Quelle  ctofisc1.tbl   Sprache: unbekannt

#############################################################################
##
#W  ctofisc1.tbl                GAP table library               Thomas Breuer
##
##  This file contains the ordinary character tables related to the
##  Fischer group $Fi_{22}$ of the ATLAS.
##
#H  ctbllib history
#H  ---------------
#H  $Log: ctofisc1.tbl,v $
#H  Revision 4.20  2012/01/30 08:31:42  gap
#H  removed #H entries from the headers
#H      TB
#H
#H  Revision 4.19  2011/09/28 12:28:28  gap
#H  - removed revision entry and SET_TABLEFILENAME call,
#H  - added tables of Isoclinic(2.Fi22.2), Isoclinic(6.Fi22.2)
#H      TB
#H
#H  Revision 4.18  2010/11/15 16:28:26  gap
#H  added comments to the fusions 2.Fi22 -> 2.2E6(2), 6.Fi22 -> 6.2E6(2)
#H      TB
#H
#H  Revision 4.17  2010/05/05 13:20:00  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 4.16  2010/01/19 17:05:31  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 4.15  2009/07/29 13:52:54  gap
#H  break a too long line
#H      TB
#H
#H  Revision 4.14  2009/06/15 15:12:12  gap
#H  added tables of 2E6(2)M3, 2E6(2)M4, 2E6(2)M5, 2E6(2)M7, 2E6(2)M8,
#H  2E6(2)M9, and corresponding fusions
#H      TB
#H
#H  Revision 4.13  2009/04/27 08:27:21  gap
#H  removed some superfluous explicit <nam>M<n> names,
#H  which are created automatically
#H      TB
#H
#H  Revision 4.12  2009/01/12 17:33:57  gap
#H  added missing maxes of Fi22.2 and their fusions
#H      TB
#H
#H  Revision 4.11  2006/06/07 07:54:27  gap
#H  unified ConstructMixed and ConstructMGA (for better programmatic access)
#H      TB
#H
#H  Revision 4.10  2004/01/20 10:26:13  gap
#H  added several names of the forms `<name>C<class>', `<name>N<class>'
#H      TB
#H
#H  Revision 4.9  2003/03/31 16:33:22  gap
#H  added fusions BN31 -> B, L2(31) -> B,
#H  added some names and tables of maxes of 2.B,
#H  added table of 2.(S3xFi22.2) < 2.B (J. An had asked for it)
#H      TB
#H
#H  Revision 4.8  2002/07/12 06:45:55  gap
#H  further tidying up: removed `irredinfo' stuff, rearranged constructions
#H      TB
#H
#H  Revision 4.7  2002/07/08 16:06:56  gap
#H  changed `construction' component from function (call) to list of function
#H  name and arguments
#H      TB
#H
#H  Revision 4.6  2001/05/04 16:47:18  gap
#H  first revision for ctbllib
#H
#H
#H  tbl history (GAP 4)
#H  -------------------
#H  (Rev. 4.6 of ctbllib coincides with Rev. 4.5 of tbl in GAP 4)
#H  
#H  RCS file: /gap/CVS/GAP/4.0/tbl/ctofisc1.tbl,v
#H  Working file: ctofisc1.tbl
#H  head: 4.5
#H  branch:
#H  locks: strict
#H  access list:
#H  symbolic names:
#H   GAP4R2: 4.5.0.6
#H   GAP4R2PRE2: 4.5.0.4
#H   GAP4R2PRE1: 4.5.0.2
#H   GAP4R1: 4.3.0.2
#H  keyword substitution: kv
#H  total revisions: 6; selected revisions: 6
#H  description:
#H  ----------------------------
#H  revision 4.5
#H  date: 2000/02/02 11:49:07;  author: gap;  state: Exp;  lines: +3 -3
#H  added table of the preimage of Fi22.2N2B in 3.Fi22
#H  (Eamonn had asked me for this table)
#H  
#H      TB
#H  ----------------------------
#H  revision 4.4
#H  date: 2000/02/01 09:23:07;  author: gap;  state: Exp;  lines: +3 -3
#H  corrected name of FI22M7 from `(2x2^(1+8):U4(2)):2' to
#H  `(2x2^(1+8)):U4(2):2'
#H  (see incremental ``Improvements to the ATLAS'')
#H  
#H      TB
#H  ----------------------------
#H  revision 4.3
#H  date: 1999/07/14 11:37:12;  author: gap;  state: Exp;  lines: +8 -7
#H  removed `maxes' of Fi22.2 for the moment
#H  (will be added again when the missing tables are added)
#H  
#H      TB
#H  ----------------------------
#H  revision 4.2
#H  date: 1997/11/25 16:17:16;  author: gap;  state: Exp;  lines: +7 -6
#H  fixed succession of maxes for Fi22.2, J3.2, M12.2, M22.2
#H      (The simple group itself had not been contained before.)
#H          TB
#H  ----------------------------
#H  revision 4.1
#H  date: 1997/07/17 15:38:43;  author: fceller;  state: Exp;  lines: +2 -2
#H  for version 4
#H  ----------------------------
#H  revision 1.1
#H  date: 1996/10/21 15:59:14;  author: sam;  state: Exp;
#H  first proposal of the table library
#H  ==========================================================================
##

MOT("2.Fi22",
[
"origin: ATLAS of finite groups, tests: 1.o.r."
],
[129123503308800,129123503308800,36787322880,36787322880,106168320,106168320,
1769472,39191040,39191040,5038848,5038848,279936,279936,34992,34992,110592,
92160,92160,12288,9216,9216,3072,1200,1200,311040,311040,186624,186624,20736,
20736,13824,13824,7776,7776,3456,6912,6912,3456,3456,1728,1728,864,864,432,
432,84,84,384,384,128,64,64,648,648,324,324,54,54,120,120,80,80,44,44,44,44,
864,1152,1152,576,576,576,288,288,288,288,288,288,96,96,144,144,72,72,26,26,
26,26,28,28,60,60,32,32,216,216,216,216,108,108,72,72,40,40,42,42,44,44,44,44,
48,48,60,60],
[,[1,1,1,1,1,1,1,8,8,10,10,12,12,14,14,6,5,5,6,7,7,5,23,23,8,8,10,10,10,10,8,
8,12,12,8,10,10,12,12,12,12,12,12,14,14,46,46,16,16,19,20,20,53,53,55,55,57,
57,23,23,23,23,65,65,63,63,30,32,32,32,31,31,36,36,37,37,38,38,30,31,40,40,45,
45,87,87,85,85,46,46,91,91,50,50,53,53,53,53,55,55,53,53,61,61,105,105,65,65,
63,63,69,68,91,91],[1,2,3,4,5,6,7,1,2,1,2,1,2,1,2,16,17,18,19,20,21,22,23,24,
3,4,3,4,5,6,5,6,3,4,7,7,7,7,7,5,6,7,7,7,7,46,47,48,49,50,51,52,10,11,10,11,14,
15,59,60,61,62,63,64,65,66,16,16,16,16,17,18,21,20,21,20,20,21,19,22,17,18,20,
21,85,86,87,88,89,90,23,24,93,94,27,28,27,28,27,28,29,30,103,104,46,47,107,
108,109,110,49,48,59,60],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,
21,22,1,2,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,
47,48,49,50,51,52,53,54,55,56,57,58,3,4,5,6,63,64,65,66,67,68,69,70,71,72,73,
74,75,76,77,78,79,80,81,82,83,84,87,88,85,86,89,90,8,9,94,93,97,98,95,96,99,
100,101,102,17,18,105,106,107,108,109,110,111,112,25,26],,[1,2,3,4,5,6,7,8,9,
10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,
36,37,38,39,40,41,42,43,44,45,1,2,48,49,50,51,52,53,54,55,56,57,58,59,60,61,
62,65,66,63,64,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,87,88,85,
86,3,4,91,92,94,93,95,96,97,98,99,100,101,102,103,104,8,9,109,110,107,108,111,
112,113,114],,,,[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,
50,51,52,53,54,55,56,57,58,59,60,61,62,1,2,1,2,67,68,69,70,71,72,73,74,75,76,
77,78,79,80,81,82,83,84,87,88,85,86,89,90,91,92,93,94,97,98,95,96,99,100,101,
102,103,104,105,106,3,4,3,4,111,112,113,114],,[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,
40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,65,66,63,
64,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,1,2,1,2,89,90,91,92,
94,93,95,96,97,98,99,100,101,102,103,104,105,106,109,110,107,108,111,112,113,
114]],
0,
[(95,97)(96,98),(93,94),(85,87)(86,88),( 63, 65)( 64, 66)(107,109)(108,110),
(  3,  4)( 17, 18)( 25, 26)( 27, 28)( 33, 34)( 36, 37)( 42, 43)( 51, 52)
( 59, 60)( 71, 72)( 73, 75)( 74, 76)( 81, 82)( 89, 90)( 95, 96)( 97, 98)
( 99,100)(103,104)(107,108)(109,110)(113,114)],
["ConstructProj",[["Fi22",[]],["2.Fi22",[]]]]);
ARC("2.Fi22","CAS",[rec(name:="2.f22",
permchars:=( 42, 44, 43)( 67, 68)( 69, 71)( 85, 86)( 93, 94)(100,101)(107,108)
(111,112),
permclasses:=(  2, 66, 72, 87,  6, 68, 25, 21,113, 19, 60, 79, 35, 23, 14, 45,
 103, 18,112, 29, 32, 86, 69, 88, 70, 27, 31, 22, 56, 95, 41,107,  9, 84,104,
  82,110, 74, 36, 33, 49, 62, 80, 26, 85,  5,  3)(  4, 67, 34,106, 77, 54, 97,
 42, 52,114, 83, 47, 75, 94, 65,  8, 20, 57, 44, 46, 11, 89, 12, 48, 61, 16,
  59, 15,102,100, 96, 98, 99, 39,108, 73, 93, 64, 71, 24, 78,111, 28, 90, 76,
  37, 92, 81, 53, 40, 50, 63,  7)( 10, 30, 91, 17, 55, 38, 51, 58,101, 43,109)
( 13,105))]);
ARC("2.Fi22","maxes",["2^2.U6(2)","2xO7(3)","2.Fi22M3","O8+(2):S3x2",
"2.Fi22M5","S8(2)M3","2.(2x2^(1+8)):U4(2):2","S3x2.U4(3).2_2","2x2F4(2)'",
"2^(1+5+8).(S3xA6)","2.(3^(1+6):2^(3+4):3^2:2)","S10x2","2.Fi22M13","2xm12"]);
ALF("2.Fi22","Fi22",[1,1,2,2,3,3,4,5,5,6,6,7,7,8,8,9,10,10,11,12,12,13,14,
14,15,15,16,16,17,17,18,18,19,19,20,21,21,22,22,23,23,24,24,25,25,26,26,
27,28,29,30,30,31,31,32,32,33,33,34,34,35,35,36,36,37,37,38,39,39,40,41,
