File: ctoorth2.tbl

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#############################################################################
##
#W  ctoorth2.tbl                GAP table library               Thomas Breuer
##
##  This file contains the ordinary character tables related to the
##  orthogonal groups $O_8^+(2)$ and $O_8^+(3)$.
##
#H  ctbllib history
#H  ---------------
#H  $Log: ctoorth2.tbl,v $
#H  Revision 4.33  2012/01/30 08:31:59  gap
#H  removed #H entries from the headers
#H      TB
#H
#H  Revision 4.32  2011/09/28 12:55:44  gap
#H  - removed revision entry and SET_TABLEFILENAME call,
#H  - renamed (6x2.U4(2)):2 and (6xU4(2)):2 to 2x(3x2.U4(2)):2 and
#H    2x(3xU4(2)):2, respectively (and changed the constructions accordingly)
#H  - renamed 2.(3^(1+2)+:2S4), 2^2.(7:3xS3), and 2^2.(L2(7)x2)
#H    to 2x3^(1+2)_+:2S4, 7:3xS4, and D8xL3(2), respectively
#H    (and changed the construction accordingly)
#H  - added tables of 2^{3+6}:(L3(2)x3), 2^{1+8}_+:(S3xA5),
#H  - added maxes entry for O8-(2)
#H      TB
#H
#H  Revision 4.31  2010/12/01 17:45:29  gap
#H  added text to the ambiguous fusion O8+(3).2_1 -> O8+(3).D8
#H      TB
#H
#H  Revision 4.30  2010/05/05 13:20:08  gap
#H  - added many class fusions,
#H  - changed several class fusions according to consistency conditions,
#H    after systematic checks of consistency
#H    - with Brauer tables w.r.t. the restriction of characters,
#H    - of subgroup fusions with the corresponding subgroup fusions between
#H      proper factors where the factor fusions are stored,
#H    - of subgroup fusions from maximal subgroups with subgroup fusions of
#H      extensions inside automorphic extensions
#H
#H      TB
#H
#H  Revision 4.29  2010/01/19 17:05:35  gap
#H  added several tables of maximal subgroups of central extensions of
#H  simple groups (many of them were contributed by S. Dany)
#H      TB
#H
#H  Revision 4.28  2009/04/22 12:39:07  gap
#H  added missing maxes of He.2, ON.2, HN.2, Fi24, and B
#H      TB
#H
#H  Revision 4.27  2009/03/31 16:34:48  gap
#H  added tables of 2.O8+(3), 2^2.O8+(3) (contributed by Max), 2^2.O8+(3).3
#H      TB
#H
#H  Revision 4.26  2008/06/24 16:23:06  gap
#H  added several fusions and names
#H      TB
#H
#H  Revision 4.25  2006/06/07 07:54:27  gap
#H  unified ConstructMixed and ConstructMGA (for better programmatic access)
#H      TB
#H
#H  Revision 4.24  2005/08/10 14:39:55  gap
#H  corrected InfoText values of GV4 constructed tables
#H      TB
#H
#H  Revision 4.23  2004/08/31 12:33:33  gap
#H  added tables of 4.L2(25).2_3,
#H                  L2(49).2^2,
#H                  L2(81).2^2,
#H                  L2(81).(2x4),
#H                  3.L3(4).3.2_2,
#H                  L3(9).2^2,
#H                  L4(4).2^2,
#H                  2x2^3:L3(2)x2,
#H                  (2xA6).2^2,
#H                  2xL2(11).2,
#H                  S3xTh,
#H                  41:40,
#H                  7^(1+4):(3x2.S7),
#H                  7xL2(8),
#H                  (7xL2(8)).3,
#H                  O7(3)N3A,
#H                  O8+(3).2_1',
#H                  O8+(3).2_1'',
#H                  O8+(3).2_2',
#H                  O8+(3).(2^2)_{122},
#H                  S4(9),
#H                  S4(9).2_i,
#H                  2.U4(3).2_2',
#H                  2.U4(3).(2^2)_{133},
#H                  2.U4(3).D8,
#H                  3.U6(2).S3,
#H  added fusions 3.A6.2_i -> 3.A6.2^2,
#H                L2(49).2_i -> L2(49).2^2,
#H                L3(9).2_i -> L3(9).2^2,
#H                L4(4).2_i -> L4(4).2^2,
#H                G2(3) -> O7(3),
#H                L2(17) -> S8(2),
#H                2.L3(4).2_2 -> 2.M22.2
#H                3.L3(4).2_2 -> 3.L3(4).3.2_2
#H                3.L3(4).3 -> 3.L3(4).3.2_2
#H                2^5:S6 -> 2.M22.2
#H                O8+(3) -> O8+(3).2_1',
#H                O8+(3) -> O8+(3).2_1'',
#H                O8+(3) -> O8+(3).2_2',
#H                O8+(3) -> O8+(3).(2^2)_{122},
#H                O8+(3).2_1 -> O8+(3).(2^2)_{122},
#H                O8+(3).2_2 -> O8+(3).(2^2)_{122},
#H                2.U4(3) -> 2.U4(3).2_2',
#H                2.U4(3).2_1 -> 2.U4(3).(2^2)_{133},
#H                2.U4(3).2_2 -> O7(3),
#H                2.U4(3).2_2' -> U4(3).2_2,
#H                2.U4(3).2_3 -> 2.U4(3).(2^2)_{133},
#H                2.U4(3).2_3' -> 2.U4(3).(2^2)_{133},
#H                2.U4(3).4 -> 2.U4(3).D8,
#H                3.U6(2).2 -> 3.U6(2).S3,
#H                3.U6(2).3 -> 3.U6(2).S3,
#H  replaced table of psl(3,4):d12 by L3(4).D12,
#H  changed table of O8+(3).S4 to a construction table,
#H  changed encoding of the table of 12.A6.2_3,
#H  added maxes of Sz(8), Sz(8).3,
#H      TB
#H
#H  Revision 4.22  2003/09/23 16:30:45  gap
#H  added fusions O8+(3).2_1 -> O8+(3).D8, O8+(3).2_2 -> O8+(3).D8
#H  (needed for `AtlasClassNames( "O8+(3).D8" )')
#H      TB
#H
#H  Revision 4.21  2003/06/20 15:03:10  gap
#H  added several fusions
#H      TB
#H
#H  Revision 4.20  2003/05/15 17:38:20  gap
#H  next step towards the closer connection to the library of tables of marks:
#H  added fusions tbl -> tom, adjusted fusions between character tables
#H  in order to make the diagrams commute, adjusted orderings of maxes
#H      TB
#H
#H  Revision 4.19  2003/04/23 08:00:57  gap
#H  added table of O8+(3).D8
#H      TB
#H
#H  Revision 4.18  2003/01/24 15:57:35  gap
#H  replaced several fusions by ones that are compatible with Brauer tables
#H      TB
#H
#H  Revision 4.17  2003/01/14 17:28:50  gap
#H  changed `InfoText' values (for a better programmatic access)
#H  and replaced `ConstructDirectProduct' by `ConstructPermuted' where
#H  there is only one factor (again better programmatic handling)
#H      TB
#H
#H  Revision 4.16  2002/10/22 12:44:13  gap
#H  added 215 factor fusions for cases <tbl> -> <tbl> / O_{<p>}(<tbl>)
#H  (they make it possible to construct <p>-modular Brauer tables
#H  for tables of the type [p^n].<fact> where the <p>-modular Brauer table
#H  of <fact> is in the library)
#H      TB
#H
#H  Revision 4.15  2002/09/30 13:19:49  gap
#H  added tables of 2^2.O8+(2).2, 2^2.O8+(2).3, 2^2.O8+(2).3.2
#H      TB
#H
#H  Revision 4.14  2002/09/18 15:22:01  gap
#H  changed the `text' components of many fusions,
#H  in order to use them as a status information (for evaluation)
#H      TB
#H
#H  Revision 4.13  2002/07/12 06:45:57  gap
#H  further tidying up: removed `irredinfo' stuff, rearranged constructions
#H      TB
#H
#H  Revision 4.12  2002/07/08 16:06:56  gap
#H  changed `construction' component from function (call) to list of function
#H  name and arguments
#H      TB
#H
#H  Revision 4.11  2001/05/04 16:49:31  gap
#H  first revision for ctbllib
#H
#H
#H  tbl history (GAP 4)
#H  -------------------
#H  (Rev. 4.11 of ctbllib coincides with Rev. 4.10 of tbl in GAP 4)
#H  
#H  RCS file: /gap/CVS/GAP/4.0/tbl/ctoorth2.tbl,v
#H  Working file: ctoorth2.tbl
#H  head: 4.10
#H  branch:
#H  locks: strict
#H  access list:
#H  symbolic names:
#H  	GAP4R2: 4.7.0.6
#H  	GAP4R2PRE2: 4.7.0.4
#H  	GAP4R2PRE1: 4.7.0.2
#H  	GAP4R1: 4.5.0.2
#H  keyword substitution: kv
#H  total revisions: 11;	selected revisions: 11
#H  description:
#H  ----------------------------
#H  revision 4.10
#H  date: 2001/03/02 18:30:17;  author: gap;  state: Exp;  lines: +28 -2
#H  for G = O8+(3),
#H  added fusions of G.2_1, G.2_2, G.3 into G.S4,
#H  and fusion of G.2_1 into G.A4
#H  
#H      TB
#H  ----------------------------
#H  revision 4.9
#H  date: 2001/01/10 16:35:28;  author: gap;  state: Exp;  lines: +5 -5
#H  typo in the version I had committed a few seconds ago ...
#H  
#H      TB
#H  ----------------------------
#H  revision 4.8
#H  date: 2001/01/10 16:33:07;  author: gap;  state: Exp;  lines: +6 -2
#H  added fusion of the table of O8+(2) into the table of marks
#H  (nontrivial to find it)
#H  
#H      TB
#H  ----------------------------
#H  revision 4.7
#H  date: 1999/10/21 14:15:48;  author: gap;  state: Exp;  lines: +5 -8
#H  added many `tomidentifer' and `tomfusion' values, which yields a better
#H  interface between `tom' and `tbl';
#H  
#H  added maxes of McL.2,
#H  
#H  unified tables `J2.2M4', `2^(2+4):(3x3):2^2', `2^(2+4):(S3xS3)'.
#H  
#H      TB
#H  ----------------------------
#H  revision 4.6
#H  date: 1999/07/28 14:25:50;  author: gap;  state: Exp;  lines: +5 -5
#H  fixed a ``too long line''
#H  
#H      TB
#H  ----------------------------
#H  revision 4.5
#H  date: 1999/07/12 14:53:29;  author: gap;  state: Exp;  lines: +4 -4
#H  fixed CAS components of a few tables
#H  (now more restrictive than in GAP 3)
#H  
#H      TB
#H  ----------------------------
#H  revision 4.4
#H  date: 1999/05/31 15:14:25;  author: gap;  state: Exp;  lines: +7 -2
#H  added `maxes' entry for O8+(3)
#H  
#H      TB
#H  ----------------------------
#H  revision 4.3
#H  date: 1999/05/14 08:05:56;  author: gap;  state: Exp;  lines: +59 -2
#H  added the tables of some maxes of O8+(3)
#H  (yes, these tables are not relevant for the release of GAP 4,
#H  but Bob Guralnick had asked for them ...)
#H  
#H      TB
#H  ----------------------------
#H  revision 4.2
#H  date: 1998/12/07 13:11:52;  author: gap;  state: Exp;  lines: +9 -3
#H  added new table of S8(2)M3, added some fusions into S8(2)
#H  
#H      TB
#H  ----------------------------
#H  revision 4.1
#H  date: 1997/07/17 15:46:15;  author: fceller;  state: Exp;  lines: +2 -2
#H  for version 4
#H  ----------------------------
#H  revision 1.1
#H  date: 1996/10/21 16:01:17;  author: sam;  state: Exp;
#H  first proposal of the table library
#H  ==========================================================================
##

MOT("2.O8+(2)",
[
"origin: ATLAS of finite groups, tests: 1.o.r."
],
[348364800,348364800,110592,92160,92160,46080,46080,3072,155520,155520,155520,
155520,155520,155520,3888,3888,1296,1296,9216,9216,512,384,384,192,192,64,600,
600,600,600,600,600,3456,3456,1728,1728,576,576,288,288,432,432,216,216,216,
144,144,72,72,24,14,14,32,64,64,54,54,54,54,54,54,40,40,20,20,288,288,288,288,
288,288,72,72,48,48,24,24,30,30,30,30,30,30],
[,[1,1,1,1,1,2,2,1,9,9,11,11,13,13,15,15,17,17,3,3,3,4,4,6,7,8,27,27,29,29,31,
31,9,9,11,13,9,9,12,14,15,15,17,17,17,17,17,18,18,17,51,51,19,21,21,56,56,58,
58,60,60,27,27,30,32,33,33,35,35,36,36,41,41,37,37,39,40,78,78,80,80,82,82],[
1,2,3,4,5,6,7,8,1,2,1,2,1,2,1,2,1,2,19,20,21,22,23,24,25,26,27,28,29,30,31,32,
3,3,3,3,4,5,6,7,3,3,3,3,3,4,5,6,7,8,51,52,53,54,55,15,16,15,16,15,16,62,63,64,
65,19,20,19,20,19,20,19,20,22,23,24,25,27,28,29,30,31,32],,[1,2,3,4,5,6,7,8,9,
10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,1,2,1,2,1,2,33,34,35,36,37,
38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,4,5,6,
7,66,67,68,69,70,71,72,73,74,75,76,77,9,10,11,12,13,14],,[1,2,3,4,5,6,7,8,9,
10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,
36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,1,2,53,54,55,56,57,58,59,60,61,
62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83]],
0,
[( 6, 7)(11,13)(12,14)(24,25)(29,31)(30,32)(35,36)(39,40)(44,45)(48,49)(58,60)
(59,61)(64,65)(68,70)(69,71)(76,77)(80,82)(81,83)],
["ConstructProj",[["O8+(2)",[]],["2.O8+(2)",[]]]]);
ARC("2.O8+(2)","maxes",["2xS6(2)","2.S6(2)","2.O8+(2)M3","P31/G1/L1/V1/ext2",
"2^(1+6)_+.A8","2.O8+(2)M6","2xA9","2.A9","2.O8+(2)M9","2x(3xU4(2)):2",
"(3x2.U4(2)):2","2.O8+(2)M12","2.2^(1+8)_+:(S3xS3xS3)","(2x3^4:2^3).S4",
"(A5xA5).(2x4)","2.(A5xA5).2^2","2.O8+(2)M17"]);
ALF("2.O8+(2)","O8+(2)",[1,1,2,3,3,4,5,6,7,7,8,8,9,9,10,10,11,11,12,12,13,
14,14,15,16,17,18,18,19,19,20,20,21,21,22,23,24,24,25,26,27,27,28,29,30,
31,31,32,33,34,35,35,36,37,37,38,38,39,39,40,40,41,41,42,43,44,44,45,45,
46,46,47,47,48,48,49,50,51,51,52,52,53,53]);
ALF("2.O8+(2)","2.O8+(2).2",[1,2,3,4,5,6,6,7,8,9,10,11,10,11,12,13,14,15,
16,17,18,19,20,21,21,22,23,24,25,26,25,26,27,28,29,29,30,31,32,32,33,34,
35,36,36,37,38,39,39,40,41,42,43,44,45,46,47,48,49,48,49,50,51,52,52,53,
54,55,56,55,56,57,58,59,60,61,61,62,63,64,65,64,65]);

MOT("2.O8+(2).2",
[
"origin: ATLAS of finite groups, tests: 1.o.r."
],
[696729600,696729600,221184,184320,184320,46080,6144,311040,311040,155520,
155520,7776,7776,2592,2592,18432,18432,1024,768,768,192,128,1200,1200,600,600,
6912,6912,1728,1152,1152,288,864,864,432,216,288,288,72,48,28,28,64,128,128,
108,108,54,54,80,80,20,576,576,288,288,144,144,96,96,24,60,60,30,30,5806080,
5806080,18432,18432,15360,15360,4608,1536,1536,768,256,8640,8640,2592,2592,
576,576,432,432,288,288,144,144,384,384,64,16,120,120,576,576,192,192,72,24,
48,48,28,28,36,36,40,40,48,48,60,60],
[,[1,1,1,1,1,2,1,8,8,10,10,12,12,14,14,3,3,3,4,4,6,7,23,23,25,25,8,8,10,8,8,
11,12,12,14,14,14,14,15,14,41,41,16,18,18,46,46,48,48,23,23,26,27,27,29,29,33,
33,30,30,32,62,62,64,64,1,1,1,1,4,4,4,3,3,5,4,8,8,12,12,8,8,14,14,12,12,14,14,
16,16,18,22,23,23,30,30,30,30,37,38,33,33,41,41,46,46,50,50,53,53,62,62],[1,2,
3,4,5,6,7,1,2,1,2,1,2,1,2,16,17,18,19,20,21,22,23,24,25,26,3,3,3,4,5,6,3,3,3,
3,4,5,6,7,41,42,43,44,45,12,13,12,13,50,51,52,16,17,16,17,16,17,19,20,21,23,
24,25,26,66,67,68,69,70,71,72,73,74,75,76,66,67,66,67,68,69,66,67,68,69,68,69,
89,90,91,92,93,94,72,72,70,71,72,75,73,74,103,104,79,80,107,108,89,90,93,
94],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,1,2,1,2,27,28,
29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,4,5,6,53,54,55,
56,57,58,59,60,61,8,9,10,11,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,
82,83,84,85,86,87,88,89,90,91,92,66,67,95,96,97,98,99,100,101,102,103,104,105,
106,70,71,109,110,77,78],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,
21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,1,2,43,44,45,46,
47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,
73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,
99,100,101,102,66,67,105,106,107,108,109,110,111,112]],
0,
[( 66, 67)( 68, 69)( 70, 71)( 73, 74)( 77, 78)( 79, 80)( 81, 82)( 83, 84)
( 85, 86)( 87, 88)( 89, 90)( 93, 94)( 95, 96)( 97, 98)(101,102)(103,104)
(105,106)(107,108)(109,110)(111,112)],
["ConstructProj",[["O8+(2).2",[]],["2.O8+(2).2",[]]]]);
ALF("2.O8+(2).2","O8+(2).2",[1,1,2,3,3,4,5,6,6,7,7,8,8,9,9,10,10,11,12,12,
13,14,15,15,16,16,17,17,18,19,19,20,21,21,22,23,24,24,25,26,27,27,28,29,
29,30,30,31,31,32,32,33,34,34,35,35,36,36,37,37,38,39,39,40,40,41,41,42,
42,43,43,44,45,45,46,47,48,48,49,49,50,50,51,51,52,52,53,53,54,54,55,56,
57,57,58,58,59,59,60,61,62,62,63,63,64,64,65,65,66,66,67,67]);
ALN("2.O8+(2).2",["w(e8)"]);

MOT("Isoclinic(2.O8+(2).2)",
[
"isoclinic group of the 2.O8+(2).2 given in the ATLAS"
],
0,
0,
0,
[(66,67)(68,69)(70,71)(73,74)(77,78)(79,80)(81,82)(83,84)(85,86)(87,88)(89,90)
(93,94)(95,96)(97,98)(101,102)(103,104)(105,106)(107,108)(109,110)(111,112)],
["ConstructIsoclinic",[["2.O8+(2).2"]]]);
ALF("Isoclinic(2.O8+(2).2)","O8+(2).2",[1,1,2,3,3,4,5,6,6,7,7,8,8,9,9,10,
10,11,12,12,13,14,15,15,16,16,17,17,18,19,19,20,21,21,22,23,24,24,25,26,
27,27,28,29,29,30,30,31,31,32,32,33,34,34,35,35,36,36,37,37,38,39,39,40,
40,41,41,42,42,43,43,44,45,45,46,47,48,48,49,49,50,50,51,51,52,52,53,53,
54,54,55,56,57,57,58,58,59,59,60,61,62,62,63,63,64,64,65,65,66,66,67,67]);

