7,8,9,10],[1,1,1,1,1,1,1,1,1,1],["elab",
10,12]],[[1,2,3,4,4,5,5,6,6,6,7,8,9,9,9,10],[2,2,4,2,4,2,4,2,4,5,3,3,2,3,4,2],
["elab",16,7]],[[1,3,4,7],[3,2,3,2],["elab",4,23,(2,3),(2,4,3)]],[[1,2,3,5],
[4,3,3,3],["elab",4,23,,(2,4)]],[[1,3,3,4,5,6,8,8],[5,5,6,5,5,3,2,4],["elab",
8,6,(2,5,6,7,3,8,4)]],[[1,2],[7,5],[[1,1],[1,-1]]],[[1,2],[6,4],[[1,1],[1,
-1]]]]]]);
ALF("P21/G2/L2/V1/ext2","A6",[1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,
2,2,2,2,3,3,3,3,4,4,4,4,5,5,5,5,5,5,5,5,7,7,6,6]);
ALN("P21/G2/L2/V1/ext2",["2^9.A6v4"]);

MOT("P21/G2/L2/V2/ext2",
[
"origin: Hanrath library,\n",
"structure is 2^9.A6"
],
0,
0,
0,
0,
["ConstructPermuted",["P21/G2/L2/V1/ext2"],(11,16)(12,14)(13,15)(17,20)(18,19)
(35,36)(37,38)(39,40)(41,42)(43,45)(44,46),(4,5)(9,10)(13,16,14,15)(19,20)(22,
23)(29,32)(30,31)(37,40,38,39)(41,43,44,42)(45,46)]);
ALF("P21/G2/L2/V2/ext2","A6",[1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,
2,2,2,2,3,3,3,3,4,4,4,4,5,5,5,5,5,5,5,5,7,7,6,6]);
ALN("P21/G2/L2/V2/ext2",["2^9.A6v5"]);

MOT("P21/G2/L2/V3/ext2",
[
"origin: Hanrath library,\n",
"structure is 2^9.A6"
],
[184320,4096,2048,1024,12288,3072,2048,30720,18432,12288,64,64,64,64,128,128,
128,128,128,128,128,128,24,72,72,24,72,24,24,72,32,32,32,32,32,32,32,32,10,10,
10,10],
[,[1,1,1,1,1,1,1,1,1,1,3,4,8,4,2,7,9,9,10,7,10,2,24,24,24,24,27,27,27,27,17,
18,20,16,16,20,18,17,42,42,39,39],[1,2,3,4,5,6,7,8,9,10,11,14,13,12,22,20,18,
17,21,16,19,15,5,1,9,8,1,10,6,9,32,31,35,36,33,34,38,37,42,41,40,39],,[1,2,3,
4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,38,
37,36,35,34,33,32,31,1,8,8,1]],
0,
[(39,42)(40,41),(31,38)(32,37)(33,36)(34,35),(12,14)(15,22)(16,20)(17,18)
(19,21)(31,32)(33,35)(34,36)(37,38)],
["ConstructClifford",[[[1,2,3,4,5,7,6],[1,2,4,7,6],[1,3,4,
2,5,5],[1,2,3,2,5],[1,2,4,2,5],[1,2,5,2,2],[1,3,2],[1,5,2,5],[1,2,2,2],[1,
2]],[["A6"],["projectives","A5","2.A5"],["3^2:4"],["Symm(4)"],["Symm(4)"],
["D8"],["S3"],["C4"],["projectives","V4","Q8"],["Cyclic",2]],[[[1,2,3,4,5,6,7,
8,9,10],[1,1,1,1,1,1,1,1,1,1],["elab",10,12]],[[1,3,4,4,5,5,6,6,6,7,8,10],[2,
4,2,4,2,4,2,4,5,3,3,2],["elab",12,6]],[[1,3,4,7],[3,2,3,2],["elab",4,23,(2,3),
(1,2,3)]],[[1,2,3,5],[4,3,3,3],["elab",4,23,,(2,4)]],[[1,3,3,4,5,6,8,8],[5,5,
6,5,5,3,2,4],["elab",8,12]],[[1,2],[7,5],[[1,1],[1,-1]]],[[1,2],[6,4],[[1,1],[
-1,1]]]]]]);
ALF("P21/G2/L2/V3/ext2","A6",[1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,
3,3,3,3,4,4,4,4,5,5,5,5,5,5,5,5,7,7,6,6]);
ALN("P21/G2/L2/V3/ext2",["2^9.A6v6"]);

MOT("P21/G2/L5/V2/ext2",
[
"origin: Hanrath library,\n",
"structure is 2^9.A6"
],
[184320,4096,1024,12288,12288,2048,3072,3072,5120,18432,128,128,128,128,64,64,
64,64,64,64,72,24,24,72,24,24,72,72,32,32,32,32,32,32,32,32,10,10,10,10],
[,[1,1,1,1,1,1,1,1,1,1,10,10,6,6,7,7,8,8,9,9,21,21,21,21,27,27,27,27,14,13,12,
11,13,14,11,12,40,40,38,38],[1,2,3,4,5,6,7,8,9,10,12,11,14,13,16,15,18,17,20,
19,1,8,5,10,7,4,1,10,30,29,32,31,34,33,36,35,39,40,37,38],,[1,2,3,4,5,6,7,8,9,
10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,34,33,36,35,30,29,32,
31,9,1,9,1]],
0,
[(37,39)(38,40),(29,34)(30,33)(31,36)(32,35),(19,20),(11,12)(13,14)(15,16)
(17,18)(29,30)(31,32)(33,34)(35,36),( 4, 5)( 7, 8)(13,14)(15,18)(16,17)(21,27)
(22,25)(23,26)(24,28)(29,30)(31,36)(32,35)(33,34)],
["ConstructClifford",[[[1,2,3,4,5,7,6],[1,2,4,3,5,7,6],[1,
2,3,2,5],[1,2,3,2,5],[1,2,4,2,5],[1,2,4,2,5],[1,2,5,2,2],[1,2,5,2,2],[1,2],[1,
2]],[["A6"],["projectives","A6","2.A6"],["Symm(4)"],["projectives","Symm(4)",
"2.Symm(4)"],["Symm(4)"],["projectives","Symm(4)","2.Symm(4)"],["D8"],
["projectives","D8","2.D8"],["Cyclic",2],["Cyclic",2]],[[[1,2,3,4,5,6,7,8,9,
10],[1,1,1,1,1,1,1,1,1,1],["elab",10,13]],[[1,3,3,5,5,7,7,7,9,10],[2,2,4,2,4,
2,4,5,2,2],["elab",10,14]],[[1,2,3,4],[3,4,3,3],["elab",4,23,(2,3),(2,4)]],
[[1,2,5,6],[4,3,3,3],["elab",4,23,(2,3),(1,3,2,4)]],[[1,2,3,4,5,6,7,8],[5,5,5,
5,5,5,3,3],["elab",8,13]],[[1,2],[7,7],[[1,1],[-1,1]]],[[1,2],[6,6],[[1,1],
[-1,1]]]]]]);
ALF("P21/G2/L5/V2/ext2","A6",[1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,3,3,
3,3,4,4,4,4,5,5,5,5,5,5,5,5,7,7,6,6]);
ALN("P21/G2/L5/V2/ext2",["2^9.A6v7"]);

MOT("P21/G3/L2/V1/ext2",
[
"origin: Hanrath library,\n",
"structure is 2^10.A6"
],
[368640,8192,6144,4096,2048,8192,6144,2048,4096,18432,2048,24576,61440,24576,
24576,61440,24576,368640,512,256,128,256,256,512,128,128,128,128,128,128,128,
256,256,256,256,512,256,512,128,128,256,256,144,144,48,48,48,48,144,144,144,
48,48,48,144,48,144,144,32,32,32,32,32,32,32,32,20,20,20,20,20,20,20,20],
[,[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,6,6,1,6,1,4,3,3,4,3,3,14,17,17,14,14,
12,12,12,9,9,2,2,43,43,43,43,43,43,43,43,51,51,51,51,51,51,51,51,19,36,32,41,
32,41,24,38,71,71,71,71,67,67,67,67],[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,
1,10,14,13,12,16,18,10,1,15,3,7,10,17,10,18,59,60,63,64,61,62,65,66,71,74,73,
72,67,70,69,68],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,
24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,
50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,1,13,18,16,1,16,18,13]],
0,
[(67,71)(68,74)(69,73)(70,72),(61,63)(62,64),( 4, 9)(13,16)(25,40)(28,39)
(34,35)(44,50)(46,48)(68,70)(72,74),(19,24)(20,23)(25,28)(26,30)(27,29)(34,35)
(36,38)(39,40)(59,65)(60,66)],
["ConstructClifford",[[[1,2,3,4,5,7,6],[1,2,4,7,6],[1,3,4,2,5,5],[1,2,3,2,5],
[1,2,4,2,5],[1,3,3,4,4,2],[1,6,7,2],[1,6,7,2],[1,2,5,2,2],[1,3,2],[1,3,2],[1,
3,2],[1,4,2],[1,4,2],[1,5,2,5],[1,2,2,2],[1,2],[1,2]],[["A6"],["A5"],
["3^2:4"],["Symm(4)"],["Symm(4)"],["3^2:2"],["Dihedral",10],["Dihedral",
10],["D8"],["S3"],["S3"],["S3"],["S3"],["S3"],["C4"],["V4"],["Cyclic",
2],["Cyclic",2]],[[[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18],[1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1],["elab",18,2]],[[1,2,3,4,4,5,5,6,7,8,9,9,9,10,11,
12,13,14,15,16,16,16,17,18],[2,2,4,2,4,2,4,6,4,4,2,4,5,3,3,3,3,3,3,2,3,4,2,
2],["elab",24,3]],[[1,3,4,6,6,10,11,12],[3,2,3,2,3,2,2,2],["elab",8,2,
(3,6,7,4)(5,8),(3,7)(4,8)]],[[1,2,3,5,6,6,13,14],[4,3,3,3,4,5,2,2],["elab",8,
2,(2,6)(3,4,7,5,8),(2,5)(3,7)(4,8,6)]],[[1,3,3,4,5,9,15,15],[5,5,6,5,5,3,2,
4],["elab",8,6,(2,5)(3,8)(4,6,7)]],[[1,2,7,8],[7,5,2,2],["elab",4,12,
(2,4)]],[[1,2,7,8],[6,4,3,3],["elab",4,12,(2,3,4)]]]]]);
ALF("P21/G3/L2/V1/ext2","A6",[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,
2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,5,
5,5,5,5,5,5,5,7,7,7,7,6,6,6,6]);
ALN("P21/G3/L2/V1/ext2",["2^10.A6v1"]);

MOT("P21/G3/L5/V1/ext2",
[
"origin: Hanrath library,\n",
"structure is 2^10.A6"
],
0,
0,
0,
0,
["ConstructPermuted",["P21/G3/L2/V1/ext2"],(2,8,6,3,4,7,16,15,17)(5,11)(10,14)
(20,40,36,42,37,34,27,32,21,28)(22,29)(23,24,41,39,35,33,31)(25,30,26)(44,49,
47)(45,48,46)(52,53,56,54)(61,62)(63,64)(68,70,69)(72,73),(15,16)(33,34)(35,
39)(36,40)(37,41)(38,42)(57,60)(58,61)(59,62)(68,69,70)]);
ALF("P21/G3/L5/V1/ext2","A6",[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,
2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,5,
5,5,5,5,5,5,5,7,7,7,7,6,6,6,6]);
ALN("P21/G3/L5/V1/ext2",["2^10.A6v2"]);

MOT("P27/G1/L1/V1/ext2",
[
"origin: Hanrath library,\n",
"structure is 2^6.A7,\n",
"characters sorted with permutation (19,21,22,23)"
],
[161280,7680,4608,23040,384,192,128,64,128,384,576,576,96,144,144,36,36,36,36,
16,16,16,16,20,20,20,20,48,48,24,7,7],
[,[1,1,1,1,1,2,1,2,3,3,11,11,11,11,11,16,16,16,16,5,7,10,9,24,24,24,24,11,12,
13,31,32],[1,2,3,4,5,6,7,8,9,10,1,3,2,3,4,1,3,3,4,20,21,22,23,24,27,26,25,5,
10,6,32,31],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,1,4,
2,4,28,29,30,32,31],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,
22,23,24,27,26,25,28,29,30,1,1]],
0,
[(25,27),(17,18),(31,32)],
["ConstructClifford",[[[1,2,3,4,5,6,7,8,9],[1,2,4,3,5,6,6],[1,2,3,6,2,5,7],[1,
3,2,7,4,4,3,2,5]],[["A7"],["A6"],["S5"],["(A4x3):2"]],[[[1,2,3,4],[1,1,1,1],
["elab",4,24]],[[1,2,3,3,4,4],[2,2,2,5,3,8],["elab",6,9,(2,3,5,6,4),(2,6,4,5,
3)]],[[1,2,3,4,4],[3,4,3,2,7],["elab",5,15,(3,4,5),(3,4,5)]],[[1,2,4,4],[4,3,
5,6],["elab",4,12,(2,4,3)]],[[1,2,3,4],[5,5,6,9],["elab",4,12,(2,4,3)]],[[1,2,
2,3],[6,6,7,4],["elab",4,12]],[[1,3,4],[7,7,4],["elab",3,8,(2,3)]],[[1],[8]],
[[1],[9]]]]]);
ALF("P27/G1/L1/V1/ext2","A7",[1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,4,4,4,4,5,5,5,
5,6,6,6,6,7,7,7,8,9]);
ALN("P27/G1/L1/V1/ext2",["2^6.A7"]);

