|
#############################################################################
##
#W ctosylno.tbl GAP table library Thomas Breuer
##
## This file contains the ordinary character tables of the Sylow normalizers
## of sporadic simple groups.
## Many of these tables have been published in~\cite{Ost86},
## they are marked by `"origin: Ostermann"' in their `InfoText' value.
##
#T change: The primes are listed up in brackets after the group names.
##
## $M_{11}$, $M_{12}$, $M_{22}$, $M_{23}$, $M_{24}$ (2,3 for each),
##
## $J_1$ (2), $J_2$ (2,3,5), $J_3$ (2,3), $J_4$ (3,11),
##
## $HS$, $McL$, $Suz$, $Ru$ and $Ly$ (2,3,5 for each),
##
## $ON$ (2,3,7), $He$ (2,3,5,7), $Co_1$ (3,7), $Co_2$ (5),
## $Co_3$ (2,3,5), $Fi_{22}$ (3,5) and $Th$ (2).
##
## *Note* the isomorphisms $M22N2 \cong M23N2$, $M24N2 \cong HeN2$,
## $M24N3 \cong HeN3$, and $Co2N5 \cong ThN5$.
##
#H ctbllib history
#H ---------------
#H $Log: ctosylno.tbl,v $
#H Revision 4.56 2012/06/20 14:45:32 gap
#H added tables and fusions, as documented in ctbldiff.dat
#H TB
#H
#H Revision 4.55 2012/06/06 12:44:28 gap
#H added the table of "ThN3"
#H TB
#H
#H Revision 4.54 2012/04/23 16:16:16 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 4.53 2012/03/28 13:11:43 gap
#H added missing fusion Fi22N5 -> 2F4(2)'.2
#H TB
#H
#H Revision 4.52 2011/09/28 14:08:59 gap
#H - removed revision entry and SET_TABLEFILENAME call,
#H - added tables of Fi22N2, S4x5^2:4S4,
#H - added fusions 3^(1+2):8","U3(3), 3^(1+2):D8","3.A6.2_1,
#H 3^(1+2):D8 -> 3.A7.2, 3^(1+2):D8 -> 2^6:3^(1+2).D8,
#H 3^(1+2):SD16 -> 2F4(2)'.2, 3^4:(3^2:Q8) -> McL.2N3,
#H 3^4:2^(1+4)D10 -> 3^4:2^(1+4).(5:4), 4^3.D8 -> ON.2N2,
#H 5^(1+2):3:8 -> 5^(1+2):(24:2), 7^(1+2):(D8x3) -> 7^(1+2)_+:(3xD16),
#H 7^(1+2):(S3x6) -> 7^(1+2)_+:(6xS3).2, Co1N3 -> Co1,
#H Fi22N5 -> O8+(2).3.2, McLN2 -> McL.2N2, 2.HSN3 -> 2.HS.2N3,
#H Co1N5 -> 5^(1+2):GL2(5), F3+N5 -> S4x5^2:4S4,
#H TB
#H
#H Revision 4.51 2011/02/09 15:56:57 gap
#H name 11^2:(5x2A5) (used in AtlasRep) for 11^2:(5x2.A5)
#H TB
#H
#H Revision 4.50 2010/12/01 17:47:57 gap
#H renamed "Sym(4)" to "Symm(4)";
#H note that the table constructed with `CharacterTable( "Symmetric", 4 )'
#H gets the identifier `"Sym(4)"', and this table is sorted differently
#H TB
#H
#H Revision 4.49 2010/05/05 13:20:08 gap
#H - added many class fusions,
#H - changed several class fusions according to consistency conditions,
#H after systematic checks of consistency
#H - with Brauer tables w.r.t. the restriction of characters,
#H - of subgroup fusions with the corresponding subgroup fusions between
#H proper factors where the factor fusions are stored,
#H - of subgroup fusions from maximal subgroups with subgroup fusions of
#H extensions inside automorphic extensions
#H
#H TB
#H
#H Revision 4.48 2010/01/19 17:05:35 gap
#H added several tables of maximal subgroups of central extensions of
#H simple groups (many of them were contributed by S. Dany)
#H TB
#H
#H Revision 4.47 2009/07/29 14:00:54 gap
#H added fusions 13:12 -> 2F4(2)'.2, 13:12 -> A13.2
#H TB
#H
#H Revision 4.46 2009/05/11 15:28:36 gap
#H added table of MN7
#H TB
#H
#H Revision 4.45 2009/04/22 12:39:07 gap
#H added missing maxes of He.2, ON.2, HN.2, Fi24, and B
#H TB
#H
#H Revision 4.44 2009/03/31 16:33:40 gap
#H added fusion 3^2:Q8 -> L3(4)
#H TB
#H
#H Revision 4.43 2009/01/07 09:37:38 gap
#H added table of HNN2,
#H added fusion 3^4:2^(1+4).(5:4) -> ON.2
#H TB
#H
#H Revision 4.42 2008/06/24 16:12:49 gap
#H "2.HS.2N5" is "2.HS.2M9" not "2.HS.2M3"
#H added table of ON.2M5
#H TB
#H
#H Revision 4.41 2007/07/03 08:51:54 gap
#H added fusions,
#H encoded several tables as index two subdirect products
#H TB
#H
#H Revision 4.40 2007/06/05 07:52:55 gap
#H unified the tables of "3^2:Q8.2" and "3^2:SD16"
#H TB
#H
#H Revision 4.39 2006/06/07 07:29:37 gap
#H added comment to the fusion BN7 -> B
#H TB
#H
#H Revision 4.38 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 4.37 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 4.36 2004/01/09 08:36:42 gap
#H replaced fusion F3+N5 -> F3+ by a smaller one (had not been available
#H in GAP 4.3)
#H TB
#H
#H Revision 4.35 2003/11/17 15:49:55 gap
#H added a few obvious fusions
#H TB
#H
#H Revision 4.34 2003/11/14 08:38:47 gap
#H fixed an InfoText
#H TB
#H
#H Revision 4.33 2003/11/12 17:38:37 gap
#H removed name "HS.2M2" for "HS.2N5"
#H corrected name F3+17 to F3+N17 (for 17:16)
#H TB
#H
#H Revision 4.32 2003/05/15 17:38:24 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 4.31 2003/03/07 15:53:41 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 4.30 2003/01/24 15:57:39 gap
#H replaced several fusions by ones that are compatible with Brauer tables
#H TB
#H
#H Revision 4.29 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 4.28 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 4.27 2003/01/13 17:18:37 gap
#H added fusion 2.HS.2N5 -> 5^(1+4):2^(1+4).5.4
#H TB
#H
#H Revision 4.26 2003/01/03 10:10:22 gap
#H added fusions M24N2 -> M24 and -> He
#H TB
#H
#H Revision 4.25 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 4.24 2002/10/14 15:19:43 gap
#H added a fusion text
#H TB
#H
#H Revision 4.23 2002/09/23 15:06:00 gap
#H added fusions SuzN3 -> Suz, Co3N5 -> Co3,
#H and names "McL.2N5", "U3(5).3.2N5"
#H TB
#H
#H Revision 4.22 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 4.21 2002/09/05 15:12:16 gap
#H fixed fusion comments (will be used programmatically in the future),
#H corrected fusion (2^2xD14):3 -> Ru,
#H removed name `rvn2' for `RuN2',
#H removed names `mcn2', `mcn3', `mcn5',
#H added fusions 2^4:D8 -> M23,
#H 3^(1+2):8 -> J2,
#H 3^(1+2):D8 -> M24,
#H 3^(1+2):D8 -> He,
#H 3^(1+2):SD16 -> Ru,
#H 3^2:SD16 -> M23,
#H 3^4:(3^2:Q8) -> McL,
#H 4^3.D8 -> ON,
#H 5^2:(4xS3) -> Suz,
#H 7^(1+2):(D8x3) -> ON,
#H Co3N2 -> Co3,
#H Co3N3 -> Co3,
#H J2N2 -> J2,
#H J3N2 -> J3,
#H TB
#H
#H Revision 4.20 2002/08/21 13:53:51 gap
#H removed names of the form `c1m<n>', `c2m<n>', `c3m<n>'
#H TB
#H
#H Revision 4.19 2002/08/01 13:20:55 gap
#H removed names c3n5, c1n3, c3n2, c3n3
#H TB
#H
#H Revision 4.18 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 4.17 2002/07/24 16:41:46 gap
#H added power maps and fusion for Fi22N3,
#H added table of MN11
#H TB
#H
#H Revision 4.16 2002/07/18 17:19:04 gap
#H ... and adjusted the table automorphisms!
#H TB
#H
#H Revision 4.15 2002/07/18 17:14:36 gap
#H added power map and fusion for ThN2
#H TB
#H
#H Revision 4.14 2002/07/17 15:19:30 gap
#H added missing power maps and fusion to SuzN2,
#H added tables of RuN7, RuN13
#H TB
#H
#H Revision 4.13 2002/07/12 06:45:57 gap
#H further tidying up: removed `irredinfo' stuff, rearranged constructions
#H TB
#H
#H Revision 4.12 2002/07/08 16:06:57 gap
#H changed `construction' component from function (call) to list of function
#H name and arguments
#H TB
#H
#H Revision 4.11 2002/05/16 15:08:14 gap
#H replaced the new 2nd power map of RuN2 by an equivalent one
#H that is compatible with the stored fusion
#H TB
#H
#H Revision 4.10 2002/04/18 16:32:59 gap
#H added fusion M22N3 -> M22, nd 2nd power map of RuN2
#H TB
#H
#H Revision 4.9 2002/03/25 18:17:00 gap
#H added J4N3 (the correct table!), F3+N7, M24N5, Co2N2, Co2N3, Co2N7, MN13
#H TB
#H
#H Revision 4.8 2002/03/04 17:14:34 gap
#H added tables of 2x5:4, 11:5, 2x11:5, 17:8, 17:16, 19:9, M23N5,
#H 7:3xS3, S3x7:6, Co1N5, F3+N5, BN7
#H TB
#H
#H Revision 4.7 2001/05/04 16:50:08 gap
#H first revision for ctbllib
#H
#H
#H tbl history (GAP 4)
#H -------------------
#H (Rev. 4.7 of ctbllib coincides with Rev. 4.6 of tbl in GAP 4)
#H
#H RCS file: /gap/CVS/GAP/4.0/tbl/ctosylno.tbl,v
#H Working file: ctosylno.tbl
#H head: 4.6
#H branch:
#H locks: strict
#H access list:
#H symbolic names:
#H GAP4R2: 4.6.0.6
#H GAP4R2PRE2: 4.6.0.4
#H GAP4R2PRE1: 4.6.0.2
#H GAP4R1: 4.4.0.2
#H keyword substitution: kv
#H total revisions: 8; selected revisions: 8
#H description:
#H ----------------------------
#H revision 4.6
#H date: 1999/10/22 13:24:48; author: gap; state: Exp; lines: +10 -3
#H added maxes of J2.2
#H
#H TB
#H ----------------------------
#H revision 4.5
#H date: 1999/10/21 14:15:48; author: gap; state: Exp; lines: +15 -3
#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 4.4
#H date: 1999/07/14 11:39:42; author: gap; state: Exp; lines: +4 -3
#H cosmetic changes for the release ...
