#############################################################################
##
#W ctonews.tbl GAP table library Thomas Breuer
##
## This file contains new ordinary character tables
##
#H ctbllib history
#H ---------------
#H $Log: ctonews.tbl,v $
#H Revision 4.73 2012/06/20 14:45:32 gap
#H added tables and fusions, as documented in ctbldiff.dat
#H TB
#H
#H Revision 4.72 2012/05/07 15:26:48 gap
#H revert three changes:
#H - use direct product constructions from `[["Symmetric",4],["S6(2)"]]' and
#H `[["Symmetric",4],["U4(2).2"]]' instead of `[["s4"],["S6(2)"]]' and
#H `[["s4"],["U4(2).2"]]', respectively
#H - use the name `"D62x2"' instead of `"D124"'
#H TB
#H
#H Revision 4.71 2012/04/23 16:16:15 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 4.70 2012/03/12 17:01:47 gap
#H omit the fourth argument of `ConstructV4G'
#H TB
#H
#H Revision 4.69 2012/01/30 08:31:58 gap
#H removed #H entries from the headers
#H TB
#H
#H Revision 4.68 2012/01/26 11:09:07 gap
#H added fusions "2xS6(2)" -> "O8-(2).2", "A6.D8" -> "2.Ru"
#H added table of (S3xS3):2xS5 < O8-(2).2
#H TB
#H
#H Revision 4.67 2011/11/23 14:42:15 gap
#H added fusions 2^(3+8):(S3xS6) ->> S3xS6, 2^(6+6):(S3xL3(2)) -> L3(2)xS3
#H TB
#H
#H Revision 4.66 2011/09/28 13:59:20 gap
#H - removed revision entry and SET_TABLEFILENAME call,
#H - added tables of 2x3^4:A6, 3^4:2.A6, 2.(2x3^4:A6), 4.3^(1+4)_+.2S4,
#H 3^2.(3^4:A6), 3^2.(3^(1+4)_+.2S4),
#H - changed the construction of the table of 2^6:U4(2).2
#H (use `ConstructAdjusted' not `ConstructPermuted'),
#H - added fusions 3.ONM6 -> 3.ON.2N3, M12C4 -> U3(3)
#H TB
#H
#H Revision 4.65 2010/11/15 16:48:26 gap
#H added missing maxes (fusions) of S8(2)
#H TB
#H
#H Revision 4.64 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 4.63 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 4.62 2009/05/12 08:01:04 gap
#H fixed a typo
#H TB
#H
#H Revision 4.61 2009/05/11 15:29:27 gap
#H added fusion 7^1+4.2A7 -> M (determined using the table of MN7)
#H TB
#H
#H Revision 4.60 2009/04/27 08:27:24 gap
#H removed some superfluous explicit <nam>M<n> names,
#H which are created automatically
#H TB
#H
#H Revision 4.59 2009/04/22 12:39:06 gap
#H added missing maxes of He.2, ON.2, HN.2, Fi24, and B
#H TB
#H
#H Revision 4.58 2009/01/07 09:49:14 gap
#H added fusion 2^6:S8 -> O8+(2).2
#H TB
#H
#H Revision 4.57 2008/06/24 16:23:05 gap
#H added several fusions and names
#H TB
#H
#H Revision 4.56 2007/07/03 08:50:15 gap
#H added fusions,
#H encoded several tables as index two subdirect products
#H TB
#H
#H Revision 4.55 2006/06/07 07:54:27 gap
#H unified ConstructMixed and ConstructMGA (for better programmatic access)
#H TB
#H
#H Revision 4.54 2006/04/20 11:54:08 gap
#H fixed the known bug in the 2nd power map of the table of 13^1+2.2A4
#H TB
#H
#H Revision 4.53 2005/04/27 07:51:04 gap
#H corrected the table of 7^1+4.2A7 (the one that had been contributed by
#H Simon Norton was wrong, the correct table has been computed directly from
#H a permutation representation, using hardware resources provided by
#H Frank Himstedt
#H TB
#H
#H Revision 4.52 2005/04/20 15:35:07 gap
#H added tables of 2^(1+8):S8 and its factor group 2^8:S8
#H (a maximal subgroup of 2^(1+8).S6(2) < Co2,
#H the group occurs as an inertia factor group of 2^(1+22).Co2 < B),
#H contributed by H. Pahlings
#H TB
#H
#H Revision 4.51 2004/11/24 15:20:20 gap
#H added missing maxes of U4(3) --Max had asked for them--
#H and their class fusions,
#H fixed construction entry for "(2xA6).2^2",
#H fixed fusion "2.U4(3).2_2' -> U4(3).2_2"
#H TB
#H
#H Revision 4.50 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 4.49 2004/03/30 08:02:57 gap
#H changed a fusion text
#H TB
#H
#H Revision 4.48 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 4.47 2003/11/19 09:09:06 gap
#H added links to the generic tables of double covers of altern./symm. groups
#H TB
#H
#H Revision 4.46 2003/11/10 08:08:37 gap
#H added tables of 2x3.A6, 7^1+2.6, M12C4, 1/2(8xS3), (2^2x3).2, 4.2^2,
#H (4xA6).2^2, 5^1+2.2A4, 13^1+2.2A4, 7^1+4.2A7
#H (Simon Norton uses them)
#H TB
#H
#H Revision 4.45 2003/10/30 09:17:59 gap
#H corrected table automorphisms of 2.(A4xA4), 3^3:A4, 3^7.O7(3)
#H TB
#H
#H Revision 4.44 2003/07/22 15:02:02 gap
#H corrected an InfoText:
#H the "2^8:S6(2)" given is *not* contained in "2^8:O8-(2)"
#H TB
#H
#H Revision 4.43 2003/06/10 16:19:12 gap
#H store in several fusions between character tables to which subgroup number
#H in the table of marks of the supergroup the subgroup belongs
#H (in order to make the commutative diagrams testable)
#H TB
#H
#H Revision 4.42 2003/05/15 17:38:19 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 4.41 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 4.40 2003/01/24 15:57:35 gap
#H replaced several fusions by ones that are compatible with Brauer tables
#H TB
#H
#H Revision 4.39 2003/01/22 12:32:52 gap
#H added fusion 2^8:S6(2) -> 2^8:O8+(2)
#H TB
#H
#H Revision 4.38 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 4.37 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 4.36 2002/11/18 17:18:58 gap
#H determined fusion D8xL4(3).2_2 -> O8-(3).2_1
#H TB
#H
#H Revision 4.35 2002/11/18 16:19:06 gap
#H adjusted fusion O7(3).2x2 -> O8-(3).2_1 to the table of O8-(3).2_1
#H (up to now, the fusion had been contained but the table of O8-(3).2_1 not)
#H TB
#H
#H Revision 4.34 2002/11/04 16:33:47 gap
#H added fusions of maxes of U3(3).2,
#H added fusion U3(3).2 -> Fi24' (this took me a whole afternoon ...)