MOT("P27/G1/L1/V1/ext3",
[
"origin: Hanrath library,\n",
"structure is 3^6.A7,\n",
"characters sorted with permutation (26,28,29,30)(33,35,36,37)(64,65)(69,70)"
],
[1837080,43740,52488,52488,8748,17496,17496,262440,13122,262440,87480,87480,
1944,972,972,324,324,648,324,648,324,972,1944,648,324,648,324,1944,648,648,
162,324,2916,2916,2916,243,243,243,729,729,729,486,486,486,729,729,729,81,81,
81,81,81,81,81,81,81,36,36,36,36,36,36,36,36,36,45,45,45,45,45,45,45,45,45,
108,108,108,54,54,54,7,7],
[,[1,2,4,3,5,7,6,10,9,8,12,11,1,12,11,4,7,8,3,10,6,5,3,11,5,7,5,4,6,12,9,2,33,
35,34,36,38,37,45,47,46,43,42,44,39,41,40,48,50,49,54,56,55,51,53,52,13,24,30,
26,28,18,29,20,23,66,68,67,69,71,70,72,74,73,33,34,35,43,44,42,81,82],[1,1,1,
1,1,1,1,1,1,1,1,1,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,
1,4,3,1,4,3,4,3,1,4,3,1,3,1,4,1,8,10,4,3,9,3,9,4,57,57,57,57,57,57,57,57,57,
66,66,66,66,66,66,66,66,66,13,28,23,23,13,28,82,81],,[1,2,4,3,5,7,6,10,9,8,12,
11,13,15,14,19,21,20,16,18,17,22,28,30,27,29,25,23,26,24,31,32,33,35,34,36,38,
37,45,47,46,43,42,44,39,41,40,48,50,49,54,56,55,51,53,52,57,59,58,63,65,64,60,
62,61,1,11,12,2,8,10,2,8,10,75,77,76,80,79,78,82,81],,[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,
63,64,65,66,67,68,72,73,74,69,70,71,75,76,77,78,79,80,1,1]],
0,
[(81,82),(69,72)(70,73)(71,74),(51,56)(52,54)(53,55),( 3, 4)( 6, 7)( 8,10)
(11,12)(14,15)(16,19)(17,21)(18,20)(23,28)(24,30)(25,27)(26,29)(34,35)(37,38)
(39,45)(40,47)(41,46)(42,43)(49,50)(51,52)(54,56)(58,59)(60,63)(61,65)(62,64)
(67,68)(70,71)(73,74)(76,77)(78,80)],
["ConstructClifford",[[[1,2,3,4,5,6,7,8,9],[1,2,4,3,5,6,
6],[1,2,4,3,5,6,6],[1,2,3,6,2,5,7],[1,2,3,6,2,5,7],[1,3,2,7,4,4,3,2,5],[1,3,2,
7,4,4,3,2,5],[1,2,3,6,6],[1,2,3,2,5],[1,2,3,2,5],[1,4,3,3,4,2],[1,2,3,7,2,
2]],[["A7"],["A6"],["A6"],["S5"],["S5"],["(A4x3):2"],["(A4x3):2"],["A5"],
["Symm(4)"],["Symm(4)"],["3^2:2"],["S3x2"]],[[[1,2,3,4,5,6,7,8,9,10,11,12],[1,
1,1,1,1,1,1,1,1,1,1,1],["elab",12,7]],[[1,2,3,4,4,5,5,6,6,7,7,8,9,9,10,10,11,
12,12,12],[2,2,2,2,5,2,5,3,8,3,8,2,2,4,2,4,6,2,5,6],["elab",20,4]],[[1,2,3,4,
5,6,6,7,7,8,9,10,11,11,12],[3,4,4,3,3,2,7,2,7,3,3,3,3,4,3],["elab",15,4]],[[1,
2,3,6,6,7,7,11,11],[4,3,3,5,6,5,6,2,5],["elab",9,5,(2,5,6,3,4,7)]],[[1,2,3,4,
5,6,7,9,10],[5,5,5,6,6,9,9,5,5],["elab",9,5,(2,7)(3,4,6)(8,9)]],[[1,2,2,3,3,4,
5,8,8],[6,6,7,6,7,4,4,4,5],["elab",9,5,(3,7)(5,6)(8,9)]],[[1,4,5,6,7,12],[7,7,
7,4,4,4],["elab",6,15,(2,4)(3,5),(4,5,6)]],[[1],[8]],[[1],[9]]]]]);
ALF("P27/G1/L1/V1/ext3","A7",[1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,
2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,
5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,9]);
ALN("P27/G1/L1/V1/ext3",["3^6.A7"]);

MOT("P27/G1/L1/V1/ext4",
[
"origin: Hanrath library,\n",
"structure is 4^6.A7,\n",
"characters sorted with permutation (33,35,36,37)(40,42,43,44)\n",
"(47,49,50,51)(97,98)(102,103)(107,108)(112,113)(117,118)(122,123)"
],
[10321920,245760,491520,98304,98304,294912,49152,24576,294912,294912,24576,
49152,24576,49152,245760,98304,73728,16384,49152,245760,1474560,98304,1474560,
98304,73728,491520,98304,73728,491520,1474560,6144,3072,3072,3072,1024,512,
512,512,2048,1024,1024,1024,1024,1024,1024,2048,512,512,1024,1024,1024,2048,
1024,1024,2048,1024,1024,2048,1024,1024,2048,2048,512,1024,1024,3072,3072,
6144,1024,1024,2048,2048,1024,2048,1024,2048,6144,3072,2048,6144,9216,9216,
9216,9216,768,768,1536,1536,768,768,768,768,1536,1536,1536,1536,2304,2304,
2304,2304,768,768,768,768,768,768,768,768,2304,2304,2304,2304,2304,2304,2304,
2304,144,144,144,144,144,144,144,144,144,144,144,144,144,144,144,144,64,64,64,
64,64,64,64,64,64,64,64,64,64,64,64,64,80,80,80,80,80,80,80,80,80,80,80,80,80,
80,80,80,192,192,192,192,96,96,96,96,96,96,7,7],
[,[1,3,1,3,3,9,9,3,1,9,9,3,9,3,21,9,21,9,3,21,1,9,21,21,9,3,21,9,3,21,1,12,3,
14,21,14,9,12,1,12,3,14,4,9,5,3,4,5,3,14,12,21,9,12,21,14,5,3,4,18,22,16,18,
22,16,7,29,10,7,29,10,22,18,16,26,9,9,26,6,6,81,83,81,83,87,87,81,83,87,87,87,
87,87,87,87,87,113,115,113,115,113,115,113,115,113,115,113,115,113,115,113,
115,81,83,81,83,117,119,117,119,125,127,125,127,117,119,117,119,125,127,125,
127,31,55,39,52,71,74,68,62,77,58,76,46,79,72,80,61,149,159,149,159,157,151,
157,151,149,159,149,159,157,151,157,151,81,82,83,84,94,95,96,93,87,88,175,
176],[1,2,3,5,4,10,7,8,9,6,13,14,11,12,20,22,17,18,19,15,21,16,30,27,28,29,24,
25,26,23,31,34,33,32,35,38,37,36,39,42,41,40,57,53,59,58,48,47,49,54,56,55,44,
50,52,51,43,46,45,73,74,72,63,65,64,66,78,80,69,75,79,62,60,61,70,76,77,67,71,
68,1,10,9,6,19,19,3,7,2,5,8,4,12,14,29,26,10,30,28,17,11,24,16,15,13,20,22,27,
6,17,25,23,9,28,21,25,1,25,9,28,10,23,28,17,9,6,21,10,6,17,25,30,133,136,135,
134,145,148,147,146,141,144,143,142,137,140,139,138,149,164,159,154,153,152,
163,158,157,156,151,162,161,160,155,150,31,68,77,80,34,67,78,32,33,66,176,
175],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,
27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,
53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,
79,80,81,82,83,84,86,85,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,
103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,
122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,
141,142,143,144,145,146,147,148,1,23,21,30,2,23,29,20,3,15,21,20,2,15,26,30,
165,166,167,168,169,170,171,172,173,174,176,175],,[1,2,3,5,4,10,7,8,9,6,13,14,
11,12,20,22,17,18,19,15,21,16,30,27,28,29,24,25,26,23,31,34,33,32,35,38,37,36,
39,42,41,40,57,53,59,58,48,47,49,54,56,55,44,50,52,51,43,46,45,73,74,72,63,65,
64,66,78,80,69,75,79,62,60,61,70,76,77,67,71,68,81,84,83,82,86,85,87,88,89,92,
91,90,94,93,96,95,109,112,111,110,105,108,107,106,101,104,103,102,97,100,99,
98,113,116,115,114,117,120,119,118,129,132,131,130,125,128,127,126,121,124,
123,122,133,136,135,134,145,148,147,146,141,144,143,142,137,140,139,138,149,
164,159,154,153,152,163,158,157,156,151,162,161,160,155,150,165,168,167,166,
172,171,170,169,173,174,1,1]],
0,
[(175,176),(150,154)(151,159)(152,164)(153,161)(156,160)(158,162),(118,131)
(119,125)(120,123)(121,128)(124,130)(126,129),( 85, 86),(  4,  5)(  6, 10)
( 11, 13)( 12, 14)( 15, 20)( 16, 22)( 23, 30)( 24, 27)( 25, 28)( 26, 29)
( 32, 34)( 36, 38)( 40, 42)( 43, 57)( 44, 53)( 45, 59)( 46, 58)( 47, 48)
( 50, 54)( 51, 56)( 52, 55)( 60, 73)( 61, 74)( 62, 72)( 64, 65)( 67, 78)
( 68, 80)( 70, 75)( 71, 79)( 82, 84)( 90, 92)( 93, 94)( 95, 96)( 97,109)
( 98,112)( 99,111)(100,110)(101,105)(102,108)(103,107)(104,106)(114,116)
(118,120)(121,129)(122,132)(123,131)(124,130)(126,128)(134,136)(137,145)
(138,148)(139,147)(140,146)(142,144)(150,152)(153,161)(154,164)(155,163)
(156,162)(158,160)(166,168)(169,172)(170,171)],
["ConstructClifford",[[[1,2,3,4,5,6,7,8,9],[1,2,4,3,5,6,
6],[1,2,4,3,5,6,6],[1,2,4,3,5,6,6],[1,2,3,6,2,5,7],[1,2,3,6,2,5,7],[1,2,3,6,2,
5,7],[1,3,2,7,4,4,3,2,5],[1,3,2,7,4,4,3,2,5],[1,3,2,7,4,4,3,2,5],[1,2,3,6,6],[
1,2,3,6,6],[1,2,3,6,6],[1,2,3,2,5],[1,2,3,2,5],[1,2,3,2,5],[1,2,3,2,5],[1,2,3,
2,5],[1,2,3,2,5],[1,4,3,3,4,2],[1,4,3,3,4,2],[1,4,3,3,4,2],[1,2,3,3],[1,2,3,7,
2,2],[1,2,3,7,2,2],[1,2,3,7,2,2],[1,3,2],[1,3,2],[1,3,2],[1,2,2,
2]],[["A7"],["A6"],["A6"],["A6"],["S5"],["S5"],["S5"],["(A4x3):2"],["(A4x3):2"
],["(A4x3):2"],["A5"],["A5"],["A5"],["Symm(4)"],["Symm(4)"],["Symm(4)"],
["Symm(4)"],["Symm(4)"],["Symm(4)"],["3^2:2"],["3^2:2"],["3^2:2"],["A4"],
["S3x2"],["S3x2"],["S3x2"],["S3"],["S3"],["S3"],["V4"]],[[[1,2,3,4,5,6,7,8,9,
10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30],[1,1,1,1,1,1,
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",30,1]],[[1,2,3,4,5,5,
6,6,7,7,8,8,9,9,10,10,11,12,13,14,14,15,15,16,16,17,17,18,18,19,19,20,21,22,
23,24,24,24,25,25,25,26,26,26,27,28,29,30,30,30],[2,2,2,2,2,5,2,5,2,5,3,8,3,8,
3,8,2,2,2,2,4,2,4,2,4,2,4,2,4,2,4,6,6,6,2,2,5,6,2,5,6,2,5,6,3,3,3,2,3,4],
["elab",50,1]],[[1,2,3,4,5,6,7,8,8,9,9,10,10,11,12,13,14,15,16,17,18,19,20,20,
21,21,22,22,23,23,24,25,26,27,28,29],[3,4,4,4,3,3,3,2,7,2,7,2,7,3,3,3,3,3,3,3,
3,3,3,4,3,4,3,4,3,4,3,3,3,2,2,2],["elab",36,6]],[[1,2,3,4,8,8,9,9,10,10,20,20,
21,21,22,22],[4,3,3,3,5,6,5,6,5,6,2,5,2,5,2,5],["elab",16,1,( 2, 6,10)( 3, 5,
 7, 9)( 4, 8)(11,13,15)(12,14,16)]],[[1,2,3,4,5,6,7,8,9,10,14,15,16,17,18,19],
[5,5,5,5,6,6,6,9,9,9,5,5,5,5,5,5],["elab",16,1,( 2,10)( 3, 5, 6, 8, 4, 9)(11,
16)(14,15)]],[[1,2,2,3,3,4,4,5,6,7,11,11,12,12,13,13],[6,6,7,6,7,6,7,4,4,4,4,
5,4,5,4,5],["elab",16,1,( 3,10)( 5, 9)( 7, 8)(11,14)(12,15)(13,16)]],[[1,5,6,
7,8,9,10,24,25,26],[7,7,7,7,4,4,4,4,4,4],["elab",10,4,( 2, 7,10, 9)( 3, 6)( 4,
 5, 8),( 2, 5,10, 4, 8, 3, 9, 7, 6)]],[[1],[8]],[[1],[9]]]]]);
ALF("P27/G1/L1/V1/ext4","A7",[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
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,
2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,
3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,
5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,
7,7,7,7,8,9]);
ALN("P27/G1/L1/V1/ext4",["4^6.A7"]);