#H
#H TB
#H ----------------------------
#H revision 4.3
#H date: 1999/03/25 12:33:26; author: gap; state: Exp; lines: +3 -3
#H added fusions into S10(2)
#H
#H TB
#H ----------------------------
#H revision 4.2
#H date: 1997/11/25 15:45:50; author: gap; state: Exp; lines: +15 -7
#H first attempt to link the library of character tables and the
#H library of tables of marks
#H TB
#H ----------------------------
#H revision 4.1
#H date: 1997/07/17 15:47:20; author: fceller; state: Exp; lines: +2 -2
#H for version 4
#H ----------------------------
#H revision 1.2
#H date: 1996/12/17 12:49:22; author: sam; state: Exp; lines: +55 -2
#H added some fusions into '2.HS', and table of '2.HSN3'
#H ----------------------------
#H revision 1.1
#H date: 1996/10/21 16:01:44; author: sam; state: Exp;
#H first proposal of the table library
#H ==========================================================================
##
MOT("(3^(1+2)x2).SD16",
[
"origin: Ostermann, tests: 1.o.r., pow[2,3]\n",
"Note that this is NOT the table of the Sylow 3 normalizer J4,\n",
"contrary to the claim in Ostermann's book"
],
[864,864,864,864,24,24,432,72,72,48,48,24,24,432,432,432,72,72,72,72,72,72,24,
24,24,24,48,48,48,48,48,48,48,48,24,24,24,24,48,48,48,48,48,48,48,48],
[,[1,1,1,1,1,1,7,8,9,2,2,2,2,7,7,7,8,8,9,9,8,9,8,8,8,8,10,10,10,10,15,15,15,
15,20,20,20,20,32,32,31,31,32,32,31,31],[1,2,3,4,5,6,1,1,1,10,11,12,13,3,2,4,
3,2,3,2,4,4,5,5,6,6,27,28,29,30,10,10,11,11,12,12,13,13,27,28,28,27,29,30,30,
29]],
[[1,1,-1,-1,-1,1,1,1,1,1,-1,1,-1,-1,1,-1,-1,1,-1,1,-1,-1,-1,-1,1,1,-1,-1,1,1,
1,1,-1,-1,1,1,-1,-1,-1,-1,-1,-1,1,1,1,1],[1,1,1,1,-1,-1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1],[1,
1,-1,-1,1,-1,1,1,1,1,-1,-1,1,-1,1,-1,-1,1,-1,1,-1,-1,1,1,-1,-1,-1,-1,1,1,1,1,
-1,-1,-1,-1,1,1,-1,-1,-1,-1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,-1,-1,1,1,1,1,1,1,
1,1,1,1,1,1,1,-1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],
[TENSOR,[1,4]],
[TENSOR,[1,3]],
[TENSOR,[1,2]],
[TENSOR,[1,1]],[2,-2,-2,2,0,0,2,2,2,0,0,0,0,-2,-2,2,-2,-2,-2,-2,2,2,0,0,0,0,
E(8)+E(8)^3,-E(8)-E(8)^3,-E(8)-E(8)^3,E(8)+E(8)^3,0,0,0,0,0,0,0,0,E(8)+E(8)^3,
-E(8)-E(8)^3,-E(8)-E(8)^3,E(8)+E(8)^3,-E(8)-E(8)^3,E(8)+E(8)^3,E(8)+E(8)^3,
-E(8)-E(8)^3],
[TENSOR,[9,5]],
[TENSOR,[9,2]],
[TENSOR,[9,1]],[2,2,-2,-2,0,0,2,2,2,-2,2,0,0,-2,2,-2,-2,2,-2,2,-2,-2,0,0,0,0,
0,0,0,0,-2,-2,2,2,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[13,1]],[4,-4,-4,4,0,0,4,-2,1,0,0,0,0,-4,-4,4,2,2,-1,-1,-2,1,0,0,0,0,
0,0,0,0,0,0,0,0,E(12)^7-E(12)^11,-E(12)^7+E(12)^11,-E(12)^7+E(12)^11,
E(12)^7-E(12)^11,0,0,0,0,0,0,0,0],
[TENSOR,[15,4]],
[TENSOR,[15,1]],
[TENSOR,[15,3]],[4,4,-4,-4,0,0,4,-2,1,0,0,-2,2,-4,4,-4,2,-2,-1,1,2,-1,0,0,0,0,
0,0,0,0,0,0,0,0,1,1,-1,-1,0,0,0,0,0,0,0,0],
[TENSOR,[19,1]],
[TENSOR,[19,4]],
[TENSOR,[19,3]],[4,-4,-4,4,0,0,4,1,-2,0,0,0,0,-4,-4,4,-1,-1,2,2,1,-2,
E(3)-E(3)^2,-E(3)+E(3)^2,-E(3)+E(3)^2,E(3)-E(3)^2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0],
[TENSOR,[23,3]],
[TENSOR,[23,2]],
[TENSOR,[23,1]],[4,4,-4,-4,-2,2,4,1,-2,0,0,0,0,-4,4,-4,-1,1,2,-2,-1,2,1,1,-1,
-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[27,3]],
[TENSOR,[27,2]],
[TENSOR,[27,1]],[6,-6,6,-6,0,0,-3,0,0,0,0,0,0,-3,3,3,0,0,0,0,0,0,0,0,0,0,
E(8)+E(8)^3,-E(8)-E(8)^3,E(8)+E(8)^3,-E(8)-E(8)^3,-E(12)^7+E(12)^11,
E(12)^7-E(12)^11,-E(12)^7+E(12)^11,E(12)^7-E(12)^11,0,0,0,0,E(24)+E(24)^11,
-E(24)-E(24)^11,-E(24)^17-E(24)^19,E(24)^17+E(24)^19,E(24)+E(24)^11,
-E(24)-E(24)^11,-E(24)^17-E(24)^19,E(24)^17+E(24)^19],
[TENSOR,[31,5]],
[GALOIS,[31,17]],
[TENSOR,[33,5]],
[TENSOR,[31,2]],
[TENSOR,[31,1]],
[TENSOR,[33,2]],
[TENSOR,[33,1]],[6,6,6,6,0,0,-3,0,0,-2,-2,0,0,-3,-3,-3,0,0,0,0,0,0,0,0,0,0,-2,
-2,-2,-2,1,1,1,1,0,0,0,0,1,1,1,1,1,1,1,1],
[TENSOR,[39,5]],
[TENSOR,[39,2]],
[TENSOR,[39,1]],[6,6,6,6,0,0,-3,0,0,2,2,0,0,-3,-3,-3,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,-1,-1,-1,-1,0,0,0,0,E(12)^7-E(12)^11,E(12)^7-E(12)^11,-E(12)^7+E(12)^11,
-E(12)^7+E(12)^11,E(12)^7-E(12)^11,E(12)^7-E(12)^11,-E(12)^7+E(12)^11,
-E(12)^7+E(12)^11],
[TENSOR,[43,5]],
[TENSOR,[43,2]],
[TENSOR,[43,1]]],
[(35,36)(37,38),(31,32)(33,34)(35,36)(37,38)(39,42)(40,41)(43,46)(44,45),
(27,28)(29,30)(31,32)(33,34)(35,36)(37,38)(39,41)(40,42)(43,45)(44,46),(23,24)
(25,26),(23,24)(25,26)(31,32)(33,34)(35,36)(37,38)(39,42)(40,41)(43,46)
(44,45),( 5, 6)(12,13)(23,25)(24,26)(35,37)(36,38),(31,32)(33,34)(39,42)
(40,41)(43,46)(44,45),(27,28)(29,30)(39,40)(41,42)(43,44)(45,46),(12,13)
(27,29)(28,30)(35,37)(36,38)(39,43)(40,44)(41,45)(42,46),( 3, 4)(14,16)(17,21)
(19,22)(25,26)(29,30)(33,34)(37,38)(43,44)(45,46)]);
ARC("(3^(1+2)x2).SD16","CAS",[rec(name:="j4n3",
permchars:=(),
permclasses:=(),
text:="")]);
MOT("(2x3^(1+2)_+:8):2",
[
"origin: Dixon's Algorithm,\n",
"Sylow 3 normalizer in the sporadic simple Janko group J4\n",
"(Note that the table printed in Ostermann's book is not related to J4.),\n",
"maximal subgroup of 6.L3(4).2_2"
],
[864,864,432,432,36,36,96,96,48,48,48,48,24,24,16,16,16,16,24,24,24,24,12,12,
24,24,24,24],
[,[1,1,3,3,5,5,1,1,3,3,7,7,9,9,12,12,12,12,1,1,8,8,5,5,10,10,10,10],[1,2,1,2,1
,2,7,8,7,8,11,12,11,12,18,17,16,15,19,20,22,21,19,20,22,22,21,21]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,
-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,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[2,2,2,2,2,2,-2,-2,-2,-2,0,0,0,0,-E(8)-E(8)^3,E(8)+E(8)^3,E(8)+E(8)^3,
-E(8)-E(8)^3,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[6,3]],[8,8,8,8,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,-2,-2,0,0,1,1,0,0,0,0],
[TENSOR,[8,2]],[6,6,-3,-3,0,0,-2,-2,1,1,2,2,-1,-1,0,0,0,0,0,0,2,2,0,0,-1,-1,
-1,-1],
[TENSOR,[10,2]],[6,6,-3,-3,0,0,-2,-2,1,1,-2,-2,1,1,0,0,0,0,0,0,0,0,0,0,
-E(3)+E(3)^2,E(3)-E(3)^2,-E(3)+E(3)^2,E(3)-E(3)^2],
[TENSOR,[12,2]],[12,12,-6,-6,0,0,4,4,-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0],[1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,E(4),E(4),-E(4),-E(4),1,-1,E(4),-E(4),1
,-1,E(4),E(4),-E(4),-E(4)],
[TENSOR,[15,4]],
[TENSOR,[2,16]],
[TENSOR,[2,15]],
[TENSOR,[5,15]],
[TENSOR,[6,16]],
[TENSOR,[6,15]],
[TENSOR,[12,16]],
[TENSOR,[12,15]],
[TENSOR,[10,16]],
[TENSOR,[10,15]],
[TENSOR,[8,15]],
[TENSOR,[8,17]],
[TENSOR,[14,15]]],
[(15,16)(17,18),(25,26)(27,28),(15,17)(16,18)(19,20)(23,24),
(15,17)(16,18)(21,22)(25,27)(26,28)]);
ALF("(2x3^(1+2)_+:8):2","J4",[1,2,4,9,4,10,2,3,10,11,6,5,22,21,14,14,14,
14,2,3,7,7,10,11,23,23,23,23],[
"determined by factorization through 6.L3(4).2_2 and 6.M22.2"
]);
ALF("(2x3^(1+2)_+:8):2","2.Ru",[1,2,6,7,6,7,3,4,18,19,8,9,30,31,22,22,23,
23,3,4,10,11,18,19,32,32,33,33],[
"fusion map is unique up to table automorphisms"
]);
ALF("(2x3^(1+2)_+:8):2","6.L3(4).2_2",[1,4,3,2,9,10,5,8,7,6,11,14,13,12,
38,38,39,39,32,33,15,15,36,37,16,17,16,17],[
"fusion map is unique up to table automorphisms"
]);
ALF("(2x3^(1+2)_+:8):2","C4",[1,3,1,3,1,3,1,3,1,3,1,3,1,3,2,2,4,4,1,3,2,4,
1,3,2,2,4,4]);
ALF("(2x3^(1+2)_+:8):2","3^(1+2):SD16",[1,1,4,4,5,5,2,2,8,8,6,6,14,14,10,
11,11,10,3,3,7,7,9,9,12,13,12,13]);
ALN("(2x3^(1+2)_+:8):2",["J4N3","6.L3(4).2_2M6","6.L3(4).2_2N3","2.RuN3"]);
MOT("11+^(1+2):(5x2S4)",
[
"origin: Ostermann\n",
"tests: 1.o.r., pow[2,3,5,11]\n",
"Maximal subgroup in sporadic Janko group J4."
