SSL ctomisc2.tbl   Interaktion und
Portierbarkeitunbekannt

#############################################################################
##
#W  ctomisc2.tbl                GAP table library               Thomas Breuer
##
##  This file contains the ordinary character tables of miscellaneous
##  CAS tables (alphabetical order, 'f' to 'o')
##
#H  ctbllib history
#H  ---------------
#H  $Log: ctomisc2.tbl,v $
#H  Revision 4.36  2012/04/23 16:16:14  gap
#H  next step of consolidation:
#H
#H  - removed a few unnecessary duplicate tables,
#H    and changed some related fusions, names of maxes, table constructions
#H  - make sure that duplicate tables arise only via `ConstructPermuted'
#H    constructions
#H  - added some relative names
#H  - added fusions A11.2 -> A12.2, L2(11).2 -> A12.2, D8x2F4(2)'.2 -> B,
#H    L2(41) -> M, (A5xA12):2 -> A17,
#H  - added maxes of A12.2, L6(2), 2.M22.2
#H  - added table of QD16.2,
#H  - fixed the syntax of two `ALN' calls
#H      TB
#H
#H  Revision 4.35  2012/01/30 08:31:57  gap
#H  removed #H entries from the headers
#H      TB
#H
#H  Revision 4.34  2011/09/28 13:26:41  gap
#H  - removed revision entry and SET_TABLEFILENAME call,
#H  - added fusions hed3 -> He.2d3, hed3 -> He,
#H  - fixed the InfoText of 2.Fi22M5
#H      TB
#H
#H  Revision 4.33  2010/05/05 13:20:07  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 4.32  2010/01/19 17:05:34  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 4.31  2009/04/22 12:39:05  gap
#H  added missing maxes of He.2, ON.2, HN.2, Fi24, and B
#H      TB
#H
#H  Revision 4.30  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 4.29  2004/03/30 08:10:59  gap
#H  turned u4q3.s3 into an explicit direct product called S3xU4(3)
#H      TB
#H
#H  Revision 4.28  2003/11/12 17:41:14  gap
#H  renamed Fi22.2M6 to Fi22.2M4
#H      TB
#H
#H  Revision 4.27  2003/10/06 07:16:34  gap
#H  corrected table automorphisms of `"group3"' (why was it wrong?)
#H      TB
#H
#H  Revision 4.26  2003/07/22 15:11:17  gap
#H  added table of 2^(1+6)_+.A8 (maximal in 2.O8+(2))
#H      TB
#H
#H  Revision 4.25  2003/06/20 15:03:09  gap
#H  added several fusions
#H      TB
#H
#H  Revision 4.24  2003/05/23 15:06:16  gap
#H  added some fusions
#H      TB
#H
#H  Revision 4.23  2003/05/15 17:38:17  gap
#H  next step towards the closer connection to the library of tables of marks:
#H  added fusions tbl -> tom, adjusted fusions between character tables
#H  in order to make the diagrams commute, adjusted orderings of maxes
#H      TB
#H
#H  Revision 4.22  2003/03/07 15:53:40  gap
#H  added tables of `Isoclinic(2.A5.2)' and `L2(125)',
#H  and many `tomidentifier' components (still several are missing)
#H      TB
#H
#H  Revision 4.21  2003/01/22 12:32:12  gap
#H  made "2^6:S6(2)" an admissible name for "2^6:s6f2"
#H      TB
#H
#H  Revision 4.20  2003/01/21 16:25:32  gap
#H  further standardizations of `InfoText' strings,
#H  added and corrected `Maxes' infos,
#H  added some fusions
#H      TB
#H
#H  Revision 4.19  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 4.18  2002/10/22 12:44:12  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 4.17  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 4.16  2002/07/17 15:25:32  gap
#H  added missing table automorphisms
#H      TB
#H
#H  Revision 4.15  2002/07/12 06:45:56  gap
#H  further tidying up: removed `irredinfo' stuff, rearranged constructions
#H      TB
#H
#H  Revision 4.14  2001/05/04 16:48:54  gap
#H  first revision for ctbllib
#H
#H
#H  tbl history (GAP 4)
#H  -------------------
#H  (Rev. 4.14 of ctbllib coincides with Rev. 4.13 of tbl in GAP 4)
#H  
#H  RCS file: /gap/CVS/GAP/4.0/tbl/ctomisc2.tbl,v
#H  Working file: ctomisc2.tbl
#H  head: 4.13
#H  branch:
#H  locks: strict
#H  access list:
#H  symbolic names:
#H   GAP4R2: 4.10.0.4
#H   GAP4R2PRE2: 4.10.0.2
#H   GAP4R2PRE1: 4.8.0.2
#H   GAP4R1: 4.6.0.2
#H  keyword substitution: kv
#H  total revisions: 14; selected revisions: 14
#H  description:
#H  ----------------------------
#H  revision 4.13
#H  date: 2000/03/27 11:42:00;  author: gap;  state: Exp;  lines: +148 -3
#H  added table of 6.Fi22M5 (Eamonn had asked for it ...)
#H  
#H      TB
#H  ----------------------------
#H  revision 4.12
#H  date: 2000/03/27 09:54:45;  author: gap;  state: Exp;  lines: +117 -3
#H  added some tables of maxes of 2.Suz and corresponding fusions,
#H  added table of 3.Fi22M5
#H  
#H      TB
#H  ----------------------------
#H  revision 4.11
#H  date: 2000/03/07 15:33:57;  author: gap;  state: Exp;  lines: +4 -2
#H  added factor fusion Fi22M5 -> M22 (needed for a table construction)
#H  
#H      TB
#H  ----------------------------
#H  revision 4.10
#H  date: 2000/02/21 12:41:47;  author: gap;  state: Exp;  lines: +76 -3
#H  added tables of Fi22.2M6 and 2.Fi22M5
#H  (Eamonn had asked for them)
#H  
#H      TB
#H  ----------------------------
#H  revision 4.9
#H  date: 2000/02/17 08:38:28;  author: gap;  state: Exp;  lines: +7 -2
#H  added table of 2^10:M22:2 < Fi22.2
#H  
#H      TB
#H  ----------------------------
#H  revision 4.8
#H  date: 1999/10/21 14:15:47;  author: gap;  state: Exp;  lines: +5 -2
#H  added many `tomidentifer' and `tomfusion' values, which yields a better
#H  interface between `tom' and `tbl';
#H  
#H  added maxes of McL.2,
#H  
#H  unified tables `J2.2M4', `2^(2+4):(3x3):2^2', `2^(2+4):(S3xS3)'.
#H  
#H      TB
#H  ----------------------------
#H  revision 4.7
#H  date: 1999/09/14 13:28:19;  author: gap;  state: Exp;  lines: +2 -108
#H  really removed corrupted tables (had only been commented out before)
#H  
#H      TB
#H  ----------------------------
#H  revision 4.6
#H  date: 1999/07/14 14:19:56;  author: gap;  state: Exp;  lines: +107 -107
#H  removed incomplete CAS table of `iu332' (for the moment ...)
#H  
#H      TB
#H  ----------------------------
#H  revision 4.5
#H  date: 1999/07/14 11:39:40;  author: gap;  state: Exp;  lines: +4 -3
#H  cosmetic changes for the release ...
#H  
#H      TB
#H  ----------------------------
#H  revision 4.4
#H  date: 1998/12/14 12:51:19;  author: gap;  state: Exp;  lines: +6 -6
#H  fixed the name of a fusion destination
#H  
#H      TB
#H  ----------------------------
#H  revision 4.3
#H  date: 1998/03/12 15:52:18;  author: gap;  state: Exp;  lines: +89 -74
#H  tables with names `mo81p' and `y' are both `2^6:A8';
#H  cleaned this situation, added some fusions
#H  
#H      TB
#H  ----------------------------
#H  revision 4.2
#H  date: 1997/11/25 15:45:30;  author: gap;  state: Exp;  lines: +5 -4
#H  first attempt to link the library of character tables and the
#H      library of tables of marks
#H          TB
#H  ----------------------------
#H  revision 4.1
#H  date: 1997/07/17 15:43:57;  author: fceller;  state: Exp;  lines: +2 -2
#H  for version 4
#H  ----------------------------
#H  revision 1.1
#H  date: 1996/10/21 16:00:25;  author: sam;  state: Exp;
#H  first proposal of the table library
#H  ==========================================================================
##

MOT("2^10:m22",
[
"origin: CAS library,\n",
"2..10.m22\n",
"2nd power map determined only up to matrix automorphisms,\n",
"tests: 1.o.r., pow[2,3,5,7,11],"
],
[454164480,20643840,1966080,589824,24576,8192,3072,1024,4096,1536,4096,512,
512,256,128,128,128,128,128,32,64,576,144,576,144,96,20,20,20,20,48,24,48,14,
14,14,14,32,32,32,32,11,11],
[,[1,1,1,1,1,1,3,3,3,4,3,5,5,5,9,9,11,5,6,10,11,22,22,22,22,22,27,27,27,27,22,
26,24,34,34,36,36,12,13,17,17,43,42],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,
17,18,19,20,21,1,2,4,4,3,27,29,28,30,5,7,10,36,37,34,35,38,39,40,41,42,43],,[
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,1,2,2,3,
31,32,33,36,37,34,35,38,39,41,40,42,43],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,
16,17,18,19,20,21,22,23,24,25,26,27,29,28,30,31,32,33,1,2,1,2,38,39,41,40,43,
42],,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,
27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,1,1]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1],[21,21,21,21,5,5,5,5,5,5,5,1,1,1,1,1,1,1,1,1,1,3,3,3,3,3,1,1,1,1,
-1,-1,-1,0,0,0,0,-1,-1,-1,-1,-1,-1],[45,45,45,45,-3,-3,-3,-3,-3,-3,-3,1,1,1,1,
1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,E(7)+E(7)^2+E(7)^4,E(7)+E(7)^2+E(7)^4,
E(7)^3+E(7)^5+E(7)^6,E(7)^3+E(7)^5+E(7)^6,-1,-1,-1,-1,1,1],
[GALOIS,[3,3]],[55,55,55,55,7,7,7,7,7,7,7,3,3,3,3,3,3,-1,-1,-1,-1,1,1,1,1,1,0,
0,0,0,1,1,1,-1,-1,-1,-1,1,1,1,1,0,0],[99,99,99,99,3,3,3,3,3,3,3,3,3,3,3,3,3,
-1,-1,-1,-1,0,0,0,0,0,-1,-1,-1,-1,0,0,0,1,1,1,1,-1,-1,-1,-1,0,0],[154,154,154,
154,10,10,10,10,10,10,10,-2,-2,-2,-2,-2,-2,2,2,2,2,1,1,1,1,1,-1,-1,-1,-1,1,1,
1,0,0,0,0,0,0,0,0,0,0],[210,210,210,210,2,2,2,2,2,2,2,-2,-2,-2,-2,-2,-2,-2,-2,
-2,-2,3,3,3,3,3,0,0,0,0,-1,-1,-1,0,0,0,0,0,0,0,0,1,1],[231,231,231,231,7,7,7,
7,7,7,7,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-3,-3,-3,-3,-3,1,1,1,1,1,1,1,0,0,0,0,-1,
-1,-1,-1,0,0],[385,385,385,385,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-2,-2,-2,-2,
-2,0,0,0,0,-2,-2,-2,0,0,0,0,1,1,1,1,0,0],[280,280,280,280,-8,-8,-8,-8,-8,-8,
-8,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0,0,0,
E(11)+E(11)^3+E(11)^4+E(11)^5+E(11)^9,E(11)^2+E(11)^6+E(11)^7+E(11)^8+E(11)^10
 ],
[GALOIS,[11,2]],[77,-35,13,-3,13,-3,-7,1,5,1,-3,5,-3,1,1,-3,1,1,1,-1,1,5,1,-3,
-3,1,2,0,0,-2,1,-1,1,0,0,0,0,1,1,-1,-1,0,0],[385,-175,65,-15,17,1,-11,-3,9,5,
1,-3,5,1,-3,1,1,1,1,-1,1,7,5,-9,-3,-1,0,0,0,0,-1,1,-1,0,0,0,0,-1,-1,1,1,0,0],[
385,-175,65,-15,17,1,-11,-3,9,5,1,-3,5,1,-3,1,1,1,1,-1,1,-2,-4,6,0,2,0,0,0,0,
2,-2,2,0,0,0,0,-1,-1,1,1,0,0],[693,-315,117,-27,21,5,-15,-7,13,9,5,5,-3,1,1,
-3,1,1,1,-1,1,0,0,0,0,0,-2,0,0,2,0,0,0,0,0,0,0,1,1,-1,-1,0,0],[770,-350,130,
-30,-14,18,2,-14,2,10,18,-2,-2,-2,2,2,-2,-2,-2,2,-2,5,1,-3,-3,1,0,0,0,0,1,-1,
1,0,0,0,0,0,0,0,0,0,0],[1155,-525,195,-45,35,-13,-17,7,11,-1,-13,3,-5,-1,3,-1,
-1,-1,-1,1,-1,3,-3,3,-3,3,0,0,0,0,-1,1,-1,0,0,0,0,-1,-1,1,1,0,0],[1155,-525,
195,-45,-13,3,7,-1,-5,-1,3,-1,7,3,-5,-1,3,-1,-1,1,-1,3,-3,3,-3,3,0,0,0,0,-1,1,
-1,0,0,0,0,1,1,-1,-1,0,0],[616,-56,-24,8,24,-8,0,0,-8,0,8,4,4,-4,0,0,0,4,-4,0,
0,4,-2,-4,2,0,1,-1,-1,1,0,0,0,0,0,0,0,2,-2,0,0,0,0],[616,-56,-24,8,24,-8,0,0,
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0,0,0,0,0,0,0,-4,2,0,0,0,0,0,0,0,0,0,0,2,2,2,1,-1,1,-1,0,0,0,0,0,0],[2640,-960
,240,0,48,0,-24,0,0,12,0,0,0,0,0,0,0,0,4,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1,1,
-1,0,0,0,0,0,0],[3360,0,-160,0,32,0,0,0,0,-8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-4,
0,0,0,0,2,0,-2,0,0,0,0,0,0,0,0,E(11)+E(11)^3+E(11)^4+E(11)^5+E(11)^9,
E(11)^2+E(11)^6+E(11)^7+E(11)^8+E(11)^10],
[GALOIS,[8,2]],[3696,1344,336,0,-48,0,-24,0,0,-12,0,0,0,0,0,0,0,0,4,2,0,0,0,0
,0,0,1,-1,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0],[3696,1344,336,0,16,0,8,0,0,4,0,0,0,
0,0,0,0,0,-4,-2,0,0,0,0,0,0,1,-1,-1,1,-2,2,-2,0,0,0,0,0,0,0,0,0,0],[3696,-1344
,336,0,-48,0,24,0,0,-12,0,0,0,0,0,0,0,0,4,-2,0,0,0,0,0,0,1,1,1,1,0,0,0,0,0,0,0
,0,0,0,0,0,0],[3696,-1344,336,0,16,0,-8,0,0,4,0,0,0,0,0,0,0,0,-4,2,0,0,0,0,0,0
,1,1,1,1,-2,-2,-2,0,0,0,0,0,0,0,0,0,0],[4224,1536,384,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,-1,1,1,-1,0,0,0,E(7)+E(7)^2+E(7)^4,E(7)+E(7)^2+E(7)^4,
E(7)^3+E(7)^5+E(7)^6,E(7)^3+E(7)^5+E(7)^6,0,0,0,0,0,0],[4224,-1536,384,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,-1,0,0,0,E(7)+E(7)^2+E(7)^4,
-E(7)-E(7)^2-E(7)^4,E(7)^3+E(7)^5+E(7)^6,-E(7)^3-E(7)^5-E(7)^6,0,0,0,0,0,0],
[GALOIS,[14,3]],
[GALOIS,[15,3]],[6720,0,-320,0,64,0,0,0,0,-16,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,4
,0,0,0,0,-2,0,2,0,0,0,0,0,0,0,0,-1,-1],[6720,0,-320,0,-64,0,0,0,0,16,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,4,0,0,0,0,2,0,-2,0,0,0,0,0,0,0,0,-1,-1],[7392,0,-352,0,
-32,0,0,0,0,8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-4,2,0,0,-2,-2,0,2,0,0,0,0,0,0,0,0
,0,0],[8064,0,-384,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,
-E(5)+E(5)^2+E(5)^3-E(5)^4,E(5)-E(5)^2-E(5)^3+E(5)^4,1,0,0,0,0,0,0,0,0,0,0,0,1
,1],
[GALOIS,[21,2]]],]);
ALF("2^10:m22","Fi22",[1,2,3,4,3,4,10,13,9,12,11,9,11,13,27,28,29,13,12,
30,29,7,19,22,24,23,14,34,34,35,23,47,44,26,51,26,51,27,29,53,54,36,37],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("2^10:m22","Fi22.2M4",[1,2,3,4,5,6,9,11,7,10,8,17,18,19,21,22,20,24,
23,26,25,12,14,13,15,16,27,29,29,28,30,32,31,33,34,35,36,37,38,39,39,40,
40],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("2^10:m22","M22",[1,1,1,1,2,2,2,2,2,2,2,4,4,4,4,4,4,5,5,5,5,3,3,3,3,3,
6,6,6,6,7,7,7,8,8,9,9,10,10,10,10,11,12]);
ALN("2^10:m22",["f22m5"]);

MOT("2.Fi22M5",
[
"origin: computed from the character tables of Fi22M5, Fi22, and 2.Fi22,\n",
"the table is sorted w.r.t. the normal series 2 < 2^11 < 2^11.M22"
],
[908328960,908328960,41287680,41287680,3932160,3932160,589824,49152,49152,
8192,6144,6144,1024,4096,3072,3072,4096,512,512,256,128,128,128,128,256,256,
64,64,64,1152,1152,288,288,1152,1152,288,288,192,192,40,40,40,40,40,40,40,40,
96,96,48,48,96,96,28,28,28,28,28,28,28,28,32,32,32,32,22,22,22,22],
[,[1,1,1,1,1,1,1,1,1,1,5,5,5,6,7,7,6,9,9,8,14,14,17,8,10,10,15,15,17,30,30,30,
30,30,30,30,30,30,30,40,40,40,40,40,40,40,40,30,30,38,38,34,34,54,54,54,54,58,
58,58,58,18,19,23,23,68,68,66,66],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,
18,19,20,21,22,23,24,25,26,27,28,29,1,2,3,4,7,7,7,7,5,6,40,41,44,45,42,43,46,
47,8,9,11,12,15,16,58,59,60,61,54,55,56,57,62,63,64,65,66,67,68,69],,[1,2,3,4,
5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,
32,33,34,35,36,37,38,39,1,2,3,4,3,4,5,6,48,49,50,51,52,53,58,59,60,61,54,55,
56,57,62,63,65,64,66,67,68,69],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,
19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,44,45,42,
43,46,47,48,49,50,51,52,53,1,2,3,4,1,2,3,4,62,63,65,64,68,69,66,67],,,,[1,2,3,
4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,
32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,
58,59,60,61,62,63,64,65,1,2,1,2]],
0,
[(66,68)(67,69),(64,65),(42,44)(43,45),(54,58)(55,59)(56,60)(57,61),( 3, 4)
(11,12)(27,28)(32,33)(36,37)(42,43)(44,45)(50,51)(56,57)(60,61)],
["ConstructProj",[["2^10:m22",[]],["2.Fi22M5",[]]]]);
ALF("2.Fi22M5","2^10:m22",[1,1,2,2,3,3,4,5,5,6,7,7,8,9,10,10,11,12,13,14,15,
16,17,18,19,19,20,20,21,22,22,23,23,24,24,25,25,26,26,27,27,28,28,29,29,30,30,
31,31,32,32,33,33,34,34,35,35,36,36,37,37,38,39,40,41,42,42,43,43]);
ALF("2.Fi22M5","2.Fi22",[1,2,3,4,5,6,7,5,6,7,17,18,22,16,20,21,19,16,19,
22,48,49,50,22,20,21,51,52,50,12,13,33,34,38,39,42,43,40,41,23,24,59,60,
59,60,61,62,40,41,81,82,77,78,46,47,89,90,46,47,89,90,48,50,93,94,63,64,
65,66],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("2.Fi22M5","M22",[1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,5,5,5,
5,5,5,3,3,3,3,3,3,3,3,3,3,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,9,9,9,9,10,
10,10,10,11,11,12,12]);