MOT("2^2.O8+(2)",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[696729600,696729600,696729600,696729600,110592,92160,92160,92160,92160,92160,
92160,3072,311040,311040,311040,311040,311040,311040,311040,311040,311040,
311040,311040,311040,7776,7776,7776,7776,2592,2592,2592,2592,18432,18432,
18432,18432,512,384,384,384,384,384,384,64,1200,1200,1200,1200,1200,1200,1200,
1200,1200,1200,1200,1200,3456,3456,3456,3456,3456,3456,576,576,576,576,576,
576,864,864,864,864,216,216,216,144,144,144,144,144,144,24,28,28,28,28,32,128,
128,128,128,108,108,108,108,108,108,108,108,108,108,108,108,40,40,40,40,40,40,
576,576,576,576,576,576,576,576,576,576,576,576,144,144,144,144,48,48,48,48,
48,48,60,60,60,60,60,60,60,60,60,60,60,60],
[,[1,1,1,1,1,2,2,3,3,4,4,1,13,13,13,13,17,17,17,17,21,21,21,21,25,25,25,25,29,
29,29,29,5,5,5,5,5,6,6,8,8,10,10,12,45,45,45,45,49,49,49,49,53,53,53,53,13,13,
17,17,21,21,14,14,19,19,24,24,25,25,25,25,29,29,29,30,30,31,31,32,32,29,83,83,
83,83,33,37,37,37,37,92,92,92,92,96,96,96,96,100,100,100,100,46,46,51,51,56,
56,57,57,57,57,59,59,59,59,61,61,61,61,69,69,69,69,63,63,65,65,67,67,132,132,
132,132,136,136,136,136,140,140,140,140],[1,2,3,4,5,6,7,8,9,10,11,12,1,2,3,4,
1,2,3,4,1,2,3,4,1,2,3,4,1,2,3,4,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,
48,49,50,51,52,53,54,55,56,5,5,5,5,5,5,6,7,8,9,10,11,5,5,5,5,5,5,5,6,7,8,9,10,
11,12,83,84,85,86,87,88,89,90,91,25,26,27,28,25,26,27,28,25,26,27,28,104,105,
106,107,108,109,33,34,35,36,33,34,35,36,33,34,35,36,33,34,35,36,38,39,40,41,
42,43,45,46,47,48,49,50,51,52,53,54,55,56],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,
15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,
41,42,43,44,1,2,3,4,1,2,3,4,1,2,3,4,57,58,59,60,61,62,63,64,65,66,67,68,69,70,
71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,
97,98,99,100,101,102,103,6,7,8,9,10,11,110,111,112,113,114,115,116,117,118,
119,120,121,122,123,124,125,126,127,128,129,130,131,13,14,15,16,17,18,19,20,
21,22,23,24],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,
25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,
51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,
77,78,79,80,81,82,1,2,3,4,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,
103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,
122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,
141,142,143]],
0,
[(  3,  4)(  8, 10)(  9, 11)( 15, 16)( 17, 21)( 18, 22)( 19, 24)( 20, 23)
( 27, 28)( 31, 32)( 35, 36)( 40, 42)( 41, 43)( 47, 48)( 49, 53)( 50, 54)
( 51, 56)( 52, 55)( 59, 61)( 60, 62)( 65, 67)( 66, 68)( 71, 72)( 74, 75)
( 78, 80)( 79, 81)( 85, 86)( 90, 91)( 94, 95)( 96,100)( 97,101)( 98,103)
( 99,102)(106,108)(107,109)(112,113)(114,118)(115,119)(116,121)(117,120)
(124,125)(128,130)(129,131)(134,135)(136,140)(137,141)(138,143)(139,142),
(  2,  3)(  6,  8)(  7,  9)( 13, 17)( 14, 19)( 15, 18)( 16, 20)( 22, 23)
( 26, 27)( 30, 31)( 34, 35)( 38, 40)( 39, 41)( 45, 49)( 46, 51)( 47, 50)
( 48, 52)( 54, 55)( 57, 59)( 58, 60)( 63, 65)( 64, 66)( 70, 71)( 73, 74)
( 76, 78)( 77, 79)( 84, 85)( 89, 90)( 92, 96)( 93, 98)( 94, 97)( 95, 99)
(101,102)(104,106)(105,107)(110,114)(111,116)(112,115)(113,117)(119,120)
(123,124)(126,128)(127,129)(132,136)(133,138)(134,137)(135,139)(141,142)],
["ConstructV4G","2.O8+(2)",(  2,  3,  4)(  6,  8, 10)
(  7,  9, 11)( 13, 17, 21)( 14, 19, 24)( 15, 20, 22)( 16, 18, 23)( 26, 27,
 28)( 30, 31, 32)( 34, 35, 36)( 38, 40, 42)( 39, 41, 43)( 45, 49, 53)( 46,
 51, 56)( 47, 52, 54)( 48, 50, 55)( 57, 59, 61)( 58, 60, 62)( 63, 65, 67)
( 64, 66, 68)( 70, 71, 72)( 73, 74, 75)( 76, 78, 80)( 77, 79, 81)( 84, 85,
 86)( 89, 90, 91)( 92, 96,100)( 93, 98,103)( 94, 99,101)( 95, 97,102)(104,
106,108)(105,107,109)(110,114,118)(111,116,121)(112,117,119)(113,115,120)
(123,124,125)(126,128,130)(127,129,131)(132,136,140)(133,138,143)(134,139,
141)(135,137,142)]);
ARC("2^2.O8+(2)","maxes",["2x2.S6(2)","2^2.O8+(2)M2","2^2.O8+(2)M3",
"(2x2^(1+6)_+).A8","2^2.O8+(2)M5","2^2.O8+(2)M6","2x2.A9","2^2.O8+(2)M8",
"2^2.O8+(2)M9","2x(3x2.U4(2)):2","2^2.O8+(2)M11","2^2.O8+(2)M12",
"2^2.(2^(1+8)_+:(S3xS3xS3))","(2^2x3^4).2^3.S4","(2x2.(A5xA5)):2^2",
"2^2.O8+(2)M16","2^2.O8+(2)M17"]);
ALF("2^2.O8+(2)","O8+(2)",[1,1,1,1,2,3,3,4,4,5,5,6,7,7,7,7,8,8,8,8,9,9,9,
9,10,10,10,10,11,11,11,11,12,12,12,12,13,14,14,15,15,16,16,17,18,18,18,18,
19,19,19,19,20,20,20,20,21,21,22,22,23,23,24,24,25,25,26,26,27,27,27,27,
28,29,30,31,31,32,32,33,33,34,35,35,35,35,36,37,37,37,37,38,38,38,38,39,
39,39,39,40,40,40,40,41,41,42,42,43,43,44,44,44,44,45,45,45,45,46,46,46,
46,47,47,47,47,48,48,49,49,50,50,51,51,51,51,52,52,52,52,53,53,53,53]);
ALF("2^2.O8+(2)","2.O8+(2)",[1,1,2,2,3,4,5,6,6,7,7,8,9,9,10,10,11,11,12,
12,13,13,14,14,15,15,16,16,17,17,18,18,19,19,20,20,21,22,23,24,24,25,25,
26,27,27,28,28,29,29,30,30,31,31,32,32,33,34,35,35,36,36,37,38,39,39,40,
40,41,41,42,42,43,44,45,46,47,48,48,49,49,50,51,51,52,52,53,54,54,55,55,
56,56,57,57,58,58,59,59,60,60,61,61,62,63,64,64,65,65,66,66,67,67,68,68,
69,69,70,70,71,71,72,72,73,73,74,75,76,76,77,77,78,78,79,79,80,80,81,81,
82,82,83,83]);
ALF("2^2.O8+(2)","2^2.O8+(2).2",[1,2,3,3,4,5,6,7,8,7,8,9,10,11,12,12,13,
14,15,16,13,14,16,15,17,18,19,19,20,21,22,22,23,24,25,25,26,27,28,29,30,
29,30,31,32,33,34,34,35,36,37,38,35,36,38,37,39,40,41,42,41,42,43,44,45,
46,45,46,47,48,49,49,50,51,51,52,53,54,55,54,55,56,57,58,59,59,60,61,62,
63,63,64,65,66,66,67,68,69,70,67,68,70,69,71,72,73,74,73,74,75,76,77,77,
78,79,80,81,78,79,81,80,82,83,84,84,85,86,87,88,87,88,89,90,91,91,92,93,
94,95,92,93,95,94],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("2^2.O8+(2)","2^2.O8+(2).3",[1,2,2,2,3,4,5,4,5,4,5,6,7,8,9,10,7,10,8,
9,7,9,10,8,11,12,12,12,13,14,14,14,15,16,16,16,17,18,19,18,19,18,19,20,21,
22,23,24,21,24,22,23,21,23,24,22,25,26,25,26,25,26,27,28,27,28,27,28,29,
30,30,30,31,31,31,32,33,32,33,32,33,34,35,36,36,36,37,38,39,39,39,40,41,
42,43,40,43,41,42,40,42,43,41,44,45,44,45,44,45,46,47,48,49,46,49,47,48,
46,48,49,47,50,51,51,51,52,53,52,53,52,53,54,55,56,57,54,57,55,56,54,56,
57,55]);

MOT("2^2.O8+(2).2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[1393459200,1393459200,696729600,221184,184320,184320,92160,92160,6144,622080,
622080,311040,311040,311040,311040,311040,15552,15552,7776,5184,5184,2592,
36864,36864,18432,1024,768,768,384,384,128,2400,2400,1200,1200,1200,1200,1200,
6912,6912,3456,3456,1152,1152,576,576,1728,1728,864,432,216,288,288,144,144,48
,56,56,28,64,256,256,128,216,216,108,108,108,108,108,80,80,40,40,1152,1152,576
,576,576,576,576,288,288,144,96,96,48,48,120,120,60,60,60,60,60,5806080,
5806080,18432,18432,15360,15360,4608,1536,1536,768,256,8640,8640,2592,2592,576
,576,432,432,288,288,144,144,384,384,64,16,120,120,576,576,192,192,72,24,48,48
,28,28,36,36,40,40,48,48,60,60],
[,[1,1,1,1,2,2,3,3,1,10,10,10,13,13,13,13,17,17,17,20,20,20,4,4,4,4,5,5,7,7,9,
32,32,32,35,35,35,35,10,10,13,13,11,11,15,15,17,17,17,20,20,21,21,22,22,20,57,
57,57,23,26,26,26,64,64,64,67,67,67,67,33,33,37,37,39,39,39,41,41,41,41,47,47,
47,43,43,45,45,89,89,89,92,92,92,92,1,2,2,1,5,5,5,4,4,6,5,10,11,17,18,11,10,20
,21,18,17,21,20,24,23,26,31,32,33,43,43,43,43,52,53,47,48,57,58,64,65,71,71,76
,75,89,90],[1,2,3,4,5,6,7,8,9,1,2,3,1,2,3,3,1,2,3,1,2,3,23,24,25,26,27,28,29,
30,31,32,33,34,35,36,37,38,4,4,4,4,5,6,7,8,4,4,4,4,4,5,6,7,8,9,57,58,59,60,61,
62,63,17,18,19,17,18,19,19,71,72,73,74,23,24,25,23,24,25,25,23,24,25,27,28,29,
30,32,33,34,35,36,37,38,96,97,98,99,100,101,102,103,104,105,106,96,97,96,97,98
,99,96,97,98,99,98,99,119,120,121,122,123,124,102,102,100,101,102,105,103,104,
133,134,109,110,137,138,119,120,123,124],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15
,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,1,2,3,1,2,3,3,39,40,41,42,43,
44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,
70,5,6,7,8,75,76,77,78,79,80,81,82,83,84,85,86,87,88,10,11,12,13,14,15,16,96,
97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,
117,118,119,120,121,122,96,97,125,126,127,128,129,130,131,132,133,134,135,136,
100,101,139,140,107,108],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,
21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,
47,48,49,50,51,52,53,54,55,56,1,2,3,60,61,62,63,64,65,66,67,68,69,70,71,72,73,
74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,
100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,
119,120,121,122,123,124,125,126,127,128,129,130,131,132,96,97,135,136,137,138,
139,140,141,142]],
0,
[],
["ConstructMGA","2^2.O8+(2)","2.O8+(2).2",[[84,114],[85,115],[86,116],[87,
117],[88,119],[89,118],[90,120],[91,121],[92,122],[93,124],[94,123],[95,125],
[96,126],[97,128],[98,127],[99,129],[100,130],[101,131],[102,132],[103,133],
[104,135],[105,134],[106,136],[107,137],[108,139],[109,138],[110,140],[111,
141],[112,142],[113,143]],()]);
ALF("2^2.O8+(2).2","2.O8+(2).2",[1,1,2,3,4,5,6,6,7,8,8,9,10,10,11,11,12,
12,13,14,14,15,16,16,17,18,19,20,21,21,22,23,23,24,25,25,26,26,27,28,29,
29,30,31,32,32,33,33,34,35,36,37,38,39,39,40,41,41,42,43,44,44,45,46,46,
47,48,48,49,49,50,51,52,52,53,53,54,55,55,56,56,57,57,58,59,60,61,61,62,
62,63,64,64,65,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,
84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,
106,107,108,109,110,111,112]);
ALF("2^2.O8+(2).2","2^2.O8+(2).3.2",[1,2,2,3,4,5,4,5,6,7,8,9,7,9,8,9,10,
11,11,12,13,13,14,15,15,16,17,18,17,18,19,20,21,22,20,22,21,22,23,24,23,
24,25,26,25,26,27,28,28,29,29,30,31,30,31,32,33,34,34,35,36,37,37,38,39,
40,38,40,39,40,41,42,41,42,43,44,45,43,45,44,45,46,47,47,48,49,48,49,50,
51,52,50,52,51,52,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,
85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,
107,108,109,110,111,112,113]);
ALF("2^2.O8+(2).2","O8+(2).2",[1,1,1,2,3,3,4,4,5,6,6,6,7,7,7,7,8,8,8,9,9,
9,10,10,10,11,12,12,13,13,14,15,15,15,16,16,16,16,17,17,18,18,19,19,20,20,
21,21,21,22,23,24,24,25,25,26,27,27,27,28,29,29,29,30,30,30,31,31,31,31,
32,32,33,33,34,34,34,35,35,35,35,36,36,36,37,37,38,38,39,39,39,40,40,40,
40,41,41,42,42,43,43,44,45,45,46,47,48,48,49,49,50,50,51,51,52,52,53,53,
54,54,55,56,57,57,58,58,59,59,60,61,62,62,63,63,64,64,65,65,66,66,67,67]);