MOT("P31/G1/L1/V1/ext2",
[
"origin: Hanrath library,\n",
"structure is 2^7.A8,\n",
"characters sorted with permutation (26,29)(27,28)(30,31,32,33,34)(36,37)\n",
"(39,40,42,41)(44,45)(46,49,48,47)(54,55)(56,57)"
],
[2580480,92160,36864,92160,2580480,3072,3072,256,3072,3072,3072,3072,512,512,
384,384,3072,3072,5760,5760,576,576,1152,1152,144,144,144,144,72,72,64,64,64,
64,64,64,32,32,64,64,120,120,40,40,96,96,48,48,96,96,24,24,24,24,14,14,14,14,
30,30,30,30],
[,[1,1,1,1,1,1,5,3,1,5,1,3,1,3,2,2,3,1,19,19,19,19,19,19,25,25,25,25,25,25,6,
7,10,9,11,14,17,13,14,11,41,41,41,41,19,24,21,21,24,19,25,26,25,26,55,55,57,
57,59,59,61,61],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,1,5,2,4,3,3,1,5,
4,2,3,3,31,32,33,34,35,36,37,38,39,40,41,42,43,44,11,12,16,15,17,18,6,7,9,10,
57,58,55,56,41,42,41,42],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,
21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,1,5,4,2,45,46,47,
48,49,50,51,52,53,54,57,58,55,56,19,20,19,20],,[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,
40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,1,5,1,5,61,62,59,60]],
0,
[(59,61)(60,62),(55,57)(56,58),( 7,10)(29,30)(32,33)(52,54),( 6, 9)(29,30)
(31,34)(51,53)],
["ConstructClifford",[[[1,2,3,4,5,6,7,8,9,10,11,12,13,14],[1,3,4,5,7,8,9,11,
12],[1,3,5,4,7,8,2,3,7,10,9],[1,3,2,3,6,7,4,9,5,5,2,2,6,6,10,10],[1,3,4,8,4,9,
5,13,14,3,7,9]],[["A8"],["A7"],["S6"],["2^4:(S3xS3)"],["(A5x3):2"]],[[[1,2,3,
4,5],[1,1,1,1,1],["elab",5,21]],[[1,3,4,4,4],[2,7,3,11,12],["elab",5,14,,(3,4,
5)]],[[1,2,3,3,4,4,5,5],[3,2,2,8,2,4,2,10],["elab",8,14]],[[1,2,3,4,5,5],[4,3,
4,7,3,5],["elab",6,20]],[[1,2,3,4,4,5],[5,4,3,9,10,7],["elab",6,16,(2,6,3),
(2,3,5,4,6)]],[[1,4,4,4],[6,5,13,14],["elab",4,12,(2,3)]],[[1,2,3,3,4,5],[7,5,
5,9,6,11],["elab",6,16,(3,6)]],[[1,2,3,5],[8,6,6,4],["elab",4,23,(3,4),
(3,4)]],[[1,2,3,4,5,5],[9,7,11,8,6,12],["elab",6,16,(2,3,6,4),(5,6)]],[[1,3,4,
4],[10,10,15,16],["elab",4,12,(2,4)]],[[1,2],[11,8],[[1,1],[1,-1]]],[[1,2],[
12,9],[[1,1],[1,-1]]],[[1,5],[13,8],[[1,1],[1,-1]]],[[1,5],[14,9],[[1,1],[1,
-1]]]]]]);
ALF("P31/G1/L1/V1/ext2","A8",[1,1,1,1,1,2,2,2,2,2,3,3,3,3,3,3,3,3,4,4,4,4,
4,4,5,5,5,5,5,5,6,6,6,6,7,7,7,7,7,7,8,8,8,8,9,9,9,9,9,9,10,10,10,10,11,11,
12,12,13,13,14,14]);
ALF("P31/G1/L1/V1/ext2","2^6:A8",[1,2,3,2,1,4,5,8,7,6,9,11,10,12,13,13,11,
9,14,14,16,16,15,15,17,17,20,20,19,18,21,23,24,22,25,28,27,26,28,25,29,29,
30,30,31,32,33,33,32,31,34,36,37,35,38,38,39,39,40,40,41,41]);
ALF("P31/G1/L1/V1/ext2","2.O8+(2)",[1,4,3,5,2,3,6,21,8,7,4,20,8,21,22,23,
19,5,9,10,37,38,34,33,17,18,47,46,44,45,21,24,25,26,22,55,53,26,54,23,27,
28,63,62,37,67,75,74,66,38,43,48,50,49,51,52,51,52,78,79,78,79],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALN("P31/G1/L1/V1/ext2",["2^7.A8"]);

MOT("P31/G1/L1/V1/ext3",
[
"origin: Hanrath library,\n",
"structure is 3^7.A8,\n",
"characters sorted with permutation (35,38)(36,37)(39,40,41,42,43)(46,49)\n",
"(47,48)(50,51,52,53,54)(58,59)(60,61)(70,71)(72,73)(80,81)\n",
"(102,104,105,106)(109,111,112,113)(120,121)(129,130)\n",
"(134,137,139,135,138,140,136)(146,148,147)"
],
[44089920,787320,787320,787320,104976,157464,157464,1574640,78732,1574640,
262440,262440,5511240,629856,5511240,5184,1296,1296,432,864,23328,23328,23328,
3888,3888,3888,11664,11664,11664,1944,1944,1944,972,972,972,1944,1944,1944,
2916,2916,2916,2916,2916,2916,5832,5832,5832,5832,5832,5832,43740,43740,43740,
1458,1458,1458,8748,8748,8748,4374,4374,4374,8748,8748,8748,4374,4374,4374,
2187,2187,2187,486,243,243,243,243,243,243,243,243,243,243,486,243,243,486,48,
24,216,216,216,108,108,108,216,216,216,108,108,108,216,216,216,108,108,108,
405,405,405,135,135,135,135,135,135,135,135,324,324,324,162,162,162,162,162,
162,324,324,324,162,162,162,324,324,324,18,18,18,21,21,21,21,21,21,45,45,45,
45,45,45],
[,[1,2,4,3,5,7,6,10,9,8,12,11,15,14,13,1,8,10,5,14,1,14,14,10,5,8,5,10,8,5,14,
5,7,6,9,11,12,2,4,9,11,3,12,9,6,15,3,7,4,13,51,53,52,56,55,54,63,65,64,68,67,
66,57,59,58,62,61,60,70,69,71,72,74,73,78,79,77,75,76,80,85,82,86,84,81,83,16,
20,21,25,25,47,38,49,24,23,24,48,46,37,26,26,22,36,50,45,107,109,108,110,111,
115,117,116,112,114,113,51,58,65,55,62,66,60,67,56,59,63,52,68,54,61,64,53,57,
72,83,86,139,141,140,142,144,143,145,147,146,148,150,149],[1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,16,16,16,16,16,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,
21,21,21,21,21,21,21,21,21,21,21,21,21,1,3,4,4,1,3,4,1,3,3,4,1,3,4,1,1,3,4,3,
4,1,1,3,4,3,4,1,4,3,9,10,9,10,9,8,8,87,87,89,89,89,89,89,89,89,89,89,89,89,89,
89,89,89,89,89,89,107,107,107,107,107,107,107,107,107,107,107,21,21,21,21,21,
21,47,47,47,47,47,47,49,49,49,49,49,49,16,18,17,142,142,142,139,139,139,107,
109,108,107,109,108],,[1,2,4,3,5,7,6,10,9,8,12,11,15,14,13,16,18,17,19,20,21,
23,22,26,25,24,27,29,28,32,31,30,34,33,35,37,36,38,42,44,43,39,41,40,48,50,49,
45,47,46,51,53,52,56,55,54,63,65,64,68,67,66,57,59,58,62,61,60,70,69,71,72,74,
73,78,79,77,75,76,80,85,82,86,84,81,83,87,88,89,91,90,94,93,92,101,103,102,
106,105,104,95,97,96,100,99,98,1,4,3,2,2,10,15,12,8,11,13,118,120,119,121,123,
122,130,132,131,133,135,134,124,126,125,127,129,128,136,138,137,142,144,143,
139,141,140,51,52,53,51,52,53],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,
19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,
45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,
71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,
97,98,99,100,101,102,103,104,105,106,107,108,109,111,110,112,113,114,115,116,
117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,
136,137,138,1,15,13,1,15,13,148,149,150,145,146,147]],
0,
[(145,148)(146,149)(147,150),(139,142)(140,143)(141,144),(110,111),( 75, 79)
( 76, 78)( 80, 84),(  3,  4)(  6,  7)(  8, 10)( 11, 12)( 13, 15)( 17, 18)
( 22, 23)( 24, 26)( 28, 29)( 30, 32)( 33, 34)( 36, 37)( 39, 42)( 40, 44)
( 41, 43)( 45, 48)( 46, 50)( 47, 49)( 52, 53)( 54, 56)( 57, 63)( 58, 65)
( 59, 64)( 60, 68)( 61, 67)( 62, 66)( 69, 70)( 73, 74)( 75, 76)( 78, 79)
( 80, 84)( 81, 85)( 83, 86)( 90, 91)( 92, 94)( 95,101)( 96,103)( 97,102)
( 98,106)( 99,105)(100,104)(108,109)(112,115)(113,117)(114,116)(119,120)
(122,123)(124,130)(125,132)(126,131)(127,133)(128,135)(129,134)(137,138)
(140,141)(143,144)(146,147)(149,150)],
["ConstructClifford",[[[1,2,3,4,5,6,7,8,9,10,11,12,13,14],[
1,3,4,5,7,8,9,11,12],[1,3,4,5,7,8,9,11,12],[1,3,5,4,7,8,2,3,7,10,9],[1,3,5,4,
7,8,2,3,7,10,9],[1,3,4,8,4,9,5,13,14,3,7,9],[1,3,4,8,4,9,5,13,14,3,7,9],[1,3,
4,5,7,8,8],[1,3,3,2,4,9,4,9,5,5,3,7,7,6],[1,3,4,8,3,7,9],[1,3,4,8,3,7,9],[1,4,
3,9,4,5,5,3,7],[1,4,3,9,4,5,5,3,7],[1,3,3,2,4,9,3,3,7,7],[1,4,4,5,3,9,3,9,
3]],[["A8"],["A7"],["A7"],["S6"],["S6"],["(A5x3):2"],["(A5x3):2"],["A6"],
["2^4:(3x3):2"],["S5"],["S5"],["(A4x3):2"],["(A4x3):2"],["2xSymm(4)"],["S3xS3"
]],
[[[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",15,5]],[[1,4,5,9,14],[2,7,7,4,4],["elab",5,5,(2,4,3),(2,4,5,3)]],[[1,
2,3,4,4,5,5,6,6,7,7,8,9,9,9,10,10,11,11,12,12,13,13,14,14,14,14,15,15,15],[3,
2,2,2,8,2,8,2,10,2,10,2,2,3,11,2,5,2,5,3,8,3,8,2,3,7,8,5,7,9],["elab",30,2]],
[[1,2,3,4,5,6,6,7,7,8,9,9,10,11,12,12,13,13,14,15,15],[4,3,3,4,4,3,5,3,5,3,5,
7,3,3,2,5,2,5,5,2,3],["elab",21,3]],[[1,2,3,4,5,6,7,8,9,9,12,12,13,13,15],[5,
4,4,3,3,7,7,4,9,10,6,7,6,7,4],["elab",15,3,( 4, 9,12, 8, 7, 6, 5)(10,14,13)
(11,15),( 4, 5, 6)( 7, 8)( 9,15,10,11,14,12)]],[[1,9],[6,14],[[1,1],[2,-1]]],
[[1,2,3,4,4,5,5,6,7,8,9,9,10,11,12,13,14,14],[7,5,5,5,9,5,9,11,11,5,12,13,6,6,
9,9,9,10],["elab",18,1,( 2,11, 5, 3,12,17, 9,18, 8, 7,14,10, 4)( 6,13),
( 2, 4, 7,13,15, 3, 6,12,17)( 5,10,11, 9,18, 8,16,14)]],[[1,2,3,4,5,6,7,8,8,
10,11],[8,6,6,6,6,4,4,6,7,4,4],["elab",11,4,( 2, 4,10, 3, 5,11)( 8, 9),
( 2, 6, 7, 5, 4,11, 3, 9)( 8,10)]],[[1,2,3,4,5,6,6,7,7,9,9,10,11,12,13,14,15,
15],[9,7,7,11,11,6,12,6,12,6,8,7,7,4,4,6,6,8],["elab",18,1,( 2, 6,13,14,16,17,
 5, 9,10,15,18, 4, 7,12,11, 3, 8),( 2, 5, 7,17, 3, 6, 8,15)( 4,12,14)
( 9,13,18,11,10)]],[[1,4,5],[10,10,10],["elab",3,1]],[[1,2,3],[11,8,
8],["elab",3,1]],[[1,2,3],[12,9,9],["elab",3,1]],[[1,6,7],[13,8,8],["elab",3,
1,(2,3)]],[[1,6,7],[14,9,9],["elab",3,1,(2,3)]]]]]);
ALF("P31/G1/L1/V1/ext3","A8",[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,3,3,
3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,
4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,7,7,7,7,7,7,7,7,
7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,
9,9,10,10,10,11,11,11,12,12,12,13,13,13,14,14,14]);
ALN("P31/G1/L1/V1/ext3",["3^7.A8"]);

