Spracherkennung für: .tbl vermutete Sprache: Unknown {[0] [0] [0]} [Methode: Schwerpunktbildung, einfache Gewichte, sechs Dimensionen]
#############################################################################
##
#W ctoalter.tbl GAP table library Thomas Breuer
##
## This file contains the ordinary character tables related to the
## alternating groups of the ATLAS.
## These are the tables of $G$, $G.2$, $2.G$, and $2.G.2$
## for $G \in \{ A_5, A_7, A_8, \ldots, A_13 \}$
## and the tables of $A_6, A_6.2_1, A_6.2_2, A_6.2_3, A_6.2^2, 2.A_6,
## 2.A_6.2_1, 2.A_6.2_2, 3.A_6, 3.A_6.2_1, 3.A_6.2_2, 3.A_6.2_3, 3.A_6.2^2,
## 6.A_6, 6.A_6.2_1, 6.A_6.2_2$ and of $3.A_7, 3.A_7.2, 6.A_7, 6.A_7.2$.
##
## Additionally, the tables of $A_{14}$, $A_{15}$, $A_{16}$, $S_{14}$,
## $S_{15}$, $S_{16}$, $S_{17}$ are contained in this file.
## These tables except the last one had been available already in the
## {\sf CAS} system.
## They are encoded via the generic table of symmetric groups,
## and are explicitly listed here mainly because of the available Brauer
## tables for these groups.
##
## The `ClassParameters' values of symmetric groups in this file are equal
## to the class parameters computed from the generic table of symmetric
## groups in {\GAP}.
##
#H ctbllib history
#H ---------------
#H $Log: ctoalter.tbl,v $
#H Revision 4.76 2012/06/20 13:54:20 gap
#H added character parameters for the table of S3 and several alternating
#H groups
#H TB
#H
#H Revision 4.75 2012/04/23 16:16:04 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 4.74 2012/03/28 15:36:00 gap
#H sort the table of S19 as the other tables of symmetric groups
#H TB
#H
#H Revision 4.73 2012/03/28 11:44:54 gap
#H - added tables of A19, S19 (needed for adding the Brauer tables
#H computed by J"urgen and Lukas)
#H - added the fusion Isoclinic(6.A6x2) -> 3.A6
#H - added a permutation to the fusion into the table of marks of S13
#H TB
#H
#H Revision 4.72 2012/03/02 08:21:59 gap
#H added fusions 2.A7.2 -> 2.Suz.2, Isoclinic(2.A7.2) -> Isoclinic(2.Suz.2)
#H TB
#H
#H Revision 4.71 2012/01/30 08:31:41 gap
#H removed #H entries from the headers
#H TB
#H
#H Revision 4.70 2012/01/26 10:59:41 gap
#H added fusion A14.2 -> S12(2)
#H TB
#H
#H Revision 4.69 2011/09/28 12:16:38 gap
#H removed revision entry and SET_TABLEFILENAME call,
#H added
#H - table of Isoclinic(2.A11.2), Isoclinic(2.A12.2), Isoclinic(2.A13.2),
#H Isoclinic(6.A7.2),
#H - maxes entry for 2.A12,
#H - fusions 3.A6.2_1 -> M24, A5 -> 2^4:A5
#H - fusion from A13.2 to the table of marks
#H TB
#H
#H Revision 4.68 2011/02/09 15:53:50 gap
#H added fusion Isoclinic(2.A5.2) -> 2.J2.2
#H TB
#H
#H Revision 4.67 2010/12/01 17:47:55 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 4.66 2010/09/15 08:00:26 gap
#H changed the class parameters of A6 and S6, since they did not fit to the
#H fusions into the tables of marks (thanks to Klaus Lux for reporting this)
#H TB
#H
#H Revision 4.65 2010/05/05 13:20:00 gap
#H - added many class fusions,
#H - changed several class fusions according to consistency conditions,
#H after systematic checks of consistency
#H - with Brauer tables w.r.t. the restriction of characters,
#H - of subgroup fusions with the corresponding subgroup fusions between
#H proper factors where the factor fusions are stored,
#H - of subgroup fusions from maximal subgroups with subgroup fusions of
#H extensions inside automorphic extensions
#H
#H TB
#H
#H Revision 4.64 2010/01/19 17:05:30 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 4.63 2009/07/29 13:51:33 gap
#H added maxes of A12, A13, S13
#H TB
#H
#H Revision 4.62 2009/04/22 12:39:00 gap
#H added missing maxes of He.2, ON.2, HN.2, Fi24, and B
#H TB
#H
#H Revision 4.61 2009/03/02 16:44:37 gap
#H moved the tables of A15, A16 from ctomisc1.tbl to ctoalter.tbl
#H TB
#H
#H Revision 4.60 2008/06/24 16:23:05 gap
#H added several fusions and names
#H TB
#H
#H Revision 4.59 2007/07/03 08:50:15 gap
#H added fusions,
#H encoded several tables as index two subdirect products
#H TB
#H
#H Revision 4.58 2006/06/07 07:54:26 gap
#H unified ConstructMixed and ConstructMGA (for better programmatic access)
#H TB
#H
#H Revision 4.57 2006/05/03 14:48:59 gap
#H added fusions to tables of marks of S12, A13
#H TB
#H
#H Revision 4.56 2005/04/27 07:38:02 gap
#H added maxes entry for S9 (the tables were already available)
#H TB
#H
#H Revision 4.55 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 4.54 2004/02/17 17:33:14 gap
#H added certain tables of isoclinic groups of ATLAS groups
#H (which are available in atlasrep),
#H added missing maxes of U5(2)
#H TB
#H
#H Revision 4.53 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 4.52 2003/11/10 07:59:11 gap
#H removed a superfluous `tomfusion' entry for 3.A6.2_2
#H TB
#H
#H Revision 4.51 2003/10/30 09:12:54 gap
#H added fusion A10 -> O9(3)
#H TB
#H
#H Revision 4.50 2003/06/20 15:02:55 gap
#H added several fusions
#H TB
#H
#H Revision 4.49 2003/06/10 16:19:06 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 4.48 2003/05/23 15:06:16 gap
#H added some fusions
#H TB
#H
#H Revision 4.47 2003/05/15 17:38:02 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 4.46 2003/05/05 14:20:42 gap
#H adjusted fusion texts (no longer ambiguous when s.c. are used)
#H TB
#H
#H Revision 4.45 2003/03/07 15:53:33 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 4.44 2003/01/29 15:51:50 gap
#H added admissible names, fusions, tables for certain maxes (which are
#H available in Rob's ATLAS and thus should be available in the table
#H library, too)
#H TB
#H
#H Revision 4.43 2003/01/21 16:25:31 gap
#H further standardizations of `InfoText' strings,
#H added and corrected `Maxes' infos,
#H added some fusions
#H TB
#H
#H Revision 4.42 2003/01/14 17:28:49 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 4.41 2002/10/22 12:44:06 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 4.40 2002/09/18 15:22:00 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 4.39 2002/08/21 14:48:27 gap
#H added fusion A6.2^2 -> M22.2
#H TB
#H
#H Revision 4.38 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 4.37 2002/07/12 06:45:54 gap
#H further tidying up: removed `irredinfo' stuff, rearranged constructions
#H TB
#H
#H Revision 4.36 2002/07/08 16:06:55 gap
#H changed `construction' component from function (call) to list of function
#H name and arguments
#H TB
#H
#H Revision 4.35 2001/05/04 16:47:00 gap
#H first revision for ctbllib
#H
#H
#H tbl history (GAP 4)
#H -------------------
#H (Rev. 4.35 of ctbllib coincides with Rev. 4.34 of tbl in GAP 4)
#H
#H RCS file: /gap/CVS/GAP/4.0/tbl/ctoalter.tbl,v
#H Working file: ctoalter.tbl
#H head: 4.34
#H branch:
#H locks: strict
#H access list:
#H symbolic names:
#H GAP4R2: 4.28.0.6
#H GAP4R2PRE2: 4.28.0.4
#H GAP4R2PRE1: 4.28.0.2
#H GAP4R1: 4.19.0.2
#H keyword substitution: kv
#H total revisions: 35; selected revisions: 35
#H description:
#H ----------------------------
#H revision 4.34
#H date: 2000/12/27 14:20:15; author: gap; state: Exp; lines: +5 -2
#H added fusion A5 -> S6(3)
#H
#H TB
#H ----------------------------
#H revision 4.33
#H date: 2000/05/13 12:12:24; author: gap; state: Exp; lines: +4 -2
#H added fusion 6.A7 -> 6.Suz
#H
#H TB
#H ----------------------------
#H revision 4.32
#H date: 2000/04/06 12:30:41; author: gap; state: Exp; lines: +774 -2
#H added table of 2.S18 (computed by Gunter Malle)
#H
#H TB
#H ----------------------------
#H revision 4.31
#H date: 2000/04/06 11:47:05; author: gap; state: Exp; lines: +55 -2
#H added table of S18 (needed for 2.S18 that will be added afterwards)
#H
#H TB
#H ----------------------------
#H revision 4.30
#H date: 2000/04/05 15:15:49; author: gap; state: Exp; lines: +1305 -2
#H added tables of 2.S14, 2.S15, 2.S16, 2.S17
#H (computed by Gunter Malle)
#H
#H TB
#H ----------------------------
#H revision 4.29
#H date: 2000/03/27 09:54:44; author: gap; state: Exp; lines: +5 -2
#H added some tables of maxes of 2.Suz and corresponding fusions,
#H added table of 3.Fi22M5
#H
#H TB
#H ----------------------------
#H revision 4.28
#H date: 2000/01/06 13:52:06; author: gap; state: Exp; lines: +22 -3
#H added maxes of S5 with fusions (I needed them ...)
#H
#H TB
#H ----------------------------
#H revision 4.27
#H date: 1999/10/22 13:24:48; author: gap; state: Exp; lines: +8 -2
#H added maxes of J2.2
#H
#H TB
#H ----------------------------
#H revision 4.26
#H date: 1999/10/21 14:15:46; author: gap; state: Exp; lines: +15 -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 4.25
#H date: 1999/10/04 15:57:14; author: gap; state: Exp; lines: +10 -5
#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 4.24
#H date: 1999/09/22 11:23:18; author: gap; state: Exp; lines: +4 -2
#H fixed problem to read the file (due to a ``typo'' in the wrong place ...)
#H
#H TB
#H ----------------------------
#H revision 4.23
#H date: 1999/09/22 07:46:53; author: gap; state: Exp; lines: +44 -2
#H added table of 12.A6.2_3
#H
#H TB
#H ----------------------------
#H revision 4.22
#H date: 1999/08/31 13:16:13; author: gap; state: Exp; lines: +5 -2
#H added missing tables and fusions of maximal subgroups of Suz.2
#H
#H TB
#H ----------------------------
#H revision 4.21
#H date: 1999/08/25 17:31:38; author: gap; state: Exp; lines: +5 -5
#H typo in file header
#H
#H TB
#H ----------------------------
#H revision 4.20
#H date: 1999/08/17 13:56:45; author: gap; state: Exp; lines: +11 -2
#H added fusions 3.A7 -> 3.Suz, 3.A7.2 -> 3.Suz.2
#H
#H TB
#H ----------------------------
#H revision 4.19
#H date: 1999/07/21 11:09:53; author: gap; state: Exp; lines: +41 -2
#H added table of A17 (needed for forthcoming Brauer tables ...)