#H TB
#H
#H Revision 4.33 2002/10/22 12:44:13 gap
#H added 215 factor fusions for cases <tbl> -> <tbl> / O_{<p>}(<tbl>)
#H (they make it possible to construct <p>-modular Brauer tables
#H for tables of the type [p^n].<fact> where the <p>-modular Brauer table
#H of <fact> is in the library)
#H TB
#H
#H Revision 4.32 2002/09/25 16:09:26 gap
#H fixed syntax problem in table of O7(3).2x2 (since the previous change)
#H TB
#H
#H Revision 4.31 2002/09/23 15:01:38 gap
#H removed trailing blanks,
#H corrected table of O7(3).2x2 (and its table automorphisms,
#H the fusion was o.k.)
#H TB
#H
#H Revision 4.30 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 4.29 2002/08/21 14:55:19 gap
#H added fusion 3^4:A6 -> U4(3)
#H TB
#H
#H Revision 4.28 2002/07/26 16:58:05 gap
#H added more missing table automorphisms,
#H removed a few inconvenient names such as `c2' for `Co2'
#H (note that `c2' is used for the cyclic group of order 2,
#H which occurs in direct product constructions ...)
#H TB
#H
#H Revision 4.27 2002/07/12 06:45:57 gap
#H further tidying up: removed `irredinfo' stuff, rearranged constructions
#H TB
#H
#H Revision 4.26 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 4.25 2002/03/04 17:10:43 gap
#H moved table of 5:4 to `ctosylno.tbl'
#H TB
#H
#H Revision 4.24 2001/10/22 15:51:04 gap
#H added two new tables (contributed by Faryad Ali)
#H TB
#H
#H Revision 4.23 2001/05/04 16:49:21 gap
#H first revision for ctbllib
#H
#H
#H tbl history (GAP 4)
#H -------------------
#H (Rev. 4.23 of ctbllib coincides with Rev. 4.22 of tbl in GAP 4)
#H
#H RCS file: /gap/CVS/GAP/4.0/tbl/ctonews.tbl,v
#H Working file: ctonews.tbl
#H head: 4.22
#H branch:
#H locks: strict
#H access list:
#H symbolic names:
#H GAP4R2: 4.17.0.4
#H GAP4R2PRE2: 4.17.0.2
#H GAP4R2PRE1: 4.16.0.2
#H GAP4R1: 4.9.0.2
#H keyword substitution: kv
#H total revisions: 23; selected revisions: 23
#H description:
#H ----------------------------
#H revision 4.22
#H date: 2000/04/03 11:06:50; author: gap; state: Exp; lines: +207 -2
#H added tables of 6.U6(2)M3 and (2^2x3).U6(2)M3 (constructed for Eamonn)
#H
#H TB
#H ----------------------------
#H revision 4.21
#H date: 2000/03/31 13:02:42; author: gap; state: Exp; lines: +123 -3
#H added table of 6.U6(2)M3 (= 6.U6(2) \cap 3.Fi22M5 \leq 3.Fi22)
#H
#H TB
#H ----------------------------
#H revision 4.20
#H date: 2000/03/31 11:45:13; author: gap; state: Exp; lines: +14 -2
#H added fusions x.U6(2)M3 -> x.U6(2)
#H
#H TB
#H ----------------------------
#H revision 4.19
#H date: 2000/03/31 11:25:43; author: gap; state: Exp; lines: +56 -9
#H added table of 2.U6(2)M3 (< 2^10.M22)
#H
#H TB
#H ----------------------------
#H revision 4.18
#H date: 2000/03/30 10:12:51; author: gap; state: Exp; lines: +89 -2
#H added table of 3.U6(2)M3 (structure 2^9.3L3(4))
#H
#H TB
#H ----------------------------
#H revision 4.17
#H date: 2000/02/15 10:09:46; author: gap; state: Exp; lines: +180 -2
#H added table of 2^8:S6(2) (computed by Faryad Ali)
#H
#H TB
#H ----------------------------
#H revision 4.16
#H date: 2000/02/02 11:49:08; author: gap; state: Exp; lines: +2 -319
#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 4.15
#H date: 2000/02/01 09:23:07; author: gap; state: Exp; lines: +4 -4
#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 4.14
#H date: 2000/01/06 13:52:06; author: gap; state: Exp; lines: +16 -2
#H added maxes of S5 with fusions (I needed them ...)