MOT("2^2.O8+(2).3",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[2090188800,696729600,331776,92160,92160,9216,311040,311040,311040,311040,
23328,7776,7776,2592,55296,18432,1536,384,384,192,1200,1200,1200,1200,3456,
3456,576,576,2592,864,216,144,144,72,84,28,96,384,128,108,108,108,108,40,40,
576,576,576,576,432,144,48,48,60,60,60,60,36288,36288,648,648,576,576,144,144,
72,72,54,54,288,288,144,144,96,96,12,12,18,18,21,21,24,24,24,24],
[,[1,1,1,2,2,1,7,7,7,7,11,11,13,13,3,3,3,4,4,6,21,21,21,21,7,7,8,8,11,11,13,14
,14,13,35,35,15,17,17,40,40,40,40,22,22,25,25,25,25,29,29,27,27,54,54,54,54,59
,58,61,60,59,58,59,58,61,60,69,68,63,62,63,62,63,62,67,66,69,68,81,80,71,70,75
,74],[1,2,3,4,5,6,1,2,2,2,1,2,1,2,15,16,17,18,19,20,21,22,23,24,3,3,4,5,3,3,3,
4,5,6,35,36,37,38,39,11,12,12,12,44,45,15,16,16,16,15,16,18,19,21,22,23,24,1,1
,1,1,3,3,6,6,6,6,11,11,15,15,15,15,17,17,20,20,29,29,35,35,37,37,38,38],,[1,2,
3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,1,2,2,2,25,26,27,28,29,30,31,32
,33,34,35,36,37,38,39,40,41,42,43,4,5,46,47,48,49,50,51,52,53,7,8,9,10,59,58,
61,60,63,62,65,64,67,66,69,68,71,70,73,72,75,74,77,76,79,78,81,80,83,82,85,84]
,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,
29,30,31,32,33,34,1,2,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55
,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,58,59
,82,83,84,85]],
0,
[(58,59)(60,61)(62,63)(64,65)(66,67)(68,69)(70,71)(72,73)(74,75)(76,77)(78,79)
(80,81)(82,83)(84,85),(9,10)(23,24)(42,43)(48,49)(56,57)(58,59)(60,61)(62,63)
(64,65)(66,67)(68,69)(70,71)(72,73)(74,75)(76,77)(78,79)(80,81)(82,83)(84,85)
],
["ConstructMGA","2^2.O8+(2)","O8+(2).3",[[54,84,114],[55,85,115],[56,86,
116],[57,87,117],[58,88,118],[59,89,119],[60,90,120],[61,91,121],[62,92,122],
[63,93,123],[64,94,124],[65,95,125],[66,96,126],[67,97,127],[68,98,128],[69,
99,129],[70,100,130],[71,101,131],[72,102,132],[73,103,133],[74,104,134],[75,
105,135],[76,106,136],[77,107,137],[78,108,138],[79,109,139],[80,110,140],[81,
111,141],[82,112,142],[83,113,143]],()]);
ALF("2^2.O8+(2).3","O8+(2).3",[1,1,2,3,3,4,5,5,5,5,6,6,7,7,8,8,9,10,10,11,
12,12,12,12,13,13,14,14,15,15,16,17,17,18,19,19,20,21,21,22,22,22,22,23,
23,24,24,24,24,25,25,26,26,27,27,27,27,28,29,30,31,32,33,34,35,36,37,38,
39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55]);
ALF("2^2.O8+(2).3","2^2.O8+(2).3.2",[1,2,3,4,5,6,7,8,9,9,10,11,12,13,14,
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MOT("2^2.O8+(2).3.2",
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"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
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ALF("2^2.O8+(2).3.2","O8+(2).3.2",[1,1,2,3,3,4,5,5,5,6,6,7,7,8,8,9,10,10,
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MOT("O8+(2)",
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"origin: ATLAS of finite groups, tests: 1.o.r."
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1,0,0,3,0,0,0,1,0,0,-1,0,0],[2835,-45,-45,51,-45,3,0,-81,0,0,0,3,3,3,-5,3,-1,
0,5,0,0,-9,0,0,3,0,0,0,0,0,0,0,0,0,0,-1,-1,0,0,0,0,1,0,0,3,0,0,0,1,0,0,-1,0],[
2835,-45,-45,-45,51,3,0,0,-81,0,0,3,3,3,3,-5,-1,0,0,5,0,0,-9,0,0,3,0,0,0,0,0,
0,0,0,0,-1,-1,0,0,0,0,0,1,0,0,3,0,0,0,1,0,0,-1],[3200,128,0,0,0,0,-40,-40,-40,
14,-4,0,0,0,0,0,0,0,0,0,8,8,8,0,0,0,2,-4,-4,-4,0,0,0,0,1,0,0,-1,-1,-1,0,0,0,0,
0,0,0,0,0,0,0,0,0],[4096,0,0,0,0,0,64,64,64,-8,-8,0,0,0,0,0,0,-4,-4,-4,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0,-1,-1,-1],[4200,-24,40,
40,40,8,-30,-30,-30,15,-3,-8,-8,0,0,0,0,0,0,0,-6,-6,-6,-2,-2,-2,3,3,3,3,1,1,1,
-1,0,0,0,0,0,0,0,0,0,-2,-2,-2,1,0,0,0,0,0,0],[6075,27,-45,-45,-45,-21,0,0,0,0,
0,-9,-1,3,3,3,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,1,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0]],
[( 4, 5)( 8, 9)(15,16)(19,20)(22,23)(25,26)(29,30)(32,33)(39,40)(42,43)(45,46)
(49,50)(52,53),( 3, 4)( 7, 8)(14,15)(18,19)(21,22)(24,25)(28,29)(31,32)(38,39)
(41,42)(44,45)(48,49)(51,52)]);
ARC("O8+(2)","CAS",[rec(name:="o8p2",
permchars:=(),
permclasses:=(),
text:=[
" test:= 1. o.r., sym 2 decompose correctly      \n",
""])]);
ARC("O8+(2)","projectives",["2.O8+(2)",[[8,0,4,0,0,0,5,-4,-4,-1,2,4,0,2,0,0,0,
3,-2,-2,-3,0,0,1,0,0,3,0,0,0,-2,0,0,0,1,0,2,2,-1,-1,-1,0,0,1,-2,-2,1,-1,0,0,0,
1,1],[56,0,-4,0,0,0,11,-16,-16,2,2,12,0,-2,0,0,0,1,-4,-4,3,0,0,-1,0,0,6,0,0,0,
2,0,0,0,0,0,2,-1,-1,-1,1,0,0,3,0,0,0,1,0,0,1,-1,-1],[112,0,24,0,0,0,31,4,4,4,
4,8,0,4,0,0,0,7,2,2,-9,0,0,3,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,-1,0,0,-1,2,2,2,
1,0,0,1,-1,-1],[160,0,16,0,0,0,34,-20,-20,-2,-2,16,0,0,0,0,0,5,0,0,-6,0,0,-2,
0,0,6,0,0,0,-2,0,0,0,-1,0,0,1,1,1,1,0,0,-2,-2,-2,-2,0,0,0,-1,0,0],[224,0,-16,
0,0,0,14,-40,-4,-1,2,16,0,0,0,0,0,-1,-6,4,6,0,0,2,0,0,3,0,0,0,2,0,0,0,0,0,0,
-1,-1,2,-1,0,0,-2,4,-2,1,0,0,0,-1,0,1],[224,0,-16,0,0,0,14,-4,-40,-1,2,16,0,0,
0,0,0,-1,4,-6,6,0,0,2,0,0,3,0,0,0,2,0,0,0,0,0,0,-1,2,-1,-1,0,0,-2,-2,4,1,0,0,
0,-1,1,0],[400,0,40,0,0,0,25,-20,-20,4,10,-8,0,4,0,0,0,0,0,0,9,0,0,1,0,0,0,0,
0,0,-2,0,0,0,1,0,0,-2,1,1,0,0,0,1,-2,-2,-2,1,0,0,0,0,0],[448,0,32,0,0,0,16,16,
16,16,-2,0,0,0,0,0,0,-2,-2,-2,0,0,0,8,0,0,0,0,0,0,2,0,0,0,0,0,0,1,1,1,2,0,0,0,
0,0,0,0,0,0,1,1,1],[560,0,56,0,0,0,74,20,20,-7,2,8,0,4,0,0,0,5,0,0,-6,0,0,2,0,
0,-3,0,0,0,2,0,0,0,0,0,0,-1,-1,-1,1,0,0,2,2,2,-1,-2,0,0,-1,0,0],[672,0,16,0,0,
0,-30,-84,24,-3,6,16,0,0,0,0,0,-3,-8,2,-6,0,0,-2,0,0,-3,0,0,0,-2,0,0,0,0,0,0,
0,0,0,1,0,0,-2,-2,4,1,0,0,0,0,1,-1],[672,0,16,0,0,0,-30,24,-84,-3,6,16,0,0,0,
0,0,-3,2,-8,-6,0,0,-2,0,0,-3,0,0,0,-2,0,0,0,0,0,0,0,0,0,1,0,0,-2,4,-2,1,0,0,0,
0,-1,1],[840,0,4,0,0,0,21,-60,-60,3,-6,20,0,2,0,0,0,-5,0,0,-3,0,0,1,0,0,3,0,0,
0,-2,0,0,0,0,0,-2,0,0,0,-1,0,0,5,2,2,-1,-1,0,0,1,0,0],[1008,0,24,0,0,0,90,36,
36,9,0,8,0,-4,0,0,0,3,-2,-2,-6,0,0,-6,0,0,-3,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,
2,2,2,-1,2,0,0,0,1,1],[1008,0,24,0,0,0,-45,36,-72,9,0,8,0,-4,0,0,0,3,-2,-2,3,
0,0,3,0,0,-3,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,-1,2,-4,-1,-1,0,0,0,1,-2],[1008,
0,24,0,0,0,-45,-72,36,9,0,8,0,-4,0,0,0,3,-2,-2,3,0,0,3,0,0,-3,0,0,0,0,0,0,0,0,
0,0,0,0,0,-1,0,0,-1,-4,2,-1,-1,0,0,0,-2,1],[1296,0,-24,0,0,0,81,0,0,0,0,24,0,
-4,0,0,0,1,6,6,9,0,0,-3,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,-3,0,0,0,-1,0,0,
1,0,0],[1400,0,60,0,0,0,-25,20,20,-13,8,-4,0,-2,0,0,0,0,0,0,15,0,0,3,0,0,3,0,
0,0,0,0,0,0,0,0,-2,2,-1,-1,0,0,0,-1,2,2,-1,1,0,0,0,0,0],[1400,0,60,0,0,0,95,
-40,-40,-4,-4,-4,0,-2,0,0,0,0,0,0,-9,0,0,3,0,0,0,0,0,0,0,0,0,0,0,0,-2,-1,-1,
-1,0,0,0,-1,-4,-4,2,1,0,0,0,0,0],[2400,0,-80,0,0,0,60,60,60,-3,6,16,0,0,0,0,0,
0,0,0,12,0,0,4,0,0,-3,0,0,0,-2,0,0,0,-1,0,0,0,0,0,0,0,0,4,-2,-2,1,0,0,0,0,0,
0],[2800,0,-40,0,0,0,55,-80,-80,-8,10,-24,0,-4,0,0,0,0,0,0,-9,0,0,-1,0,0,0,0,
0,0,2,0,0,0,0,0,0,1,1,1,0,0,0,3,0,0,0,-1,0,0,0,0,0],[2800,0,-40,0,0,0,-5,40,
-140,1,-2,8,0,4,0,0,0,0,0,0,3,0,0,-1,0,0,-3,0,0,0,2,0,0,0,0,0,0,1,-2,1,0,0,0,
-1,-4,2,-1,1,0,0,0,0,0],[2800,0,-40,0,0,0,-5,-140,40,1,-2,8,0,4,0,0,0,0,0,0,3,
0,0,-1,0,0,-3,0,0,0,2,0,0,0,0,0,0,1,1,-2,0,0,0,-1,2,-4,-1,1,0,0,0,0,0],[3240,
0,84,0,0,0,81,0,0,0,0,-12,0,2,0,0,0,-5,0,0,9,0,0,-3,0,0,0,0,0,0,0,0,0,0,-1,0,
2,0,0,0,-1,0,0,-3,0,0,0,-1,0,0,1,0,0],[3360,0,16,0,0,0,-6,-60,-60,12,-6,-16,0,
0,0,0,0,5,0,0,18,0,0,-2,0,0,0,0,0,0,-2,0,0,0,0,0,0,0,0,0,1,0,0,2,2,2,2,0,0,0,
-1,0,0],[3584,0,0,0,0,0,-64,80,-64,-16,-4,0,0,0,0,0,0,4,-6,4,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,-1,2,-1,0,0,0,0,0,0,0,0,0,0,1,0,1],[3584,0,0,0,0,0,-64,-64,
80,-16,-4,0,0,0,0,0,0,4,4,-6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,2,0,0,0,
0,0,0,0,0,0,0,1,1,0],[4096,0,0,0,0,0,64,64,64,-8,-8,0,0,0,0,0,0,-4,-4,-4,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0,-1,-1,-1],[4200,0,20,
0,0,0,-75,60,60,15,6,4,0,2,0,0,0,0,0,0,-3,0,0,-7,0,0,3,0,0,0,2,0,0,0,0,0,-2,0,
0,0,0,0,0,1,-2,-2,1,-1,0,0,0,0,0],[4536,0,60,0,0,0,-81,0,0,0,0,12,0,-2,0,0,0,
-4,6,6,-9,0,0,3,0,0,0,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,3,0,0,0,1,0,0,-1,0,0],[
5600,0,-80,0,0,0,20,20,20,11,2,-16,0,0,0,0,0,0,0,0,-12,0,0,4,0,0,3,0,0,0,-2,0,
0,0,0,0,0,-1,-1,-1,0,0,0,-4,2,2,-1,0,0,0,0,0,0]],]);
ARC("O8+(2)","isSimple",true);
ARC("O8+(2)","extInfo",["2^2","3.2"]);
ARC("O8+(2)","tomfusion",rec(name:="O8+(2)",map:=[1,2,3,4,5,6,8,7,9,10,11,
43,44,46,45,47,48,49,50,51,68,69,67,71,70,72,76,74,73,75,79,78,77,80,81,
291,290,301,302,303,312,311,310,329,330,331,332,334,333,335,409,410,411],
text:=[
"fusion map is unique up to table automorphisms, hard to determine"
],
perm:=(1,3,2)(4,5)(7,9,8)));
ARC("O8+(2)","maxes",["S6(2)","O8+(2)M2","O8+(2)M3","2^6:A8","O8+(2)M5",
"O8+(2)M6","A9","O8+(2)M8","O8+(2)M9","(3xU4(2)):2","O8+(2)M11","O8+(2)M12",
"2^(1+8)_+:(S3xS3xS3)","3^4:2^3.S4(a)","(A5xA5):2^2","O8+(2)M16",
"O8+(2)M17"]);
ALF("O8+(2)","O8+(2).2",[1,2,3,4,4,5,6,7,7,8,9,10,11,12,13,13,14,15,16,16,
17,18,18,19,20,20,21,22,23,23,24,25,25,26,27,28,29,30,31,31,32,33,33,34,
35,35,36,37,38,38,39,40,40],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("O8+(2)","O8+(2).3",[1,2,3,3,3,4,5,5,5,6,7,8,9,10,10,10,11,12,12,12,
13,13,13,14,14,14,15,16,16,16,17,17,17,18,19,20,21,22,22,22,23,23,23,24,
24,24,25,26,26,26,27,27,27],[
"fusion map is unique, equal to that on the CAS table"
]);
ALF("O8+(2)","O8+(3)",[1,5,2,3,4,5,7,8,12,16,17,19,23,20,21,22,23,24,25,26,
37,38,42,31,32,36,49,52,51,50,43,44,45,53,55,56,57,71,71,71,72,73,74,78,79,
83,88,89,90,94,100,101,105],[
"fusion map is unique up to table automorphisms,\n",
"the representative is the one mentioned in the ATLAS"
]);
ALF("O8+(2)","2^8:O8+(2)",[1,4,8,13,15,17,21,24,25,26,28,31,34,39,45,47,
49,52,55,56,57,60,61,62,67,68,69,71,74,76,78,81,83,85,88,92,95,98,100,101,
102,105,106,107,109,110,111,113,117,118,119,123,124],[
"fusion map is unique up to table automorphisms"
]);
ALN("O8+(2)",["o8p2","O8+(2).2M1","O8+(2).3M1"]);

MOT("O8+(3)M11",
[
"11th maximal subgroup of O8+(3),\n",
"differs from O8+(2) only by fusion map"
],
0,
0,
0,
0,
["ConstructPermuted",["O8+(2)"]]);
ALF("O8+(3)M11","O8+(3)",[1,5,2,3,4,5,7,11,9,15,17,19,23,20,21,22,23,24,25,
26,37,41,39,31,35,33,48,53,50,51,43,44,45,52,55,56,57,70,70,70,72,73,74,78,
82,80,87,89,93,91,100,104,102],[
"fusion O8+(2) -> O8+(3) mapped under O8+(3).2_1"
]);

MOT("O8+(3)M12",
[
"12th maximal subgroup of O8+(3),\n",
"differs from O8+(2) only by fusion map"
],
0,
0,
0,
0,
["ConstructPermuted",["O8+(2)"]]);
ALF("O8+(3)M12","O8+(3)",[1,5,2,3,4,5,10,8,9,14,17,19,23,20,21,22,23,24,25,
26,40,38,39,34,32,33,47,50,53,52,43,44,45,51,55,56,57,69,69,69,72,73,74,81,
79,80,86,92,90,91,103,101,102],[
"fusion O8+(2) -> O8+(3) mapped under O8+(3).2_1'"
]);

MOT("O8+(3)M13",
[
"13th maximal subgroup of O8+(3),\n",
"differs from O8+(2) only by fusion map"
],
0,
0,
0,
0,
["ConstructPermuted",["O8+(2)"]]);
ALF("O8+(3)M13","O8+(3)",[1,5,2,3,4,5,10,11,12,13,17,19,23,20,21,22,23,24,
25,26,40,41,42,34,35,36,46,51,52,53,43,44,45,50,55,56,57,68,68,68,72,73,74,
81,82,83,85,92,93,94,103,104,105],[
"fusion map is unique up to table automorphisms,\n",
"equal to the map from O8+(2), mapped under an outer autom.;\n",
"compatible with the ATLAS"
]);

MOT("O8+(2).2",
[
"origin: ATLAS of finite groups, tests: 1.o.r."
],
[348364800,221184,92160,46080,6144,155520,77760,3888,1296,9216,1024,384,192,
128,600,300,3456,1728,576,288,432,432,216,144,72,48,14,64,64,54,27,40,20,288,
144,72,48,24,30,15,2903040,9216,7680,4608,768,768,256,4320,1296,288,216,144,
72,192,64,16,60,288,96,72,24,24,14,18,20,24,30],
[,[1,1,1,1,1,6,7,8,9,2,2,3,4,5,15,16,6,7,6,7,8,9,9,9,9,9,27,10,11,30,31,15,16,
17,18,21,19,20,39,40,1,1,3,3,2,3,3,6,8,6,9,8,9,10,11,14,15,19,19,24,24,21,27,
30,32,34,39],[1,2,3,4,5,1,1,1,1,10,11,12,13,14,15,16,2,2,3,4,2,2,2,3,4,5,27,
28,29,8,8,32,33,10,10,10,12,13,15,16,41,42,43,44,45,46,47,41,41,42,41,42,42,
54,55,56,57,44,43,44,46,45,63,49,65,54,57],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,
1,1,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,3,4,34,35,36,37,38,6,7,41,42,
43,44,45,46,47,48,49,50,51,52,53,54,55,56,41,58,59,60,61,62,63,64,43,66,48],,[
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,1,28,29,
30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,
56,57,58,59,60,61,62,41,64,65,66,67]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[28,-4,4,4,
-4,10,10,1,1,8,0,0,0,0,3,3,2,2,-2,-2,5,-1,-1,1,1,-1,0,-2,2,1,1,-1,-1,2,2,-1,0,
0,0,0,14,-2,6,-2,2,2,-2,2,5,-2,-1,1,1,0,0,0,-1,4,0,1,-1,-1,0,-1,1,0,2],
[TENSOR,[3,2]],[35,3,11,-5,3,14,5,-1,2,7,-1,3,-1,-1,5,0,6,-3,2,1,3,0,0,2,-2,0,
0,1,1,2,-1,1,0,-2,1,1,0,-1,-1,0,21,5,9,1,1,-3,1,6,3,2,0,-1,2,3,-1,-1,1,4,0,-2,
0,1,0,0,-1,0,1],
[TENSOR,[5,2]],[70,6,-10,6,6,10,19,-2,4,14,-2,-2,2,-2,0,5,-6,3,2,3,6,0,0,-4,0,
0,0,2,2,-2,1,0,1,2,-1,2,-2,-1,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0],[50,18,10,10,2,5,5,-4,5,-2,6,2,2,2,0,0,-3,-3,1,1,0,3,3,1,1,-1,1,
0,0,-1,-1,0,0,1,1,-2,-1,-1,0,0,20,4,0,8,0,4,0,5,2,1,-1,-2,1,-2,2,0,0,-1,3,-1,
1,0,-1,-1,0,1,0],
[TENSOR,[8,2]],[84,20,20,4,4,21,-6,3,3,4,4,4,0,0,4,-1,5,2,5,-2,-1,5,-1,-1,1,1,
0,0,0,0,0,0,-1,1,-2,1,1,0,1,-1,42,10,10,10,2,2,2,9,-3,1,3,1,1,2,2,0,2,1,1,1,
-1,-1,0,0,0,-1,-1],
[TENSOR,[10,2]],[168,40,8,24,8,-12,15,6,6,8,8,0,4,0,-2,3,4,7,-4,3,-2,-2,4,2,0,
2,0,0,0,0,0,-2,-1,-4,-1,2,0,1,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0],[175,-17,15,15,-1,-5,-5,13,4,-1,-1,-1,-1,3,0,0,-5,-5,3,3,1,-2,-2,
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[]);
ARC("O8+(2).2","CAS",[rec(name:="o8p2b",
permchars:=( 7, 9, 8)(17,21,20,19,18)(26,36,33,31,41,38,35,32,30,29,28,27)
(34,44,40,37)(39,47,55,51,48,45,42,52,49,46,43)(50,62,58,54)(53,63,59,65,61,57
 )(56,64,60),
permclasses:=(),
text:=[
" test:= 1. o.r., sym 2 decompose correctly \n",
""])]);
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0,0,0,-1,0],[4536,0,60,0,0,-81,0,0,0,12,0,-2,0,0,-4,6,-9,0,3,0,0,0,0,0,0,0,0,
0,2,0,0,0,0,3,0,0,1,0,-1,0,378,30,-20,0,6,0,0,-9,0,3,0,0,0,2,0,0,-2,-3,1,0,0,
0,0,0,0,-1,1],[5600,0,-80,0,0,20,20,11,2,-16,0,0,0,0,0,0,-12,0,4,0,3,0,0,-2,0,
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0,0,0,1,0,1,0,0,0]],]);
ALF("O8+(2).2","Fi22",[1,3,3,3,4,5,5,6,7,9,9,13,13,12,14,14,18,18,18,18,
17,23,23,23,23,22,26,28,27,32,32,35,35,39,39,38,46,46,52,52,2,4,10,10,11,
10,13,15,16,20,19,21,24,27,28,30,34,41,41,47,47,45,51,57,59,64,65],[
"fusion map is unique, equal to that on the CAS table"
]);
ALF("O8+(2).2","O8+(2).3.2",[1,2,3,3,4,5,5,6,7,8,9,10,10,11,12,12,13,13,
14,14,15,16,16,17,17,18,19,20,21,22,22,23,23,24,24,25,26,26,27,27,42,43,
44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,
68],[
"fusion map is unique, equal to that on the CAS table"
]);
ALF("O8+(2).2","S8(2)",[1,3,4,5,7,8,9,11,10,14,15,19,21,23,24,25,27,30,28,
36,35,29,34,37,38,41,42,45,46,49,50,53,54,55,59,63,62,67,69,71,2,6,13,12,
18,17,20,26,31,32,33,40,39,43,44,48,51,56,57,60,65,66,68,74,76,78,80],[
"fusion map is unique"
]);
ALF("O8+(2).2","2^8:O8+(2):2",[1,4,8,13,15,19,22,23,25,28,32,37,42,44,47,
50,51,54,55,60,61,63,66,68,71,73,76,80,83,85,87,88,91,92,94,95,98,101,102,
105,106,110,116,120,125,128,132,136,140,142,146,150,152,156,159,163,165,
169,172,176,178,180,182,184,186,189,190],[
"fusion map is unique"
]);
ALN("O8+(2).2",["f22u4","o8p2b"]);