41,42,42,43,43,44,44,45,46,47,47,48,48,49,49,50,50,51,51,52,52,53,54,55,
55,56,56,57,57,58,58,59,59,60,60,61,61,62,62,63,64,65,65]);
ALF("2.Fi22","2E6(2)M8",[1,1,2,2,3,3,4,5,5,6,6,7,7,8,8,9,10,10,11,12,12,
13,14,14,15,15,16,16,17,17,18,18,19,19,20,21,21,22,22,23,23,24,24,25,25,
26,26,27,28,29,30,30,31,31,32,32,33,33,34,34,35,35,36,36,37,37,38,39,39,
40,41,41,42,42,43,43,44,44,45,46,47,47,48,48,49,49,50,50,51,51,52,52,53,
54,55,55,56,56,57,57,58,58,59,59,60,60,61,61,62,62,63,64,65,65]);
ALF("2.Fi22","2.Fi22.2",[1,2,3,3,4,5,6,7,8,9,10,11,12,13,14,15,16,16,17,
18,19,20,21,22,23,23,24,24,25,26,27,28,29,29,30,31,31,32,33,34,35,36,36,
37,38,39,40,41,42,43,44,44,45,46,47,48,49,50,51,51,52,53,54,55,54,55,56,
57,58,59,60,60,61,62,61,62,63,64,65,66,67,67,68,69,70,71,70,71,72,72,73,
74,75,75,76,77,77,76,78,78,79,80,81,81,82,83,84,85,85,84,86,87,88,88]);
ALF("2.Fi22","Fi23",[1,2,2,3,3,4,4,5,14,6,15,7,18,8,23,10,9,11,12,10,12,
11,13,38,14,16,15,17,17,21,16,22,18,24,22,21,19,25,20,24,26,26,25,27,28,
29,59,31,30,32,30,31,35,66,34,67,37,73,38,39,39,40,41,78,41,79,46,44,48,
48,42,50,52,46,47,43,49,53,52,50,51,55,54,56,58,86,57,85,59,60,61,90,63,
64,66,71,66,71,67,70,71,68,74,75,76,97,79,77,78,77,84,82,90,89],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("2.Fi22","2.2E6(2)",[1,2,4,3,5,6,7,8,9,12,13,10,11,12,13,20,24,23,27,
29,30,31,34,35,37,36,43,42,47,48,40,41,39,38,46,52,51,49,50,44,45,50,49,
51,52,55,56,64,64,69,75,75,78,79,80,81,80,81,83,82,84,85,86,87,88,89,105,
101,101,101,108,107,120,119,116,115,113,114,123,109,112,111,117,118,127,
128,127,128,132,131,135,136,142,142,153,152,155,154,157,156,158,159,167,
166,170,171,173,172,175,174,183,183,194,193],[
"fusion map is unique up to table autom.,\n",
"representative compatible with relevant factors"
]);
ALN("2.Fi22",["2.f22","f23m1","Fi23C2A","Fi23N2A","2.2E6(2)M8"]);

MOT("2.Fi22.2",
[
"origin: ATLAS of finite groups, tests: 1.o.r."
],
[258247006617600,258247006617600,36787322880,212336640,212336640,3538944,
78382080,78382080,10077696,10077696,559872,559872,69984,69984,221184,92160,
24576,18432,18432,6144,2400,2400,311040,186624,41472,41472,27648,27648,7776,
6912,6912,6912,6912,3456,3456,864,864,864,168,168,768,768,256,64,1296,1296,
648,648,108,108,120,160,160,44,44,1728,2304,2304,1152,576,288,288,576,576,192,
192,144,144,144,26,26,28,120,120,32,216,216,108,144,144,40,84,84,44,44,96,96,
60,2090188800,6635520,5806080,1327104,245760,18432,12288,3072,311040,145152,
145152,23328,8640,7776,6912,2592,2592,2592,2592,2592,864,432,768,768,768,192,
1200,120,80,6912,2592,1152,864,768,576,288,144,96,48,48,84,28,32,216,216,108,
36,36,36,40,96,96,48,48,48,48,60,60,72,72,84,84],
[,[1,1,1,1,1,1,7,7,9,9,11,11,13,13,5,4,5,6,6,4,21,21,7,9,9,9,7,7,11,7,9,11,11,
11,11,11,13,13,39,39,15,15,17,18,45,45,47,47,49,49,21,21,21,54,54,26,28,28,28,
27,31,31,32,32,26,27,34,38,38,70,70,39,73,73,43,45,45,47,45,45,52,82,82,54,54,
58,57,73,1,1,2,5,5,4,5,6,7,7,7,9,8,11,7,10,13,13,13,13,11,12,15,15,17,19,21,
22,21,28,26,28,35,28,27,25,34,35,38,38,39,40,43,45,45,47,48,49,49,53,58,57,65,
65,64,64,73,74,80,80,82,82],[1,2,3,4,5,6,1,2,1,2,1,2,1,2,15,16,17,18,19,20,21,
22,3,3,4,5,4,5,3,6,6,6,6,4,5,6,6,6,39,40,41,42,43,44,9,10,9,10,13,14,51,52,53,
54,55,15,15,15,15,16,19,18,18,19,17,20,16,18,19,70,71,72,21,22,75,24,24,24,25,
26,81,39,40,84,85,42,41,51,89,90,91,92,93,94,95,96,89,89,89,89,91,89,90,91,89,
89,90,90,90,91,111,112,113,114,115,116,117,92,92,92,92,93,94,94,94,95,96,96,
129,130,131,100,100,100,104,107,108,138,111,112,113,113,114,114,115,116,119,
119,129,129],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,1,2,23,24,
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,
3,4,5,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,7,8,75,77,76,
78,79,80,16,82,83,84,85,86,87,23,89,90,91,92,93,94,95,96,97,99,98,100,101,102,
103,104,106,105,108,107,109,110,111,112,113,114,89,91,90,118,119,120,121,122,
123,124,125,126,128,127,129,130,131,133,132,134,135,137,136,93,139,140,142,
141,144,143,97,101,147,148,150,149],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,
17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,1,2,41,42,
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,
69,70,71,3,73,74,75,76,77,78,79,80,81,7,8,85,84,86,87,88,89,90,91,92,93,94,95,
96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,
116,117,118,119,120,121,122,123,124,125,126,127,128,89,91,131,132,133,134,135,
136,137,138,139,140,142,141,144,143,145,146,147,148,98,99],,,,[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,
34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,1,2,56,57,58,59,
60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,77,76,78,79,80,81,82,83,3,3,
86,87,88,89,90,91,92,93,94,95,96,97,99,98,100,101,102,103,104,106,105,108,107,
109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,128,
127,129,130,131,133,132,134,135,137,136,138,139,140,141,142,143,144,145,146,
147,148,150,149],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,
23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,
49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,1,2,72,73,74,
75,76,77,78,79,80,81,82,83,85,84,86,87,88,89,90,91,92,93,94,95,96,97,98,99,
100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,
119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,
138,139,140,141,142,143,144,145,146,147,148,149,150]],
0,
[(143,144),(141,142),(141,142)(143,144),(84,85),( 76, 77)( 98, 99)(105,106)
(107,108)(127,128)(132,133)(136,137)(141,142)(143,144)(149,150),( 76, 77)
( 98, 99)(105,106)(107,108)(127,128)(132,133)(136,137)(149,150),( 76, 77)
(147,148)],
["ConstructProj",[["Fi22.2",[]],["2.Fi22.2",[]]]]);
ALF("2.Fi22.2","F3+",[1,2,2,2,3,3,4,13,5,15,6,18,7,19,9,10,11,9,11,10,12,
35,13,15,15,17,13,16,18,16,17,21,14,18,21,21,20,22,24,52,26,26,27,26,31,
60,30,62,34,64,35,35,36,37,73,39,38,40,40,41,45,39,42,48,45,41,49,43,50,
51,83,52,54,90,57,60,60,62,60,59,67,69,103,73,73,77,76,90,2,3,10,9,9,10,
11,11,13,13,13,15,41,18,16,44,19,19,20,20,21,49,26,26,27,28,35,67,36,38,
39,40,42,40,41,44,49,48,50,50,52,87,57,60,60,62,98,65,66,68,77,76,80,80,
81,82,90,108,95,96,103,103],[
"fusion map is unique up to table automorphisms"
]);
ALF("2.Fi22.2","Fi22.2",[1,1,2,3,3,4,5,5,6,6,7,7,8,8,9,10,11,12,12,13,14,
14,15,16,17,17,18,18,19,20,21,22,22,23,23,24,25,25,26,26,27,28,29,30,31,
31,32,32,33,33,34,35,35,36,36,37,38,38,39,40,41,41,42,42,43,44,45,46,46,
47,47,48,49,49,50,51,51,52,53,53,54,55,55,56,56,57,58,59,60,61,62,63,64,
65,66,67,68,69,69,70,71,72,73,74,75,75,76,76,77,78,79,80,81,82,83,84,85,
86,87,88,89,90,91,92,93,94,95,95,96,97,98,99,99,100,101,102,102,103,104,
105,106,107,108,108,109,110,111,111,112,112]);
ALF("2.Fi22.2","2^2.Fi22.2",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,
19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,
43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,
67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,168,169,
170,171,172,173,174,175,176,177,177,178,179,180,181,182,183,183,184,184,
185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,
203,203,204,205,206,207,207,208,209,210,210,211,212,213,214,215,216,216,
217,218,219,219,220,220],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables"
]);
ALN("2.Fi22.2",["F3+C2A","F3+N2A"]);

MOT("Isoclinic(2.Fi22.2)",
[
"isoclinic group of the 2.Fi22.2 given in the ATLAS"
],
0,
0,
0,
[(143,144),(141,142),(84,85),( 76, 77)(147,148),
( 98, 99)(105,106)(107,108)(127,128)(132,133)(136,137)(147,148)(149,150)],
["ConstructIsoclinic",[["2.Fi22.2"]]]);
ALF("Isoclinic(2.Fi22.2)","Fi22.2",[1,1,2,3,3,4,5,5,6,6,7,7,8,8,9,10,11,
12,12,13,14,14,15,16,17,17,18,18,19,20,21,22,22,23,23,24,25,25,26,26,27,
28,29,30,31,31,32,32,33,33,34,35,35,36,36,37,38,38,39,40,41,41,42,42,43,
44,45,46,46,47,47,48,49,49,50,51,51,52,53,53,54,55,55,56,56,57,58,59,60,
61,62,63,64,65,66,67,68,69,69,70,71,72,73,74,75,75,76,76,77,78,79,80,81,
82,83,84,85,86,87,88,89,90,91,92,93,94,95,95,96,97,98,99,99,100,101,102,
102,103,104,105,106,107,108,108,109,110,111,111,112,112]);

MOT("3.Fi22",
[
"origin: ATLAS of finite groups, tests: 1.o.r."