MOT("3.Fi22M5",
[
"5th maximal subgroup of 3.Fi22,\n",
"computed in March 2000 by Thomas Breuer using character theoretic methods\n",
"from the known tables of Fi22, 3.Fi22, and Fi22M5"
],
[1362493440,1362493440,1362493440,61931520,61931520,61931520,5898240,5898240,
5898240,1769472,1769472,1769472,73728,73728,73728,24576,24576,24576,9216,9216,
9216,3072,3072,3072,12288,12288,12288,4608,4608,4608,12288,12288,12288,1536,
1536,1536,1536,1536,1536,768,768,768,384,384,384,384,384,384,384,384,384,384,
384,384,384,384,384,96,96,96,192,192,192,576,144,576,144,288,288,288,60,60,60,
60,60,60,60,60,60,60,60,60,144,144,144,72,72,72,144,144,144,42,42,42,42,42,42,
42,42,42,42,42,42,96,96,96,96,96,96,96,96,96,96,96,96,33,33,33,33,33,33],
[,[1,3,2,1,3,2,1,3,2,1,3,2,1,3,2,1,3,2,7,9,8,7,9,8,7,9,8,10,12,11,7,9,8,13,15,
14,13,15,14,13,15,14,25,27,26,25,27,26,31,33,32,13,15,14,16,18,17,28,30,29,31,
33,32,64,64,64,64,64,64,64,71,73,72,71,73,72,71,73,72,71,73,72,64,64,64,68,70,
69,66,66,66,92,94,93,92,94,93,98,100,99,98,100,99,34,36,35,37,39,38,49,51,50,
49,51,50,119,121,120,116,118,117],[1,1,1,4,4,4,7,7,7,10,10,10,13,13,13,16,16,
16,19,19,19,22,22,22,25,25,25,28,28,28,31,31,31,34,34,34,37,37,37,40,40,40,43,
43,43,46,46,46,49,49,49,52,52,52,55,55,55,58,58,58,61,61,61,1,4,10,10,7,7,7,
71,71,71,77,77,77,74,74,74,80,80,80,13,13,13,19,19,19,28,28,28,98,98,98,101,
101,101,92,92,92,95,95,95,104,104,104,107,107,107,110,110,110,113,113,113,116,
116,116,119,119,119],,[1,3,2,4,6,5,7,9,8,10,12,11,13,15,14,16,18,17,19,21,20,
22,24,23,25,27,26,28,30,29,31,33,32,34,36,35,37,39,38,40,42,41,43,45,44,46,48,
47,49,51,50,52,54,53,55,57,56,58,60,59,61,63,62,64,65,66,67,68,70,69,1,3,2,4,
6,5,4,6,5,7,9,8,83,85,84,86,88,87,89,91,90,98,100,99,101,103,102,92,94,93,95,
97,96,104,106,105,107,109,108,113,115,114,110,112,111,116,118,117,119,121,
120],,[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,
53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,77,78,79,74,75,
76,80,81,82,83,84,85,86,87,88,89,90,91,1,2,3,4,5,6,1,2,3,4,5,6,104,105,106,
107,108,109,113,114,115,110,111,112,119,120,121,116,117,118],,,,[1,3,2,4,6,5,
7,9,8,10,12,11,13,15,14,16,18,17,19,21,20,22,24,23,25,27,26,28,30,29,31,33,32,
34,36,35,37,39,38,40,42,41,43,45,44,46,48,47,49,51,50,52,54,53,55,57,56,58,60,
59,61,63,62,64,65,66,67,68,70,69,71,73,72,74,76,75,77,79,78,80,82,81,83,85,84,
86,88,87,89,91,90,92,94,93,95,97,96,98,100,99,101,103,102,104,106,105,107,109,
108,110,112,111,113,115,114,1,3,2,1,3,2]],
0,
[(110,113)(111,114)(112,115),( 92, 98)( 93, 99)( 94,100)( 95,101)( 96,102)
( 97,103),( 74, 77)( 75, 78)( 76, 79),(116,119)(117,120)(118,121),(  2,  3)
(  5,  6)(  8,  9)( 11, 12)( 14, 15)( 17, 18)( 20, 21)( 23, 24)( 26, 27)
( 29, 30)( 32, 33)( 35, 36)( 38, 39)( 41, 42)( 44, 45)( 47, 48)( 50, 51)
( 53, 54)( 56, 57)( 59, 60)( 62, 63)( 69, 70)( 72, 73)( 75, 76)( 78, 79)
( 81, 82)( 84, 85)( 87, 88)( 90, 91)( 93, 94)( 96, 97)( 99,100)(102,103)
(105,106)(108,109)(111,112)(114,115)(117,118)(120,121)],
["ConstructProj",[["2^10:m22",[]],,["3.Fi22M5",[2,8,8,2,23,23,2,2,2,2,2,11,11,
2,2,2,8,8,2,2,2,2,2,2,2,2,2,2,2,17,2,17,2,2,2,2,2,2,2]]]]);
ALF("3.Fi22M5","2^10:m22",[1,1,1,2,2,2,3,3,3,4,4,4,5,5,5,6,6,6,7,7,7,8,8,
8,9,9,9,10,10,10,11,11,11,12,12,12,13,13,13,14,14,14,15,15,15,16,16,16,17,
17,17,18,18,18,19,19,19,20,20,20,21,21,21,22,23,24,25,26,26,26,27,27,27,
28,28,28,29,29,29,30,30,30,31,31,31,32,32,32,33,33,33,34,34,34,35,35,35,
36,36,36,37,37,37,38,38,38,39,39,39,40,40,40,41,41,41,42,42,42,43,43,43]);
ALF("3.Fi22M5","3.Fi22",[1,3,2,4,6,5,7,9,8,10,12,11,7,9,8,10,12,11,22,24,
23,31,33,32,19,21,20,28,30,29,25,27,26,19,21,20,25,27,26,31,33,32,63,65,
64,66,68,67,69,71,70,31,33,32,28,30,29,72,74,73,69,71,70,17,49,54,58,55,
57,56,34,36,35,80,82,81,80,82,81,83,85,84,55,57,56,113,115,114,106,106,
106,60,62,61,123,125,124,60,62,61,123,125,124,63,65,64,69,71,70,129,131,
130,132,134,133,86,88,87,89,91,90],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);
ALF("3.Fi22M5","3.M22",[1,2,3,1,2,3,1,2,3,1,2,3,4,5,6,4,5,6,4,5,6,4,5,6,4,
5,6,4,5,6,4,5,6,8,9,10,8,9,10,8,9,10,8,9,10,8,9,10,8,9,10,11,12,13,11,12,
13,11,12,13,11,12,13,7,7,7,7,7,7,7,14,15,16,14,15,16,14,15,16,14,15,16,17,
18,19,17,18,19,17,18,19,20,21,22,20,21,22,23,24,25,23,24,25,26,27,28,26,
27,28,26,27,28,26,27,28,29,30,31,32,33,34]);

MOT("6.Fi22M5",
[
"5th maximal subgroup of 6.Fi22,\n",
"constructed in March 2000 by Thomas Breuer, using the known tables of\n",
"3.Fi22M5, 2.Fi22M5, and 6.Fi22"
],
[2724986880,2724986880,2724986880,2724986880,2724986880,2724986880,123863040,
123863040,123863040,123863040,123863040,123863040,11796480,11796480,11796480,
11796480,11796480,11796480,1769472,1769472,1769472,147456,147456,147456,
147456,147456,147456,24576,24576,24576,18432,18432,18432,18432,18432,18432,
3072,3072,3072,12288,12288,12288,9216,9216,9216,9216,9216,9216,12288,12288,
12288,1536,1536,1536,1536,1536,1536,768,768,768,384,384,384,384,384,384,384,
384,384,384,384,384,768,768,768,768,768,768,192,192,192,192,192,192,192,192,
192,1152,1152,288,288,1152,1152,288,288,576,576,576,576,576,576,120,120,120,
120,120,120,120,120,120,120,120,120,120,120,120,120,120,120,120,120,120,120,
120,120,288,288,288,288,288,288,144,144,144,144,144,144,288,288,288,288,288,
288,84,84,84,84,84,84,84,84,84,84,84,84,84,84,84,84,84,84,84,84,84,84,84,84,
96,96,96,96,96,96,96,96,96,96,96,96,66,66,66,66,66,66,66,66,66,66,66,66],
[,[1,3,5,1,3,5,1,3,5,1,3,5,1,3,5,1,3,5,1,3,5,1,3,5,1,3,5,1,3,5,13,15,17,13,15,
17,13,15,17,16,18,14,19,21,20,19,21,20,16,18,14,25,27,23,25,27,23,22,24,26,40,
42,41,40,42,41,49,51,50,22,24,26,28,30,29,28,30,29,43,45,47,43,45,47,49,51,50,
88,88,88,88,88,88,88,88,88,88,88,88,88,88,102,104,106,102,104,106,102,104,106,
102,104,106,102,104,106,102,104,106,102,104,106,102,104,106,88,88,88,88,88,88,
96,98,100,96,98,100,92,92,92,92,92,92,144,146,148,144,146,148,144,146,148,144,
146,148,156,158,160,156,158,160,156,158,160,156,158,160,52,54,53,55,57,56,67,
69,68,67,69,68,186,188,190,186,188,190,180,182,184,180,182,184],[1,4,1,4,1,4,
7,10,7,10,7,10,13,16,13,16,13,16,19,19,19,22,25,22,25,22,25,28,28,28,31,34,31,
34,31,34,37,37,37,40,40,40,43,46,43,46,43,46,49,49,49,52,52,52,55,55,55,58,58,
58,61,61,61,64,64,64,67,67,67,70,70,70,73,76,73,76,73,76,79,82,79,82,79,82,85,
85,85,1,4,7,10,19,19,19,19,13,16,13,16,13,16,102,105,102,105,102,105,114,117,
114,117,114,117,108,111,108,111,108,111,120,123,120,123,120,123,22,25,22,25,
22,25,31,34,31,34,31,34,43,46,43,46,43,46,156,159,156,159,156,159,162,165,162,
165,162,165,144,147,144,147,144,147,150,153,150,153,150,153,168,168,168,171,
171,171,174,174,174,177,177,177,180,183,180,183,180,183,186,189,186,189,186,
189],,[1,6,5,4,3,2,7,12,11,10,9,8,13,18,17,16,15,14,19,21,20,22,27,26,25,24,
23,28,30,29,31,36,35,34,33,32,37,39,38,40,42,41,43,48,47,46,45,44,49,51,50,52,
54,53,55,57,56,58,60,59,61,63,62,64,66,65,67,69,68,70,72,71,73,78,77,76,75,74,
79,84,83,82,81,80,85,87,86,88,89,90,91,92,93,94,95,96,101,100,99,98,97,1,6,5,
4,3,2,7,12,11,10,9,8,7,12,11,10,9,8,13,18,17,16,15,14,126,131,130,129,128,127,
132,137,136,135,134,133,138,143,142,141,140,139,156,161,160,159,158,157,162,
167,166,165,164,163,144,149,148,147,146,145,150,155,154,153,152,151,168,170,
169,171,173,172,177,179,178,174,176,175,180,185,184,183,182,181,186,191,190,
189,188,187],,[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,
102,103,104,105,106,107,114,115,116,117,118,119,108,109,110,111,112,113,120,
121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,
140,141,142,143,1,2,3,4,5,6,7,8,9,10,11,12,1,2,3,4,5,6,7,8,9,10,11,12,168,169,
170,171,172,173,177,178,179,174,175,176,186,187,188,189,190,191,180,181,182,
183,184,185],,,,[1,6,5,4,3,2,7,12,11,10,9,8,13,18,17,16,15,14,19,21,20,22,27,
26,25,24,23,28,30,29,31,36,35,34,33,32,37,39,38,40,42,41,43,48,47,46,45,44,49,
51,50,52,54,53,55,57,56,58,60,59,61,63,62,64,66,65,67,69,68,70,72,71,73,78,77,
76,75,74,79,84,83,82,81,80,85,87,86,88,89,90,91,92,93,94,95,96,101,100,99,98,
97,102,107,106,105,104,103,108,113,112,111,110,109,114,119,118,117,116,115,
120,125,124,123,122,121,126,131,130,129,128,127,132,137,136,135,134,133,138,
143,142,141,140,139,144,149,148,147,146,145,150,155,154,153,152,151,156,161,
160,159,158,157,162,167,166,165,164,163,168,170,169,171,173,172,174,176,175,
177,179,178,1,6,5,4,3,2,1,6,5,4,3,2]],
0,
[(180,186)(181,187)(182,188)(183,189)(184,190)(185,191),(174,177)(175,178)
(176,179),(108,114)(109,115)(110,116)(111,117)(112,118)(113,119),(144,156)
(145,157)(146,158)(147,159)(148,160)(149,161)(150,162)(151,163)(152,164)
(153,165)(154,166)(155,167),(  7, 10)(  8, 11)(  9, 12)( 31, 34)( 32, 35)
( 33, 36)( 79, 82)( 80, 83)( 81, 84)( 90, 91)( 94, 95)(108,111)(109,112)
(110,113)(114,117)(115,118)(116,119)(132,135)(133,136)(134,137)(150,153)
(151,154)(152,155)(162,165)(163,166)(164,167),(  2,  6)(  3,  5)(  8, 12)
(  9, 11)( 14, 18)( 15, 17)( 20, 21)( 23, 27)( 24, 26)( 29, 30)( 32, 36)
( 33, 35)( 38, 39)( 41, 42)( 44, 48)( 45, 47)( 50, 51)( 53, 54)( 56, 57)
( 59, 60)( 62, 63)( 65, 66)( 68, 69)( 71, 72)( 74, 78)( 75, 77)( 80, 84)
( 81, 83)( 86, 87)( 97,101)( 98,100)(103,107)(104,106)(109,113)(110,112)
(115,119)(116,118)(121,125)(122,124)(127,131)(128,130)(133,137)(134,136)
(139,143)(140,142)(145,149)(146,148)(151,155)(152,154)(157,161)(158,160)
(163,167)(164,166)(169,170)(172,173)(175,176)(178,179)(181,185)(182,184)
(187,191)(188,190)],
["ConstructProj",[["2^10:m22",[]],["2.Fi22M5",[]],["3.Fi22M5",[2,8,8,2,23,23,
2,2,2,2,2,11,11,2,2,2,8,8,2,2,2,2,2,2,2,2,2,2,2,17,2,17,2,2,2,2,2,2,2]],,,
["6.Fi22M5",[5,5,5,5,5,5,5,23,23,5,5,5,5,29,29,29,29,5,5,5,11,11]]]]);
ALF("6.Fi22M5","2^10:m22",[1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,5,5,
5,5,5,5,6,6,6,7,7,7,7,7,7,8,8,8,9,9,9,10,10,10,10,10,10,11,11,11,12,12,12,
13,13,13,14,14,14,15,15,15,16,16,16,17,17,17,18,18,18,19,19,19,19,19,19,
20,20,20,20,20,20,21,21,21,22,22,23,23,24,24,25,25,26,26,26,26,26,26,27,
27,27,27,27,27,28,28,28,28,28,28,29,29,29,29,29,29,30,30,30,30,30,30,31,
31,31,31,31,31,32,32,32,32,32,32,33,33,33,33,33,33,34,34,34,34,34,34,35,
35,35,35,35,35,36,36,36,36,36,36,37,37,37,37,37,37,38,38,38,39,39,39,40,
40,40,41,41,41,42,42,42,42,42,42,43,43,43,43,43,43]);
ALF("6.Fi22M5","2.Fi22M5",[1,2,1,2,1,2,3,4,3,4,3,4,5,6,5,6,5,6,7,7,7,8,9,
8,9,8,9,10,10,10,11,12,11,12,11,12,13,13,13,14,14,14,15,16,15,16,15,16,17,
17,17,18,18,18,19,19,19,20,20,20,21,21,21,22,22,22,23,23,23,24,24,24,25,
26,25,26,25,26,27,28,27,28,27,28,29,29,29,30,31,32,33,34,35,36,37,38,39,
38,39,38,39,40,41,40,41,40,41,42,43,42,43,42,43,44,45,44,45,44,45,46,47,
46,47,46,47,48,49,48,49,48,49,50,51,50,51,50,51,52,53,52,53,52,53,54,55,
54,55,54,55,56,57,56,57,56,57,58,59,58,59,58,59,60,61,60,61,60,61,62,62,
62,63,63,63,64,64,64,65,65,65,66,67,66,67,66,67,68,69,68,69,68,69]);
ALF("6.Fi22M5","3.Fi22M5",[1,2,3,1,2,3,4,5,6,4,5,6,7,8,9,7,8,9,10,11,12,
13,14,15,13,14,15,16,17,18,19,20,21,19,20,21,22,23,24,25,26,27,28,29,30,
28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,
52,53,54,55,56,57,55,56,57,58,59,60,58,59,60,61,62,63,64,64,65,65,66,66,
67,67,68,69,70,68,69,70,71,72,73,71,72,73,74,75,76,74,75,76,77,78,79,77,
78,79,80,81,82,80,81,82,83,84,85,83,84,85,86,87,88,86,87,88,89,90,91,89,
90,91,92,93,94,92,93,94,95,96,97,95,96,97,98,99,100,98,99,100,101,102,103,
101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,
116,117,118,119,120,121,119,120,121]);
ALF("6.Fi22M5","6.Fi22",[1,6,5,4,3,2,7,12,11,10,9,8,13,18,17,16,15,14,19,
21,20,13,18,17,16,15,14,19,21,20,37,42,41,40,39,38,52,54,53,34,36,35,46,
51,50,49,48,47,43,45,44,34,36,35,43,45,44,52,54,53,110,112,111,113,115,
114,116,118,117,52,54,53,46,51,50,49,48,47,119,124,123,122,121,120,116,
118,117,30,31,85,86,92,93,100,101,94,99,98,97,96,95,55,60,59,58,57,56,135,
140,139,138,137,136,135,140,139,138,137,136,141,146,145,144,143,142,94,99,
98,97,96,95,189,194,193,192,191,190,181,182,181,182,181,182,104,109,108,
107,106,105,209,214,213,212,211,210,104,109,108,107,106,105,209,214,213,
212,211,210,110,112,111,116,118,117,221,223,222,224,226,225,147,152,151,
150,149,148,153,158,157,156,155,154],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);
ALF("6.Fi22M5","3.M22",[1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,4,5,6,4,
5,6,4,5,6,4,5,6,4,5,6,4,5,6,4,5,6,4,5,6,4,5,6,4,5,6,8,9,10,8,9,10,8,9,10,
8,9,10,8,9,10,8,9,10,11,12,13,11,12,13,11,12,13,11,12,13,11,12,13,11,12,
13,7,7,7,7,7,7,7,7,7,7,7,7,7,7,14,15,16,14,15,16,14,15,16,14,15,16,14,15,
16,14,15,16,14,15,16,14,15,16,17,18,19,17,18,19,17,18,19,17,18,19,17,18,
19,17,18,19,20,21,22,20,21,22,20,21,22,20,21,22,23,24,25,23,24,25,23,24,
25,23,24,25,26,27,28,26,27,28,26,27,28,26,27,28,29,30,31,29,30,31,32,33,
34,32,33,34]);