#H
#H TB
#H ----------------------------
#H revision 4.18
#H date: 1999/07/19 16:07:22; author: gap; state: Exp; lines: +105 -17
#H added character parameters for ATLAS tables of symmetric groups
#H
#H TB
#H ----------------------------
#H revision 4.17
#H date: 1999/07/16 10:53:37; author: gap; state: Exp; lines: +171 -231
#H changed `classtext' components of tables of alternating and symmetric
#H groups to `ClassParameters' values (same format as computed from
#H generic tables)
#H
#H TB
#H ----------------------------
#H revision 4.16
#H date: 1999/07/15 10:23:06; author: gap; state: Exp; lines: +51 -4
#H added table of S17 (needed for the Brauer tables)
#H
#H TB
#H ----------------------------
#H revision 4.15
#H date: 1999/07/14 11:37:49; author: gap; state: Exp; lines: +16 -35
#H removed obsolete `irredinfo.charparam' of A14
#H
#H TB
#H ----------------------------
#H revision 4.14
#H date: 1999/03/25 12:32:28; author: gap; state: Exp; lines: +5 -2
#H added fusions and tables for completing maxes of M12.2
#H
#H TB
#H ----------------------------
#H revision 4.13
#H date: 1998/12/10 15:56:31; author: gap; state: Exp; lines: +22 -125
#H removed some now obsolete `irredinfo' components
#H
#H TB
#H ----------------------------
#H revision 4.12
#H date: 1998/12/07 13:11:52; author: gap; state: Exp; lines: +8 -3
#H added new table of S8(2)M3, added some fusions into S8(2)
#H
#H TB
#H ----------------------------
#H revision 4.11
#H date: 1998/10/28 15:05:52; author: gap; state: Exp; lines: +8 -2
#H added fusions from S12 and U3(8).6 into HN.2
#H
#H TB
#H ----------------------------
#H revision 4.10
#H date: 1998/10/06 13:27:42; author: gap; state: Exp; lines: +62 -2
#H added table of S16 mod 3 (computed by Juergen Mueller)
#H
#H TB
#H ----------------------------
#H revision 4.9
#H date: 1998/08/18 13:54:53; author: gap; state: Exp; lines: +274 -5
#H added table of S15 mod 3 (constructed by J"urgen M"uller)
#H
#H TB
#H ----------------------------
#H revision 4.8
#H date: 1998/03/11 08:05:11; author: gap; state: Exp; lines: +33 -22
#H mainly new fusions to tables of marks added
#H
#H TB
#H ----------------------------
#H revision 4.7
#H date: 1998/01/16 14:49:36; author: gap; state: Exp; lines: +74 -84
#H corrected table automorphisms of 4.A6.2_3 (very strange bug ...),
#H
#H added some identifiers of tables of marks,
#H
#H added some fusions
#H
#H TB
#H ----------------------------
#H revision 4.6
#H date: 1997/11/25 15:44:31; author: gap; state: Exp; lines: +30 -2
#H first attempt to link the library of character tables and the
#H library of tables of marks
#H TB
#H ----------------------------
#H revision 4.5
#H date: 1997/10/31 13:02:13; author: gap; state: Exp; lines: +6 -3
#H added missing blocks ...
#H TB
#H ----------------------------
#H revision 4.4
#H date: 1997/10/31 12:50:04; author: gap; state: Exp; lines: +32 -2
#H added blocks info for A14
#H TB
#H ----------------------------
#H revision 4.3
#H date: 1997/08/05 15:03:41; author: gap; state: Exp; lines: +3 -3
#H removed unnecessary (and ugly) `return' statements in the calls of
#H `ConstructPermuted' and `ConstructSubdirect'
#H ----------------------------
#H revision 4.2
#H date: 1997/08/01 15:42:52; author: gap; state: Exp; lines: +40 -2
#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 15:37:43; author: fceller; state: Exp; lines: +2 -2
#H for version 4
#H ----------------------------
#H revision 1.1
#H date: 1996/10/21 15:59:02; author: sam; state: Exp;
#H first proposal of the table library
#H ==========================================================================
##
MOT("(2xA6).2_3",
[
"non-split extension of 2xA6 with 2, factor group of 4.A6.2_3"
],
0,
0,
0,
[(13,15)(14,16),(11,12)(13,14)(15,16)],
["ConstructIsoclinic",[["A6.2_3"],["Cyclic",2]],(),(2,9,5,3)(4,10,13,7)(6,11)
(8,12,14,15)]);
ARC("(2xA6).2_3","projectives",["4.A6.2_3",[[8,0,0,0,-1,-3*E(4),0,0,-2,0,0,0,
0,0,0,0],[16,0,0,0,-2,0,0,0,1,-E(20)-E(20)^9+E(20)^13+E(20)^17,0,0,0,0,0,0],[
20,0,0,0,2,0,0,2*E(8)+2*E(8)^3,0,0,0,0,0,0,0,0]],]);
ALF("(2xA6).2_3","A6.2_3",[1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8]);
ALF("(2xA6).2_3","C4",[1,3,1,3,1,3,1,3,1,3,2,4,2,4,2,4]);
ALF("(2xA6).2_3","2.M22",[1,2,3,4,5,6,8,7,10,11,9,9,18,19,18,19],[
"fusion map is unique up to table automorphisms"
]);
MOT("2.A10",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[3628800,3628800,2880,384,15120,15120,432,432,162,162,96,96,32,600,600,50,50,
72,72,12,42,42,16,16,18,18,18,18,20,24,24,24,24,30,30,42,42,42,42],
[,[1,1,2,1,5,5,7,7,9,9,3,3,4,14,14,16,16,6,8,7,21,21,13,13,25,25,27,27,15,18,
18,19,19,34,34,38,38,36,36],[1,2,3,4,1,2,1,2,1,2,11,12,13,14,15,16,17,3,3,4,
21,22,23,24,9,10,9,10,29,12,12,11,11,14,15,21,22,21,22],,[1,2,3,4,5,6,7,8,9,
10,11,12,13,1,2,1,2,18,19,20,21,22,23,24,25,26,27,28,3,30,31,32,33,5,6,36,37,
38,39],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,1,2,23,24,25,26,
27,28,29,30,31,33,32,34,35,5,6,5,6]],
0,
[(36,38)(37,39),(32,33),(30,31),(30,31)(32,33)(36,38)(37,39),(23,24),(25,27)
(26,28)],
["ConstructProj",[["A10",[]],["2.A10",[]]]]);
ARC("2.A10","maxes",["2.A9","Isoclinic(2.A8.2)","(2.A7x3).2","2.(A5xA5).4",
"2.(A6xA4).2","2^(1+4).S5","M10x2"]);
ALF("2.A10","A10",[1,1,2,3,4,4,5,5,6,6,7,8,9,10,10,11,11,12,13,14,15,15,
16,16,17,17,18,18,19,20,20,21,21,22,22,23,23,24,24]);
ALF("2.A10","2.A10.2",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,
21,22,23,23,24,25,24,25,26,27,27,28,28,29,30,31,32,31,32]);
ALF("2.A10","2.A11",[1,2,3,4,5,6,7,8,9,10,13,11,12,14,15,16,17,19,20,21,
24,25,26,27,28,29,28,29,30,36,36,37,38,40,41,46,47,48,49],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);
MOT("2.A10.2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[7257600,7257600,5760,768,30240,30240,864,864,324,324,192,192,64,1200,1200,
100,100,144,144,24,84,84,16,18,18,40,24,24,60,60,42,42,80640,3840,1152,2880,
64,64,720,144,144,72,48,36,36,16,60,20,20,72,72,28,28,40,40,60,60],
[,[1,1,2,1,5,5,7,7,9,9,3,3,4,14,14,16,16,6,8,7,21,21,13,24,24,15,18,19,29,29,
31,31,1,1,2,3,3,4,5,8,6,7,7,10,10,13,14,16,16,18,19,21,21,26,26,29,29],[1,2,3,
4,1,2,1,2,1,2,11,12,13,14,15,16,17,3,3,4,21,22,23,9,10,26,12,11,14,15,21,22,
33,34,35,36,37,38,33,35,35,33,34,35,35,46,47,49,48,36,36,53,52,55,54,47,47],,[
1,2,3,4,5,6,7,8,9,10,11,12,13,1,2,1,2,18,19,20,21,22,23,24,25,3,27,28,5,6,31,
32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,33,34,34,50,51,53,52,36,36,39,
39],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,1,2,23,24,25,26,27,
28,29,30,5,6,33,34,35,36,37,38,39,40,41,42,43,45,44,46,47,49,48,50,51,33,33,
54,55,57,56]],
0,
[(56,57),(54,55),(52,53),(48,49)(54,55)(56,57),(44,45),(44,45)(54,55),
(48,49)],
["ConstructProj",[["A10.2",[]],["2.A10.2",[]]]]);
ALF("2.A10.2","A10.2",[1,1,2,3,4,4,5,5,6,6,7,8,9,10,10,11,11,12,13,14,15,
15,16,17,17,18,19,20,21,21,22,22,23,24,25,26,27,28,29,30,31,32,33,34,34,
35,36,37,37,38,39,40,40,41,41,42,42]);
ALN("2.A10.2",["2.S10"]);
MOT("Isoclinic(2.A10.2)",
[
"isoclinic group of the 2.A10.2 given in the ATLAS"
],
0,
0,
0,
[(56,57),(54,55),(52,53),(48,49)(54,55)(56,57),(48,49)(52,53)(56,57),(44,45),
(48,49)],
["ConstructIsoclinic",[["2.A10.2"]]]);
ALF("Isoclinic(2.A10.2)","A10.2",[1,1,2,3,4,4,5,5,6,6,7,8,9,10,10,11,11,
12,13,14,15,15,16,17,17,18,19,20,21,21,22,22,23,24,25,26,27,28,29,30,31,
32,33,34,34,35,36,37,37,38,39,40,40,41,41,42,42]);
ALF("Isoclinic(2.A10.2)","2.A12",[1,2,3,5,6,7,8,9,12,13,16,14,15,18,19,20,
21,22,24,26,30,31,32,35,36,41,48,51,53,54,59,60,3,4,5,14,16,17,22,26,23,
24,25,28,29,32,41,42,43,48,49,52,52,57,58,61,61]);
MOT("2.A11",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11]"
],
[39916800,39916800,20160,1152,120960,120960,2160,2160,324,324,480,96,96,3600,
3600,50,50,576,288,72,36,36,36,168,168,16,16,18,18,40,22,22,22,22,48,24,24,24,
28,90,90,90,90,40,40,42,42,42,42],
[,[1,1,2,1,5,5,7,7,9,9,3,4,3,14,14,16,16,5,6,8,7,9,9,24,24,12,12,28,28,15,33,
33,31,31,18,19,20,20,25,40,40,42,42,30,30,48,48,46,46],[1,2,3,4,1,2,1,2,1,2,
11,12,13,14,15,16,17,4,3,3,4,4,4,24,25,26,27,9,10,30,31,32,33,34,12,11,13,13,
39,14,15,14,15,44,45,24,25,24,25],,[1,2,3,4,5,6,7,8,9,10,11,12,13,1,2,1,2,18,
19,20,21,22,23,24,25,26,27,28,29,3,31,32,33,34,35,36,37,38,39,5,6,7,8,11,11,
46,47,48,49],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,1,
2,26,27,28,29,30,33,34,31,32,35,36,38,37,3,40,41,42,43,45,44,5,6,5,6],,,,[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,
1,2,1,2,35,36,38,37,39,40,41,42,43,45,44,48,49,46,47]],
0,
[(46,48)(47,49),(44,45),(37,38),(37,38)(46,48)(47,49),(31,33)(32,34),(26,27),
(22,23)],
["ConstructProj",[["A11",[]],["2.A11",[]]]]);
ARC("2.A11","maxes",["2.A10","Isoclinic(2.A9.2)","(2.A8x3).2","2.(A7xA4).2",
"2.(A6xA5).2","2xM11","2.A11M7"]);
ALF("2.A11","A11",[1,1,2,3,4,4,5,5,6,6,7,8,9,10,10,11,11,12,13,14,15,16,
16,17,17,18,18,19,19,20,21,21,22,22,23,24,25,25,26,27,27,28,28,29,29,30,
30,31,31]);
ALF("2.A11","2.A11.2",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,
21,22,22,23,24,25,25,26,27,28,29,30,29,30,31,32,33,33,34,35,36,37,38,39,
39,40,41,40,41]);
ALF("2.A11","2.A12",[1,2,3,5,6,7,8,9,12,13,14,15,16,18,19,20,21,23,22,24,
26,28,29,30,31,32,32,35,36,41,44,45,46,47,50,48,51,51,52,53,54,55,56,57,
58,59,60,59,60],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("2.A11","Ly",[1,2,5,2,3,8,4,9,4,10,12,5,13,6,15,7,16,8,19,20,10,9,10,
11,21,13,12,14,25,26,17,29,18,30,19,31,32,33,35,22,36,23,37,47,48,27,49,
28,50],[
"fusion map is unique up to table autom."