#H
#H TB
#H ----------------------------
#H revision 4.13
#H date: 1999/10/21 14:15:47; author: gap; state: Exp; lines: +8 -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 4.12
#H date: 1999/10/04 15:57:15; author: gap; state: Exp; lines: +2 -91
#H added and corrected several fusions from character tables
#H to their tables of marks,
#H unified two instances of the table of (A6xA6):2^2,
#H corrected the name of the table of marks of 2F4(2).
#H
#H TB
#H ----------------------------
#H revision 4.11
#H date: 1999/09/14 13:28:19; author: gap; state: Exp; lines: +62 -62
#H really removed corrupted tables (had only been commented out before)
#H
#H TB
#H ----------------------------
#H revision 4.10
#H date: 1999/07/30 08:01:14; author: gap; state: Exp; lines: +2 -7
#H removed superfluous `galomorphism' components from a few tables
#H
#H TB
#H ----------------------------
#H revision 4.9
#H date: 1999/07/12 17:04:05; author: gap; state: Exp; lines: +66 -66
#H removed incomplete fusion (causes problems in attempts to construct
#H Brauer tables)
#H
#H TB
#H ----------------------------
#H revision 4.8
#H date: 1999/05/14 08:05:56; author: gap; state: Exp; lines: +49 -10
#H added the tables of some maxes of O8+(3)
#H (yes, these tables are not relevant for the release of GAP 4,
#H but Bob Guralnick had asked for them ...)
#H
#H TB
#H ----------------------------
#H revision 4.7
#H date: 1998/12/07 13:11:52; author: gap; state: Exp; lines: +464 -3
#H added new table of S8(2)M3, added some fusions into S8(2)
#H
#H TB
#H ----------------------------
#H revision 4.6
#H date: 1998/04/03 09:34:38; author: gap; state: Exp; lines: +17 -2
#H added table of 2^3.L3(2) (subgroup of G2(3))
#H
#H TB
#H ----------------------------
#H revision 4.5
#H date: 1997/11/25 16:17:24; author: gap; state: Exp; lines: +5 -5
#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 4.4
#H date: 1997/11/25 15:45:39; author: gap; state: Exp; lines: +7 -4
#H first attempt to link the library of character tables and the
#H library of tables of marks
#H TB
#H ----------------------------
#H revision 4.3
#H date: 1997/09/05 12:33:44; author: gap; state: Exp; lines: +32 -2
#H added table of 2^6:U4(2).2 (subgroup of 2^6:S6(2) = Fi22M6)
#H TB
#H ----------------------------
#H revision 4.2
#H date: 1997/08/01 15:43:20; author: gap; state: Exp; lines: +3 -3
#H added table of 2^7:S6(2)
#H (subgroup of Fi22.2; stored using Clifford matrices);
#H added tables of A14 mod p for p = 2, 11, 13
#H (moved ordinary table from `ctomisc1.tbl' to `ctoalter.tbl' for that);
#H added maxes of 2.M12;
#H updated the ``table of contents''.
#H ----------------------------
#H revision 4.1
#H date: 1997/07/17 15:45:53; author: fceller; state: Exp; lines: +2 -2
#H for version 4
#H ----------------------------
#H revision 1.1
#H date: 1996/10/21 16:01:06; author: sam; state: Exp;
#H first proposal of the table library
#H ==========================================================================
##
MOT("(3^2:2xG2(3)).2",
[
"origin: constructed using tables of G2(3), 3^2:2 and F3+,\n",
"17th maximal subgroup of F3+,\n",
"tests: 1.o.r., pow[2,3,7,13]"
],
[152845056,20736,104976,26244,5832,5832,1728,1296,648,648,252,144,972,972,972,
216,234,38211264,5184,52488,52488,6561,1458,1458,864,864,648,648,162,162,63,
72,72,243,243,243,108,108,117,117,38211264,5184,52488,52488,6561,1458,1458,
864,864,648,648,162,162,63,72,72,243,243,243,108,108,117,117,16982784,2304,
11664,2916,648,648,192,144,72,72,28,16,108,108,108,24,26,6048,96,108,72,72,24,
24,28,36,36,36,6048,96,108,72,72,24,24,28,36,36,36],
[,[1,1,3,4,5,6,2,3,5,6,11,7,13,15,14,8,17,18,18,20,21,22,23,24,19,19,20,21,23,
24,31,25,26,34,36,35,27,28,40,39,41,41,43,44,45,46,47,42,42,43,44,46,47,54,48,
49,57,59,58,50,51,63,62,1,1,3,4,5,6,2,3,5,6,11,7,13,15,14,8,17,64,65,67,69,69,