MOT("2^6:s6f2",
[
"origin: CAS library,\n",
"maximal subgroup of Fi22,\n",
"1987   O.B.\n",
"tests: 1.o.r., pow[2,3,5,7]"
],
[92897280,1474560,737280,49152,46080,73728,24576,6144,24576,8192,6144,3072,
3072,3072,1024,1024,34560,2304,648,432,144,1536,512,1536,512,384,1536,512,384,
512,512,256,128,128,128,128,120,40,576,192,1152,384,288,72,192,192,96,72,72,
24,24,7,32,32,32,32,9,20,20,48,48,48,48,12,15,144,48],
[,[1,1,1,1,2,1,1,2,1,1,2,2,1,2,2,2,17,17,19,20,20,6,7,9,9,11,9,9,11,6,7,7,9,
10,11,11,37,37,17,18,17,17,18,19,17,18,18,20,21,20,21,52,30,31,22,23,57,37,38,
45,46,45,46,44,65,20,20],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,1,2,1,1,2,22,
23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,6,8,3,4,5,6,9,11,12,3,5,13,14,
52,53,54,55,56,19,58,59,24,26,27,29,22,37,6,7],,[1,2,3,4,5,6,7,8,9,10,11,12,
13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,1,2,
39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,3,5,60,61,62,63,64,
17,66,67],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,
26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,
1,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67]],
[[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],[7,7,-5,-5,-5,-1,
-1,-1,3,3,3,3,-1,-1,-1,-1,4,4,-2,1,1,3,3,1,1,1,-3,-3,-3,-1,-1,-1,1,1,1,1,2,2,
2,2,-2,-2,-2,2,0,0,0,1,1,-1,-1,0,1,1,-1,-1,1,0,0,-2,-2,0,0,0,-1,-1,-1],[15,15,
-5,-5,-5,7,7,7,3,3,3,3,-1,-1,-1,-1,0,0,-3,3,3,-1,-1,-3,-3,-3,1,1,1,3,3,3,1,1,
1,1,0,0,-2,-2,-2,-2,-2,1,0,0,0,1,1,-1,-1,1,-1,-1,1,1,0,0,0,0,0,-2,-2,-1,0,1,
1],[21,21,9,9,9,-3,-3,-3,1,1,1,1,-3,-3,-3,-3,6,6,3,0,0,5,5,-1,-1,-1,3,3,3,1,1,
1,-1,-1,-1,-1,1,1,0,0,0,0,0,3,-2,-2,-2,0,0,0,0,0,1,1,-1,-1,0,-1,-1,2,2,0,0,-1,
1,0,0],[21,21,-11,-11,-11,5,5,5,5,5,5,5,-3,-3,-3,-3,6,6,3,0,0,1,1,-3,-3,-3,-3,
-3,-3,1,1,1,1,1,1,1,1,1,2,2,-2,-2,-2,-1,2,2,2,-2,-2,0,0,0,-1,-1,-1,-1,0,-1,-1,
0,0,0,0,1,1,2,2],[27,27,15,15,15,3,3,3,7,7,7,7,3,3,3,3,9,9,0,0,0,3,3,1,1,1,5,
5,5,-1,-1,-1,1,1,1,1,2,2,3,3,3,3,3,0,1,1,1,0,0,0,0,-1,-1,-1,1,1,0,0,0,1,1,-1,
-1,0,-1,0,0],[35,35,-5,-5,-5,3,3,3,-5,-5,-5,-5,3,3,3,3,5,5,-1,2,2,7,7,-1,-1,
-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,0,0,-3,-3,1,1,1,3,1,1,1,-2,-2,0,0,0,1,1,1,1,
-1,0,0,-1,-1,-1,-1,1,0,0,0],[35,35,15,15,15,11,11,11,7,7,7,7,3,3,3,3,5,5,-1,2,
2,-1,-1,5,5,5,1,1,1,3,3,3,1,1,1,1,0,0,-1,-1,3,3,3,-1,1,1,1,0,0,0,0,0,1,1,-1,
-1,-1,0,0,-1,-1,1,1,-1,0,2,2],[56,56,-24,-24,-24,-8,-8,-8,8,8,8,8,0,0,0,0,11,
11,2,2,2,0,0,4,4,4,-4,-4,-4,0,0,0,0,0,0,0,1,1,1,1,-3,-3,-3,-2,-1,-1,-1,0,0,0,
0,0,0,0,0,0,-1,1,1,1,1,-1,-1,0,1,-2,-2],[70,70,-10,-10,-10,-10,-10,-10,6,6,6,
6,-2,-2,-2,-2,-5,-5,7,1,1,2,2,2,2,2,2,2,2,2,2,2,-2,-2,-2,-2,0,0,-1,-1,-1,-1,
-1,-1,3,3,3,-1,-1,1,1,0,0,0,0,0,1,0,0,-1,-1,-1,-1,-1,0,-1,-1],[84,84,4,4,4,20,
20,20,4,4,4,4,4,4,4,4,-6,-6,3,3,3,4,4,0,0,0,0,0,0,4,4,4,0,0,0,0,-1,-1,2,2,-2,
-2,-2,-1,-2,-2,-2,1,1,1,1,0,0,0,0,0,0,-1,-1,0,0,0,0,1,-1,-1,-1],[105,105,-35,
-35,-35,1,1,1,5,5,5,5,1,1,1,1,15,15,-3,-3,-3,5,5,-1,-1,-1,-5,-5,-5,1,1,1,-1,
-1,-1,-1,0,0,1,1,1,1,1,1,-1,-1,-1,1,1,1,1,0,-1,-1,1,1,0,0,0,-1,-1,1,1,-1,0,1,
1],[105,105,5,5,5,17,17,17,-3,-3,-3,-3,-7,-7,-7,-7,0,0,6,3,3,-3,-3,3,3,3,-1,
-1,-1,1,1,1,-1,-1,-1,-1,0,0,2,2,2,2,2,2,0,0,0,-1,-1,-1,-1,0,-1,-1,1,1,0,0,0,0,
0,2,2,0,0,-1,-1],[105,105,25,25,25,-7,-7,-7,9,9,9,9,1,1,1,1,0,0,6,3,3,-3,-3,
-3,-3,-3,-3,-3,-3,-3,-3,-3,1,1,1,1,0,0,-4,-4,4,4,4,2,0,0,0,1,1,1,1,0,-1,-1,-1,
-1,0,0,0,0,0,0,0,0,0,-1,-1],[120,120,40,40,40,-8,-8,-8,8,8,8,8,0,0,0,0,15,15,
-6,0,0,0,0,-4,-4,-4,4,4,4,0,0,0,0,0,0,0,0,0,1,1,1,1,1,-2,-1,-1,-1,-2,-2,0,0,1,
0,0,0,0,0,0,0,-1,-1,1,1,0,0,-2,-2],[168,168,40,40,40,8,8,8,8,8,8,8,8,8,8,8,6,
6,6,-3,-3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,-2,2,2,-2,-2,-2,2,2,2,2,1,1,-1,-1,
0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1,-1],[189,189,21,21,21,-3,-3,-3,-11,-11,-11,-11,
-3,-3,-3,-3,9,9,0,0,0,9,9,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-3,-3,-3,-3,-3,0,1,
1,1,0,0,0,0,0,-1,-1,-1,-1,0,1,1,1,1,1,1,0,-1,0,0],[189,189,-39,-39,-39,21,21,
21,1,1,1,1,-3,-3,-3,-3,9,9,0,0,0,-3,-3,-5,-5,-5,-1,-1,-1,1,1,1,-1,-1,-1,-1,-1,
-1,3,3,3,3,3,0,1,1,1,0,0,0,0,0,1,1,-1,-1,0,1,1,1,1,-1,-1,0,-1,0,0],[189,189,
-51,-51,-51,-3,-3,-3,13,13,13,13,-3,-3,-3,-3,9,9,0,0,0,-3,-3,1,1,1,1,1,1,-3,
-3,-3,1,1,1,1,-1,-1,-3,-3,-3,-3,-3,0,1,1,1,0,0,0,0,0,1,1,1,1,0,-1,-1,1,1,1,1,
0,-1,0,0],[210,210,50,50,50,2,2,2,2,2,2,2,-6,-6,-6,-6,15,15,3,0,0,-2,-2,2,2,2,
2,2,2,-2,-2,-2,-2,-2,-2,-2,0,0,-1,-1,-1,-1,-1,-1,-1,-1,-1,2,2,0,0,0,0,0,0,0,0,
0,0,-1,-1,-1,-1,1,0,2,2],[210,210,10,10,10,-14,-14,-14,10,10,10,10,2,2,2,2,
-15,-15,-6,3,3,6,6,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,0,0,1,1,1,1,1,-2,1,
1,1,1,1,-1,-1,0,0,0,0,0,0,0,0,1,1,1,1,0,0,1,1],[216,216,-24,-24,-24,24,24,24,
8,8,8,8,0,0,0,0,-9,-9,0,0,0,0,0,-4,-4,-4,4,4,4,0,0,0,0,0,0,0,1,1,-3,-3,-3,-3,
-3,0,-1,-1,-1,0,0,0,0,-1,0,0,0,0,0,1,1,-1,-1,1,1,0,1,0,0],[280,280,-40,-40,
-40,-8,-8,-8,-8,-8,-8,-8,8,8,8,8,10,10,10,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,-2,-2,2,2,2,-2,-2,-2,-2,-1,-1,-1,-1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,1],[280,
280,40,40,40,24,24,24,8,8,8,8,0,0,0,0,-5,-5,-8,-2,-2,0,0,4,4,4,-4,-4,-4,0,0,0,
0,0,0,0,0,0,-3,-3,1,1,1,0,-1,-1,-1,-2,-2,0,0,0,0,0,0,0,1,0,0,1,1,-1,-1,0,0,0,
0],[315,315,-45,-45,-45,-21,-21,-21,3,3,3,3,3,3,3,3,0,0,-9,0,0,-5,-5,3,3,3,3,
3,3,3,3,3,-1,-1,-1,-1,0,0,0,0,0,0,0,3,0,0,0,0,0,0,0,0,-1,-1,-1,-1,0,0,0,0,0,0,
0,1,0,0,0],[336,336,-16,-16,-16,16,16,16,-16,-16,-16,-16,0,0,0,0,6,6,-6,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,-2,-2,2,2,2,-2,2,2,2,2,2,0,0,0,0,0,0,0,0,-1,
-1,0,0,0,0,0,1,-2,-2],[378,378,-30,-30,-30,-6,-6,-6,2,2,2,2,-6,-6,-6,-6,-9,-9,
0,0,0,6,6,2,2,2,2,2,2,-2,-2,-2,2,2,2,2,-2,-2,3,3,3,3,3,0,-1,-1,-1,0,0,0,0,0,0,
0,0,0,0,0,0,-1,-1,-1,-1,0,1,0,0],[405,405,45,45,45,-27,-27,-27,-3,-3,-3,-3,-3,
-3,-3,-3,0,0,0,0,0,-3,-3,-3,-3,-3,-3,-3,-3,5,5,5,1,1,1,1,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,-1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0],[420,420,20,20,20,4,4,4,-12,-12,
-12,-12,4,4,4,4,0,0,-3,3,3,-4,-4,0,0,0,0,0,0,-4,-4,-4,0,0,0,0,0,0,4,4,-4,-4,
-4,1,0,0,0,-1,-1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,1,1],[512,512,0,0,0,0,0,0,0,
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0,0,0,0,0,0,1,0,0,0,0,-1,0,0,0,0,0,0,0,-1,0,0],[63,-1,31,-1,-1,15,-1,-1,15,-1,
-1,-1,7,-1,-1,-1,15,-1,0,3,-1,3,-1,7,-1,-1,7,-1,-1,3,-1,-1,3,-1,-1,-1,3,-1,3,
-1,7,-1,-1,0,3,-1,-1,1,-1,1,-1,0,1,-1,1,-1,0,1,-1,1,-1,1,-1,0,0,3,-1],[63,-1,
-29,3,-1,-9,7,-1,11,-5,3,-1,-1,-5,3,-1,15,-1,0,3,-1,3,-1,5,-3,1,-7,1,1,-1,3,
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1,0,0,-3,1],[315,-5,95,-1,-5,3,19,-5,23,7,-1,-5,11,7,-1,-5,30,-2,0,-3,1,3,-1,
-3,5,-3,9,1,-3,-1,3,-1,1,1,-3,1,0,0,6,-2,2,2,-2,0,2,2,-2,-1,1,-1,1,0,-1,1,1,
-1,0,0,0,0,0,0,0,0,0,-3,1],[315,-5,-85,11,-5,27,11,-5,11,-5,11,-5,-5,-13,3,3,
30,-2,0,-3,1,3,-1,-9,-1,3,-9,-1,3,3,-1,-1,-1,3,-1,-1,0,0,6,-2,2,2,-2,0,2,2,-2,
-1,1,1,-1,0,-1,1,-1,1,0,0,0,0,0,0,0,0,0,3,-1],[315,-5,35,3,-5,-21,27,-5,19,3,
3,-5,3,3,3,-5,-15,1,0,6,-2,3,-1,-5,3,-1,-5,3,-1,-5,7,-1,-1,3,-1,-1,0,0,-3,1,5,
-3,1,0,1,-3,1,2,-2,0,0,0,-1,1,-1,1,0,0,0,1,-1,1,-1,0,0,0,0],[315,-5,-25,7,-5,
51,3,-5,15,-1,7,-5,3,-9,-1,3,-15,1,0,6,-2,3,-1,-7,1,1,5,-3,1,7,-5,-1,1,1,-3,1,
0,0,-3,1,-7,1,1,0,-3,1,1,2,-2,0,0,0,-1,1,1,-1,0,0,0,-1,1,-1,1,0,0,0,0],[567,
-9,99,3,-9,63,15,-9,27,11,3,-9,15,3,-5,-1,0,0,0,0,0,3,-1,9,1,-3,-3,5,-3,7,-5,
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0],[567,-9,-81,15,-9,-9,39,-9,15,-1,15,-9,-9,-9,7,-1,0,0,0,0,0,3,-1,3,-5,3,3,
-5,3,-5,7,-1,3,-1,-1,-1,-3,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1,1,-1,0,-1,1,0,0,
0,0,0,0,0,0],[630,-10,70,6,-10,6,38,-10,-10,22,6,-10,-2,14,-2,-2,15,-1,0,3,-1,
-6,2,2,2,-2,2,2,-2,-6,2,2,-2,-2,2,2,0,0,3,-1,-5,3,-1,0,-1,3,-1,1,-1,1,-1,0,0,
0,0,0,0,0,0,-1,1,-1,1,0,0,3,-1],[630,-10,-50,14,-10,54,22,-10,-18,14,14,-10,
-10,-2,-2,6,15,-1,0,3,-1,-6,2,-2,-2,2,-2,-2,2,2,-6,2,-2,-2,2,2,0,0,3,-1,7,-1,
-1,0,3,-1,-1,1,-1,-1,1,0,0,0,0,0,0,0,0,1,-1,1,-1,0,0,-3,1],[1008,-16,16,16,
-16,48,48,-16,16,16,16,-16,0,0,0,0,-30,2,0,-6,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
3,-1,-6,2,-2,-2,2,0,-2,-2,2,-2,2,0,0,0,0,0,0,0,0,1,-1,0,0,0,0,0,0,0,0],[378,
-6,114,-14,6,-6,-6,2,18,-14,10,-2,-6,6,-2,2,45,-3,0,0,0,6,-2,-2,-2,2,14,-2,-2,
-2,-2,2,-2,2,2,-2,3,-1,3,-1,3,-5,3,0,-3,1,1,0,0,0,0,0,0,0,0,0,0,-1,1,1,-1,-1,
1,0,0,0,0],[378,-6,-126,2,6,-6,-6,2,34,2,-6,-2,-6,6,-2,2,45,-3,0,0,0,6,-2,2,2,
-2,-14,2,2,-2,-2,2,2,-2,-2,2,3,-1,3,-1,-9,-1,3,0,1,-3,1,0,0,0,0,0,0,0,0,0,0,
-1,1,-1,1,1,-1,0,0,0,0],[1512,-24,216,-40,24,-24,-24,8,-8,-8,24,-8,0,0,0,0,45,
-3,0,0,0,0,0,-4,-4,4,4,4,-4,0,0,0,0,0,0,0,-3,1,3,-1,-9,-1,3,0,1,-3,1,0,0,0,0,
0,0,0,0,0,0,1,-1,-1,1,1,-1,0,0,0,0],[1512,-24,-264,-8,24,-24,-24,8,24,24,-8,
-8,0,0,0,0,45,-3,0,0,0,0,0,4,4,-4,-4,-4,4,0,0,0,0,0,0,0,-3,1,3,-1,3,-5,3,0,-3,
1,1,0,0,0,0,0,0,0,0,0,0,1,-1,1,-1,-1,1,0,0,0,0],[1890,-30,90,-38,30,-30,-30,
10,26,-6,18,-10,-6,6,-2,2,-45,3,0,0,0,6,-2,-2,-2,2,-10,6,-2,-2,-2,2,2,-2,-2,2,
0,0,-3,1,9,1,-3,0,-1,3,-1,0,0,0,0,0,0,0,0,0,0,0,0,1,-1,-1,1,0,0,0,0],[1890,
-30,-150,-22,30,-30,-30,10,42,10,2,-10,-6,6,-2,2,-45,3,0,0,0,6,-2,2,2,-2,10,
-6,2,-2,-2,2,-2,2,2,-2,0,0,-3,1,-3,5,-3,0,3,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,-1,
1,1,-1,0,0,0,0],[2268,-36,-36,-36,36,-36,-36,12,-36,28,12,-12,12,-12,4,-4,0,0,
0,0,0,-12,4,0,0,0,0,0,0,4,4,-4,0,0,0,0,3,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,-1,1,0,0,0,0,0,0,0,0],[630,-10,110,-18,10,-42,22,-2,14,-18,6,2,-2,2,-6,6,
15,-1,0,3,-1,-6,2,-10,6,-2,-2,-2,2,2,2,-2,2,-2,2,-2,0,0,-3,1,5,-3,1,0,-1,3,-1,
-1,1,1,-1,0,0,0,0,0,0,0,0,-1,1,1,-1,0,0,-3,1],[630,-10,-130,-2,10,54,-10,-2,
30,-2,-10,2,-10,10,2,-2,15,-1,0,3,-1,-6,2,-14,2,2,2,2,-2,2,2,-2,2,-2,2,-2,0,0,
-3,1,-7,1,1,0,3,-1,-1,-1,1,-1,1,0,0,0,0,0,0,0,0,1,-1,-1,1,0,0,3,-1],[630,-10,
110,-18,10,54,-10,-2,14,-18,6,2,-10,10,2,-2,15,-1,0,3,-1,-6,2,14,-2,-2,-2,-2,
2,2,2,-2,-2,2,-2,2,0,0,-3,1,5,-3,1,0,-1,3,-1,-1,1,-1,1,0,0,0,0,0,0,0,0,-1,1,1,
-1,0,0,3,-1],[630,-10,-130,-2,10,-42,22,-2,30,-2,-10,2,-2,2,-6,6,15,-1,0,3,-1,
-6,2,10,-6,2,2,2,-2,2,2,-2,-2,2,-2,2,0,0,-3,1,-7,1,1,0,3,-1,-1,-1,1,1,-1,0,0,
0,0,0,0,0,0,1,-1,-1,1,0,0,-3,1],[1260,-20,-20,-20,20,12,12,-4,-52,12,-4,4,12,
-12,4,-4,30,-2,0,6,-2,12,-4,0,0,0,0,0,0,-4,-4,4,0,0,0,0,0,0,-6,2,-2,-2,2,0,2,
2,-2,-2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[2520,-40,200,-56,40,24,24,-8,
-24,-24,8,8,0,0,0,0,15,-1,0,-6,2,0,0,4,4,-4,-4,-4,4,0,0,0,0,0,0,0,0,0,-3,1,-7,
1,1,0,3,-1,-1,2,-2,0,0,0,0,0,0,0,0,0,0,1,-1,-1,1,0,0,0,0],[2520,-40,-280,-24,
40,24,24,-8,8,8,-24,8,0,0,0,0,15,-1,0,-6,2,0,0,-4,-4,4,4,4,-4,0,0,0,0,0,0,0,0,
0,-3,1,5,-3,1,0,-1,3,-1,2,-2,0,0,0,0,0,0,0,0,0,0,-1,1,1,-1,0,0,0,0],[2520,-40,
-40,-40,40,-72,56,-8,-8,-8,-8,8,8,-8,-8,8,-30,2,0,3,-1,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,6,-2,2,2,-2,0,-2,-2,2,-1,1,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,3,
-1],[2520,-40,-40,-40,40,120,-8,-8,-8,-8,-8,8,-8,8,8,-8,-30,2,0,3,-1,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,6,-2,2,2,-2,0,-2,-2,2,-1,1,1,-1,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,-3,1],[945,-15,225,1,-15,33,-15,1,49,1,-15,1,9,-15,1,1,45,-3,0,0,0,-3,
1,5,-3,1,5,-3,1,-3,1,1,1,-3,1,1,0,0,-3,1,9,1,-3,0,1,-3,1,0,0,0,0,0,-1,1,-1,1,
0,0,0,-1,1,-1,1,0,0,0,0],[945,-15,165,5,-15,-39,9,1,-3,13,-11,1,-15,-3,5,1,45,
-3,0,0,0,9,-3,-5,3,-1,7,-1,-1,5,1,-3,-1,-1,-1,3,0,0,-3,1,-3,5,-3,0,-3,1,1,0,0,
0,0,0,1,-1,-1,1,0,0,0,1,-1,1,-1,0,0,0,0],[945,-15,-135,25,-15,33,-15,1,-23,-7,
9,1,9,9,-7,1,45,-3,0,0,0,9,-3,-7,1,1,-7,1,1,1,5,-3,-3,1,1,1,0,0,-3,1,9,1,-3,0,
1,-3,1,0,0,0,0,0,1,-1,1,-1,0,0,0,-1,1,-1,1,0,0,0,0],[945,-15,-195,29,-15,-39,
9,1,21,-27,13,1,9,-3,5,-7,45,-3,0,0,0,-3,1,7,-1,-1,-5,3,-1,1,-3,1,-1,-1,3,-1,
0,0,-3,1,-3,5,-3,0,-3,1,1,0,0,0,0,0,-1,1,1,-1,0,0,0,1,-1,1,-1,0,0,0,0],[1890,
-30,90,26,-30,66,-30,2,26,-6,-6,2,18,-6,-6,2,-45,3,0,0,0,6,-2,-2,-2,2,-2,-2,2,
-2,6,-2,-2,-2,2,2,0,0,3,-1,-9,-1,3,0,-1,3,-1,0,0,0,0,0,0,0,0,0,0,0,0,1,-1,1,
-1,0,0,0,0],[1890,-30,-30,34,-30,-78,18,2,18,-14,2,2,-6,-6,10,-6,-45,3,0,0,0,
6,-2,2,2,-2,2,2,-2,6,-2,-2,-2,-2,2,2,0,0,3,-1,3,-5,3,0,3,-1,-1,0,0,0,0,0,0,0,
0,0,0,0,0,-1,1,-1,1,0,0,0,0],[2835,-45,315,27,-45,-45,3,3,27,11,-21,3,3,3,3,
-5,0,0,0,0,0,-9,3,-9,-1,3,-9,-1,3,-1,-5,3,-1,3,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,1,-1,1,-1,0,0,0,0,0,0,0,0,0,0,0],[2835,-45,135,39,-45,27,-21,3,-33,15,
-9,3,-21,-9,-1,11,0,0,0,0,0,3,-1,9,1,-3,-3,5,-3,-1,3,-1,1,1,1,-3,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,-1,1,1,-1,0,0,0,0,0,0,0,0,0,0,0],[2835,-45,-45,51,-45,-45,
3,3,-45,3,3,3,3,27,-5,-5,0,0,0,0,0,3,-1,3,-5,3,3,-5,3,3,-1,-1,3,-1,-1,-1,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,-1,1,0,0,0,0,0,0,0,0,0,0,0],[2835,-45,-225,
63,-45,27,-21,3,-9,-25,15,3,3,-9,-1,3,0,0,0,0,0,-9,3,-3,5,-3,9,1,-3,-5,-1,3,1,
1,-3,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1,-1,1,0,0,0,0,0,0,0,0,0,0,0]],
[]);
ALF("2^6:s6f2","Fi22",[1,3,2,4,10,4,3,9,3,4,9,13,4,10,13,11,5,18,8,7,23,
12,11,13,10,28,10,13,27,12,9,13,13,12,27,28,14,35,20,40,15,20,41,25,18,39,
46,19,47,24,47,26,30,28,30,29,33,34,59,46,63,41,64,48,52,22,23],[
"fusion map is unique, equal to that on the CAS table"
]);
ALF("2^6:s6f2","2^7:S6(2)",[1,2,5,6,7,11,12,13,17,18,19,20,25,26,27,28,33,
34,37,39,40,43,44,47,48,49,53,54,55,59,60,61,65,66,67,68,73,74,77,78,81,
82,83,87,89,90,91,95,96,99,100,103,105,106,109,110,113,115,116,119,120,
123,124,127,129,131,132],[
"fusion map is unique"
]);
ALF("2^6:s6f2","S6(2)",[1,1,2,2,2,3,3,3,4,4,4,4,5,5,5,5,6,6,7,8,8,9,9,10,
10,10,11,11,11,12,12,12,13,13,13,13,14,14,16,16,15,15,15,17,18,18,18,19,
19,21,21,22,24,24,23,23,25,26,26,27,27,28,28,29,30,20,20]);
ALN("2^6:s6f2",["2^6:S6(2)","f22m6"]);