]);
ALN("2.A11",["LyC2A","LyN2A"]);
MOT("2.A11.2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11]"
],
[79833600,79833600,40320,2304,241920,241920,4320,4320,648,648,960,192,192,
7200,7200,100,100,1152,576,144,72,36,336,336,16,36,36,80,22,22,96,48,24,56,
180,180,180,180,40,42,42,725760,5760,3840,20160,192,64,4320,720,324,288,216,
48,36,48,240,240,20,20,288,96,72,28,36,36,40,48,48,56,56,60,60,60,60],
[,[1,1,2,1,5,5,7,7,9,9,3,4,3,14,14,16,16,5,6,8,7,9,23,23,12,26,26,15,29,29,18,
19,20,24,35,35,37,37,28,40,40,1,2,1,3,3,4,5,8,9,6,7,7,10,12,14,15,16,16,19,19,
20,23,26,26,28,31,31,34,34,35,35,38,38],[1,2,3,4,1,2,1,2,1,2,11,12,13,14,15,
16,17,4,3,3,4,4,23,24,25,9,10,28,29,30,12,11,13,34,14,15,14,15,39,23,24,42,43,
44,45,46,47,42,43,42,43,42,44,43,55,56,57,59,58,45,46,45,63,50,50,66,55,55,70,
69,56,56,57,57],,[1,2,3,4,5,6,7,8,9,10,11,12,13,1,2,1,2,18,19,20,21,22,23,24,
25,26,27,3,29,30,31,32,33,34,5,6,7,8,11,40,41,42,43,44,45,46,47,48,49,50,51,
52,53,54,55,42,43,44,44,60,61,62,63,64,65,45,68,67,69,70,48,48,49,49],,[1,2,3,
4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,1,2,25,26,27,28,29,30,31,
32,33,3,35,36,37,38,39,5,6,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,59,
58,60,61,62,42,64,65,66,68,67,45,45,72,71,73,74],,,,[1,2,3,4,5,6,7,8,9,10,11,
12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,1,2,31,32,33,34,35,36,37,
38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,
64,65,66,67,68,69,70,72,71,73,74]],
0,
[(73,74),(71,72),(69,70),(67,68),(67,68)(73,74),(67,68)(71,72)(73,74),(67,68)
(69,70)(73,74),(64,65),(58,59)(71,72)(73,74),(58,59)],
["ConstructProj",[["A11.2",[]],["2.A11.2",[]]]]);
ALF("2.A11.2","A11.2",[1,1,2,3,4,4,5,5,6,6,7,8,9,10,10,11,11,12,13,14,15,
16,17,17,18,19,19,20,21,21,22,23,24,25,26,26,27,27,28,29,29,30,31,32,33,
34,35,36,37,38,39,40,41,42,43,44,45,46,46,47,48,49,50,51,51,52,53,53,54,
54,55,55,56,56]);
ALN("2.A11.2",["2.S11"]);
MOT("Isoclinic(2.A11.2)",
[
"isoclinic group of the 2.A11.2 given in the ATLAS"
],
0,
0,
0,
[(73,74),(71,72),(69,70),(67,68),(64,65),(58,59)],
["ConstructIsoclinic",[["2.A11.2"]]]);
ALF("Isoclinic(2.A11.2)","A11.2",[1,1,2,3,4,4,5,5,6,6,7,8,9,10,10,11,11,
12,13,14,15,16,17,17,18,19,19,20,21,21,22,23,24,25,26,26,27,27,28,29,29,
30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,46,47,48,49,50,51,51,
52,53,53,54,54,55,55,56,56]);
MOT("2.A12",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11]"
],
[479001600,479001600,161280,23040,4608,1088640,1088640,12960,12960,1944,1944,
972,972,2880,384,192,128,25200,25200,100,100,1440,576,144,144,144,36,36,36,
840,840,16,32,32,54,54,54,54,54,54,120,20,20,22,22,22,22,72,72,48,24,28,360,
360,90,90,40,40,42,42,60,70,70,70,70],
[,[1,1,2,2,1,6,6,8,8,10,10,12,12,3,5,3,5,18,18,20,20,7,6,9,9,8,11,12,12,30,30,
15,17,17,35,35,39,39,37,37,19,21,21,46,46,44,44,22,24,23,24,31,53,53,55,55,41,
41,59,59,54,64,64,62,62],[1,2,3,4,5,1,2,1,2,1,2,1,2,14,15,16,17,18,19,20,21,3,
5,3,4,5,4,5,5,30,31,32,33,34,12,13,12,13,12,13,41,42,43,44,45,46,47,14,14,15,
16,52,18,19,18,19,57,58,30,31,41,62,63,64,65],,[1,2,3,4,5,6,7,8,9,10,11,12,13,
14,15,16,17,1,2,1,2,22,23,24,25,26,27,28,29,30,31,32,34,33,35,36,39,40,37,38,
3,4,4,44,45,46,47,48,49,50,51,52,6,7,8,9,14,14,59,60,22,30,31,30,31],,[1,2,3,
4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,1,2,
32,34,33,35,36,37,38,39,40,41,42,43,46,47,44,45,48,49,50,51,3,53,54,55,56,58,
57,6,7,61,18,19,18,19],,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,
21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,39,40,37,38,41,43,42,1,2,1,2,
48,49,50,51,52,53,54,55,56,58,57,59,60,61,62,63,64,65]],
0,
[(62,64)(63,65),(57,58),(44,46)(45,47),(42,43),(42,43)(57,58),(42,43)(57,58)
(62,64)(63,65),(37,39)(38,40),(33,34),(33,34)(42,43),(28,29)],
["ConstructProj",[["A12",[]],["2.A12",[]]]]);
ARC("2.A12","maxes",["2.A11","Isoclinic(2.A10.2)","(2.A9x3).2",
"2.(A6xA6).2^2","2.(A8xA4).2","2.(A7xA5).2","2.M12","2.A12M8",
"2^(1+6)_-.3^3.S4","2.2^5.S6","2.3^4.2^3.S4"]);
ALF("2.A12","A12",[1,1,2,3,4,5,5,6,6,7,7,8,8,9,10,11,12,13,13,14,14,15,16,
17,18,19,20,21,21,22,22,23,24,24,25,25,26,26,27,27,28,29,29,30,30,31,31,
32,33,34,35,36,37,37,38,38,39,39,40,40,41,42,42,43,43]);
ALF("2.A12","2.A12.2",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,
21,22,23,24,25,26,27,28,28,29,30,31,32,32,33,34,35,36,35,36,37,38,38,39,
40,39,40,41,42,43,44,45,46,47,48,49,50,50,51,52,53,54,55,54,55]);
MOT("2.A12.2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11]"
],
[958003200,958003200,322560,46080,9216,2177280,2177280,25920,25920,3888,3888,
1944,1944,5760,768,384,256,50400,50400,200,200,2880,1152,288,288,288,72,36,
1680,1680,32,32,108,108,54,54,240,20,22,22,144,144,96,48,56,720,720,180,180,
40,84,84,120,70,70,7257600,34560,7680,161280,1536,768,384,128,30240,4320,864,
864,864,324,108,108,96,192,64,1200,240,100,20,1440,144,96,96,96,24,24,84,36,
36,120,48,48,56,56,60,60,60,84,84,120,120],
[,[1,1,2,2,1,6,6,8,8,10,10,12,12,3,5,3,5,18,18,20,20,7,6,9,9,8,11,12,29,29,15,
17,33,33,35,35,19,21,39,39,22,24,23,24,30,46,46,48,48,37,51,51,47,54,54,1,2,1,
3,3,3,4,5,6,9,7,8,9,12,11,13,8,15,15,18,19,20,20,22,24,22,24,24,27,27,29,33,
33,37,43,43,45,45,46,49,49,51,51,53,53],[1,2,3,4,5,1,2,1,2,1,2,1,2,14,15,16,
17,18,19,20,21,3,5,3,4,5,4,5,29,30,31,32,12,13,12,13,37,38,39,40,14,14,15,16,
45,18,19,18,19,50,29,30,37,54,55,56,57,58,59,60,61,62,63,56,57,57,56,57,56,57,
57,58,73,74,75,76,77,78,59,59,61,60,60,62,62,86,69,69,89,73,73,93,92,75,76,76,
86,86,89,89],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,1,2,1,2,22,23,24,25,
26,27,28,29,30,31,32,33,34,35,36,3,4,39,40,41,42,43,44,45,6,7,8,9,14,51,52,22,
29,30,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,56,57,56,58,79,
80,81,82,83,84,85,86,87,88,59,91,90,92,93,64,65,65,97,98,79,79],,[1,2,3,4,5,6,
7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,1,2,31,32,33,
34,35,36,37,38,39,40,41,42,43,44,3,46,47,48,49,50,6,7,53,18,19,56,57,58,59,60,
61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,83,82,84,85,56,
87,88,89,91,90,59,59,94,95,96,64,64,99,100],,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,
14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,1,
2,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,
66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,83,82,84,85,86,87,88,89,90,91,
92,93,94,95,96,98,97,100,99]],
0,
[( 99,100),(97,98),(95,96),( 95, 96)( 99,100),(92,93),(92,93)(97,98),(90,91),
(87,88),(84,85)(90,91)(95,96),(82,83),( 82, 83)( 90, 91)( 92, 93)( 95, 96)
( 99,100),( 82, 83)( 84, 85)( 90, 91)( 95, 96)( 97, 98)( 99,100),(84,85)],
["ConstructProj",[["A12.2",[]],["2.A12.2",[]]]]);
ALF("2.A12.2","A12.2",[1,1,2,3,4,5,5,6,6,7,7,8,8,9,10,11,12,13,13,14,14,
15,16,17,18,19,20,21,22,22,23,24,25,25,26,26,27,28,29,29,30,31,32,33,34,
35,35,36,36,37,38,38,39,40,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,
55,56,57,58,59,60,61,62,63,64,65,66,67,67,68,68,69,70,70,71,72,72,73,73,
74,75,75,76,76,77,77]);
ALN("2.A12.2",["2.S12"]);
MOT("Isoclinic(2.A12.2)",
[
"isoclinic group of the 2.A12.2 given in the ATLAS"
],
0,
0,
0,
[( 99,100),(97,98),(95,96),(92,93),(90,91),(87,88),(82,83),(84,85)],
["ConstructIsoclinic",[["2.A12.2"]]]);
ALF("Isoclinic(2.A12.2)","A12.2",[1,1,2,3,4,5,5,6,6,7,7,8,8,9,10,11,12,13,
13,14,14,15,16,17,18,19,20,21,22,22,23,24,25,25,26,26,27,28,29,29,30,31,
32,33,34,35,35,36,36,37,38,38,39,40,40,41,42,43,44,45,46,47,48,49,50,51,
52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,67,68,68,69,70,70,71,72,
72,73,73,74,75,75,76,76,77,77]);
MOT("2.A13",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11,13]"
],
[6227020800,6227020800,1451520,23040,23040,10886400,10886400,90720,90720,3888,
3888,1944,1944,20160,1920,576,128,201600,201600,300,300,8640,1152,720,648,432,
144,36,36,5040,5040,48,32,32,216,216,54,54,54,54,960,480,20,20,22,22,288,288,
96,72,72,72,72,26,26,26,26,56,1800,1800,180,180,150,150,36,80,40,126,126,126,
126,48,48,56,56,60,60,60,70,70,70,70],
[,[1,1,2,1,2,6,6,8,8,10,10,12,12,3,4,3,4,18,18,20,20,7,6,8,11,9,9,10,13,30,30,
15,17,17,35,35,39,39,37,37,18,19,21,21,45,45,22,22,23,26,26,25,25,56,56,54,54,
31,59,59,61,61,63,63,36,41,42,68,68,70,70,49,49,58,58,60,61,61,81,81,79,79],[
1,2,3,4,5,1,2,1,2,1,2,1,2,14,15,16,17,18,19,20,21,3,4,4,3,3,5,4,5,30,31,32,33,
34,10,11,10,11,10,11,41,42,43,44,45,46,14,16,15,14,16,16,16,54,55,56,57,58,18,
19,18,19,20,21,25,66,67,30,31,30,31,32,32,74,75,42,41,41,79,80,81,82],,[1,2,3,
4,5,6,7,8,9,10,11,12,13,14,15,16,17,1,2,1,2,22,23,24,25,26,27,28,29,30,31,32,
34,33,35,36,39,40,37,38,4,3,5,5,45,46,47,48,49,50,51,53,52,56,57,54,55,58,6,7,
8,9,6,7,65,15,14,68,69,70,71,73,72,74,75,22,24,24,30,31,30,31],,[1,2,3,4,5,6,
7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,1,2,32,34,
33,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,53,52,56,57,54,55,3,59,
60,61,62,63,64,65,66,67,6,7,8,9,72,73,14,14,76,78,77,18,19,18,19],,,,[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,
32,33,34,35,36,39,40,37,38,41,42,44,43,1,2,47,48,49,50,51,52,53,56,57,54,55,
58,59,60,61,62,63,64,65,66,67,68,69,70,71,73,72,75,74,76,78,77,79,80,81,82],,[
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,
30,31,32,34,33,35,36,37,38,39,40,41,42,44,43,45,46,47,48,49,50,51,53,52,1,2,1,
2,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,78,77,79,80,81,
82]],
0,
[(79,81)(80,82),(77,78),(74,75),(74,75)(79,81)(80,82),(72,73),(54,56)(55,57),
(52,53),(43,44),(43,44)(77,78)(79,81)(80,82),(43,44)(74,75),(37,39)(38,40),
(37,39)(38,40)(72,73)(77,78),(33,34),(33,34)(43,44)(52,53)],
["ConstructProj",[["A13",[]],["2.A13",[]]]]);
ALF("2.A13","A13",[1,1,2,3,4,5,5,6,6,7,7,8,8,9,10,11,12,13,13,14,14,15,16,
17,18,19,20,21,22,23,23,24,25,25,26,26,27,27,28,28,29,30,31,31,32,32,33,
34,35,36,37,38,38,39,39,40,40,41,42,42,43,43,44,44,45,46,47,48,48,49,49,
50,50,51,51,52,53,53,54,54,55,55]);
ALF("2.A13","2.A13.2",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,
21,22,23,24,25,26,27,28,29,30,31,32,33,33,34,35,36,37,36,37,38,39,40,40,
41,42,43,44,45,46,47,48,48,49,50,49,50,51,52,53,54,55,56,57,58,59,60,61,
62,63,64,65,65,66,66,67,68,68,69,70,69,70]);
MOT("2.A13.2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11,13]"
],
[12454041600,12454041600,2903040,46080,46080,21772800,21772800,181440,181440,