MOT("O8+(2).3",
[
"origin: ATLAS of finite groups, tests: 1.o.r."
],
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648,216,72,72,21,96,96,27,20,144,108,24,15,36288,36288,648,648,576,576,144,
144,72,72,54,54,288,288,144,144,96,96,12,12,18,18,21,21,24,24,24,24],
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29,28,29,28,31,30,39,38,33,32,33,32,33,32,37,36,39,38,51,50,41,40,45,44],[1,2,
3,4,1,1,1,8,9,10,11,12,2,3,2,2,3,4,19,20,21,6,23,8,8,10,12,1,1,1,1,2,2,4,4,4,
4,6,6,8,8,8,8,9,9,11,11,15,15,19,19,20,20,21,21],,[1,2,3,4,5,6,7,8,9,10,11,1,
13,14,15,16,17,18,19,20,21,22,3,24,25,26,5,29,28,31,30,33,32,35,34,37,36,39,
38,41,40,43,42,45,44,47,46,49,48,51,50,53,52,55,54],,[1,2,3,4,5,6,7,8,9,10,11,
12,13,14,15,16,17,18,1,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,
38,39,40,41,42,43,44,45,46,47,48,49,28,29,52,53,54,55]],
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[TENSOR,[26,2]],
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0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[3200,128,0,0,-40,14,-4,0,0,0,0,0,8,0,
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[TENSOR,[44,2]],
[TENSOR,[44,3]],[4096,0,0,0,64,-8,-8,0,0,0,0,-4,0,0,0,0,0,0,1,0,0,1,0,0,0,0,
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[TENSOR,[47,2]],
[TENSOR,[47,3]],[4200,-24,40,8,-30,15,-3,-8,-8,0,0,0,-6,-2,3,3,1,-1,0,0,0,0,0,
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[TENSOR,[50,2]],
[TENSOR,[50,3]],[6075,27,-45,-21,0,0,0,-9,-1,3,3,0,0,0,0,0,0,0,-1,1,1,0,0,0,0,
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[TENSOR,[53,2]],
[TENSOR,[53,3]]],
[(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)(40,41)(42,43)(44,45)(46,47)(48,49)
(50,51)(52,53)(54,55)]);
ARC("O8+(2).3","CAS",[rec(name:="o8p2d",
permchars:=(),
permclasses:=(),
text:=[
"  test:= 1. o.r., sym 2 decompose correctly      \n",
""])]);
ALF("O8+(2).3","O8+(2).3.2",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,
19,20,21,22,23,24,25,26,27,28,28,29,29,30,30,31,31,32,32,33,33,34,34,35,
35,36,36,37,37,38,38,39,39,40,40,41,41]);
ALN("O8+(2).3",["o8p2d"]);

MOT("O8+(2).3.2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7],\n",
"constructions: Aut(O8+(2))"
],
[1045094400,663552,92160,18432,155520,11664,3888,27648,3072,384,384,600,3456,
576,1296,432,144,144,42,192,192,54,40,288,216,48,30,36288,648,576,144,72,54,
288,144,96,12,18,21,24,24,2903040,9216,7680,4608,768,768,256,4320,1296,288,
216,144,72,192,64,16,60,288,96,72,24,24,14,18,20,24,30],
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29,33,30,30,30,32,33,39,34,36,1,1,3,3,2,3,3,5,6,5,7,6,7,8,9,11,12,14,14,17,17,
15,19,22,23,24,27],[1,2,3,4,1,1,1,8,9,10,11,12,2,3,2,2,3,4,19,20,21,6,23,8,8,
10,12,1,1,2,4,4,6,8,8,9,11,15,19,20,21,42,43,44,45,46,47,48,42,42,43,42,43,43,
55,56,57,58,45,44,45,47,46,64,50,66,55,58],,[1,2,3,4,5,6,7,8,9,10,11,1,13,14,
15,16,17,18,19,20,21,22,3,24,25,26,5,28,29,30,31,32,33,34,35,36,37,38,39,40,
41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,42,59,60,61,62,63,64,65,44,
67,49],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,1,20,21,22,23,24,25,26,
27,28,29,30,31,32,33,34,35,36,37,38,28,40,41,42,43,44,45,46,47,48,49,50,51,52,
53,54,55,56,57,58,59,60,61,62,63,42,65,66,67,68]],
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-2],
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[]);
ARC("O8+(2).3.2","CAS",[rec(permchars:=( 4, 5)( 6, 8,10, 7,11, 9)(12,15)(13,
14)(16,18,24,28,36,40,44,34,38,30,26,21,23,19,17,25,22,20)(27,31)(29,35,41,43,
47,54,62,64,51,61,49,58,46,42,48,53,63,52,60,50,57,45,33,39,37)(55,67)(56,66),
permclasses:=(10,11)(14,15)(17,18)(28,30,39,64,60,54,44,32,45,33,49,37,59,51,
 40,67,65,61,56,47,34,52,41,66,63,58,50,38,62,57,48,36,55,46,35,53,42)
(29,31,43),
name:="o8p2s3")]);
ALF("O8+(2).3.2","Fi22",[1,3,3,4,5,6,7,9,9,13,12,14,18,18,17,23,23,22,26,
28,27,32,35,39,38,46,52,5,8,18,20,25,31,39,40,39,48,58,60,63,64,2,4,10,10,
11,10,13,15,16,20,19,21,24,27,28,30,34,41,41,47,47,45,51,57,59,64,65],[
"fusion map is unique, equal to that on the CAS table"
]);
ALF("O8+(2).3.2","F4(2)",[1,2,4,5,7,8,6,9,11,19,20,24,28,32,29,25,31,33,
37,42,40,50,53,55,56,65,75,7,8,28,34,35,49,55,55,63,68,82,87,91,89,3,5,14,
13,15,18,21,26,30,34,27,35,33,42,40,47,52,59,61,58,64,66,73,83,85,91,95],[
"fusion map is unique up to table automorphisms"
]);
ALN("O8+(2).3.2",["O8+(2).S3","O8+(2):S3","o8p2s3","f22m4"]);

MOT("F4(2)M8",
[
"differs from O8+(2).3.2 only by fusion into F4(2)"
],
0,
0,
0,
0,
["ConstructPermuted",["O8+(2).3.2"]]);
ALF("F4(2)M8","F4(2)",[1,3,4,5,6,8,7,10,12,18,20,24,27,31,30,26,32,34,36,
43,41,49,53,54,57,64,74,6,8,27,33,35,50,54,54,62,68,83,86,90,88,2,5,14,13,
16,19,21,25,29,33,28,35,34,43,41,47,51,58,60,59,65,67,72,82,85,90,94],[
"fusion O8+(2).3.2 -> F4(2) mapped under F4(2).2"
]);

MOT("O8+(3)",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,13]"
],
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20,20],
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E(28)^3-E(28)^11-E(28)^15+E(28)^19-E(28)^23+E(28)^27,
-E(28)^3+E(28)^11+E(28)^15-E(28)^19+E(28)^23-E(28)^27,0,0,0,0,0,0,-2,0,0,-2,0,
0,0,0,0],
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0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0],[716800,0,0,0,0,1408,-320,
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E(13)^2+E(13)^5+E(13)^6+E(13)^7+E(13)^8+E(13)^11,
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0,0,0],
[GALOIS,[79,2]]],]);
ARC("O8+(3)","CAS",[rec(name:="o8p3",
permchars:=(),
permclasses:=(  6, 13, 20)(  7, 14, 21)(  8, 16, 23, 10, 15, 22)
(  9, 18, 24, 94, 73, 98,111, 92, 69, 37, 53, 65, 35, 46, 59, 29, 42, 58, 27,
  40, 54, 67, 34, 44, 50, 63, 30, 52, 64, 32, 45, 51, 66, 33, 47, 60, 31, 43,
  49, 62, 28, 41, 56, 11, 17, 25, 95,113,101,105,108, 93, 71, 39, 57, 12, 19)
( 26, 96,114,102,107, 91, 72, 97,110, 90, 70, 38, 55,109, 88, 87, 86, 85, 84,
  83, 82, 80, 81, 78, 77, 76, 75, 74, 99,112,100,103,104,106, 89, 68, 36, 48,
  61),
text:=[
"names:=o8p3; pom8[3,+]\n",
"               d4[3]     [lie-not.]\n",
"    order: 2^12.3^12.5^2.7.13 = 4,952,179,814,400\n",
"    number of classes: 114\n",
"    source:hunt, d.c.\n",
"          the character table of an eight-dimensional\n",
"          orthogonal group\n",
"          math.comp. 28\n",
"          [1974],659-660\n",
"          loose microfiche suppl. d1-e5\n",
"    test: 1. o.r., sym 2 decompose correctly\n",
"    comments: -\n",
""])]);
ARC("O8+(3)","isSimple",true);
ARC("O8+(3)","extInfo",["2^2","S4"]);
ARC("O8+(3)","maxes",["O7(3)","O8+(3)M2","O8+(3)M3","O8+(3)M4","O8+(3)M5",
"O8+(3)M6","3^6:L4(3)","O8+(3)M8","O8+(3)M9","O8+(2)","O8+(3)M11",
"O8+(3)M12","O8+(3)M13","O8+(3)M14","2.U4(3).(2^2)_{122}","O8+(3)M16",
"O8+(3)M17","(A4xU4(2)):2","O8+(3)M19","O8+(3)M20","O8+(3)M21","O8+(3)M22",
"O8+(3)M23","(A6xA6):2^2","O8+(3)M25","O8+(3)M26","O8+(3)M27"]);
ALF("O8+(3)","O8+(3).2_1",[1,2,3,4,5,6,7,8,9,10,8,9,11,11,12,12,13,14,15,
16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,28,29,31,32,33,34,32,33,35,
36,37,38,38,39,39,40,40,41,41,42,43,44,45,46,47,48,49,47,48,50,50,51,51,
52,52,53,53,54,55,56,57,58,59,60,61,62,63,61,62,64,65,65,66,66,67,68,69,
70,68,69,71,72,73,74,75,76,77,78,79,77,78,80,81,82,83,81,82,84,85,86]);
ALF("O8+(3)","O8+(3).2_1'",[1,4,2,3,5,6,9,7,8,9,10,8,11,12,11,12,13,14,15,
18,16,17,19,22,20,21,25,23,24,26,29,27,28,29,30,28,33,31,32,33,34,32,37,
35,36,38,39,38,39,40,41,40,41,42,43,44,45,48,46,47,48,49,47,50,51,50,51,
52,53,52,53,56,54,55,59,57,58,62,60,61,62,63,61,64,65,66,65,66,69,67,68,
69,70,68,71,72,75,73,74,78,76,77,78,79,77,82,80,81,82,83,81,86,84,85]);
ALF("O8+(3)","O8+(3).2_1''",[1,3,4,2,5,6,8,9,7,8,9,10,11,12,12,11,13,14,
15,17,18,16,19,21,22,20,24,25,23,26,28,29,27,28,29,30,32,33,31,32,33,34,
36,37,35,38,39,39,38,40,41,41,40,42,43,44,45,47,48,46,47,48,49,50,51,51,
50,52,53,53,52,55,56,54,58,59,57,61,62,60,61,62,63,64,65,66,66,65,68,69,
67,68,69,70,71,72,74,75,73,77,78,76,77,78,79,81,82,80,81,82,83,85,86,84]);
ALF("O8+(3)","O8+(3).2_2",[1,2,3,3,4,5,6,7,7,8,9,9,10,11,12,12,13,14,15,
16,17,17,18,19,20,20,21,22,22,23,24,25,25,26,27,27,28,29,29,30,31,31,32,
33,33,34,35,36,36,37,38,39,39,40,41,42,43,44,45,45,46,47,47,48,49,50,50,
51,52,53,53,54,55,55,56,57,57,58,59,59,60,61,61,62,63,64,65,65,66,67,67,
68,69,69,70,71,72,73,73,74,75,75,76,77,77,78,79,79,80,81,81,82,83,83]);
ALF("O8+(3)","O8+(3).2_2'",[1,2,3,3,4,5,8,7,9,6,9,7,12,12,10,11,13,14,15,
16,17,17,18,19,20,20,21,22,22,23,26,25,27,24,27,25,30,29,31,28,31,29,32,
33,33,36,36,34,35,39,39,37,38,40,41,42,43,46,45,47,44,47,45,50,50,48,49,
53,53,51,52,54,55,55,56,57,57,60,59,61,58,61,59,62,65,65,63,64,68,67,69,
66,69,67,70,71,72,73,73,76,75,77,74,77,75,80,79,81,78,81,79,82,83,83]);
ALF("O8+(3)","O8+(3).3",[1,2,2,2,3,4,5,5,5,6,6,6,7,8,8,8,9,10,11,12,12,12,
13,14,14,14,15,15,15,16,17,17,17,18,18,18,19,19,19,20,20,20,21,21,21,22,
23,23,23,24,25,25,25,26,27,28,29,30,30,30,31,31,31,32,33,33,33,34,35,35,
35,36,36,36,37,37,37,38,38,38,39,39,39,40,41,42,42,42,43,43,43,44,44,44,
45,46,47,47,47,48,48,48,49,49,49,50,50,50,51,51,51,52,52,52]);
ALF("O8+(3)","O8+(3).4",[1,2,3,3,4,5,6,7,7,6,7,7,8,8,8,8,9,10,11,12,13,13,
14,15,16,16,17,18,18,19,20,21,21,20,21,21,22,23,23,22,23,23,24,25,25,26,
26,26,26,27,27,27,27,28,29,30,31,32,33,33,32,33,33,34,34,34,34,35,35,35,
35,36,37,37,38,39,39,40,41,41,40,41,41,42,43,43,43,43,44,45,45,44,45,45,
46,47,48,49,49,50,51,51,50,51,51,52,53,53,52,53,53,54,55,55]);
ALF("O8+(3)","O8+(3).(2^2)_{111}",[1,2,3,4,5,6,7,8,9,7,8,9,10,10,10,10,11,
12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,25,26,27,28,29,30,28,29,
30,31,32,33,34,34,34,34,35,35,35,35,36,37,38,39,40,41,42,40,41,42,43,43,
43,43,44,44,44,44,45,46,47,48,49,50,51,52,53,51,52,53,54,55,55,55,55,56,
57,58,56,57,58,59,60,61,62,63,64,65,66,64,65,66,67,68,69,67,68,69,70,71,
72]);
ALF("O8+(3)","B",[1,3,3,3,5,7,6,6,6,6,6,6,7,7,7,7,6,7,12,14,14,14,12,18,
18,18,26,26,26,28,22,22,22,22,22,22,27,27,27,27,27,27,22,22,22,29,29,29,
29,24,24,24,24,28,31,41,41,47,47,47,47,47,47,46,46,46,46,47,47,47,47,49,
49,49,60,60,60,64,64,64,64,64,64,60,68,68,68,68,66,66,66,66,66,66,75,75,
79,79,79,81,81,81,81,81,81,94,94,94,94,94,94,104,104,104],[
"fusion map is unique"
]);
ALN("O8+(3)",["o8p3"]);

MOT("O8+(3).2_1",
[
"origin: ATLAS of finite groups, tests: 1.o.r.,\n",
"constructions: PSO(+1,8,3)"
],
[9904359628800,52254720,52254720,52254720,663552,136048896,37791360,18895680,
18895680,37791360,472392,472392,104976,26244,27648,5760,5760,5760,3072,3600,
3600,3600,93312,93312,93312,20736,15552,7776,7776,15552,10368,5184,5184,10368,
1296,1296,1296,648,648,648,648,324,56,64,64,5832,2916,2916,5832,729,729,81,81,
80,80,80,3456,3456,3456,864,432,432,864,384,108,108,144,72,72,144,26,26,56,56,
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E(13)^2+E(13)^5+E(13)^6+E(13)^7+E(13)^8+E(13)^11,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[141,2]],
[GALOIS,[141,2]],
[TENSOR,[143,2]]],
[(143,144),(141,142)(143,144),(133,134)(135,136),( 71, 72)(131,132),(  7, 10)
( 11, 12)( 27, 30)( 31, 34)( 38, 39)( 40, 41)( 46, 49)( 50, 51)( 52, 53)
( 60, 63)( 65, 66)( 67, 70)( 76, 79)( 80, 83)( 94, 95)( 96, 97)( 98, 99)
(113,114)(118,119)(122,123)(129,130)(137,138)(139,140),(  3,  4)(  8,  9)
( 17, 18)( 21, 22)( 24, 25)( 28, 29)( 32, 33)( 36, 37)( 47, 48)( 55, 56)
( 58, 59)( 61, 62)( 68, 69)( 74, 75)( 77, 78)( 81, 82)( 85, 86)(103,104)
(106,107)(109,110)(125,126)(127,128)(135,136)(141,143)(142,144)]);
ALF("O8+(3).2_1","O8+(3).4",[1,2,3,3,4,5,6,7,7,6,8,8,9,10,11,12,13,13,14,
15,16,16,17,18,18,19,20,21,21,20,22,23,23,22,24,25,25,26,26,27,27,28,29,
30,31,32,33,33,32,34,34,35,35,36,37,37,38,39,39,40,41,41,40,42,43,43,44,
45,45,44,46,47,48,49,49,50,51,51,50,52,53,53,52,54,55,55,56,57,58,59,60,
61,62,63,63,64,64,65,65,66,67,68,69,69,70,71,71,72,73,73,74,75,76,76,77,
78,79,80,80,81,82,83,83,84,85,85,86,86,87,87,88,89,90,90,91,92,93,93,94,
94,95,96,95,96]);
ALF("O8+(3).2_1","O8+(3).(2^2)_{111}",[1,2,3,4,5,6,7,8,9,7,10,10,11,12,13,
14,15,16,17,18,19,20,21,22,23,24,25,26,27,25,28,29,30,28,31,32,33,34,34,
35,35,36,37,38,39,40,41,42,40,43,43,44,44,45,46,47,48,49,50,51,52,53,51,
54,55,55,56,57,58,56,59,60,61,62,63,64,65,66,64,67,68,69,67,70,71,72,73,
74,75,76,77,78,79,80,80,81,81,82,82,83,84,85,86,87,88,89,90,91,92,93,94,
95,96,96,97,98,99,100,100,101,102,103,103,104,105,106,107,108,109,109,110,
111,112,113,114,115,116,116,117,117,118,119,120,121]);
ALF("O8+(3).2_1","O8+(3).(2^2)_{122}",[1,2,3,3,4,5,6,7,7,8,9,10,11,12,13,
14,15,15,16,17,18,18,19,20,20,21,22,23,23,24,25,26,26,27,28,29,29,30,31,
32,33,34,35,36,37,38,39,39,40,41,42,43,44,45,46,46,47,48,48,49,50,50,51,
52,53,54,55,56,56,57,58,59,60,61,61,62,63,63,64,65,66,66,67,68,69,69,70,
71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,86,87,88,88,89,90,90,91,
92,93,94,95,96,97,98,99,100,101,102,103,104,105,105,106,106,107,108,109,
110,111,111,112,113,114,115,116,117,118,119,118,119]);
ALF("O8+(3).2_1","O8+(3).A4",[1,2,2,2,3,4,5,5,5,5,6,6,7,8,9,10,10,10,11,
12,12,12,13,13,13,14,15,15,15,15,16,16,16,16,17,17,17,18,18,19,19,20,21,
22,23,24,24,24,24,25,25,26,26,27,27,27,28,28,28,29,29,29,29,30,31,31,32,
32,32,32,33,34,35,35,35,36,36,36,36,37,37,37,37,38,38,38,39,40,41,42,43,
44,45,46,46,47,47,48,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,62,63,
64,65,66,66,67,68,69,69,70,71,72,73,74,75,75,76,77,78,79,80,81,82,82,83,
83,84,85,86,87]);
ALF("O8+(3).2_1","O8+(3).D8",[1,2,3,3,4,5,6,7,7,6,8,8,9,10,11,12,13,13,14,
15,16,16,17,18,18,19,20,21,21,20,22,23,23,22,24,25,25,26,26,27,27,28,29,
30,31,32,33,33,32,34,34,35,35,36,37,37,38,39,39,40,41,41,40,42,43,43,44,
45,45,44,46,47,48,49,49,50,51,51,50,52,53,53,52,54,55,55,56,57,58,59,60,
61,62,63,63,64,64,65,65,66,67,68,69,69,70,71,71,72,73,73,74,75,76,76,77,
78,79,80,80,81,82,83,83,84,85,85,86,86,87,87,88,89,90,90,91,92,93,93,94,
94,95,96,95,96],[
"fusion map determined up to table automorphisms as the one that maps\n",
"to the extension of O8+(3) by the central involution of D8"
]);
ALF("O8+(3).2_1","O8+(3).S4",[1,2,2,2,3,4,5,5,5,5,6,6,7,8,9,10,10,10,11,
12,12,12,13,13,13,14,15,15,15,15,16,16,16,16,17,17,17,18,18,19,19,20,21,
22,23,24,24,24,24,25,25,26,26,27,27,27,28,28,28,29,29,29,29,30,31,31,32,
32,32,32,33,34,35,35,35,36,36,36,36,37,37,37,37,38,38,38,39,40,41,42,43,
44,45,46,46,47,47,48,48,49,50,51,52,52,53,54,54,55,56,56,57,58,59,59,60,
61,62,63,63,64,65,66,66,67,68,68,69,69,70,70,71,72,73,73,74,75,76,76,77,
77,78,79,78,79]);