],
[193685254963200,193685254963200,193685254963200,55180984320,55180984320,
55180984320,159252480,159252480,159252480,5308416,5308416,5308416,58786560,
58786560,58786560,2519424,139968,17496,331776,331776,331776,138240,138240,
138240,36864,36864,36864,13824,13824,13824,9216,9216,9216,1800,1800,1800,
466560,466560,466560,279936,279936,279936,31104,31104,31104,20736,20736,20736,
3888,10368,10368,10368,3456,1728,2592,2592,2592,432,216,126,126,126,1152,1152,
1152,1152,1152,1152,384,384,384,96,96,96,972,972,972,162,27,180,180,180,120,
120,120,66,66,66,66,66,66,2592,2592,2592,1728,1728,1728,1728,1728,1728,864,
864,864,144,144,144,288,288,288,288,288,288,216,216,216,36,39,39,39,39,39,39,
42,42,42,90,90,90,96,96,96,96,96,96,324,324,324,324,324,324,54,108,108,108,60,
60,60,63,63,63,66,66,66,66,66,66,144,144,144,144,144,144,90,90,90],
[,[1,3,2,1,3,2,1,3,2,1,3,2,13,15,14,16,17,18,7,9,8,7,9,8,7,9,8,10,12,11,7,9,8,
34,36,35,13,15,14,16,16,16,16,16,16,13,15,14,17,13,15,14,16,17,17,17,17,17,18,
60,62,61,19,21,20,19,21,20,25,27,26,28,30,29,75,77,76,78,79,34,36,35,34,36,35,
89,91,90,86,88,87,43,45,44,46,48,47,46,48,47,46,48,47,53,53,54,43,45,44,46,48,
47,55,57,56,59,120,122,121,117,119,118,60,62,61,126,128,127,69,71,70,69,71,70,
75,77,76,75,77,76,78,75,77,76,83,85,84,148,150,149,89,91,90,86,88,87,95,97,96,
95,97,96,126,128,127],[1,1,1,4,4,4,7,7,7,10,10,10,1,1,1,1,1,1,19,19,19,22,22,
22,25,25,25,28,28,28,31,31,31,34,34,34,4,4,4,4,4,4,7,7,7,7,7,7,4,10,10,10,10,
10,7,7,7,10,10,60,60,60,63,63,63,66,66,66,69,69,69,72,72,72,16,16,16,16,18,80,
80,80,83,83,83,86,86,86,89,89,89,19,19,19,19,19,19,19,19,19,22,22,22,28,28,28,
25,25,25,31,31,31,22,22,22,28,117,117,117,120,120,120,123,123,123,34,34,34,
129,129,129,132,132,132,41,41,41,42,42,42,40,43,43,43,145,145,145,60,60,60,
151,151,151,154,154,154,66,66,66,63,63,63,80,80,80],,[1,3,2,4,6,5,7,9,8,10,12,
11,13,15,14,16,17,18,19,21,20,22,24,23,25,27,26,28,30,29,31,33,32,1,3,2,37,39,
38,40,42,41,43,45,44,46,48,47,49,50,52,51,53,54,55,57,56,58,59,60,62,61,63,65,
64,66,68,67,69,71,70,72,74,73,75,77,76,78,79,4,6,5,7,9,8,86,88,87,89,91,90,92,
94,93,95,97,96,98,100,99,101,103,102,104,105,106,107,109,108,110,112,111,113,
115,114,116,120,122,121,117,119,118,123,125,124,13,15,14,132,134,133,129,131,
130,138,140,139,135,137,136,141,142,144,143,22,24,23,148,150,149,151,153,152,
154,156,155,157,159,158,160,162,161,37,39,38],,[1,2,3,4,5,6,7,8,9,10,11,12,13,
14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,
40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,1,2,3,63,64,65,66,
67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,89,90,91,86,87,88,92,
93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,
114,115,116,120,121,122,117,118,119,4,5,6,126,127,128,132,133,134,129,130,131,
135,136,137,138,139,140,141,142,143,144,145,146,147,13,14,15,154,155,156,151,
152,153,157,158,159,160,161,162,163,164,165],,,,[1,3,2,4,6,5,7,9,8,10,12,11,
13,15,14,16,17,18,19,21,20,22,24,23,25,27,26,28,30,29,31,33,32,34,36,35,37,39,
38,40,42,41,43,45,44,46,48,47,49,50,52,51,53,54,55,57,56,58,59,60,62,61,63,65,
64,66,68,67,69,71,70,72,74,73,75,77,76,78,79,80,82,81,83,85,84,1,3,2,1,3,2,92,
94,93,95,97,96,98,100,99,101,103,102,104,105,106,107,109,108,110,112,111,113,
115,114,116,120,122,121,117,119,118,123,125,124,126,128,127,129,131,130,132,
134,133,138,140,139,135,137,136,141,142,144,143,145,147,146,148,150,149,4,6,5,
4,6,5,157,159,158,160,162,161,163,165,164],,[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,
67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,89,90,91,86,87,88,92,
93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,
114,115,116,1,2,3,1,2,3,123,124,125,126,127,128,132,133,134,129,130,131,135,
136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,154,155,156,151,
152,153,157,158,159,160,161,162,163,164,165]],
0,
[(129,132)(130,133)(131,134),(117,120)(118,121)(119,122),(104,105),( 86, 89)
( 87, 90)( 88, 91)(151,154)(152,155)(153,156),(  2,  3)(  5,  6)(  8,  9)
( 11, 12)( 14, 15)( 20, 21)( 23, 24)( 26, 27)( 29, 30)( 32, 33)( 35, 36)
( 38, 39)( 41, 42)( 44, 45)( 47, 48)( 51, 52)( 56, 57)( 61, 62)( 64, 65)
( 67, 68)( 70, 71)( 73, 74)( 76, 77)( 81, 82)( 84, 85)( 87, 88)( 90, 91)
( 93, 94)( 96, 97)( 99,100)(102,103)(108,109)(111,112)(114,115)(118,119)
(121,122)(124,125)(127,128)(130,131)(133,134)(135,138)(136,140)(137,139)
(143,144)(146,147)(149,150)(152,153)(155,156)(158,159)(161,162)(164,165)],
["ConstructProj",[["Fi22",[]],,["3.Fi22",[-1,-1,-25,-25,-1,-1,-1,-1,-1,-1,-1,
-1,-1,-1,-1,-1,-1,23,23,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,17,17,-1,-1,
-1,-1,-1,23,23,-1,-1,-1,-1,-1,-1,-1,-1]]]]);
ARC("3.Fi22","maxes",["6.U6(2)","3.O7(3)","3.Fi22M3","3xO8+(2):S3","3.Fi22M5",
"3x2^6:S6(2)","3x(2x2^(1+8)):U4(2):2","S3x3_1.U4(3).2_2","3x2F4(2)'",
"2^(5+8):(S3x3.A6)","3.3^(1+6):2^(3+4):3^2:2","3xA10.2","3xA10.2","3xM12"]);
ALF("3.Fi22","Fi22",[1,1,1,2,2,2,3,3,3,4,4,4,5,5,5,6,7,8,9,9,9,10,10,10,
11,11,11,12,12,12,13,13,13,14,14,14,15,15,15,16,16,16,17,17,17,18,18,18,
19,20,20,20,21,22,23,23,23,24,25,26,26,26,27,27,27,28,28,28,29,29,29,30,
30,30,31,31,31,32,33,34,34,34,35,35,35,36,36,36,37,37,37,38,38,38,39,39,
39,40,40,40,41,41,41,42,43,44,45,45,45,46,46,46,47,47,47,48,49,49,49,50,
50,50,51,51,51,52,52,52,53,53,53,54,54,54,55,55,55,56,56,56,57,58,58,58,
59,59,59,60,60,60,61,61,61,62,62,62,63,63,63,64,64,64,65,65,65]);
ALF("3.Fi22","3.Fi22.2",[1,2,2,3,4,4,5,6,6,7,8,8,9,10,10,11,12,13,14,15,
15,16,17,17,18,19,19,20,21,21,22,23,23,24,25,25,26,27,27,28,29,29,30,31,
31,32,33,33,34,35,36,36,37,38,39,40,40,41,42,43,44,44,45,46,46,47,48,48,
49,50,50,51,52,52,53,54,54,55,56,57,58,58,59,60,60,61,62,63,61,63,62,64,
65,65,66,67,67,68,69,69,70,71,71,72,72,73,74,75,75,76,77,77,78,79,79,80,
81,82,83,81,83,82,84,85,85,86,87,87,88,89,90,88,90,89,91,92,93,91,93,92,
94,95,96,96,97,98,98,99,100,100,101,102,103,101,103,102,104,105,105,106,
107,107,108,109,109],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables"
]);
ALF("3.Fi22","3.2E6(2)",[1,3,2,4,6,5,7,9,8,10,12,11,13,15,14,17,16,17,27,
29,28,39,41,40,42,44,43,51,53,52,54,56,55,63,65,64,66,68,67,73,75,74,82,
84,83,70,72,71,69,79,81,80,86,85,76,78,77,85,86,90,92,91,105,107,106,105,
107,106,117,119,118,135,137,136,141,143,142,144,144,145,147,146,148,150,
149,151,153,152,154,156,155,183,185,184,174,176,175,174,176,175,192,194,
193,206,207,204,208,210,209,195,197,196,201,203,202,205,223,225,224,223,
225,224,229,231,230,235,237,236,247,249,248,247,249,248,271,273,272,274,
276,275,277,278,280,279,290,292,291,294,296,295,297,299,298,300,302,301,
308,310,309,308,310,309,332,334,333],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALN("3.Fi22",["3.2E6(2)M7","3.Fi22.2M1"]);

MOT("3.Fi22.2",
[
"origin: ATLAS of finite groups, tests: 1.o.r."