MOT("P41/G1/L1/V1/ext2",
[
"origin: Hanrath library,\n",
"structure is 2^7.L2(8),\n",
"characters sorted with permutation (12,14,15,13)(19,20)"
],
[64512,1024,1024,64512,128,128,64,64,64,64,64,64,128,128,18,18,14,14,14,14,14,
14,18,18,18,18,18,18],
[,[1,1,1,1,1,2,2,3,2,3,3,2,1,2,15,15,19,19,21,21,17,17,25,25,27,27,23,23],[1,
2,3,4,5,6,7,8,9,10,11,12,13,14,1,4,21,22,17,18,19,20,15,16,15,16,15,16],,,,[1,
2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,1,4,1,4,1,4,25,26,27,28,23,24]],
0,
[(23,25,27)(24,26,28),( 7, 9,12)( 8,10,11),( 5,13)( 6,14),(17,19,21)
(18,20,22)],
["ConstructClifford",[[[1,2,3,4,5,6,7,8,9],[1,7,8,3,9,2],[
1,4,5,6,2],[1,2,2,2,2,2,2,2]],[["L2(8)"],["Dihedral",18],["Dihedral",
14],["2^3"]],[[[1,2,3,4],[1,1,1,1],["elab",4,25]],[[1,2,3,4,4,4,4,4,4,4],[2,6,
5,2,3,4,5,6,7,8],["elab",10,15]],[[1,2],[3,4],[[1,1],[1,-1]]],[[1,3],[4,2],[[
1,1],[1,-1]]],[[1,3],[5,3],[[1,1],[1,-1]]],[[1,3],[6,4],[[1,1],[1,-1]]],[[1,
2],[7,2],[[1,1],[1,-1]]],[[1,2],[8,3],[[1,1],[1,-1]]],[[1,2],[9,5],[[1,1],[1,
-1]]]]]]);
ALF("P41/G1/L1/V1/ext2","L2(8)",[1,1,1,1,2,2,2,2,2,2,2,2,2,2,3,3,4,4,5,5,
6,6,7,7,8,8,9,9]);
ALN("P41/G1/L1/V1/ext2",["2^7.L2(8)v1"]);

MOT("P41/G1/L1/V1/ext3",
[
"origin: Hanrath library,\n",
"structure is 3^7.L2(8),\n",
"characters sorted with permutation (11,13)(12,16,15,14)"
],
[1102248,8748,6561,4374,4374,6561,13122,6561,4374,13122,2187,15309,19683,216,
54,54,54,54,54,108,108,108,243,81,81,243,81,81,243,81,81,81,81,21,21,21,21,21,
21,21,21,21,27,27,27,27,27,27,27,27,27],
[,[1,2,3,4,5,6,10,8,9,7,11,12,13,1,10,7,5,4,9,2,2,2,23,24,25,26,27,28,29,30,
31,33,32,37,39,38,40,41,42,34,35,36,46,48,47,49,51,50,43,44,45],[1,1,1,1,1,1,
1,1,1,1,1,1,1,14,14,14,14,14,14,14,14,14,1,13,13,1,13,13,1,13,13,1,1,40,40,40,
34,34,34,37,37,37,23,29,26,23,26,29,23,29,26],,,,[1,2,3,4,5,6,7,8,9,10,11,12,
13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,1,12,12,1,12,
12,1,12,12,46,48,47,49,51,50,43,44,45]],
0,
[(43,46,49)(44,48,50)(45,47,51),(35,36)(38,39)(41,42),(34,37,40)(35,38,42)
(36,39,41),( 7,10)(15,16)(32,33),(24,25)(26,29)(27,31)(28,30)(44,45)(47,48)
(50,51),( 3, 6, 8)( 4, 5, 9)(17,19,18)(20,22,21)(24,28,27,25,30,31)(26,29)
(44,45)(47,48)(50,51),(23,29)(24,31)(25,30)(27,28)(43,44)(46,48)(49,50)],
["ConstructClifford",[[[1,2,3,4,5,6,7,8,9],[1,7,8,3,9,9,3,
8,7],[1,4,5,6,6,5,4],[1,3,2],[1,3,2],[1,2,2,2],[1,3,3],[1,3,3],[1,3,3],[1,2],[
1,2],[1,2],[1]],[["L2(8)"],["Cyclic",9],["Cyclic",
7],["S3"],["S3"],["V4"],["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],[
1,1,1,1,1,1,1,1,1,1,1,1,1],["elab",13,1]],[[1,4,5,6,6,6,10,11,12],[2,3,3,2,3,
4,2,2,2],["elab",9,10,(2,4,3,5)(7,8)]],[[1,2,2,4,5,7,7,8,8,9,9],[3,4,7,2,2,2,
3,2,3,2,3],["elab",11,4,( 2,11, 8, 5, 7, 3,10, 9, 4, 6),( 4, 6, 8, 9, 7,11)
( 5,10)]],[[1,3,3],[4,2,7],["elab",3,1]],[[1,3,3],[5,3,6],["elab",3,1]],[[1,3,
3],[6,4,5],["elab",3,1]],[[1,2,2],[7,2,9],["elab",3,1]],[[1,2,2],[8,3,
8],["elab",3,1]],[[1,2,2],[9,5,6],["elab",3,1]]]]]);
ALF("P41/G1/L1/V1/ext3","L2(8)",[1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,
2,2,3,3,3,3,3,3,3,3,3,3,3,4,4,4,5,5,5,6,6,6,7,7,7,8,8,8,9,9,9]);
ALN("P41/G1/L1/V1/ext3",["3^7.L2(8)v1"]);

MOT("P41/G1/L1/V2/ext2",
[
"origin: Hanrath library,\n",
"structure is 2^7.L2(8),\n",
"characters sorted with permutation (12,14,15,13)(19,20)"
],
[64512,1024,1024,64512,64,64,128,128,64,64,64,64,128,128,18,18,14,14,14,14,14,
14,18,18,18,18,18,18],
[,[1,1,1,1,1,2,2,3,2,3,3,2,2,3,15,15,19,19,22,22,18,18,25,25,27,27,23,23],[1,
2,3,4,5,6,7,8,9,10,11,12,13,14,1,4,21,22,18,17,20,19,15,16,15,16,15,16],,,,[1,
2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,4,1,1,4,4,1,25,26,27,28,23,24]],
0,
[(23,25,27)(24,26,28),( 7,13)( 8,14),(17,20,21)(18,19,22)],
["ConstructClifford",[[[1,2,3,4,5,6,7,8,9],[1,7,8,3,9,2],[
1,4,5,6,2],[1,2,2,2,2,2,2,2]],[["L2(8)"],["Dihedral",18],["Dihedral",
14],["2^3"]],[[[1,2,3,4],[1,1,1,1],["elab",4,25]],[[1,2,3,4,4,4,4,4,4,4],[2,6,
5,2,3,4,5,6,7,8],["elab",10,16]],[[1,2],[3,4],[[1,1],[1,-1]]],[[1,3],[4,2],[[
1,1],[-1,1]]],[[1,3],[5,3],[[1,1],[1,-1]]],[[1,3],[6,4],[[1,1],[-1,1]]],[[1,
2],[7,2],[[1,1],[1,-1]]],[[1,2],[8,3],[[1,1],[1,-1]]],[[1,2],[9,5],[[1,1],[1,
-1]]]]]]);
ALF("P41/G1/L1/V2/ext2","L2(8)",[1,1,1,1,2,2,2,2,2,2,2,2,2,2,3,3,4,4,5,5,
6,6,7,7,8,8,9,9]);
ALN("P41/G1/L1/V2/ext2",["2^7.L2(8)v2"]);

MOT("P41/G1/L1/V3/ext3",
[
"origin: Hanrath library,\n",
"structure is 3^7.L2(8),\n",
"characters sorted with permutation (11,13)(12,16,15,14)"
],
[1102248,8748,6561,4374,4374,6561,13122,6561,4374,13122,2187,15309,19683,108,
54,54,54,108,54,108,54,216,81,81,81,81,81,81,81,81,243,243,243,21,21,21,21,21,
21,21,21,21,27,27,27,27,27,27,27,27,27],
[,[1,2,3,4,5,6,10,8,9,7,11,12,13,2,7,5,4,2,9,2,10,1,30,24,25,26,27,28,29,23,
31,32,33,38,37,39,40,41,42,34,35,36,47,46,48,51,50,49,45,43,44],[1,1,1,1,1,1,
1,1,1,1,1,1,1,22,22,22,22,22,22,22,22,22,13,13,1,13,1,13,1,13,13,13,13,42,42,
42,36,36,36,39,39,39,31,33,32,33,31,32,32,31,33],,,,[1,2,3,4,5,6,7,8,9,10,11,
12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,12,12,1,12,
12,1,12,12,1,47,46,48,51,50,49,45,43,44]],
0,
[(34,35)(37,38)(40,41),(34,37,41)(35,38,40)(36,39,42),( 7,10)(15,21)(23,30),
(24,26,28)(25,27,29)(31,32,33)(43,48,51)(44,47,49)(45,46,50),(43,47,50)
(44,46,51)(45,48,49),( 3, 6, 8)( 4, 5, 9)(14,20,18)(16,19,17)(24,28,26)
(25,27,29)],
["ConstructClifford",[[[1,2,3,4,5,6,7,8,9],[1,7,8,3,9,9,3,
8,7],[1,4,5,6,6,5,4],[1,3,2],[1,3,2],[1,2,2,2],[1,3,3],[1,3,3],[1,3,3],[1,2],[
1,2],[1,2],[1]],[["L2(8)"],["Cyclic",9],["Cyclic",
7],["S3"],["S3"],["V4"],["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],[
1,1,1,1,1,1,1,1,1,1,1,1,1],["elab",13,1]],[[1,4,5,6,6,6,10,11,12],[2,3,3,2,3,
4,2,2,2],["elab",9,15]],[[1,2,2,4,5,7,7,8,8,9,9],[3,4,7,2,2,2,3,2,3,2,
3],["elab",11,5]],[[1,3,3],[4,2,7],["elab",3,1,,(1,3,2)]],[[1,3,3],[5,3,
6],["elab",3,1,,(1,3,2)]],[[1,3,3],[6,4,5],["elab",3,1,,(1,3,2)]],[[1,2,2],[7,
2,9],["elab",3,12]],[[1,2,2],[8,3,8],["elab",3,12,(2,3),(2,3)]],[[1,2,2],[9,5,
6],["elab",3,12]]]]]);
ALF("P41/G1/L1/V3/ext3","L2(8)",[1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,
2,2,3,3,3,3,3,3,3,3,3,3,3,4,4,4,5,5,5,6,6,6,7,7,7,8,8,8,9,9,9]);
ALN("P41/G1/L1/V3/ext3",["3^7.L2(8)v2"]);

MOT("P41/G1/L1/V4/ext2",
[
"origin: computed from PerfectGroup(64512,4),\n",
"structure is 2^7.L2(8).\n",
"NOTE: The table 2.4.7 in the microfiche of [HP89] is not correct,\n",
"the 2A Clifford matrix and the table head had to be changed."
],
[64512,1024,1024,64512,128,128,128,128,64,64,64,64,64,64,18,18,14,14,14,14,14,
14,18,18,18,18,18,18],
[,[1,1,1,1,2,2,3,3,2,2,4,3,3,3,16,16,20,20,22,22,18,18,26,26,27,27,23,23],[1,
2,3,4,6,5,8,7,9,10,11,12,13,14,4,1,21,22,17,18,19,20,16,15,15,16,16,15],,,,[1,
2,3,4,6,5,8,7,9,10,11,12,13,14,15,16,4,1,4,1,4,1,26,25,28,27,23,24]],
0,
[(23,26,27)(24,25,28),(5,6)(7,8),(17,19,21)(18,20,22)],
["ConstructClifford",[[[1,2,3,4,5,6,7,8,9],[1,7,8,3,9,2],[
1,4,5,6,2],[1,2,2,2,2,2,2,2]],[["L2(8)"],["Dihedral",18],["Dihedral",
14],["2^3"]],[[[1,2,3,4],[1,1,1,1],["elab",4,25]],[[1,2,3,4,4,4,4,4,4,4],[2,6,
5,2,3,4,5,6,7,8],["elab",10,23]],[[1,2],[3,4],[[1,1],[-1,1]]],[[1,3],[4,2],[[
1,1],[-1,1]]],[[1,3],[5,3],[[1,1],[-1,1]]],[[1,3],[6,4],[[1,1],[-1,1]]],[[1,
2],[7,2],[[1,1],[1,-1]]],[[1,2],[8,3],[[1,1],[-1,1]]],[[1,2],[9,5],[[1,1],[1,
-1]]]]]]);
ALF("P41/G1/L1/V4/ext2","L2(8)",[1,1,1,1,2,2,2,2,2,2,2,2,2,2,3,3,4,4,5,5,
6,6,7,7,8,8,9,9]);
ALN("P41/G1/L1/V4/ext2",["2^7.L2(8)v3"]);

MOT("P41/G1/L1/V4/ext3",
[
"origin: Hanrath library,\n",
"structure is 3^7.L2(8),\n",
"characters sorted with permutation (11,13)(12,16,15,14)"
],
0,
0,
0,
0,
["ConstructPermuted",["P41/G1/L1/V3/ext3"],(23,33,32,30,24,26)(25,27)(43,47,
51,45,46,50)(44,48,49),(3,4,5)(10,13)(11,18,17,12,14,15)(36,38)(39,41)(42,44)
]);
ALF("P41/G1/L1/V4/ext3","L2(8)",[1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,
2,2,3,3,3,3,3,3,3,3,3,3,3,4,4,4,5,5,5,6,6,6,7,7,7,8,8,8,9,9,9]);
ALN("P41/G1/L1/V4/ext3",["3^7.L2(8)v3"]);