MOT("O8+(3).2_1'",
[
"differs from O8+(3).2_1 only by fusion into O8+(3).(2^2)_{111}"
],
0,
0,
0,
0,
["ConstructPermuted",["O8+(3).2_1"]]);
ALF("O8+(3).2_1'","O8+(3).(2^2)_{111}",[1,3,4,2,5,6,8,9,7,8,10,10,11,12,
13,15,16,14,17,19,20,18,22,23,21,24,26,27,25,26,29,30,28,29,32,33,31,34,
34,35,35,36,37,38,39,41,42,40,41,43,43,44,44,46,47,45,49,50,48,52,53,51,
52,54,55,55,57,58,56,57,59,60,62,63,61,65,66,64,65,68,69,67,68,71,72,70,
122,123,124,125,126,127,128,129,129,130,130,131,131,132,133,134,136,135,
137,139,138,140,142,141,143,144,145,145,146,147,148,149,149,150,151,152,
152,153,155,154,157,156,158,158,159,160,162,161,163,164,165,165,166,166,
170,169,167,168],[
"fusion map is unique up to table automorphisms,\n",
"equal to the map from O8+(3).2_1, mapped under an outer autom."
]);

MOT("O8+(3).2_1''",
[
"differs from O8+(3).2_1 only by fusion into O8+(3).(2^2)_{111}"
],
0,
0,
0,
0,
["ConstructPermuted",["O8+(3).2_1"]]);
ALF("O8+(3).2_1''","O8+(3).(2^2)_{111}",[1,4,2,3,5,6,9,7,8,9,10,10,11,12,
13,16,14,15,17,20,18,19,23,21,22,24,27,25,26,27,30,28,29,30,33,31,32,34,
34,35,35,36,37,38,39,42,40,41,42,43,43,44,44,47,45,46,50,48,49,53,51,52,
53,54,55,55,58,56,57,58,59,60,63,61,62,66,64,65,66,69,67,68,69,72,70,71,
171,172,173,174,175,176,177,178,178,179,179,180,180,181,182,183,184,185,
186,187,188,189,190,191,192,193,194,194,195,196,197,198,198,199,200,201,
201,202,203,204,205,206,207,207,208,209,211,210,213,212,214,214,215,215,
217,216,219,218],[
"fusion map is unique up to table automorphisms,\n",
"equal to the map from O8+(3).2_1', mapped under an outer autom."
]);

MOT("O8+(3).2_2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,13]"
],
[9904359628800,52254720,26127360,663552,136048896,37791360,18895680,37791360,
18895680,944784,944784,472392,104976,26244,27648,5760,2880,3072,3600,1800,
93312,46656,20736,15552,7776,15552,7776,10368,5184,10368,5184,1296,648,1296,
1296,648,1296,1296,648,324,56,64,64,5832,2916,5832,2916,1458,1458,729,162,162,
81,80,40,3456,1728,864,432,864,432,384,216,216,108,144,72,144,72,26,26,56,28,
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[TENSOR,[132,2]],
[GALOIS,[132,2]],
[TENSOR,[134,2]]],
[( 70, 71)(130,131),(  7,  9)( 10, 11)( 25, 27)( 29, 31)( 34, 35)( 37, 38)
( 45, 47)( 48, 49)( 51, 52)( 59, 61)( 63, 64)( 67, 69)( 75, 77)( 79, 81)
( 94, 95)( 99,100)(118,119)(124,125)(126,127)]);
ALF("O8+(3).2_2","O8+(3).(2^2)_{122}",[1,2,3,4,5,6,7,8,7,9,9,10,11,12,13,
14,15,16,17,18,19,20,21,22,23,24,23,25,26,27,26,28,29,30,30,31,32,32,33,
34,35,36,37,38,39,40,39,41,41,42,43,43,44,45,46,47,48,49,50,51,50,52,53,
53,54,55,56,57,56,58,59,60,61,62,63,64,63,65,66,67,66,68,69,120,121,122,
123,124,125,126,127,128,129,130,130,131,132,133,134,134,135,136,137,138,
139,140,141,142,143,144,145,146,147,148,149,150,151,152,152,153,154,155,
156,157,157,158,158,159,160,161,162,163,164,165,166]);
ALF("O8+(3).2_2","O8+(3).3.2",[1,2,2,3,4,5,5,6,6,7,8,8,9,10,11,12,12,13,
14,14,15,15,16,17,17,18,18,19,19,20,20,21,21,22,23,23,24,25,25,26,27,28,
29,30,30,31,31,32,33,33,34,35,35,36,36,37,37,38,38,39,39,40,41,42,42,43,
43,44,44,45,46,47,47,48,48,49,49,50,50,51,51,52,52,74,75,76,77,78,79,80,
81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,
104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,
122,123,124,125]);
ALF("O8+(3).2_2","O8+(3).D8",[1,2,3,4,5,6,7,6,7,8,8,8,9,10,11,12,13,14,15,
16,17,18,19,20,21,20,21,22,23,22,23,24,25,26,26,26,27,27,27,28,29,30,31,
32,33,32,33,34,34,34,35,35,35,36,37,38,39,40,41,40,41,42,43,43,43,44,45,
44,45,46,47,48,49,50,51,50,51,52,53,52,53,54,55,146,147,148,149,150,151,
152,153,154,155,156,156,157,158,159,160,160,161,162,163,164,165,166,167,
168,169,170,171,172,173,174,175,176,177,178,178,179,180,181,182,183,183,
184,184,185,186,187,188,189,190,191,192],[
"fusion map is unique up to table automorphisms"
]);
ALF("O8+(3).2_2","O8+(3).S4",[1,2,2,3,4,5,5,5,5,6,6,6,7,8,9,10,10,11,12,
12,13,13,14,15,15,15,15,16,16,16,16,17,17,18,18,18,19,19,19,20,21,22,23,
24,24,24,24,25,25,25,26,26,26,27,27,28,28,29,29,29,29,30,31,31,31,32,32,
32,32,33,34,35,35,36,36,36,36,37,37,37,37,38,38,101,102,103,104,105,106,
107,108,109,110,111,111,112,113,114,115,115,116,117,118,119,120,121,122,
123,124,125,126,127,128,129,130,131,132,133,133,134,135,136,137,138,138,
139,139,140,141,142,143,144,145,146,147]);

MOT("O8+(3).2_2'",
[
"differs from O8+(3).2_2 only by fusion into O8+(3).2^2"
],
0,
0,
0,
0,
["ConstructPermuted",["O8+(3).2_2"]]);
ALF("O8+(3).2_2'","O8+(3).(2^2)_{122}",[1,2,3,4,5,8,7,6,7,10,10,9,11,12,
13,14,15,16,17,18,19,20,21,24,23,22,23,27,26,25,26,28,29,31,31,30,33,33,
32,34,35,36,37,40,39,38,39,42,42,41,44,44,43,45,46,47,48,51,50,49,50,52,
54,54,53,57,56,55,56,58,59,60,61,64,63,62,63,67,66,65,66,68,69,167,168,
169,170,171,172,173,174,175,176,177,177,178,179,180,181,181,182,183,184,
185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,199,200,201,
202,203,204,204,205,205,206,207,208,209,210,211,212,213]);

MOT("O8+(3).3",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,13]"
],
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108,72,72,39,39,28,45,45,108,108,20,12737088,12737088,17496,17496,1728,1728,
216,216,1944,1944,1458,1458,729,729,486,486,288,288,288,288,36,36,216,216,54,
54,54,54,21,21,24,24,24,24,27,27,36,36,39,39,39,39],
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56,55,62,61,64,63,66,65,68,67,58,57,58,57,60,59,62,61,64,63,68,67,82,81,70,69,
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38,39,40,41,42,43,44,1,1,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,
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,
90,53,54,53,54]],
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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]);
ALF("O8+(3).3","O8+(3).S4",[1,2,3,4,5,5,6,6,7,8,9,10,11,12,13,14,15,15,16,
16,17,18,18,19,19,20,21,22,23,24,24,25,25,26,26,27,28,29,29,30,31,31,32,
32,33,34,35,36,36,37,37,38,80,80,81,81,82,82,83,83,84,84,85,85,86,86,87,
87,88,88,89,89,90,90,91,91,92,92,93,93,94,94,95,95,96,96,97,97,98,98,99,
99,100,100]);

MOT("O8+(3).3.2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,13]"
],
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[( 45, 46)( 72, 73)(120,121)]);
ALF("O8+(3).3.2","Fi23",[1,3,4,6,7,5,6,8,7,8,10,11,10,13,17,19,24,16,25,
22,24,21,28,20,26,27,29,30,31,34,35,33,36,34,37,39,43,49,44,43,46,54,55,
50,57,58,60,62,61,70,71,75,5,8,22,28,33,36,36,35,48,44,54,69,72,68,76,84,
82,87,93,95,96,2,4,9,9,11,12,15,14,18,20,15,23,21,18,26,19,27,23,22,25,28,
31,30,38,40,45,42,45,51,50,47,53,51,55,52,56,59,66,67,68,67,73,69,72,74,
82,85,86,88,90,91,94],[
"fusion map is unique up to table automorphisms"
]);
ALN("O8+(3).3.2",["O8+(3).S3","o8+(3):s3"]);

MOT("O8+(3).4",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,13],\n",
"2nd power map determined only up to matrix automorphism (141,143)(142,144)"
],
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[TENSOR,[121,2]],[465920,-1792,0,0,-640,656,-640,8,8,8,0,0,0,0,10,0,-64,0,0,8,
0,0,0,8,0,0,0,0,0,0,0,-10,8,-1,-1,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,0,0,0,
832,-320,0,0,0,0,-32,4,4,4,4,4,0,0,0,0,-10,0,2,0,0,0,0,0,0,0,0,-2,0,0,0,0,0,0,
0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,-E(40)^7+E(40)^13-E(40)^21-E(40)^23-E(40)^29+E(40)^31+E(40)^37
 +E(40)^39,-E(40)^7+E(40)^13-E(40)^21-E(40)^23-E(40)^29+E(40)^31+E(40)^37
 +E(40)^39,E(40)^7-E(40)^13+E(40)^21+E(40)^23+E(40)^29-E(40)^31-E(40)^37
 -E(40)^39,E(40)^7-E(40)^13+E(40)^21+E(40)^23+E(40)^29-E(40)^31-E(40)^37
 -E(40)^39,0,0,0,0,0,0,0,0],
[TENSOR,[123,2]],
[TENSOR,[123,3]],
[TENSOR,[123,4]],[931840,0,-1792,0,-1280,-1280,16,16,16,16,0,0,0,0,0,10,0,-64,
0,0,8,0,0,0,8,0,0,0,0,0,0,16,-2,-2,-2,0,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,-E(40)^7+E(40)^13-E(40)^21-E(40)^23-E(40)^29+E(40)^31+E(40)^37+E(40)^39,
E(40)^7-E(40)^13+E(40)^21+E(40)^23+E(40)^29-E(40)^31-E(40)^37-E(40)^39,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0],
[TENSOR,[127,2]],[491400,-840,-840,200,-675,540,540,54,-27,-27,0,0,0,16,0,0,
-3,-3,-19,-12,-12,-4,-4,-3,-3,2,-1,-1,0,0,0,0,0,0,0,0,0,9,9,0,0,1,0,0,0,0,0,0,
0,0,0,0,0,0,0,780,-100,420,28,4,4,-3,-10,6,-1,-3,-1,-12,-4,4,0,0,0,0,-39,6,1,
-3,1,-2,1,1,0,0,3,-1,0,0,0,0,0,0,0,0,0,0,26,26,10,10,14,14,-10,-10,-2,-2,-2,
-2,-2,-2,-2,-2,-1,-1,-1,-1,1,1,0,0,5,5,1,1,-1,-1,-1,-1,1,1,1,1,0,0,0,0,0,0,0,
0,0,0,0,0],
[TENSOR,[129,2]],
[TENSOR,[129,3]],
[TENSOR,[129,4]],[531441,729,729,81,0,0,0,0,0,0,-27,9,9,-3,-9,-9,0,0,0,0,0,0,
0,0,0,0,0,0,1,-1,-1,0,0,0,0,-1,-1,0,0,0,0,0,0,0,0,1,1,1,1,0,0,0,0,-1,-1,729,
81,729,-27,9,-3,0,0,0,0,0,0,-9,3,-1,-1,-9,1,-1,0,0,0,0,0,0,0,0,0,-1,0,0,0,1,1,
1,1,1,0,0,-1,-1,27,27,-9,-9,27,27,9,9,3,3,-3,-3,-3,-3,1,1,0,0,0,0,0,0,1,1,0,0,
0,0,0,0,0,0,0,0,0,0,-1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1],
[TENSOR,[133,2]],
[TENSOR,[133,3]],
[TENSOR,[133,4]],[716800,0,0,0,1408,-320,-320,-104,-32,-14,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,4,4,4,1,0,0,0,0,0,0,0,0,0,0,E(13)+E(13)^3+E(13)^4
 +E(13)^9+E(13)^10+E(13)^12,E(13)^2+E(13)^5+E(13)^6+E(13)^7+E(13)^8+E(13)^11,
0,0,0,0,0,0,0,0,1280,0,0,0,0,0,-16,0,-16,0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
2,0,0,0,0,E(13)+E(13)^3+E(13)^4+E(13)^9+E(13)^10+E(13)^12,
E(13)^2+E(13)^5+E(13)^6+E(13)^7+E(13)^8+E(13)^11,0,0,0,0,0,0,0,32,32,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,-4,-4,2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
E(13)+E(13)^3+E(13)^4+E(13)^9+E(13)^10+E(13)^12,E(13)+E(13)^3+E(13)^4+E(13)^9
 +E(13)^10+E(13)^12,E(13)^2+E(13)^5+E(13)^6+E(13)^7+E(13)^8+E(13)^11,
E(13)^2+E(13)^5+E(13)^6+E(13)^7+E(13)^8+E(13)^11,0,0,0,0],
[TENSOR,[137,2]],
[TENSOR,[137,3]],
[TENSOR,[137,4]],
[GALOIS,[137,2]],
[TENSOR,[141,2]],
[TENSOR,[141,3]],
[TENSOR,[141,4]]],
[(133,135)(134,136),( 95, 96)(133,135)(134,136),( 91, 92)(141,143)(142,144),
( 91, 92)( 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),( 46, 47)( 88, 89)(137,139)(138,140),( 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)(141,144)(142,143)]);
ALF("O8+(3).4","O8+(3).D8",[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,
91,92,93,94,95,96,193,193,194,194,195,195,196,196,197,197,198,198,199,199,
200,200,201,201,202,202,203,203,204,204,205,205,206,206,207,207,208,208,
209,209,210,210,211,211,212,212,213,213,214,214,215,216,216,215]);
ALF("O8+(3).4","O8+(3).S4",[1,2,2,3,4,5,5,6,7,8,9,10,10,11,12,12,13,13,14,
15,15,16,16,17,17,18,19,20,21,22,23,24,24,25,26,27,27,28,28,29,29,30,31,
32,32,33,34,35,35,36,36,37,37,38,38,39,40,41,42,43,44,45,46,47,48,49,50,
51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,
75,76,77,79,78,148,148,149,149,150,150,151,151,152,152,153,153,154,154,
155,155,156,156,157,157,158,158,159,159,160,160,161,161,162,162,163,163,
164,164,165,165,166,166,167,167,168,168,169,169,170,171,171,170]);