],
[387370509926400,193685254963200,110361968640,55180984320,318504960,159252480,
10616832,5308416,117573120,58786560,5038848,279936,34992,663552,331776,276480,
138240,73728,36864,27648,13824,18432,9216,3600,1800,933120,466560,559872,
279936,62208,31104,41472,20736,7776,20736,10368,6912,3456,5184,2592,864,432,
252,126,2304,1152,2304,1152,768,384,192,96,1944,972,324,54,360,180,240,120,66,
66,66,5184,2592,3456,1728,3456,1728,1728,864,144,288,576,288,576,288,432,216,
72,39,39,39,84,42,180,90,96,96,96,324,324,324,108,216,108,120,60,126,63,66,66,
66,288,144,288,144,180,90,2090188800,6635520,5806080,1327104,245760,18432,
12288,3072,311040,72576,23328,8640,7776,6912,2592,1296,1296,864,432,768,768,
768,192,1200,120,80,6912,2592,1152,864,768,576,288,144,96,24,84,28,32,108,108,
36,18,40,96,96,48,48,24,60,60,36,42],
[,[1,2,1,2,1,2,1,2,9,10,11,12,13,5,6,5,6,5,6,7,8,5,6,24,25,9,10,11,11,11,11,9,
10,12,9,10,11,12,12,12,12,13,43,44,14,15,14,15,18,19,20,21,53,54,55,56,24,25,
24,25,61,62,63,30,31,32,33,32,33,32,33,37,38,30,31,32,33,39,40,42,81,82,83,43,
44,86,87,49,50,50,53,54,54,55,53,54,59,60,99,100,61,62,63,66,67,66,67,86,87,1,
1,1,5,5,5,5,7,9,9,11,9,12,9,11,13,13,12,12,14,14,18,20,24,24,24,32,30,32,39,
32,32,30,39,39,42,43,43,49,53,55,55,56,59,66,66,74,74,73,86,86,95,99],[1,1,3,
3,5,5,7,7,1,1,1,1,1,14,14,16,16,18,18,20,20,22,22,24,24,3,3,3,3,5,5,5,5,3,7,7,
7,7,5,5,7,7,43,43,45,45,47,47,49,49,51,51,11,11,11,13,57,57,59,59,61,61,61,14,
14,14,14,14,14,16,16,20,20,18,18,22,22,16,16,20,81,81,81,84,84,24,24,88,88,88,
29,29,29,28,30,30,97,97,43,43,101,101,101,47,47,45,45,57,57,110,111,112,113,
114,115,116,117,110,110,110,112,110,111,112,110,111,111,112,129,130,131,132,
133,134,135,113,113,113,113,114,115,115,115,116,117,146,147,148,120,120,124,
126,153,129,130,131,131,132,133,134,137,146],,[1,2,3,4,5,6,7,8,9,10,11,12,13,
14,15,16,17,18,19,20,21,22,23,1,2,26,27,28,29,30,31,32,33,34,35,36,37,38,39,
40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,3,4,5,6,61,63,62,64,65,66,
67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,9,10,88,89,90,91,92,
93,94,95,96,16,17,99,100,101,103,102,104,105,106,107,26,27,110,111,112,113,
114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,
110,112,111,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,
152,114,154,155,157,156,158,118,121,161,162],,[1,2,3,4,5,6,7,8,9,10,11,12,13,
14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,
40,41,42,1,2,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,63,62,64,65,
66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,83,82,3,4,86,87,88,90,89,91,
92,93,94,95,96,97,98,9,10,101,103,102,104,105,106,107,108,109,110,111,112,113,
114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,
133,134,135,136,137,138,139,140,141,142,143,144,145,110,112,148,149,150,151,
152,153,154,155,157,156,158,159,160,161,119],,,,[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,
39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,1,2,2,64,65,
66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,90,89,91,
92,93,94,95,96,97,98,99,100,3,4,4,104,105,106,107,108,109,110,111,112,113,114,
115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,
134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,
153,154,155,156,157,158,159,160,161,162],,[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,
41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,63,62,64,65,66,
67,68,69,70,71,72,73,74,75,76,77,78,79,80,1,2,2,84,85,86,87,88,90,89,91,92,93,
94,95,96,97,98,99,100,101,103,102,104,105,106,107,108,109,110,111,112,113,114,
115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,
134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,
153,154,155,156,157,158,159,160,161,162]],
0,
[(156,157),(89,90),( 89, 90)(156,157),(82,83),( 62, 63)(102,103),( 62, 63)
( 82, 83)( 89, 90)(102,103)(156,157)],
["ConstructMGA","3.Fi22","Fi22.2",[[66,67],[68,69],[70,73],[71,72],[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],[100,103],[101,102],[104,105],[106,107],[108,109],[110,
111],[112,113],[114,115],[116,117],[118,119],[120,121],[122,123],[124,125],
[126,127],[128,129],[130,131],[132,135],[133,134],[136,137],[138,139],[140,
141],[142,143],[144,145],[146,149],[147,148],[150,151],[152,153],[154,155],
[156,157],[158,159],[160,161],[162,163],[164,165]],()]);
ALF("3.Fi22.2","Fi22.2",[1,1,2,2,3,3,4,4,5,5,6,7,8,9,9,10,10,11,11,12,12,
13,13,14,14,15,15,16,16,17,17,18,18,19,20,20,21,22,23,23,24,25,26,26,27,
27,28,28,29,29,30,30,31,31,32,33,34,34,35,35,36,36,36,37,37,38,38,39,39,
40,40,41,42,43,43,44,44,45,45,46,47,47,47,48,48,49,49,50,50,50,51,51,51,
52,53,53,54,54,55,55,56,56,56,57,57,58,58,59,59,60,61,62,63,64,65,66,67,
68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,
92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,
112]);

MOT("6.Fi22",
[
"origin: ATLAS of finite groups, tests: 1.o.r."
],
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318504960,318504960,318504960,5308416,5308416,5308416,117573120,117573120,
117573120,117573120,117573120,117573120,5038848,5038848,279936,279936,34992,
34992,331776,331776,331776,276480,276480,276480,276480,276480,276480,36864,
36864,36864,27648,27648,27648,27648,27648,27648,9216,9216,9216,3600,3600,3600,
3600,3600,3600,933120,933120,933120,933120,933120,933120,559872,559872,559872,
559872,559872,559872,62208,62208,62208,62208,62208,62208,41472,41472,41472,
41472,41472,41472,7776,7776,10368,10368,10368,6912,6912,3456,3456,5184,5184,
5184,5184,5184,5184,864,864,432,432,252,252,252,252,252,252,1152,1152,1152,
1152,1152,1152,384,384,384,192,192,192,192,192,192,1944,1944,1944,1944,1944,
1944,324,324,54,54,360,360,360,360,360,360,240,240,240,240,240,240,132,132,
132,132,132,132,132,132,132,132,132,132,2592,2592,2592,3456,3456,3456,3456,
3456,3456,1728,1728,1728,1728,1728,1728,1728,1728,1728,288,288,288,288,288,
288,288,288,288,288,288,288,432,432,432,432,432,432,72,72,78,78,78,78,78,78,
78,78,78,78,78,78,84,84,84,84,84,84,180,180,180,180,180,180,96,96,96,96,96,96,
648,648,648,648,648,648,648,648,648,648,648,648,108,108,216,216,216,216,216,
216,120,120,120,120,120,120,126,126,126,126,126,126,132,132,132,132,132,132,
132,132,132,132,132,132,144,144,144,144,144,144,180,180,180,180,180,180],
[,[1,3,5,1,3,5,1,3,5,1,3,5,1,3,5,1,3,5,1,3,5,22,24,26,22,24,26,28,28,30,30,32,
32,16,18,14,13,15,17,13,15,17,16,18,14,19,21,20,19,21,20,13,15,17,55,57,59,55,
57,59,22,24,26,22,24,26,28,28,28,28,28,28,28,28,28,28,28,28,22,24,26,22,24,26,
30,30,22,24,26,28,28,30,30,30,30,30,30,30,30,30,30,32,32,104,106,108,104,106,
108,34,36,35,34,36,35,43,45,44,46,48,50,46,48,50,125,127,129,125,127,129,131,
131,133,133,55,57,59,55,57,59,55,57,59,55,57,59,153,155,157,153,155,157,147,
149,151,147,149,151,76,78,74,82,84,80,82,84,80,82,84,80,79,81,83,79,81,83,90,
90,91,91,92,92,76,78,74,79,81,83,94,96,98,94,96,98,103,103,203,205,207,203,
205,207,197,199,201,197,199,201,104,106,108,104,106,108,215,217,219,215,217,
219,116,118,117,116,118,117,125,127,129,125,127,129,125,127,129,125,127,129,
131,131,125,127,129,125,127,129,141,143,145,141,143,145,253,255,257,253,255,
257,153,155,157,153,155,157,147,149,151,147,149,151,165,167,163,162,164,166,
215,217,219,215,217,219],[1,4,1,4,1,4,7,10,7,10,7,10,13,16,13,16,13,16,19,19,
19,1,4,1,4,1,4,1,4,1,4,1,4,34,34,34,37,40,37,40,37,40,43,43,43,46,49,46,49,46,
49,52,52,52,55,58,55,58,55,58,7,10,7,10,7,10,7,10,7,10,7,10,13,16,13,16,13,16,
13,16,13,16,13,16,7,10,19,19,19,19,19,19,19,13,16,13,16,13,16,19,19,19,19,104,
107,104,107,104,107,110,110,110,113,113,113,116,116,116,119,122,119,122,119,
122,28,29,28,29,28,29,28,29,32,33,135,138,135,138,135,138,141,144,141,144,141,
144,147,150,147,150,147,150,153,156,153,156,153,156,34,34,34,34,34,34,34,34,
34,34,34,34,37,40,37,40,37,40,49,46,49,46,46,49,43,43,43,52,52,52,37,40,37,40,
37,40,46,49,197,200,197,200,197,200,203,206,203,206,203,206,209,212,209,212,
209,212,55,58,55,58,55,58,221,221,221,224,224,224,71,68,71,68,71,68,69,72,69,
72,69,72,67,70,73,76,73,76,73,76,247,250,247,250,247,250,104,107,104,107,104,
107,259,262,259,262,259,262,265,268,265,268,265,268,113,113,113,110,110,110,
135,138,135,138,135,138],,[1,6,5,4,3,2,7,12,11,10,9,8,13,18,17,16,15,14,19,21,
20,22,27,26,25,24,23,28,29,30,31,32,33,34,36,35,37,42,41,40,39,38,43,45,44,46,