MOT("f22s2",
[
"Sylow 2-subgroup and Sylow 2 normalizer in Fi22,\n",
"origin: CAS library,\n",
"tests: 1.o.r., pow[2],\n",
"2nd power map determined only up to matrix automorphisms,"
],
[131072,131072,65536,65536,65536,32768,32768,32768,32768,16384,16384,16384,
8192,8192,8192,8192,8192,8192,8192,4096,4096,4096,4096,4096,4096,4096,4096,
4096,2048,2048,2048,2048,2048,2048,2048,2048,2048,2048,2048,2048,2048,2048,
1024,1024,1024,1024,1024,1024,1024,1024,1024,1024,1024,512,512,4096,4096,2048,
2048,2048,2048,2048,2048,1024,1024,1024,1024,1024,1024,1024,1024,1024,1024,
1024,1024,1024,1024,1024,1024,1024,1024,1024,1024,1024,1024,1024,512,512,512,
512,512,512,512,512,512,512,512,512,512,512,512,512,512,512,512,512,512,512,
512,512,512,512,512,512,512,512,512,512,512,512,512,512,512,512,512,512,512,
512,512,512,512,512,256,256,256,256,256,256,256,256,256,256,256,256,256,256,
256,256,256,256,256,256,256,256,256,256,256,256,256,256,256,256,128,128,128,
128,128,128,128,128,128,128,128,128,128,128,128,128,128,128,64,64,128,128,128,
128,128,128,128,128,128,128,128,64,64,64,64,64,64,64,64,64,64,64,64,64,32,32,
32,32,32,32,32,32,32],
[,[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,4,2,2,4,2,10,6,10,4,10,4,10,2,4,4,4,
10,10,4,10,2,4,10,2,4,2,6,2,13,7,10,8,18,10,10,6,10,10,8,12,6,18,4,18,18,18,
10,5,18,4,13,7,10,12,10,10,18,12,10,18,6,2,18,10,4,10,2,6,18,18,18,12,12,12,
20,28,11,18,10,14,13,14,18,18,7,21,6,13,8,14,11,13,18,14,7,21,8,28,13,28,5,13,
20,28,30,20,21,20,13,28,32,16,30,20,25,28,25,30,30,32,32,32,31,40,57,59,60,59,
56,60,59,59,56,60,60,75,65,58,64,58,58,62,57,74,64,75,74,65,87,106,88,90,97,
109,110,183,183]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
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[(214,215),(202,205),(202,205)(214,215),( 45, 52)( 51, 53)(112,131)(116,132)
(169,179)(178,180),( 38, 42)( 51, 53)( 88,110)(112,116)(131,132)(143,153)
(178,180)(209,213),( 17, 19)( 29, 39)(156,162)(169,179)(178,180),( 44, 48)
( 84, 86)( 91,118)( 94,119)( 96,124)(103,121)(104,128)(107,129)(133,161)
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ALF("f22s2","2^(5+8):(S3xA6)",[1,2,3,2,4,2,4,4,3,5,6,2,5,6,6,6,14,5,17,5,
6,6,6,15,6,17,16,5,16,20,6,5,17,6,6,21,16,6,15,5,6,6,20,21,6,6,21,20,17,
22,6,6,5,22,22,7,8,8,7,24,7,8,23,28,7,30,25,19,25,31,29,26,7,8,27,18,23,
32,26,26,33,25,24,23,8,24,28,9,30,9,32,28,34,25,19,35,9,8,7,35,37,19,33,
35,34,9,27,37,27,9,33,8,34,27,36,7,32,30,26,37,31,31,29,36,29,8,18,36,28,
7,7,8,28,35,38,40,40,38,28,39,19,34,9,38,37,34,9,39,39,27,40,38,9,38,9,18,
34,36,9,34,27,19,77,40,39,40,40,19,19,39,79,34,39,40,39,78,80,19,19,18,39,
40,43,45,84,45,44,81,44,44,45,83,82,85,45,43,88,43,43,43,43,43,86,87,43,
44,88,46,46,46,46,87,46,91,92],[
"determined by the fusion 2.Fi22N2 -> 2.Fi22M10"
]);
ALF("f22s2","Fi22",[1,3,2,3,4,3,4,4,2,3,4,3,3,4,4,4,2,3,4,3,4,4,4,3,4,4,4,
3,4,3,4,3,4,4,4,4,4,4,3,3,4,4,3,4,4,4,4,3,4,4,4,4,3,4,4,9,11,11,9,9,9,11,
9,9,9,9,10,13,10,10,11,13,9,11,11,10,9,11,13,13,13,10,9,9,11,9,9,12,9,12,
11,9,13,10,13,13,12,11,9,13,13,13,13,13,13,12,11,13,11,12,13,11,13,11,10,
9,11,9,13,13,10,10,11,10,11,11,10,10,9,9,9,11,9,13,12,13,13,12,9,12,13,13,
12,12,13,13,12,12,12,11,13,12,12,12,12,10,13,10,12,13,11,13,13,13,12,13,
13,13,13,12,11,13,12,13,12,9,13,13,13,10,12,13,29,27,28,27,28,27,28,28,27,
27,28,29,27,29,27,29,29,29,29,29,28,29,29,28,27,30,30,30,30,29,30,53,54],[
"determined by the fusion 2.Fi22N2 -> 2.Fi22"
]);
ALN("f22s2",["Fi22N2"]);

MOT("g61",
[
"origin: CAS library,\n",
"names;g61\n",
"order: 2^4.3.5^4.13 = 390,000\n",
"number of classes: 61\n",
"source:generated by cayley-algorithms\n",
"and cas-system\n",
"aachen [1979]\n",
"test: 1. o.r., sym 2 decompose correctly\n",
"comments:frobenius-group \n",
"tests: 1.o.r., pow[2,3,5,13]"
],
[390000,156,156,156,156,156,156,156,156,156,156,156,156,156,156,156,156,156,
156,156,156,156,156,156,156,156,156,156,156,156,156,156,156,156,156,156,156,
312,312,312,624,624,312,624,16,16,16,16,16,16,16,16,48,48,48,48,24,24,24,24,
625],
[,[1,14,15,16,17,18,19,16,17,19,18,14,15,26,27,31,30,28,29,32,32,33,33,34,34,
28,29,30,31,26,27,35,36,37,36,37,35,40,40,43,44,44,43,1,53,54,55,56,56,55,54,
53,41,42,42,41,38,39,38,39,61],[1,20,21,24,25,22,23,25,24,22,23,21,20,32,32,
34,34,33,33,22,23,25,24,20,21,35,35,36,36,37,37,33,34,32,36,37,35,41,42,44,42,
41,1,44,47,48,52,51,46,45,49,50,55,56,53,54,56,55,53,54,61],,[1,2,3,4,5,6,7,8,
9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,
35,36,37,38,39,40,41,42,43,44,49,50,46,45,52,51,47,48,56,55,54,53,59,60,57,58,
1],,,,,,,,[1,38,39,39,38,39,38,38,39,39,38,39,38,40,40,40,40,40,40,41,42,42,
41,42,41,43,43,43,43,43,43,44,44,44,1,1,1,38,39,40,41,42,43,44,48,47,51,52,45,
46,50,49,56,55,54,53,59,60,57,58,61]],
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1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
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-1,-1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
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-E(4),-1,-1,-1,-1,-1,-1,-1,-1,1],
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[TENSOR,[2,5]],
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1],
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[TENSOR,[17,12]],
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E(13)+E(13)^5+E(13)^8+E(13)^12,E(13)+E(13)^5+E(13)^8+E(13)^12,
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E(13)+E(13)^5+E(13)^8+E(13)^12,E(13)+E(13)^5+E(13)^8+E(13)^12,
E(13)^2+E(13)^3+E(13)^10+E(13)^11,E(13)^2+E(13)^3+E(13)^10+E(13)^11,
E(13)^4+E(13)^6+E(13)^7+E(13)^9,E(13)^4+E(13)^6+E(13)^7+E(13)^9,
E(13)^2+E(13)^3+E(13)^10+E(13)^11,E(13)^2+E(13)^3+E(13)^10+E(13)^11,
E(13)^4+E(13)^6+E(13)^7+E(13)^9,E(13)^4+E(13)^6+E(13)^7+E(13)^9,
E(13)+E(13)^5+E(13)^8+E(13)^12,E(13)+E(13)^5+E(13)^8+E(13)^12,
E(13)^2+E(13)^3+E(13)^10+E(13)^11,E(13)^4+E(13)^6+E(13)^7+E(13)^9,
E(13)+E(13)^5+E(13)^8+E(13)^12,E(13)^4+E(13)^6+E(13)^7+E(13)^9,
E(13)+E(13)^5+E(13)^8+E(13)^12,E(13)^2+E(13)^3+E(13)^10+E(13)^11,4,4,4,4,4,4,
4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,4],
[GALOIS,[25,2]],
[GALOIS,[25,4]],
[TENSOR,[25,5]],
[TENSOR,[26,5]],
[TENSOR,[27,5]],[4,E(39)^4+E(39)^20+E(39)^22+E(39)^32,E(39)^7+E(39)^17
 +E(39)^19+E(39)^35,E(39)^23+E(39)^28+E(39)^29+E(39)^37,E(39)^2+E(39)^10
 +E(39)^11+E(39)^16,E(39)+E(39)^5+E(39)^8+E(39)^25,E(39)^14+E(39)^31+E(39)^34
 +E(39)^38,E(39)^23+E(39)^28+E(39)^29+E(39)^37,E(39)^2+E(39)^10+E(39)^11
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E(39)^4+E(39)^20+E(39)^22+E(39)^32,E(39)^7+E(39)^17+E(39)^19+E(39)^35,
E(39)+E(39)^5+E(39)^8+E(39)^25,E(39)^14+E(39)^31+E(39)^34+E(39)^38,
E(39)^7+E(39)^17+E(39)^19+E(39)^35,E(39)^4+E(39)^20+E(39)^22+E(39)^32,
E(39)^2+E(39)^10+E(39)^11+E(39)^16,E(39)^23+E(39)^28+E(39)^29+E(39)^37,
E(13)^4+E(13)^6+E(13)^7+E(13)^9,E(13)^4+E(13)^6+E(13)^7+E(13)^9,
E(13)+E(13)^5+E(13)^8+E(13)^12,E(13)+E(13)^5+E(13)^8+E(13)^12,
E(13)^2+E(13)^3+E(13)^10+E(13)^11,E(13)^2+E(13)^3+E(13)^10+E(13)^11,
E(39)^2+E(39)^10+E(39)^11+E(39)^16,E(39)^23+E(39)^28+E(39)^29+E(39)^37,
E(39)^4+E(39)^20+E(39)^22+E(39)^32,E(39)^7+E(39)^17+E(39)^19+E(39)^35,
E(39)+E(39)^5+E(39)^8+E(39)^25,E(39)^14+E(39)^31+E(39)^34+E(39)^38,
E(13)+E(13)^5+E(13)^8+E(13)^12,E(13)^2+E(13)^3+E(13)^10+E(13)^11,
E(13)^4+E(13)^6+E(13)^7+E(13)^9,E(13)^2+E(13)^3+E(13)^10+E(13)^11,
E(13)^4+E(13)^6+E(13)^7+E(13)^9,E(13)+E(13)^5+E(13)^8+E(13)^12,-2,-2,-2,4,4,
-2,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,4],
[GALOIS,[31,14]],
[GALOIS,[31,2]],
[GALOIS,[31,23]],
[GALOIS,[31,7]],
[GALOIS,[31,4]],
[TENSOR,[31,5]],
[TENSOR,[32,5]],
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[TENSOR,[25,10]],
[TENSOR,[26,9]],
[TENSOR,[26,10]],
[TENSOR,[27,9]],
[TENSOR,[27,10]],[624,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
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,-1]],
[(45,49,52,48)(46,50,51,47)(53,56)(54,55)(57,59)(58,60),(45,52)(46,51)(47,50)
(48,49),( 2, 7, 5,13,11, 8)( 3, 6, 4,12,10, 9)(14,19,17,15,18,16)(20,23,25)
(21,22,24)(26,29,30,27,28,31)(32,33,34)(35,36,37),( 2,12)( 3,13)( 4, 8)( 5, 9)
( 6,11)( 7,10)(20,21)(22,23)(24,25)(38,39)(41,42)(45,46)(47,48)(49,50)(51,52)
(53,54)(55,56)(57,58)(59,60),( 2,12)( 3,13)( 4, 8)( 5, 9)( 6,11)( 7,10)(20,21)
(22,23)(24,25)(38,39)(41,42)(45,50,52,47)(46,49,51,48)(53,55)(54,56)(57,60)
(58,59),( 2,13)( 3,12)( 4, 9)( 5, 8)( 6,10)( 7,11)(14,15)(16,17)(18,19)(26,27)
(28,29)(30,31),( 2,11, 5)( 3,10, 4)( 6, 9,12)( 7, 8,13)(14,18,17)(15,19,16)
(20,23,25)(21,22,24)(26,28,30)(27,29,31)(32,33,34)(35,36,37),( 2, 8,11,13, 5,
  7)( 3, 9,10,12, 4, 6)(14,16,18,15,17,19)(20,25,23)(21,24,22)(26,31,28,27,30,
 29)(32,34,33)(35,37,36)]);