MOT("P41/G2/L1/V1/ext2",
[
"origin: Hanrath library,\n",
"structure is 2^8.L2(8),\n",
"characters sorted with permutation (21,22)"
],
[129024,3584,1024,1536,14336,128,32,32,64,64,64,128,36,12,28,28,28,28,28,28,
28,28,28,28,28,28,9,9,9],
[,[1,1,1,1,1,1,4,2,3,3,3,5,13,13,19,19,19,19,23,23,23,23,15,15,15,15,28,29,
27],[1,2,3,4,5,6,7,8,9,10,11,12,1,4,23,24,25,26,15,16,18,17,19,20,21,22,13,13,
13],,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,1,2,5,5,1,2,5,5,1,2,5,5,28,29,27]],
0,
[(27,28,29),(10,11),( 9,10),(17,18)(21,22)(25,26),(15,19,23)(16,20,24)
(17,21,26)(18,22,25)],
["ConstructClifford",[[[1,2,3,4,5,6,7,8,9],[1,2,4,5,6,6,5,
4],[1,4,5,6,2],[1,3,2],[1,2,2,2]],[["L2(8)"],["2^3:7"],["Dihedral",
14],["S3"],["V4"]],[[[1,2,3,4,5],[1,1,1,1,1],["elab",5,22]],[[1,2,3,4,5,5,5],[
2,2,5,3,2,3,4],["elab",7,5,(2,4,3)(5,6,7),(2,7,3,4,5,6)]],[[1,4],[3,2],[[1,
1],[3,-1]]],[[1,2,2,3],[4,3,8,2],["elab",4,12,(2,4,3)]],[[1,2,2,3],[5,4,7,
3],["elab",4,12,(2,4,3)]],[[1,2,2,3],[6,5,6,4],["elab",4,12,(2,4,3)]],[[1],[
7]],[[1],[8]],[[1],[9]]]]]);
ALF("P41/G2/L1/V1/ext2","L2(8)",[1,1,1,1,1,2,2,2,2,2,2,2,3,3,4,4,4,4,5,5,
5,5,6,6,6,6,7,8,9]);
ALN("P41/G2/L1/V1/ext2",["2^8.L2(8)"]);

MOT("P41/G2/L1/V1/ext3",
[
"origin: Hanrath library,\n",
"structure is 3^8.L2(8),\n",
"characters sorted with permutation (29,30)(34,35)(37,39)(38,42,41,40)"
],
[3306744,45927,39366,39366,13122,13122,13122,6561,26244,6561,26244,39366,6561,
6561,6561,19683,39366,13122,13122,13122,13122,13122,13122,45927,26244,6561,
45927,3306744,39366,39366,3306744,648,162,162,162,162,324,162,162,162,324,648,
162,162,324,648,162,324,162,324,162,324,324,162,162,162,324,324,243,81,81,81,
81,81,81,81,243,81,243,63,63,63,63,63,63,63,63,63,63,63,63,63,63,63,63,63,63,
63,63,63,63,63,63,63,63,63,27,27,27,27,27,27,27,27,27],
[,[1,2,4,3,5,6,7,10,11,8,9,17,13,14,15,16,12,23,22,21,20,19,18,27,25,26,24,31,
30,29,28,1,29,30,4,19,25,3,22,6,11,28,17,12,9,31,5,11,20,25,21,11,9,18,7,23,9,
25,59,61,60,62,63,64,65,66,67,68,69,79,81,80,85,87,86,82,84,83,88,90,89,93,92,
91,95,94,96,70,72,71,75,74,73,77,76,78,100,101,102,103,104,105,97,98,99],[1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,32,32,32,32,32,32,
32,32,32,32,32,32,32,32,32,32,32,32,32,32,32,32,32,32,32,32,32,1,31,28,16,16,
16,16,16,1,16,1,88,88,88,88,88,88,88,88,88,70,70,70,70,70,70,70,70,70,79,79,
79,79,79,79,79,79,79,59,67,69,59,67,69,59,67,69],,,,[1,2,3,4,5,6,7,8,9,10,11,
12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,
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,
64,65,66,67,68,69,1,28,31,27,2,24,24,27,2,1,28,31,27,2,24,24,27,2,1,28,31,27,
2,24,24,27,2,100,101,102,103,104,105,97,98,99]],
0,
[( 97,100,103)( 98,101,104)( 99,102,105),( 62, 64)( 63, 65)( 66, 68)( 67, 69)
( 98, 99)(101,102)(104,105),(  5,  6,  7)( 13, 15, 14)( 18, 19, 20)
( 21, 23, 22)( 36, 49, 54)( 37, 50, 58)( 39, 51, 56)( 40, 55, 47)( 41, 52, 48)
( 45, 57, 53)( 62, 66, 63, 64, 68, 65)( 67, 69)( 98, 99)(101,102)(104,105),
( 73, 77)( 74, 78)( 75, 76)( 82, 86)( 83, 87)( 84, 85)( 91, 95)( 92, 96)
( 93, 94),( 70, 79, 88)( 71, 80, 89)( 72, 81, 90)( 73, 82, 95)( 74, 83, 96)
( 75, 84, 94)( 76, 85, 93)( 77, 86, 91)( 78, 87, 92),(  3,  4)(  8, 10)
(  9, 11)( 12, 17)( 18, 23)( 19, 22)( 20, 21)( 24, 27)( 28, 31)( 29, 30)
( 33, 34)( 35, 38)( 36, 39)( 41, 45)( 42, 46)( 43, 44)( 48, 53)( 49, 51)
( 52, 57)( 54, 56)( 60, 61)( 71, 72)( 73, 75)( 76, 77)( 80, 81)( 82, 84)
( 85, 86)( 89, 90)( 91, 93)( 94, 95),(  5,  7,  6)( 13, 14, 15)( 18, 20, 19)
( 21, 22, 23)( 36, 54, 49)( 37, 58, 50)( 39, 56, 51)( 40, 47, 55)( 41, 48, 52)
( 45, 53, 57)( 62, 63, 68)( 64, 65, 66),( 59, 67)( 62, 65)( 63, 66)( 64, 68)
( 97, 98)(100,101)(103,104)],
["ConstructClifford",[[[1,2,3,4,5,6,7,8,9],[1,2,4,5,6,6,5,
4],[1,2,4,5,6,6,5,4],[1,4,5,6,2],[1,4,5,6,2],[1,7,8,3,9,9,3,8,7],[1,4,5,6,6,5,
4],[1,3,2],[1,3,2],[1,2,2,2],[1,2,2,2],[1,2,2,2],[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],[1,2],[1],[1],[1],[
1],[1]],[["L2(8)"],["2^3:7"],["2^3:7"],["Dihedral",14],["Dihedral",
14],["Cyclic",9],["Cyclic",7],["S3"],["S3"],["V4"],["V4"],["V4"],["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",2],["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],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1],["elab",31,1]],[[1,2,3,4,5,8,9,10,10,10,11,11,11,12,12,12,16,17,18,19,20,
21,22,23,24,25,26],[2,2,2,5,5,3,3,2,3,4,2,3,4,2,3,4,2,2,2,2,2,2,2,2,2,2,
2],["elab",27,6,( 2,16,26,25,21, 5, 9,13, 8,12,14,11, 7, 3,15,23, 4)( 6,10)
(17,19,24,22,27,20,18),( 2, 5,22,26,11, 4,19,12, 6,17,14,20,15,25,10, 3, 8)
( 7,18,13)( 9,16,24,23,27,21)]],[[1,6,6,8,9,13,13,14,14,15,15],[3,4,7,2,2,2,3,
2,3,2,3],["elab",11,4,( 2,11, 8, 5, 7, 3,10, 9, 4, 6),( 2, 4, 8, 7, 3, 6,10, 5
 )]],[[1,2,2,3,3,4,5,7,7],[4,3,8,3,8,2,2,2,7],["elab",9,5,(2,7)(4,6)(8,9)]],[[
1,2,2,3,3,4,5,7,7],[5,4,7,4,7,3,3,3,6],["elab",9,5,(2,7)(4,6)(8,9)]],[[1,2,2,
3,3,4,5,7,7],[6,5,6,5,6,4,4,4,5],["elab",9,5,(2,7)(4,6)(8,9)]],[[1,6,6],[7,2,
9],["elab",3,1]],[[1,6,6],[8,3,8],["elab",3,1,(2,3)]],[[1,6,6],[9,5,
6],["elab",3,1]]]]]);
ALF("P41/G2/L1/V1/ext3","L2(8)",[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
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,
2,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,
6,6,7,7,7,8,8,8,9,9,9]);
ALN("P41/G2/L1/V1/ext3",["3^8.L2(8)"]);

MOT("P43/G1/L1/V1/ext2",
[
"origin: Hanrath library,\n",
"structure is 2^10.L2(11),\n",
"characters sorted with permutation (2,6,4,3)"
],
[675840,12288,2048,12288,4096,6144,6144,61440,12288,61440,12288,10240,768,128,
256,256,256,256,128,256,256,128,128,256,256,256,256,768,256,256,768,768,96,48,
48,48,48,96,48,96,48,96,20,20,20,20,20,20,20,20,24,24,24,24,11,11],
[,[1,1,1,1,1,1,1,1,1,1,1,1,1,9,9,5,11,2,4,11,9,11,5,11,5,9,4,9,1,4,11,2,33,33,
33,33,33,33,33,33,33,33,47,47,47,47,43,43,43,43,33,42,38,40,56,55],[1,2,3,4,5,
6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,
1,4,8,10,7,9,4,2,6,11,47,50,49,48,43,46,45,44,13,31,28,32,55,56],,[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,
33,39,35,36,37,38,34,40,41,42,1,8,12,10,1,10,12,8,51,52,53,54,55,56],,,,,,[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,
30,31,32,33,39,35,36,37,38,34,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,1,
1]],
0,
[(55,56),(43,47)(44,50)(45,49)(46,48),(34,39),( 6, 7)( 8,10)( 9,11)(14,22)
(15,20)(16,25)(17,26)(21,24)(27,30)(28,31)(35,36)(37,41)(38,42)(44,46)(48,50)
(52,53)],
["ConstructClifford",[[[1,2,3,5,4,6,7,8],[1,2,3,5,4],[1,2,
3,5,4],[1,6,3,2,2,2],[1,6,3,2,2,2],[1,6,3,2,2,2],[1,2,3,3],[1,4,5,2],[1,3,2],[
1,3,2],[1,2,2,2],[1,2]],[["L2(11)"],["A5"],["A5"],["Dihedral",12],["Dihedral",
12],["Dihedral",12],["A4"],["Dihedral",10],["S3"],["S3"],["V4"],["Cyclic",
2]],[[[1,2,3,4,5,6,7,8,9,10,11,12],[1,1,1,1,1,1,1,1,1,1,1,1],["elab",12,8]],[[
1,2,3,4,4,4,5,5,5,6,6,6,7,8,9,10,11,11,11,12],[2,2,2,4,5,6,4,5,6,4,5,6,2,4,3,
3,2,3,4,2],["elab",20,5]],[[1,2,3,4,5,6,7,7,9,10],[3,3,3,3,3,3,3,4,2,
2],["elab",10,1,( 2, 7, 3, 5, 4, 8),( 2, 6, 7, 3, 8, 4,10, 9, 5)]],[[1,2,3,
8],[5,5,5,2],["elab",4,12]],[[1,2,3,8],[4,4,4,3],["elab",4,12,(2,3)]],[[1,4,5,
6],[6,2,2,2],["elab",4,12,(2,4,3)]],[[1],[7]],[[1],[8]]]]]);
ALF("P43/G1/L1/V1/ext2","L2(11)",[1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,
2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,5,5,5,5,4,4,4,4,6,6,6,6,7,8]);
ALN("P43/G1/L1/V1/ext2",["2^10.L2(11)v1"]);

MOT("P43/G2/L1/V1/ext2",
[
"origin: Hanrath library,\n",
"structure is 2^10.L2(11),\n",
"characters sorted with permutation (2,6,4,3)"
],
0,
0,
0,
0,
["ConstructPermuted",["P43/G1/L1/V1/ext2"],(2,11,7,10,8,12,9)(3,6)(4,5)(14,30,
23,15,18)(16,17,28,32,26,29,27)(19,25,24,22,21,20,31)(34,35,42,38,37,40)(36,
39)(44,45)(48,50,49)(52,54)(55,56),(2,3)(19,25,31)(20,26,32)(21,27,33)(22,28,
34)(23,29,35)(24,30,36)(38,39)]);
ALF("P43/G2/L1/V1/ext2","L2(11)",[1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,
2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,5,5,5,5,4,4,4,4,6,6,6,6,7,8]);
ALN("P43/G2/L1/V1/ext2",["2^10.L2(11)v2"]);