51,50,49,48,47,52,54,53,1,6,5,4,3,2,61,66,65,64,63,62,67,72,71,70,69,68,73,78,
77,76,75,74,79,84,83,82,81,80,85,86,87,89,88,90,91,92,93,94,99,98,97,96,95,
100,101,102,103,104,109,108,107,106,105,110,112,111,113,115,114,116,118,117,
119,124,123,122,121,120,125,130,129,128,127,126,131,132,133,134,7,12,11,10,9,
8,13,18,17,16,15,14,147,152,151,150,149,148,153,158,157,156,155,154,159,161,
160,162,167,166,165,164,163,168,170,169,171,176,175,174,173,172,177,178,179,
180,181,182,183,185,184,186,188,187,189,194,193,192,191,190,195,196,203,208,
207,206,205,204,197,202,201,200,199,198,209,214,213,212,211,210,22,27,26,25,
24,23,224,226,225,221,223,222,233,238,237,236,235,234,227,232,231,230,229,228,
239,240,241,246,245,244,243,242,37,42,41,40,39,38,253,258,257,256,255,254,259,
264,263,262,261,260,265,270,269,268,267,266,271,273,272,274,276,275,61,66,65,
64,63,62],,[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,
103,1,2,3,4,5,6,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,
125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,
144,145,146,153,154,155,156,157,158,147,148,149,150,151,152,159,160,161,162,
163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,
182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,203,204,205,206,
207,208,197,198,199,200,201,202,7,8,9,10,11,12,215,216,217,218,219,220,224,
225,226,221,222,223,227,228,229,230,231,232,233,234,235,236,237,238,239,240,
241,242,243,244,245,246,247,248,249,250,251,252,22,23,24,25,26,27,265,266,267,
268,269,270,259,260,261,262,263,264,271,272,273,274,275,276,277,278,279,280,
281,282],,,,[1,6,5,4,3,2,7,12,11,10,9,8,13,18,17,16,15,14,19,21,20,22,27,26,
25,24,23,28,29,30,31,32,33,34,36,35,37,42,41,40,39,38,43,45,44,46,51,50,49,48,
47,52,54,53,55,60,59,58,57,56,61,66,65,64,63,62,67,72,71,70,69,68,73,78,77,76,
75,74,79,84,83,82,81,80,85,86,87,89,88,90,91,92,93,94,99,98,97,96,95,100,101,
102,103,104,109,108,107,106,105,110,112,111,113,115,114,116,118,117,119,124,
123,122,121,120,125,130,129,128,127,126,131,132,133,134,135,140,139,138,137,
136,141,146,145,144,143,142,1,6,5,4,3,2,1,6,5,4,3,2,159,161,160,162,167,166,
165,164,163,168,170,169,171,176,175,174,173,172,177,178,179,180,181,182,183,
185,184,186,188,187,189,194,193,192,191,190,195,196,203,208,207,206,205,204,
197,202,201,200,199,198,209,214,213,212,211,210,215,220,219,218,217,216,221,
223,222,224,226,225,233,238,237,236,235,234,227,232,231,230,229,228,239,240,
241,246,245,244,243,242,247,252,251,250,249,248,253,258,257,256,255,254,7,12,
11,10,9,8,7,12,11,10,9,8,271,273,272,274,276,275,277,282,281,280,279,278],,[1,
2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,
30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,
56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,
82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,
106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,
125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,
144,145,146,153,154,155,156,157,158,147,148,149,150,151,152,159,160,161,162,
163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,
182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,1,2,3,4,5,6,1,2,3,
4,5,6,209,210,211,212,213,214,215,216,217,218,219,220,224,225,226,221,222,223,
227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,
246,247,248,249,250,251,252,253,254,255,256,257,258,265,266,267,268,269,270,
259,260,261,262,263,264,271,272,273,274,275,276,277,278,279,280,281,282]],
0,
[(221,224)(222,225)(223,226),(197,203)(198,204)(199,205)(200,206)(201,207)
(202,208),(147,153)(148,154)(149,155)(150,156)(151,157)(152,158)(259,265)
(260,266)(261,267)(262,268)(263,269)(264,270),(  2,  6)(  3,  5)(  8, 12)
(  9, 11)( 14, 18)( 15, 17)( 20, 21)( 23, 27)( 24, 26)( 35, 36)( 38, 42)
( 39, 41)( 44, 45)( 47, 51)( 48, 50)( 53, 54)( 56, 60)( 57, 59)( 62, 66)
( 63, 65)( 68, 72)( 69, 71)( 74, 78)( 75, 77)( 80, 84)( 81, 83)( 88, 89)
( 95, 99)( 96, 98)(105,109)(106,108)(111,112)(114,115)(117,118)(120,124)
(121,123)(126,130)(127,129)(136,140)(137,139)(142,146)(143,145)(148,152)
(149,151)(154,158)(155,157)(160,161)(163,167)(164,166)(169,170)(172,176)
(173,175)(184,185)(187,188)(190,194)(191,193)(198,202)(199,201)(204,208)
(205,207)(210,214)(211,213)(216,220)(217,219)(222,223)(225,226)(227,233)
(228,238)(229,237)(230,236)(231,235)(232,234)(242,246)(243,245)(248,252)
(249,251)(254,258)(255,257)(260,264)(261,263)(266,270)(267,269)(272,273)
(275,276)(278,282)(279,281),(  7, 10)(  8, 11)(  9, 12)( 37, 40)( 38, 41)
( 39, 42)( 61, 64)( 62, 65)( 63, 66)( 67, 70)( 68, 71)( 69, 72)( 85, 86)
( 90, 91)(100,101)(119,122)(120,123)(121,124)(135,138)(136,139)(137,140)
(171,174)(172,175)(173,176)(177,179)(178,180)(189,192)(190,193)(191,194)
(209,212)(210,213)(211,214)(227,230)(228,231)(229,232)(233,236)(234,237)
(235,238)(239,240)(247,250)(248,251)(249,252)(259,262)(260,263)(261,264)
(265,268)(266,269)(267,270)(277,280)(278,281)(279,282)],
["ConstructProj",[["Fi22",[]],["2.Fi22",[]],["3.Fi22",[-1,-1,-25,-25,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,23,23,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
17,17,-1,-1,-1,-1,-1,23,23,-1,-1,-1,-1,-1,-1,-1,-1]],,,["6.Fi22",[-1,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,23,23,23,23,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-25,-25,
-1,-1,-1,-1,-1]]]]);
ALF("6.Fi22","Fi22",[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,
5,6,6,7,7,8,8,9,9,9,10,10,10,10,10,10,11,11,11,12,12,12,12,12,12,13,13,13,
14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,17,17,17,17,17,17,
18,18,18,18,18,18,19,19,20,20,20,21,21,22,22,23,23,23,23,23,23,24,24,25,
25,26,26,26,26,26,26,27,27,27,28,28,28,29,29,29,30,30,30,30,30,30,31,31,
31,31,31,31,32,32,33,33,34,34,34,34,34,34,35,35,35,35,35,35,36,36,36,36,
36,36,37,37,37,37,37,37,38,38,38,39,39,39,39,39,39,40,40,40,41,41,41,41,
41,41,42,42,43,43,44,44,45,45,45,46,46,46,47,47,47,47,47,47,48,48,49,49,
49,49,49,49,50,50,50,50,50,50,51,51,51,51,51,51,52,52,52,52,52,52,53,53,
53,54,54,54,55,55,55,55,55,55,56,56,56,56,56,56,57,57,58,58,58,58,58,58,
59,59,59,59,59,59,60,60,60,60,60,60,61,61,61,61,61,61,62,62,62,62,62,62,
63,63,63,64,64,64,65,65,65,65,65,65]);
ALF("6.Fi22","2E6(2)M8",[1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,5,5,5,
5,5,5,6,6,7,7,8,8,9,9,9,10,10,10,10,10,10,11,11,11,12,12,12,12,12,12,13,
13,13,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,17,17,17,17,
17,17,18,18,18,18,18,18,19,19,20,20,20,21,21,22,22,23,23,23,23,23,23,24,
24,25,25,26,26,26,26,26,26,27,27,27,28,28,28,29,29,29,30,30,30,30,30,30,
31,31,31,31,31,31,32,32,33,33,34,34,34,34,34,34,35,35,35,35,35,35,36,36,
36,36,36,36,37,37,37,37,37,37,38,38,38,39,39,39,39,39,39,40,40,40,41,41,
41,41,41,41,42,42,43,43,44,44,45,45,45,46,46,46,47,47,47,47,47,47,48,48,
49,49,49,49,49,49,50,50,50,50,50,50,51,51,51,51,51,51,52,52,52,52,52,52,
53,53,53,54,54,54,55,55,55,55,55,55,56,56,56,56,56,56,57,57,58,58,58,58,
58,58,59,59,59,59,59,59,60,60,60,60,60,60,61,61,61,61,61,61,62,62,62,62,
62,62,63,63,63,64,64,64,65,65,65,65,65,65]);
ALF("6.Fi22","2.Fi22",[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,
8,9,10,11,12,13,14,15,16,16,16,17,18,17,18,17,18,19,19,19,20,21,20,21,20,
21,22,22,22,23,24,23,24,23,24,25,26,25,26,25,26,27,28,27,28,27,28,29,30,
29,30,29,30,31,32,31,32,31,32,33,34,35,35,35,36,37,38,39,40,41,40,41,40,
41,42,43,44,45,46,47,46,47,46,47,48,48,48,49,49,49,50,50,50,51,52,51,52,
51,52,53,54,53,54,53,54,55,56,57,58,59,60,59,60,59,60,61,62,61,62,61,62,
63,64,63,64,63,64,65,66,65,66,65,66,67,67,67,68,69,68,69,68,69,70,70,70,
71,72,71,72,71,72,73,74,75,76,77,78,79,79,79,80,80,80,81,82,81,82,81,82,
83,84,85,86,85,86,85,86,87,88,87,88,87,88,89,90,89,90,89,90,91,92,91,92,
91,92,93,93,93,94,94,94,95,96,95,96,95,96,97,98,97,98,97,98,99,100,101,
102,101,102,101,102,103,104,103,104,103,104,105,106,105,106,105,106,107,
108,107,108,107,108,109,110,109,110,109,110,111,111,111,112,112,112,113,
114,113,114,113,114]);
ALF("6.Fi22","3.Fi22",[1,2,3,1,2,3,4,5,6,4,5,6,7,8,9,7,8,9,10,11,12,13,14,
15,13,14,15,16,16,17,17,18,18,19,20,21,22,23,24,22,23,24,25,26,27,28,29,
30,28,29,30,31,32,33,34,35,36,34,35,36,37,38,39,37,38,39,40,41,42,40,41,
42,43,44,45,43,44,45,46,47,48,46,47,48,49,49,50,51,52,53,53,54,54,55,56,