72,72,74,76,78,77,64,65,67,69,69,72,72,74,76,78,77],[1,2,1,1,1,1,7,2,2,2,11,
12,4,4,4,7,17,1,2,1,1,1,1,1,7,7,2,2,2,2,11,12,12,4,4,4,7,7,17,17,1,2,1,1,1,1,
1,7,7,2,2,2,2,11,12,12,4,4,4,7,7,17,17,64,65,64,64,64,64,70,65,65,65,74,75,67,
67,67,70,80,92,93,92,92,92,93,93,99,94,94,94,81,82,81,81,81,82,82,88,83,83,
83],,,,[1,2,3,4,5,6,7,8,9,10,1,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,
27,28,29,30,18,32,33,34,35,36,37,38,40,39,41,42,43,44,45,46,47,48,49,50,51,52,
53,41,55,56,57,58,59,60,61,63,62,64,65,66,67,68,69,70,71,72,73,64,75,76,77,78,
79,80,92,93,94,95,96,98,97,92,100,101,102,81,82,83,84,85,87,86,81,89,90,
91],,,,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,1,18,19,20,21,22,23,24,25,26,
27,28,29,30,31,32,33,34,35,36,37,38,18,18,41,42,43,44,45,46,47,48,49,50,51,52,
53,54,55,56,57,58,59,60,61,41,41,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,
79,64,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102]],
0,
[(86,87)(97,98),(62,63),(43,44)(48,49)(50,51)(55,56)(60,61),(39,40),(20,21)
(25,26)(27,28)(32,33)(37,38),(18,41)(19,42)(20,43)(21,44)(22,45)(23,46)(24,47)
(25,48)(26,49)(27,50)(28,51)(29,52)(30,53)(31,54)(32,55)(33,56)(34,57)(35,58)
(36,59)(37,60)(38,61)(39,62)(40,63),( 81, 92)( 82, 93)( 83, 94)( 84, 95)
( 85, 96)( 86, 97)( 87, 98)( 88, 99)( 89,100)( 90,101)( 91,102),( 14, 15)
( 35, 36)( 58, 59)( 77, 78)( 84, 85)( 90, 91)( 95, 96)(101,102)],
["ConstructIndexTwoSubdirectProduct","3^2:2","3^2:4","G2(3)","G2(3).2",[130,
131,132,133,134,135,136,137,138,139,140,158,159,160,161,162,163,164,165,166,
167,168],(),(29,30)(31,32)(33,34)(35,36)(37,38)(39,40)(42,43)(44,45)(51,52)
(53,54)(55,56)(63,81,69,90,84,72,93,87,80,68,85,73,97,96,95,91,83,71,94,92,88,
74,98,100,76,101,77,65)(64,82,70,89,75,102,78,66)(67,86,79)]);
ALF("(3^2:2xG2(3)).2","3^2:4",[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,
2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,
3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,
6,6,6,6,6,6,6]);
ALF("(3^2:2xG2(3)).2","G2(3).2",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,
17,1,2,3,3,4,5,6,7,7,8,8,9,10,11,12,12,13,14,15,16,16,17,17,1,2,3,3,4,5,6,
7,7,8,8,9,10,11,12,12,13,14,15,16,16,17,17,1,2,3,4,5,6,7,8,9,10,11,12,13,
14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,18,19,20,21,22,23,24,25,26,
27,28]);
ALF("(3^2:2xG2(3)).2","F3+",[1,3,5,5,7,6,9,17,20,14,24,26,30,30,30,39,51,
4,16,4,7,7,7,7,40,38,16,22,22,22,69,77,76,33,33,33,40,43,99,100,8,23,8,8,
8,8,8,46,47,23,23,23,23,70,78,79,29,32,32,46,47,101,102,2,3,15,15,19,18,
11,17,22,21,52,26,62,62,62,45,83,10,11,44,49,49,50,50,87,98,98,98,10,11,
44,49,49,50,50,87,98,98,98],[
"fusion map is unique up to table automorphisms"
]);
MOT("(3xA6).2_1",
[
"origin: Dixon's Algorithm\n",
" subgroup of U5(2).2"
],
[2160,15,15,15,1080,27,54,27,54,24,12,6,6,48,48,8,24,48],
[,[1,2,3,4,5,6,7,8,9,5,10,7,9,1,1,15,15,1],[1,2,2,2,1,1,1,1,1,15,17,14,18,14,
15,16,17,18],,[1,1,5,5,5,6,7,8,9,10,11,12,13,14,15,16,17,18]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,1,-1,1,
-1],[2,2,-1,-1,-1,-1,2,-1,2,-1,-1,0,0,0,2,0,2,0],[5,0,0,0,5,-1,-1,2,2,1,-1,1,
0,1,1,-1,-1,-3],
[TENSOR,[4,2]],[5,0,0,0,5,2,2,-1,-1,1,-1,0,-1,3,1,1,-1,-1],
[TENSOR,[6,2]],[9,-1,-1,-1,9,0,0,0,0,1,1,0,0,3,1,-1,1,3],
[TENSOR,[8,2]],[10,0,0,0,10,1,1,1,1,-2,0,-1,1,2,-2,0,0,-2],
[TENSOR,[10,2]],[10,0,0,0,-5,1,-2,-2,4,-1,1,0,0,0,2,0,-2,0],[10,0,0,0,-5,-2,4,
1,-2,-1,1,0,0,0,2,0,-2,0],[16,1,1,1,16,-2,-2,-2,-2,0,0,0,0,0,0,0,0,0],[16,1,
-E(15)^7-E(15)^11-E(15)^13-E(15)^14,-E(15)-E(15)^2-E(15)^4-E(15)^8,-8,1,-2,1,
-2,0,0,0,0,0,0,0,0,0],
[GALOIS,[15,7]],[18,-2,1,1,-9,0,0,0,0,-1,-1,0,0,0,2,0,2,0],[20,0,0,0,-10,-1,2,
-1,2,2,0,0,0,0,-4,0,0,0]],
[(3,4),(6,8)(7,9)(12,13)(14,18)]);
ARC("(3xA6).2_1","tomfusion",rec(name:="(A6x3):2",map:=[1,17,55,55,5,8,6,
9,7,20,52,27,28,3,4,13,12,2],text:=[
"fusion map is unique up to table autom."