MOT("O8+(3).(2^2)_{111}",
[
"table of the normal subgroup O8+(3).V4 in O8+(3).S4,\n",
"constructed by T. Breuer using the tables of O8+(3), O8+(3).2_1"
],
[19808719257600,104509440,104509440,104509440,1327104,272097792,37791360,
37791360,37791360,472392,209952,52488,55296,11520,11520,11520,6144,7200,7200,
7200,186624,186624,186624,41472,15552,15552,15552,10368,10368,10368,2592,2592,
2592,648,648,648,112,128,128,5832,5832,5832,729,81,160,160,160,6912,6912,6912,
864,864,864,768,108,144,144,144,52,52,112,112,112,90,90,90,216,216,216,80,80,
80,48522240,2073600,52254720,96768,18432,1536,46656,12960,7776,648,648,648,
4608,1536,1536,512,160,160,7200,200,200,160,93312,7776,1728,1296,1152,288,192,
144,108,80,576,576,192,192,72,52,52,112,112,112,112,90,108,80,80,80,80,
48522240,2073600,52254720,96768,18432,1536,46656,12960,7776,648,648,648,4608,
1536,1536,512,160,160,7200,200,200,160,93312,7776,1728,1296,1152,288,192,144,
108,80,576,576,192,192,72,52,52,112,112,112,112,90,108,80,80,80,80,48522240,
2073600,52254720,96768,18432,1536,46656,12960,7776,648,648,648,4608,1536,1536,
512,160,160,7200,200,200,160,93312,7776,1728,1296,1152,288,192,144,108,80,576,
576,192,192,72,52,52,112,112,112,112,90,108,80,80,80,80],
[,[1,1,1,1,1,6,7,8,9,10,11,12,5,2,3,4,5,18,19,20,6,6,6,6,7,8,9,7,8,9,11,11,11,
10,11,12,37,13,17,40,41,42,43,44,18,19,20,24,24,24,28,29,30,24,34,25,26,27,60,
59,37,37,37,64,65,66,40,41,42,45,46,47,1,1,2,2,2,5,6,7,7,11,12,12,13,13,13,13,
15,16,18,19,20,18,21,25,21,31,21,25,24,31,40,45,49,50,49,50,51,60,59,61,61,61,
61,64,67,71,71,72,72,1,1,3,3,3,5,6,8,8,11,12,12,13,13,13,13,14,16,19,18,20,19,
22,26,22,32,22,26,24,32,41,46,48,50,48,50,52,60,59,62,62,62,62,65,68,70,70,72,
72,1,1,4,4,4,5,6,9,9,11,12,12,13,13,13,13,14,15,20,18,19,20,23,27,23,33,23,27,
24,33,42,47,48,49,48,49,53,60,59,63,63,63,63,66,69,70,70,71,71],[1,2,3,4,5,1,
1,1,1,1,1,1,13,14,15,16,17,18,19,20,2,3,4,5,2,3,4,5,5,5,2,3,4,5,5,5,37,38,39,
6,6,6,6,10,45,46,47,13,13,13,13,13,13,17,13,14,15,16,59,60,61,62,63,18,19,20,
21,22,23,70,71,72,73,74,75,76,77,78,73,74,73,74,73,74,85,86,87,88,89,90,91,92,
93,94,75,75,76,75,77,77,78,76,79,104,85,85,86,87,85,110,111,112,113,114,115,
91,95,118,119,120,121,122,123,124,125,126,127,122,123,122,123,122,123,134,135,
136,137,138,139,140,141,142,143,124,124,125,124,126,126,127,125,128,153,134,
134,135,136,134,159,160,161,162,163,164,140,144,167,168,169,170,171,172,173,
174,175,176,171,172,171,172,171,172,183,184,185,186,187,188,189,190,191,192,
173,173,174,173,175,175,176,174,177,202,183,183,184,185,183,208,209,210,211,
212,213,189,193,216,217,218,219],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,
1,1,1,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,
2,3,4,48,49,50,51,52,53,54,55,56,57,58,60,59,61,62,63,7,8,9,67,68,69,14,15,16,
73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,74,74,74,73,95,96,97,98,
99,100,101,102,103,75,105,106,107,108,109,111,110,113,112,115,114,80,117,89,
89,90,90,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,
139,123,123,123,122,144,145,146,147,148,149,150,151,152,124,154,155,156,157,
158,160,159,162,161,164,163,129,166,138,138,139,139,171,172,173,174,175,176,
177,178,179,180,181,182,183,184,185,186,187,188,172,172,172,171,193,194,195,
196,197,198,199,200,201,173,203,204,205,206,207,209,208,211,210,213,212,178,
215,187,187,188,188],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,
22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,1,38,39,40,41,42,43,44,45,46,47,
48,49,50,51,52,53,54,55,56,57,58,60,59,2,3,4,64,65,66,67,68,69,70,71,72,73,74,
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,
100,101,102,103,104,105,106,107,108,109,111,110,75,75,76,76,116,117,119,118,
121,120,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,
139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,
158,160,159,124,124,125,125,165,166,168,167,170,169,171,172,173,174,175,176,
177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,
196,197,198,199,200,201,202,203,204,205,206,207,209,208,173,173,174,174,214,
215,217,216,219,218],,,,,,[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,
47,48,49,50,51,52,53,54,55,56,57,58,1,1,61,62,63,64,65,66,67,68,69,70,71,72,
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,
99,100,101,102,103,104,105,106,107,108,109,73,73,113,112,115,114,116,117,118,
119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,
138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,
157,158,122,122,162,161,164,163,165,166,167,168,169,170,171,172,173,174,175,
176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,
195,196,197,198,199,200,201,202,203,204,205,206,207,171,171,211,210,213,212,
214,215,216,217,218,219]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
-1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],
[TENSOR,[2,3]],[520,72,40,40,8,34,61,-20,-20,7,16,-2,8,8,0,0,8,10,0,0,18,-14,
-14,2,9,4,4,5,-4,-4,0,4,4,-1,2,2,2,0,0,7,-2,-2,-2,1,2,0,0,2,2,2,5,-4,-4,2,-1,
-1,0,0,0,0,2,-2,-2,1,0,0,3,-2,-2,-2,0,0,52,20,68,-12,4,4,-2,11,7,2,-2,2,4,4,4,
4,0,0,10,0,0,2,14,5,6,-4,-2,1,-2,0,1,-2,-2,-2,-2,-2,1,0,0,-2,-2,2,2,1,-1,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
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 -E(40)^23-E(40)^29+E(40)^31+E(40)^37+E(40)^39,E(40)^7-E(40)^13+E(40)^21
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E(40)^7-E(40)^13+E(40)^21+E(40)^23+E(40)^29-E(40)^31-E(40)^37-E(40)^39,
-E(40)^7+E(40)^13-E(40)^21-E(40)^23-E(40)^29+E(40)^31+E(40)^37+E(40)^39,832,
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[TENSOR,[200,2]],
[TENSOR,[200,4]],
[TENSOR,[200,3]],[491400,-840,-840,-840,200,-675,540,540,540,54,-27,-27,0,0,0,
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420,28,4,4,-3,-10,6,-1,-3,-1,-12,-4,-4,4,0,0,0,0,0,0,-39,6,1,-3,1,-2,1,1,0,0,
3,3,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[204,2]],
[TENSOR,[204,4]],
[TENSOR,[204,3]],[531441,729,729,729,81,0,0,0,0,0,0,0,-27,9,9,9,-3,-9,-9,-9,0,
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[TENSOR,[208,2]],
[TENSOR,[208,4]],
[TENSOR,[208,3]],[716800,0,0,0,0,1408,-320,-320,-320,-104,-32,-14,0,0,0,0,0,0,
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0,E(13)+E(13)^3+E(13)^4+E(13)^9+E(13)^10+E(13)^12,E(13)^2+E(13)^5+E(13)^6
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2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,E(13)+E(13)^3+E(13)^4
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0,0,0,0,0,0,0,0,0,0,1280,0,0,0,0,0,-16,0,-16,0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,2,0,0,0,0,0,0,E(13)+E(13)^3+E(13)^4+E(13)^9+E(13)^10+E(13)^12,
E(13)^2+E(13)^5+E(13)^6+E(13)^7+E(13)^8+E(13)^11,0,0,0,0,0,0,0,0,0,0,1280,0,0,
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E(13)+E(13)^3+E(13)^4+E(13)^9+E(13)^10+E(13)^12,E(13)^2+E(13)^5+E(13)^6
 +E(13)^7+E(13)^8+E(13)^11,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[212,2]],
[TENSOR,[212,4]],
[TENSOR,[212,3]],
[GALOIS,[212,2]],
[TENSOR,[216,2]],
[TENSOR,[216,3]],
[TENSOR,[216,4]]],
[(167,168)(216,217),(120,121)(169,170),(118,119)(120,121)(167,168)(169,170)
(216,217)(218,219),(112,113)(114,115)(161,162)(163,164)(210,211)(212,213),
( 59, 60)(110,111)(159,160)(208,209),(  3,  4)(  8,  9)( 15, 16)( 19, 20)
( 22, 23)( 26, 27)( 29, 30)( 32, 33)( 41, 42)( 46, 47)( 49, 50)( 52, 53)
( 57, 58)( 62, 63)( 65, 66)( 68, 69)( 71, 72)( 86, 87)( 89, 90)( 92, 93)
(105,106)(107,108)(114,115)(118,120)(119,121)(122,171)(123,172)(124,173)
(125,174)(126,175)(127,176)(128,177)(129,178)(130,179)(131,180)(132,181)
(133,182)(134,183)(135,184)(136,185)(137,186)(138,187)(139,188)(140,189)
(141,190)(142,191)(143,192)(144,193)(145,194)(146,195)(147,196)(148,197)
(149,198)(150,199)(151,200)(152,201)(153,202)(154,203)(155,204)(156,205)
(157,206)(158,207)(159,208)(160,209)(161,210)(162,211)(163,212)(164,213)
(165,214)(166,215)(167,216)(168,217)(169,218)(170,219),(  2,  3)(  7,  8)
( 14, 15)( 18, 19)( 21, 22)( 25, 26)( 28, 29)( 31, 32)( 40, 41)( 45, 46)
( 48, 49)( 51, 52)( 56, 57)( 61, 62)( 64, 65)( 67, 68)( 70, 71)( 73,122)
( 74,123)( 75,124)( 76,125)( 77,126)( 78,127)( 79,128)( 80,129)( 81,130)
( 82,131)( 83,132)( 84,133)( 85,134)( 86,135)( 87,136)( 88,137)( 89,138)
( 90,139)( 91,140)( 92,141)( 93,142)( 94,143)( 95,144)( 96,145)( 97,146)
( 98,147)( 99,148)(100,149)(101,150)(102,151)(103,152)(104,153)(105,154)
(106,155)(107,156)(108,157)(109,158)(110,159)(111,160)(112,161)(113,162)
(114,163)(115,164)(116,165)(117,166)(118,167)(119,168)(120,169)(121,170)
(184,185)(187,188)(190,191)(203,204)(205,206)(212,213)(216,218)(217,219)]);
ALF("O8+(3).(2^2)_{111}","O8+(3).A4",[1,2,2,2,3,4,5,5,5,6,7,8,9,10,10,10,
11,12,12,12,13,13,13,14,15,15,15,16,16,16,17,17,17,18,19,20,21,22,23,24,
24,24,25,26,27,27,27,28,28,28,29,29,29,30,31,32,32,32,33,34,35,35,35,36,
36,36,37,37,37,38,38,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,
55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,
79,80,81,82,83,84,85,87,86,39,40,41,42,43,44,45,46,47,48,49,50,51,53,52,
54,56,55,57,59,58,60,61,62,63,64,65,66,67,68,69,70,72,71,74,73,75,76,77,
78,79,81,80,82,83,86,87,85,84,39,40,41,42,43,44,45,46,47,48,49,50,51,52,
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]);
ALF("O8+(3).(2^2)_{111}","O8+(3).D8",[1,2,3,3,4,5,6,7,7,8,9,10,11,12,13,
13,14,15,16,16,17,18,18,19,20,21,21,22,23,23,24,25,25,26,27,28,29,30,31,
32,33,33,34,35,36,37,37,38,39,39,40,41,41,42,43,44,45,45,46,47,48,49,49,
50,51,51,52,53,53,54,55,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,69,
70,71,71,72,73,73,74,75,76,77,78,79,80,81,82,83,84,85,85,86,86,87,88,89,
90,90,91,92,93,94,95,96,95,96,97,98,99,100,101,102,103,104,105,106,107,
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,
144,145,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,
114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,
132,133,134,135,137,136,139,138,140,141,143,142,144,145]);


MOT("O8+(3).(2^2)_{122}",
[
"constructed using `PossibleCharacterTablesOfTypeGV4',\n",
"constructions: PGO(+1,8,3)"
],
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75582720,944784,944784,209952,52488,55296,11520,5760,6144,7200,3600,186624,
93312,41472,31104,7776,31104,20736,5184,20736,2592,1296,1296,1296,1296,1296,
648,112,128,128,11664,2916,11664,1458,1458,162,162,160,80,6912,3456,1728,432,
1728,768,216,216,288,72,288,52,52,112,56,180,45,180,432,108,432,80,40,48522240
,2073600,52254720,96768,18432,1536,46656,25920,25920,15552,15552,1296,1296,648
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,144,216,216,80,288,96,144,144,52,52,56,112,112,180,180,216,216,40,40,
18341406720,2488320,414720,96768,9216,4608,2519424,699840,559872,311040,34992,
31104,11664,10368,3888,5832,5184,1296,648,384,128,480,480,5184,1728,1728,864,
576,576,576,144,144,72,56,1296,648,432,54,54,80,48,52,52,56,60,60,72,
18341406720,2488320,414720,96768,9216,4608,2519424,699840,559872,311040,34992,
31104,11664,10368,3888,5832,5184,1296,648,384,128,480,480,5184,1728,1728,864,
576,576,576,144,144,72,56,1296,648,432,54,54,80,48,52,52,56,60,60,72],
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145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,120,120,163,
164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,
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ALF("O8+(3).(2^2)_{122}","O8+(3).D8",[1,2,3,4,5,6,7,6,8,8,9,10,11,12,13,
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MOT("O8+(3).D8",
[
"constructed (by accident) in April 2003 using Dixon's algorithm and\n",
"character theoretic methods"
],
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ALF("O8+(3).D8","O8+(3).S4",[1,2,2,3,4,5,5,6,7,8,9,10,10,11,12,12,13,13,
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168,169,170,171]);

MOT("O8+(3).A4",
[
"origin: constructed by T. Breuer using the tables of O8+(3), O8+(3).3,\n",
"O8+(3).(2^2)_{111},\n",
"tests: 1.o.r., pow[2,3,5,7,13,]"
],
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E(40)^7-E(40)^13+E(40)^21+E(40)^23+E(40)^29-E(40)^31-E(40)^37-E(40)^39,
E(40)^7-E(40)^13+E(40)^21+E(40)^23+E(40)^29-E(40)^31-E(40)^37-E(40)^39,
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0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[1594323,2187,243,0,0,0,0,0,-81,27,-9,-27,0,0,
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-3*E(3)^2,-3*E(3),0,0,0,0,0,0,0,0,E(3)^2,E(3),-E(3)^2,-E(3),-E(3)^2,-E(3),0,0,
0,0,E(3)^2,E(3),E(3)^2,E(3)],
[TENSOR,[119,3]],
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E(13)+E(13)^3+E(13)^4+E(13)^9+E(13)^10+E(13)^12,E(13)^2+E(13)^5+E(13)^6
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16*E(3)^2,0,0,0,0,-8*E(3),-8*E(3)^2,4*E(3),4*E(3)^2,-5*E(3),-5*E(3)^2,-2*E(3),
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E(39)+E(39)^4+E(39)^10+E(39)^16+E(39)^22+E(39)^25,E(39)^14+E(39)^17+E(39)^23
 +E(39)^29+E(39)^35+E(39)^38,E(39)^7+E(39)^19+E(39)^28+E(39)^31+E(39)^34
 +E(39)^37,E(39)^2+E(39)^5+E(39)^8+E(39)^11+E(39)^20+E(39)^32],
[TENSOR,[122,3]],
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0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[122,2]],
[TENSOR,[126,3]],
[TENSOR,[126,2]],
[GALOIS,[125,2]]],
[( 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),(84,85)(86,87),(80,81),(78,79)
(80,81),(52,53)(55,56)(58,59)(71,72)(73,74)(84,86)(85,87),( 33, 34)( 76, 77)
(126,128)(127,129)]);
ALF("O8+(3).A4","O8+(3).S4",[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,
43,44,45,46,47,48,49,50,51,52,52,53,54,54,55,56,56,57,58,59,60,61,62,63,
64,65,66,67,68,68,69,69,70,71,72,73,73,74,75,76,77,78,79,79,78,80,80,81,
81,82,82,83,83,84,84,85,85,86,86,87,87,88,88,89,89,90,90,91,91,92,92,93,
93,94,94,95,95,96,96,97,97,98,98,99,99,100,100]);

MOT("O8+(3).S4",
[
"origin: constructed by T. Breuer using the tables of O8+(3), O8+(3).A4,\n",
"O8+(3).2_2, O8+(3).4, B\n",
"tests: 1.o.r., pow[2,3,5,7,13,],\n",
"constructions: Aut(O8+(3))"
],
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331776,23040,36864,14400,373248,248832,31104,20736,5184,3888,3888,3888,672,768
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97044480,4147200,104509440,193536,36864,3072,93312,25920,15552,1296,1296,1296,
9216,1536,1024,160,14400,200,320,186624,15552,3456,2592,2304,576,384,288,216,
160,576,192,144,104,104,112,224,224,180,216,80,80,12737088,17496,1728,216,1944
,1458,729,486,288,288,36,216,54,54,21,24,24,27,36,39,39,18341406720,2488320,
414720,96768,9216,4608,2519424,699840,559872,311040,34992,31104,11664,10368,
3888,5832,5184,1296,648,384,128,480,480,5184,1728,1728,864,576,576,576,144,144
,72,56,1296,648,432,54,54,80,48,52,52,56,60,60,72,44928,5760,48384,5760,768,
384,384,128,432,72,72,40,864,96,72,72,48,48,80,80,52,52,56,56],
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,34,33,21,36,24,27,1,1,2,2,2,3,4,5,5,7,8,8,9,9,9,10,12,12,12,13,15,13,17,13,15
,14,17,24,27,28,28,29,34,33,35,35,35,36,37,38,38,80,81,80,81,84,85,86,87,82,82
,83,84,85,87,94,88,89,97,91,100,99,1,1,2,2,2,3,4,5,5,5,6,4,7,5,6,8,5,7,8,9,11,
12,12,13,15,13,15,15,14,16,17,17,18,21,24,24,24,26,25,27,29,34,33,35,36,36,37,
39,39,42,41,42,43,44,44,45,49,49,57,60,60,65,61,62,64,67,67,72,71,74,75],[1,2,
3,1,1,1,1,1,9,10,11,12,2,3,2,3,2,3,3,3,21,22,23,4,4,6,27,9,9,11,9,10,33,34,35,
12,13,38,39,40,41,42,43,44,39,40,39,40,39,40,51,52,53,54,55,56,57,41,41,42,41,
43,43,44,42,45,67,51,52,51,71,72,73,74,75,55,58,78,79,1,1,3,3,6,6,6,6,9,11,11,
18,18,18,21,22,23,25,31,33,34,101,102,103,104,105,106,101,101,101,102,101,102,
101,102,102,101,102,102,102,120,121,122,123,103,103,104,103,105,106,106,104,
105,106,134,107,107,112,111,112,140,120,142,143,144,122,123,124,148,149,150,
151,152,153,154,155,148,148,149,159,150,152,150,151,153,154,166,167,168,169,
170,171],,[1,2,3,4,5,6,7,8,9,10,11,1,13,14,15,16,17,18,19,20,21,22,23,24,25,26
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53,54,40,40,39,58,59,60,61,62,63,64,65,66,41,68,69,70,72,71,73,75,74,46,77,54,
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102,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,103,141,
143,142,144,108,110,147,148,149,150,151,152,153,154,155,156,157,158,149,160,
161,162,163,164,165,151,151,169,168,171,170],,[1,2,3,4,5,6,7,8,9,10,11,12,13,
14,15,16,17,18,19,20,1,22,23,24,25,26,27,28,29,30,31,32,34,33,2,36,37,38,39,40
,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
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133,101,135,136,137,138,139,140,141,143,142,104,145,146,147,148,149,150,151,
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26,27,28,29,30,31,32,1,1,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52
,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,39,39,73,75,74,76,77,78
,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,80,80,101,102,103
,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,
101,101,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,
161,162,163,164,165,166,167,148,148,171,170]],
0,
[(78,79)(166,167),(74,75)(170,171),(33,34)(71,72)(99,100)(142,143)(168,169)],
["ConstructGS3","O8+(3).D8","O8+(3).A4",[3,4,6,7,8,9,12,13,17,18,19,20,21,30,
31,33,34,35,36,41,42,46,47,51,52,56,57,58,59,62,63,67,68,72,73,74,75,78,79,80,
81,84,85,86,87,88,93,94,95,96,101,102,103,104,105,110,111,112,113,114,119,120,
121,122,123,130,131,132,133,138,139,141,142,143,144,147,148,152,153,154,155,
160,161,165,166,170,171,172,173,174,179,180,181,182,183,188,189,190,191,192,
199,200,202,203,209,210,214,215],[[2,3],[8,10],[16,17],[19,20],[24,25],[28,
30],[33,34],[36,37],[42,44],[47,48],[59,61],[75,76],[79,80],[86,88],[91,92],
[96,97],[99,100],[114,116],[119,121],[122,123],[126,128]],[[1,1],[9,14],[15,
26],[18,28],[26,39],[29,44],[32,49],[38,54],[43,64],[46,69],[60,99],[74,128],
[81,136],[87,149],[93,158],[95,163],[101,167],[115,197],[120,204],[124,207],
[127,212]],(1,4,7,10,16,28,52,85,133,14,26,50,80,122,117,56,89,140,38,68,104,
158,125,134,20,35,65,98,149,62,95,146,57,90,141,39,69,105,165,154,107,170,168,
163,136,23,41,71,110,12,18,30,54,87,138,33,60,93,144,48,78,120,101,155,108,
171,169,164,153,100,151,83,128,162,135,21,36,66,102,156,118,63,96,147,58,91,
142,42,72,111,22,40,70,109,3,6,9,15,27,51,84,132,13,19,31,55,88,139,34,64,97,
148,61,94,145,49,79,121,106,166,160,129,167,161,130)(2,5,8,11,17,29,53,86,137,
24,45,75,114,37,67,103,157,119,81,123,124,131)(25,46,76,115,44,74,113,32,59,
92,143,43,73,112)(47,77,116)(82,127,159,126,152,99,150)]);
ALF("O8+(3).S4","B",[1,3,5,7,6,7,6,7,12,14,12,18,26,28,22,27,22,29,24,28,
31,41,41,47,46,47,49,60,64,60,68,66,75,75,79,81,94,104,4,4,9,10,13,17,30,
25,25,25,30,30,38,38,38,43,50,50,50,56,55,67,58,69,63,72,61,97,102,121,
121,122,129,129,132,133,133,139,156,164,164,6,7,27,29,46,46,46,47,64,64,
68,96,96,95,109,123,123,131,158,160,160,2,5,11,11,14,15,23,20,21,24,23,29,
21,24,28,23,27,27,29,41,41,48,52,65,59,65,62,66,71,70,62,66,73,77,92,93,
95,93,96,103,123,130,130,135,138,141,157,16,16,32,33,37,40,45,45,74,74,74,
106,119,124,118,114,126,127,161,161,176,176,178,179]);