MOT("g61s1",
[
"origin: CAS library,\n",
"names:=g61s1\n",
" order: 2^4.3.13 = 624\n",
" number of classes: 60\n",
" source:generated by cayley-algorithms\n",
"       and cas-system\n",
"       aachen [1979]\n",
" comments:factorgroup of index 625 in g61 \n",
"tests: 1.o.r., pow[2,3,13]"
],
[624,156,156,156,156,156,156,156,156,156,156,156,156,156,156,156,156,156,156,
156,156,156,156,156,156,156,156,156,156,156,156,156,156,156,156,156,156,312,
312,312,624,624,312,624,16,16,16,16,16,16,16,16,48,24,24,24,48,48,24,48],
[,[1,14,15,16,17,18,19,16,17,19,18,14,15,26,27,31,30,28,29,32,32,33,33,34,34,
28,29,30,31,26,27,35,36,37,36,37,35,40,40,43,44,44,43,1,53,53,60,60,53,53,60,
60,1,40,40,43,44,44,43,1],[1,20,21,24,25,22,23,25,24,22,23,21,20,32,32,34,34,
33,33,22,23,25,24,20,21,35,35,36,36,37,37,33,34,32,36,37,35,41,42,44,42,41,1,
44,46,45,48,47,50,49,52,51,53,57,58,60,58,57,53,60],,,,,,,,,,[1,38,39,39,38,
39,38,38,39,39,38,39,38,40,40,40,40,40,40,41,42,42,41,42,41,43,43,43,43,43,43,
44,44,44,1,1,1,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,
59,60]],
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[TENSOR,[2,3]],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
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E(13)^2+E(13)^3+E(13)^10+E(13)^11,E(13)^2+E(13)^3+E(13)^10+E(13)^11,
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E(13)^4+E(13)^6+E(13)^7+E(13)^9,E(13)^4+E(13)^6+E(13)^7+E(13)^9,
E(13)^2+E(13)^3+E(13)^10+E(13)^11,E(13)^2+E(13)^3+E(13)^10+E(13)^11,
E(13)^4+E(13)^6+E(13)^7+E(13)^9,E(13)^4+E(13)^6+E(13)^7+E(13)^9,
E(13)+E(13)^5+E(13)^8+E(13)^12,E(13)+E(13)^5+E(13)^8+E(13)^12,
E(13)^4+E(13)^6+E(13)^7+E(13)^9,E(13)^4+E(13)^6+E(13)^7+E(13)^9,
E(13)+E(13)^5+E(13)^8+E(13)^12,E(13)+E(13)^5+E(13)^8+E(13)^12,
E(13)^2+E(13)^3+E(13)^10+E(13)^11,E(13)^2+E(13)^3+E(13)^10+E(13)^11,
E(13)^4+E(13)^6+E(13)^7+E(13)^9,E(13)+E(13)^5+E(13)^8+E(13)^12,
E(13)^2+E(13)^3+E(13)^10+E(13)^11,E(13)+E(13)^5+E(13)^8+E(13)^12,
E(13)^2+E(13)^3+E(13)^10+E(13)^11,E(13)^4+E(13)^6+E(13)^7+E(13)^9,4,4,4,4,4,4,
4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[25,2]],
[GALOIS,[25,4]],
[TENSOR,[25,2]],
[TENSOR,[26,2]],
[TENSOR,[27,2]],
[TENSOR,[25,9]],
[TENSOR,[26,9]],
[TENSOR,[27,9]],
[TENSOR,[25,10]],
[TENSOR,[26,10]],
[TENSOR,[27,10]],[4,-E(39)^23-E(39)^28-E(39)^29-E(39)^37,-E(39)^2-E(39)^10
 -E(39)^11-E(39)^16,-E(39)-E(39)^5-E(39)^8-E(39)^25,-E(39)^14-E(39)^31
 -E(39)^34-E(39)^38,-E(39)^7-E(39)^17-E(39)^19-E(39)^35,-E(39)^4-E(39)^20
 -E(39)^22-E(39)^32,-E(39)-E(39)^5-E(39)^8-E(39)^25,-E(39)^14-E(39)^31
 -E(39)^34-E(39)^38,-E(39)^4-E(39)^20-E(39)^22-E(39)^32,-E(39)^7-E(39)^17
 -E(39)^19-E(39)^35,-E(39)^23-E(39)^28-E(39)^29-E(39)^37,-E(39)^2-E(39)^10
 -E(39)^11-E(39)^16,E(39)^7+E(39)^17+E(39)^19+E(39)^35,E(39)^4+E(39)^20
 +E(39)^22+E(39)^32,E(39)^2+E(39)^10+E(39)^11+E(39)^16,E(39)^23+E(39)^28
 +E(39)^29+E(39)^37,E(39)^14+E(39)^31+E(39)^34+E(39)^38,E(39)+E(39)^5+E(39)^8
 +E(39)^25,-E(13)^2-E(13)^3-E(13)^10-E(13)^11,-E(13)^2-E(13)^3-E(13)^10
 -E(13)^11,-E(13)^4-E(13)^6-E(13)^7-E(13)^9,-E(13)^4-E(13)^6-E(13)^7-E(13)^9,
-E(13)-E(13)^5-E(13)^8-E(13)^12,-E(13)-E(13)^5-E(13)^8-E(13)^12,
E(39)^14+E(39)^31+E(39)^34+E(39)^38,E(39)+E(39)^5+E(39)^8+E(39)^25,
E(39)^23+E(39)^28+E(39)^29+E(39)^37,E(39)^2+E(39)^10+E(39)^11+E(39)^16,
E(39)^7+E(39)^17+E(39)^19+E(39)^35,E(39)^4+E(39)^20+E(39)^22+E(39)^32,
E(13)^4+E(13)^6+E(13)^7+E(13)^9,E(13)+E(13)^5+E(13)^8+E(13)^12,
E(13)^2+E(13)^3+E(13)^10+E(13)^11,E(13)+E(13)^5+E(13)^8+E(13)^12,
E(13)^2+E(13)^3+E(13)^10+E(13)^11,E(13)^4+E(13)^6+E(13)^7+E(13)^9,2,2,-2,-4,
-4,-2,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[37,2]],
[TENSOR,[37,9]],
[TENSOR,[37,10]],
[GALOIS,[38,2]],
[TENSOR,[41,2]],
[GALOIS,[38,4]],
[GALOIS,[38,14]],
[TENSOR,[44,9]],
[TENSOR,[44,2]],
[TENSOR,[44,10]],
[TENSOR,[43,2]],
[TENSOR,[43,9]],
[TENSOR,[43,10]],
[TENSOR,[41,9]],
[TENSOR,[41,10]],
[GALOIS,[38,23]],
[TENSOR,[53,2]],
[GALOIS,[38,7]],
[TENSOR,[55,2]],
[TENSOR,[55,10]],
[TENSOR,[55,9]],
[TENSOR,[53,10]],
[TENSOR,[53,9]]],
[( 2, 7, 5,13,11, 8)( 3, 6, 4,12,10, 9)(14,19,17,15,18,16)(20,23,25)(21,22,24)
(26,29,30,27,28,31)(32,33,34)(35,36,37),( 2,12)( 3,13)( 4, 8)( 5, 9)( 6,11)
( 7,10)(20,21)(22,23)(24,25)(38,39)(41,42)(45,46)(47,48)(49,50)(51,52)(54,55)
(57,58),( 2,13)( 3,12)( 4, 9)( 5, 8)( 6,10)( 7,11)(14,15)(16,17)(18,19)(26,27)
(28,29)(30,31),( 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)(38,39)(41,42)(45,46)(47,48)(49,50)
(51,52)(54,55)(57,58),( 2,10, 5, 3,11, 4)( 6, 8,12, 7, 9,13)(14,19,17,15,18,16
 )(20,22,25,21,23,24)(26,29,30,27,28,31)(32,33,34)(35,36,37)(38,39)(41,42)
(45,46)(47,48)(49,50)(51,52)(54,55)(57,58),( 2, 9,11,12, 5, 6)( 3, 8,10,13, 4,
 7)(14,17,18)(15,16,19)(20,24,23,21,25,22)(26,30,28)(27,31,29)(32,34,33)
(35,37,36)(38,39)(41,42)(45,46)(47,48)(49,50)(51,52)(54,55)(57,58),( 2,11, 5)
( 3,10, 4)( 6, 9,12)( 7, 8,13)(14,18,17)(15,19,16)(20,23,25)(21,22,24)
(26,28,30)(27,29,31)(32,33,34)(35,36,37),( 2, 8,11,13, 5, 7)( 3, 9,10,12, 4, 6
 )(14,16,18,15,17,19)(20,25,23)(21,24,22)(26,31,28,27,30,29)(32,34,33)
(35,37,36),( 2,12)( 3,13)( 4, 8)( 5, 9)( 6,11)( 7,10)(20,21)(22,23)(24,25)
(38,39)(41,42)(47,51)(48,52)(54,55)(57,58),( 2,12)( 3,13)( 4, 8)( 5, 9)( 6,11)
( 7,10)(20,21)(22,23)(24,25)(38,39)(41,42)(45,49)(46,50)(54,55)(57,58),( 2,12)
( 3,13)( 4, 8)( 5, 9)( 6,11)( 7,10)(20,21)(22,23)(24,25)(38,39)(41,42)(45,47)
(46,48)(49,51)(50,52)(53,60)(56,59)]);

MOT("g72x16",
[
"origin: CAS library,\n",
" test:= 1. o.r., sym 2 decompose correctly  \n",
"tests: 1.o.r., pow[2,3]"
],
[1152,384,384,128,384,1152,384,144,48,144,144,1152,48,48,48,48,48,48,48,48,
288,288,192,128,384,48,48,96,96,192,48,48,48,48,384,64,128,64,144,384,48,48,
96,96,192,1152,48,48,288,288,192,48,384,64,36,36,192,192,64,36,36,192,36,36,
96,96,128,288,288,64,36,36,64,64,64,192,96,96,288,288],
[,[1,1,1,1,1,1,1,11,11,11,11,1,21,22,28,29,21,22,21,22,22,21,1,1,1,28,29,22,
21,2,28,29,11,11,1,1,1,2,11,1,28,29,22,21,1,1,21,22,22,21,2,11,1,1,64,63,2,1,
1,64,63,1,64,63,21,22,1,22,21,1,64,63,2,2,2,2,22,21,22,21],[1,2,3,4,5,6,7,12,
35,46,1,12,23,23,30,30,45,45,58,58,1,1,23,24,25,51,51,2,2,30,57,57,53,3,35,36,
37,38,6,40,76,76,5,5,45,46,62,62,6,6,51,7,53,54,12,12,57,58,59,46,46,62,1,1,
25,25,67,12,12,70,6,6,73,74,75,76,40,40,46,46]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,E(3)^2,E(3),E(3)^2,E(3),E(3)^2,E(3),E(3)^2,
E(3),E(3),E(3)^2,1,1,1,E(3)^2,E(3),E(3),E(3)^2,1,E(3)^2,E(3),1,1,1,1,1,1,1,1,
E(3)^2,E(3),E(3),E(3)^2,1,1,E(3)^2,E(3),E(3),E(3)^2,1,1,1,1,E(3),E(3)^2,1,1,1,
E(3),E(3)^2,1,E(3),E(3)^2,E(3)^2,E(3),1,E(3),E(3)^2,1,E(3),E(3)^2,1,1,1,1,
E(3),E(3)^2,E(3),E(3)^2],[1,1,1,1,1,1,1,1,1,1,1,1,-E(3),-E(3)^2,-E(3),-E(3)^2,
-E(3),-E(3)^2,-E(3),-E(3)^2,E(3)^2,E(3),-1,1,1,-E(3),-E(3)^2,E(3)^2,E(3),-1,
-E(3),-E(3)^2,1,1,1,-1,1,-1,1,1,-E(3),-E(3)^2,E(3)^2,E(3),-1,1,-E(3),-E(3)^2,
E(3)^2,E(3),-1,1,1,-1,E(3)^2,E(3),-1,-1,-1,E(3)^2,E(3),-1,E(3)^2,E(3),E(3),
E(3)^2,1,E(3)^2,E(3),-1,E(3)^2,E(3),-1,-1,-1,-1,E(3)^2,E(3),E(3)^2,E(3)],
[TENSOR,[2,2]],
[TENSOR,[2,3]],
[TENSOR,[2,5]],[1,1,1,1,1,1,1,-1,-1,-1,1,-1,E(3)^2,E(3),E(3)^2,E(3),E(3)^2,
E(3),-E(3)^2,-E(3),E(3),E(3)^2,1,1,-1,E(3)^2,E(3),E(3),E(3)^2,1,-E(3)^2,-E(3),
-1,1,-1,1,-1,1,1,-1,-E(3)^2,-E(3),E(3),E(3)^2,1,-1,-E(3)^2,-E(3),E(3),E(3)^2,
1,1,-1,1,-E(3),-E(3)^2,-1,-1,-1,-E(3),-E(3)^2,-1,E(3),E(3)^2,-E(3)^2,-E(3),-1,
-E(3),-E(3)^2,-1,E(3),E(3)^2,-1,1,-1,-1,-E(3),-E(3)^2,-E(3),-E(3)^2],
[TENSOR,[7,4]],
[TENSOR,[3,8]],
[TENSOR,[2,7]],
[TENSOR,[2,9]],
[TENSOR,[2,11]],[1,1,1,1,-1,-1,-1,1,1,-1,1,1,E(3)^2,E(3),E(3)^2,E(3),-E(3)^2,
-E(3),E(3)^2,E(3),E(3),E(3)^2,1,-1,1,-E(3)^2,-E(3),E(3),E(3)^2,1,E(3)^2,E(3),
-1,1,1,1,1,1,-1,-1,-E(3)^2,-E(3),-E(3),-E(3)^2,-1,-1,-E(3)^2,-E(3),-E(3),
-E(3)^2,-1,-1,-1,-1,E(3),E(3)^2,1,1,1,-E(3),-E(3)^2,-1,E(3),E(3)^2,E(3)^2,
E(3),-1,E(3),E(3)^2,-1,-E(3),-E(3)^2,1,-1,-1,-1,-E(3),-E(3)^2,-E(3),-E(3)^2],
[TENSOR,[13,4]],
[TENSOR,[3,14]],
[TENSOR,[2,13]],
[TENSOR,[2,15]],
[TENSOR,[2,17]],
[TENSOR,[7,14]],
[TENSOR,[7,16]],
[TENSOR,[3,20]],
[TENSOR,[2,19]],
[TENSOR,[2,21]],
[TENSOR,[2,23]],[2,2,2,2,2,2,2,-1,-1,-1,-1,2,0,0,0,0,0,0,0,0,2,2,0,2,2,0,0,2,
2,0,0,0,-1,-1,2,0,2,0,-1,2,0,0,2,2,0,2,0,0,2,2,0,-1,2,0,-1,-1,0,0,0,-1,-1,0,
-1,-1,2,2,2,2,2,0,-1,-1,0,0,0,0,2,2,2,2],
[TENSOR,[25,2]],
[TENSOR,[25,3]],
[TENSOR,[25,20]],
[TENSOR,[25,19]],
[TENSOR,[25,21]],
[TENSOR,[25,7]],
[TENSOR,[25,8]],
[TENSOR,[25,9]],
[TENSOR,[25,14]],
[TENSOR,[25,13]],
[TENSOR,[25,15]],[3,3,-1,-1,3,3,-1,3,-1,3,3,3,0,0,0,0,0,0,0,0,0,0,3,-1,3,0,0,
0,0,3,0,0,-1,-1,-1,-1,-1,-1,3,3,0,0,0,0,3,3,0,0,0,0,3,-1,-1,-1,0,0,3,3,-1,0,0,
3,0,0,0,0,-1,0,0,-1,0,0,-1,-1,-1,3,0,0,0,0],
[TENSOR,[37,3]],
[TENSOR,[37,7]],
[TENSOR,[37,9]],
[TENSOR,[37,13]],
[TENSOR,[37,15]],
[TENSOR,[37,19]],
[TENSOR,[37,21]],[3,-1,3,-1,1,-3,-3,0,0,0,0,3,E(3)^2,E(3),-E(3)^2,-E(3),
-E(3)^2,-E(3),E(3)^2,E(3),3*E(3),3*E(3)^2,1,1,-1,E(3)^2,E(3),-E(3),-E(3)^2,-1,
-E(3)^2,-E(3),0,0,3,1,-1,-1,0,1,E(3)^2,E(3),E(3),E(3)^2,-1,-3,-E(3)^2,-E(3),
-3*E(3),-3*E(3)^2,1,0,-3,-1,0,0,-1,1,1,0,0,-1,0,0,-E(3)^2,-E(3),1,3*E(3),
3*E(3)^2,-1,0,0,-1,1,1,1,E(3),E(3)^2,-3*E(3),-3*E(3)^2],
[TENSOR,[45,4]],
[TENSOR,[45,6]],
[TENSOR,[45,2]],
[TENSOR,[45,3]],
[TENSOR,[45,5]],
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[TENSOR,[45,12]],
[TENSOR,[45,7]],
[TENSOR,[45,9]],
[TENSOR,[45,11]],
[TENSOR,[45,14]],
[TENSOR,[45,16]],
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[TENSOR,[45,20]],
[TENSOR,[45,22]],
[TENSOR,[45,24]],
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[TENSOR,[45,21]],
[TENSOR,[45,23]],[6,6,-2,-2,6,6,-2,-3,1,-3,-3,6,0,0,0,0,0,0,0,0,0,0,0,-2,6,0,
0,0,0,0,0,0,1,1,-2,0,-2,0,-3,6,0,0,0,0,0,6,0,0,0,0,0,1,-2,0,0,0,0,0,0,0,0,0,0,
0,0,0,-2,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[69,19]],
[TENSOR,[69,7]],
[TENSOR,[69,13]],[9,-3,-3,1,3,-9,3,0,0,0,0,9,0,0,0,0,0,0,0,0,0,0,3,-1,-3,0,0,
0,0,-3,0,0,0,0,-3,-1,1,1,0,3,0,0,0,0,-3,-9,0,0,0,0,3,0,3,1,0,0,-3,3,-1,0,0,-3,
0,0,0,0,-1,0,0,1,0,0,1,-1,-1,3,0,0,0,0],
[TENSOR,[73,3]],
[TENSOR,[73,7]],
[TENSOR,[73,9]],
[TENSOR,[73,13]],
[TENSOR,[73,15]],
[TENSOR,[73,19]],
[TENSOR,[73,21]]],
[(13,14)(15,16)(17,18)(19,20)(21,22)(26,27)(28,29)(31,32)(41,42)(43,44)(47,48)
(49,50)(55,56)(60,61)(63,64)(65,66)(68,69)(71,72)(77,78)(79,80),( 8,10)( 9,33)
(12,46)(19,47)(20,48)(25,40)(31,41)(32,42)(35,53)(37,67)(55,60)(56,61)(57,76)
(58,62)(59,70)(65,78)(66,77)(68,79)(69,80)(73,75),( 5,25)( 6,12)( 7,35)( 8,39)
( 9,52)(17,19)(18,20)(24,37)(26,31)(27,32)(43,66)(44,65)(45,58)(49,68)(50,69)
(51,57)(54,59)(55,71)(56,72)(73,74),( 8,10)( 9,33)(12,46)(13,17)(14,18)(15,26)
(16,27)(23,45)(25,40)(30,51)(35,53)(36,54)(37,67)(38,74)(55,60)(56,61)(65,78)
(66,77)(68,79)(69,80)]);

MOT("ghh",
[
"origin: CAS library,\n",
"tests: 1.o.r., pow[2,3,5]"
],
0,
0,
0,
0,
["ConstructPermuted",["5^(1+2):4S4"],(2,4,20,26,24,9,12)(3,6,15,18,7,8,10,16,
19,27,25,13)(5,14,23,11,17)(21,22),(1,4)(2,3)(5,9)(6,10)(7,8)(11,14)(17,26,18,
27,19)(20,23,21,22)]);

MOT("gl25",
[
"origin: CAS library,\n",
"names:=gl25\n",
" order: 2^5.3.5 = 480\n",
" number of classes: 24\n",
" source:generated by cas-algorithms\n",
"        aachen [1981]\n",
" comments: - \n",
"tests: 1.o.r., pow[2,3,5]"
],
[480,480,480,480,20,20,20,20,16,16,16,16,16,16,24,24,24,24,24,24,24,24,24,24],
[,[1,3,1,3,5,7,5,7,10,1,10,10,3,10,16,18,2,20,23,20,4,16,18,23],[1,4,3,2,5,8,
7,6,11,10,9,14,13,12,17,2,21,3,21,1,17,17,4,21],,[1,2,3,4,1,2,3,4,9,10,11,12,
13,14,15,16,17,18,19,20,21,22,23,24]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,-1,1,-1,1,-1,1,-1,E(4),
-1,-E(4),-E(4),1,E(4),E(4),-1,-E(4),1,-E(4),1,E(4),E(4),-1,-E(4)],
[TENSOR,[2,2]],
[TENSOR,[2,3]],[5,5,5,5,0,0,0,0,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],
[TENSOR,[5,2]],
[TENSOR,[5,3]],
[TENSOR,[5,4]],[6,6*E(4),-6,-6*E(4),1,E(4),-1,-E(4),1+E(4),0,1-E(4),-1+E(4),0,
-1-E(4),0,0,0,0,0,0,0,0,0,0],[6,-6,6,-6,1,-1,1,-1,0,2,0,0,-2,0,0,0,0,0,0,0,0,
0,0,0],
[TENSOR,[9,4]],
[TENSOR,[9,2]],
[TENSOR,[10,2]],
[TENSOR,[9,3]],[4,4*E(4),-4,-4*E(4),-1,-E(4),1,E(4),0,0,0,0,0,0,
-E(24)+E(24)^17,-E(4),0,-1,-E(24)^11+E(24)^19,1,0,E(24)-E(24)^17,E(4),
E(24)^11-E(24)^19],[4,-4,4,-4,-1,1,-1,1,0,0,0,0,0,0,-E(4),-1,-2*E(4),1,E(4),1,
2*E(4),-E(4),-1,E(4)],[4,-4*E(4),-4,4*E(4),-1,E(4),1,-E(4),0,0,0,0,0,0,0,
-2*E(4),0,2,0,-2,0,0,2*E(4),0],
[TENSOR,[16,4]],
[TENSOR,[15,2]],
[TENSOR,[16,2]],
[TENSOR,[17,2]],
[TENSOR,[15,3]],
[TENSOR,[16,3]],
[TENSOR,[15,4]]],
[(15,22)(19,24),( 9,14)(11,12),( 2, 4)( 6, 8)( 9,11)(12,14)(15,19)(16,23)
(17,21)(22,24),( 2, 4)( 6, 8)( 9,11)(12,14)(15,24)(16,23)(17,21)(19,22)]);
ALF("gl25","A5.2",[1,1,1,1,4,4,4,4,6,2,6,6,2,6,7,3,5,3,7,3,5,7,3,7]);