],
[319440,2640,220,330,440,240,240,240,240,330,40,40,240,240,240,240,20,20,20,
20,30,30,30,30,40,40,40,40,30,30,30,30,40,40,40,40,40,40,40,40,31944,242,264,
22,66,66,44,66,66],
[,[1,1,1,4,2,7,9,6,8,4,5,5,7,6,9,8,7,6,9,8,22,23,24,21,13,14,15,16,21,22,24,
23,25,26,27,28,26,27,25,28,41,42,41,42,45,46,43,45,46],[1,2,3,1,5,8,6,9,7,2,
11,12,14,16,13,15,18,20,17,19,6,7,9,8,26,28,25,27,14,13,16,15,34,36,39,38,40,
33,37,35,41,42,43,44,41,41,47,43,43],,[1,2,3,4,5,1,1,1,1,10,12,11,2,2,2,2,3,3,
3,3,4,4,4,4,5,5,5,5,10,10,10,10,11,11,12,11,12,11,12,12,41,42,43,44,46,45,47,
49,48],,[1,2,3,4,5,7,9,6,8,10,12,11,15,13,16,14,19,17,20,18,22,23,24,21,27,25,
28,26,30,32,29,31,35,39,36,37,33,40,38,34,41,42,43,44,46,45,47,49,48],,,,[1,2,
3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,
31,32,33,34,35,36,37,38,39,40,1,1,2,3,4,4,5,10,10],,[1,2,3,4,5,8,6,9,7,10,12,
11,14,16,13,15,18,20,17,19,24,21,22,23,26,28,25,27,31,29,32,30,37,40,33,35,36,
39,34,38,41,42,43,44,46,45,47,49,48],,,,[1,2,3,4,5,7,9,6,8,10,11,12,15,13,16,
14,19,17,20,18,22,23,24,21,27,25,28,26,30,32,29,31,38,33,40,34,39,36,35,37,41,
42,43,44,45,46,47,48,49],,[1,2,3,4,5,9,8,7,6,10,11,12,16,15,14,13,20,19,18,17,
23,24,21,22,28,27,26,25,32,31,30,29,36,38,37,33,35,34,40,39,41,42,43,44,46,45,
47,49,48],,,,[1,2,3,4,5,8,6,9,7,10,12,11,14,16,13,15,18,20,17,19,24,21,22,23,
26,28,25,27,31,29,32,30,37,40,33,35,36,39,34,38,41,42,43,44,46,45,47,49,
48],,,,,,[1,2,3,4,5,9,8,7,6,10,12,11,16,15,14,13,20,19,18,17,23,24,21,22,28,
27,26,25,32,31,30,29,40,35,34,39,38,37,36,33,41,42,43,44,45,46,47,48,49],,[1,
2,3,4,5,6,7,8,9,10,12,11,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,
30,31,32,39,37,38,40,34,35,33,36,41,42,43,44,45,46,47,48,49],,,,,,[1,2,3,4,5,
7,9,6,8,10,12,11,15,13,16,14,19,17,20,18,22,23,24,21,27,25,28,26,30,32,29,31,
35,39,36,37,33,40,38,34,41,42,43,44,45,46,47,48,49],,,,[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],,[1,2,3,4,5,8,6,9,7,10,11,12,14,16,13,
15,18,20,17,19,24,21,22,23,26,28,25,27,31,29,32,30,34,36,39,38,40,33,37,35,41,
42,43,44,46,45,47,49,48],,,,[1,2,3,4,5,7,9,6,8,10,12,11,15,13,16,14,19,17,20,
18,22,23,24,21,27,25,28,26,30,32,29,31,35,39,36,37,33,40,38,34,41,42,43,44,46,
45,47,49,48],,,,,,[1,2,3,4,5,8,6,9,7,10,12,11,14,16,13,15,18,20,17,19,24,21,
22,23,26,28,25,27,31,29,32,30,37,40,33,35,36,39,34,38,41,42,43,44,46,45,47,49,
48],,,,,,[1,2,3,4,5,9,8,7,6,10,11,12,16,15,14,13,20,19,18,17,23,24,21,22,28,
27,26,25,32,31,30,29,36,38,37,33,35,34,40,39,41,42,43,44,46,45,47,49,48],,[1,
2,3,4,5,6,7,8,9,10,12,11,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,
30,31,32,39,37,38,40,34,35,33,36,41,42,43,44,46,45,47,49,48]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1],[1,1,-1,1,1,E(5)^4,E(5)^3,E(5)^2,E(5),1,-1,-1,E(5)^4,
E(5)^2,E(5)^3,E(5),-E(5)^4,-E(5)^2,-E(5)^3,-E(5),E(5)^3,E(5),E(5)^2,E(5)^4,
E(5)^2,E(5),E(5)^4,E(5)^3,E(5)^4,E(5)^3,E(5)^2,E(5),-E(5),-E(5)^3,-E(5)^2,
-E(5)^4,-E(5)^3,-E(5)^2,-E(5),-E(5)^4,1,1,1,-1,1,1,1,1,1],[1,1,1,1,1,E(5)^4,
E(5)^3,E(5)^2,E(5),1,1,1,E(5)^4,E(5)^2,E(5)^3,E(5),E(5)^4,E(5)^2,E(5)^3,E(5),
E(5)^3,E(5),E(5)^2,E(5)^4,E(5)^2,E(5),E(5)^4,E(5)^3,E(5)^4,E(5)^3,E(5)^2,E(5),
E(5),E(5)^3,E(5)^2,E(5)^4,E(5)^3,E(5)^2,E(5),E(5)^4,1,1,1,1,1,1,1,1,1],
[GALOIS,[2,4]],
[GALOIS,[3,4]],
[TENSOR,[4,5]],
[TENSOR,[4,4]],
[TENSOR,[2,3]],
[TENSOR,[2,2]],
[TENSOR,[2,5]],[2,-2,0,-1,0,2*E(5)^4,2*E(5)^3,2*E(5)^2,2*E(5),1,E(8)+E(8)^3,
-E(8)-E(8)^3,-2*E(5)^4,-2*E(5)^2,-2*E(5)^3,-2*E(5),0,0,0,0,-E(5)^3,-E(5),
-E(5)^2,-E(5)^4,0,0,0,0,E(5)^4,E(5)^3,E(5)^2,E(5),-E(40)^13-E(40)^23,
-E(40)^29-E(40)^39,E(40)^21+E(40)^31,-E(40)^7-E(40)^37,E(40)^29+E(40)^39,
-E(40)^21-E(40)^31,E(40)^13+E(40)^23,E(40)^7+E(40)^37,2,2,-2,0,-1,-1,0,1,1],
[TENSOR,[11,10]],[2,2,0,-1,2,2*E(5)^4,2*E(5)^3,2*E(5)^2,2*E(5),-1,0,0,
2*E(5)^4,2*E(5)^2,2*E(5)^3,2*E(5),0,0,0,0,-E(5)^3,-E(5),-E(5)^2,-E(5)^4,
2*E(5)^2,2*E(5),2*E(5)^4,2*E(5)^3,-E(5)^4,-E(5)^3,-E(5)^2,-E(5),0,0,0,0,0,0,0,
0,2,2,2,0,-1,-1,2,-1,-1],
[TENSOR,[11,7]],
[TENSOR,[11,6]],
[TENSOR,[13,6]],
[TENSOR,[11,8]],
[TENSOR,[11,9]],
[TENSOR,[13,8]],
[TENSOR,[11,3]],
[TENSOR,[11,2]],
[TENSOR,[13,2]],
[TENSOR,[11,5]],
[TENSOR,[11,4]],
[TENSOR,[13,4]],[3,3,-1,0,-1,3*E(5)^4,3*E(5)^3,3*E(5)^2,3*E(5),0,1,1,3*E(5)^4,
3*E(5)^2,3*E(5)^3,3*E(5),-E(5)^4,-E(5)^2,-E(5)^3,-E(5),0,0,0,0,-E(5)^2,-E(5),
-E(5)^4,-E(5)^3,0,0,0,0,E(5),E(5)^3,E(5)^2,E(5)^4,E(5)^3,E(5)^2,E(5),E(5)^4,3,
3,3,-1,0,0,-1,0,0],
[TENSOR,[26,10]],
[TENSOR,[26,7]],
[TENSOR,[26,6]],
[TENSOR,[26,9]],
[TENSOR,[26,8]],
[TENSOR,[26,3]],
[TENSOR,[26,2]],
[TENSOR,[26,4]],
[TENSOR,[26,5]],[4,-4,0,1,0,4*E(5)^4,4*E(5)^3,4*E(5)^2,4*E(5),-1,0,0,
-4*E(5)^4,-4*E(5)^2,-4*E(5)^3,-4*E(5),0,0,0,0,E(5)^3,E(5),E(5)^2,E(5)^4,0,0,0,
0,-E(5)^4,-E(5)^3,-E(5)^2,-E(5),0,0,0,0,0,0,0,0,4,4,-4,0,1,1,0,-1,-1],
[TENSOR,[36,6]],
[TENSOR,[36,8]],
[TENSOR,[36,2]],
[TENSOR,[36,4]],[110,-10,0,5,10,0,0,0,0,5,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,-11,0,1,0,-E(33)-E(33)^2-E(33)^4-E(33)^8-E(33)^16
-E(33)^17-E(33)^25-E(33)^29-E(33)^31-E(33)^32,-E(33)^5-E(33)^7-E(33)^10
-E(33)^13-E(33)^14-E(33)^19-E(33)^20-E(33)^23-E(33)^26-E(33)^28,-1,
-E(33)-E(33)^2-E(33)^4-E(33)^8-E(33)^16-E(33)^17-E(33)^25-E(33)^29-E(33)^31
-E(33)^32,-E(33)^5-E(33)^7-E(33)^10-E(33)^13-E(33)^14-E(33)^19-E(33)^20
-E(33)^23-E(33)^26-E(33)^28],[110,-10,0,-10,10,0,0,0,0,-10,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-11,0,1,0,1,1,-1,1,1],
[GALOIS,[41,5]],[120,0,10,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,120,-1,0,-1,0,0,0,0,0],
[TENSOR,[44,2]],[220,20,0,10,0,0,0,0,0,-10,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,-22,0,-2,0,-1,-1,0,1,1],[220,20,0,-5,0,0,0,0,0,5,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-22,0,-2,0,
E(33)+E(33)^2+E(33)^4+E(33)^8+E(33)^16+E(33)^17+E(33)^25+E(33)^29+E(33)^31
+E(33)^32,E(33)^5+E(33)^7+E(33)^10+E(33)^13+E(33)^14+E(33)^19+E(33)^20
+E(33)^23+E(33)^26+E(33)^28,0,-E(33)-E(33)^2-E(33)^4-E(33)^8-E(33)^16
-E(33)^17-E(33)^25-E(33)^29-E(33)^31-E(33)^32,-E(33)^5-E(33)^7-E(33)^10
-E(33)^13-E(33)^14-E(33)^19-E(33)^20-E(33)^23-E(33)^26-E(33)^28],
[GALOIS,[47,5]],[330,-30,0,0,-10,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,-33,0,3,0,0,0,1,0,0]],
[(45,46)(48,49),(11,12)(33,39)(34,37)(35,38)(36,40),( 6, 7, 9, 8)(13,15,16,14)
(17,19,20,18)(21,22,23,24)(25,27,28,26)(29,30,32,31)(33,38,36,34)
(35,40,37,39)]);
ARC("11+^(1+2):(5x2S4)","CAS",[rec(name:="j4n11",
permchars:=(),
permclasses:=(),
text:=[
"Maximal subgroup of sporadic Janko group j4.\n",
"Table received from Essen; fusion into j4 by O.Bonten and K.Lux\n",
"test: restricted characters decompose properly.\n",
""])]);
ALF("11+^(1+2):(5x2S4)","J4",[1,2,3,4,5,8,8,8,8,9,14,14,17,17,17,17,18,18,
18,18,28,28,28,28,30,31,31,30,42,42,42,42,54,53,53,54,53,53,54,54,19,20,
34,35,46,47,60,61,62],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALN("11+^(1+2):(5x2S4)",["J4N11"]);
MOT("2.HS.2N5",
[
"origin: Dixon's Algorithm,\n",
"Sylow 5 normalizer in 2.HS.2,\n",
"maximal subgroup of 2.HS.2,\n",
"table is sorted w.r. to normal series 2.5.5^2.8.2.2,\n",
"tests: 1.o.r., pow[2,5]"
],
[8000,8000,2000,2000,200,200,100,100,320,320,80,80,32,32,16,16,16,16,80,40,40,
160,160,40,40,40,20,20,80,40,40,80,40,40,40,40,40,40,40,16,16],
[,[1,1,3,3,5,5,7,7,1,1,3,3,10,10,13,13,14,14,9,11,11,2,2,6,6,1,7,7,23,25,25,
22,24,24,11,11,9,11,11,23,22],,,[1,2,1,2,1,2,1,2,9,10,9,10,13,14,15,16,17,18,
19,19,19,22,23,22,23,26,26,26,29,29,29,32,32,32,37,37,37,37,37,40,41]],
0,
[(35,36)(38,39),(30,31)(33,34),(27,28),(20,21)(27,28)(30,31)(33,34)
(35,39,36,38),(13,14)(15,17)(16,18)(22,23)(24,25)(29,32)(30,33)(31,34)(40,41),
(15,16)(17,18)],
["ConstructProj",[["HS.2N5",[]],["2.HS.2N5",[]]]]);
ALF("2.HS.2N5","HS.2N5",[1,1,2,2,3,3,4,4,5,5,6,6,7,8,9,9,10,10,11,12,12,
13,13,14,14,15,16,16,17,18,18,19,20,20,21,21,22,23,23,24,25]);
ALF("2.HS.2N5","2.HS.2",[1,2,11,12,13,14,15,16,4,3,25,24,10,10,23,23,23,
23,8,32,33,5,5,26,26,35,46,45,38,51,50,38,50,51,54,55,36,53,52,38,38],[
"compatible with 5^(1+2):8:4 -> 2.HS"
]);
ALF("2.HS.2N5","5^(1+4):2^(1+4).5.4",[1,10,2,12,3,13,4,14,8,10,9,12,31,30,
45,43,44,42,11,15,16,31,30,39,38,29,34,33,42,52,50,43,51,53,16,16,11,15,
15,44,45],[
"fusion map determined by explicit computations from the groups"
]);
ALN("2.HS.2N5",["2.HS.2M9","HNN10A"]);
MOT("2^3.7.3",
[
"origin: Ostermann, tests: 1.o.r., pow[2,3,7]\n",
"Sylow 2 normalizer in sporadic Janko group J1"
],
[168,24,7,7,6,6,6,6],
[,[1,1,3,4,7,7,5,5],[1,2,4,3,1,2,1,2],,,,[1,2,1,1,5,6,7,8]],
[[1,1,1,1,1,1,1,1],[1,1,1,1,E(3),E(3),E(3)^2,E(3)^2],
[TENSOR,[2,2]],[3,3,E(7)+E(7)^2+E(7)^4,E(7)^3+E(7)^5+E(7)^6,0,0,0,0],
[GALOIS,[4,3]],[7,-1,0,0,1,-1,1,-1],
[TENSOR,[6,2]],
[TENSOR,[6,3]]],
[(5,7)(6,8),(3,4)]);
ARC("2^3.7.3","CAS",[rec(name:="j1n2",
permchars:=(1,2)(4,5)(6,8),
permclasses:=(3,7,4,8,5),
text:=[
" test:= 1. o.r., sym 2 decompose correctly \n",
""])]);
ARC("2^3.7.3","tomfusion",rec(name:="2^3:7:3",map:=[1,2,6,6,3,5,3,5],text:=[
"fusion map is unique"
]));
ALF("2^3.7.3","J1",[1,2,7,7,3,6,3,6],[
"fusion map is unique, equal to that on the CAS table"
]);
ALF("2^3.7.3","L2(8).3",[1,2,4,4,6,8,7,9],[
"fusion map is unique up to table autom."