57,55,56,57,58,58,59,59,60,61,62,60,61,62,63,64,65,66,67,68,69,70,71,72,
73,74,72,73,74,75,76,77,75,76,77,78,78,79,79,80,81,82,80,81,82,83,84,85,
83,84,85,86,87,88,86,87,88,89,90,91,89,90,91,92,93,94,95,96,97,95,96,97,
98,99,100,101,102,103,101,102,103,104,104,105,105,106,106,107,108,109,110,
111,112,113,114,115,113,114,115,116,116,117,118,119,117,118,119,120,121,
122,120,121,122,123,124,125,123,124,125,126,127,128,126,127,128,129,130,
131,132,133,134,135,136,137,135,136,137,138,139,140,138,139,140,141,141,
142,143,144,142,143,144,145,146,147,145,146,147,148,149,150,148,149,150,
151,152,153,151,152,153,154,155,156,154,155,156,157,158,159,160,161,162,
163,164,165,163,164,165]);
ALF("6.Fi22","3.2E6(2)M8",[1,2,3,1,2,3,4,5,6,4,5,6,7,8,9,7,8,9,10,11,12,
13,14,15,13,14,15,16,16,17,17,18,18,19,20,21,22,23,24,22,23,24,25,26,27,
28,29,30,28,29,30,31,32,33,34,35,36,34,35,36,37,38,39,37,38,39,40,41,42,
40,41,42,43,44,45,43,44,45,46,47,48,46,47,48,49,49,50,51,52,53,53,54,54,
55,56,57,55,56,57,58,58,59,59,60,61,62,60,61,62,63,64,65,66,67,68,69,70,
71,72,73,74,72,73,74,75,76,77,75,76,77,78,78,79,79,80,81,82,80,81,82,83,
84,85,83,84,85,86,87,88,86,87,88,89,90,91,89,90,91,92,93,94,95,96,97,95,
96,97,98,99,100,101,102,103,101,102,103,104,104,105,105,106,106,107,108,
109,110,111,112,113,114,115,113,114,115,116,116,117,118,119,117,118,119,
120,121,122,120,121,122,123,124,125,123,124,125,126,127,128,126,127,128,
129,130,131,132,133,134,135,136,137,135,136,137,138,139,140,138,139,140,
141,141,142,143,144,142,143,144,145,146,147,145,146,147,148,149,150,148,
149,150,151,152,153,151,152,153,154,155,156,154,155,156,157,158,159,160,
161,162,163,164,165,163,164,165]);
ALF("6.Fi22","6.Fi22.2",[1,2,3,4,3,2,5,6,6,5,7,7,8,9,10,11,10,9,12,13,13,
14,15,16,17,16,15,18,19,20,21,22,23,24,25,25,26,27,27,26,28,28,29,30,30,
31,32,33,34,33,32,35,36,36,37,38,39,40,39,38,41,42,42,41,43,43,44,45,45,
44,46,46,47,48,49,50,49,48,51,52,53,54,53,52,55,55,56,57,57,58,58,59,60,
61,62,63,64,63,62,65,65,66,67,68,69,70,71,70,69,72,73,73,74,75,75,76,77,
77,78,79,79,78,80,80,81,82,83,84,83,82,85,86,87,88,89,90,90,89,91,91,92,
93,94,95,94,93,96,97,98,99,100,101,96,101,100,99,98,97,102,103,103,104,
105,106,107,106,105,108,109,109,110,111,111,110,112,112,113,114,113,114,
115,116,117,118,118,119,120,120,121,122,122,121,123,123,124,125,126,127,
128,129,130,131,126,131,130,129,128,127,132,133,133,132,134,134,135,136,
137,138,137,136,139,140,141,139,141,140,142,143,144,145,146,147,145,144,
143,142,147,146,148,148,149,150,151,152,151,150,153,154,154,153,155,155,
156,157,158,159,158,157,160,161,162,163,164,165,163,162,161,160,165,164,
166,167,167,168,169,169,170,171,171,170,172,172],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);
ALF("6.Fi22","6.2E6(2)",[1,6,5,4,3,2,10,9,8,7,12,11,13,18,17,16,15,14,19,
21,20,22,27,26,25,24,23,30,31,28,29,30,31,50,52,51,62,61,60,59,64,63,71,
73,72,77,82,81,80,79,78,83,85,84,92,97,96,95,94,93,101,100,99,98,103,102,
115,114,113,112,117,116,127,132,131,130,129,128,106,111,110,109,108,107,
105,104,124,126,125,136,135,133,134,118,123,122,121,120,119,134,133,135,
136,143,148,147,146,145,144,170,172,171,170,172,171,185,187,186,203,205,
204,203,205,204,212,217,216,215,214,213,218,219,218,219,223,222,221,220,
225,224,226,231,230,229,228,227,232,237,236,235,234,233,238,243,242,241,
240,239,281,283,282,269,271,270,269,271,270,269,271,270,290,289,288,287,
292,291,312,311,308,307,305,306,319,321,320,293,295,294,302,301,300,299,
304,303,309,310,331,336,335,334,333,332,331,336,335,334,333,332,346,345,
344,343,348,347,355,360,359,358,357,356,376,378,377,376,378,377,409,408,
407,406,411,410,415,414,413,412,417,416,419,418,420,425,424,423,422,421,
447,446,445,444,449,448,452,457,456,455,454,453,461,460,459,458,463,462,
467,466,465,464,469,468,483,485,484,483,485,484,516,515,514,513,518,517],[
"fusion map is unique up to table autom.,\n",
"representative compatible with relevant factors"
]);
ALN("6.Fi22",["6.2E6(2)M8","6.Fi22.2M1"]);

MOT("6.Fi22.2",
[
"origin: ATLAS of finite groups, tests: 1.o.r."
],
[774741019852800,387370509926400,387370509926400,774741019852800,110361968640,
110361968640,110361968640,637009920,318504960,318504960,637009920,10616832,
5308416,235146240,117573120,117573120,235146240,10077696,10077696,559872,
559872,69984,69984,663552,331776,276480,276480,276480,73728,36864,55296,27648,
27648,55296,18432,9216,7200,3600,3600,7200,933120,933120,933120,559872,559872,
559872,124416,62208,62208,124416,82944,41472,41472,82944,7776,20736,10368,
6912,6912,6912,10368,5184,5184,10368,864,864,864,504,252,252,504,2304,1152,
2304,1152,768,384,192,192,192,3888,1944,1944,3888,648,648,108,108,360,360,360,
480,240,240,480,132,132,132,132,132,132,5184,2592,6912,3456,3456,6912,3456,
1728,1728,1728,1728,288,288,576,576,576,288,576,288,432,432,432,144,144,78,78,
78,78,78,78,84,84,84,360,180,180,360,96,96,96,648,648,648,648,648,648,108,432,
216,216,432,120,120,120,252,126,126,252,132,132,132,132,132,132,288,144,288,
144,180,180,180,2090188800,6635520,5806080,1327104,245760,18432,12288,3072,
311040,145152,145152,23328,8640,7776,6912,2592,2592,2592,2592,2592,864,432,
768,768,768,192,1200,120,80,6912,2592,1152,864,768,576,288,144,96,48,48,84,28,
32,216,216,108,36,36,36,40,96,96,48,48,48,48,60,60,72,72,84,84],
[,[1,3,3,1,1,3,3,1,3,3,1,1,3,14,16,16,14,18,18,20,20,22,22,11,9,8,10,10,11,9,
12,13,13,12,8,10,37,39,39,37,14,16,16,18,18,18,18,18,18,18,14,16,16,14,20,14,
16,18,20,20,20,20,20,20,20,22,22,68,70,70,68,24,25,24,25,29,30,31,33,33,81,83,
83,81,85,85,87,87,37,39,39,37,39,39,37,96,100,98,96,100,98,50,48,54,52,52,54,
54,52,51,53,53,58,58,59,59,50,48,51,53,61,63,63,67,67,126,130,128,126,130,128,
68,70,70,135,137,137,135,76,77,77,81,83,83,81,83,83,85,81,83,83,81,92,94,94,
156,158,158,156,96,100,98,96,100,98,107,105,104,106,135,137,137,1,1,4,11,11,8,
11,12,14,14,14,18,17,20,14,19,22,22,22,22,20,21,24,24,29,34,37,40,37,54,50,54,
64,54,51,47,61,64,67,67,68,71,76,81,81,85,86,87,87,95,107,104,117,117,116,116,
135,138,152,152,156,156],[1,4,1,4,5,5,5,8,11,8,11,12,12,1,4,1,4,1,4,1,4,1,4,
24,24,26,26,26,29,29,31,34,31,34,35,35,37,40,37,40,5,5,5,5,5,5,8,11,8,11,8,11,
8,11,5,12,12,12,12,12,8,11,8,11,12,12,12,68,71,68,71,72,72,74,74,76,76,78,78,
78,18,19,18,19,18,19,22,23,89,89,89,92,95,92,95,96,99,96,99,96,99,24,24,24,24,
24,24,24,24,26,26,26,34,31,31,34,29,29,35,35,26,26,26,31,34,126,129,126,129,
126,129,132,132,132,37,40,37,40,139,139,139,46,45,46,45,46,45,44,47,50,47,50,
153,153,153,68,71,68,71,160,163,160,163,160,163,74,74,72,72,89,89,89,173,174,
175,176,177,178,179,180,173,173,173,173,175,173,174,175,173,173,174,174,174,
175,195,196,197,198,199,200,201,176,176,176,176,177,178,178,178,179,180,180,
213,214,215,184,184,184,188,191,192,222,195,196,197,197,198,198,199,200,203,
203,213,213],,[1,2,3,4,5,7,6,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,
25,26,28,27,29,30,31,32,33,34,35,36,1,2,3,4,41,43,42,44,46,45,47,48,49,50,51,
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,
78,80,79,81,82,83,84,85,86,87,88,5,7,6,8,9,10,11,96,101,100,99,98,97,102,103,
104,105,106,107,108,109,110,112,111,113,114,115,116,117,118,119,120,121,123,
122,124,125,126,127,128,129,130,131,132,134,133,14,15,16,17,139,140,141,145,
146,147,142,143,144,148,149,150,151,152,26,28,27,156,157,158,159,160,165,164,
163,162,161,166,167,168,169,41,43,42,173,174,175,176,177,178,179,180,181,183,
182,184,185,186,187,188,190,189,192,191,193,194,195,196,197,198,173,175,174,
202,203,204,205,206,207,208,209,210,212,211,213,214,215,217,216,218,219,221,
220,177,223,224,226,225,228,227,181,185,231,232,234,233],,[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,
62,63,64,65,66,67,1,2,3,4,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,
89,90,91,92,93,94,95,96,101,100,99,98,97,102,103,104,105,106,107,108,109,110,
111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,131,130,129,
128,127,5,6,7,135,136,137,138,139,141,140,142,143,144,145,146,147,148,149,150,
151,152,153,154,155,14,15,16,17,163,162,161,160,165,164,166,167,168,169,170,
171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,
190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,
209,210,211,212,173,175,215,216,217,218,219,220,221,222,223,224,226,225,228,