MOT("2.O8+(3)",
[
"constructed by Max Neunh\"offer, April 2008"
],
[9904359628800,9904359628800,52254720,52254720,26127360,26127360,331776,
136048896,136048896,37791360,37791360,37791360,37791360,37791360,37791360,
37791360,37791360,37791360,37791360,37791360,37791360,944784,944784,944784,
944784,944784,944784,944784,944784,104976,104976,26244,26244,27648,27648,5760,
5760,2880,2880,1536,3600,3600,3600,3600,3600,3600,93312,93312,46656,46656,
20736,20736,15552,15552,7776,7776,15552,15552,7776,7776,10368,10368,5184,5184,
10368,10368,5184,5184,1296,1296,648,648,1296,1296,1296,1296,1296,1296,1296,
1296,648,648,648,648,324,324,56,56,32,64,64,5832,5832,5832,5832,5832,5832,5832
,5832,5832,5832,5832,5832,1458,1458,1458,1458,1458,1458,1458,1458,162,162,162,
162,162,162,162,162,80,80,40,40,3456,3456,3456,3456,3456,3456,864,864,864,864,
864,864,864,864,864,864,864,864,192,216,216,216,216,216,216,216,216,144,144,72
,72,144,144,72,72,26,26,26,26,56,56,56,56,56,56,90,90,90,90,90,90,90,90,90,90,
90,90,216,216,108,108,216,216,108,108,40,40,40,40,40,40],
[,[1,1,1,1,2,2,1,8,8,10,10,12,12,14,14,16,16,18,18,20,20,22,22,24,24,26,26,28,
28,30,30,32,32,7,7,3,3,5,6,7,41,41,43,43,45,45,8,8,9,9,8,8,10,10,13,15,16,16,
19,21,10,10,12,14,16,16,18,20,30,30,31,31,22,22,24,24,26,26,28,28,30,30,30,30,
32,32,87,87,35,40,40,92,92,94,94,96,96,98,98,100,100,102,102,104,104,106,106,
108,108,110,110,112,112,114,114,116,116,118,118,41,41,44,46,52,52,51,51,51,51,
62,62,63,63,64,64,66,66,67,67,68,68,52,74,74,76,76,78,78,79,79,53,53,55,56,57,
57,59,60,161,161,159,159,87,87,88,88,88,88,169,169,171,171,173,173,175,175,177
,177,179,179,92,92,95,97,98,98,101,103,121,121,122,122,123,123],[1,2,3,4,5,6,7
,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,34,35,36,37,38,39,40,41,
42,43,44,45,46,4,3,5,6,7,7,3,4,5,6,3,4,5,6,7,7,7,7,7,7,7,7,3,4,5,6,7,7,7,7,7,7
,7,7,7,7,7,7,7,7,87,88,89,90,91,8,9,8,9,8,9,8,9,8,9,8,9,8,9,8,9,8,9,8,9,22,23,
24,25,26,27,28,29,120,121,122,123,34,35,35,34,34,35,34,35,35,34,34,35,35,34,34
,35,34,35,40,35,34,34,35,34,35,34,35,36,37,38,39,36,37,38,39,159,160,161,162,
163,164,165,166,167,168,41,42,43,44,45,46,41,42,43,44,45,46,47,48,49,50,47,48,
49,50,189,190,191,192,193,194],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,
19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,1,2,1,2,1,2,
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
,119,4,3,5,6,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,
140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,
161,162,159,160,163,164,166,165,168,167,10,11,12,13,14,15,16,17,18,19,20,21,
181,182,183,184,185,186,187,188,37,36,38,38,39,39],,[1,2,3,4,5,6,7,8,9,10,11,
12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,
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,
64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,1,2,89,90
,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,
131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,
150,151,152,153,154,155,156,157,158,161,162,159,160,3,4,5,5,6,6,169,170,171,
172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,
192,191,194,193],,,,,,[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,
119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,
138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,
157,158,1,2,1,2,163,164,166,165,168,167,169,170,171,172,173,174,175,176,177,
178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194]],
0,
[(193,194),(191,192),(165,166)(167,168),(159,161)(160,162),
( 12, 18)( 13, 19)( 14, 20)( 15, 21)( 22, 24)( 23, 25)( 26, 28)( 27, 29)
( 55, 59)( 56, 60)( 63, 67)( 64, 68)( 73, 75)( 74, 76)( 77, 80)( 78, 79)
( 81, 82)( 83, 84)( 94,100)( 95,101)( 96,102)( 97,103)(104,106)(105,107)
(108,110)(109,111)(112,114)(113,115)(116,118)(117,119)(132,139)(133,138)
(134,140)(135,141)(143,146)(144,145)(147,149)(148,150)(153,157)(154,158)
(171,177)(172,178)(173,179)(174,180)(183,187)(184,188)
,
( 10, 16)( 11, 17)( 14, 20)( 15, 21)( 22, 26)( 23, 27)( 24, 28)( 25, 29)
( 53, 57)( 54, 58)( 56, 60)( 61, 65)( 62, 66)( 64, 68)( 73, 77)( 74, 78)
( 75, 80)( 76, 79)( 81, 83)( 82, 84)( 85, 86)( 92, 98)( 93, 99)( 96,102)
( 97,103)(104,108)(105,109)(106,110)(107,111)(112,116)(113,117)(114,118)
(115,119)(130,137)(131,136)(134,140)(135,141)(143,148)(144,147)(145,149)
(146,150)(151,155)(152,156)(154,158)(169,175)(170,176)(173,179)(174,180)
(181,185)(182,186)(184,188)
,
(  5,  6)( 12, 14)( 13, 15)( 18, 20)( 19, 21)( 26, 28)( 27, 29)( 38, 39)
( 43, 45)( 44, 46)( 49, 50)( 55, 56)( 59, 60)( 63, 64)( 67, 68)( 71, 72)
( 77, 80)( 78, 79)( 83, 84)( 94, 96)( 95, 97)(100,102)(101,103)(108,110)
(109,111)(116,118)(117,119)(122,123)(126,129)(127,128)(132,135)(133,134)
(138,140)(139,141)(147,149)(148,150)(153,154)(157,158)(165,167)(166,168)
(171,173)(172,174)(177,179)(178,180)(183,184)(187,188)(191,193)(192,194)
],
["ConstructProj",[["O8+(3)",[]],["2.O8+(3)",[]]]]);
ALF("2.O8+(3)","O8+(3)",[1,1,2,2,3,4,5,6,6,7,7,8,8,9,9,10,10,11,11,12,12,
13,13,14,14,15,15,16,16,17,17,18,18,19,19,20,20,21,22,23,24,24,25,25,26,
26,27,27,28,29,30,30,31,31,32,33,34,34,35,36,37,37,38,39,40,40,41,42,43,
43,44,45,46,46,47,47,48,48,49,49,50,51,52,53,54,54,55,55,56,57,57,58,58,
59,59,60,60,61,61,62,62,63,63,64,64,65,65,66,66,67,67,68,68,69,69,70,70,
71,71,72,72,73,74,75,75,76,76,77,77,78,78,79,79,80,80,81,81,82,82,83,83,
84,85,85,86,86,87,87,88,88,89,89,90,91,92,92,93,94,95,95,96,96,97,97,98,
98,99,99,100,100,101,101,102,102,103,103,104,104,105,105,106,106,107,108,
109,109,110,111,112,112,113,113,114,114]);