]);
ALN("2^3.7.3",["J1N2"]);
MOT("2^4:D8",
[
"origin: Ostermann, tests: 1.o.r., pow[2],\n",
"2nd power map determined only up to matrix automorphisms,\n",
"Sylow 2 normalizer in sporadic Mathieu group M22\n",
"Sylow 2 normalizer in sporadic Mathieu group M23"
],
[128,128,64,32,32,16,16,16,32,16,16,16,16,16,8,8,8],
[,[1,1,1,1,1,1,1,1,2,2,3,3,2,3,4,5,9]],
[[1,1,1,1,1,-1,-1,-1,1,-1,-1,-1,1,1,1,1,-1],[1,1,1,1,1,-1,-1,1,1,-1,-1,1,-1,
-1,1,-1,1],[1,1,1,1,1,-1,1,-1,1,-1,1,-1,-1,-1,-1,1,1],[1,1,1,1,1,-1,1,1,1,-1,
1,1,1,1,-1,-1,-1],
[TENSOR,[1,4]],
[TENSOR,[1,3]],
[TENSOR,[1,2]],
[TENSOR,[1,1]],[2,2,2,-2,-2,0,0,0,2,0,0,0,-2,2,0,0,0],
[TENSOR,[9,2]],[2,2,2,-2,2,0,0,-2,-2,0,0,2,0,0,0,0,0],
[TENSOR,[11,1]],[2,2,2,2,-2,0,-2,0,-2,0,2,0,0,0,0,0,0],
[TENSOR,[13,1]],[4,4,-4,0,0,-2,0,0,0,2,0,0,0,0,0,0,0],
[TENSOR,[15,1]],[8,-8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]],
[( 4, 5)( 7, 8)(11,12)(15,16)]);
ARC("2^4:D8","CAS",[rec(name:="m22n2",
permchars:=(),
permclasses:=(),
text:=""),rec(name:="m23n2",
permchars:=( 1, 5)( 2, 3)( 4, 8)( 6, 7)( 9,11)(10,12),
permclasses:=( 4, 5)( 6, 8)(10,12)(11,13),
text:="")]);
ALF("2^4:D8","s61p",[1,1,2,3,4,5,11,12,6,7,13,14,8,9,15,16,10]);
ALF("2^4:D8","2.A8",[1,2,3,3,3,3,3,3,4,4,9,9,4,9,9,9,10],[
"fusion map is unique"
]);
ALF("2^4:D8","LyN2",[1,2,3,5,5,7,11,11,4,8,16,16,6,13,19,19,17],[
"fusion map is unique"
]);
ALF("2^4:D8","M22",[1,2,2,2,2,2,2,2,4,4,5,5,5,4,4,5,10],[
"determined using that exactly one roots class of the central involution\n",
"fuses in 4B of M22; together with that, the map is unique up to table\n",
"automorphisms"
]);
ALF("2^4:D8","M23",[1,2,2,2,2,2,2,2,4,4,4,4,4,4,4,4,9],[
"fusion map is unique"
]);
ALF("2^4:D8","U4(3)",[1,2,2,2,2,2,2,2,7,7,8,8,8,7,8,8,15],[
"fusion map determined by the groups"
]);
ALN("2^4:D8",["2.A8N2","M22N2","M23N2","U4(3)N2"]);
MOT("2x(3^2.QD16)",
[
"origin: Ostermann, tests: 1.o.r., pow[2,3]\n",
"Sylow 3 normalizer in sporadic Higman Sims group HS"
],
[288,288,32,32,24,24,36,16,16,8,8,36,12,12,16,16,16,16],
[,[1,1,1,1,1,1,7,3,3,3,3,7,7,7,9,9,9,9],[1,2,3,4,5,6,1,8,9,10,11,2,6,5,15,16,
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],[1,-1,1,-1,-1,1,1,-1,1,-1,1,-1,1,-1,-1,-1,1,1],[1,1,1,1,1,1,1,
1,1,-1,-1,1,1,1,-1,-1,-1,-1],
[TENSOR,[1,4]],
[TENSOR,[1,3]],
[TENSOR,[1,2]],
[TENSOR,[1,1]],[2,2,2,2,0,0,2,-2,-2,0,0,2,0,0,0,0,0,0],
[TENSOR,[9,1]],[2,2,-2,-2,0,0,2,0,0,0,0,2,0,0,E(8)+E(8)^3,-E(8)-E(8)^3,
E(8)+E(8)^3,-E(8)-E(8)^3],
[TENSOR,[11,1]],
[TENSOR,[11,3]],
[TENSOR,[11,4]],[8,-8,0,0,-2,2,-1,0,0,0,0,1,-1,1,0,0,0,0],
[TENSOR,[15,3]],
[TENSOR,[15,1]],
[TENSOR,[15,2]]],
[(15,16)(17,18),(10,11)(15,17)(16,18),( 5, 6)(10,11)(13,14)]);
ARC("2x(3^2.QD16)","CAS",[rec(name:="hsn3",
permchars:=(),
permclasses:=(),
text:="")]);
ALN("2x(3^2.QD16)",["HSN3"]);
ALF("2x(3^2.QD16)","HS",[1,3,2,3,2,3,4,6,7,7,7,11,11,12,15,15,16,16],[
"fusion map is unique up to table automorphisms"
]);
MOT("3^(1+2):8",
[
"origin: Ostermann, tests: 1.o.r., pow[2,3]\n",
"Sylow 3 normalizer in sporadic Janko group J2"
],
[216,24,108,9,24,24,12,8,8,8,8,12,12],
[,[1,1,3,4,2,2,3,6,5,6,5,7,7],[1,2,1,1,6,5,2,9,8,11,10,5,6]],
[[1,-1,1,1,E(4),-E(4),-1,E(8)^3,E(8),-E(8)^3,-E(8),-E(4),E(4)],
[GALOIS,[1,5]],
[GALOIS,[1,3]],
[GALOIS,[1,7]],
[TENSOR,[1,1]],
[TENSOR,[1,2]],
[TENSOR,[1,3]],
[TENSOR,[1,4]],[6,2,-3,0,2*E(4),-2*E(4),-1,0,0,0,0,E(4),-E(4)],
[TENSOR,[9,5]],
[TENSOR,[9,3]],
[TENSOR,[9,1]],[8,0,8,-1,0,0,0,0,0,0,0,0,0]],
[( 5, 6)( 8, 9)(10,11)(12,13),( 5, 6)( 8,11)( 9,10)(12,13),( 8,10)( 9,11)]);
ARC("3^(1+2):8","CAS",[rec(name:="j2n3",
permchars:=(),
permclasses:=(),
text:=""),rec(name:="3^1+2:8",
permchars:=( 1, 7, 2, 8)( 3, 5, 4, 6)( 9,12)(10,11),
permclasses:=( 2, 4, 3)( 5, 6)( 9,11,10),
text:=[
" test:= 1. o.r., sym 2 decompose correctly \n",
""])]);
ALF("3^(1+2):8","3^(1+2):SD16",[1,2,4,5,6,6,8,10,10,11,11,14,14],[
"fusion map is unique up to table autom."
]);
ALF("3^(1+2):8","J2",[1,2,4,5,6,6,11,14,14,14,14,19,19],[
"fusion map is unique"
]);
ALF("3^(1+2):8","U3(3)",[1,2,3,4,5,6,8,12,11,12,11,14,13],[
"fusion map is unique up to table autom."
]);
ALN("3^(1+2):8",["J2N3","U3(3)N3","3^1+2:8"]);
MOT("3^(1+2):D8",
[
"origin: Ostermann, tests: 1.o.r., pow[2,3]\n",
"Sylow 3 normalizer in sporadic Mathieu group M24,\n",
"Sylow 3 normalizer in sporadic Held group He,\n",
"5th maximal subgroup (novelty) in M12.2"
],
[216,24,12,12,108,18,18,12,12,6,6,12,12],
[,[1,1,1,1,5,6,7,2,5,6,7,9,9],[1,2,3,4,1,1,1,8,2,3,4,8,8]],
[[1,1,1,-1,1,1,1,-1,1,1,-1,-1,-1],
[TENSOR,[1,1]],[1,1,-1,1,1,1,1,-1,1,-1,1,-1,-1],
[TENSOR,[1,3]],[2,-2,0,0,2,2,2,0,-2,0,0,0,0],[4,0,-2,0,4,1,-2,0,0,1,0,0,0],
[TENSOR,[6,3]],[4,0,0,-2,4,-2,1,0,0,0,1,0,0],
[TENSOR,[8,1]],[6,-2,0,0,-3,0,0,-2,1,0,0,1,1],
[TENSOR,[10,1]],[6,2,0,0,-3,0,0,0,-1,0,0,E(12)^7-E(12)^11,-E(12)^7+E(12)^11],
[TENSOR,[12,1]]],
[(12,13),( 3, 4)( 6, 7)(10,11)]);
ARC("3^(1+2):D8","CAS",[rec(name:="m24n3",
permchars:=(),
permclasses:=(),
text:=""),rec(name:="hen3",
permchars:=( 1, 4, 2, 3)( 6, 9, 7, 8)(10,11),
permclasses:=(),
text:="")]);
ARC("3^(1+2):D8","tomfusion",rec(name:="3^(1+2)+:D8",map:=[1,2,3,4,5,7,6,8,
15,17,18,25,25],text:=[
"fusion map is unique up to table autom."
]));
ALF("3^(1+2):D8","M12.2",[1,3,3,13,4,4,5,14,9,9,16,20,21],[
"fusion map is unique up to table automorphisms"
]);
ALF("3^(1+2):D8","M24",[1,2,2,3,4,4,5,6,10,10,11,17,17],[
"fusion map is unique up to table autom."
]);
ALF("3^(1+2):D8","He",[1,2,2,3,4,4,5,6,10,10,11,19,19],[
"fusion map is unique up to table autom."
]);
ALF("3^(1+2):D8","L3(3).2",[1,2,2,10,3,3,4,11,6,6,12,14,15],[
"fusion map is unique up to table autom."
]);
ALF("3^(1+2):D8","3.A6.2_1",[1,3,12,13,2,5,6,7,4,15,16,8,8],[
"fusion map is unique up to table autom."
]);
ALF("3^(1+2):D8","3.A7.2",[1,3,16,17,2,5,6,7,4,19,20,8,8],[
"fusion map is unique up to table autom."
]);
ALF("3^(1+2):D8","2^6:3^(1+2).D8",[1,10,19,25,5,6,8,15,14,23,29,17,18],[
"fusion map is unique up to table autom."
]);
ALF("3^(1+2):D8","3^(1+2):SD16",[1,2,3,3,4,5,5,6,8,9,9,14,14],[
"fusion map is unique"
]);
ALF("3^(1+2):D8","2F4(2)'",[1,3,3,3,4,4,4,5,9,9,9,15,16],[
"fusion map is unique up to table aut."