227,229,230,231,232,182,183],,,,[1,2,3,4,5,7,6,8,9,10,11,12,13,14,15,16,17,18,
19,20,21,22,23,24,25,26,28,27,29,30,31,32,33,34,35,36,37,38,39,40,41,43,42,44,
46,45,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,
71,72,73,74,75,76,77,78,80,79,81,82,83,84,85,86,87,88,89,91,90,92,93,94,95,1,
2,3,4,3,2,102,103,104,105,106,107,108,109,110,112,111,113,114,115,116,117,118,
119,120,121,123,122,124,125,126,127,128,129,130,131,132,134,133,135,136,137,
138,139,141,140,145,146,147,142,143,144,148,149,150,151,152,153,155,154,156,
157,158,159,5,7,7,5,6,6,166,167,168,169,170,172,171,173,174,175,176,177,178,
179,180,181,183,182,184,185,186,187,188,190,189,192,191,193,194,195,196,197,
198,199,200,201,202,203,204,205,206,207,208,209,210,212,211,213,214,215,217,
216,218,219,221,220,222,223,224,225,226,227,228,229,230,231,232,234,233],,[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,
82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,101,100,99,98,97,102,103,104,105,
106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,
125,1,2,3,4,3,2,132,133,134,135,136,137,138,139,141,140,142,143,144,145,146,
147,148,149,150,151,152,153,154,155,156,157,158,159,163,162,161,160,165,164,
166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,
185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,
204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,
223,224,225,226,227,228,229,230,231,232,233,234]],
0,
[(227,228),(225,226),(225,226)(227,228),(140,141),(140,141)(225,226)(227,228),
(127,131)(128,130),( 97,101)( 98,100)(160,163)(161,162)(164,165),(  6,  7)
( 27, 28)( 42, 43)( 45, 46)( 79, 80)( 90, 91)( 97,101)( 98,100)(111,112)
(122,123)(127,131)(128,130)(133,134)(140,141)(142,145)(143,146)(144,147)
(154,155)(161,165)(162,164)(171,172)(182,183)(189,190)(191,192)(211,212)
(216,217)(220,221)(225,226)(227,228)(233,234),(  6,  7)( 27, 28)( 42, 43)
( 45, 46)( 79, 80)( 90, 91)(111,112)(122,123)(133,134)(142,145)(143,146)
(144,147)(154,155)(160,163)(161,164)(162,165)(171,172)(182,183)(189,190)
(191,192)(211,212)(216,217)(220,221)(233,234),(182,183)(189,190)(191,192)
(211,212)(216,217)(220,221)(231,232)(233,234)],
["ConstructMGA","6.Fi22","2.Fi22.2",[[115,116],[117,118],[119,122],[120,
121],[123,124],[125,126],[127,128],[129,130],[131,132],[133,134],[135,136],
[137,138],[139,140],[141,142],[143,144],[145,146],[147,148],[149,152],[150,
151],[153,154],[155,156],[157,158],[159,160],[161,162],[163,164],[165,166],
[167,168],[169,170],[171,172],[173,174],[175,176],[177,178],[179,180],[181,
184],[182,183],[185,186],[187,188],[189,190],[191,192],[193,194],[195,198],
[196,197],[199,200],[201,202],[203,204],[205,206],[207,208],[209,210],[211,
212],[213,214],[215,218],[216,217],[219,222],[220,221],[223,226],[224,225],
[227,230],[228,229],[231,232],[233,236],[234,235],[237,240],[238,239],[241,
244],[242,243],[245,248],[246,247],[249,252],[250,251],[253,256],[254,255],
[257,260],[258,259],[261,264],[262,263],[265,268],[266,267],[269,272],[270,
271],[273,274],[275,278],[276,277],[279,282],[280,281]],()]);
ALF("6.Fi22.2","Fi22.2",[1,1,1,1,2,2,2,3,3,3,3,4,4,5,5,5,5,6,6,7,7,8,8,9,
9,10,10,10,11,11,12,12,12,12,13,13,14,14,14,14,15,15,15,16,16,16,17,17,17,
17,18,18,18,18,19,20,20,21,22,22,23,23,23,23,24,25,25,26,26,26,26,27,27,
28,28,29,29,30,30,30,31,31,31,31,32,32,33,33,34,34,34,35,35,35,35,36,36,
36,36,36,36,37,37,38,38,38,38,39,39,40,40,40,41,41,42,42,43,43,44,44,45,
45,45,46,46,47,47,47,47,47,47,48,48,48,49,49,49,49,50,50,50,51,51,51,51,
51,51,52,53,53,53,53,54,54,54,55,55,55,55,56,56,56,56,56,56,57,57,58,58,
59,59,59,60,61,62,63,64,65,66,67,68,69,69,70,71,72,73,74,75,75,76,76,77,
78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,95,96,97,98,99,99,
100,101,102,102,103,104,105,106,107,108,108,109,110,111,111,112,112]);
ALF("6.Fi22.2","2.Fi22.2",[1,2,1,2,3,3,3,4,5,4,5,6,6,7,8,7,8,9,10,11,12,
13,14,15,15,16,16,16,17,17,18,19,18,19,20,20,21,22,21,22,23,23,23,24,24,
24,25,26,25,26,27,28,27,28,29,30,30,31,32,33,34,35,34,35,36,37,38,39,40,
39,40,41,41,42,42,43,43,44,44,44,45,46,45,46,47,48,49,50,51,51,51,52,53,
52,53,54,55,54,55,54,55,56,56,57,58,57,58,59,59,60,60,60,61,62,63,64,65,
65,66,66,67,67,67,68,69,70,71,70,71,70,71,72,72,72,73,74,73,74,75,75,75,
76,77,76,77,76,77,78,79,80,79,80,81,81,81,82,83,82,83,84,85,84,85,84,85,
86,86,87,87,88,88,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,
105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,
123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,
141,142,143,144,145,146,147,148,149,150]);
ALF("6.Fi22.2","3.Fi22.2",[1,2,2,1,3,4,4,5,6,6,5,7,8,9,10,10,9,11,11,12,
12,13,13,14,15,16,17,17,18,19,20,21,21,20,22,23,24,25,25,24,26,27,27,28,
29,29,30,31,31,30,32,33,33,32,34,35,36,37,38,38,39,40,40,39,41,42,42,43,
44,44,43,45,46,47,48,49,50,51,52,52,53,54,54,53,55,55,56,56,57,58,58,59,
60,60,59,61,62,63,61,62,63,64,65,66,67,67,66,68,69,70,71,71,72,72,73,73,
74,75,76,77,78,79,79,80,80,81,82,83,81,82,83,84,85,85,86,87,87,86,88,89,
90,91,92,93,91,92,93,94,95,96,96,95,97,98,98,99,100,100,99,101,102,103,
101,102,103,104,105,106,107,108,109,109,110,111,112,113,114,115,116,117,
118,119,119,120,121,122,123,124,125,125,126,126,127,128,129,130,131,132,
133,134,135,136,137,138,139,140,141,142,143,144,145,145,146,147,148,149,
149,150,151,152,152,153,154,155,156,157,158,158,159,160,161,161,162,162]);

MOT("Isoclinic(6.Fi22.2)",
[
"isoclinic group of the 6.Fi22.2 given in the ATLAS"
],
0,
0,
0,
[(227,228),(225,226),(140,141),(127,131)(128,130),
( 97,101)( 98,100)(160,163)(161,162)(164,165),
(182,183)(189,190)(191,192)(211,212)(216,217)(220,221)(231,232)(233,234),
(  6,  7)( 27, 28)( 42, 43)( 45, 46)( 79, 80)( 90, 91)(111,112)(122,123)
(133,134)(142,145)(143,146)(144,147)(154,155)(160,163)(161,164)(162,165)
(171,172)(231,232)
],
["ConstructIsoclinic",[["6.Fi22.2"]]]);
ALF("Isoclinic(6.Fi22.2)","Fi22.2",[1,1,1,1,2,2,2,3,3,3,3,4,4,5,5,5,5,6,6,
7,7,8,8,9,9,10,10,10,11,11,12,12,12,12,13,13,14,14,14,14,15,15,15,16,16,
16,17,17,17,17,18,18,18,18,19,20,20,21,22,22,23,23,23,23,24,25,25,26,26,
26,26,27,27,28,28,29,29,30,30,30,31,31,31,31,32,32,33,33,34,34,34,35,35,
35,35,36,36,36,36,36,36,37,37,38,38,38,38,39,39,40,40,40,41,41,42,42,43,
43,44,44,45,45,45,46,46,47,47,47,47,47,47,48,48,48,49,49,49,49,50,50,50,
51,51,51,51,51,51,52,53,53,53,53,54,54,54,55,55,55,55,56,56,56,56,56,56,
57,57,58,58,59,59,59,60,61,62,63,64,65,66,67,68,69,69,70,71,72,73,74,75,
75,76,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,95,96,
97,98,99,99,100,101,102,102,103,104,105,106,107,108,108,109,110,111,111,
112,112]);
ALF("Isoclinic(6.Fi22.2)","Isoclinic(2.Fi22.2)",[1,2,1,2,3,3,3,4,5,4,5,6,
6,7,8,7,8,9,10,11,12,13,14,15,15,16,16,16,17,17,18,19,18,19,20,20,21,22,
21,22,23,23,23,24,24,24,25,26,25,26,27,28,27,28,29,30,30,31,32,33,34,35,
34,35,36,37,38,39,40,39,40,41,41,42,42,43,43,44,44,44,45,46,45,46,47,48,
49,50,51,51,51,52,53,52,53,54,55,54,55,54,55,56,56,57,58,57,58,59,59,60,
60,60,61,62,63,64,65,65,66,66,67,67,67,68,69,70,71,70,71,70,71,72,72,72,
73,74,73,74,75,75,75,76,77,76,77,76,77,78,79,80,79,80,81,81,81,82,83,82,
83,84,85,84,85,84,85,86,86,87,87,88,88,88,89,90,91,92,93,94,95,96,97,98,
99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,
117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,
135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150]);
ALF("Isoclinic(6.Fi22.2)","3.Fi22.2",[1,2,2,1,3,4,4,5,6,6,5,7,8,9,10,10,9,
11,11,12,12,13,13,14,15,16,17,17,18,19,20,21,21,20,22,23,24,25,25,24,26,
27,27,28,29,29,30,31,31,30,32,33,33,32,34,35,36,37,38,38,39,40,40,39,41,
42,42,43,44,44,43,45,46,47,48,49,50,51,52,52,53,54,54,53,55,55,56,56,57,
58,58,59,60,60,59,61,62,63,61,62,63,64,65,66,67,67,66,68,69,70,71,71,72,
72,73,73,74,75,76,77,78,79,79,80,80,81,82,83,81,82,83,84,85,85,86,87,87,
86,88,89,90,91,92,93,91,92,93,94,95,96,96,95,97,98,98,99,100,100,99,101,
102,103,101,102,103,104,105,106,107,108,109,109,110,111,112,113,114,115,
116,117,118,119,119,120,121,122,123,124,125,125,126,126,127,128,129,130,
131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,145,146,147,
148,149,149,150,151,152,152,153,154,155,156,157,158,158,159,160,161,161,
162,162]);

MOT("Fi22",
[
"origin: ATLAS of finite groups, tests: 1.o.r."