7776,7776,3888,3888,40320,3840,1152,256,403200,403200,600,600,17280,2304,1440,
1296,864,288,72,72,10080,10080,96,32,432,432,54,54,1920,960,20,44,44,576,576,
192,144,144,72,26,26,112,3600,3600,360,360,300,300,72,160,80,252,252,252,252,
48,56,120,60,70,70,79833600,241920,23040,1451520,3840,1536,384,384,241920,
30240,11520,4320,3456,864,648,432,288,144,108,960,64,7200,480,100,60,8640,648,
432,192,192,96,96,24,24,336,336,36,480,160,44,44,48,56,180,180,60,60,60,72,72,
80,80,84,84,84,84,120,120],
[,[1,1,2,1,2,6,6,8,8,10,10,12,12,3,4,3,4,18,18,20,20,7,6,8,11,9,9,10,13,30,30,
15,17,34,34,36,36,18,19,21,41,41,22,22,23,26,26,25,49,49,31,52,52,54,54,56,56,
35,38,39,61,61,63,63,45,51,53,54,69,69,1,2,1,3,3,3,4,5,6,9,6,8,7,9,10,11,8,10,
13,15,15,18,19,20,20,22,25,26,22,23,26,26,29,29,30,31,34,39,39,41,41,45,51,52,
54,55,56,56,58,58,59,59,61,61,64,64,67,67],[1,2,3,4,5,1,2,1,2,1,2,1,2,14,15,
16,17,18,19,20,21,3,4,4,3,3,5,4,5,30,31,32,33,10,11,10,11,38,39,40,41,42,14,
16,15,14,16,16,49,50,51,18,19,18,19,20,21,25,59,60,30,31,30,31,32,66,39,38,69,
70,71,72,73,74,75,76,77,78,71,72,73,71,72,72,71,72,73,73,72,90,91,92,93,94,95,
74,74,74,75,77,76,76,78,78,105,106,85,108,109,110,111,90,113,92,92,93,95,95,
97,97,121,122,105,105,106,106,108,108],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,
16,17,1,2,1,2,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,4,3,5,41,42,43,
44,45,46,47,48,49,50,51,6,7,8,9,6,7,58,15,14,61,62,63,64,65,66,22,24,30,31,71,
72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,71,72,71,73,96,97,
98,99,100,101,102,103,104,105,106,107,74,75,110,111,112,113,79,82,80,81,81,
120,119,90,90,123,124,125,126,96,96],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,
17,18,19,20,21,22,23,24,25,26,27,28,29,1,2,32,33,34,35,36,37,38,39,40,41,42,
43,44,45,46,47,48,49,50,3,52,53,54,55,56,57,58,59,60,6,7,8,9,65,14,67,68,18,
19,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,
96,97,98,99,100,102,101,103,104,71,72,107,108,109,111,110,112,74,114,115,116,
118,117,120,119,121,122,79,79,80,80,127,128],,,,[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,
39,40,1,2,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,
65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,
91,92,93,94,95,96,97,98,99,100,102,101,103,104,105,106,107,108,109,71,71,112,
113,114,115,116,118,117,119,120,122,121,124,123,125,126,128,127],,[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,
33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,1,2,51,52,53,54,55,56,57,58,
59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,
85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,102,101,104,103,105,106,107,
108,109,111,110,112,113,114,115,116,118,117,120,119,122,121,124,123,126,125,
127,128]],
0,
[(127,128),(125,126),(123,124),(123,124)(125,126),(121,122),(119,120),
(117,118),(117,118)(121,122)(127,128),(110,111),(103,104)(121,122)(125,126),
(101,102),(101,102)(119,120)(121,122)(125,126)(127,128),(101,102)(103,104)
(117,118)(123,124)(125,126)(127,128),(103,104)],
["ConstructProj",[["A13.2",[]],["2.A13.2",[]]]]);
ALF("2.A13.2","A13.2",[1,1,2,3,4,5,5,6,6,7,7,8,8,9,10,11,12,13,13,14,14,
15,16,17,18,19,20,21,22,23,23,24,25,26,26,27,27,28,29,30,31,31,32,33,34,
35,36,37,38,38,39,40,40,41,41,42,42,43,44,45,46,46,47,47,48,49,50,51,52,
52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,
76,77,78,79,80,81,82,83,83,84,84,85,86,87,88,89,90,90,91,92,93,94,95,96,
96,97,97,98,98,99,99,100,100,101,101]);
ALN("2.A13.2",["2.S13"]);
MOT("Isoclinic(2.A13.2)",
[
"isoclinic group of the 2.A13.2 given in the ATLAS"
],
0,
0,
0,
[(127,128),(125,126),(123,124),(121,122),(119,120),(117,118),(110,111),
(101,102),(103,104)],
["ConstructIsoclinic",[["2.A13.2"]]]);
ALF("Isoclinic(2.A13.2)","A13.2",[1,1,2,3,4,5,5,6,6,7,7,8,8,9,10,11,12,13,
13,14,14,15,16,17,18,19,20,21,22,23,23,24,25,26,26,27,27,28,29,30,31,31,
32,33,34,35,36,37,38,38,39,40,40,41,41,42,42,43,44,45,46,46,47,47,48,49,
50,51,52,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,
73,74,75,76,77,78,79,80,81,82,83,83,84,84,85,86,87,88,89,90,90,91,92,93,
94,95,96,96,97,97,98,98,99,99,100,100,101,101]);
MOT("2.A14.2",
[
"Schur cover of S14,\n",
"constructed by Gunter Malle"
],
[174356582400,174356582400,29030400,276480,92160,239500800,239500800,1451520,
1451520,38880,38880,7776,7776,322560,23040,15360,4608,768,512,3628800,3628800,
2400,2400,120960,8640,6912,6912,3456,1296,576,216,216,144,70560,70560,196,196,
384,384,64,2160,2160,108,108,4800,1920,400,40,132,132,2880,576,576,576,576,
288,192,72,24,26,26,336,21600,21600,1620,1620,1080,1080,300,300,72,240,160,40,
1008,1008,252,252,48,48,56,240,60,66,66,140,140,168,90,90,120,958003200,
1935360,645120,92160,14515200,23040,3072,1536,1536,768,2177280,241920,25920,
17280,11520,3888,2304,2160,1944,1728,1152,216,144,144,5760,128,128,128,50400,
1440,240,200,80,60480,1728,648,576,576,192,192,96,24,1680,336,28,28,108,108,
108,2400,200,160,44,44,144,144,168,720,720,180,180,180,180,60,60,72,72,80,80,
84,84,84,120,140,140,168,168],
[,[1,1,2,1,2,6,6,8,8,10,10,12,12,3,4,3,3,5,4,20,20,22,22,7,8,6,8,9,11,9,10,12,
13,34,34,36,36,15,15,19,41,41,43,43,21,20,23,23,49,49,24,28,26,24,27,28,28,29,
33,60,60,35,63,63,65,65,67,67,69,69,42,45,46,47,75,75,77,77,53,55,62,64,67,84,
84,86,86,76,89,89,82,1,2,2,1,3,3,3,4,4,5,6,9,8,7,6,12,9,11,10,9,8,13,10,13,15,
15,19,19,20,21,22,22,23,24,28,29,24,28,26,27,28,33,34,35,37,37,41,43,43,45,47,
45,49,49,53,55,62,63,64,68,67,66,66,69,69,71,71,73,73,75,78,78,82,86,86,88,
88],[1,2,3,4,5,1,2,1,2,1,2,1,2,14,15,16,17,18,19,20,21,22,23,3,4,4,4,3,3,5,4,
4,5,34,35,36,37,38,39,40,10,11,10,11,45,46,47,48,49,50,14,17,15,17,15,14,16,
17,18,60,61,62,20,21,20,21,20,21,22,23,29,72,73,74,34,35,34,35,38,39,81,45,46,
49,50,86,87,62,65,66,72,92,93,94,95,96,97,98,99,100,101,92,93,92,93,95,92,94,
93,92,93,95,93,95,94,116,117,118,119,120,121,122,123,124,96,96,96,97,97,99,
100,98,101,134,135,136,137,110,110,110,141,142,143,144,145,116,116,148,120,
121,121,120,121,121,122,122,127,127,159,160,134,135,135,141,165,166,148,
148],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,1,2,1,2,24,25,26,27,28,
29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,3,4,3,5,49,50,51,52,53,54,55,
56,57,58,59,60,61,62,6,7,10,11,8,9,6,7,71,14,15,16,75,76,77,78,79,80,81,24,25,
84,85,34,35,88,41,42,51,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,
107,108,109,110,111,112,113,114,115,116,117,119,118,92,93,95,92,94,125,126,
127,128,129,130,131,132,133,134,135,137,136,138,140,139,96,96,97,144,145,146,
147,148,102,105,103,104,109,109,106,106,158,157,116,116,161,162,163,125,134,
134,168,167],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,
25,26,27,28,29,30,31,32,33,1,2,1,2,38,39,40,41,42,43,44,45,46,47,48,49,50,51,
52,53,54,55,56,57,58,59,60,61,3,63,64,65,66,67,68,69,70,71,72,73,74,6,7,8,9,
79,80,14,82,83,84,85,20,21,24,89,90,91,92,93,94,95,96,97,98,99,100,101,102,
103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,119,118,120,121,
122,123,124,125,126,127,128,129,130,131,132,133,92,93,94,94,138,139,140,141,
142,143,145,144,146,147,96,149,150,151,152,153,154,156,155,158,157,159,160,
102,103,103,164,120,120,125,125],,,,[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,
43,44,45,46,47,48,1,2,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,
69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,6,7,86,87,88,89,90,91,92,93,94,
95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,
115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,
134,135,137,136,138,140,139,141,142,143,92,92,146,147,148,149,150,151,152,154,
153,156,155,157,158,160,159,161,162,163,164,165,166,168,167],,[1,2,3,4,5,6,7,
8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,
34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,
1,2,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,
86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,
109,110,111,112,113,114,115,116,117,119,118,120,121,122,123,124,125,126,127,
128,129,130,131,132,133,134,135,137,136,138,139,140,141,142,143,145,144,146,
147,148,149,150,151,152,154,153,156,155,158,157,160,159,161,163,162,164,165,
166,167,168]],
0,
[(167,168),(165,166),(162,163),(159,160),(157,158),(155,156),(153,154),(144,
145),(139,140),(118,119),(136,137)],
["ConstructProj",[["A14.2",[]],["2.A14.2",[]]]]);
ALF("2.A14.2","A14.2",[1,1,2,3,4,5,5,6,6,7,7,8,8,9,10,11,12,13,14,
15,15,16,16,17,18,19,20,21,22,23,24,25,26,27,27,28,28,29,30,31,32,32,33,
33,34,35,36,37,38,38,39,40,41,42,43,44,45,46,47,48,48,49,50,50,51,51,52,
52,53,53,54,55,56,57,58,58,59,59,60,61,62,63,64,65,65,66,66,67,68,68,69,
70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,
94,95,96,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,
113,113,114,115,115,116,117,118,119,119,120,121,122,123,124,125,126,127,
127,128,128,129,129,130,130,131,132,132,133,134,134,135,135]);
ALN("2.A14.2",["2.S14"]);
MOT("Isoclinic(2.A14.2)",
0,
0,
0,
0,
[(167,168),(165,166),(162,163),(159,160),(157,158),(155,156),(153,154),(144,
145),(139,140),(118,119),(136,137)],
["ConstructIsoclinic",[["2.A14.2"]]]);
ALF("Isoclinic(2.A14.2)","A14.2",[1,1,2,3,4,5,5,6,6,7,7,8,8,9,10,11,12,13,14,
15,15,16,16,17,18,19,20,21,22,23,24,25,26,27,27,28,28,29,30,31,32,32,33,
33,34,35,36,37,38,38,39,40,41,42,43,44,45,46,47,48,48,49,50,50,51,51,52,
52,53,53,54,55,56,57,58,58,59,59,60,61,62,63,64,65,65,66,66,67,68,68,69,
70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,
94,95,96,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,
113,113,114,115,115,116,117,118,119,119,120,121,122,123,124,125,126,127,
127,128,128,129,129,130,130,131,132,132,133,134,134,135,135]);
MOT("2.A15.2",
[
"Schur cover of S15,\n",
"constructed by Gunter Malle"
],
[2615348736000,2615348736000,319334400,1935360,276480,2874009600,2874009600,
13063680,13063680,233280,233280,58320,58320,23328,23328,2903040,161280,23040,
15360,1536,768,36288000,36288000,12000,12000,1500,1500,967680,138240,60480,
27648,17280,6912,2592,1728,864,864,432,216,216,564480,564480,196,196,1920,384,
192,12960,12960,324,324,324,324,28800,3840,400,120,528,528,17280,2880,2304,
1296,1152,864,768,576,192,144,24,52,52,2688,1344,151200,151200,4320,4320,1620,