MOT("P43/G3/L1/V1/ext2",
[
"origin: Hanrath library,\n",
"structure is 2^10.L2(11),\n",
"characters sorted with permutation (2,6,4,3)"
],
[675840,12288,2048,4096,4096,10240,10240,10240,12288,12288,768,256,256,128,
128,256,128,256,256,256,256,256,256,256,256,128,256,768,768,768,24,24,24,24,
20,20,20,20,20,20,20,20,24,24,24,24,11,11],
[,[1,1,1,1,1,1,1,1,1,1,1,4,4,3,3,4,3,4,4,4,4,4,4,4,4,3,4,1,1,1,31,31,31,31,39,
39,39,39,35,35,35,35,31,31,31,31,48,47],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,
16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,1,9,2,10,39,40,41,42,35,36,37,38,
11,28,30,29,47,48],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,
23,24,25,26,27,28,29,30,31,32,33,34,1,8,6,7,1,8,6,7,43,44,45,46,47,48],,,,,,[
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,
30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,1,1]],
0,
[(47,48),(35,39)(36,40)(37,41)(38,42),(11,28)(12,23)(13,27)(14,26)(15,17)
(16,18)(19,24)(20,25)(21,22)(29,30)(43,44)(45,46),(11,29)(12,24)(13,22)(14,15)
(16,20)(17,26)(18,25)(19,23)(21,27)(28,30)(43,46)(44,45),( 6, 7)( 9,10)(12,16)
(13,21)(14,17)(18,24)(19,25)(20,23)(28,29)(32,34)(37,38)(41,42)(44,46),
( 2, 9,10)( 6, 7, 8)(12,13,18)(14,26,17)(16,24,21)(19,27,25)(20,23,22)
(28,29,30)(32,34,33)(36,37,38)(40,41,42)(44,46,45)],
["ConstructClifford",[[[1,2,3,5,4,6,7,8],[1,6,3,2,2,2],[1,
6,3,2,2,2],[1,6,3,2,2,2],[1,4,5,2],[1,4,5,2],[1,4,5,2],[1,2,2,2],[1,2,2,2],[1,
2]],[["L2(11)"],["Dihedral",12],["Dihedral",12],["Dihedral",12],["Dihedral",
10],["Dihedral",10],["Dihedral",10],["V4"],["V4"],["Cyclic",2]],[[[1,2,3,4,5,
6,7,8,9,10],[1,1,1,1,1,1,1,1,1,1],["elab",10,18]],[[1,2,2,2,3,3,3,4,4,4,5,6,7,
8,8,8,9,9,9,10],[2,4,5,6,4,5,6,4,5,6,4,4,4,2,3,4,2,3,4,2],["elab",20,5,
( 2, 3,19,10, 5,17, 7)( 4, 8,15,13,16,11, 6, 9,18)(12,14,20),( 2, 4, 3)
( 5, 6,14,11, 7)( 8,13,10,16,20,18,17, 9)]],[[1,2,3,4],[3,3,3,3],["elab",4,12,
(2,4)]],[[1,5,6,7],[5,2,2,2],["elab",4,12,(2,4,3)]],[[1,5,6,7],[4,3,3,
3],["elab",4,12,(2,4,3)]],[[1,2,3,4],[6,2,2,2],["elab",4,12,(2,4)]],[[1],[
7]],[[1],[8]]]]]);
ALF("P43/G3/L1/V1/ext2","L2(11)",[1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,
2,2,2,2,2,2,2,2,2,2,3,3,3,3,5,5,5,5,4,4,4,4,6,6,6,6,7,8]);
ALN("P43/G3/L1/V1/ext2",["2^10.L2(11)v3"]);

MOT("P43/G3/L1/V2/ext2",
[
"origin: Hanrath library,\n",
"structure is 2^10.L2(11),\n",
"characters sorted with permutation (2,6,4,3)"
],
[675840,12288,2048,4096,4096,10240,10240,10240,12288,12288,256,128,128,128,
256,768,256,256,256,256,256,256,256,256,256,128,256,768,768,768,24,24,24,24,
20,20,20,20,20,20,20,20,24,24,24,24,11,11],
[,[1,1,1,1,1,1,1,1,1,1,5,6,6,6,10,9,2,2,5,2,5,10,5,10,10,6,2,9,9,9,34,34,34,
34,42,42,42,42,38,38,38,38,33,33,33,33,48,47],[1,2,3,4,5,6,7,8,9,10,21,14,26,
12,25,28,27,20,23,18,11,24,19,22,15,13,17,16,30,29,10,2,9,1,39,40,41,42,35,36,
37,38,28,16,29,30,47,48],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,
21,22,23,24,25,26,27,28,29,30,31,32,33,34,7,6,8,1,7,6,8,1,43,44,45,46,47,
48],,,,,,[1,2,3,4,5,6,7,8,9,10,21,14,26,12,25,28,27,20,23,18,11,24,19,22,15,
13,17,16,30,29,31,32,33,34,35,36,37,38,39,40,41,42,44,43,46,45,1,1]],
0,
[(47,48),(35,39)(36,40)(37,41)(38,42),(11,19)(12,13)(14,26)(15,24)(16,29)
(17,20)(18,27)(21,23)(22,25)(28,30)(43,46)(44,45),(11,21)(12,14)(13,26)(15,25)
(16,28)(17,27)(18,20)(19,23)(22,24)(29,30)(43,44)(45,46),( 2,10)( 7, 8)(12,14)
(15,20)(16,28)(17,22)(18,25)(19,23)(24,27)(31,32)(35,37)(39,41)(43,44)],
["ConstructClifford",[[[1,2,3,5,4,6,7,8],[1,6,3,2,2,2],[1,
6,3,2,2,2],[1,6,3,2,2,2],[1,4,5,2],[1,4,5,2],[1,4,5,2],[1,2,2,2],[1,2,2,2],[1,
2]],[["L2(11)"],["Dihedral",12],["Dihedral",12],["Dihedral",12],["Dihedral",
10],["Dihedral",10],["Dihedral",10],["V4"],["V4"],["Cyclic",2]],[[[1,2,3,4,5,
6,7,8,9,10],[1,1,1,1,1,1,1,1,1,1],["elab",10,18]],[[1,2,2,2,3,3,3,4,4,4,5,6,7,
8,8,8,9,9,9,10],[2,4,5,6,4,5,6,4,5,6,4,4,4,2,3,4,2,3,4,2],["elab",20,6]],[[1,
2,3,4],[3,3,3,3],["elab",4,12,(2,3,4),(1,4,3,2)]],[[1,5,6,7],[5,2,2,
2],["elab",4,12,(3,4),(1,4,3,2)]],[[1,5,6,7],[4,3,3,3],["elab",4,12,(3,4),
(1,4,3,2)]],[[1,2,3,4],[6,2,2,2],["elab",4,21,(2,4),(1,3)]],[[1],[7]],[[1],[
8]]]]]);
ALF("P43/G3/L1/V2/ext2","L2(11)",[1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,
2,2,2,2,2,2,2,2,2,2,3,3,3,3,5,5,5,5,4,4,4,4,6,6,6,6,7,8]);
ALN("P43/G3/L1/V2/ext2",["2^10.L2(11)v4"]);

MOT("P48/G1/L1/V1/ext2",
[
"origin: Hanrath library,\n",
"structure is 2^10.M11,\n",
"characters sorted with permutation (13,15)(14,16,17,18)(20,21)(23,24)\n",
"(30,31,32,33,34)(39,42)(49,50)"
],
[8110080,147456,24576,20480,122880,49152,737280,3072,1024,256,768,256,256,512,
768,512,1024,3072,288,96,48,96,288,144,128,64,64,64,128,64,64,64,128,128,20,
20,20,20,24,24,24,24,32,32,32,32,32,32,32,32,11,11],
[,[1,1,1,1,1,1,1,1,6,5,2,2,3,3,5,3,1,6,19,19,19,19,19,19,8,18,16,16,18,8,16,
16,8,18,35,35,35,35,19,23,22,20,25,29,34,33,25,29,34,33,52,51],[1,2,3,4,5,6,7,
8,9,10,11,12,13,14,15,16,17,18,1,6,3,5,2,7,25,26,31,28,29,30,27,32,33,34,35,
36,37,38,8,11,15,18,43,44,45,46,47,48,49,50,51,52],,[1,2,3,4,5,6,7,8,9,10,11,
12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,1,4,7,5,
39,40,41,42,47,48,49,50,43,44,45,46,51,52],,,,,,[1,2,3,4,5,6,7,8,9,10,11,12,
13,14,15,16,17,18,19,20,21,22,23,24,25,26,31,28,29,30,27,32,33,34,35,36,37,38,
39,40,41,42,43,44,45,46,47,48,49,50,1,1]],
0,
[(51,52),(43,47)(44,48)(45,49)(46,50),(27,31),(25,33)(28,32)(29,34)(43,46)
(44,45)(47,50)(48,49)],
["ConstructClifford",[[[1,2,3,4,5,6,7,8,9,10],[1,2,3,4,5,4,
7,8],[1,2,2,3,4,4,6,7,8],[1,2,3,5,2,4,6],[1,2,4,2,7,8,3,6],[1,2,3,2,4],[1,5,4,
2,4]],[["M11"],["A6.2_3"],["3^2:Q8.2"],["A5.2"],["M8:S3"],["Symm(4)"],["P:Q",
[5,4]]],[[[1,2,3,4,5,6,7],[1,1,1,1,1,1,1],["elab",7,13]],[[1,2,3,3,4,4,5,5,6,
6,7],[2,2,2,3,2,5,2,4,2,4,4],["elab",11,3,( 3, 6)( 4, 7, 9,11, 8,10),( 2, 3,
 4)( 5, 7)( 8, 9)]],[[1,2,3,4,5,6],[3,3,4,3,7,3],["elab",6,9,(2,4,5,6),(2,5,4)
(3,6)]],[[1,2,2,3,3,4,5,6,7,7],[4,4,6,5,6,6,3,5,3,5],["elab",10,19]],[[1,2,4,
7],[5,5,4,2],["elab",4,12,(2,4)]],[[1,3,4,5],[6,7,7,8],["elab",4,12,
(2,3,4)]],[[1,2,3,5],[7,7,8,5],["elab",4,22,(2,4),(2,3)]],[[1,2,3,5],[8,8,9,
6],["elab",4,22,(2,4),(2,3)]],[[1],[9]],[[1],[10]]]]]);
ALF("P48/G1/L1/V1/ext2","M11",[1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,3,3,3,
3,3,3,4,4,4,4,4,4,4,4,4,4,5,5,5,5,6,6,6,6,7,7,7,7,8,8,8,8,9,10]);
ALN("P48/G1/L1/V1/ext2",["2^10.M11v1"]);

MOT("P48/G1/L1/V2/ext2",
[
"origin: Hanrath library,\n",
"structure is 2^10.M11,\n",
"characters sorted with permutation (13,15)(14,16,17,18)(20,21)(23,24)\n",
"(30,31,32,33,34)(39,42)(49,50)"
],
[8110080,147456,24576,20480,122880,49152,737280,512,256,256,768,256,512,3072,
1024,768,1024,3072,288,96,48,96,288,144,64,64,64,128,64,64,128,128,64,128,20,
20,20,20,24,24,24,24,32,32,32,32,32,32,32,32,11,11],
[,[1,1,1,1,1,1,1,3,3,5,2,2,3,1,6,5,1,6,19,19,19,19,19,19,13,13,17,15,13,15,17,
15,13,17,35,35,35,35,19,23,22,20,34,32,28,31,34,32,28,31,52,51],[1,2,3,4,5,6,
7,8,9,10,11,12,13,14,15,16,17,18,1,6,3,5,2,7,33,26,27,32,29,30,34,28,25,31,35,
36,37,38,14,11,16,18,46,45,44,43,50,49,48,47,51,52],,[1,2,3,4,5,6,7,8,9,10,11,
12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,1,4,7,5,
39,40,41,42,47,48,49,50,43,44,45,46,51,52],,,,,,[1,2,3,4,5,6,7,8,9,10,11,12,
13,14,15,16,17,18,19,20,21,22,23,24,33,26,27,32,29,30,34,28,25,31,35,36,37,38,
39,40,41,42,46,45,44,43,50,49,48,47,1,1]],
0,
[(51,52),(43,47)(44,48)(45,49)(46,50),(26,29),(25,33)(28,32)(31,34)(43,46)
(44,45)(47,50)(48,49)],
["ConstructClifford",[[[1,2,3,4,5,6,7,8,9,10],[1,2,3,4,5,4,
7,8],[1,2,2,3,4,4,6,7,8],[1,2,3,5,2,4,6],[1,2,4,2,7,8,3,6],[1,2,3,2,4],[1,5,4,
2,4]],[["M11"],["A6.2_3"],["3^2:Q8.2"],["A5.2"],["M8:S3"],["Symm(4)"],["P:Q",
[5,4]]],[[[1,2,3,4,5,6,7],[1,1,1,1,1,1,1],["elab",7,13]],[[1,2,3,3,4,4,5,5,6,
6,7],[2,2,2,3,2,5,2,4,2,4,4],["elab",11,3,( 3, 6)( 4, 7, 9,11, 8,10),
( 1, 7, 5, 6, 2, 3, 4, 8)]],[[1,2,3,4,5,6],[3,3,4,3,7,3],["elab",6,9,
(2,4,5,6),(2,5,4)(3,6)]],[[1,2,2,3,3,4,5,6,7,7],[4,4,6,5,6,6,3,5,3,5],["elab",
10,20]],[[1,2,4,7],[5,5,4,2],["elab",4,12,(2,4)]],[[1,3,4,5],[6,7,7,
8],["elab",4,12,(2,3,4)]],[[1,2,3,5],[7,7,8,5],["elab",4,26]],[[1,2,3,5],[8,8,
9,6],["elab",4,26]],[[1],[9]],[[1],[10]]]]]);
ALF("P48/G1/L1/V2/ext2","M11",[1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,3,3,3,
3,3,3,4,4,4,4,4,4,4,4,4,4,5,5,5,5,6,6,6,6,7,7,7,7,8,8,8,8,9,10]);
ALN("P48/G1/L1/V2/ext2",["2^10.M11v2"]);