]);
ALN("3^(1+2):D8",["M24N3","HeN3","2F4(2)'N3","3.A6.2_1N3","3.A7.2N3"]);
MOT("3^(1+2):SD16",
[
"origin: Ostermann, tests: 1.o.r., pow[2,3]\n",
"Sylow 3 normalizer in sporadic Rudvalis group Ru,"
],
[432,48,12,216,18,24,12,24,6,8,8,12,12,12],
[,[1,1,1,4,5,2,2,4,5,6,6,8,8,8],[1,2,3,1,1,6,7,2,3,10,11,7,7,6]],
[[1,1,1,1,1,1,-1,1,1,-1,-1,-1,-1,1],[1,1,-1,1,1,1,-1,1,-1,1,1,-1,-1,1],
[TENSOR,[1,1]],
[TENSOR,[1,2]],[2,-2,0,2,2,0,0,-2,0,-E(8)-E(8)^3,E(8)+E(8)^3,0,0,0],
[TENSOR,[5,1]],[2,2,0,2,2,-2,0,2,0,0,0,0,0,-2],[6,-2,0,-3,0,-2,0,1,0,0,0,
E(3)-E(3)^2,-E(3)+E(3)^2,1],
[TENSOR,[8,1]],[6,-2,0,-3,0,2,2,1,0,0,0,-1,-1,-1],
[TENSOR,[10,1]],[8,0,2,8,-1,0,0,0,-1,0,0,0,0,0],
[TENSOR,[12,2]],[12,4,0,-6,0,0,0,-2,0,0,0,0,0,0]],
[(12,13),(10,11)]);
ARC("3^(1+2):SD16","CAS",[rec(name:="run3",
permchars:=(),
permclasses:=(),
text:="")]);
ALF("3^(1+2):SD16","G2(4)",[1,2,3,4,5,6,7,13,14,16,16,23,24,22],[
"fusion map determined up to table aut. by the fact that\n",
"the order 12 elements are not all conjugate in G2(4)"
]);
ALF("3^(1+2):SD16","J2.2",[1,2,17,4,5,6,18,9,20,12,12,23,23,15],[
"fusion map determined by the fact that\n",
"the order 12 elements are not all conjugate in J2.2"
]);
ALF("3^(1+2):SD16","Ru",[1,2,2,4,4,5,6,11,11,13,13,19,19,18],[
"fusion map is unique"
]);
ALF("3^(1+2):SD16","U3(3).2",[1,2,11,3,4,5,12,7,13,9,9,15,16,10],[
"fusion map is unique up to table automorphisms"
]);
ALF("3^(1+2):SD16","2F4(2)'.2",[1,3,3,4,4,5,20,9,9,23,23,24,25,14],[
"fusion map is unique up to table automorphisms"
]);
ALF("3^(1+2):SD16","3.M22.2",[1,3,23,2,5,6,8,4,27,28,28,9,9,7],[
"fusion map is unique"
]);
ALN("3^(1+2):SD16",["G2(4)N3","J2.2N3","RuN3"]);
MOT("3^2.3^(1+2):8",
[
"origin: CAS library,\n",
"Sylow 3 normalizer in sporadic Janko group J3,\n",
"maximal subgroup of J3,\n",
"tests: 1.o.r., pow[2,3]"
],
[1944,243,108,27,27,27,24,12,24,12,24,12,8,8,8,8],
[,[1,2,3,5,6,4,1,3,7,8,7,8,9,11,9,11],[1,1,1,2,2,2,7,7,11,11,9,9,14,13,16,
15]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1],[1,1,
1,1,1,1,1,1,-1,-1,-1,-1,E(4),-E(4),E(4),-E(4)],
[TENSOR,[2,3]],[1,1,1,1,1,1,-1,-1,E(4),E(4),-E(4),-E(4),E(8),E(8)^3,-E(8),
-E(8)^3],
[TENSOR,[5,4]],
[TENSOR,[2,5]],
[TENSOR,[2,6]],[6,6,-3,0,0,0,-2,1,2,-1,2,-1,0,0,0,0],
[TENSOR,[9,3]],
[TENSOR,[9,5]],
[TENSOR,[9,6]],[8,8,8,-1,-1,-1,0,0,0,0,0,0,0,0,0,0],[24,-3,0,-2*E(9)^2-E(9)^4
-E(9)^5-2*E(9)^7,E(9)^2-E(9)^4-E(9)^5+E(9)^7,E(9)^2+2*E(9)^4+2*E(9)^5+E(9)^7,
0,0,0,0,0,0,0,0,0,0],
[GALOIS,[14,4]],
[GALOIS,[14,2]]],
[( 9,11)(10,12)(13,14)(15,16),( 9,11)(10,12)(13,16)(14,15),(4,5,6),(4,6,5),
(13,15)(14,16)]);
ARC("3^2.3^(1+2):8","CAS",[rec(name:="j3n3",
permchars:=( 1, 2)( 3, 7)( 4, 8, 5)( 9,10)(14,16),
permclasses:=( 2, 3, 4,12,15,10,16,11, 6,14, 9, 5,13, 8, 7),
text:=""),rec(name:="j3m7",
permchars:=(),
permclasses:=(),
text:="")]);
ARC("3^2.3^(1+2):8","tomfusion",rec(name:="3^2.3^(1+2):8",map:=[1,3,4,11,
11,11,2,6,5,12,5,12,8,8,8,8],text:=[
"fusion map is unique"
]));
ALF("3^2.3^(1+2):8","3^2.3^(1+2):8.2",[1,2,3,4,5,6,7,8,9,10,9,10,11,11,12,
12],[
"fusion map is unique up to table automorphisms"
]);
ALF("3^2.3^(1+2):8","J3",[1,4,3,10,11,12,2,8,5,15,5,15,9,9,9,9],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALN("3^2.3^(1+2):8",["J3N3"]);
MOT("3^2:Q8",
[
"origin: Ostermann, tests: 1.o.r., pow[2,3]\n",
"Sylow 3 normalizer in sporadic Mathieu group M22"
],
[72,8,9,4,4,4],
[,[1,1,3,2,2,2],[1,2,1,4,5,6]],
[[1,1,1,-1,-1,1],[1,1,1,-1,1,-1],
[TENSOR,[1,2]],
[TENSOR,[1,1]],[2,-2,2,0,0,0],[8,0,-1,0,0,0]],
[(5,6),(4,5)]);
ARC("3^2:Q8","projectives",["3^(1+2)_+:Q8",[[3,-1,0,-1,-1,1],[6,2,0,0,0,0]],
]);
ARC("3^2:Q8","CAS",[rec(name:="m22n3",
permchars:=(),
permclasses:=(),
text:="")]);
ARC("3^2:Q8","tomfusion",rec(name:="3^2:Q8",map:=[1,2,3,4,5,6],text:=[
"fusion map is unique up to table automorphisms"
]));
ALF("3^2:Q8","A6.2_3",[1,2,3,4,6,6],[
"fusion map is unique up to table autom."
]);
ALF("3^2:Q8","M22",[1,2,3,4,5,5],[
"fusion map determined up to table automorphisms\n",
"by factorization through M10"
]);
ALF("3^2:Q8","L3(4)",[1,2,3,4,5,6],[
"fusion map determined by the fact that the class of subgroups\n",
"is invariant under the automorphism group"
]);
ALF("3^2:Q8","L3(7)",[1,2,3,4,4,4],[
"fusion map is unique"
]);
ALF("3^2:Q8","U3(11)",[1,2,3,6,6,6],[
"fusion map is unique"
]);
ALF("3^2:Q8","U3(5)",[1,2,3,4,4,4],[
"fusion map is unique"
]);
ALF("3^2:Q8","3^2:Q8.2",[1,2,4,5,6,6],[
"fusion map is unique up to table automorphisms"
]);
ALF("3^2:Q8","3^2:2A4",[1,3,2,4,4,4],[
"fusion map is unique"
]);
ALN("3^2:Q8",["L3(4)N3","M22N3","U3(5)N3"]);
MOT("3^2:Q8.2",
[
"origin: Ostermann, tests: 1.o.r., pow[2,3]\n",
"Sylow 3 normalizer in sporadic Mathieu group M11,\n",
"maximal subgroup of M11,\n",
"Sylow 3 normalizer in sporadic Mathieu group M23,\n",
"Sylow 3 normalizer in M22.2"
],
[144,16,12,18,8,4,6,8,8],
[,[1,1,1,4,2,2,4,5,5],[1,2,3,1,5,6,3,8,9]],
[[1,1,1,1,1,-1,1,-1,-1],[1,1,-1,1,1,1,-1,-1,-1],
[TENSOR,[1,2]],
[TENSOR,[1,1]],[2,-2,0,2,0,0,0,E(8)+E(8)^3,-E(8)-E(8)^3],
[TENSOR,[5,1]],[2,2,0,2,-2,0,0,0,0],[8,0,-2,-1,0,0,1,0,0],
[TENSOR,[8,2]]],
[(8,9)]);
ARC("3^2:Q8.2","CAS",[rec(name:="m11n3",
permchars:=(),
permclasses:=(),
text:=""),rec(name:="m23n3",
permchars:=(2,3),
permclasses:=(),
text:="")]);
ARC("3^2:Q8.2","tomfusion",rec(name:="M9:2",map:=[1,3,2,4,6,7,10,13,13],
text:=[
"fusion map is unique"
]));
ALF("3^2:Q8.2","A6.2^2",[1,2,6,3,4,12,8,10,10],[
"fusion map is unique"
]);
ALF("3^2:Q8.2","L3(4).2_2",[1,2,9,3,4,5,11,12,12],[
"fusion map is unique"
]);
ALF("3^2:Q8.2","L3(4).2_3",[1,2,9,3,4,5,10,11,11],[
"fusion map uniquely determined by Brauer tables"
]);
ALF("3^2:Q8.2","M11",[1,2,2,3,4,4,6,7,8],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("3^2:Q8.2","M23",[1,2,2,3,4,4,6,9,9],[
"fusion map is unique"
]);
ALF("3^2:Q8.2","M22.2",[1,2,12,3,4,5,16,17,17],[
"determined by the embedding of 3^2:Q8 = M22N3"
]);
ALN("3^2:Q8.2",["3^2:SD16","M11N3","M22.2N3","M23N3"]);
MOT("3^4:(3^2:Q8)",
[
"origin: Ostermann, tests: 1.o.r., pow[2,3]\n",
"Sylow 3 normalizer in sporadic McLaughlin group McL,"
],
0,
0,
0,
0,
["ConstructPermuted",["3^4.3^2.Q8"],(2,3,5,6,7,8,9,16,10,17,18,19,20,21,11,14,
15,12),(1,4)(2,3)(6,10,7,9)(13,17,15,19,14,18)]);
ARC("3^4:(3^2:Q8)","CAS",[rec(name:="mcn3",
permchars:=(),
permclasses:=(),
text:="")]);
ALF("3^4:(3^2:Q8)","McL",[1,2,3,3,4,4,4,4,4,5,5,5,8,8,9,13,14,18,18,18,18],[
"fusion map is unique up to table autom."