MOT("group2",
[
"origin: CAS library,\n",
"names:group2\n",
"order: 2^9 = 512\n",
"number of classes: 41\n",
"source;generated by cas-algorithms\n",
"aachen [1980]\n",
"test: 1. o.r. satisfied\n",
"comments:p-group \n",
"tests: 1.o.r., pow[2]"
],
[512,64,128,32,16,32,128,64,256,512,64,64,256,512,512,64,16,64,32,32,32,32,32,
32,32,64,64,16,16,16,16,32,64,64,128,128,128,16,128,64,64],
[,[1,3,1,1,7,10,10,3,10,1,3,3,1,10,10,1,9,10,10,1,35,36,13,36,35,10,10,41,16,
41,16,13,1,1,13,13,13,7,13,10,1],[1,2,3,4,5,6,7,8,9,10,12,11,13,15,14,16,17,
18,19,20,22,21,23,25,24,27,26,28,29,30,31,32,33,34,36,35,37,38,39,40,41],,[1,
2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,
30,31,32,33,34,35,36,37,38,39,40,41]],
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1,1,1,1,1,-1,-1,-1,-1,1,1,1,1,1,1,-1,1,1,1],
[TENSOR,[2,3]],[1,-1,1,1,-1,1,1,-1,1,1,-1,-1,1,1,1,1,-1,1,-1,-1,1,1,-1,1,1,-1,
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[TENSOR,[2,5]],
[TENSOR,[3,5]],
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0,0,0,0,0,0,-2,0,2,0,0,0,0,2,2,-2,0,-2,-2,2],
[TENSOR,[10,2]],[2,2,2,0,0,0,2,2,2,2,2,2,2,2,2,-2,-2,-2,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,2,2,2,0,2,-2,-2],[2,0,-2,0,0,0,2,0,-2,2,0,0,2,-2,-2,2,0,-2,0,0,0,0,
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[TENSOR,[15,2]],
[TENSOR,[12,5]],[2,0,2,2,0,2,2,0,2,2,0,0,2,2,2,2,0,2,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,-2,-2,-2,-2,-2,-2,-2],
[TENSOR,[9,3]],
[TENSOR,[18,3]],[2,0,-2,0,0,0,2,0,-2,2,0,0,2,-2,-2,-2,0,2,0,0,2*E(4),-2*E(4),
0,-2*E(4),2*E(4),0,0,0,0,0,0,0,0,0,-2,-2,2,0,2,2,-2],
[TENSOR,[21,2]],[4,0,-4,0,0,0,-4,0,4,4,0,0,4,4,4,0,0,0,0,0,0,0,-2,0,0,2,2,0,0,
0,0,-2,2,2,0,0,0,0,0,0,0],
[TENSOR,[23,2]],[4,2,0,-2,0,2,0,2,4,4,-2,-2,-4,-4,-4,0,0,0,2,-2,0,0,0,0,0,0,0,
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[TENSOR,[25,3]],
[TENSOR,[25,5]],
[TENSOR,[25,7]],[4,0,4,0,0,0,-4,0,-4,4,0,0,4,-4,-4,0,0,0,0,0,0,0,2,0,0,2,2,0,
0,0,0,-2,-2,-2,0,0,0,0,0,0,0],
[TENSOR,[29,2]],[4,-2,0,0,0,0,0,2,0,-4,-2*E(4),2*E(4),0,4*E(4),-4*E(4),0,0,0,
0,0,-1-E(4),-1+E(4),0,1-E(4),1+E(4),2*E(4),-2*E(4),0,0,0,0,0,-2,2,-2*E(4),
2*E(4),-2,0,2,0,0],
[TENSOR,[31,2]],
[TENSOR,[31,5]],
[TENSOR,[31,6]],
[GALOIS,[31,3]],
[TENSOR,[35,2]],
[TENSOR,[35,5]],
[TENSOR,[35,6]],[8,0,0,0,0,0,0,0,-8,8,0,0,-8,8,8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0],[8,0,0,0,0,0,0,0,0,-8,0,0,0,8*E(4),-8*E(4),0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,4*E(4),-4*E(4),4,0,-4,0,0],
[GALOIS,[40,3]]],
[(29,31),(28,30),(11,12)(14,15)(21,22)(24,25)(26,27)(35,36),( 4,20)( 5,38)
( 6,19)(16,41)(18,40)(28,29)(30,31),( 2, 8)(14,15)(21,24)(22,25)(26,27)
(35,36),(11,12)(14,15)(21,24)(22,25)(33,34)(35,36)]);

MOT("group3",
[
"origin: CAS library,\n",
"names:=group3\n",
" order:3^2.7 = 63\n",
" number of classes:15\n",
" source:generated by dixon-algorithm\n",
"        aachen  [1981]\n",
" test: 1. o.r. satisfied\n",
" comments:-\n",
"tests: 1.o.r., pow[3,7]"
],
[63,63,63,21,21,21,21,9,9,9,9,9,9,21,21],
[,,[1,1,1,15,14,15,14,2,3,3,2,2,3,15,14],,,,[1,2,3,2,3,3,2,11,10,13,12,8,9,1,
1]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,E(3)^2,E(3),E(3)^2,E(3),E(3),E(3)^2,
-E(9)^2-E(9)^5,-E(9)^4-E(9)^7,E(9)^7,E(9)^2,E(9)^5,E(9)^4,1,1],
[GALOIS,[2,5]],
[GALOIS,[2,7]],
[TENSOR,[2,4]],
[TENSOR,[3,5]],
[TENSOR,[2,2]],
[TENSOR,[2,7]],
[TENSOR,[2,3]],[3,3,3,E(7)+E(7)^2+E(7)^4,E(7)^3+E(7)^5+E(7)^6,
E(7)+E(7)^2+E(7)^4,E(7)^3+E(7)^5+E(7)^6,0,0,0,0,0,0,E(7)+E(7)^2+E(7)^4,
E(7)^3+E(7)^5+E(7)^6],
[GALOIS,[10,3]],
[TENSOR,[10,2]],
[TENSOR,[10,3]],
[TENSOR,[11,2]],
[TENSOR,[11,3]]],
[(4,7)(5,6)(14,15),(2,3)(4,6)(5,7)(8,9)(10,11)(12,13),(8,11,12)(9,10,13)]);

MOT("group5",
[
"origin: CAS library,\n",
"tests: 1.o.r., pow[2,3,7]"
],
[1176,49,49,49,49,49,49,49,49,49,49,49,49,49,49,392,392,6,6,168,6,6,56,56],
[,[1,4,5,8,9,10,11,7,6,14,15,2,3,13,12,16,17,19,18,1,18,19,16,17],[1,6,7,10,
11,12,13,14,15,2,3,9,8,4,5,17,16,1,1,20,20,20,24,23],,[1,6,7,10,11,12,13,14,
15,2,3,9,8,4,5,17,16,19,18,20,22,21,24,23],,[1,16,17,16,17,17,16,16,17,17,16,
16,17,17,16,1,1,18,19,20,21,22,20,20]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,E(3)^2,E(3),1,E(3),E(3)^2,1,1],
[TENSOR,[2,2]],[3,E(49)^5-E(49)^10-E(49)^17-E(49)^24-E(49)^31-E(49)^38
 +E(49)^41-E(49)^45,-E(49)^4+E(49)^8-E(49)^11-E(49)^18-E(49)^25-E(49)^32
 -E(49)^39+E(49)^44,E(49)^6+E(49)^10+E(49)^33,E(49)^16+E(49)^39+E(49)^43,
E(49)^9+E(49)^15+E(49)^25,E(49)^24+E(49)^34+E(49)^40,E(49)^12+E(49)^17
 +E(49)^20,E(49)^29+E(49)^32+E(49)^37,-E(49)^8-E(49)^15+E(49)^18-E(49)^22
 -E(49)^29+E(49)^30-E(49)^36-E(49)^43,-E(49)^6-E(49)^13+E(49)^19-E(49)^20
 -E(49)^27+E(49)^31-E(49)^34-E(49)^41,E(49)^26+E(49)^27+E(49)^45,
E(49)^4+E(49)^22+E(49)^23,-E(49)^9+E(49)^11-E(49)^16-E(49)^23-E(49)^30
 +E(49)^36-E(49)^37-E(49)^44,-E(49)^5-E(49)^12+E(49)^13-E(49)^19-E(49)^26
 -E(49)^33+E(49)^38-E(49)^40,E(7)^3+E(7)^5+E(7)^6,E(7)+E(7)^2+E(7)^4,0,0,3,0,
0,E(7)^3+E(7)^5+E(7)^6,E(7)+E(7)^2+E(7)^4],
[GALOIS,[4,2]],[3,E(7)^3+E(7)^5+E(7)^6,E(7)+E(7)^2+E(7)^4,E(7)^3+E(7)^5+E(7)^6
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E(7)^3+E(7)^5+E(7)^6,E(7)+E(7)^2+E(7)^4,E(7)+E(7)^2+E(7)^4,
E(7)^3+E(7)^5+E(7)^6,E(7)^3+E(7)^5+E(7)^6,E(7)+E(7)^2+E(7)^4,
E(7)+E(7)^2+E(7)^4,E(7)^3+E(7)^5+E(7)^6,3,3,0,0,3,0,0,3,3],
[GALOIS,[4,4]],
[GALOIS,[4,3]],
[GALOIS,[4,13]],
[GALOIS,[4,26]],
[GALOIS,[4,24]],
[GALOIS,[4,29]],
[GALOIS,[4,12]],
[GALOIS,[6,3]],
[GALOIS,[4,19]],
[GALOIS,[4,6]],
[GALOIS,[4,8]],
[GALOIS,[4,16]],
[GALOIS,[4,9]],[7,0,0,0,0,0,0,0,0,0,0,0,0,0,0,7,7,1,1,-1,-1,-1,-1,-1],
[TENSOR,[20,3]],
[TENSOR,[20,2]],[21,0,0,0,0,0,0,0,0,0,0,0,0,0,0,7*E(7)+7*E(7)^2+7*E(7)^4,
7*E(7)^3+7*E(7)^5+7*E(7)^6,0,0,-3,0,0,-E(7)-E(7)^2-E(7)^4,
-E(7)^3-E(7)^5-E(7)^6],
[GALOIS,[23,3]]],
[(18,19)(21,22),( 2, 6,12, 9,15, 5,11, 3, 7,13, 8,14, 4,10)(16,17)(23,24)]);

MOT("group6",
[
"origin: CAS library,\n",
"names:=group6\n",
" order: 2^5.3 = 96\n",
" number of classes: 13\n",
" source:generated by dixon-algorithm\n",
"        aachen [1982]\n",
" comments:generators:a,b\n",
"          relations: (a*b)^2=(a^3*b^2)^2=(a^2*b^3)^2=(a^-1*b^2)^2=1 \n",
"tests: 1.o.r., pow[2,3]"
],
[96,12,12,8,8,12,12,8,8,16,48,16,96],
[,[1,6,6,1,10,7,7,1,10,13,13,1,1],[1,11,11,4,5,13,1,8,9,10,11,12,13]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,-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]],[2,1,1,0,0,-1,-1,0,0,2,-2,-2,2],
[TENSOR,[5,3]],[3,0,0,1,1,0,0,-1,-1,-1,-3,1,3],
[TENSOR,[7,3]],
[TENSOR,[7,4]],
[TENSOR,[7,2]],[4,0,0,0,0,2,-2,0,0,0,0,0,-4],[4,-E(12)^7+E(12)^11,
E(12)^7-E(12)^11,0,0,-1,1,0,0,0,0,0,-4],
[TENSOR,[12,3]]],
[(4,8)(5,9),(2,3)]);
ALF("group6","L3(3).2",[1,14,15,2,13,6,3,10,7,5,11,10,2],[
"fusion map is unique up to table aut."
]);

MOT("gs4",
[
"origin: CAS library,\n",
"tests: 1.o.r., pow[2,3]"
],
0,
0,
0,
0,
["ConstructPermuted",["4.s4"],(5,7,9,11,13,16,6,8,10,12,14,15),(3,5,11,9,12,
10,14,8,6,4,13,7)(15,16)]);

MOT("h4",
[
"origin: CAS library,\n",
"names:=h4\n",
"       order: 2^6.3^2.5^2 = 14,400\n",
"       number of classes: 34\n",
"       source:grove, l.c.\n",
"             the characters of the\n",
"             hecatonicosahedroidal group\n",
"             j.reine angew. math. 265\n",
"             [1974],160-169\n",
"       comments: -\n",
"tests: 1.o.r., pow[2,3,5]"
],
[14400,14400,32,360,36,240,600,600,100,100,50,360,36,600,600,100,100,50,12,30,
30,20,20,30,30,240,240,8,12,12,20,20,20,20],
[,[1,1,1,4,5,2,8,7,10,9,11,4,5,7,8,9,10,11,12,21,20,14,15,21,20,1,1,3,5,5,10,
10,9,9],[1,2,3,1,1,6,8,7,10,9,11,2,2,15,14,17,16,18,6,8,7,23,22,14,15,26,27,
28,27,26,33,34,31,32],,[1,2,3,4,5,6,1,1,1,1,1,12,13,2,2,2,2,2,19,4,4,6,6,12,
12,26,27,28,29,30,27,26,27,26]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[4,-4,
0,-2,1,0,2*E(5)^2+2*E(5)^3,2*E(5)+2*E(5)^4,-2*E(5)-E(5)^2-E(5)^3-2*E(5)^4,
-E(5)-2*E(5)^2-2*E(5)^3-E(5)^4,-1,2,-1,-2*E(5)-2*E(5)^4,-2*E(5)^2-2*E(5)^3,
E(5)+2*E(5)^2+2*E(5)^3+E(5)^4,2*E(5)+E(5)^2+E(5)^3+2*E(5)^4,1,0,
-E(5)^2-E(5)^3,-E(5)-E(5)^4,0,0,E(5)^2+E(5)^3,E(5)+E(5)^4,2,-2,0,1,-1,
-E(5)^2-E(5)^3,E(5)^2+E(5)^3,-E(5)-E(5)^4,E(5)+E(5)^4],
[TENSOR,[3,2]],
[GALOIS,[3,2]],
[TENSOR,[5,2]],[6,6,-2,3,0,2,-3*E(5)-4*E(5)^2-4*E(5)^3-3*E(5)^4,
-4*E(5)-3*E(5)^2-3*E(5)^3-4*E(5)^4,-2*E(5)-2*E(5)^4,-2*E(5)^2-2*E(5)^3,1,3,0,
-4*E(5)-3*E(5)^2-3*E(5)^3-4*E(5)^4,-3*E(5)-4*E(5)^2-4*E(5)^3-3*E(5)^4,
-2*E(5)^2-2*E(5)^3,-2*E(5)-2*E(5)^4,1,-1,-E(5)^2-E(5)^3,-E(5)-E(5)^4,
E(5)+E(5)^4,E(5)^2+E(5)^3,-E(5)^2-E(5)^3,-E(5)-E(5)^4,0,0,0,0,0,0,0,0,0],
[GALOIS,[7,2]],[8,8,0,5,2,4,3,3,-2,-2,-2,5,2,3,3,-2,-2,-2,1,0,0,-1,-1,0,0,0,0,
0,0,0,0,0,0,0],[8,-8,0,-4,2,0,-2,-2,-2,-2,3,4,-2,2,2,2,2,-3,0,1,1,0,0,-1,-1,0,
0,0,0,0,0,0,0,0],[9,9,1,0,0,-3,-3*E(5)-3*E(5)^4,-3*E(5)^2-3*E(5)^3,
-E(5)-2*E(5)^2-2*E(5)^3-E(5)^4,-2*E(5)-E(5)^2-E(5)^3-2*E(5)^4,-1,0,0,
-3*E(5)^2-3*E(5)^3,-3*E(5)-3*E(5)^4,-2*E(5)-E(5)^2-E(5)^3-2*E(5)^4,
-E(5)-2*E(5)^2-2*E(5)^3-E(5)^4,-1,0,0,0,E(5)+E(5)^4,E(5)^2+E(5)^3,0,0,3,3,-1,
0,0,-E(5)-E(5)^4,-E(5)-E(5)^4,-E(5)^2-E(5)^3,-E(5)^2-E(5)^3],
[TENSOR,[11,2]],
[GALOIS,[11,2]],
[TENSOR,[13,2]],[10,10,2,4,-2,6,5,5,0,0,0,4,-2,5,5,0,0,0,0,-1,-1,1,1,-1,-1,0,
0,0,0,0,0,0,0,0],[16,-16,0,-2,-2,0,6*E(5)+2*E(5)^2+2*E(5)^3+6*E(5)^4,
2*E(5)+6*E(5)^2+6*E(5)^3+2*E(5)^4,-2*E(5)^2-2*E(5)^3,-2*E(5)-2*E(5)^4,1,2,2,
-2*E(5)-6*E(5)^2-6*E(5)^3-2*E(5)^4,-6*E(5)-2*E(5)^2-2*E(5)^3-6*E(5)^4,
2*E(5)+2*E(5)^4,2*E(5)^2+2*E(5)^3,-1,0,-E(5)^2-E(5)^3,-E(5)-E(5)^4,0,0,
E(5)^2+E(5)^3,E(5)+E(5)^4,0,0,0,0,0,0,0,0,0],
[GALOIS,[16,2]],[16,-16,0,4,1,0,-4,-4,1,1,1,-4,-1,4,4,-1,-1,-1,0,-1,-1,0,0,1,
1,4,-4,0,-1,1,1,-1,1,-1],
[TENSOR,[18,2]],[16,16,0,4,1,0,-4,-4,1,1,1,4,1,-4,-4,1,1,1,0,-1,-1,0,0,-1,-1,
4,4,0,1,1,-1,-1,-1,-1],
[TENSOR,[20,2]],[18,18,2,0,0,-6,3,3,-2,-2,3,0,0,3,3,-2,-2,3,0,0,0,-1,-1,0,0,0,
0,0,0,0,0,0,0,0],[24,24,0,3,0,-4,3*E(5)-E(5)^2-E(5)^3+3*E(5)^4,
-E(5)+3*E(5)^2+3*E(5)^3-E(5)^4,2*E(5)+2*E(5)^4,2*E(5)^2+2*E(5)^3,-1,3,0,
-E(5)+3*E(5)^2+3*E(5)^3-E(5)^4,3*E(5)-E(5)^2-E(5)^3+3*E(5)^4,2*E(5)^2+2*E(5)^3
 ,2*E(5)+2*E(5)^4,-1,-1,-E(5)^2-E(5)^3,-E(5)-E(5)^4,1,1,-E(5)^2-E(5)^3,
-E(5)-E(5)^4,0,0,0,0,0,0,0,0,0],
[GALOIS,[23,2]],[24,-24,0,-6,0,0,4*E(5)-2*E(5)^2-2*E(5)^3+4*E(5)^4,
-2*E(5)+4*E(5)^2+4*E(5)^3-2*E(5)^4,2*E(5)^2+2*E(5)^3,2*E(5)+2*E(5)^4,-1,6,0,
2*E(5)-4*E(5)^2-4*E(5)^3+2*E(5)^4,-4*E(5)+2*E(5)^2+2*E(5)^3-4*E(5)^4,
-2*E(5)-2*E(5)^4,-2*E(5)^2-2*E(5)^3,1,0,-1,-1,0,0,1,1,0,0,0,0,0,0,0,0,0],
[GALOIS,[25,2]],[25,25,1,-5,1,5,0,0,0,0,0,-5,1,0,0,0,0,0,-1,0,0,0,0,0,0,5,5,1,
-1,-1,0,0,0,0],
[TENSOR,[27,2]],[30,30,-2,-3,0,-2,-5*E(5)^2-5*E(5)^3,-5*E(5)-5*E(5)^4,0,0,0,
-3,0,-5*E(5)-5*E(5)^4,-5*E(5)^2-5*E(5)^3,0,0,0,1,E(5)^2+E(5)^3,E(5)+E(5)^4,
-E(5)^2-E(5)^3,-E(5)-E(5)^4,E(5)^2+E(5)^3,E(5)+E(5)^4,0,0,0,0,0,0,0,0,0],
[GALOIS,[29,2]],[36,-36,0,0,0,0,6,6,1,1,1,0,0,-6,-6,-1,-1,-1,0,0,0,0,0,0,0,6,
-6,0,0,0,-1,1,-1,1],
[TENSOR,[31,2]],[40,40,0,1,-2,4,-5,-5,0,0,0,1,-2,-5,-5,0,0,0,1,1,1,-1,-1,1,1,
0,0,0,0,0,0,0,0,0],[48,-48,0,6,0,0,-2,-2,-2,-2,-2,-6,0,2,2,2,2,2,0,1,1,0,0,-1,
-1,0,0,0,0,0,0,0,0,0]],
[( 7, 8)( 9,10)(14,15)(16,17)(20,21)(22,23)(24,25)(31,33)(32,34),(26,27)
(29,30)(31,32)(33,34)]);
#I  store the following tomfusion `h4' -> `2.(A5xA5).2':
ARC("h4","tomfusion",rec(name:="2.(A5xA5).2",map:=[1,2,5,6,7,8,17,17,18,
18,19,20,21,41,41,43,43,42,58,65,65,79,79,103,103,3,4,15,28,27,49,47,49,47],
text:=[
"fusion map is unique up to table autom."
]));
ALF("h4","a5wc2",[1,1,4,5,6,2,9,8,10,11,12,5,6,8,9,11,10,12,13,20,19,15,
16,20,19,3,3,7,14,14,18,18,17,17]);
ALF("h4","S4(5)",[1,2,3,5,4,6,8,9,11,11,10,14,15,18,17,19,20,21,24,28,29,
31,32,33,34,2,3,7,16,15,22,19,22,20],[
"fusion map is unique up to table autom."
]);