MOT("2^2.O8+(3)",
[
"group Spin8+(3),\n",
"constructed using `PossibleCharacterTablesOfTypeV4G'"
],
[19808719257600,19808719257600,19808719257600,19808719257600,52254720,52254720
,52254720,52254720,52254720,52254720,331776,272097792,272097792,272097792,
272097792,75582720,75582720,75582720,75582720,75582720,75582720,75582720,
75582720,75582720,75582720,75582720,75582720,75582720,75582720,75582720,
75582720,75582720,75582720,75582720,75582720,75582720,75582720,75582720,
75582720,1889568,1889568,1889568,1889568,1889568,1889568,1889568,1889568,
1889568,1889568,1889568,1889568,1889568,1889568,1889568,1889568,209952,209952,
209952,209952,52488,52488,52488,52488,55296,55296,55296,55296,5760,5760,5760,
5760,5760,5760,1536,7200,7200,7200,7200,7200,7200,7200,7200,7200,7200,7200,
7200,93312,93312,93312,93312,93312,93312,41472,41472,41472,41472,15552,15552,
15552,15552,15552,15552,15552,15552,15552,15552,15552,15552,10368,10368,10368,
10368,10368,10368,10368,10368,10368,10368,10368,10368,1296,1296,1296,1296,1296
,1296,2592,2592,2592,2592,2592,2592,2592,2592,2592,2592,2592,2592,2592,2592,
2592,2592,648,648,648,648,648,648,648,648,112,112,112,112,32,128,128,128,128,
11664,11664,11664,11664,11664,11664,11664,11664,11664,11664,11664,11664,11664,
11664,11664,11664,11664,11664,11664,11664,11664,11664,11664,11664,2916,2916,
2916,2916,2916,2916,2916,2916,2916,2916,2916,2916,2916,2916,2916,2916,324,324,
324,324,324,324,324,324,324,324,324,324,324,324,324,324,80,80,80,80,80,80,6912
,6912,6912,6912,6912,6912,6912,6912,6912,6912,6912,6912,1728,1728,1728,1728,
1728,1728,1728,1728,1728,1728,1728,1728,1728,1728,1728,1728,1728,1728,1728,
1728,1728,1728,1728,1728,192,432,432,432,432,432,432,432,432,432,432,432,432,
432,432,432,432,144,144,144,144,144,144,144,144,144,144,144,144,52,52,52,52,52
,52,52,52,112,112,112,112,112,112,112,112,112,112,112,112,180,180,180,180,180,
180,180,180,180,180,180,180,180,180,180,180,180,180,180,180,180,180,180,180,
216,216,216,216,216,216,216,216,216,216,216,216,80,80,80,80,80,80,80,80,80,80,
80,80],
[,[1,1,1,1,2,2,3,3,4,4,1,12,12,12,12,16,16,16,16,20,20,20,20,24,24,24,24,28,28
,28,28,32,32,32,32,36,36,36,36,40,40,40,40,44,44,44,44,48,48,48,48,52,52,52,52
,56,56,56,56,60,60,60,60,11,11,11,11,5,5,7,7,9,9,11,75,75,75,75,79,79,79,79,83
,83,83,83,13,13,14,14,15,15,12,12,12,12,17,17,22,22,27,27,29,29,34,34,39,39,16
,16,20,20,24,24,28,28,32,32,36,36,57,57,58,58,59,59,40,40,40,40,44,44,44,44,48
,48,48,48,52,52,52,52,56,56,56,56,60,60,60,60,151,151,151,151,67,74,74,74,74,
160,160,160,160,164,164,164,164,168,168,168,168,172,172,172,172,176,176,176,
176,180,180,180,180,184,184,184,184,188,188,188,188,192,192,192,192,196,196,
196,196,200,200,200,200,204,204,204,204,208,208,208,208,212,212,212,212,76,76,
81,81,86,86,95,95,95,95,94,94,94,94,93,93,93,93,110,110,110,110,112,112,112,
112,114,114,114,114,116,116,116,116,118,118,118,118,120,120,120,120,96,130,130
,130,130,133,133,133,133,138,138,138,138,140,140,140,140,97,97,99,99,101,101,
103,103,105,105,107,107,291,291,291,291,287,287,287,287,152,152,152,152,153,
153,153,153,154,154,154,154,307,307,307,307,311,311,311,311,315,315,315,315,
319,319,319,319,323,323,323,323,327,327,327,327,161,161,166,166,171,171,173,
173,178,178,183,183,217,217,217,217,219,219,219,219,221,221,221,221],[1,2,3,4,
5,6,7,8,9,10,11,1,2,3,4,1,2,3,4,1,2,3,4,1,2,3,4,1,2,3,4,1,2,3,4,1,2,3,4,1,2,3,
4,1,2,3,4,1,2,3,4,1,2,3,4,1,2,3,4,1,2,3,4,64,65,66,67,68,69,70,71,72,73,74,75,
76,77,78,79,80,81,82,83,84,85,86,6,5,8,7,10,9,11,11,11,11,5,6,7,8,9,10,5,6,7,8
,9,10,11,11,11,11,11,11,11,11,11,11,11,11,5,6,7,8,9,10,11,11,11,11,11,11,11,11
,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,151,152,153,154,155,156,157,
158,159,12,13,14,15,12,13,14,15,12,13,14,15,12,13,14,15,12,13,14,15,12,13,14,
15,12,13,14,15,12,13,14,15,12,13,14,15,12,13,14,15,40,41,42,43,44,45,46,47,48,
49,50,51,52,53,54,55,216,217,218,219,220,221,64,65,66,67,66,67,64,65,65,64,67,
66,64,65,66,67,66,67,64,65,65,64,67,66,66,67,64,65,65,64,67,66,64,65,66,67,74,
67,66,65,64,64,65,66,67,64,65,66,67,64,65,66,67,68,69,70,71,72,73,68,69,70,71,
72,73,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,
305,306,75,76,77,78,79,80,81,82,83,84,85,86,75,76,77,78,79,80,81,82,83,84,85,
86,87,88,89,90,91,92,87,88,89,90,91,92,343,344,345,346,347,348,349,350,351,352
,353,354],,[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,
52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,1,2,3,4,1
,2,3,4,1,2,3,4,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,
106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,
125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,
144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,
163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,
182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,
201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,6,5,8,7,10,9,222,
223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,
242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,
261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,
280,281,282,283,284,285,286,291,292,293,294,287,288,289,290,296,295,298,297,
301,302,299,300,306,305,304,303,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,
31,32,33,34,35,36,37,38,39,331,332,333,334,335,336,337,338,339,340,341,342,69,
69,68,68,71,70,71,70,73,72,72,73],,[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,
70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,
96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,
116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,
135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,1,2,3,4,155,
156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,
175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,
194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,
213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,
232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,
251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,
270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,291,292,
293,294,287,288,289,290,5,5,6,6,7,8,7,8,9,10,10,9,307,308,309,310,311,312,313,
314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,
333,334,335,336,337,338,339,340,341,342,344,343,346,345,349,350,347,348,354,
353,352,351],,,,,,[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,
120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,
139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,
158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,
177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,
196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,
215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,
234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,
253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,
272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,1,2,3,4,1,2,3,4,
296,295,298,297,301,302,299,300,306,305,304,303,307,308,309,310,311,312,313,
314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,
333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,
352,353,354]],
0,
[(351,354)(352,353),(347,349)(348,350),(343,344)(345,346),
(295,296)(297,298)(299,301)(300,302)(303,306)(304,305),
(287,291)(288,292)(289,293)(290,294),
( 20, 32)( 21, 33)( 22, 34)( 23, 35)( 24, 36)( 25, 37)( 26, 38)( 27, 39)
( 40, 44)( 41, 45)( 42, 46)( 43, 47)( 48, 52)( 49, 53)( 50, 54)( 51, 55)
( 99,105)(100,106)(101,107)(102,108)(111,117)(112,118)(113,119)(114,120)
(127,132)(128,131)(129,134)(130,133)(135,141)(136,142)(137,139)(138,140)
(143,144)(145,146)(147,148)(149,150)(164,176)(165,177)(166,178)(167,179)
(168,180)(169,181)(170,182)(171,183)(184,188)(185,189)(186,190)(187,191)
(192,196)(193,197)(194,198)(195,199)(200,204)(201,205)(202,206)(203,207)
(208,212)(209,213)(210,214)(211,215)(238,253)(239,252)(240,251)(241,250)
(242,255)(243,254)(244,257)(245,256)(259,266)(260,265)(261,264)(262,263)
(267,271)(268,272)(269,273)(270,274)(277,283)(278,284)(279,285)(280,286)
(311,323)(312,324)(313,325)(314,326)(315,327)(316,328)(317,329)(318,330)
(333,339)(334,340)(335,341)(336,342)
,
( 16, 28)( 17, 29)( 18, 30)( 19, 31)( 24, 36)( 25, 37)( 26, 38)( 27, 39)
( 40, 48)( 41, 49)( 42, 50)( 43, 51)( 44, 52)( 45, 53)( 46, 54)( 47, 55)
( 97,103)( 98,104)(101,107)(102,108)(109,115)(110,116)(113,119)(114,120)
(127,135)(128,136)(129,137)(130,138)(131,142)(132,141)(133,140)(134,139)
(143,145)(144,146)(147,149)(148,150)(160,172)(161,173)(162,174)(163,175)
(168,180)(169,181)(170,182)(171,183)(184,192)(185,193)(186,194)(187,195)
(188,196)(189,197)(190,198)(191,199)(200,208)(201,209)(202,210)(203,211)
(204,212)(205,213)(206,214)(207,215)(234,248)(235,249)(236,246)(237,247)
(242,255)(243,254)(244,257)(245,256)(259,270)(260,269)(261,268)(262,267)
(263,271)(264,272)(265,273)(266,274)(275,281)(276,282)(279,285)(280,286)
(307,319)(308,320)(309,321)(310,322)(315,327)(316,328)(317,329)(318,330)
(331,337)(332,338)(335,341)(336,342)
,
(  3,  4)(  7,  9)(  8, 10)( 14, 15)( 18, 19)( 20, 24)( 21, 25)( 22, 27)
( 23, 26)( 30, 31)( 32, 36)( 33, 37)( 34, 39)( 35, 38)( 42, 43)( 46, 47)
( 48, 52)( 49, 53)( 50, 55)( 51, 54)( 58, 59)( 62, 63)( 64, 65)( 70, 72)
( 71, 73)( 77, 78)( 79, 83)( 80, 84)( 81, 86)( 82, 85)( 89, 91)( 90, 92)
( 93, 94)( 99,101)(100,102)(105,107)(106,108)(111,113)(112,114)(117,119)
(118,120)(123,125)(124,126)(127,128)(131,132)(135,142)(136,141)(137,139)
(138,140)(145,146)(149,150)(153,154)(158,159)(162,163)(164,168)(165,169)
(166,171)(167,170)(174,175)(176,180)(177,181)(178,183)(179,182)(186,187)
(190,191)(192,196)(193,197)(194,199)(195,198)(202,203)(206,207)(208,212)
(209,213)(210,215)(211,214)(218,220)(219,221)(222,223)(226,233)(227,232)
(228,230)(229,231)(234,235)(238,245)(239,244)(240,242)(241,243)(248,249)
(250,254)(251,255)(252,257)(253,256)(261,262)(263,264)(267,272)(268,271)
(269,273)(270,274)(277,279)(278,280)(283,285)(284,286)(289,290)(293,294)
(297,298)(299,303)(300,304)(301,306)(302,305)(309,310)(311,315)(312,316)
(313,318)(314,317)(321,322)(323,327)(324,328)(325,330)(326,329)(333,335)
(334,336)(339,341)(340,342)(345,346)(347,351)(348,352)(349,354)(350,353)
,
(  2,  3)(  5,  7)(  6,  8)( 13, 14)( 16, 20)( 17, 22)( 18, 21)( 19, 23)
( 25, 26)( 28, 32)( 29, 34)( 30, 33)( 31, 35)( 37, 38)( 41, 42)( 44, 48)
( 45, 50)( 46, 49)( 47, 51)( 53, 54)( 57, 58)( 61, 62)( 65, 66)( 68, 70)
( 69, 71)( 75, 79)( 76, 81)( 77, 80)( 78, 82)( 84, 85)( 87, 89)( 88, 90)
( 94, 95)( 97, 99)( 98,100)(103,105)(104,106)(109,111)(110,112)(115,117)
(116,118)(121,123)(122,124)(128,129)(131,137)(132,135)(133,138)(134,136)
(139,142)(144,145)(148,149)(152,153)(157,158)(160,164)(161,166)(162,165)
(163,167)(169,170)(172,176)(173,178)(174,177)(175,179)(181,182)(185,186)
(188,192)(189,194)(190,193)(191,195)(197,198)(201,202)(204,208)(205,210)
(206,209)(207,211)(213,214)(216,218)(217,219)(222,228)(223,226)(224,229)
(225,227)(230,233)(234,240)(235,238)(236,241)(237,239)(242,245)(246,250)
(247,252)(248,251)(249,253)(255,256)(260,261)(263,267)(264,269)(265,268)
(266,270)(272,273)(275,277)(276,278)(281,283)(282,284)(288,289)(292,293)
(295,299)(296,301)(297,300)(298,302)(304,305)(307,311)(308,313)(309,312)
(310,314)(316,317)(319,323)(320,325)(321,324)(322,326)(328,329)(331,333)
(332,334)(337,339)(338,340)(343,347)(344,349)(345,348)(346,350)(352,353)
],
["ConstructV4G","2.O8+(3)",
(  2,  3,  4)(  5,  7,  9)(  6,  8, 10)( 13, 14, 15)( 16, 20, 24)( 17, 22, 27)
( 18, 23, 25)( 19, 21, 26)( 28, 32, 36)( 29, 34, 39)( 30, 35, 37)( 31, 33, 38)
( 41, 42, 43)( 44, 48, 52)( 45, 50, 55)( 46, 51, 53)( 47, 49, 54)( 57, 58, 59)
( 61, 62, 63)( 64, 66, 65)( 68, 70, 72)( 69, 71, 73)( 75, 79, 83)( 76, 81, 86)
( 77, 82, 84)( 78, 80, 85)( 87, 89, 91)( 88, 90, 92)( 93, 95, 94)( 97, 99,101)
( 98,100,102)(103,105,107)(104,106,108)(109,111,113)(110,112,114)(115,117,119)
(116,118,120)(121,123,125)(122,124,126)(127,129,128)(131,135,139)(132,137,142)
(133,138,140)(134,136,141)(144,145,146)(148,149,150)(152,153,154)(157,158,159)
(160,164,168)(161,166,171)(162,167,169)(163,165,170)(172,176,180)(173,178,183)
(174,179,181)(175,177,182)(185,186,187)(188,192,196)(189,194,199)(190,195,197)
(191,193,198)(201,202,203)(204,208,212)(205,210,215)(206,211,213)(207,209,214)
(216,218,220)(217,219,221)(222,226,230)(223,228,233)(224,229,231)(225,227,232)
(234,238,242)(235,240,245)(236,241,243)(237,239,244)(246,250,254)(247,252,257)
(248,253,255)(249,251,256)(260,261,262)(263,269,272)(264,267,273)(265,268,271)
(266,270,274)(275,277,279)(276,278,280)(281,283,285)(282,284,286)(288,289,290)
(292,293,294)(295,299,303)(296,301,306)(297,302,304)(298,300,305)(307,311,315)
(308,313,318)(309,314,316)(310,312,317)(319,323,327)(320,325,330)(321,326,328)
(322,324,329)(331,333,335)(332,334,336)(337,339,341)(338,340,342)(343,347,351)
(344,349,354)(345,350,352)(346,348,353)
]);
ALF("2^2.O8+(3)","2.O8+(3)",[1,1,2,2,3,4,5,5,6,6,7,8,8,9,9,10,10,11,11,12,
12,13,13,14,14,15,15,16,16,17,17,18,18,19,19,20,20,21,21,22,22,23,23,24,
24,25,25,26,26,27,27,28,28,29,29,30,30,31,31,32,32,33,33,34,34,35,35,36,
37,38,38,39,39,40,41,41,42,42,43,43,44,44,45,45,46,46,47,48,49,49,50,50,
51,51,52,52,53,54,55,55,56,56,57,58,59,59,60,60,61,62,63,63,64,64,65,66,
67,67,68,68,69,70,71,71,72,72,73,73,74,74,75,75,76,76,77,77,78,78,79,79,
80,80,81,82,83,84,85,85,86,86,87,87,88,88,89,90,90,91,91,92,92,93,93,94,
94,95,95,96,96,97,97,98,98,99,99,100,100,101,101,102,102,103,103,104,104,
105,105,106,106,107,107,108,108,109,109,110,110,111,111,112,112,113,113,
114,114,115,115,116,116,117,117,118,118,119,119,120,121,122,122,123,123,
124,124,125,125,126,126,127,127,128,128,129,129,130,130,131,131,132,132,
133,133,134,134,135,135,136,136,137,137,138,138,139,139,140,140,141,141,
142,143,143,144,144,145,145,146,146,147,147,148,148,149,149,150,150,151,
152,153,153,154,154,155,156,157,157,158,158,159,159,160,160,161,161,162,
162,163,163,164,164,165,165,166,166,167,167,168,168,169,169,170,170,171,
171,172,172,173,173,174,174,175,175,176,176,177,177,178,178,179,179,180,
180,181,182,183,183,184,184,185,186,187,187,188,188,189,189,190,190,191,
191,192,192,193,193,194,194]);
ALF("2^2.O8+(3)","O8+(3)",[1,1,1,1,2,2,3,3,4,4,5,6,6,6,6,7,7,7,7,8,8,8,8,
9,9,9,9,10,10,10,10,11,11,11,11,12,12,12,12,13,13,13,13,14,14,14,14,15,15,
15,15,16,16,16,16,17,17,17,17,18,18,18,18,19,19,19,19,20,20,21,21,22,22,
23,24,24,24,24,25,25,25,25,26,26,26,26,27,27,28,28,29,29,30,30,30,30,31,
31,32,32,33,33,34,34,35,35,36,36,37,37,38,38,39,39,40,40,41,41,42,42,43,
43,44,44,45,45,46,46,46,46,47,47,47,47,48,48,48,48,49,49,49,49,50,51,52,
53,54,54,54,54,55,55,55,55,56,57,57,57,57,58,58,58,58,59,59,59,59,60,60,
60,60,61,61,61,61,62,62,62,62,63,63,63,63,64,64,64,64,65,65,65,65,66,66,
66,66,67,67,67,67,68,68,68,68,69,69,69,69,70,70,70,70,71,71,71,71,72,72,
73,73,74,74,75,75,75,75,76,76,76,76,77,77,77,77,78,78,78,78,79,79,79,79,
80,80,80,80,81,81,81,81,82,82,82,82,83,83,83,83,84,85,85,85,85,86,86,86,
86,87,87,87,87,88,88,88,88,89,89,90,90,91,91,92,92,93,93,94,94,95,95,95,
95,96,96,96,96,97,97,97,97,98,98,98,98,99,99,99,99,100,100,100,100,101,
101,101,101,102,102,102,102,103,103,103,103,104,104,104,104,105,105,105,
105,106,106,107,107,108,108,109,109,110,110,111,111,112,112,112,112,113,
113,113,113,114,114,114,114]);
ALF("2^2.O8+(3)","2^2.O8+(3).3",[1,2,2,2,3,4,3,4,3,4,5,6,7,7,7,8,9,10,11,
8,11,9,10,8,10,11,9,12,13,14,15,12,15,13,14,12,14,15,13,16,17,17,17,18,19,
20,21,18,21,19,20,18,20,21,19,22,23,23,23,24,25,25,25,26,26,26,27,28,29,
28,29,28,29,30,31,32,33,34,31,34,32,33,31,33,34,32,35,36,35,36,35,36,37,
37,37,38,39,40,39,40,39,40,41,42,41,42,41,42,43,44,43,44,43,44,45,46,45,
46,45,46,47,48,47,48,47,48,49,49,49,50,51,52,53,54,51,54,52,53,51,53,54,
52,55,56,56,56,57,58,58,58,59,60,60,60,61,62,63,63,63,64,65,66,67,64,67,
65,66,64,66,67,65,68,69,70,71,68,71,69,70,68,70,71,69,72,73,73,73,74,75,
76,77,74,77,75,76,74,76,77,75,78,79,79,79,80,81,82,83,80,83,81,82,80,82,
83,81,84,85,84,85,84,85,86,87,88,89,86,89,87,88,86,88,89,87,90,91,92,93,
90,93,91,92,90,92,93,91,94,95,96,97,94,97,95,96,94,96,97,95,98,99,100,100,
100,101,102,103,104,102,103,101,104,103,101,102,104,105,106,105,106,105,
106,107,108,107,108,107,108,109,110,110,110,111,112,112,112,113,114,115,
116,113,116,114,115,113,115,116,114,117,118,119,120,117,120,118,119,117,
119,120,118,121,122,123,124,121,124,122,123,121,123,124,122,125,126,125,
126,125,126,127,128,127,128,127,128,129,130,131,132,129,132,130,131,129,
131,132,130],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALN("2^2.O8+(3)",["Spin8+(3)"]);

MOT("2^2.O8+(3).3",
[
"constructed using `PossibleCharacterTablesOfTypeMGA'"
],
[59426157772800,19808719257600,52254720,52254720,995328,816293376,272097792,
75582720,75582720,75582720,75582720,75582720,75582720,75582720,75582720,
5668704,1889568,1889568,1889568,1889568,1889568,629856,209952,157464,52488,
55296,165888,5760,5760,4608,7200,7200,7200,7200,93312,93312,41472,124416,15552
,15552,15552,15552,10368,10368,10368,10368,1296,1296,2592,7776,2592,2592,2592,
2592,1944,648,1944,648,336,112,96,384,128,11664,11664,11664,11664,11664,11664,
11664,11664,8748,2916,2916,2916,2916,2916,972,324,324,324,324,324,80,80,6912,
6912,6912,6912,1728,1728,1728,1728,1728,1728,1728,1728,576,1296,432,432,432,
432,432,144,144,144,144,156,52,156,52,112,112,112,112,180,180,180,180,180,180,
180,180,216,216,216,216,80,80,80,80,12737088,12737088,17496,17496,1728,1728,
216,216,1944,1944,1458,1458,729,729,486,486,288,288,288,288,36,36,216,216,54,
54,54,54,21,21,24,24,24,24,27,27,36,36,39,39,39,39],
[,[1,1,2,2,1,6,6,8,8,8,8,12,12,12,12,16,16,18,18,18,18,22,22,24,24,5,5,3,3,5,
31,31,31,31,7,7,6,6,9,9,13,13,8,8,12,12,23,23,16,16,18,18,18,18,22,22,24,24,59
,59,27,30,30,64,64,64,64,68,68,68,68,72,72,74,74,74,74,78,78,80,80,80,80,32,32
,37,37,37,37,44,44,44,44,46,46,46,46,38,50,50,53,53,53,53,39,39,41,41,111,111,
109,109,60,60,60,60,117,117,117,117,121,121,121,121,65,65,69,69,85,85,85,85,
134,133,136,135,134,133,136,135,142,141,144,143,146,145,148,147,138,137,138,
137,140,139,142,141,144,143,148,147,162,161,150,149,152,151,168,167,156,155,
174,173,172,171],[1,2,3,4,5,1,2,1,2,2,2,1,2,2,2,1,2,1,2,2,2,1,2,1,2,26,27,28,
29,30,31,32,33,34,4,3,5,5,3,4,3,4,5,5,5,5,3,4,5,5,5,5,5,5,5,5,5,5,59,60,61,62,
63,6,7,7,7,6,7,7,7,6,7,6,7,7,7,16,17,18,19,20,21,84,85,26,26,26,27,26,26,26,27
,26,27,26,26,30,27,26,26,26,26,27,28,29,28,29,109,110,111,112,113,114,115,116,
31,32,33,34,31,32,33,34,35,36,35,36,129,130,131,132,1,1,1,1,5,5,5,5,16,16,16,
16,16,16,16,16,27,27,30,30,30,30,50,50,50,50,50,50,59,59,61,61,62,62,72,72,99,
99,109,109,111,111],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22
,23,24,25,26,27,28,29,30,1,2,2,2,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,
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,
76,77,78,79,80,81,82,83,4,3,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,
102,103,104,105,106,107,108,111,112,109,110,114,113,116,115,8,9,10,11,12,13,14
,15,125,126,127,128,29,29,28,28,134,133,136,135,138,137,140,139,142,141,144,
143,146,145,148,147,150,149,152,151,154,153,156,155,158,157,160,159,162,161,
164,163,166,165,168,167,170,169,174,173,172,171],,[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,
39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,1,2,61,62,63,64,65
,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
,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,111,112,109,110,3
,3,4,4,117,118,119,120,121,122,123,124,125,126,127,128,130,129,132,131,133,134
,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,
154,155,156,157,158,159,160,133,134,163,164,165,166,167,168,169,170,173,174,
171,172],,,,,,[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,
102,103,104,105,106,107,108,1,2,1,2,114,113,116,115,117,118,119,120,121,122,
123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,
142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,
161,162,163,164,165,166,167,168,169,170,133,134,133,134]],
0,
[(129,130)(131,132),(115,116),(113,114),
(109,111)(110,112)(133,134)(135,136)(137,138)(139,140)(141,142)(143,144)
(145,146)(147,148)(149,150)(151,152)(153,154)(155,156)(157,158)(159,160)
(161,162)(163,164)(165,166)(167,168)(169,170)(171,174)(172,173)
,(109,111)(110,112)(171,173)(172,174),
( 10, 11)( 14, 15)( 20, 21)( 33, 34)( 51, 52)( 66, 67)( 70, 71)( 76, 77)
( 82, 83)( 86, 87)( 90, 91)( 96, 97)(101,102)(109,111)(110,112)(119,120)
(123,124)(131,132)(133,134)(135,136)(137,138)(139,140)(141,142)(143,144)
(145,146)(147,148)(149,150)(151,152)(153,154)(155,156)(157,158)(159,160)
(161,162)(163,164)(165,166)(167,168)(169,170)(171,174)(172,173)
],
["ConstructMGA","2^2.O8+(3)","O8+(3).3",[[115,195..275],[116,196..276],[117,
197..277],[118,198..278],[119,199..279],[120,200..280],[121,201..281],[122,202
..282],[123,203..283],[124,204..284],[125,205..285],[126,206..286],[127,207..
287],[128,208..288],[129,209..289],[130,210..290],[131,211..291],[132,212..292
],[133,213..293],[134,214..294],[135,215..295],[136,216..296],[137,217..297],[
138,218..298],[139,219..299],[140,220..300],[141,221..301],[142,222..302],[143
,223..303],[144,224..304],[145,225..305],[146,226..306],[147,227..307],[148,
228..308],[149,229..309],[150,230..310],[151,231..311],[152,232..312],[153,233
..313],[154,234..314],[155,235..315],[156,236..316],[157,237..317],[158,238..
318],[159,239..319],[160,240..320],[161,241..321],[162,242..322],[163,243..323
],[164,244..324],[165,245..325],[166,246..326],[167,247..327],[168,248..328],[
169,249..329],[170,250..330],[171,251..331],[172,252..332],[173,253..333],[174
,254..334],[175,255..335],[176,256..336],[177,257..337],[178,258..338],[179,
259..339],[180,260..340],[181,261..341],[182,262..342],[183,263..343],[184,264
..344],[185,265..345],[186,266..346],[187,267..347],[188,268..348],[189,269..
349],[190,270..350],[191,271..351],[192,272..352],[193,273..353],[194,274..354
]],()]);
ALF("2^2.O8+(3).3","O8+(3).3",[1,1,2,2,3,4,4,5,5,5,5,6,6,6,6,7,7,8,8,8,8,
9,9,10,10,11,11,12,12,13,14,14,14,14,15,15,16,16,17,17,18,18,19,19,20,20,
21,21,22,22,23,23,23,23,24,25,26,26,27,27,28,29,29,30,30,30,30,31,31,31,
31,32,32,33,33,33,33,34,34,35,35,35,35,36,36,37,37,37,37,38,38,38,38,39,
39,39,39,40,41,41,42,42,42,42,43,43,44,44,45,45,46,46,47,47,47,47,48,48,
48,48,49,49,49,49,50,50,51,51,52,52,52,52,53,54,55,56,57,58,59,60,61,62,
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]);


LIBTABLE.LOADSTATUS.ctoorth2:="userloaded";

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