]);
ALF("3^4:(3^2:Q8)","McL.2N3",[1,11,2,6,3,7,4,5,5,16,17,12,14,13,15,8,8,18,
18,19,19]);
ALN("3^4:(3^2:Q8)",["McLN3"]);
MOT("3^4:2^(1+4)D10",
[
"origin: Ostermann, tests: 1.o.r., pow[2,3,5]\n",
"Sylow 3 normalizer in sporadic O'Nan group ON,\n",
"maximal subgroup of ON"
],
[25920,320,288,324,144,32,32,16,8,10,10,36,8,8,10,10,36,36],
[,[1,1,1,4,3,2,2,3,2,11,10,4,6,7,10,11,12,12],[1,2,3,1,5,6,7,8,9,11,10,3,13,
14,16,15,5,5],,[1,2,3,4,5,6,7,8,9,1,1,12,13,14,2,2,17,18]],
[[1,1,1,1,-1,1,1,-1,-1,1,1,1,-1,-1,1,1,-1,-1],
[TENSOR,[1,1]],[2,2,2,2,0,2,2,0,0,E(5)^2+E(5)^3,E(5)+E(5)^4,2,0,0,E(5)+E(5)^4,
E(5)^2+E(5)^3,0,0],
[GALOIS,[3,2]],[4,-4,0,4,2,0,0,-2,0,-1,-1,0,0,0,1,1,2,2],
[TENSOR,[5,1]],[5,5,-3,5,1,1,1,1,1,0,0,-3,-1,-1,0,0,1,1],[5,5,1,5,-1,1,-3,-1,
1,0,0,1,-1,1,0,0,-1,-1],[5,5,1,5,1,-3,1,1,-1,0,0,1,-1,1,0,0,1,1],
[TENSOR,[7,1]],
[TENSOR,[8,1]],
[TENSOR,[9,1]],[8,-8,0,8,0,0,0,0,0,-E(5)-E(5)^4,-E(5)^2-E(5)^3,0,0,0,
E(5)^2+E(5)^3,E(5)+E(5)^4,0,0],
[GALOIS,[13,2]],[80,0,8,-1,8,0,0,0,0,0,0,-1,0,0,0,0,-1,-1],
[TENSOR,[15,1]],[80,0,-8,-1,0,0,0,0,0,0,0,1,0,0,0,0,-3*E(4),3*E(4)],
[TENSOR,[17,1]]],
[(17,18),(10,11)(15,16),( 6, 7)(13,14)]);
ARC("3^4:2^(1+4)D10","CAS",[rec(name:="onn3",
permchars:=(),
permclasses:=(),
text:="")]);
ALF("3^4:2^(1+4)D10","ON",[1,2,2,3,4,5,5,5,5,6,6,7,10,11,12,12,14,14],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("3^4:2^(1+4)D10","3^4:2^(1+4).(5:4)",[1,3,5,2,9,4,4,10,11,7,7,6,12,12,
8,8,13,14]);
ALN("3^4:2^(1+4)D10",["ONN3"]);
MOT("3^4:2^(1+4).(5:4)",
[
"Sylow 3 normalizer in ON.2,\n",
"5th maximal subgroup of ON.2,\n,",
"origin: Dixon's Algorithm"
],
[51840,648,640,32,576,72,10,10,288,32,16,8,72,72,48,48,8,24,24,48,48,8,24,24],
[,[1,2,1,3,1,2,7,7,5,5,3,4,6,6,9,9,11,14,14,9,9,11,13,13],[1,1,3,4,5,5,7,8,9,
10,11,12,9,9,20,21,22,20,21,15,16,17,15,16],,[1,2,3,4,5,6,1,3,9,10,11,12,13,14
,16,15,17,19,18,21,20,22,24,23]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,-1,-1,-1,
-1,-1,-1,E(4),E(4),E(4),E(4),E(4),-E(4),-E(4),-E(4),-E(4),-E(4)],
[TENSOR,[2,2]],
[TENSOR,[2,3]],[4,4,4,4,4,4,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[5,5,5,1,
-3,-3,0,0,1,1,1,-1,1,1,1,1,-1,1,1,1,1,-1,1,1],
[TENSOR,[6,2]],
[TENSOR,[6,3]],
[TENSOR,[6,4]],[10,10,10,-2,2,2,0,0,2,2,-2,0,2,2,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[10,2]],[4,4,-4,0,0,0,-1,1,-2,2,0,0,-2,-2,E(8)-E(8)^3,-E(8)+E(8)^3,0,
E(8)-E(8)^3,-E(8)+E(8)^3,-E(8)+E(8)^3,E(8)-E(8)^3,0,-E(8)+E(8)^3,E(8)-E(8)^3],
[TENSOR,[12,2]],
[TENSOR,[12,3]],
[TENSOR,[12,4]],[16,16,-16,0,0,0,1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[80,-1
,0,0,8,-1,0,0,8,0,0,0,-1,-1,2,2,0,-1,-1,2,2,0,-1,-1],
[TENSOR,[17,2]],
[TENSOR,[17,3]],
[TENSOR,[17,4]],[80,-1,0,0,-8,1,0,0,0,0,0,0,-3*E(4),3*E(4),2*E(8),-2*E(8),0,
-E(8),E(8),2*E(8)^3,-2*E(8)^3,0,-E(8)^3,E(8)^3],
[TENSOR,[21,2]],
[TENSOR,[21,3]],
[TENSOR,[21,4]]],
[(15,16)(18,19)(20,21)(23,24),(13,14)(15,21)(16,20)(17,22)(18,24)(19,23)]);
ALF("3^4:2^(1+4).(5:4)","ON.2",[1,3,2,5,2,7,6,11,4,5,5,10,13,13,28,29,30,
35,36,29,28,30,36,35],[
"fusion map is unique up to table automorphisms"
]);
ALN("3^4:2^(1+4).(5:4)",["ON.2N3"]);
MOT("3^5:(3^2:SD16)",
[
"origin: Ostermann, tests: 1.o.r., pow[2,3]\n",
"Sylow 3 normalizer in sporadic Suzuki group Suz,"
],
[34992,432,324,8748,8748,1944,972,972,486,486,162,81,24,12,324,324,216,108,
108,108,108,108,108,108,108,108,108,54,54,18,8,8,54,54,12,12,12,18,18],
[,[1,1,1,4,5,6,8,7,9,10,11,12,2,2,5,5,6,8,7,8,7,6,6,4,5,8,7,9,10,11,13,13,34,
33,24,24,17,33,34],[1,2,3,1,1,1,1,1,1,1,1,1,13,14,3,3,2,3,3,2,2,3,3,2,2,3,3,2,
3,3,31,32,5,5,14,14,13,15,16]],
[[1,1,-1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,1,-1,-1,1,1,-1,-1,1,1,-1,-1,1,-1,-1,-1,
-1,1,1,1,1,1,-1,-1],[1,1,1,1,1,1,1,1,1,1,1,1,1,-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,-1,-1,1,1,-1,-1,1,1,1],
[TENSOR,[1,1]],
[TENSOR,[1,2]],[2,-2,0,2,2,2,2,2,2,2,2,2,0,0,0,0,-2,0,0,-2,-2,0,0,-2,-2,0,0,
-2,0,0,-E(8)-E(8)^3,E(8)+E(8)^3,2,2,0,0,0,0,0],
[TENSOR,[5,1]],[2,2,2,2,2,-1,-1,-1,-1,2,2,2,2,0,2,2,-1,-1,-1,-1,-1,-1,-1,2,2,
-1,-1,-1,2,2,0,0,-1,-1,0,0,-1,-1,-1],
[TENSOR,[7,1]],[2,2,0,2,2,-1,-1,-1,-1,2,2,2,-2,0,0,0,-1,-E(3)+E(3)^2,
E(3)-E(3)^2,-1,-1,E(3)-E(3)^2,-E(3)+E(3)^2,2,2,-E(3)+E(3)^2,E(3)-E(3)^2,-1,0,
0,0,0,-1,-1,0,0,1,-E(3)+E(3)^2,E(3)-E(3)^2],
[TENSOR,[9,1]],[2,2,0,2,2,2,2,2,2,2,2,2,-2,0,0,0,2,0,0,2,2,0,0,2,2,0,0,2,0,0,
0,0,2,2,0,0,-2,0,0],[4,-4,0,4,4,-2,-2,-2,-2,4,4,4,0,0,0,0,2,0,0,2,2,0,0,-4,-4,
0,0,2,0,0,0,0,-2,-2,0,0,0,0,0],[8,0,-2,8,8,8,8,8,8,8,-1,-1,0,0,-2,-2,0,-2,-2,
0,0,-2,-2,0,0,-2,-2,0,-2,1,0,0,-1,-1,0,0,0,1,1],
[TENSOR,[13,1]],[8,0,2,8,8,-4,-4,-4,-4,8,-1,-1,0,0,2,2,0,2*E(3)^2,2*E(3),0,0,
2*E(3),2*E(3)^2,0,0,2*E(3)^2,2*E(3),0,2,-1,0,0,E(3)-2*E(3)^2,-2*E(3)+E(3)^2,0,
0,0,-E(3)^2,-E(3)],
[TENSOR,[15,1]],
[GALOIS,[15,2]],
[TENSOR,[17,1]],[24,0,-6,24,24,0,0,0,0,-3,6,-3,0,0,-6,-6,0,0,0,0,0,0,0,0,0,0,
0,0,3,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[19,1]],[36,-4,0,9,-18,-12,6,6,-3,0,0,0,0,0,0,0,-4,0,0,2,2,0,0,-1,2,0,
0,-1,0,0,0,0,0,0,E(12)^7-E(12)^11,-E(12)^7+E(12)^11,0,0,0],
[TENSOR,[21,2]],[36,4,0,9,-18,-12,6,6,-3,0,0,0,0,2,0,0,4,0,0,-2,-2,0,0,1,-2,0,
0,1,0,0,0,0,0,0,-1,-1,0,0,0],
[TENSOR,[23,2]],[36,4,6,-18,9,12,3,3,-6,0,0,0,0,0,-3,-3,4,-3,-3,1,1,0,0,-2,1,
3,3,-2,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[25,1]],[36,-4,0,-18,9,12,3,3,-6,0,0,0,0,0,-3*E(3)+3*E(3)^2,
3*E(3)-3*E(3)^2,-4,-E(3)+E(3)^2,E(3)-E(3)^2,-1,-1,-2*E(3)+2*E(3)^2,
2*E(3)-2*E(3)^2,2,-1,-E(3)+E(3)^2,E(3)-E(3)^2,2,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[27,1]],[36,-4,0,-18,9,-6,-3*E(3)+6*E(3)^2,6*E(3)-3*E(3)^2,3,0,0,0,0,
0,3*E(3)-3*E(3)^2,-3*E(3)+3*E(3)^2,2,E(3)+2*E(3)^2,2*E(3)+E(3)^2,
E(3)-2*E(3)^2,-2*E(3)+E(3)^2,-4*E(3)-2*E(3)^2,-2*E(3)-4*E(3)^2,2,-1,
E(3)+2*E(3)^2,2*E(3)+E(3)^2,-1,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[29,1]],
[GALOIS,[30,2]],
[TENSOR,[31,1]],[36,4,-6,-18,9,-6,6*E(3)-3*E(3)^2,-3*E(3)+6*E(3)^2,3,0,0,0,0,
0,3,3,-2,3*E(3)^2,3*E(3),2*E(3)-E(3)^2,-E(3)+2*E(3)^2,0,0,-2,1,-3*E(3)^2,
-3*E(3),1,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[33,1]],
[GALOIS,[34,2]],
[TENSOR,[35,1]],[48,0,0,48,48,0,0,0,0,-6,-6,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0],[72,8,0,18,-36,12,-6,-6,3,0,0,0,0,0,0,0,-4,0,0,2,2,0,0,
2,-4,0,0,-1,0,0,0,0,0,0,0,0,0,0,0],[72,-8,0,18,-36,12,-6,-6,3,0,0,0,0,0,0,0,4,
0,0,-2,-2,0,0,-2,4,0,0,1,0,0,0,0,0,0,0,0,0,0,0]],
[(35,36),(31,32),(31,32)(35,36),( 7, 8)(15,16)(18,19)(20,21)(22,23)(26,27)
(33,34)(35,36)(38,39),( 7, 8)(15,16)(18,19)(20,21)(22,23)(26,27)(33,34)
(38,39)]);
ARC("3^5:(3^2:SD16)","CAS",[rec(name:="suzn3",
permchars:=(),
permclasses:=(),
text:="")]);
ALF("3^5:(3^2:SD16)","Suz",[1,2,2,4,5,4,5,5,5,5,5,6,9,9,14,15,13,16,16,14,
15,13,13,13,16,15,14,16,16,16,21,21,23,22,29,29,29,38,39],[
"determined up to table automorphisms by factorization through 3^5:M11"
]);
ALF("3^5:(3^2:SD16)","LyN3",[1,2,3,7,8,9,11,11,10,12,13,14,17,18,20,20,19,
28,28,24,24,29,29,21,22,23,23,25,27,34,38,39,40,40,48,48,47,49,49],[
"fusion map is unique up to table aut."
]);
ALN("3^5:(3^2:SD16)",["SuzN3"]);
MOT("4^3.D8",
[
"origin: Ostermann, tests: 1.o.r., pow[2]\n",
"Sylow 2 normalizer in sporadic O'Nan group ON,"
],
[512,512,256,128,32,32,32,16,256,256,128,128,128,64,64,64,64,64,32,32,32,16,
32,32,16,16,16,16,16,16,16,16],
[,[1,1,1,1,1,1,1,1,2,2,3,2,3,4,3,4,4,4,2,2,2,3,9,9,12,12,11,11,23,23,24,24]],
[[1,1,1,1,1,-1,-1,-1,1,1,1,1,1,-1,1,-1,-1,-1,1,-1,-1,-1,1,1,-1,1,1,1,-1,-1,1,
1],[1,1,1,1,-1,1,-1,1,1,1,1,1,1,-1,1,-1,-1,-1,-1,1,-1,1,1,1,1,-1,-1,-1,-1,-1,
1,1],[1,1,1,1,1,-1,-1,1,1,1,1,1,1,-1,1,-1,-1,-1,1,-1,-1,1,1,1,-1,1,-1,-1,1,1,
-1,-1],[1,1,1,1,-1,1,-1,-1,1,1,1,1,1,-1,1,-1,-1,-1,-1,1,-1,-1,1,1,1,-1,1,1,1,
1,-1,-1],
[TENSOR,[1,4]],
[TENSOR,[1,3]],
[TENSOR,[1,2]],
[TENSOR,[1,1]],[2,2,2,2,0,0,2,0,2,2,2,2,2,-2,2,-2,-2,-2,0,0,2,0,-2,-2,0,0,0,0,
0,0,0,0],
[TENSOR,[9,1]],[2,2,2,-2,0,0,-2,0,-2,-2,2,2,2,0,-2,0,0,0,0,0,2,0,0,0,0,0,0,0,
-E(8)+E(8)^3,E(8)-E(8)^3,-E(8)+E(8)^3,E(8)-E(8)^3],
[TENSOR,[11,3]],
[TENSOR,[11,1]],
[TENSOR,[11,5]],[2,2,2,2,0,2,0,0,2,2,-2,2,-2,0,-2,0,0,0,0,2,0,0,-2,2,-2,0,0,0,
0,0,0,0],
[TENSOR,[15,1]],[2,2,2,2,-2,0,0,0,2,2,-2,2,-2,0,-2,0,0,0,-2,0,0,0,2,-2,0,2,0,
0,0,0,0,0],
[TENSOR,[17,2]],[4,4,-4,0,-2,2,0,0,4,-4,0,0,0,-2,0,2,2,-2,2,-2,0,0,0,0,0,0,0,
0,0,0,0,0],
[TENSOR,[19,5]],
[TENSOR,[19,1]],
[TENSOR,[19,2]],[4,4,4,-4,0,0,0,0,-4,-4,-4,4,-4,0,4,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0],[4,4,4,-4,0,0,0,-2,4,4,0,-4,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[24,1]],[4,4,4,4,0,0,0,0,-4,-4,0,-4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,2,
0,0,0,0],
[TENSOR,[26,2]],[8,-8,0,0,0,0,0,0,0,0,4,0,-4,-4,0,0,0,4,0,0,0,0,0,0,0,0,0,0,0,
0,0,0],
[TENSOR,[28,1]],[8,8,-8,0,0,0,0,0,-8,8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0],[8,-8,0,0,0,0,0,0,0,0,-4,0,4,0,0,-4*E(4),4*E(4),0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0],
[TENSOR,[31,1]]],
[(29,30)(31,32),(27,28),(16,17),(16,17)(29,30)(31,32),(14,18),( 5, 6)(19,20)
(23,24)(25,26)(29,31)(30,32)]);
ARC("4^3.D8","CAS",[rec(name:="onn2",
permchars:=(),
permclasses:=(),
text:="")]);
ALF("4^3.D8","ON",[1,2,2,2,2,2,2,2,5,4,5,5,4,4,5,5,5,5,5,5,5,5,10,11,11,
10,10,11,18,19,20,21],[
"fusion map is unique up to table autom."