]));
ALF("(3xA6).2_1","A9",[1,9,17,18,4,5,6,6,4,10,16,11,10,3,2,7,7,2],[
"fusion map is unique up to table autom."
]);
ALF("(3xA6).2_1","U5(2).2",[1,11,29,29,4,5,7,7,6,15,27,34,33,31,3,32,10,
31]);
ALF("(3xA6).2_1","A6.2_1",[1,6,6,6,1,3,3,4,4,2,5,10,11,7,2,9,5,8]);
ALF("(3xA6).2_1","S3",[1,1,2,2,2,2,1,2,1,2,2,3,3,3,1,3,1,3]);
MOT("(A6xA6).D8",
[
"origin: Dixon's Algorithm,\n",
"8th maximal subgroup of HN"
],
[1036800,11520,512,6480,324,324,5760,128,128,3600,50,144,80,72,45,40,2304,
2304,192,128,144,144,36,36,24,1440,32,36,36,16,10,96,96,16,12,12,80,80,32,32,
16,20,40,40],
[,[1,1,1,4,5,6,2,3,2,10,11,4,10,12,15,13,1,1,2,3,4,4,5,6,12,1,3,5,5,8,11,18,
18,20,24,24,2,7,8,8,9,13,16,16],[1,2,3,1,1,1,7,8,9,10,11,2,13,7,10,16,17,18,
19,20,17,18,17,18,19,26,27,26,26,30,31,33,32,34,32,33,37,38,40,39,41,42,44,
43],,[1,2,3,4,5,6,7,8,9,1,1,12,2,14,4,7,17,18,19,20,21,22,23,24,25,26,27,28,
29,30,26,32,33,34,35,36,37,38,39,40,41,37,38,38]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1],
[TENSOR,[2,3]],[2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,-2,-2,-2,-2,-2,-2,-2,-2,-2,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[20,12,4,11,2,2,8,-4,0,10,0,3,2,-1,1,-2,
-4,-4,-4,-4,-1,-1,2,2,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[20,12,4,11,2,
2,8,-4,0,10,0,3,2,-1,1,-2,4,4,4,4,1,1,-2,-2,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0],[18,10,2,9,0,0,10,2,2,8,-2,1,0,1,-1,0,-6,-6,-2,2,-3,-3,0,0,1,0,0,0,0,0,
0,0,0,0,0,0,-2,0,2,2,0,-2,0,0],
[TENSOR,[8,2]],[18,10,2,9,0,0,10,2,2,8,-2,1,0,1,-1,0,6,6,2,-2,3,3,0,0,-1,0,0,
0,0,0,0,0,0,0,0,0,0,-2,0,0,2,0,-2,-2],
[TENSOR,[10,2]],[40,16,-8,22,4,4,20,0,-4,20,0,-2,-4,2,2,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[50,10,2,5,5,-4,-10,2,-2,0,0,1,0,-1,0,0,
10,-6,2,2,1,-3,1,0,-1,10,2,1,1,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[13,3]],[50,10,2,5,5,-4,-10,2,-2,0,0,1,0,-1,0,0,-10,6,-2,-2,-1,3,-1,0,
1,0,0,-3,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[15,3]],[32,16,0,14,-4,-4,16,0,0,17,2,-2,1,-2,-1,1,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,-4,-4,0,0,0,1,1,1],
[TENSOR,[17,2]],[50,10,2,5,-4,5,-10,2,-2,0,0,1,0,-1,0,0,-6,10,2,2,-3,1,0,1,-1,
0,0,0,0,0,0,2,2,2,-1,-1,0,0,0,0,0,0,0,0],
[TENSOR,[19,2]],[50,10,2,5,-4,5,-10,2,-2,0,0,1,0,-1,0,0,6,-10,-2,-2,3,-1,0,-1,
1,0,0,0,0,0,0,4*E(4),-4*E(4),0,-E(4),E(4),0,0,0,0,0,0,0,0],
[TENSOR,[21,2]],[81,9,1,0,0,0,9,1,1,-9,1,0,-1,0,0,-1,9,9,-3,1,0,0,0,0,0,9,1,0,
0,1,-1,-3,-3,1,0,0,1,-1,1,1,-1,1,-1,-1],
[TENSOR,[23,2]],
[TENSOR,[23,4]],
[TENSOR,[23,3]],[162,18,2,0,0,0,18,2,2,-18,2,0,-2,0,0,-2,-18,-18,6,-2,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[180,28,4,9,0,0,-8,-4,0,-10,0,1,-2,1,
-1,2,-12,-12,-4,4,3,3,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[180,28,4,
9,0,0,-8,-4,0,-10,0,1,-2,1,-1,2,12,12,4,-4,-3,-3,0,0,1,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0],[200,0,-8,20,2,2,-20,0,4,0,0,0,0,-2,0,0,-16,16,0,0,2,-2,2,-2,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[200,0,-8,20,2,2,-20,0,4,0,0,0,0,-2,
0,0,16,-16,0,0,-2,2,-2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[200,-40,8,
20,2,2,0,0,0,0,0,-4,0,0,0,0,-8,8,0,0,4,-4,-2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0],[100,-20,4,10,1,1,0,0,0,0,0,-2,0,0,0,0,4,-4,0,0,-2,2,1,-1,0,-10,2,
