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## #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]" ], [264905352699586176614400,31267361914880,67645734912,1908408320,1908408320, 16777216,2097152,1572864,524288,786432,8192,16384,16384,1024,1024,256,256,256, 256,203840,203840,203840,448,448,448,112,112,112,112,112,112,3528,3528,3528, 56,56,56,16547328,4608,192,192,192,4536,4536,4536,72,72,72,63,63,63,63,63,63, 63,63,63,63,63,63,145600,320,80,80,35,35,35,378560,378560,378560,832,832,832, 208,208,208,208,208,208,91,91,91,91,91,91,91,91,91,65,65,65,169,57,57,57,57, 57,57,57,57,57,37,37,37,109,109,109,109,109,109,109,109,109], [,[1,1,1,2,2,2,2,3,3,3,6,6,6,9,8,12,13,13,12,21,22,20,21,22,20,24,25,23,24,25, 23,34,32,33,32,34,33,38,38,39,39,39,44,45,43,43,44,45,50,51,49,53,54,52,56,60, 58,59,57,55,61,61,62,62,66,67,65,69,70,68,69,70,68,72,73,71,72,73,71,84,85,83, 87,88,86,81,82,80,90,91,89,92,94,95,93,97,98,96,100,101,99,103,104,102,108, 109,110,111,112,113,105,106,107],[1,2,3,5,4,6,7,8,9,10,11,13,12,14,15,17,16, 19,18,22,20,21,25,23,24,31,29,30,28,26,27,33,34,32,37,35,36,1,3,8,10,10,38,38, 38,39,39,39,32,34,33,49,50,51,50,51,51,49,50,49,61,62,64,63,67,65,66,69,70,68, 72,73,71,78,79,77,75,76,74,87,88,86,81,82,80,84,85,83,90,91,89,92,94,95,93,93, 94,95,94,95,93,104,102,103,112,113,105,106,107,108,109,110,111],,[1,2,3,4,5,6, 7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,20,24,25,23,27,28,26,30,31,29,34,32, 33,36,37,35,38,39,40,42,41,45,43,44,48,46,47,50,51,49,55,56,60,57,58,52,53,54, 59,1,2,4,5,21,22,20,68,69,70,71,72,73,74,75,76,77,78,79,83,84,85,86,87,88,80, 81,82,68,69,70,92,94,95,93,99,100,101,98,96,97,104,102,103,109,110,111,112, 113,105,106,107,108],,[1,2,3,5,4,6,7,8,9,10,11,13,12,14,15,17,16,19,18,1,1,1, 2,2,2,5,5,5,4,4,4,1,1,1,3,3,3,38,39,40,41,42,44,45,43,47,48,46,38,38,38,43,44, 45,45,43,44,45,43,44,61,62,64,63,61,61,61,70,68,69,73,71,72,79,77,78,76,74,75, 70,68,69,70,68,69,70,68,69,91,89,90,92,93,94,95,96,97,98,99,100,101,104,102, 103,109,110,111,112,113,105,106,107,108],,,,,,[1,2,3,4,5,6,7,8,9,10,11,12,13, 14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39, 40,41,42,45,43,44,48,46,47,49,50,51,58,59,57,53,54,56,60,55,52,61,62,63,64,65, 66,67,1,1,1,2,2,2,4,4,4,5,5,5,20,20,20,21,21,21,22,22,22,61,61,61,1,95,93,94, 100,101,99,96,97,98,104,102,103,109,110,111,112,113,105,106,107,108],,,,,,[1, 2,3,5,4,6,7,8,9,10,11,13,12,14,15,17,16,19,18,21,22,20,24,25,23,30,31,29,27, 28,26,34,32,33,36,37,35,38,39,40,41,42,43,44,45,46,47,48,50,51,49,59,57,58,54, 52,60,55,56,53,61,62,64,63,66,67,65,70,68,69,73,71,72,79,77,78,76,74,75,85,83, 84,88,86,87,82,80,81,91,89,90,92,1,1,1,38,38,38,38,38,38,104,102,103,108,109, 110,111,112,113,105,106,107],,,,,,,,,,,,,,,,,,[1,2,3,4,5,6,7,8,9,10,11,12,13, 14,15,16,17,18,19,21,22,20,24,25,23,27,28,26,30,31,29,34,32,33,36,37,35,38,39, 40,41,42,43,44,45,46,47,48,50,51,49,59,57,58,54,52,60,55,56,53,61,62,63,64,66, 67,65,69,70,68,72,73,71,75,76,74,78,79,77,84,85,83,87,88,86,81,82,80,90,91,89, 92,93,94,95,101,99,100,97,98,96,1,1,1,110,111,112,113,105,106,107,108, 109],,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,[ 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,22,20,21,25,23,24,28,26,27,31, 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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 --> -------------------- [ zur Elbe Produktseite wechseln0.127Quellennavigators ] |
2026-04-02