]);
ALF("4^3.D8","ON.2N2",[1,2,3,5,18,18,16,22,7,6,9,4,10,12,8,11,11,13,19,19,
15,21,14,14,17,17,20,20,23,24,23,24]);
ALN("4^3.D8",["ONN2"]);
MOT("5^(1+2):(24:2)",
[
"origin: Ostermann, tests: 1.o.r., pow[2,3,5]\n",
"Sylow 5 normalizer in sporadic Conway group Co3,\n",
"10th maximal subgroup of McL.2"
],
[6000,240,40,120,48,48,40,1500,50,120,24,24,8,8,60,10,24,24,30,20,20,24,24,24,
24,30],
[,[1,1,1,4,2,2,2,8,9,4,6,5,5,6,8,9,10,10,19,15,15,18,17,18,17,19],[1,2,3,1,6,
5,7,8,9,2,12,11,14,13,15,16,5,6,8,20,21,11,12,11,12,15],,[1,2,3,4,5,6,7,1,1,
10,11,12,13,14,2,3,17,18,4,7,7,22,23,24,25,10]],
[[1,1,-1,1,-1,-1,1,1,1,1,E(4),-E(4),-E(4),E(4),1,-1,-1,-1,1,1,1,-E(4),E(4),
-E(4),E(4),1],[1,1,1,1,-1,-1,-1,1,1,1,-E(4),E(4),-E(4),E(4),1,1,-1,-1,1,-1,-1,
E(4),-E(4),E(4),-E(4),1],
[GALOIS,[1,3]],
[GALOIS,[2,3]],
[TENSOR,[1,1]],
[TENSOR,[1,2]],
[TENSOR,[1,3]],
[TENSOR,[1,4]],[2,2,0,-1,2,2,0,2,2,-1,-2,-2,0,0,2,0,-1,-1,-1,0,0,1,1,1,1,-1],
[TENSOR,[9,5]],
[TENSOR,[9,1]],
[TENSOR,[9,2]],[2,-2,0,2,-2*E(4),2*E(4),0,2,2,-2,0,0,0,0,-2,0,2*E(4),-2*E(4),
2,0,0,0,0,0,0,-2],[2,-2,0,-1,-2*E(4),2*E(4),0,2,2,1,0,0,0,0,-2,0,-E(4),E(4),
-1,0,0,-E(24)+E(24)^17,-E(24)^11+E(24)^19,E(24)-E(24)^17,E(24)^11-E(24)^19,1],
[TENSOR,[14,5]],
[TENSOR,[13,1]],
[TENSOR,[14,2]],
[TENSOR,[14,1]],[20,-4,0,-4,0,0,0,-5,0,-4,0,0,0,0,1,0,0,0,1,
E(20)+E(20)^9-E(20)^13-E(20)^17,-E(20)-E(20)^9+E(20)^13+E(20)^17,0,0,0,0,1],
[TENSOR,[19,2]],[20,4,0,-4,0,0,-4,-5,0,4,0,0,0,0,-1,0,0,0,1,1,1,0,0,0,0,-1],
[TENSOR,[21,2]],[24,0,4,0,0,0,0,24,-1,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[23,1]],[40,-8,0,4,0,0,0,-10,0,4,0,0,0,0,2,0,0,0,-1,0,0,0,0,0,0,-1],[
40,8,0,4,0,0,0,-10,0,-4,0,0,0,0,-2,0,0,0,-1,0,0,0,0,0,0,1]],
[(22,24)(23,25),(20,21),( 5, 6)(11,12)(13,14)(17,18)(20,21)(22,23)(24,25),
( 5, 6)(11,12)(13,14)(17,18)(20,21)(22,25)(23,24),( 5, 6)(11,12)(13,14)(17,18)
(22,23)(24,25)]);
ARC("5^(1+2):(24:2)","CAS",[rec(name:="c3n5",
permchars:=(),
permclasses:=(),
text:="")]);
ARC("5^(1+2):(24:2)","tomfusion",rec(name:="5^(1+2)+:3:8.2",map:=[1,2,3,4,
6,6,5,8,9,10,12,12,13,13,15,18,22,22,23,28,28,31,31,31,31,35],text:=[
"fusion map is unique"
]));
ALF("5^(1+2):(24:2)","Co3",[1,2,3,4,8,8,7,9,10,11,17,17,19,19,22,23,27,27,30,
33,34,40,40,40,40,42],[
"fusion map determined up to table autom. by Brauer tables,\n",
"the representative factors through McL.2"
]);
ALF("5^(1+2):(24:2)","McL.2",[1,2,20,3,5,5,21,6,7,8,23,23,11,11,13,25,16,16,
18,28,29,32,32,33,33,19],[
"fusion map is unique up to table automorphisms"
]);
ALF("5^(1+2):(24:2)","U3(5).3.2",[1,2,22,11,4,4,23,5,6,13,9,9,25,25,10,26,15,
15,16,28,29,19,20,20,19,21],[
"fusion map is unique up to table automorphisms"
]);
ALN("5^(1+2):(24:2)",["Co3N5","McL.2N5","U3(5).3.2N5"]);
MOT("5^(1+2):(8.2)",
[
"origin: Dixon's algorithm,\n",
"maximal subgroup of U3(5).2,\n",
"Sylow 5 normalizer in sporadic Higman Sims group HS,\n",
"Sylow 5 normalizer in U3(5).2,\n",
"table is sorted w.r. to normal series 5.5^2.8.2,\n",
"2nd power map determined only up to matrix automorphisms,\n",
"tests: 1.o.r., pow[2,5]"
],
[2000,500,50,25,80,20,16,16,8,8,8,8,40,20,20,40,10],
[,[1,2,3,4,1,2,5,5,7,8,7,8,5,6,6,1,3],,,[1,1,1,1,5,5,7,8,9,10,11,12,13,13,13,
16,16]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,-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]],[1,1,1,1,1,1,-1,-1,-E(4),E(4),-E(4),E(4),1,1,1,-1,-1],
[TENSOR,[2,5]],
[TENSOR,[3,5]],
[TENSOR,[2,7]],[2,2,2,2,-2,-2,2*E(4),-2*E(4),0,0,0,0,0,0,0,0,0],
[TENSOR,[9,5]],[8,8,3,-2,0,0,0,0,0,0,0,0,0,0,0,-4,1],
[TENSOR,[11,2]],[16,16,-4,1,0,0,0,0,0,0,0,0,0,0,0,0,0],[20,-5,0,0,4,-1,0,0,0,
0,0,0,-4,1,1,0,0],
[TENSOR,[14,2]],[20,-5,0,0,-4,1,0,0,0,0,0,0,0,-E(20)-E(20)^9+E(20)^13+E(20)^17
,E(20)+E(20)^9-E(20)^13-E(20)^17,0,0],
[TENSOR,[16,2]]],
[(14,15),( 9,11)(10,12),( 7, 8)( 9,10)(11,12)(14,15),( 7, 8)( 9,10)(11,12)]);
ARC("5^(1+2):(8.2)","CAS",[rec(name:="hsn5",
permchars:=(1,4,3,7,2,8,6),
permclasses:=( 2, 7, 5)( 3, 8, 6,14,16)( 4, 9,10,11,12,13)(15,17),
text:="origin: Ostermann")]);
ARC("5^(1+2):(8.2)","tomfusion",rec(name:="5^(1+2)+:8:2",map:=[1,7,8,9,2,16,5,
5,10,10,12,12,4,23,23,3,18],text:=[
"fusion map is unique up to table automorphisms"
]));
ALF("5^(1+2):(8.2)","U3(5).2",[1,5,6,7,2,11,4,4,10,10,15,15,13,18,19,12,
16],[
"fusion map is unique up to table automorphisms"
]);
ALF("5^(1+2):(8.2)","HS",[1,8,9,10,2,17,7,7,15,15,16,16,5,23,24,3,18],[
"fusion map is unique up to table automorphisms"
]);
ALF("5^(1+2):(8.2)","HS.2N5",[1,2,3,4,5,6,7,8,9,10,9,10,11,12,12,13,14],[
"fusion map is unique up to table automorphisms"
]);
ALN("5^(1+2):(8.2)",["5^(1+2):8:2","HSN5","U3(5).2N5"]);
MOT("5^(1+2):3:8",
[
"origin: Ostermann, tests: 1.o.r., pow[2,3,5]\n",
"Sylow 5 normalizer in sporadic McLaughlin group McL,\n",
"maximal subgroup of McL"
],
[3000,120,60,24,24,750,25,60,8,8,8,8,30,12,12,30,30,30,30],
[,[1,1,3,2,2,6,7,3,4,5,4,5,6,8,8,16,17,16,17],[1,2,1,5,4,6,7,2,10,9,12,11,13,
5,4,6,6,13,13],,[1,2,3,4,5,1,1,8,11,12,9,10,2,14,15,3,3,8,8]],
[[1,-1,1,E(4),-E(4),1,1,-1,-E(8),-E(8)^3,E(8),E(8)^3,-1,E(4),-E(4),1,1,-1,-1],
[GALOIS,[1,5]],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,-1,-1,
-1,-1,1,1,1,1,1,1,1],
[TENSOR,[1,1]],
[TENSOR,[1,2]],
[TENSOR,[1,6]],
[TENSOR,[1,5]],[2,2,-1,2,2,2,2,-1,0,0,0,0,2,-1,-1,-1,-1,-1,-1],
[TENSOR,[9,5]],
[TENSOR,[9,7]],
[TENSOR,[9,1]],[20,4,2,0,0,-5,0,-2,0,0,0,0,-1,0,0,-E(15)^7-E(15)^11-E(15)^13
-E(15)^14,-E(15)-E(15)^2-E(15)^4-E(15)^8,E(15)^7+E(15)^11+E(15)^13+E(15)^14,
E(15)+E(15)^2+E(15)^4+E(15)^8],
[GALOIS,[13,7]],[20,4,-4,0,0,-5,0,4,0,0,0,0,-1,0,0,1,1,-1,-1],
[TENSOR,[13,1]],
[TENSOR,[14,1]],
[TENSOR,[15,1]],[24,0,0,0,0,24,-1,0,0,0,0,0,0,0,0,0,0,0,0]],
[(16,17)(18,19),( 4, 5)( 9,10)(11,12)(14,15),( 4, 5)( 9,12)(10,11)(14,15),
( 9,11)(10,12)]);
ARC("5^(1+2):3:8","CAS",[rec(name:="mcn5",
permchars:=(),
permclasses:=(),
text:="")]);
ARC("5^(1+2):3:8","tomfusion",rec(name:="5^(1+2)+:3:8",map:=[1,2,3,4,4,5,
6,7,8,8,8,8,9,11,11,12,12,17,17],text:=[
"fusion map is unique"
]));
ALF("5^(1+2):3:8","McL",[1,2,3,5,5,6,7,8,12,12,12,12,15,18,18,21,22,23,24],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("5^(1+2):3:8","5^(1+2):(24:2)",[1,2,4,5,6,8,9,10,13,14,13,14,15,18,17,
19,19,26,26]);
ALN("5^(1+2):3:8",["McLN5"]);
MOT("5^(1+2):4S4",
[
"origin: Ostermann, tests: 1.o.r., pow[2,3,5],\n",
"Sylow 5 normalizer in sporadic Conway group Co2,\n",
"9th maximal subgroup of Th"
],
[12000,480,80,60,96,96,80,80,80,16,16,3000,100,60,8,8,120,20,12,12,30,30,20,
20,20,30,30],
[,[1,1,1,4,2,2,3,3,2,3,3,12,13,4,5,6,12,13,14,14,21,22,18,18,17,22,21],[1,2,3,
1,6,5,8,7,9,11,10,12,13,2,16,15,17,18,5,6,12,12,24,23,25,17,17],,[1,2,3,4,5,6,
7,8,9,10,11,1,1,14,15,16,2,3,19,20,4,4,8,7,9,14,14]],
[[1,1,-1,1,-1,-1,E(4),-E(4),1,-E(4),E(4),1,1,1,-E(4),E(4),1,-1,-1,-1,1,1,
-E(4),E(4),1,1,1],
[GALOIS,[1,3]],
[TENSOR,[1,1]],
[TENSOR,[1,2]],[2,-2,0,-1,2*E(4),-2*E(4),1+E(4),1-E(4),0,-1+E(4),-1-E(4),2,2,
1,0,0,-2,0,E(4),-E(4),-1,-1,1-E(4),1+E(4),0,1,1],
[TENSOR,[5,3]],
[TENSOR,[5,2]],
[TENSOR,[5,1]],[2,2,2,-1,2,2,0,0,2,0,0,2,2,-1,0,0,2,2,-1,-1,-1,-1,0,0,2,-1,
-1],
[TENSOR,[9,1]],[3,3,1,0,-3,-3,E(4),-E(4),-1,-E(4),E(4),3,3,0,E(4),-E(4),3,1,0,
0,0,0,-E(4),E(4),-1,0,0],
[TENSOR,[11,3]],
[TENSOR,[11,2]],