1620,600,600,30,30,144,960,960,320,40,5040,5040,504,504,88,96,96,48,224,112,
720,720,120,60,66,66,420,420,72,80,168,84,90,90,120,120,210,210,12454041600,
17418240,645120,460800,159667200,161280,9216,7680,2304,1536,21772800,2177280,
181440,103680,23040,12960,7776,7776,5760,5184,3888,2304,972,648,288,144,40320,
384,128,128,403200,19200,5760,1200,600,80,100,100,483840,8640,4608,2304,1296,
1152,576,384,288,192,288,288,72,72,72,10080,672,28,28,432,432,108,108,108,108,
14400,320,320,200,44,576,192,144,52,52,672,224,3600,720,720,360,300,240,180,
180,60,72,80,252,252,84,88,88,112,112,360,360,140,140,168,168],
[,[1,1,2,1,2,6,6,8,8,10,10,12,12,14,14,3,4,3,3,4,5,22,22,24,24,26,26,7,7,8,6,
9,8,11,9,10,11,15,14,13,41,41,43,43,17,17,20,48,48,50,50,52,52,23,22,25,25,58,
58,28,32,31,34,28,32,31,33,32,34,38,71,71,41,42,75,75,77,77,79,79,81,81,83,83,
49,54,54,55,56,90,90,92,92,59,62,66,67,73,74,76,78,77,82,104,104,106,106,85,
88,91,92,112,112,100,101,116,116,1,2,2,1,3,3,3,4,5,4,6,9,8,7,6,11,10,11,8,9,
14,9,13,15,10,15,17,17,20,20,22,22,23,24,24,25,26,26,28,32,28,28,34,29,32,31,
32,33,34,34,38,40,40,41,42,44,44,48,49,50,50,53,53,54,54,55,56,58,62,62,67,71,
71,74,74,75,78,76,77,81,77,80,80,81,85,88,90,92,93,94,94,98,98,100,101,106,
106,110,110],[1,2,3,4,5,1,2,1,2,1,2,1,2,1,2,16,17,18,19,20,21,22,23,24,25,26,
27,3,5,4,4,3,4,3,5,4,5,5,4,5,41,42,43,44,45,46,47,10,11,10,11,10,11,54,55,56,
57,58,59,16,18,17,16,18,16,20,17,19,18,21,71,72,73,74,22,23,22,23,22,23,24,25,
26,27,34,86,87,88,89,41,42,41,42,94,45,47,46,98,99,54,54,55,57,58,59,106,107,
63,109,74,73,79,80,86,87,106,107,118,119,120,121,122,123,124,125,126,127,118,
119,118,119,121,119,118,119,121,119,118,120,119,119,121,120,144,145,146,147,
148,149,150,151,152,153,154,155,122,122,124,123,122,126,123,125,124,127,124,
124,126,126,126,171,172,173,174,134,135,134,134,135,135,181,182,183,184,185,
144,145,144,189,190,191,192,148,150,150,148,152,149,150,150,151,160,203,171,
171,172,207,208,209,210,181,181,213,214,191,191],,[1,2,3,4,5,6,7,8,9,10,11,12,
13,14,15,16,17,18,19,20,21,1,2,1,2,1,2,28,29,30,31,32,33,34,35,36,37,38,39,40,
41,42,43,44,45,46,47,48,49,50,51,52,53,3,4,3,5,58,59,60,61,62,63,64,65,66,67,
68,69,70,71,72,73,74,6,7,8,9,10,11,6,7,12,13,85,16,18,17,19,90,91,92,93,94,95,
96,97,98,99,28,32,30,29,104,105,41,42,108,45,110,111,48,49,60,61,90,91,118,
119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,
138,139,140,141,142,143,144,145,147,146,118,121,119,121,118,120,121,121,156,
157,158,159,160,161,162,163,164,165,167,166,168,170,169,171,172,174,173,175,
176,178,177,180,179,122,123,125,122,185,186,187,188,190,189,191,192,128,129,
131,130,128,136,133,133,132,202,144,204,205,206,208,207,210,209,156,157,171,
171,216,215],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,
25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,1,2,1,2,45,46,47,48,49,50,51,
52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,4,3,75,76,77,
78,79,80,81,82,83,84,85,86,87,88,89,6,7,8,9,94,95,96,97,17,16,100,101,102,103,
104,105,22,23,108,109,28,30,112,113,114,115,75,76,118,119,120,121,122,123,124,
125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,
144,145,147,146,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,
163,164,165,167,166,168,169,170,118,119,120,120,175,176,177,178,180,179,181,
182,183,184,185,186,187,188,190,189,122,123,193,194,195,196,197,198,199,200,
201,202,203,128,130,129,207,208,144,144,211,212,148,148,156,156],,,,[1,2,3,4,
5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,
32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,
1,2,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,
84,85,86,87,88,89,90,91,92,93,3,95,96,97,98,99,100,101,102,103,6,7,106,107,
108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,
127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,
146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,
165,166,167,168,170,169,171,172,174,173,175,176,178,177,179,180,181,182,183,
184,118,186,187,188,190,189,191,192,193,194,195,196,197,198,200,199,201,202,
203,204,205,206,122,122,210,209,211,212,213,214,216,215],,[1,2,3,4,5,6,7,8,9,
10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,
36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,
62,63,64,65,66,67,68,69,70,1,2,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,
88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,
110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,
129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,147,146,
148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,167,
166,168,170,169,171,172,174,173,175,176,177,178,179,180,181,182,183,184,185,
186,187,188,118,118,191,192,193,194,195,196,197,198,200,199,201,202,203,204,
205,206,207,208,210,209,211,212,213,214,215,216]],
0,
[(215,216),(213,214),(209,210),(207,208),(199,200),(189,190),(179,180),(177,
178),(169,170),(166,167),(154,155),(146,147),(173,174)],
["ConstructProj",[["A15.2",[]],["2.A15.2",[]]]]);
ALF("2.A15.2","A15.2",[1,1,2,3,4,5,5,6,6,7,7,8,8,9,9,10,11,12,13,
14,15,16,16,17,17,18,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,32,33,
33,34,35,36,37,37,38,38,39,39,40,41,42,43,44,44,45,46,47,48,49,50,51,52,
53,54,55,56,56,57,58,59,59,60,60,61,61,62,62,63,63,64,65,66,67,68,69,69,
70,70,71,72,73,74,75,76,77,78,79,80,81,81,82,82,83,84,85,86,87,87,88,89,
90,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,
110,111,112,113,114,115,116,117,118,119,119,120,121,122,123,124,125,126,
126,127,128,129,130,131,132,133,134,135,136,137,137,138,139,139,140,141,
142,142,143,144,145,145,146,146,147,148,149,150,151,152,153,154,155,155,
156,157,158,159,160,161,162,163,164,164,165,166,167,168,169,170,171,171,
172,172,173,174,175,175,176,176]);
ALN("2.A15.2",["2.S15"]);
MOT("2.A16.2",
[
"Schur cover of S16,\n",
"constructed by Gunter Malle"
],
[41845579776000,41845579776000,3832012800,15482880,10321920,1105920,
37362124800,37362124800,130636800,130636800,1632960,1632960,93312,93312,58320,
58320,29030400,1290240,138240,30720,12288,6144,6144,1536,399168000,399168000,
72000,72000,1500,1500,8709120,483840,138240,138240,103680,23040,15552,13824,
7776,6912,4320,1728,864,576,432,216,5080320,5080320,392,392,11520,768,768,256,
128,90720,90720,1296,1296,324,324,201600,11520,800,480,480,2640,2640,120960,
17280,11520,3456,3456,3456,1296,1152,768,432,432,384,384,48,48,156,156,6720,
2688,28,1209600,1209600,21600,21600,3240,3240,1800,1800,1800,1800,30,30,432,
216,4800,960,960,400,80,30240,30240,2268,2268,1512,1512,88,288,288,96,96,336,
224,5760,2880,720,360,180,60,60,132,132,1680,1680,72,78,78,80,336,84,180,180,
110,110,480,240,120,126,126,280,168,210,210,174356582400,174182400,2764800,
1290240,1916006400,1290240,184320,46080,36864,9216,3072,3072,239500800,
21772800,1451520,725760,90720,69120,69120,38880,34560,20736,7776,7776,4608,
2592,972,864,864,288,322560,3072,1536,256,128,3628800,28800,19200,7200,2400,
2400,160,100,100,4354560,51840,11520,7776,4608,3888,1152,1152,1152,1152,1152,
1152,384,288,288,288,288,96,72,72,70560,2016,196,28,32,32,2160,432,108,108,
108,100800,960,400,320,160,160,132,2880,288,192,192,192,52,52,3360,224,21600,
3600,1620,1440,1080,300,300,240,180,180,180,216,216,216,240,1008,1008,252,252,
252,252,88,88,112,112,1440,480,360,132,132,140,168,180,180,240,240,280,280],
[,[1,1,2,1,1,2,7,7,9,9,11,11,13,13,15,15,3,4,3,3,4,4,5,6,25,25,27,27,29,29,8,
9,7,8,10,9,14,9,12,10,11,14,12,13,13,16,47,47,49,49,18,22,18,22,23,56,56,58,
58,60,60,26,25,28,28,27,67,67,31,35,33,35,31,35,39,38,33,39,37,35,38,42,44,84,
84,48,47,49,89,89,91,91,93,93,95,95,97,97,99,99,57,59,62,63,62,64,64,108,108,
110,110,112,112,68,71,76,76,77,86,87,89,90,92,91,93,96,97,128,128,130,130,101,
133,133,104,109,112,138,138,140,140,121,122,123,145,145,131,136,149,149,1,2,1,
2,3,3,3,4,3,6,4,6,7,10,9,8,12,7,9,11,9,10,13,12,10,14,16,11,13,14,18,18,18,21,
22,25,26,25,27,27,28,28,29,29,31,35,31,37,31,39,35,33,35,34,35,38,38,42,37,39,
39,42,46,46,47,48,49,50,55,55,56,57,58,61,61,62,62,64,63,64,64,67,71,76,71,76,
76,84,84,86,86,89,92,93,90,91,95,98,91,95,94,97,101,102,102,104,108,109,113,
112,111,111,114,114,120,120,122,122,123,128,128,130,136,138,138,142,142,147,
147],[1,2,3,4,5,6,1,2,1,2,1,2,1,2,1,2,17,18,19,20,21,22,23,24,25,26,27,28,29,
30,3,4,4,6,3,5,3,4,3,6,4,6,6,5,4,6,47,48,49,50,51,52,53,54,55,11,12,11,12,11,
12,62,63,64,65,66,67,68,17,19,18,17,19,19,17,18,22,19,19,20,21,24,23,84,85,86,
87,88,25,26,25,26,25,26,27,28,27,28,29,30,39,39,103,104,105,106,107,47,48,47,
48,47,48,114,51,51,53,52,119,120,63,62,62,63,63,65,66,67,68,130,131,75,84,85,
135,86,87,93,94,140,141,104,103,105,110,111,147,119,130,131,151,152,153,154,
155,156,157,158,159,160,161,162,151,152,151,152,152,153,153,151,153,152,151,
152,154,152,152,153,153,154,181,182,183,184,185,186,187,188,189,190,191,192,
193,194,155,155,156,155,159,155,159,158,156,160,157,158,161,160,157,159,159,
162,160,160,215,216,217,218,219,220,170,174,170,174,174,226,227,228,229,230,
231,232,181,181,183,182,182,238,239,240,241,186,187,186,187,186,190,191,188,
189,187,189,200,200,200,256,215,216,216,215,216,216,263,264,265,266,226,227,
226,232,232,272,240,244,244,256,256,278,279],,[1,2,3,4,5,6,7,8,9,10,11,12,13,
14,15,16,17,18,19,20,21,22,23,24,1,2,1,2,1,2,31,32,33,34,35,36,37,38,39,40,41,
42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,3,4,3,6,5,67,68,
69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,7,8,9,10,11,12,7,
8,9,10,15,16,101,102,17,18,19,17,20,108,109,110,111,112,113,114,115,116,117,
118,119,120,33,31,35,32,41,34,36,128,129,47,48,132,133,134,51,136,137,56,57,
67,68,71,69,70,145,146,86,148,108,109,151,152,153,154,155,156,157,158,159,160,
161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,
180,181,182,183,184,185,151,152,153,153,151,152,154,153,153,195,196,197,198,
199,200,201,202,203,204,205,206,207,208,209,211,210,212,214,213,215,216,217,
218,220,219,221,222,223,225,224,155,156,155,158,157,157,232,233,234,235,237,
236,239,238,240,241,163,164,170,166,165,163,164,171,168,167,169,253,254,255,
181,257,258,259,260,262,261,264,263,266,265,195,197,196,271,270,215,273,221,
221,233,233,240,240],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,
22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,1,
2,1,2,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,