-1,-1,0,0,2*E(4),-2*E(4),0,E(4),-E(4),0,0,2*E(4),-2*E(4),0,0,0,0],
[TENSOR,[33,2]],
[TENSOR,[33,3]],
[TENSOR,[33,4]],[256,0,0,-32,4,4,0,0,0,16,1,0,0,0,-2,0,0,0,0,0,0,0,0,0,0,16,0,
-2,-2,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[37,3]],[320,32,0,-4,-4,-4,-32,0,0,10,0,-4,2,4,1,-2,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[360,-16,-8,18,0,0,20,0,-4,-20,0,2,4,2,
-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[288,16,0,-18,0,
0,16,0,0,-7,-2,-2,1,-2,2,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,4,-4,0,0,0,
-1,1,1],
[TENSOR,[41,2]],[320,-32,0,-4,-4,-4,0,0,0,10,0,4,-2,0,1,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-E(40)^7-E(40)^13+E(40)^21-E(40)^23+E(40)^29
+E(40)^31-E(40)^37+E(40)^39,E(40)^7+E(40)^13-E(40)^21+E(40)^23-E(40)^29
-E(40)^31+E(40)^37-E(40)^39],
[TENSOR,[43,2]]],
[(43,44),(32,33)(35,36)(39,40),(28,29)]);
ALF("(A6xA6).D8","HN",[1,2,3,4,4,5,7,6,7,9,13,14,22,30,34,41,2,3,7,6,14,
15,14,16,30,2,6,14,14,19,26,8,8,19,32,32,7,18,19,19,18,41,53,54],[
"fusion map is unique up to table automorphisms"
]);
ALF("(A6xA6).D8","(S6xS6).2^2",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,
18,19,20,21,22,23,24,25,43,45,46,46,48,49,54,54,65,70,70,53,59,64,64,62,
71,73,73],[
"fusion map is unique up to table aut."
]);
MOT("2.(A4xA4)",
[
"origin: Dixon's Algorithm,\n",
"normal subgroup of index 2 in U4(2)M5"
],
[288,18,18,16,18,12,12,72,72,18,18,12,12,72,72,18,18,18,48,48,72,72,72,72,
288],
[,[1,3,2,1,11,14,15,23,24,11,5,8,9,21,22,5,3,2,25,25,24,23,22,21,1],[1,1,1,4,
1,19,20,25,25,25,1,20,19,25,25,25,25,25,19,20,1,1,1,1,25]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,E(3)^2,E(3),1,E(3)^2,
E(3),1,1,E(3),E(3)^2,E(3),1,E(3)^2,E(3)^2,1,E(3),E(3)^2,E(3),1,1,E(3),1,1,
E(3)^2,1],
[TENSOR,[2,2]],[1,E(3)^2,E(3),1,E(3),1,E(3)^2,E(3)^2,1,E(3),E(3)^2,E(3),1,1,
E(3),E(3)^2,E(3)^2,E(3),1,1,1,E(3)^2,E(3),1,1],
[TENSOR,[2,4]],
[TENSOR,[2,5]],
[TENSOR,[4,4]],
[TENSOR,[2,7]],
[TENSOR,[2,8]],[3,0,0,-1,0,0,-1,3,0,0,0,-1,0,0,3,0,0,0,3,-1,0,3,3,0,3],[3,0,0,
-1,0,-1,0,0,3,0,0,0,-1,3,0,0,0,0,-1,3,3,0,0,3,3],
[TENSOR,[10,7]],
[TENSOR,[10,4]],
[TENSOR,[11,2]],
[TENSOR,[11,3]],[4,1,1,0,1,0,0,2,2,-1,1,0,0,2,2,-1,-1,-1,0,0,-2,-2,-2,-2,-4],
[TENSOR,[16,6]],
[TENSOR,[16,8]],
[TENSOR,[16,7]],
[TENSOR,[16,5]],
[TENSOR,[16,3]],
[TENSOR,[16,2]],
[TENSOR,[16,9]],
[TENSOR,[16,4]],[9,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-3,-3,0,0,0,0,9]],
[(2,3)(5,11)(6,13)(7,12)(8,15)(9,14)(10,16)(17,18)(21,24)(22,23),(2,5)(3,11)
(7,12)(8,15)(10,17)(16,18)(22,23),(2,3)(6,7)(8,9)(12,13)(14,15)(17,18)(19,20)
(21,22)(23,24)]);
ALF("2.(A4xA4)","U4(2)",[1,6,6,3,7,19,20,12,11,15,7,19,20,12,11,15,13,14,
8,8,4,5,4,5,2],[
"fusion map is unique up to table automorphisms"
]);
MOT("2.2^(2+8).(3xA5)",
[
"2nd maximal subgroup of 2.G2(4), of structure 2.2^{2+8}.(3xA5),\n",
"constructed by S. Irnich and J. M\"uller using the tables of G2(4)M2,\n",
"G2(4), 2.G2(4), and the splitting of classes computed from a perm. repr.,\n",
"tests: 1.o.r., pow[2,3,5]"
],
[368640,368640,122880,122880,6144,6144,768,3072,3072,768,512,360,360,360,360,