[TENSOR,[11,1]],[4,-4,0,1,-4*E(4),4*E(4),0,0,0,0,0,4,4,-1,0,0,-4,0,E(4),-E(4),
1,1,0,0,0,-1,-1],
[TENSOR,[15,1]],[20,4,0,2,0,0,0,0,-4,0,0,-5,0,-2,0,0,-1,0,0,0,
-E(15)^7-E(15)^11-E(15)^13-E(15)^14,-E(15)-E(15)^2-E(15)^4-E(15)^8,0,0,1,
E(15)+E(15)^2+E(15)^4+E(15)^8,E(15)^7+E(15)^11+E(15)^13+E(15)^14],
[GALOIS,[17,7]],[20,4,0,-4,0,0,0,0,-4,0,0,-5,0,4,0,0,-1,0,0,0,1,1,0,0,1,-1,
-1],[24,0,-4,0,0,0,4*E(4),-4*E(4),0,0,0,24,-1,0,0,0,0,1,0,0,0,0,E(4),-E(4),0,
0,0],
[TENSOR,[20,3]],
[TENSOR,[20,2]],
[TENSOR,[20,1]],[40,-8,0,-2,0,0,0,0,0,0,0,-10,0,-2,0,0,2,0,0,0,
E(15)^7+E(15)^11+E(15)^13+E(15)^14,E(15)+E(15)^2+E(15)^4+E(15)^8,0,0,0,
E(15)+E(15)^2+E(15)^4+E(15)^8,E(15)^7+E(15)^11+E(15)^13+E(15)^14],
[GALOIS,[24,7]],[40,-8,0,4,0,0,0,0,0,0,0,-10,0,4,0,0,2,0,0,0,-1,-1,0,0,0,-1,
-1],[60,12,0,0,0,0,0,0,4,0,0,-15,0,0,0,0,-3,0,0,0,0,0,0,0,-1,0,0]],
[(21,22)(26,27),( 5, 6)( 7, 8)(10,11)(15,16)(19,20)(23,24)]);
ARC("5^(1+2):4S4","CAS",[rec(name:="5^1+2:4s4",
permchars:=(),
permclasses:=(),
text:=[
"origin: CAS library,\n",
"Maximal subgroup of sporadic simple Conway group c2.\n",
"Test: 1.OR, JAMES, JAMES,n=3,\n",
"and restricted characters decompose properly."]),rec(name:="co2n5",
permchars:=(),
permclasses:=(),
text:="")]);
ALF("5^(1+2):4S4","Co2",[1,3,4,5,11,11,13,13,8,13,13,14,15,16,28,28,30,32,
40,40,46,47,52,52,51,60,59],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("5^(1+2):4S4","Th",[1,2,2,5,7,7,7,7,7,7,7,8,8,9,14,14,18,18,22,22,25,
26,30,30,30,41,40],[
"fusion map is unique up to table automorphisms"
]);
ALN("5^(1+2):4S4",["Co2N5","ThN5","5^1+2:2s4"]);
MOT("5^1+2:(2^5)",
[
"origin: CAS library,\n",
"maximal subgroup of Ru,\n",
"source: received from S.Mattarei\n",
"test: 1.OR, JAMES, JAMES,n=5,\n",
"and restricted characters decompose properly.\n",
"tests: 1.o.r., pow[2,5]"
],
[4000,100,1000,80,80,80,80,160,50,20,40,20,20,20,8,8,32,32,40,10,16,16,40,20,
20],
[,[1,2,3,6,6,1,8,1,9,11,3,14,14,2,17,18,8,8,1,9,6,6,8,11,11],,,[1,1,1,4,5,6,7,
8,1,7,8,4,5,6,15,16,17,18,19,19,21,22,23,23,23]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,-E(4),E(4),-1,1,1,
1,1,1,-E(4),E(4),-1,E(4),-E(4),-1,-1,1,1,-E(4),E(4),-1,-1,-1],
[TENSOR,[2,2]],
[TENSOR,[2,3]],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,1,1,-1,-1,1,1,-1,-1,-1],
[TENSOR,[2,5]],
[TENSOR,[2,6]],
[TENSOR,[2,7]],[2,2,2,0,0,-2,-2,2,2,-2,2,0,0,-2,0,0,2,2,0,0,0,0,0,0,0],
[TENSOR,[9,2]],[2,2,2,1+E(4),1-E(4),0,0,-2,2,0,-2,1+E(4),1-E(4),0,0,0,-2*E(4),
2*E(4),0,0,-1-E(4),-1+E(4),0,0,0],
[TENSOR,[11,2]],
[TENSOR,[11,3]],
[TENSOR,[11,4]],[8,3,8,4,4,4,0,0,-2,0,0,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[15,2]],
[TENSOR,[15,3]],
[TENSOR,[15,4]],[16,-4,16,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,4,-1,0,0,0,0,0],
[TENSOR,[19,5]],[20,0,-5,0,0,0,-4,4,0,1,-1,0,0,0,0,0,0,0,0,0,0,0,-4,1,1],
[TENSOR,[21,2]],[20,0,-5,0,0,0,4,4,0,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,
E(5)-E(5)^2-E(5)^3+E(5)^4,-E(5)+E(5)^2+E(5)^3-E(5)^4],
[TENSOR,[23,2]],[40,0,-10,0,0,0,0,-8,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0]],
[(24,25),( 4, 5)(12,13)(15,16)(17,18)(21,22)]);
ALF("5^1+2:(2^5)","Ru",[1,9,9,5,5,2,5,2,10,27,16,27,27,16,15,15,8,8,3,17,
8,8,6,28,29],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALN("5^1+2:(2^5)",["RuN5"]);
MOT("5^2:(4xS3)",
[
"origin: Ostermann, tests: 1.o.r., pow[2,3,5]\n",
"Sylow 5 normalizer in sporadic Suzuki group Suz,\n",
"8th maximal subgroup (and Sylow 5 normalizer) in J2:2,"
],
[600,40,40,24,12,24,24,8,8,50,50,12,10,10,12,12],
[,[1,1,1,1,5,4,4,4,4,10,11,5,10,11,12,12],[1,2,3,4,1,7,6,9,8,10,11,4,13,14,7,
6],,[1,2,3,4,5,6,7,8,9,1,1,12,2,3,15,16]],
[[1,1,-1,-1,1,E(4),-E(4),E(4),-E(4),1,1,-1,1,-1,E(4),-E(4)],
[GALOIS,[1,3]],
[TENSOR,[1,1]],
[TENSOR,[1,2]],[1,-1,1,-1,1,-E(4),E(4),E(4),-E(4),1,1,-1,-1,1,-E(4),E(4)],
[TENSOR,[5,3]],
[TENSOR,[1,5]],
[TENSOR,[1,6]],[2,0,0,-2,-1,-2*E(4),2*E(4),0,0,2,2,1,0,0,E(4),-E(4)],
[TENSOR,[9,3]],
[TENSOR,[9,1]],
[TENSOR,[9,2]],[12,4,0,0,0,0,0,0,0,-3,2,0,-1,0,0,0],
[TENSOR,[13,5]],[12,0,4,0,0,0,0,0,0,2,-3,0,0,-1,0,0],
[TENSOR,[15,1]]],
[( 6, 7)( 8, 9)(15,16),( 2, 3)( 8, 9)(10,11)(13,14)]);
ARC("5^2:(4xS3)","tomfusion",rec(name:="5^2:(4xS3)",map:=[1,2,3,4,5,6,6,7,
7,10,9,13,17,19,21,21],text:=[
"fusion map is unique up to table autom."
]));
ARC("5^2:(4xS3)","CAS",[rec(name:="suzn5",
permchars:=(),
permclasses:=(),
text:="")]);
ALF("5^2:(4xS3)","J2.2",[1,3,2,3,5,19,19,19,19,7,8,10,13,14,24,24],[
"compatible with 5^2:D12 -> J2"
]);
ALF("5^2:(4xS3)","L2(25).2_2",[1,12,13,2,3,4,4,14,14,5,6,7,17,18,8,8],[
"fusion map is unique up to table autom."
]);
ALF("5^2:(4xS3)","Suz",[1,2,3,3,6,10,10,10,10,11,12,17,24,25,30,30],[
"fusion map is unique up to table autom."
]);
ALF("5^2:(4xS3)","G2(4).2",[1,3,2,3,5,27,27,27,27,9,10,12,17,16,34,34],[
"compatible with 5^2:D12 -> G2(4)"
]);
ALF("5^2:(4xS3)","U3(4).4",[1,2,10,10,3,15,16,15,16,5,6,11,7,14,17,18],[
"fusion map is unique up to table autom."
]);
ALN("5^2:(4xS3)",["SuzN5","suzd3","J2.2N5","U3(4).4M4","U3(4).4N5"]);
MOT("5^2:4A4",
[
"origin: Ostermann, tests: 1.o.r., pow[2,3,5]\n",
"Sylow 5 normalizer in sporadic Held group He,\n",
"8th maximal subgroup and Sylow 5 normalizer in 2F4(2)',\n",
"maximal subgroup of He"
],
[1200,48,40,12,12,48,48,8,50,12,12,10,12,12,12,12],
[,[1,1,1,5,4,2,2,2,9,4,5,9,10,11,10,11],[1,2,3,1,1,7,6,8,9,2,2,12,6,6,7,7],,[
1,2,3,5,4,6,7,8,1,11,10,3,14,13,16,15]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,-1,1,1,-1,-1,1,1,1,1,-1,-1,-1,-1,-1],[
1,1,-1,E(3),E(3)^2,-1,-1,1,1,E(3)^2,E(3),-1,-E(3),-E(3)^2,-E(3),-E(3)^2],
[TENSOR,[2,3]],
[TENSOR,[3,4]],
[TENSOR,[2,5]],[2,-2,0,-E(3)^2,-E(3),-2*E(4),2*E(4),0,2,E(3),E(3)^2,0,
-E(12)^11,-E(12)^7,E(12)^11,E(12)^7],
[TENSOR,[7,2]],
[TENSOR,[7,5]],
[TENSOR,[7,6]],
[TENSOR,[7,4]],
[TENSOR,[7,3]],[3,3,-1,0,0,3,3,-1,3,0,0,-1,0,0,0,0],
[TENSOR,[13,2]],[24,0,-4,0,0,0,0,0,-1,0,0,1,0,0,0,0],
[TENSOR,[15,2]]],
[( 6, 7)(13,15)(14,16),( 4, 5)(10,11)(13,14)(15,16)]);
ARC("5^2:4A4","CAS",[rec(name:="hen5",
permchars:=(),
permclasses:=(),
text:="")]);
ARC("5^2:4A4","tomfusion",rec(name:="5^2:4A4",map:=[1,2,3,4,4,5,5,7,8,9,9,
14,16,16,16,16],text:=[
"fusion map is unique"
]));
ALF("5^2:4A4","He",[1,3,2,5,5,7,7,7,9,11,11,18,20,20,20,20],[
"fusion map is unique, equal to that on the CAS table"
]);
ALF("5^2:4A4","2F4(2)'",[1,3,2,4,4,5,5,7,8,9,9,14,15,16,16,15],[
"fusion map is unique up to table automorphisms"
]);
ALF("5^2:4A4","Fi22N5",[1,2,3,4,4,5,6,11,12,13,13,16,18,18,17,17],[
"fusion map is unique up to table automorphisms"
]);
ALN("5^2:4A4",["HeN5","2f4(2)'n5","max"]);
MOT("7^(1+2):(D8x3)",
[
"origin: Ostermann, tests: 1.o.r., pow[2,3,7]\n",
"Sylow 7 normalizer in sporadic O'Nan group ON,"
],
[8232,168,84,84,24,24,84,24,24,12,12,12,12,1372,98,98,49,12,12,28,14,14,28,
28],
[,[1,1,1,1,6,5,2,6,5,6,5,6,5,14,15,16,17,9,8,14,16,15,20,20],[1,2,3,4,1,1,7,2,
2,4,4,3,3,14,15,16,17,7,7,20,21,22,23,24],,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,1,
1,1,1,18,19,2,4,3,7,7]],
[[1,1,-1,1,E(3)^2,E(3),-1,E(3)^2,E(3),E(3)^2,E(3),-E(3)^2,-E(3),1,1,1,1,
-E(3)^2,-E(3),1,1,-1,-1,-1],[1,1,1,-1,E(3)^2,E(3),-1,E(3)^2,E(3),-E(3)^2,
--> --------------------
--> maximum size reached
--> --------------------
[ Dauer der Verarbeitung: 0.44 Sekunden
(vorverarbeitet)
]
|