75,76,77,78,79,80,81,82,83,84,85,3,4,5,89,90,91,92,93,94,95,96,97,98,99,100,
101,102,103,104,105,106,107,7,8,11,12,9,10,114,115,116,117,118,17,18,121,122,
123,124,125,126,127,128,129,25,26,132,133,134,135,31,32,138,139,140,141,142,
143,144,56,57,62,69,89,90,151,152,153,154,155,156,157,158,159,160,161,162,163,
164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,
183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,
202,203,204,205,206,207,208,209,211,210,212,213,214,151,152,151,154,220,219,
221,222,223,225,224,226,227,228,229,231,230,232,233,234,235,237,236,239,238,
155,156,242,243,244,245,246,247,248,249,250,251,252,253,255,254,256,163,166,
164,165,167,167,263,264,181,181,267,268,269,271,270,186,195,275,274,276,277,
226,226],,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,
25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,
51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,1,2,69,70,71,72,73,74,75,76,
77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,
102,103,104,105,106,107,108,109,110,111,112,113,3,115,116,117,118,119,120,121,
122,123,124,125,126,127,7,8,130,131,132,133,134,135,136,137,138,139,25,26,142,
143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,
162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,
181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,
200,201,202,203,204,205,206,207,208,209,210,211,212,214,213,215,216,217,218,
219,220,221,222,223,224,225,226,227,228,229,231,230,151,233,234,235,236,237,
239,238,240,241,242,243,244,245,246,247,248,249,250,251,252,253,255,254,256,
257,258,259,260,262,261,155,155,266,265,267,268,269,163,163,272,273,274,275,
276,277,278,279],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,
23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,
49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,
75,76,77,78,79,80,81,82,83,1,2,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,
101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,
120,121,122,123,124,125,126,127,128,129,130,131,132,7,8,135,136,137,138,139,
140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,
159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,
178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,
197,198,199,200,201,202,203,204,205,206,207,208,209,211,210,212,214,213,215,
216,217,218,220,219,221,222,223,224,225,226,227,228,229,230,231,232,233,234,
235,236,237,151,151,240,241,242,243,244,245,246,247,248,249,250,251,252,253,
255,254,256,257,258,259,260,262,261,263,264,266,265,267,268,269,271,270,272,
273,275,274,277,276,279,278]],
0,
[(278,279),(276,277),(274,275),(270,271),(265,266),(263,264),(261,262),(254,
255),(238,239),(236,237),(230,231),(224,225),(213,214),(210,211),(193,194),
(219,220)],
["ConstructProj",[["A16.2",[]],["2.A16.2",[]]]]);
ALF("2.A16.2","A16.2",[1,1,2,3,4,5,6,6,7,7,8,8,9,9,10,10,11,12,13,
14,15,16,17,18,19,19,20,20,21,21,22,23,24,25,26,27,28,29,30,31,32,33,34,
35,36,37,38,38,39,39,40,41,42,43,44,45,45,46,46,47,47,48,49,50,51,52,53,
53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,69,70,71,72,73,73,74,
74,75,75,76,76,77,77,78,78,79,80,81,82,83,84,85,86,86,87,87,88,88,89,90,
91,92,93,94,95,96,97,98,99,100,101,102,103,103,104,104,105,106,106,107,
108,109,110,110,111,111,112,113,114,115,115,116,117,118,118,119,120,121,
122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,
140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,
158,159,160,161,161,162,163,164,165,166,167,168,169,170,171,172,173,174,
175,176,177,177,178,179,179,180,181,182,183,184,184,185,186,187,188,188,
189,190,191,192,193,193,194,195,196,197,198,198,199,199,200,201,202,203,
204,205,206,207,208,209,210,211,212,213,214,214,215,216,217,218,219,220,
220,221,221,222,222,223,224,225,226,226,227,228,229,229,230,230,231,231]);
ALN("2.A16.2",["2.S16"]);
MOT("2.A17.2",
[
"Schur cover of S17,\n",
"constructed by Gunter Malle"
],
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466560,116640,116640,319334400,11612160,967680,92160,30720,12288,6144,4608,
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50803200,50803200,1176,1176,80640,3840,2304,256,128,725760,725760,6480,6480,
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144,72,48,624,624,40320,5376,28,10886400,10886400,129600,129600,19440,19440,
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192,144,104,1344,1344,448,14400,5760,1440,1440,1440,1200,360,180,120,60,396,
396,396,396,8400,8400,700,700,288,144,78,78,160,160,1008,1008,168,88,540,540,
270,270,110,110,112,720,720,480,240,120,126,126,280,168,168,420,420,
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184320,46080,9216,3072,2874009600,239500800,13063680,5806080,1935360,725760,
276480,241920,233280,103680,69120,58320,23328,15552,13824,12960,6912,3456,
1944,864,864,432,2903040,7680,3072,384,256,36288000,172800,50400,38400,12000,
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3456,2304,1440,1152,1152,1152,576,288,288,96,72,564480,26880,8064,196,84,32,
32,12960,864,324,324,108,806400,7680,3840,1920,1200,640,160,160,528,528,17280,
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1008,504,336,252,252,84,84,88,104,104,112,7200,720,600,480,480,480,120,120,
132,132,132,132,420,140,140,144,144,504,504,180,180,240,240,280,280,420,420],
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58,60,60,62,62,26,26,25,28,28,27,30,71,71,31,34,33,31,34,31,36,34,37,39,35,39,
33,34,39,42,37,43,48,47,93,93,50,49,51,98,98,100,100,102,102,104,104,106,106,
108,108,110,110,112,112,58,59,61,62,64,66,64,66,67,67,124,124,126,126,128,128,
130,130,72,75,75,81,81,85,79,94,95,95,96,99,98,101,100,101,107,103,104,107,
108,153,153,155,155,157,157,159,159,114,115,163,163,119,121,125,127,126,132,
171,171,173,173,175,175,142,143,145,144,145,148,183,183,158,167,168,188,188,1,
2,1,2,3,3,4,3,3,6,4,6,7,10,9,8,8,12,7,9,11,10,9,15,13,12,10,14,12,11,16,13,14,
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153,156,156,157,159,159,161,161,167,168,171,171,180,180,185,185,188,188],[1,2,
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82,93,94,165,166,95,95,96,170,104,105,104,105,175,176,177,118,118,119,120,123,
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195,194,197,194,197,195,196,200,195,199,199,196,198,200,200,197,198,201,199,
259,260,261,262,263,264,265,210,215,210,210,215,271,272,273,274,275,276,277,
278,279,280,224,224,224,225,227,227,226,226,289,290,291,292,229,230,230,229,
230,229,231,233,230,230,232,234,236,231,235,235,241,245,241,241,313,314,259,
261,261,259,260,261,261,263,263,324,325,326,327,271,271,275,273,272,272,274,
274,279,279,280,280,340,341,342,282,282,290,290,298,298,313,313,351,352,340,
340],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,1,2,1,2,
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55,56,57,58,59,60,61,62,63,3,6,4,3,6,5,6,71,72,73,74,75,76,77,78,79,80,81,82,
83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,7,8,9,10,13,14,11,12,7,8,9,10,15,
16,112,113,114,115,116,117,17,18,19,21,17,20,124,125,126,127,128,129,130,131,
132,133,134,135,136,137,138,139,140,141,142,31,33,34,32,38,31,43,40,35,41,153,
154,155,156,49,50,49,50,161,162,163,164,53,54,167,168,169,170,58,59,60,61,71,
72,177,73,77,75,74,76,183,184,95,186,187,124,125,190,191,192,193,194,195,196,
197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,
216,217,218,219,220,221,222,223,224,225,226,227,228,190,191,192,192,190,191,
190,193,192,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,
254,255,256,257,258,259,260,261,262,263,265,264,266,267,268,269,270,194,197,
195,199,194,196,198,198,279,280,281,282,283,284,285,286,288,287,289,290,291,
292,202,203,205,204,211,210,208,202,207,217,209,203,206,212,213,213,309,310,
311,312,224,225,315,316,317,318,319,321,320,322,323,324,325,326,327,238,239,
238,240,244,244,250,250,337,336,339,338,259,260,260,343,344,345,346,266,266,
281,281,290,290,315,315],,[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,
47,48,1,2,1,2,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,
74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,3,4,5,98,99,
100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,
119,120,121,122,123,7,8,9,10,11,12,7,8,132,133,134,135,136,137,138,139,17,19,
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162,163,164,165,166,31,34,32,170,171,172,173,174,175,176,53,178,179,180,181,
182,58,59,64,73,74,98,99,190,191,192,193,194,195,196,197,198,199,200,201,202,
203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,
222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,
241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,190,
192,191,190,193,265,264,266,267,268,269,270,271,272,273,274,275,276,278,277,
279,280,281,282,283,284,286,285,288,287,289,194,195,196,293,294,295,296,297,
298,299,300,301,302,303,304,305,306,308,307,309,310,312,311,313,314,202,205,
203,204,209,207,207,206,206,324,325,326,224,328,329,330,331,332,333,335,334,
337,336,338,339,229,231,231,344,343,238,239,348,347,349,350,271,271,293,
293],,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,
27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,
53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,1,2,73,74,75,76,77,78,
79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,
103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,
122,123,124,125,126,127,128,129,130,131,3,133,134,135,136,137,138,139,140,141,
142,143,144,145,146,147,148,149,150,151,152,7,8,9,10,157,158,159,160,161,162,
163,164,165,166,167,168,169,17,171,172,173,174,25,26,177,178,179,180,181,182,
183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,
202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,
221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,
240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,
259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,278,
277,190,191,281,282,283,284,286,285,287,288,289,290,291,292,293,294,295,296,
297,298,299,300,301,302,303,304,305,306,308,307,309,310,312,311,313,314,315,
316,317,318,319,321,320,322,323,194,326,325,327,328,329,330,331,333,332,334,
335,202,202,203,203,340,341,342,344,343,345,346,347,348,349,350,351,352,354,
353],,[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,