192,256,256,256,256,32,64,64,12,12,1152,1152,384,384,96,96,96,96,96,96,48,48,
72,72,72,72,12,12,120,120,40,40,30,30,30,30,120,120,40,40,30,30,30,30],
[,[1,1,1,1,1,1,2,3,3,4,3,14,14,13,13,2,5,5,5,5,8,11,11,15,12,27,27,27,27,27,
27,27,27,28,28,29,29,40,40,39,39,41,38,53,53,53,53,58,58,57,57,44,44,44,44,50,
50,49,49],[1,2,3,4,5,6,7,8,9,10,11,2,1,1,2,16,17,18,19,20,21,22,23,16,16,2,1,
3,4,5,6,5,6,8,9,10,10,2,1,1,2,7,7,53,52,54,55,52,53,53,52,45,44,46,47,45,44,
44,45],,[1,2,3,4,5,6,7,8,9,10,11,15,14,13,12,16,17,18,19,20,21,22,23,25,24,26,
27,28,29,32,33,30,31,34,35,37,36,41,40,39,38,43,42,1,2,3,4,15,14,13,12,2,1,3,
4,15,14,13,12]],
0,
[(36,37),(30,32)(31,33),(19,20),(44,53)(45,52)(46,54)(47,55)(48,56)(49,57)
(50,58)(51,59),(12,15)(13,14)(24,25)(38,41)(39,40)(42,43)(48,51)(49,50)(56,59)
(57,58)],
["ConstructProj",[["2^(2+8):(3xA5)",[]],["2.2^(2+8).(3xA5)",[]]]]);
ALF("2.2^(2+8).(3xA5)","2^(2+8):(3xA5)",[1,1,2,2,3,3,4,5,5,6,7,8,8,9,9,10,
11,11,12,12,13,14,14,15,16,17,17,18,18,19,19,20,20,21,21,22,23,24,24,25,
25,26,27,28,28,29,29,30,30,31,31,32,32,33,33,34,34,35,35]);
ALF("2.2^(2+8).(3xA5)","2.G2(4)",[1,2,3,4,3,4,5,10,11,12,13,9,8,8,9,5,10,
11,13,13,27,28,29,24,24,7,6,22,23,22,23,22,23,36,37,38,39,9,8,8,9,24,24,
18,19,30,31,49,48,48,49,21,20,32,33,51,50,50,51],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
MOT("2F4(8)",
[
"source: Gunter Malle, tests: 1.o.r., pow[2,3,5,7,13,19,37,109]"
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ARC("2F4(8)","extInfo",["","3"]);
MOT("2^(1+6)_-3.3.3^2:2",
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[TENSOR,[7,2]],
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[TENSOR,[9,2]],[6,-3,0,0,0,0,3,-3,0,0,-3,0,0,0,0,0,0,0,0,0,0,0,0,3,3,3,3,-3,0,
0,0,0,6,6,0,0,6,0,6,0,0],[6,-3,0,0,0,0,-3,0,3,0,-3,0,0,0,0,0,0,0,0,0,0,0,0,-3,
-3,-3,-3,0,3,3,0,0,6,6,0,0,6,0,6,0,0],[6,-3,0,0,0,0,0,3,-3,0,-3,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,3,-3,-3,0,0,6,6,0,0,6,0,6,0,0],[8,-1,-1,-1,2,2,-4,-1,2,2,1,
1,1,-2,-2,0,0,E(8)+E(8)^3,E(8)+E(8)^3,-E(8)-E(8)^3,-E(8)-E(8)^3,0,0,4,0,0,0,1,
-2,0,-2,0,-8,0,2*E(8)+2*E(8)^3,-2*E(8)-2*E(8)^3,0,0,0,0,0],
[TENSOR,[14,2]],[9,0,0,0,3,3,6,0,3,0,0,0,0,3,3,-1,-1,1,1,1,1,-1,-1,6,2,2,-2,0,
3,-1,0,0,9,5,1,1,-3,1,1,-1,-1],
[TENSOR,[16,2]],[9,0,0,0,3*E(3)^2,3*E(3),-3,0,3,0,0,0,0,3*E(3),3*E(3)^2,
-E(3)^2,-E(3),E(3),E(3)^2,E(3),E(3)^2,-E(3),-E(3)^2,-3,-E(3)+3*E(3)^2,
3*E(3)-E(3)^2,1,0,3,-1,0,0,9,5,1,1,-3,1,1,-1,-1],
[TENSOR,[18,2]],
[GALOIS,[19,2]],
[TENSOR,[20,2]],[16,-2,1,1,4,4,-8,-2,4,-2,2,-1,-1,-4,-4,0,0,0,0,0,0,0,0,8,0,0,
0,2,-4,0,2,0,-16,0,0,0,0,0,0,0,0],[16,-2,1,1,4,4,4,1,-2,4,2,-1,-1,-4,-4,0,0,0,
0,0,0,0,0,-4,0,0,0,-1,2,0,-4,0,-16,0,0,0,0,0,0,0,0],[16,-2,-2,1,4,4,4,1,-2,-2,
2,2,-1,-4,-4,0,0,0,0,0,0,0,0,-4,0,0,0,-1,2,0,2,0,-16,0,0,0,0,0,0,0,0],[16,-2,
1,-2,4,4,4,1,-2,-2,2,-1,2,-4,-4,0,0,0,0,0,0,0,0,-4,0,0,0,-1,2,0,2,0,-16,0,0,0,
0,0,0,0,0],[18,0,0,0,6,6,-6,0,-3,0,0,0,0,6,6,-2,-2,0,0,0,0,0,0,-6,-2,-2,2,0,
-3,1,0,0,18,10,0,0,-6,0,2,0,0],[18,0,0,0,6*E(3),6*E(3)^2,3,0,-3,0,0,0,0,
6*E(3)^2,6*E(3),-2*E(3),-2*E(3)^2,0,0,0,0,0,0,3,-3*E(3)+E(3)^2,E(3)-3*E(3)^2,
-1,0,-3,1,0,0,18,10,0,0,-6,0,2,0,0],
[GALOIS,[27,2]],[24,-3,0,0,6*E(3)^2,6*E(3),0,0,0,0,3,0,0,-6*E(3),-6*E(3)^2,0,