MOT("hed3",
[
"origin: CAS library,\n",
"tests: 1.o.r., pow[2,3]"
],
[1728,576,192,64,24,216,18,9,32,32,24,16,72,12,6,16,16,16,16,12],
[,[1,1,1,1,1,6,7,8,4,4,2,4,6,6,7,9,10,9,10,13],[1,2,3,4,5,1,1,1,10,9,11,12,2,
5,3,17,16,19,18,11]],
[[1,1,1,1,-1,1,1,1,1,1,-1,1,1,-1,1,-1,-1,-1,-1,-1],
[TENSOR,[1,1]],[2,2,-2,-2,0,2,-1,-1,0,0,0,0,2,0,1,-E(8)-E(8)^3,-E(8)-E(8)^3,
E(8)+E(8)^3,E(8)+E(8)^3,0],
[TENSOR,[3,1]],[2,2,2,2,0,2,-1,-1,2,2,0,2,2,0,-1,0,0,0,0,0],[3,3,3,3,1,3,0,0,
-1,-1,1,-1,3,1,0,-1,-1,-1,-1,1],
[TENSOR,[6,1]],[3,-1,3,-1,1,3,0,0,-1+2*E(4),-1-2*E(4),-1,1,-1,1,0,-E(4),E(4),
-E(4),E(4),-1],[3,-1,3,-1,-1,3,0,0,-1-2*E(4),-1+2*E(4),1,1,-1,-1,0,-E(4),E(4),
-E(4),E(4),1],
[TENSOR,[9,1]],
[TENSOR,[8,1]],[4,4,-4,-4,0,4,1,1,0,0,0,0,4,0,-1,0,0,0,0,0],[6,-2,-6,2,0,6,0,
0,0,0,0,0,-2,0,0,E(8)-E(8)^3,-E(8)+E(8)^3,-E(8)+E(8)^3,E(8)-E(8)^3,0],
[TENSOR,[13,1]],[6,-2,6,-2,0,6,0,0,2,2,0,-2,-2,0,0,0,0,0,0,0],[8,8,0,0,2,-1,2,
-1,0,0,2,0,-1,-1,0,0,0,0,0,-1],
[TENSOR,[16,1]],[16,16,0,0,0,-2,-2,1,0,0,0,0,-2,0,0,0,0,0,0,0],[24,-8,0,0,-2,
-3,0,0,0,0,2,0,1,1,0,0,0,0,0,-1],
[TENSOR,[19,1]]],
[(16,18)(17,19),( 9,10)(16,17)(18,19),( 9,10)(16,19)(17,18)]);
ARC("hed3","tomfusion",rec(name:="2^2.(3^2:2S4)",map:=[1,2,3,4,5,6,7,8,14,
14,12,15,18,23,25,36,36,36,36,47],text:=[
"fusion map is unique"
]));
ALF("hed3","NDG(He.2,3^2)",[1,5,6,3,12,2,9,10,8,8,15,7,4,13,11,16,16,17,
17,14],[
"fusion map is unique up to table automorphisms"
]);
ALF("hed3","2^2.psl(3,4).s3",[1,2,3,4,22,5,15,16,8,8,23,7,6,26,17,28,29,
28,29,27],[
"fusion map is unique up to table autom."
]);
ALF("hed3","He",[1,2,2,3,2,4,4,5,8,8,6,7,10,10,10,17,17,17,17,19],[
"fusion map is unique"
]);

MOT("hess",
[
"origin: CAS library,\n",
"names:=hess\n",
" order: 2^3.3^4 = 648\n",
" number of classes: 24\n",
" source:generated by dixon-algorithm\n",
"       aachen [1980]\n",
" comments:matrix group over gf(19) with size 3 and\n",
"         generators:\n",
"         1  0  0    0  0  1    14 14 14    16  0  0\n",
"         0  7  0    1  0  0    14  3  2     0 16  0\n",
"         0  0 11    0  1  0    14  2  3     0  0 17 \n",
"tests: 1.o.r., pow[2,3]"
],
[648,27,648,648,12,12,12,72,72,72,54,54,54,54,54,54,9,9,18,18,18,18,18,18],
[,[1,2,4,3,8,10,9,1,4,3,13,14,15,16,12,11,18,17,12,11,15,16,13,14],[1,1,1,1,5,
5,5,8,8,8,3,4,4,3,3,4,1,1,9,10,10,9,9,10]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,E(3),
E(3)^2,E(3)^2,E(3),E(3),E(3)^2,E(3),E(3)^2,E(3),E(3)^2,E(3)^2,E(3),E(3),
E(3)^2],
[TENSOR,[2,2]],[2,2,2,2,0,0,0,-2,-2,-2,-E(3),-E(3)^2,-E(3)^2,-E(3),-E(3),
-E(3)^2,-E(3),-E(3)^2,E(3),E(3)^2,E(3)^2,E(3),E(3),E(3)^2],
[TENSOR,[4,2]],
[TENSOR,[4,3]],[3,0,3*E(3)^2,3*E(3),1,E(3)^2,E(3),-1,-E(3)^2,-E(3),
2*E(9)^2+E(9)^5,E(9)^4+2*E(9)^7,E(9)^4-E(9)^7,-E(9)^2+E(9)^5,-E(9)^2-2*E(9)^5,
-2*E(9)^4-E(9)^7,0,0,-E(9)^2,-E(9)^7,E(9)^4+E(9)^7,E(9)^2+E(9)^5,-E(9)^5,
-E(9)^4],
[TENSOR,[7,3]],
[TENSOR,[7,2]],
[GALOIS,[7,5]],
[TENSOR,[10,2]],
[TENSOR,[10,3]],[3,3,3,3,-1,-1,-1,3,3,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[6,0,
6*E(3)^2,6*E(3),0,0,0,2,2*E(3)^2,2*E(3),-2*E(9)^2-E(9)^5,-E(9)^4-2*E(9)^7,
-E(9)^4+E(9)^7,E(9)^2-E(9)^5,E(9)^2+2*E(9)^5,2*E(9)^4+E(9)^7,0,0,-E(9)^2,
-E(9)^7,E(9)^4+E(9)^7,E(9)^2+E(9)^5,-E(9)^5,-E(9)^4],
[TENSOR,[14,2]],
[GALOIS,[14,2]],
[TENSOR,[16,3]],
[TENSOR,[16,2]],
[TENSOR,[14,3]],[8,-1,8,8,0,0,0,0,0,0,2,2,2,2,2,2,-1,-1,0,0,0,0,0,0],
[TENSOR,[20,2]],
[TENSOR,[20,3]],[9,0,9*E(3)^2,9*E(3),-1,-E(3)^2,-E(3),-3,-3*E(3)^2,-3*E(3),0,
0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[23,2]]],
[( 3, 4)( 6, 7)( 9,10)(11,13,15,12,14,16)(17,18)(19,24,22,20,23,21),(11,15,14)
(12,16,13)(19,22,23)(20,21,24)]);

MOT("hsd2",
[
"origin: CAS library,\n",
"tests: 1.o.r., pow[2,3,5]"
],
0,
0,
0,
0,
["ConstructPermuted",["5:4xA4"],(3,5,11,17,8,20,16,12,18,9,7,19,15,13)(4,6,
14),(1,8,12,9,7,2,16,11,3,4,10,15)(5,6,13)(17,19,18,20)]);

MOT("m12d2",
[
"origin: CAS library,\n",
"tests: 1.o.r., pow[2,3]"
],
0,
0,
0,
0,
["ConstructPermuted",["A4xS3"],(3,6,4,7,11,8,12,9,5),(1,5,2,4,10,8,11,9,7,3,
6)]);

MOT("mo61",
[
"origin: CAS library,\n",
"names:=mo61; m6[1]\n",
" order: 2^7.3^2 = 1,152\n",
" number of classes: 20\n",
" source:dye, r.h.\n",
"        the classes and characters of\n",
"        certain maximal and other subgroups\n",
"        of o 2n+2(2)\n",
"        ann.mat.pura appl.(4) 107\n",
"        (1975), 13-47\n",
" comments:semidirect product of an elementary\n",
"          abelian group of order 2^4 and o4,\n",
"          table blown up using cas-system\n",
"tests: 1.o.r., pow[2,3]"
],
0,
0,
0,
0,
["ConstructPermuted",["s4wrs2"],(4,9,6,8,5,7)(10,13,15,18,12,14,17,11,16),(2,
3,4)(6,7,8)(11,13,12)(14,18,17,15,19,16)]);
ARC("mo61","tomfusion",rec(name:="(S4xS4):2",map:=[1,2,4,3,24,17,8,33,9,7,
13,34,6,5,18,14,38,96,28,72],text:=[
"fusion map is unique"
]));
ALF("mo61","A8.2",[1,3,2,3,6,7,4,9,5,2,6,10,13,14,16,15,17,22,16,20],[
"fusion map is unique"
]);

MOT("2^4:(S3xS3)",
[
"origin: CAS library,\n",
"names:=mo61p; m6[1]+\n",
" order: 2^6.3^2 = 576\n",
" number of classes: 16\n",
" source:dye, r.h.\n",
"        the classes and characters of\n",
"        certain maximal and other subgroups\n",
"        of o 2n+2(2)\n",
"        ann.mat.pura appl.(4) 107\n",
"        (1975), 13-47\n",
" comments:semidirect product of an elementary\n",
"          abelian group of order 2^4 and o4+,\n",
"          table blown up using cas-system\n",
"tests: 1.o.r., pow[2,3]"
],
[576,96,64,16,16,8,36,12,18,18,48,48,16,16,6,6],
[,[1,1,1,1,3,2,7,7,9,10,1,1,3,3,9,10],[1,2,3,4,5,6,1,2,1,1,11,12,13,14,12,
11]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,-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]],[2,2,2,0,0,0,-1,-1,-1,2,0,2,0,2,-1,0],
[TENSOR,[5,2]],[2,2,2,0,0,0,-1,-1,2,-1,-2,0,-2,0,0,1],
[TENSOR,[7,2]],[4,4,4,0,0,0,1,1,-2,-2,0,0,0,0,0,0],[6,2,-2,2,-2,0,3,-1,0,0,0,
0,0,0,0,0],
[TENSOR,[10,3]],[9,-3,1,1,1,-1,0,0,0,0,3,3,-1,-1,0,0],
[TENSOR,[12,2]],
[TENSOR,[12,4]],
[TENSOR,[12,3]],[12,4,-4,0,0,0,-3,1,0,0,0,0,0,0,0,0]],
[( 9,10)(11,12)(13,14)(15,16)]);
ARC("2^4:(S3xS3)","tomfusion",rec(name:="2^4:(S3xS3)",map:=[1,2,4,3,20,14,8,
24,7,9,5,6,13,18,25,26],text:=[
"fusion map is unique up to table automorphisms"
]));
ALF("2^4:(S3xS3)","mo61",[1,2,3,4,5,6,7,8,9,9,10,10,11,11,12,12],[
"fusion map is unique, equal to that on the CAS table"
]);
ALF("2^4:(S3xS3)","A8",[1,3,2,3,6,7,4,9,5,5,2,2,6,6,10,10],[
"fusion map is unique"
]);
ALN("2^4:(S3xS3)",["mo61p"]);

MOT("mo62",
[
"origin: CAS library,\n",
"names:=mo62; m6[2]\n",
" order: 2^7.3.5 = 1,920\n",
" number of classes: 18\n",
" source:dye, r.h.\n",
"        the classes and characters of\n",
"        certain maximal and other subgroups\n",
"        of o 2n+2(2)\n",
"        ann.mat.pura appl.(4) 107\n",
"        (1975), 13-47\n",
" comments:semidirect product of an elementary\n",
"          abelian group of order 2^4 and o4,\n",
"          table blown up using cas-system \n",
"tests: 1.o.r., pow[2,3,5]"
],
[1920,192,384,32,32,16,24,24,12,5,96,32,32,96,12,12,8,8],
[,[1,1,1,1,3,2,7,7,7,10,1,1,2,2,7,8,4,5],[1,2,3,4,5,6,1,2,3,10,11,12,13,14,11,
14,17,18],,[1,2,3,4,5,6,7,8,9,1,11,12,13,14,15,16,17,18]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,
-1,-1],[4,4,4,0,0,0,1,1,1,-1,2,2,2,2,-1,-1,0,0],
[TENSOR,[3,2]],[5,5,5,1,1,1,-1,-1,-1,0,1,1,1,1,1,1,-1,-1],
[TENSOR,[5,2]],[5,1,-3,1,1,-1,2,-2,0,0,3,-1,1,-3,0,0,1,-1],
[TENSOR,[7,2]],[6,6,6,-2,-2,-2,0,0,0,1,0,0,0,0,0,0,0,0],[10,2,-6,2,2,-2,-2,2,
0,0,0,0,0,0,0,0,0,0],[10,-2,2,2,-2,0,1,1,-1,0,4,0,-2,2,1,-1,0,0],
[TENSOR,[11,2]],[10,-2,2,-2,2,0,1,1,-1,0,2,-2,0,4,-1,1,0,0],
[TENSOR,[13,2]],[15,3,-9,-1,-1,1,0,0,0,0,3,-1,1,-3,0,0,-1,1],
[TENSOR,[15,2]],[20,-4,4,0,0,0,-1,-1,1,0,2,2,-2,-2,-1,1,0,0],
[TENSOR,[17,2]]],
[]);
ARC("mo62","tomfusion",rec(name:="2^4:S5",map:=[1,3,2,6,15,24,7,30,34,28,
4,5,14,11,32,76,26,69],text:=[
"fusion map is unique"]));
ALF("mo62","A5.2",[1,1,1,2,2,2,3,3,3,4,5,5,5,5,7,7,6,6]);
ALF("mo62","A10",[1,2,3,3,9,7,5,13,14,11,2,3,8,7,13,21,9,16],[
"fusion map is unique"
]);
ALF("mo62","U4(2).2",[1,3,2,3,7,8,5,13,11,9,16,17,19,18,20,25,19,23],[
"fusion map is unique"
]);

MOT("mo62p",
[
"origin: CAS library,\n",
"names:=mo62p; m6[2]+\n",
" order: 2^6.3.5 = 960\n",
" number of classes: 12\n",
" source:dye, r.h.\n",
"        the classes and characters of\n",
"        certain maximal and other subgroups\n",
"        of o 2n+2(2)\n",
"        ann.mat.pura appl.(4) 107\n",
"        (1975), 13-47\n",
" comments:semidirect product of an elementary\n",
"          abelian group of order 2^4 and o4+,\n",
"          table blown up using cas-system \n",
"tests: 1.o.r., pow[2,3,5]"
],
0,
0,
0,
0,
["ConstructPermuted",["P1/G1/L1/V1/ext2"],(5,6)(8,9,10),(9,11,10)]);
ALF("mo62p","mo62",[1,2,3,4,5,6,7,8,9,9,10,10],[
"fusion map is unique, equal to that on the CAS table"
]);
ALF("mo62p","A5",[1,1,1,2,2,2,3,3,3,3,4,5]);

MOT("mo81",
[
"origin: CAS library,\n",
"names:=mo81; m8[1]\n",
" order: 2^13.3^2.5.7 = 2,580,480\n",
" number of classes: 64\n",
" source:dye, r.h.\n",
"        the classes and characters of\n",
"        certain maximal and other subgroups\n",
"        of o 2n+2(2)\n",
"        ann.mat.pura appl.(4) 107\n",
"        (1975), 13-47\n",
" comments:semidirect product of an elementary\n",
"          abelian group of order 2^6 and o6,\n",
"          table blown up using cas-system\n",
"tests: 1.o.r., pow[2,3,5,7]"
],
0,
0,
0,
0,
["ConstructPermuted",["2^6:S8"],(4,24,19,30,14,10,7,27,23,20,31,33,34,29,13,9,
6,25,21,32,35,28,12,8)(5,26,22,18,16,15,11)(37,39)(42,43)(44,48,60,64,54,46,
50,62,56,52,45,49,61,55,51)(47,59,63,53),(11,23,13,12)(14,17,24,16,31,43,63,
61,59,57,45,19,26,15,18,25)(20,27,32,37,50,36,49,30,34,42,52,39,53,40,54,46,
21,28,33,41,55,47)(22,29,35,48)(38,51)(44,62,60,58,56)]);
ALF("mo81","A8.2",[1,1,1,3,3,3,3,3,4,4,4,9,9,9,5,5,5,7,7,7,7,8,8,2,2,2,2,
12,11,6,6,6,10,10,10,13,13,13,13,14,14,14,14,17,17,17,17,15,15,15,18,18,
22,22,21,21,19,19,16,16,16,16,20,20]);