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53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,
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104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,
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239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,
258,259,260,261,262,263,265,264,266,267,268,269,270,271,272,273,274,275,276,
277,278,279,280,281,282,283,284,286,285,287,288,190,290,291,292,293,294,295,
296,297,298,299,300,301,302,303,304,305,306,308,307,309,310,312,311,313,314,
315,316,317,318,319,321,320,323,322,324,194,194,327,328,329,330,331,332,333,
334,335,337,336,339,338,340,341,342,343,344,345,346,348,347,350,349,352,351,
353,354],,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,
25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,
51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,
77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,
102,103,104,105,106,107,108,109,110,111,1,2,114,115,116,117,118,119,120,121,
122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,
141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,
160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,
179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,
198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,
217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,
236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,
255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,
274,275,276,278,277,279,280,281,282,283,284,286,285,288,287,289,290,291,292,
293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,312,
311,313,314,315,316,317,318,319,321,320,322,323,324,325,326,327,328,329,330,
331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,348,347,349,
350,351,352,354,353]],
0,
[(353,354),(351,352),(349,350),(347,348),(343,344),(341,342),(338,339),
(336,337),(334,335),(332,333),(325,326),(322,323),(320,321),(311,312),
(307,308),(287,288),(285,286),(277,278),(264,265)],
["ConstructProj",[["A17.2",[]],["2.A17.2",[]]]]);
ALF("2.A17.2","A17.2",[1,1,2,3,4,5,6,6,7,7,8,8,9,9,10,10,11,12,13,
14,15,16,17,18,19,19,20,20,21,21,22,23,24,25,26,27,28,29,30,31,32,33,34,
35,36,37,38,39,40,40,41,41,42,43,44,45,46,47,47,48,48,49,49,50,51,52,53,
54,55,56,57,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,
77,78,78,79,80,81,82,82,83,83,84,84,85,85,86,86,87,87,88,88,89,89,90,91,
92,93,94,95,96,97,98,99,100,100,101,101,102,102,103,103,104,105,106,107,
108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,
125,126,126,127,127,128,128,129,130,131,131,132,133,134,135,136,137,138,
138,139,139,140,140,141,142,143,144,145,146,147,147,148,149,150,151,151,
152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,
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296,297,297]);
ALN("2.A17.2",["2.S17"]);
MOT("2.A18.2",
[
"Schur cover of S18,\n",
"constructed by Gunter Malle"
],
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271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,
290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,
309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,328,
327,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,
347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,363,362,364,366,
365,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,
385,386,387,388,390,389,391,392,393,394,395,396,397,398,399,400,401,402,403,
404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,
423,424,425,426,427,428,429,430,431,432,434,433,435,436,437,438,439,440,441,
443,442,444,445,446,447,448,450,449,452,451,454,453]],
0,
[(453,454),(451,452),(449,450),(447,448),(444,445),(442,443),(439,440),(433,
434),(431,432),(429,430),(425,426),(422,423),(420,421),(411,412),(408,409),
(393,394),(391,392),(389,390),(365,366),(362,363),(342,343),(327,328),(344,
345)],
["ConstructProj",[["A18.2",[]],["2.A18.2",[]]]]);
ALF("2.A18.2","A18.2",[1,1,2,3,4,5,6,6,7,7,8,8,9,9,10,10,11,11,12,
13,14,15,16,17,18,19,20,21,22,22,23,23,24,24,25,26,27,28,29,30,31,32,33,
34,35,36,37,38,39,40,41,42,43,44,45,46,46,47,47,48,49,50,51,52,53,54,55,
55,56,56,57,57,58,58,59,59,60,61,62,63,64,65,66,67,68,68,69,70,71,72,73,
74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,96,
97,98,99,100,101,101,102,102,103,103,104,104,105,105,106,106,107,107,108,
108,109,109,110,111,111,112,113,114,115,116,117,118,119,120,121,122,123,
124,124,125,125,126,126,127,127,128,129,130,131,132,133,134,135,136,137,
138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,
155,156,156,157,157,158,158,159,160,161,162,162,163,164,165,166,167,168,
169,170,171,172,172,173,173,174,174,175,176,177,178,179,180,181,182,183,
183,184,184,185,186,187,187,188,189,190,191,192,192,193,193,194,195,196,
197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,
215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,
233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,
251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,
269,270,271,272,273,274,275,276,277,278,279,280,281,281,282,283,284,285,
286,287,288,289,290,291,292,293,294,295,295,296,296,297,298,299,300,301,
302,303,304,305,306,307,308,309,310,311,312,313,313,314,315,315,316,317,
318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,
336,337,338,338,339,339,340,340,341,342,343,344,345,346,347,348,349,350,
351,352,353,354,354,355,356,356,357,358,359,360,361,362,363,364,364,365,
365,366,367,367,368,369,370,370,371,371,372,372,373,374,375,376,377,377,
378,379,379,380,380,381,382,382,383,383,384,384,385,385]);
ALN("2.A18.2",["2.S18"]);
MOT("2.A5",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5]"
],
[120,120,4,6,6,10,10,10,10],
[,[1,1,2,4,4,8,8,6,6],[1,2,3,1,2,8,9,6,7],,[1,2,3,4,5,1,2,1,2]],
0,
[(6,8)(7,9)],
["ConstructProj",[["A5",[]],["2.A5",[]]]]);
ARC("2.A5","maxes",["2.L2(3)","bd10","2.S3"]);
ARC("2.A5","tomfusion",rec(name:="2.A5",map:=[1,2,4,3,6,5,8,5,8],text:=[
"fusion map is unique"
]));
ALF("2.A5","A5",[1,1,2,3,3,4,4,5,5]);
ALF("2.A5","2.A5.2",[1,2,3,4,5,6,7,6,7]);
ALF("2.A5","Isoclinic(2.A5.2)",[1,2,3,4,5,6,7,6,7],[
"fusion map is unique"
]);
ALF("2.A5","2.A6",[1,2,3,4,5,10,11,12,13],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
],"tom:26");
ALF("2.A5","2.L2(11)",[1,2,3,4,5,6,7,8,9],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("2.A5","2.L2(19)",[1,2,3,4,5,6,7,8,9],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("2.A5","2.L2(29)",[1,2,3,4,5,6,7,8,9],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("2.A5","2.L2(31)",[1,2,3,4,5,8,9,10,11],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("2.A5","2.J2",[1,2,5,8,9,16,17,18,19],[
"fusion map determined up to table aut. by compatibility\n",
"with factors"
]);
ALN("2.A5",["2.L2(4)","2.L2(5)","2.A1(4)","2.A1(5)","2.U2(4)","2.U2(5)",
"2.S2(4)","2.S2(5)","2.O3(4)","2.O3(5)","2.O4-(2)","Isoclinic(2.A5.2)M1"]);
MOT("2.A5.2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5]"
],
[240,240,8,12,12,10,10,12,8,8,12,12],
[,[1,1,2,4,4,6,6,1,3,3,4,4],[1,2,3,1,2,6,7,8,9,10,8,8],,[1,2,3,4,5,1,2,8,10,9,
12,11]],
0,
[(11,12),( 9,10)],
["ConstructProj",[["A5.2",[]],["2.A5.2",[]]]]);
ARC("2.A5.2","tomfusion",rec(name:="2.S5",map:=[1,2,6,4,8,7,14,3,12,12,10,10],
text:=[
"fusion map is unique"
]));
ARC("2.A5.2","maxes",["2.A5","2.S4","5:8","(2^2x3).2"]);
ALF("2.A5.2","A5.2",[1,1,2,3,3,4,4,5,6,6,7,7]);
ALF("2.A5.2","2.A6.2_1",[1,2,3,4,5,9,10,11,13,13,14,15],[
"fusion map is unique up to table autom."
]);
ALF("2.A5.2","U3(5)",[1,2,4,3,9,5,14,2,12,13,9,9],[
"fusion map is unique up to table autom."
]);
ALN("2.A5.2",["2.S5","U3(5)C2A","U3(5)N2A"]);
MOT("Isoclinic(2.A5.2)",
[
"isoclinic group of the 2.A5.2 given in the ATLAS"
],
0,
0,
0,
[(9,10),(11,12)],
["ConstructIsoclinic",[["2.A5.2"]]]);
ARC("Isoclinic(2.A5.2)","tomfusion",rec(name:="2.S5'",map:=[1,2,5,3,7,6,
11,4,10,10,12,12],text:=[
"fusion map is unique"
]));
ALF("Isoclinic(2.A5.2)","2.L2(25)",[1,2,3,4,5,8,9,3,7,6,12,13],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);
ALF("Isoclinic(2.A5.2)","2.A7",[1,2,3,4,5,10,11,3,8,9,12,12],[
"fusion map is unique up to table automorphisms"
]);
ALF("Isoclinic(2.A5.2)","A5.2",[1,1,2,3,3,4,4,5,6,6,7,7]);
ALF("Isoclinic(2.A5.2)","2.J2.2",[1,2,5,8,9,14,15,29,31,32,33,33],[
"fusion map is unique up to table autom."
]);
MOT("2.A6",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5]"
],
[720,720,8,18,18,18,18,8,8,10,10,10,10],
[,[1,1,2,4,4,6,6,3,3,12,12,10,10],[1,2,3,1,2,1,2,9,8,12,13,10,11],,[1,2,3,4,5,
6,7,9,8,1,2,1,2]],
0,
[(10,12)(11,13),(8,9),(4,6)(5,7)],
["ConstructProj",[["A6",[]],["2.A6",[]]]]);
ARC("2.A6","maxes",["2.A5","2.A6M2","3^2:8","2.Symm(4)","2.A6M5"]);
ARC("2.A6","tomfusion",rec(name:="2.A6",map:=[1,2,5,4,8,3,7,11,11,6,13,6,
13],text:=[
"fusion map is unique up to table autom."
],
perm:=(4,5)));
ALF("2.A6","A6",[1,1,2,3,3,4,4,5,5,6,6,7,7]);
ALF("2.A6","2.A6.2_1",[1,2,3,4,5,6,7,8,8,9,10,9,10],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("2.A6","2.A6.2_2",[1,2,3,4,5,4,5,6,7,8,9,10,11],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);
ALF("2.A6","2.A7",[1,2,3,6,7,4,5,8,9,10,11,10,11],[
"fusion map is unique up to table autom.,\n",
"compatible with tomfusion and factors"
]);
ALN("2.A6",["2.L2(9)","2.S4(2)'","2.A1(9)","2.U2(9)","2.S2(9)","2.O3(9)",
"2.O4-(3)","2.C2(2)'","2.O5(2)'"]);
MOT("2.A6.2_1",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5],\n",
"constructions: SigmaL(2,9)"
],
[1440,1440,16,36,36,36,36,8,10,10,48,48,8,12,12,12,12],
[,[1,1,2,4,4,6,6,3,9,9,1,2,3,4,4,7,7],[1,2,3,1,2,1,2,8,9,10,11,12,13,11,11,12,
12],,[1,2,3,4,5,6,7,8,1,2,11,12,13,15,14,17,16]],
0,
[(16,17),(14,15),(14,15)(16,17)],
["ConstructProj",[["A6.2_1",[]],["2.A6.2_1",[]]]]);
ARC("2.A6.2_1","tomfusion",rec(name:="2.S6",map:=[1,2,8,4,10,5,11,19,9,22,3,7,
17,13,13,27,27],text:=[
"fusion map is unique"
]));
ALF("2.A6.2_1","A6.2_1",[1,1,2,3,3,4,4,5,6,6,7,8,9,10,10,11,11]);
ALF("2.A6.2_1","Isoclinic(2.A7.2)",[1,2,3,6,7,4,5,8,9,10,15,14,16,18,19,
17,17],[
"fusion map is unique up to table autom."
]);
ALF("2.A6.2_1","2.U4(2)",[1,2,4,11,12,9,10,15,16,17,3,4,15,24,25,26,26]);
ALF("2.A6.2_1","2.A8",[1,2,4,7,8,5,6,10,11,12,3,4,10,14,15,13,13],[
"fusion map is unique up to table autom."