0,-E(24)^11-E(24)^17,-E(24)-E(24)^19,E(24)^11+E(24)^17,E(24)+E(24)^19,0,0,0,0,
0,0,0,0,0,0,0,-24,0,-2*E(8)-2*E(8)^3,2*E(8)+2*E(8)^3,0,0,0,0,0],
[TENSOR,[29,2]],
[GALOIS,[29,5]],
[TENSOR,[31,2]],[27,0,0,0,0,0,9,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,9,-3,-3,1,0,0,
0,0,0,27,3,3,3,3,-1,-5,-1,3],
[TENSOR,[33,2]],[27,0,0,0,0,0,0,0,0,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
3,-1,27,-9,3,3,-1,-1,3,1,-3],
[TENSOR,[35,2]],[48,3,0,0,0,0,-12,3,0,0,-3,0,0,0,0,0,0,0,0,0,0,0,0,12,0,0,0,
-3,0,0,0,0,-48,0,0,0,0,0,0,0,0],[48,3,0,0,0,0,0,-3,-6,0,-3,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,3,6,0,0,0,-48,0,0,0,0,0,0,0,0],[48,3,0,0,0,0,12,0,6,0,-3,0,0,0,
0,0,0,0,0,0,0,0,0,-12,0,0,0,0,-6,0,0,0,-48,0,0,0,0,0,0,0,0],[54,0,0,0,0,0,-9,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-9,3,3,-1,0,0,0,0,0,54,6,0,0,6,0,-10,0,0],[54,
0,0,0,0,0,0,0,0,-3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-3,1,54,-18,0,0,-2,
0,6,0,0]],
[(3,4)(12,13),(18,20)(19,21)(35,36),(5,6)(14,15)(16,17)(18,19)(20,21)(22,23)
(25,26)]);
ALF("2^(1+6)_-3.3.3^2:2","U5(2).2",[1,5,21,21,6,6,4,7,5,6,13,30,30,16,16,
26,26,42,42,43,43,33,33,12,24,24,15,18,14,25,16,26,2,8,36,35,8,37,3,32,31]);
MOT("2^(2+8):(3xA5)",
[
"maximal subgroup of G2(4), of structure 2^2+8:(3xA5),\n",
"tests: 1.o.r., pow[2,3,5]"
],
[184320,61440,3072,768,1536,768,512,180,180,192,128,128,32,32,12,12,576,192,
48,48,48,48,48,36,36,12,12,60,20,15,15,60,20,15,15],
[,[1,1,1,1,2,2,2,9,8,1,3,3,5,7,9,8,17,17,17,17,18,18,18,25,24,25,24,32,32,35,
34,28,28,31,30],[1,2,3,4,5,6,7,1,1,10,11,12,13,14,10,10,1,2,3,3,5,6,6,1,1,4,4,
32,33,32,32,28,29,28,28],,[1,2,3,4,5,6,7,9,8,10,11,12,13,14,16,15,17,18,20,19,
21,23,22,25,24,27,26,1,2,9,8,1,2,9,8],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,
16,17,18,19,20,21,22,23,24,25,26,27,32,33,34,35,28,29,30,31],,,,[1,2,3,4,5,6,
7,9,8,10,11,12,13,14,16,15,17,18,20,19,21,23,22,25,24,27,26,28,29,31,30,32,33,
35,34],,[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,
27,32,33,34,35,28,29,30,31]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[3,3,
3,3,3,3,3,3,3,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,-E(5)-E(5)^4,
-E(5)-E(5)^4,-E(5)-E(5)^4,-E(5)-E(5)^4,-E(5)^2-E(5)^3,-E(5)^2-E(5)^3,
-E(5)^2-E(5)^3,-E(5)^2-E(5)^3],
[GALOIS,[2,2]],[4,4,4,4,4,4,4,4,4,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,-1,-1,
-1,-1,-1,-1,-1,-1],[5,5,5,5,5,5,5,5,5,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,
-1,-1,-1,0,0,0,0,0,0,0,0],[1,1,1,1,1,1,1,E(3),E(3)^2,1,1,1,1,1,E(3),E(3)^2,1,
1,1,1,1,1,1,E(3),E(3)^2,E(3),E(3)^2,1,1,E(3),E(3)^2,1,1,E(3),E(3)^2],
[TENSOR,[6,6]],
[TENSOR,[2,6]],
[TENSOR,[3,6]],
[TENSOR,[2,7]],
[TENSOR,[3,7]],
[TENSOR,[4,6]],
[TENSOR,[4,7]],
[TENSOR,[5,6]],
[TENSOR,[5,7]],[15,15,-1,3,7,-5,-1,0,0,3,3,3,-1,-1,0,0,6,6,2,2,-2,-2,-2,0,0,0,
0,0,0,0,0,0,0,0,0],[15,15,-1,3,7,-5,-1,0,0,3,3,3,-1,-1,0,0,-3,-3,
3*E(3)-E(3)^2,-E(3)+3*E(3)^2,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[17,2]],[30,30,14,-6,6,2,-2,0,0,-6,2,2,-2,2,0,0,3,3,-1,-1,3,-1,-1,0,0,
0,0,0,0,0,0,0,0,0,0],[30,30,14,-6,6,2,-2,0,0,6,-2,-2,2,-2,0,0,3,3,-1,-1,3,-1,
--> --------------------
--> maximum size reached
--> --------------------