MOT("2^6:A8",
[
"origin: CAS library,\n",
"maximal subgroup of O8+(2),\n",
"tests: 1.o.r., pow[2,3,5,7]"
],
[1290240,46080,36864,3072,3072,3072,3072,256,1536,512,1536,512,192,2880,576,
288,72,72,72,72,64,64,64,64,32,32,32,32,60,20,48,48,24,24,24,24,24,7,7,15,15],
[,[1,1,1,1,1,1,1,3,1,1,3,3,2,14,14,14,17,17,17,17,4,7,5,6,9,10,11,12,29,29,14,
15,16,17,17,17,17,38,39,40,41],[1,2,3,4,5,6,7,8,9,10,11,12,13,1,3,2,1,3,3,2,
21,22,23,24,25,26,27,28,29,30,9,11,13,4,6,5,7,39,38,29,29],,[1,2,3,4,5,6,7,8,
9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,1,2,31,32,33,34,35,
36,37,39,38,14,14],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,
23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,1,1,41,40]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1],[7,7,7,-1,-1,-1,-1,-1,3,3,3,3,3,4,4,4,1,1,1,1,-1,-1,-1,-1,1,1,1,1,2,2,
0,0,0,-1,-1,-1,-1,0,0,-1,-1],[14,14,14,6,6,6,6,6,2,2,2,2,2,-1,-1,-1,2,2,2,2,2,
2,2,2,0,0,0,0,-1,-1,-1,-1,-1,0,0,0,0,0,0,-1,-1],[20,20,20,4,4,4,4,4,4,4,4,4,4,
5,5,5,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,-1,-1,0,0],[21,21,21,-3,
-3,-3,-3,-3,1,1,1,1,1,6,6,6,0,0,0,0,1,1,1,1,-1,-1,-1,-1,1,1,-2,-2,-2,0,0,0,0,
0,0,1,1],[21,21,21,-3,-3,-3,-3,-3,1,1,1,1,1,-3,-3,-3,0,0,0,0,1,1,1,1,-1,-1,-1,
-1,1,1,1,1,1,0,0,0,0,0,0,-E(15)^7-E(15)^11-E(15)^13-E(15)^14,
-E(15)-E(15)^2-E(15)^4-E(15)^8],
[GALOIS,[6,7]],[28,28,28,-4,-4,-4,-4,-4,4,4,4,4,4,1,1,1,1,1,1,1,0,0,0,0,0,0,0,
0,-2,-2,1,1,1,-1,-1,-1,-1,0,0,1,1],[35,35,35,3,3,3,3,3,-5,-5,-5,-5,-5,5,5,5,2,
2,2,2,-1,-1,-1,-1,-1,-1,-1,-1,0,0,1,1,1,0,0,0,0,0,0,0,0],[45,45,45,-3,-3,-3,
-3,-3,-3,-3,-3,-3,-3,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,
E(7)+E(7)^2+E(7)^4,E(7)^3+E(7)^5+E(7)^6,0,0],
[GALOIS,[10,3]],[56,56,56,8,8,8,8,8,0,0,0,0,0,-4,-4,-4,-1,-1,-1,-1,0,0,0,0,0,
0,0,0,1,1,0,0,0,-1,-1,-1,-1,0,0,1,1],[64,64,64,0,0,0,0,0,0,0,0,0,0,4,4,4,-2,
-2,-2,-2,0,0,0,0,0,0,0,0,-1,-1,0,0,0,0,0,0,0,1,1,-1,-1],[70,70,70,-2,-2,-2,-2,
-2,2,2,2,2,2,-5,-5,-5,1,1,1,1,-2,-2,-2,-2,0,0,0,0,0,0,-1,-1,-1,1,1,1,1,0,0,0,
0],[28,4,-4,4,-4,-4,4,0,8,0,4,-4,0,10,2,-2,1,-1,-1,1,0,0,0,0,2,-2,0,0,3,-1,2,
-2,0,1,-1,-1,1,0,0,0,0],[28,4,-4,-4,4,4,-4,0,4,-4,8,0,0,10,2,-2,1,-1,-1,1,0,0,
0,0,0,0,-2,2,3,-1,-2,2,0,-1,1,1,-1,0,0,0,0],[35,-5,3,11,3,3,-5,-1,7,-1,-5,3,
-1,5,-3,1,2,0,0,-2,3,-1,-1,-1,1,1,-1,-1,0,0,1,1,-1,2,0,0,-2,0,0,0,0],[35,-5,3,
-5,3,3,11,-1,7,-1,-5,3,-1,5,-3,1,2,0,0,-2,-1,3,-1,-1,1,1,-1,-1,0,0,1,1,-1,-2,
0,0,2,0,0,0,0],[35,-5,3,3,-5,11,3,-1,-5,3,7,-1,-1,5,-3,1,2,0,0,-2,-1,-1,-1,3,
-1,-1,1,1,0,0,1,1,-1,0,2,-2,0,0,0,0,0],[35,-5,3,3,11,-5,3,-1,-5,3,7,-1,-1,5,
-3,1,2,0,0,-2,-1,-1,3,-1,-1,-1,1,1,0,0,1,1,-1,0,-2,2,0,0,0,0,0],[70,-10,6,-2,
-2,14,14,-2,2,2,2,2,-2,-5,3,-1,1,-3,3,-1,-2,2,-2,2,0,0,0,0,0,0,-1,-1,1,1,-1,1,
-1,0,0,0,0],[70,-10,6,-2,14,-2,14,-2,2,2,2,2,-2,-5,3,-1,1,3,-3,-1,-2,2,2,-2,0,
0,0,0,0,0,-1,-1,1,1,1,-1,-1,0,0,0,0],[70,-10,6,14,-2,14,-2,-2,2,2,2,2,-2,-5,3,
-1,1,3,-3,-1,2,-2,-2,2,0,0,0,0,0,0,-1,-1,1,-1,-1,1,1,0,0,0,0],[70,-10,6,14,14,
-2,-2,-2,2,2,2,2,-2,-5,3,-1,1,-3,3,-1,2,-2,2,-2,0,0,0,0,0,0,-1,-1,1,-1,1,-1,1,
0,0,0,0],[140,20,-20,4,-4,-4,4,0,0,-8,12,4,0,20,4,-4,-1,1,1,-1,0,0,0,0,-2,2,0,
0,0,0,0,0,0,1,-1,-1,1,0,0,0,0],[140,20,-20,-4,4,4,-4,0,12,4,0,-8,0,20,4,-4,-1,
1,1,-1,0,0,0,0,0,0,2,-2,0,0,0,0,0,-1,1,1,-1,0,0,0,0],[140,-20,12,12,12,12,12,
-4,4,4,4,4,-4,5,-3,1,-4,0,0,4,0,0,0,0,0,0,0,0,0,0,1,1,-1,0,0,0,0,0,0,0,0],[
140,20,-20,-12,12,12,-12,0,8,0,4,-4,0,-10,-2,2,2,-2,-2,2,0,0,0,0,-2,2,0,0,0,0,
2,-2,0,0,0,0,0,0,0,0,0],[140,20,-20,12,-12,-12,12,0,4,-4,8,0,0,-10,-2,2,2,-2,
-2,2,0,0,0,0,0,0,2,-2,0,0,-2,2,0,0,0,0,0,0,0,0,0],[210,-30,18,-6,-6,-6,-6,2,
14,-2,-10,6,-2,15,-9,3,0,0,0,0,-2,-2,2,2,0,0,0,0,0,0,-1,-1,1,0,0,0,0,0,0,0,
0],[210,-30,18,-6,-6,-6,-6,2,-10,6,14,-2,-2,15,-9,3,0,0,0,0,2,2,-2,-2,0,0,0,0,
0,0,-1,-1,1,0,0,0,0,0,0,0,0],[252,36,-36,-12,12,12,-12,0,0,-8,12,4,0,0,0,0,0,
0,0,0,0,0,0,0,2,-2,0,0,-3,1,0,0,0,0,0,0,0,0,0,0,0],[252,36,-36,12,-12,-12,12,
0,12,4,0,-8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,2,-3,1,0,0,0,0,0,0,0,0,0,0,0],[280,
40,-40,8,-8,-8,8,0,-16,0,-8,8,0,10,2,-2,1,-1,-1,1,0,0,0,0,0,0,0,0,0,0,2,-2,0,
-1,1,1,-1,0,0,0,0],[280,40,-40,-8,8,8,-8,0,-8,8,-16,0,0,10,2,-2,1,-1,-1,1,0,0,
0,0,0,0,0,0,0,0,-2,2,0,1,-1,-1,1,0,0,0,0],[315,-45,27,-21,3,3,27,-1,3,-5,-9,
-1,3,0,0,0,0,0,0,0,3,-1,-1,-1,-1,-1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0],[315,-45,
27,27,3,3,-21,-1,3,-5,-9,-1,3,0,0,0,0,0,0,0,-1,3,-1,-1,-1,-1,1,1,0,0,0,0,0,0,
0,0,0,0,0,0,0],[315,-45,27,3,27,-21,3,-1,-9,-1,3,-5,3,0,0,0,0,0,0,0,-1,-1,-1,
3,1,1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0],[315,-45,27,3,-21,27,3,-1,-9,-1,3,-5,3,
0,0,0,0,0,0,0,-1,-1,3,-1,1,1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0],[420,-60,36,-12,
-12,-12,-12,4,4,4,4,4,-4,-15,9,-3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,-1,0,0,0,0,
0,0,0,0],[448,64,-64,0,0,0,0,0,0,0,0,0,0,-20,-4,4,-2,2,2,-2,0,0,0,0,0,0,0,0,3,
-1,0,0,0,0,0,0,0,0,0,0,0]],
[(38,39),(40,41),( 5, 6)(18,19)(23,24)(35,36),( 4, 7)(18,19)(21,22)(34,37)]);
ARC("2^6:A8","projectives",["2^(1+6)_+.A8",[[8,0,0,0,0,-4,0,0,0,0,-4,0,0,-4,0,
0,-2,0,0,0,0,0,0,2,0,0,0,2,2,0,0,-2,0,0,2,0,0,-1,-1,-1,-1],[56,0,0,0,0,4,0,0,
0,0,-12,0,0,-16,0,0,-2,0,0,0,0,0,0,-2,0,0,0,2,4,0,0,0,0,0,-2,0,0,0,0,1,1],
[112,0,0,0,0,-24,0,0,0,0,-8,0,0,4,0,0,-4,0,0,0,0,0,0,4,0,0,0,0,-2,0,0,2,0,0,0,
0,0,0,0,1,1],[160,0,0,0,0,-16,0,0,0,0,-16,0,0,-20,0,0,2,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,-2,0,0,2,0,0,1,1,0,0],[168,0,0,0,0,12,0,0,0,0,-4,0,0,-24,0,0,0,0,0,0,0,
0,0,2,0,0,0,-2,2,0,0,4,0,0,0,0,0,0,0,-1,-1],[168,0,0,0,0,12,0,0,0,0,-4,0,0,12,
0,0,0,0,0,0,0,0,0,2,0,0,0,-2,2,0,0,-2,0,0,0,0,0,0,0,E(15)^7+E(15)^11+E(15)^13+
E(15)^14,E(15)+E(15)^2+E(15)^4+E(15)^8],[168,0,0,0,0,12,0,0,0,0,-4,0,0,12,0,0,
0,0,0,0,0,0,0,2,0,0,0,-2,2,0,0,-2,0,0,0,0,0,0,0,E(15)+E(15)^2+E(15)^4+E(15)^8,
E(15)^7+E(15)^11+E(15)^13+E(15)^14],[224,0,0,0,0,16,0,0,0,0,-16,0,0,-4,0,0,-2,
0,0,0,0,0,0,0,0,0,0,0,-4,0,0,-2,0,0,-2,0,0,0,0,-1,-1],[280,0,0,0,0,-12,0,0,0,
0,20,0,0,-20,0,0,-4,0,0,0,0,0,0,-2,0,0,0,-2,0,0,0,-2,0,0,0,0,0,0,0,0,0],[360,
0,0,0,0,12,0,0,0,0,12,0,0,0,0,0,0,0,0,0,0,0,0,2,0,0,0,2,0,0,0,0,0,0,0,0,0,
-E(7)-E(7)^2-E(7)^4,-E(7)^3-E(7)^5-E(7)^6,0,0],[360,0,0,0,0,12,0,0,0,0,12,0,0,
0,0,0,0,0,0,0,0,0,0,2,0,0,0,2,0,0,0,0,0,0,0,0,0,-E(7)^3-E(7)^5-E(7)^6,-E(7)
-E(7)^2-E(7)^4,0,0],[448,0,0,0,0,-32,0,0,0,0,0,0,0,16,0,0,2,0,0,0,0,0,0,0,0,0,
0,0,2,0,0,0,0,0,-2,0,0,0,0,-1,-1],[512,0,0,0,0,0,0,0,0,0,0,0,0,-16,0,0,4,0,0,
0,0,0,0,0,0,0,0,0,-2,0,0,0,0,0,0,0,0,-1,-1,1,1],[560,0,0,0,0,8,0,0,0,0,-8,0,0,
20,0,0,-2,0,0,0,0,0,0,-4,0,0,0,0,0,0,0,2,0,0,2,0,0,0,0,0,0]],]);
ARC("2^6:A8","tomfusion",rec(name:="2^6:A8",map:=[1,2,3,8,6,5,4,80,9,7,78,
79,81,10,89,90,11,91,92,93,86,82,84,83,87,85,564,565,88,569,97,641,642,98,
94,95,96,109,109,643,643],text:=[
"fusion map is unique up to table autom."
]));
ALF("2^6:A8","mo81",[1,2,3,24,25,25,26,27,4,5,6,7,8,9,10,11,15,16,16,17,
30,31,32,32,18,19,20,21,22,23,12,13,14,33,34,34,35,29,29,28,28],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("2^6:A8","O8+(2)",[1,3,2,2,4,5,6,13,3,6,12,13,14,7,21,24,11,30,29,31,
13,17,15,16,14,17,36,37,18,41,24,44,48,28,33,32,34,35,35,51,51],[
"fusion is unique up to table automorphisms",
],"tom:11166");
ALF("2^6:A8","A8",[1,1,1,2,2,2,2,2,3,3,3,3,3,4,4,4,5,5,5,5,6,6,6,6,7,7,7,
7,8,8,9,9,9,10,10,10,10,11,12,13,14]);
ARC("2^6:A8","CAS",[rec(name:="mo81p",
permchars:=( 9,11,17,12,18,13,19,14,20,15)(10,16),
permclasses:=( 4,25,19,17,15,10, 5,26,20,18,16,11, 6,27,21,34,38,32,13, 8,29,
23,36,40,30,24,37,41,31,12, 7,28,22,35,39,33,14, 9),
text:=[
"names:=mo81p; m8[1]+\n",
" order: 2^12.3^2.5.7 = 1,290,240\n",
" number of classes: 41\n",
" source:dye, r.h.\n",
"        the classes and characters of\n",
"        certain maximal and other subgroups\n",
"        of o 2n+2(2)\n",
"        ann.mat.pura appl(4). 107\n",
"        (1975), 13-47\n",
" comments:semidirect product of an elementary\n",
"          abelian group of order 2^6 and o6+,\n",
"          table blown up using cas-system",
""]),rec(name:="y",
permchars:=(15,16)(17,19,18,20)(21,24)(22,23)(28,29)(30,31)(32,33)(34,35)
(36,37),
permclasses:=( 2, 3)( 4,33,21,38,23,40,13, 9, 8,34,25)( 5,35,26, 6,36,27)
( 7,37,28)(11,12)(14,17,29,15,18,31,20,32,22,41)(16,19,30)(24,39))]);

MOT("2^(1+6)_+.A8",
[
"origin: Dixon's Algorithm,\n",
"5th maximal subgroup of 2.O8+(2)"
],
[2580480,2580480,46080,36864,3072,3072,6144,6144,3072,256,1536,512,3072,3072,
512,192,5760,5760,576,288,144,144,72,72,72,64,64,64,128,128,32,32,32,64,64,120
,120,20,48,96,96,24,24,48,48,24,24,14,14,14,14,30,30,30,30],
[,[1,1,2,1,1,2,1,1,1,4,2,1,4,4,4,3,17,17,17,18,22,22,22,22,21,5,9,6,8,8,11,12,
14,15,15,37,37,36,18,19,19,20,22,22,22,21,22,49,49,51,51,53,53,55,55],[1,2,3,4
,5,6,7,8,9,10,11,12,13,14,15,16,1,2,4,3,2,1,4,4,3,26,27,28,29,30,31,32,33,34,
35,36,37,38,11,14,13,16,5,7,8,6,9,50,51,48,49,36,37,36,37],,[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
,2,1,3,39,40,41,42,43,44,45,46,47,50,51,48,49,18,17,18,17],,[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
,36,37,38,39,40,41,42,43,44,45,46,47,2,1,2,1,54,55,52,53]],
0,
[( 5, 9)(23,24)(26,27)(43,47),(48,50)(49,51),(52,54)(53,55)],
["ConstructProj",[["2^6:A8",[]],["2^(1+6)_+.A8",[]]]]);
ALF("2^(1+6)_+.A8","2^6:A8",[1,1,2,3,4,5,6,6,7,8,9,10,11,11,12,13,14,14,
15,16,17,17,18,19,20,21,22,23,24,24,25,26,27,28,28,29,29,30,31,32,32,33,
34,35,35,36,37,38,38,39,39,40,40,41,41]);
ALF("2^(1+6)_+.A8","O8+(2)M5",[1,1,2,3,4,5,6,6,7,8,9,10,11,11,12,13,14,14,
15,16,17,17,18,19,20,21,22,23,24,24,25,26,27,28,28,29,29,30,31,32,32,33,
34,35,35,36,37,38,38,39,39,40,40,41,41]);
ALF("2^(1+6)_+.A8","2.O8+(2)",[1,2,6,3,3,7,5,4,8,21,6,8,20,19,21,24,11,12,
35,39,18,17,43,45,48,21,26,25,22,23,24,26,53,54,55,30,29,64,39,68,69,76,
44,47,46,49,50,52,51,52,51,81,80,81,80],[
"fusion map is unique up to table autom.,\n",
"representative compatible with relevant factors"
]);
ALF("2^(1+6)_+.A8","A8",[1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,5,5,5,5,
5,6,6,6,6,6,7,7,7,7,7,8,8,8,9,9,9,9,10,10,10,10,10,11,11,12,12,13,13,14,
14]);

MOT("ons1",
[
"origin: CAS library,\n",
"names:=ons1\n",
" order: 2^9.3.7 = 10,752\n",
" number of classes: 18\n",
" source:o'nan, m.e.\n",
"       some evidence for the existence\n",
"       of a new finite simple group\n",
"       proc. london math. soc. [3] 32\n",
"       (1976),421-479\n",
" comments:subgroup of index 42,858,585 in on \n",
"tests: 1.o.r., pow[2,3,7]"
],
0,
0,
0,
0,
["ConstructPermuted",["4^3.L3(2)"],(9,15,12,18,14,10,16,11,17,13),(2,5,3,6,4)
(7,8)(12,18,15)(13,17,14,16)]);
ALF("ons1","L3(2)",[1,1,1,1,2,2,2,2,4,4,4,4,5,6,3,3,3,3]);

MOT("S3xU4(3)",
[
"origin: in the CAS library with the names u4q3.s3 and f22u3,\n",
"test: 1.o.r.,sym2 decompose correctly\n",
"tests: 1.o.r., pow[2,3,5,7]"
],
0,
0,
0,
[(13,14)(33,34)(53,54),(18,19)(38,39)(58,59),(16,17)(36,37)(56,57),(4,5)(11,
12)(16,18)(17,19)(24,25)(31,32)(36,38)(37,39)(44,45)(51,52)(56,58)(57,59)],
["ConstructDirectProduct",[["Dihedral",6],["U4(3)"]]]);
ARC("S3xU4(3)","CAS",[rec(name:="u4q3.s3",
permchars:=(3,4)(9,10)(11,12)(13,14)(23,24)(29,30)(31,32)(33,34)(43,44)(49,
50)(51,52)(53,54),
permclasses:=(3,6,9,18,12,15,5,7)(4,8)(10,14,20,17,11,16)(13,19)(23,26,29,38,
32,35,25,27)(24,28)(30,34,40,37,31,36)(33,39)(43,46,49,58,52,55,45,47)(44,48)
(50,54,60,57,51,56)(53,59))]);
ALF("S3xU4(3)","Fi22",[1,3,6,7,5,7,9,13,14,17,23,18,26,26,28,32,32,31,31,
38,5,18,5,6,7,8,39,46,52,18,17,23,60,60,63,32,32,31,31,39,2,4,16,19,15,19,
11,13,34,21,24,20,51,51,27,57,57,55,56,45],[
"fusion map is unique up to table automorphisms,\n",
"the representative is ocmpatible with the fusion map on the CAS tables"
]);

LIBTABLE.LOADSTATUS.ctomisc2:="userloaded";

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