MOT("P49/G1/L1/V1/ext2",
[
"origin: Hanrath library,\n",
"structure is 2^7.U3(3),\n",
"characters sorted with permutation (16,19,21,20,18)(23,25)(24,26)\n",
"(37,39,42,41,38)"
],
[774144,12288,12288,774144,3072,128,1024,1024,3072,216,216,72,24,24,72,768,
768,128,768,768,128,128,128,64,32,24,24,14,14,14,14,32,32,32,32,32,32,32,32,
24,24,24,24],
[,[1,1,1,1,1,3,1,1,1,10,10,12,12,12,12,5,5,8,5,5,8,5,5,8,7,10,10,28,28,30,30,
16,16,18,18,19,19,21,21,26,26,26,26],[1,2,3,4,5,6,7,8,9,1,4,1,3,2,4,19,20,21,
16,17,18,22,23,24,25,5,9,30,31,28,29,36,37,38,39,32,33,34,35,19,20,16,17],,,,[
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,19,20,21,16,17,18,22,23,24,25,26,27,1,4,1,
4,36,37,39,38,32,33,35,34,42,43,40,41]],
0,
[(32,33)(36,37),(28,30)(29,31),(34,35)(38,39),(16,19)(17,20)(18,21)(32,36)
(33,37)(34,38)(35,39)(40,42)(41,43)],
["ConstructClifford",[[[1,2,3,4,5,6,7,8,9,10,11,12,13,14],[
1,2,3,4,5,6,8,12,11,12,11,14,13],[1,2,4,7,9,10],[1,2,5,6,7,7,4,2,12,
11]],[["U3(3)"],["3^(1+2):8"],["L3(2)"],["4^2:S3"]],[[[1,2,3,4],[1,1,1,
1],["elab",4,25]],[[1,2,3,4,4],[2,2,2,2,8],["elab",5,23]],[[1,2],[3,3],[[1,
1],[1,-1]]],[[1,2,3,4],[4,4,3,7],["elab",4,23,(2,3),(2,4)]],[[1,2,4],[5,5,
3],["elab",3,13]],[[1,2,4],[6,6,4],["elab",3,13,,(1,2)]],[[1,3,4,4],[7,4,5,
6],["elab",4,27]],[[1,2],[8,7],[[1,1],[-1,1]]],[[1,3],[9,5],[[1,1],[1,-1]]],[[
1,3],[10,6],[[1,1],[1,-1]]],[[1,2,2,4],[11,9,11,10],["elab",4,28]],[[1,2,2,
4],[12,8,10,9],["elab",4,29]],[[1,2],[13,13],[[1,1],[-E(4),E(4)]]],[[1,2],[14,
12],[[1,1],[E(4),-E(4)]]]]]]);
ALF("P49/G1/L1/V1/ext2","U3(3)",[1,1,1,1,2,2,2,2,2,3,3,4,4,4,4,5,5,5,6,6,
6,7,7,7,7,8,8,9,9,10,10,11,11,11,11,12,12,12,12,13,13,14,14]);
ALN("P49/G1/L1/V1/ext2",["2^7.U3(3)"]);

MOT("P49/G1/L1/V1/ext3",
[
"origin: Hanrath library,\n",
"structure is 3^7.U3(3),\n",
"characters sorted with permutation (16,17)(19,20,25,22)(21,23,24,26)\n",
"(32,35,36)(40,41)(45,46)(49,50)(52,53)"
],
[13226976,104976,19683,17496,45927,45927,236196,2592,216,324,432,2916,729,324,
324,729,243,243,243,81,81,81,81,81,81,243,243,243,243,243,243,2592,324,216,
432,2592,324,216,432,48,48,48,36,36,36,21,21,21,21,21,21,24,24,24,24,24,24,36,
36,36,36,36,36],
[,[1,2,3,4,6,5,7,1,4,7,2,12,16,14,15,13,17,28,30,21,20,22,25,24,23,26,31,18,
29,19,27,8,10,9,11,8,10,9,11,8,11,11,12,15,14,46,48,47,49,51,50,32,34,34,36,
38,38,43,45,44,43,45,44],[1,1,1,1,1,1,1,8,8,8,8,1,1,7,7,1,1,7,7,3,3,3,3,3,3,1,
7,7,1,7,7,36,36,36,36,32,32,32,32,40,40,40,8,10,10,49,49,49,46,46,46,55,55,55,
52,52,52,36,37,37,32,33,33],,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,
19,20,21,22,23,24,25,26,27,28,29,30,31,36,37,38,39,32,33,34,35,40,42,41,43,44,
45,1,5,6,1,5,6,55,57,56,52,54,53,61,62,63,58,59,60]],
0,
[(53,54)(56,57),(46,49)(47,50)(48,51),(41,42),(32,36)(33,37)(34,38)(35,39)
(52,55)(53,56)(54,57)(58,61)(59,62)(60,63),(22,24),(14,15)(44,45)(59,60)
(62,63),(13,16)(20,25)(21,23),(18,30)(19,28)(26,29),(17,26)(19,31)(27,30),
( 5, 6)(18,19)(20,23)(21,25)(26,29)(27,31)(28,30)(47,48)(50,51)],
["ConstructClifford",[[[1,2,3,4,5,6,7,8,9,10,11,12,13,14],[
1,3,3,4,4,2,8,8,5,13,13,6,14,14],[1,2,5,6,7,7,4,4],[1,9,10,4,4],[1,9,10,4,4],[
1,3,3,4,4,4,4,4,4],[1,11,5,12,2,11,6,
12]],[["U3(3)"],["3^(1+2):4"],["4^2:3"],["7:3"],["7:3"],["3^2"],["Cyclic",
8]],[[[1,2,3,4,5,6,7],[1,1,1,1,1,1,1],["elab",7,14]],[[1,2,3,7],[2,6,2,
5],["elab",4,2,(2,4,3),(2,4)]],[[1,2,2,6,6],[3,2,3,2,3],["elab",5,24]],[[1,2,
2,3,3,4,4,5,5,6,6,6,6,6,6],[4,4,5,7,8,4,5,4,5,4,5,6,7,8,9],["elab",15,6]],[[1,
2,3,7],[5,9,3,3],["elab",4,2,(2,4,3),(2,4,3)]],[[1,2,3,7],[6,12,4,7],["elab",
4,2,(2,4,3),(2,4,3)]],[[1,3,3],[7,5,6],["elab",3,1,(2,3)]],[[1,2,2],[8,7,
8],["elab",3,1]],[[1,4,5],[9,2,2],["elab",3,1,(2,3)]],[[1,4,5],[10,3,
3],["elab",3,1,(2,3)]],[[1,7,7],[11,2,6],["elab",3,1,(2,3)]],[[1,7,7],[12,4,
8],["elab",3,1,(2,3)]],[[1,2,2],[13,10,11],["elab",3,1,(2,3)]],[[1,2,2],[14,
13,14],["elab",3,1,(2,3)]]]]]);
ALF("P49/G1/L1/V1/ext3","U3(3)",[1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,4,4,4,4,
4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,6,6,6,6,7,7,7,8,8,8,9,9,9,10,10,10,11,11,11,
12,12,12,13,13,13,14,14,14]);
ALN("P49/G1/L1/V1/ext3",["3^7.U3(3)v1"]);

MOT("P49/G1/L1/V2/ext3",
[
"origin: Hanrath library,\n",
"structure is 3^7.U3(3),\n",
"characters sorted with permutation (16,17)(19,20,25,22)(21,23,24,26)\n",
"(32,35,36)(40,41)(45,46)"
],
[13226976,104976,19683,17496,45927,45927,236196,216,324,432,2592,324,324,324,
81,81,81,81,81,81,81,81,81,216,324,432,2592,2592,324,216,432,48,48,48,36,36,
36,21,21,21,21,21,21,24,24,24,24,24,24,36,36,36,36,36,36],
[,[1,2,3,4,6,5,7,4,7,2,1,12,13,14,21,15,19,20,22,16,23,17,18,8,9,10,11,11,9,8,
10,10,10,11,12,14,13,39,38,40,42,41,43,24,24,27,30,30,28,35,37,36,35,37,36],[
1,1,1,1,1,1,1,11,11,11,11,1,7,7,5,6,2,6,2,5,6,2,5,28,28,28,28,27,27,27,27,34,
34,34,11,9,9,43,43,43,40,40,40,49,49,49,46,46,46,28,29,29,27,25,25],,,,[1,2,3,
4,5,6,7,8,9,10,11,12,13,14,20,18,19,21,22,23,16,17,15,30,29,31,28,27,25,24,26,
33,32,34,35,36,37,5,6,1,5,6,1,48,47,49,45,44,46,53,54,55,50,51,52]],
0,
[(44,45)(47,48),(38,41)(39,42)(40,43),(32,33),(24,30)(25,29)(26,31)(27,28)
(44,47)(45,48)(46,49)(50,53)(51,54)(52,55),(13,14)(36,37)(51,52)(54,55),
(15,20,23)(16,18,21)(17,19,22),( 5, 6)(15,16,20,18,23,21)(17,22,19)(38,39)
(41,42)],
["ConstructClifford",[[[1,2,3,4,5,6,7,8,9,10,11,12,13,14],[
1,3,3,4,4,2,8,8,5,13,13,6,14,14],[1,2,5,6,7,7,4,4],[1,9,10,4,4],[1,9,10,4,4],[
1,3,3,4,4,4,4,4,4],[1,11,5,12,2,11,6,
12]],[["U3(3)"],["3^(1+2):4"],["4^2:3"],["7:3"],["7:3"],["projectives","3^2",
"3^(1+2)_+"],["Cyclic",8]],[[[1,2,3,4,5,6,7],[1,1,1,1,1,1,1],["elab",7,14]],[[
1,2,3,7],[2,6,2,5],["elab",4,2,(2,4,3),(1,4)(2,3)]],[[1,2,2],[3,2,3],["elab",
3,1,(2,3)]],[[1,2,2,3,3,4,4,5,5],[4,4,5,7,8,4,5,4,5],["elab",9,16]],[[1,2,3,
7],[5,9,3,3],["elab",4,2,(2,4,3),(1,4)(2,3)]],[[1,2,3,7],[6,12,4,7],["elab",4,
2,(2,4,3),(2,4,3)]],[[1,3,3],[7,5,6],["elab",3,1,(2,3),(1,3,2)]],[[1,2,2],[8,
7,8],["elab",3,1]],[[1,4,5],[9,2,2],["elab",3,1,(2,3),(1,3,2)]],[[1,4,5],[10,
3,3],["elab",3,1,(2,3),(1,3,2)]],[[1,7,7],[11,2,6],["elab",3,1,(2,3),
(1,3,2)]],[[1,7,7],[12,4,8],["elab",3,1,(2,3),(1,3,2)]],[[1,2,2],[13,10,
11],["elab",3,1,(2,3)]],[[1,2,2],[14,13,14],["elab",3,1,(2,3)]]]]]);
ALF("P49/G1/L1/V2/ext3","U3(3)",[1,1,1,1,1,1,1,2,2,2,2,3,3,3,4,4,4,4,4,4,
4,4,4,5,5,5,5,6,6,6,6,7,7,7,8,8,8,9,9,9,10,10,10,11,11,11,12,12,12,13,13,
13,14,14,14]);
ALN("P49/G1/L1/V2/ext3",["3^7.U3(3)v2"]);

MOT("P50/G1/L1/V1/ext2",
[
"origin: Hanrath library,\n",
"structure is 2^6.U4(2),\n",
"characters sorted with permutation (35,38)(36,37)(39,40,41,42,43),\n",
"(table is equal to that of 2^6:U4(2) = O8-(2)M1)"
],
[1658880,46080,61440,9216,768,3072,1536,192,512,512,1536,648,648,1728,288,192,
216,72,192,64,32,32,32,32,20,20,20,20,72,72,144,48,144,48,72,24,48,24,48,9,9,
12,12],
[,[1,1,1,1,3,1,1,2,3,1,3,13,12,14,14,14,17,17,4,6,7,11,9,10,25,25,25,25,12,13,
14,16,14,16,17,17,14,15,16,41,40,29,30],[1,2,3,4,5,6,7,8,9,10,11,1,1,1,2,3,1,
2,19,20,21,22,23,24,25,27,26,28,4,4,4,5,4,5,4,6,7,8,11,12,13,19,19],,[1,2,3,4,
5,6,7,8,9,10,11,13,12,14,15,16,17,18,19,20,21,22,23,24,1,3,3,2,30,29,33,34,31,
32,35,36,37,38,39,41,40,43,42]],
0,
[(26,27),(12,13)(29,30)(31,33)(32,34)(40,41)(42,43)],
["ConstructClifford",[[[1,2,3,4,5,6,7,8,9,10,12,11,13,14,
15,16,17,18,19,20],[1,3,2,3,8,9,6,16,13,14,10,10],[1,3,6,7,9,10,3,2,9,16,
15]],[["U4(2)"],["mo62p"],["S6"]],[[[1,2,3],[1,1,1],["elab",3,3,,(2,3)]],[[1,
2,3],[2,3,8],["elab",3,6,,(2,3)]],[[1,2,2,3,3],[3,2,4,2,7],["elab",5,11,(4,5),
(2,5)(3,4)]],[[1],[4]],[[1],[5]],[[1,2,3],[6,7,3],["elab",3,7]],[[1,3],[7,
4],[[1,1],[3,-1]]],[[1,2],[8,5],[[1,1],[3,-1]]],[[1,2,3,3],[9,6,5,9],["elab",
4,12,(2,3)]],[[1,2,2,3],[10,11,12,6],["elab",4,12,(2,3,4)]],[[1],[12]],[[1],[
11]],[[1,2],[13,9],[[1,1],[3,-1]]],[[1,2],[14,10],[[1,1],[3,-1]]],[[1,3],[15,
11],[[1,1],[3,-1]]],[[1,2,3],[16,8,10],["elab",3,8,,(2,3)]],[[1],[17]],[[1],[
18]],[[1],[19]],[[1],[20]]]]]);
ALF("P50/G1/L1/V1/ext2","U4(2)",[1,1,1,2,2,2,3,3,3,3,3,4,5,6,6,6,7,7,8,8,
9,9,9,9,10,10,10,10,12,11,13,13,14,14,15,15,16,16,16,17,18,19,20]);
# ALN("P50/G1/L1/V1/ext2",["2^6.U4(2)"]);