],
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110592,46080,12288,4608,3072,600,155520,93312,10368,6912,3888,3456,3456,1728,
864,432,216,42,384,384,128,32,324,162,27,60,40,22,22,864,576,576,288,144,144,
144,96,96,72,36,13,13,14,30,32,32,108,108,54,36,20,21,22,22,48,48,30],
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14,14,37,36,17,18,18,18,21,21,22,17,18,23,25,50,49,26,52,29,29,31,31,32,31,35,
60,37,36,39,39,52],[1,2,3,4,1,1,1,1,9,10,11,12,13,14,2,2,3,3,2,4,4,4,3,4,4,26,
27,28,29,30,6,6,8,34,35,36,37,9,9,9,10,12,12,12,11,13,10,12,49,50,51,14,53,54,
16,16,16,17,59,26,61,62,28,27,34],,[1,2,3,4,5,6,7,8,9,10,11,12,13,1,15,16,17,
18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,2,3,36,37,38,39,40,41,42,43,
44,45,46,47,48,50,49,51,5,54,53,56,55,57,58,10,60,61,62,63,64,15],,[1,2,3,4,5,
6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,1,27,28,29,30,31,32,
33,34,35,37,36,38,39,40,41,42,43,44,45,46,47,48,50,49,2,52,54,53,55,56,57,58,
59,5,62,61,63,64,65],,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,
21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,1,1,38,39,40,41,42,43,44,45,46,
47,48,50,49,51,52,53,54,56,55,57,58,59,60,2,2,63,64,65],,[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,
37,36,38,39,40,41,42,43,44,45,46,47,48,1,1,51,52,54,53,55,56,57,58,59,60,62,
61,63,64,65]],
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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],[78,-34,14,-2,15,-3,6,
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-3,-1,-1,2,1,-1,0,-1,0,0,1,0,0,0,-1,-1,2,-1,-1,1,-1,-1,1,-1,-2],[429,77,45,13,
6,24,15,-3,13,5,-3,5,5,4,14,-4,0,6,5,-2,4,7,3,1,1,2,1,1,1,1,0,3,0,2,0,0,0,4,
-2,-2,2,2,2,-1,0,2,-1,-1,0,0,0,1,-1,-1,2,2,-1,0,0,-1,0,0,-2,-2,-1],[1001,-231,
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-1,0,0,-1,1,1],[3003,539,59,-37,105,6,15,6,11,11,-5,3,-5,3,17,26,14,-7,-1,-7,
2,-1,-1,-1,2,0,-1,-1,3,-1,3,0,0,-1,-1,0,0,2,5,5,5,0,0,3,-2,1,-1,0,0,0,0,0,-1,
-1,-1,-1,2,-1,1,0,0,0,-1,-1,2],[3080,616,136,40,119,2,20,2,24,24,8,0,8,5,31,
22,10,7,4,7,-2,4,4,4,-2,0,4,4,0,0,5,-1,-1,1,1,0,0,6,3,3,3,0,0,0,2,-1,0,0,-1,
-1,0,-1,0,0,1,1,1,1,-1,0,0,0,1,1,1],[10725,-715,165,-43,15,114,24,6,29,-15,
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0,0,-2,-1,0,0,0,0,-1,0,-1,-1,2,2,-1,0,0,1,0,0,3,1,0],[13650,1330,210,114,105,
123,33,15,-14,10,2,10,10,0,25,7,3,9,7,9,15,9,-3,3,3,0,-2,-2,-2,2,0,3,0,0,0,-1,
-1,-5,1,1,1,1,1,1,-1,1,1,1,0,0,0,0,0,0,-2,-2,1,0,0,0,-1,-1,1,1,0],[30030,1694,
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0,-3,-3,0,-1,1,0,0,2,-1,-7,5,0,0,0,-2,-1,2,0,0,0,0,-1,0,0,-1,-1,-1,1,1,0,0,0,
1,-1,-1],[32032,-2464,544,-32,91,-44,64,10,64,-24,0,0,8,7,-79,20,4,-5,2,1,4,
-8,4,-2,-2,0,4,-4,0,0,1,1,-2,1,-1,0,0,-8,-5,1,-3,0,0,0,0,-1,0,0,0,0,0,1,0,0,
-1,-1,-1,1,1,0,0,0,-1,1,1],[43680,-4256,416,-32,399,-60,48,-6,0,-24,0,0,8,5,
-71,-44,20,-1,10,1,4,-8,-4,-2,-2,0,-4,4,0,0,3,3,0,-1,1,-1,-1,0,3,-3,-3,0,0,0,
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2,2,2,-2,0,0,3,-2,2,1,0,0,0,0,0,1,1,0,0,0,-2,0,0,0,0,0,0,0],[75075,7315,515,
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0],[75075,-5005,-125,83,420,-12,42,15,-5,15,3,-1,-9,0,-10,-64,28,4,-10,-10,8,
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-1,-1,-1,1,0,0,0,0,0,2,0],[81081,3465,633,-87,0,162,81,0,33,5,-7,-3,-3,6,90,
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0,0,0,0,0,0,0],
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0,0,0,1,1,-2,1,0,0,0,0,1,-1,0],[205920,1056,864,160,-279,-144,72,18,64,24,0,0,
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ARC("Fi22","CAS",[rec(name:="f22",
permchars:=(15,16)(17,18)(22,23)(35,36),
permclasses:=(20,21)(42,43,44),
text:=[
"names:=f22; m[22]; fi22\n",
"       order: 2^17.3^9.5^2.7.11.13 = 64,561,751,654,400\n",
"       number of classes: 65\n",
"       source / origin:\n",
"              hunt, d.c.\n",
"              character tables of certain finite simple groups\n",
"              bull.austral.math.soc. 5\n",
"              [1971],1-42 \n",
""])]);
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ALF("Fi22","2E6(2)",[1,2,3,4,5,7,6,7,11,15,16,19,20,23,24,27,30,26,25,29,
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78,71,73,75,83,83,85,87,91,91,99,100,101,102,106,108,109,110,114,114,122],[
"fusion map is unique up to table automorphisms"
]);
ALN("Fi22",["f22","2E6(2)M7"]);

MOT("Fi22.2",
[
"origin: ATLAS of finite groups, tests: 1.o.r.,\n",
"constructions: Aut(Fi22)"
],
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ARC("Fi22.2","CAS",[rec(name:="f22.2",
permchars:=(27,28)(29,31)(30,32)(33,35)(34,36)(43,47,46,45,44)(48,49)
(58,74,70,84,82,80,78,76,72,69,67,65,63,59,75,71,68,66,64,62)(73,85,83,81,79,
 77)(86,98,97,96,95,94,93,92,91,90,89,88,87),
permclasses:=( 41, 44, 42)( 79, 80)(109,110),
text:=[
"names:=     f22.2, f22.z2, autf22\n",
"    order:     2^17.3^10.5^2.7.11.13 = 193,685,254,963,200\n",
"    number of classes:  165\n",
"    source/origin: gabrysch,th.\n",
"               unpublished\n",
"    comments:  extension of f22 with an outer\n",
"               automorphism of order 2\n",
"    test:      orth.1, min, sym[3]     \n",
""])]);
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0]],]);
ALF("Fi22.2","2E6(2).2",[1,2,3,4,5,7,6,7,11,14,15,17,18,21,22,25,28,24,23,
27,30,29,26,29,30,32,37,37,40,44,46,47,47,48,49,50,59,57,57,61,67,65,68,
62,64,66,72,74,76,79,85,86,87,90,92,93,97,97,103,106,107,107,108,109,111,
112,113,114,114,117,116,115,116,119,117,119,118,118,127,126,122,131,133,
134,134,135,138,135,137,139,141,144,142,145,146,148,149,153,155,156,157,
157,158,165,164,168,168,171,176,177,182,185],[
"fusion map is unique"
]);
ALN("Fi22.2",["f22.2","2E6(2).2M6"]);
ARC("Fi22.2","maxes",["Fi22","2.U6(2).2","O8+(2):S3x2","Fi22.2M4","2^7:S6(2)",
"(2x2^(1+8)):(U4(2):2x2)","S3xU4(3).(2^2)_{122}","2F4(2)'.2",
"2^(5+8):(S3xS6)","3^5:(2xU4(2).2)","3^(1+6)_+:2^(3+4):(S3xS3)","G2(3).2",
"M12.2"]);

LIBTABLE.LOADSTATUS.ctofisc1:="userloaded";

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