MOT("P50/G1/L1/V1/ext3",
[
"origin: Hanrath library,\n",
"structure is 3^6.U4(2),\n",
"characters sorted with permutation (46,47)(56,59)(57,60,58,61)(62,63)\n",
"(66,70,67)(68,72,69)(71,73)(74,78,79,76,75)(81,85)(82,88,87)(83,86)\n",
"(92,94,95,96)(99,101,102,103)"
],
[18895680,262440,78732,69984,262440,262440,18895680,18895680,5184,864,5184,
5184,7776,1296,1296,648,648,648,972,972,1296,972,7776,7776,17496,729,17496,
17496,17496,729,17496,17496,8748,486,486,486,729,1458,1458,8748,8748,1458,81,
729,729,729,1458,1458,432,144,144,432,432,72,72,72,36,36,36,45,45,45,45,45,45,
45,45,45,216,216,216,216,216,216,324,54,324,324,324,324,324,54,54,54,54,108,
54,54,54,108,108,27,27,27,27,27,27,36,36,36,36,36,36],
[,[1,2,3,4,6,5,8,7,1,4,8,7,1,4,4,6,2,5,3,3,4,3,7,8,29,30,32,31,25,26,28,27,33,
35,34,36,37,39,38,41,40,42,43,44,45,46,47,48,9,10,10,12,11,13,24,23,16,18,17,
60,66,63,62,68,65,61,67,64,25,28,27,29,32,31,33,38,40,41,33,40,41,39,42,47,48,
33,34,35,36,40,41,95,97,96,92,94,93,69,71,70,72,74,73],[1,1,1,1,1,1,1,1,9,9,9,
9,13,13,13,13,13,13,13,13,13,13,13,13,1,1,1,1,1,1,1,1,1,3,3,3,1,1,1,1,1,1,3,1,
1,1,1,1,49,49,49,49,49,54,54,54,54,54,54,60,60,60,60,60,60,60,60,60,9,9,9,9,9,
9,9,9,9,9,9,9,9,9,9,9,9,13,20,20,20,13,13,25,27,28,29,31,32,49,49,49,49,49,
49],,[1,2,3,4,6,5,8,7,9,10,12,11,13,15,14,18,17,16,22,20,21,19,24,23,29,30,32,
31,25,26,28,27,33,35,34,36,37,39,38,41,40,42,43,44,45,46,47,48,49,51,50,53,52,
54,56,55,58,57,59,1,6,5,6,7,2,5,2,8,72,74,73,69,71,70,79,82,81,80,75,78,77,76,
83,84,85,86,88,87,89,91,90,95,97,96,92,94,93,101,103,102,98,100,99]],
0,
[( 61, 63)( 62, 66)( 65, 67),(  5,  6)(  7,  8)( 11, 12)( 14, 15)( 16, 18)
( 19, 22)( 23, 24)( 34, 35)( 40, 41)( 52, 53)( 55, 56)( 57, 58)( 61, 62)
( 63, 66)( 64, 68)( 65, 67)( 77, 78)( 80, 81)( 87, 88)( 90, 91),( 27, 28)
( 31, 32)( 44, 45)( 47, 48)( 50, 51)( 70, 71)( 73, 74)( 84, 85)( 93, 94)
( 96, 97)( 99,100)(102,103),( 25, 27)( 29, 32)( 42, 48)( 44, 46)( 50, 51)
( 69, 71)( 72, 73)( 83, 85)( 92, 93)( 95, 97)( 98, 99)(101,103),( 25, 29)
( 26, 30)( 27, 31)( 28, 32)( 38, 39)( 44, 45)( 47, 48)( 69, 72)( 70, 73)
( 71, 74)( 75, 79)( 76, 82)( 77, 80)( 78, 81)( 84, 85)( 92, 95)( 93, 96)
( 94, 97)( 98,101)( 99,102)(100,103)],
["ConstructClifford",[[[1,2,3,4,5,6,7,8,9,10,12,11,13,14,
15,16,17,18,19,20],[1,3,2,3,8,9,6,16,13,14,10,10],[1,3,2,3,8,9,6,16,13,14,10,
10],[1,3,6,7,9,10,10],[1,6,3,16,7,7,18,17,7,18,17,4,5],[1,6,6,3,7,20,19,12,11,
15,7,20,19,12,11,15,14,13,8,8,5,4,5,4,2],[1,3,6,10,3,9,16],[1,3,6,10,3,9,
16]],[["U4(2)"],["mo62p"],["mo62p"],["A6"],["3^3:A4"],["2.(A4xA4)"],["S5"],
["S5"]],[[[1,2,3,4,5,6,7,8],[1,1,1,1,1,1,1,1],["elab",8,15]],[[1,2,3,6],[2,3,
3,25],["elab",4,30]],[[1,2,2,3,3,4,5,6,7,7,8,8],[3,2,4,2,4,2,3,4,2,5,2,
5],["elab",12,9]],[[1,5,6,6],[4,12,22,24],["elab",4,3,(3,4),(2,3,4)]],[[1,5,6,
6],[5,13,21,23],["elab",4,3,,(2,3,4)]],[[1,2,3,4,5,6,6,7,8],[6,7,7,3,2,2,3,3,
3],["elab",9,17]],[[1,4,5,5,5,6,6],[7,4,5,6,9,5,11],["elab",7,1,(4,5)(6,7),
(2,6,3,7)(4,5)]],[[1,2,3,6,6],[8,5,5,19,20],["elab",5,20,(2,5,3,4)]],[[1,2,3,
4,7,8],[9,6,6,5,6,6],["elab",6,15,(2,3)(4,5,6),(4,6,5)]],[[1,2,2,3,3,4,4,7,
8],[10,11,12,11,12,6,7,4,4],["elab",9,5,(2,6,8,5)(3,4,7,9)]],[[1,6,6],[12,9,
15],["elab",3,1,(2,3)]],[[1,6,6],[11,8,14],["elab",3,1]],[[1,2,3,6],[13,9,9,
18],["elab",4,30,(2,3)]],[[1,2,3,6],[14,10,10,17],["elab",4,30,(2,3),
(2,4,3)]],[[1,6,6],[15,10,16],["elab",3,1,(2,3)]],[[1,2,3,5,7,8],[16,8,8,4,7,
7],["elab",6,15,(2,3)(4,5,6),(2,5)(3,6)]],[[1,5,5],[17,8,11],["elab",3,1]],[[
1,5,5],[18,7,10],["elab",3,1,(2,3)]],[[1,6,6],[19,7,13],["elab",3,1]],[[1,6,
6],[20,6,12],["elab",3,1,(2,3)]]]]]);
ALF("P50/G1/L1/V1/ext3","U4(2)",[1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,
3,3,3,3,4,4,4,4,5,5,5,5,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,8,8,8,8,8,9,9,9,9,
9,9,10,10,10,10,10,10,10,10,10,12,12,12,11,11,11,13,13,13,13,14,14,14,14,
15,15,15,16,16,16,16,16,16,17,17,17,18,18,18,19,19,19,20,20,20]);
ALN("P50/G1/L1/V1/ext3",["3^6.U4(2)"]);

MOT("P50/G1/L1/V1/ext4",
[
"origin: Hanrath library,\n",
"structure is 4^6.U4(2),\n",
"characters sorted with permutation (59,62)(60,61)(63,64,65,66,67)\n",
"(77,79,80,81)(84,86,87,88)(92,95)(98,99)\n",
"(111,116,119,118,114,112,115,117,113)(122,123)(125,126,127)"
],
[106168320,1474560,2949120,147456,393216,98304,196608,3932160,245760,245760,
491520,491520,3932160,3932160,36864,12288,1536,12288,4096,3072,3072,24576,
1024,3072,1024,3072,2048,2048,1024,8192,1024,3072,2048,4096,2048,2048,3072,
3072,4096,8192,4096,4096,2048,3072,8192,24576,8192,24576,24576,648,648,27648,
768,4608,768,1536,768,3072,1536,2304,4608,1536,3072,1536,1536,4608,3072,864,
144,288,144,768,256,256,256,256,256,128,128,128,128,64,64,64,64,128,128,128,
128,80,80,80,80,80,80,80,80,80,80,80,80,80,80,80,80,72,72,576,96,192,192,192,
576,192,192,192,96,72,24,192,96,96,96,96,96,192,192,96,192,9,9,12,12],
[,[1,3,1,3,8,3,8,1,8,8,3,3,8,8,1,1,5,8,8,14,13,1,4,3,4,12,7,5,11,8,12,11,7,8,
3,8,4,4,5,1,5,8,3,7,14,13,13,8,14,51,50,52,54,52,58,54,58,52,54,54,54,58,58,
58,58,54,58,68,70,68,70,15,19,15,19,19,19,22,49,48,46,33,35,27,43,30,47,40,45,
90,98,90,98,92,100,92,100,90,98,90,98,92,100,92,100,50,51,52,62,58,67,63,52,
67,58,63,64,68,68,52,59,54,56,65,66,67,58,61,63,131,130,106,107],[1,2,3,4,5,6,
7,8,10,9,12,11,14,13,15,16,17,18,19,21,20,22,25,24,23,32,33,28,31,30,29,26,27,
42,35,36,38,37,39,40,41,34,43,44,47,49,45,48,46,1,1,1,6,3,9,11,10,8,12,2,4,5,
13,5,7,4,14,1,4,3,2,72,75,74,73,77,76,78,81,80,79,84,83,82,85,86,89,88,87,90,
102,98,94,93,105,101,97,92,104,100,96,91,103,99,95,15,15,15,17,18,20,21,15,20,
18,21,17,15,16,22,26,24,32,44,38,49,48,37,46,50,51,72,72],,[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,
36,37,38,39,40,41,42,43,44,45,46,47,48,49,51,50,52,53,54,55,56,57,58,59,60,61,
64,63,62,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,
88,89,1,14,8,13,14,11,9,2,8,9,3,10,13,2,10,12,107,106,113,117,115,114,116,108,
111,110,112,109,118,119,120,121,122,123,124,125,126,127,128,129,131,130,133,
132]],
0,
[( 73, 75),( 50, 51)( 62, 64)(106,107)(108,113)(109,117)(110,115)(111,114)
(112,116)(130,131)(132,133),( 91, 94)( 92, 98)( 93,102)( 96, 99)( 97,103)
(101,104),(  9, 10)( 11, 12)( 13, 14)( 20, 21)( 23, 25)( 26, 32)( 27, 33)
( 29, 31)( 34, 42)( 37, 38)( 45, 47)( 46, 49)( 55, 57)( 56, 59)( 61, 66)
( 63, 67)( 76, 77)( 79, 81)( 82, 84)( 87, 89)( 91, 93)( 94,102)( 95,105)
( 96,104)( 97,103)( 99,101)(111,112)(114,116)(121,123)(125,128)(126,129)],
["ConstructClifford",[[[1,2,3,4,5,6,7,8,9,10,12,11,13,14,
15,16,17,18,19,20],[1,3,2,3,8,9,6,16,13,14,10,10],[1,3,2,3,8,9,6,16,13,14,10,
10],[1,3,2,3,8,9,6,16,13,14,10,10],[1,3,6,7,9,10,3,2,9,16,15],[1,3,7,6,9,10,
10],[1,3,6,10,3,9,16],[1,3,6,10,3,9,16],[1,2,8,8,3,3,3,6,13,6,14],[1,3,6,10,
10],[1,3,6,10,10],[1,3,3,2,6,16,3,3,9,9],[1,6,6,7,3,16,3,16,3],[1,3,6,3,
9]],[["U4(2)"],["mo62p"],["mo62p"],["mo62p"],["S6"],["A6"],["S5"],["S5"],
["2.2^4:3"],["A5"],["A5"],["2xSymm(4)"],["S3xS3"],["Symm(4)"]],[[[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",14,5]],[[1,2,3,4,
5,9,12],[2,3,3,3,8,2,4],["elab",7,15]],[[1,2,2,3,3,4,4,5,5,6,7,7,8,8,9,9,9,10,
11,12,12,12,12,13,13,13,14,14],[3,2,4,2,4,2,4,2,7,2,2,5,2,5,5,6,7,2,2,2,3,7,8,
5,7,9,2,4],["elab",28,2]],[[1],[4]],[[1],[5]],[[1,2,3,4,5,6,7,8,9,9,10,11,12,
13,13,14],[6,7,7,7,3,4,3,3,8,10,3,3,5,2,3,3],["elab",16,9]],[[1,5,6,13],[7,4,
3,4],["elab",4,11,(2,4,3),(2,3)]],[[1,2,3,4,9,9],[8,5,5,5,3,4],["elab",6,21]],
[[1,2,3,4,5,5,6,7,8,12,12,14],[9,6,6,6,5,9,5,6,6,9,10,5],["elab",12,10]],[[1,
2,2,3,3,4,4,5,6,6,7,8,10,10,11,11],[10,11,12,11,12,11,12,6,6,7,4,4,4,5,4,
5],["elab",16,1,( 2,14, 9, 8,11,16,13,10,12, 3, 6,15, 7)( 4, 5)]],[[1],[
12]],[[1],[11]],[[1,2,3,4,9],[13,9,9,9,9],["elab",5,25]],[[1,2,3,4,9],[14,10,
10,10,11],["elab",5,25,,(2,5,4)]],[[1,5],[15,11],[[1,1],[3,-1]]],[[1,2,3,4,5,
7,8,12,13,13],[16,8,8,8,10,7,7,6,6,8],["elab",10,4,( 2, 4)( 5, 9, 7,10, 8, 6),
( 6,10, 7, 9)]],[[1],[17]],[[1],[18]],[[1],[19]],[[1],[20]]]]]);
ALF("P50/G1/L1/V1/ext4","U4(2)",[1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,
2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,5,6,6,6,6,6,6,
6,6,6,6,6,6,6,6,6,6,7,7,7,7,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,
10,10,10,10,10,10,10,10,10,10,10,10,10,12,11,13,13,13,13,13,14,14,14,14,
14,15,15,16,16,16,16,16,16,16,16,16,16,17,18,19,20]);
ALN("P50/G1/L1/V1/ext4",["4^6.U4(2)"]);

LIBTABLE.LOADSTATUS.ctoholpl:="userloaded";

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