]);
ALN("2.A6.2_1",["2.S6"]);
MOT("2.A6.2_2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5]"
],
[1440,1440,16,18,18,16,16,20,20,20,20,20,16,16,16,16,20,20,20,20],
[,[1,1,2,4,4,3,3,10,10,8,8,2,6,6,7,7,11,11,9,9],[1,2,3,1,2,7,6,10,11,8,9,12,
16,15,13,14,19,20,18,17],,[1,2,3,4,5,7,6,1,2,1,2,12,15,16,14,13,12,12,12,12]],
0,
[(17,18)(19,20),(13,14)(15,16),( 8,10)( 9,11)(17,19,18,20),( 6, 7)
(13,15,14,16),( 6, 7)(13,15,14,16)(17,18)(19,20),( 6, 7)(13,16,14,15)],
["ConstructProj",[["A6.2_2",[]],["2.A6.2_2",[]]]]);
ALF("2.A6.2_2","A6.2_2",[1,1,2,3,3,4,4,5,5,6,6,7,8,8,9,9,10,10,11,11]);
MOT("Isoclinic(2.A6.2_2)",
[
"isoclinic group of the 2.A6.2_2 given in the ATLAS"
],
0,
0,
0,
[(8,10)(9,11)(17,19,18,20),(6,7)(13,15,14,16)],
["ConstructIsoclinic",[["2.A6.2_2"]]]);
ALF("Isoclinic(2.A6.2_2)","A6.2_2",[1,1,2,3,3,4,4,5,5,6,6,7,8,8,9,9,10,10,
11,11]);
MOT("2.A7",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[5040,5040,24,72,72,18,18,8,8,10,10,12,14,14,14,14],
[,[1,1,2,4,4,6,6,3,3,10,10,5,13,13,15,15],[1,2,3,1,2,1,2,9,8,10,11,3,15,16,13,
14],,[1,2,3,4,5,6,7,9,8,1,2,12,15,16,13,14],,[1,2,3,4,5,6,7,8,9,10,11,12,1,2,
1,2]],
0,
[(13,15)(14,16),(8,9)],
["ConstructProj",[["A7",[]],["2.A7",[]]]]);
ARC("2.A7","maxes",["2.A6","2.L3(2)","2.L3(2)","Isoclinic(2.A5.2)",
"(2.A4x3).2"]);
ARC("2.A7","tomfusion",rec(name:="2.A7",map:=[1,2,5,3,7,4,8,12,12,6,14,15,
9,18,9,18],text:=[
"fusion map is unique"
]));
ALF("2.A7","A7",[1,1,2,3,3,4,4,5,5,6,6,7,8,8,9,9]);
ALF("2.A7","2.A7.2",[1,2,3,4,5,6,7,8,8,9,10,11,12,13,12,13]);
ALF("2.A7","Isoclinic(2.A7.2)",[1,2,3,4,5,6,7,8,8,9,10,11,12,13,12,13],[
"fusion map is unique"
]);
ALF("2.A7","2.A8",[1,2,4,5,6,7,8,10,10,11,12,13,16,17,18,19],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("2.A7","2.Suz",[1,2,5,10,11,10,11,16,16,19,20,29,30,31,30,31],[
"fusion map is unique"
]);
MOT("2.A7.2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[10080,10080,48,144,144,36,36,8,20,20,24,14,14,240,48,24,12,12,12,20,20,24,
24],
[,[1,1,2,4,4,6,6,3,9,9,5,12,12,1,2,3,4,7,7,9,9,11,11],[1,2,3,1,2,1,2,8,9,10,3,
12,13,14,15,16,14,15,15,21,20,16,16],,[1,2,3,4,5,6,7,8,1,2,11,12,13,14,15,16,
17,19,18,14,14,22,23],,[1,2,3,4,5,6,7,8,9,10,11,1,2,14,15,16,17,19,18,21,20,
23,22]],
0,
[(20,21),(18,19),(18,19)(22,23),(22,23)],
["ConstructProj",[["A7.2",[]],["2.A7.2",[]]]]);
ALF("2.A7.2","A7.2",[1,1,2,3,3,4,4,5,6,6,7,8,8,9,10,11,12,13,13,14,14,15,
15]);
ALF("2.A7.2","2.Suz.2",[1,2,5,10,11,10,11,16,19,20,27,28,29,63,62,65,69,
68,68,82,82,85,85]);
ALN("2.A7.2",["2.S7","2.Suz.2M16"]);
MOT("Isoclinic(2.A7.2)",
[
"isoclinic group of the 2.A7.2 given in the ATLAS"
],
0,
0,
0,
[(18,19),(20,21),(22,23)],
["ConstructIsoclinic",[["2.A7.2"]]]);
ARC("Isoclinic(2.A7.2)","tomfusion",rec(name:="2.S7",map:=[1,2,8,4,10,5,
11,22,9,24,27,15,36,6,3,19,31,14,14,46,46,54,54],text:=[
"fusion map is unique"
]));
ALF("Isoclinic(2.A7.2)","A7.2",[1,1,2,3,3,4,4,5,6,6,7,8,8,9,10,11,12,13,
13,14,14,15,15]);
ALF("Isoclinic(2.A7.2)","Isoclinic(2.A8.2)",[1,2,4,5,6,7,8,10,11,12,13,15,
16,19,20,21,23,25,25,28,29,30,31],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables"
]);
ALF("Isoclinic(2.A7.2)","2.A9",[1,2,3,5,6,9,10,11,13,14,15,18,19,3,4,11,
15,16,17,24,24,25,26]);
ALF("Isoclinic(2.A7.2)","Isoclinic(2.Suz.2)",[1,2,5,10,11,10,11,16,19,20,
27,28,29,63,62,65,69,68,68,82,82,85,85]);
MOT("2.A8",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[40320,40320,192,96,360,360,36,36,16,8,30,30,12,12,12,14,14,14,14,30,30,30,
30],
[,[1,1,1,2,5,5,7,7,3,4,11,11,6,7,7,16,16,18,18,20,20,22,22],[1,2,3,4,1,2,1,2,
9,10,11,12,4,3,3,18,19,16,17,11,12,11,12],,[1,2,3,4,5,6,7,8,9,10,1,2,13,15,14,
18,19,16,17,5,6,5,6],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,1,2,1,2,22,23,20,
21]],
0,
[(20,22)(21,23),(16,18)(17,19),(14,15),(14,15)(20,22)(21,23)],
["ConstructProj",[["A8",[]],["2.A8",[]]]]);
ARC("2.A8","CAS",[rec(name:="2.a8",
permchars:=( 3, 4, 5, 6, 7, 8,11,14,23,22,20,18,15)( 9,12,16)(10,13,21,19,17),
permclasses:=( 4, 6, 9, 7, 5)( 8,10,15,12,16,13,17,18,14,11)(21,22),
text:=[
"maximal subgroup of sporadic simple McLaughlin group mcl\n",
"test: 1.OR,JAMES,JAMES,n=3,\n",
"and restricted characters decompose properly.\n",
""])]);
ARC("2.A8","maxes",["2.A7","2^(1+3):L3(2)","2^(1+3):L3(2)","2.A6.2_1",
"2(A4xA4).2^2","(2.A5x3).2"]);
ARC("2.A8","tomfusion",rec(name:="2.A8",map:=[1,2,3,7,4,12,5,13,10,27,11,
30,35,15,15,16,38,16,38,39,74,39,74],text:=[
"fusion map is unique"
]));
ALF("2.A8","A8",[1,1,2,3,4,4,5,5,6,7,8,8,9,10,10,11,11,12,12,13,13,14,14],[
"factor fusion equal to that on the CAS table"
]);
ALF("2.A8","2.A8.2",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,14,15,16,15,16,17,
18,17,18]);
ALF("2.A8","Isoclinic(2.A8.2)",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,14,15,16,
15,16,17,18,17,18]);
ALF("2.A8","2.A9",[1,2,4,3,5,6,9,10,12,11,13,14,15,16,17,18,19,18,19,27,
28,29,30],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("2.A8","McL",[1,2,2,5,3,8,4,9,5,12,6,15,18,9,9,10,19,11,20,21,23,22,
24],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALN("2.A8",["McLC2A","McLN2A"]);
MOT("2.A8.2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[80640,80640,384,192,720,720,72,72,32,16,60,60,24,12,14,14,30,30,1440,96,96,
32,36,36,12,16,16,20,20,24,24],
[,[1,1,1,2,5,5,7,7,3,4,11,11,6,7,15,15,17,17,1,2,4,4,5,7,8,9,9,11,11,13,13],[
1,2,3,4,1,2,1,2,9,10,11,12,4,3,15,16,11,12,19,20,21,22,19,19,20,27,26,29,28,
21,21],,[1,2,3,4,5,6,7,8,9,10,1,2,13,14,15,16,5,6,19,20,21,22,23,24,25,26,27,
19,19,30,31],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,1,2,17,18,19,20,21,22,23,24,
25,27,26,29,28,31,30]],
0,
[(30,31),(28,29),(26,27),(26,27)(30,31)],
["ConstructProj",[["A8.2",[]],["2.A8.2",[]]]]);
ALF("2.A8.2","A8.2",[1,1,2,3,4,4,5,5,6,7,8,8,9,10,11,11,12,12,13,14,15,16,
17,18,19,20,20,21,21,22,22]);
ALN("2.A8.2",["2.S8"]);
MOT("Isoclinic(2.A8.2)",
[
"7th maximal subgroup of McL.2,\n",
"isoclinic group of the 2.A8.2 given in the ATLAS"
],
0,
0,
0,
[(30,31), (28,29), (26,27)],
["ConstructIsoclinic",[["2.A8.2"]]]);
ARC("Isoclinic(2.A8.2)","tomfusion",rec(name:="2.S8",map:=[1,2,3,9,5,15,6,16,
12,41,14,48,56,22,24,69,70,141,7,4,26,36,55,51,23,39,42,114,114,130,130],
text:=[
"fusion map is unique up to table autom."
]));
ALF("Isoclinic(2.A8.2)","2.S6(2)",[1,2,4,5,7,8,11,12,17,18,19,20,25,27,29,
30,42,43,3,6,16,15,21,26,28,32,33,36,37,39,39],[
"fusion map is unique up to table autom."
]);
ALF("Isoclinic(2.A8.2)","A8.2",[1,1,2,3,4,4,5,5,6,7,8,8,9,10,11,11,12,12,
13,14,15,16,17,18,19,20,20,21,21,22,22]);
ALF("Isoclinic(2.A8.2)","McL.2",[1,2,2,5,3,8,4,9,5,11,6,13,16,9,10,17,18,
19,21,20,23,24,26,27,22,23,24,28,29,32,33],[
"fusion map is unique up to table automorphisms"
]);
ALF("Isoclinic(2.A8.2)","2.A10",[1,2,4,3,5,6,7,8,13,12,14,15,18,20,21,22,
34,35,3,4,12,11,18,19,20,23,24,29,29,30,31]);
ALN("Isoclinic(2.A8.2)",["McL.2N2A","McL.2C2A"]);
MOT("2.A9",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[362880,362880,480,192,2160,2160,162,162,108,108,24,16,120,120,24,12,12,14,14,
18,18,18,18,20,24,24,30,30,30,30],
[,[1,1,2,1,5,5,7,7,9,9,3,4,13,13,6,9,9,18,18,20,20,22,22,14,15,15,27,27,29,
29],[1,2,3,4,1,2,1,2,1,2,11,12,13,14,3,4,4,18,19,7,8,7,8,24,11,11,13,14,13,
14],,[1,2,3,4,5,6,7,8,9,10,11,12,1,2,15,17,16,18,19,20,21,22,23,3,25,26,5,6,5,
6],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,1,2,20,21,22,23,24,25,26,29,30,
27,28]],
0,
[(27,29)(28,30),(25,26),(20,22)(21,23),(16,17),(16,17)(25,26)(27,29)(28,30)],
["ConstructProj",[["A9",[]],["2.A9",[]]]]);
ARC("2.A9","maxes",["2.A8","Isoclinic(2.A7.2)","(2.A6x3).2_1","L2(8):3x2",
"2.A9M5","2.(A5xA4).2","(2x3^3).S4","2x3^2:2A4"]);
ALF("2.A9","A9",[1,1,2,3,4,4,5,5,6,6,7,8,9,9,10,11,11,12,12,13,13,14,14,
15,16,16,17,17,18,18]);
ALF("2.A9","O8+(2)M8",[1,1,2,3,4,4,5,5,6,6,7,8,9,9,10,11,11,12,12,13,13,
14,14,15,16,16,17,17,18,18]);
ALF("2.A9","2.A9.2",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,16,17,18,19,
20,19,20,21,22,22,23,24,23,24]);
ALF("2.A9","Isoclinic(2.A9.2)",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,
16,17,18,19,20,19,20,21,22,22,23,24,23,24]);
ALF("2.A9","2.A10",[1,2,3,4,5,6,9,10,7,8,12,13,14,15,18,20,20,21,22,25,26,
27,28,29,30,31,34,35,34,35],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("2.A9","2.O8+(2)",[1,2,6,8,11,12,15,16,17,18,24,26,29,30,39,50,50,51,
52,60,61,56,57,64,76,76,80,81,80,81],[
"fusion map is unique up to table autom.,\n",
"representative compatible with relevant factors"
]);
MOT("2.A9.2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[725760,725760,960,384,4320,4320,324,324,216,216,48,32,240,240,48,12,28,28,18,
18,40,24,30,30,10080,288,480,32,144,144,36,36,36,36,16,16,20,24,28,28,40,40],
[,[1,1,2,1,5,5,7,7,9,9,3,4,13,13,6,9,17,17,19,19,14,15,23,23,1,2,3,3,5,6,9,10,
8,8,12,12,13,15,17,17,21,21],[1,2,3,4,1,2,1,2,1,2,11,12,13,14,3,4,17,18,7,8,
21,11,13,14,25,26,27,28,25,26,25,26,26,26,36,35,37,27,40,39,42,41],,[1,2,3,4,
5,6,7,8,9,10,11,12,1,2,15,16,17,18,19,20,3,22,5,6,25,26,27,28,29,30,31,32,33,
34,35,36,25,38,40,39,27,27],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,1,2,19,
20,21,22,23,24,25,26,27,28,29,30,31,32,34,33,36,35,37,38,25,25,41,42]],
0,
[(41,42),(39,40),(33,34),(33,34)(35,36),(33,34)(35,36)(41,42),(35,36)],
["ConstructProj",[["A9.2",[]],["2.A9.2",[]]]]);
ALF("2.A9.2","A9.2",[1,1,2,3,4,4,5,5,6,6,7,8,9,9,10,11,12,12,13,13,14,15,
16,16,17,18,19,20,21,22,23,24,25,25,26,26,27,28,29,29,30,30]);
ALN("2.A9.2",["2.S9"]);
MOT("Isoclinic(2.A9.2)",
[
"isoclinic group of the 2.A9.2 given in the ATLAS"
],
0,
0,
0,
[(41,42),(39,40),(33,34),(35,36)],
["ConstructIsoclinic",[["2.A9.2"]]]);
ALF("Isoclinic(2.A9.2)","A9.2",[1,1,2,3,4,4,5,5,6,6,7,8,9,9,10,11,12,12,
13,13,14,15,16,16,17,18,19,20,21,22,23,24,25,25,26,26,27,28,29,29,30,30]);
ALF("Isoclinic(2.A9.2)","2.A11",[1,2,3,4,5,6,9,10,7,8,11,12,14,15,19,21,
24,25,28,29,30,36,40,41,3,4,11,13,19,18,20,21,22,23,27,26,30,36,39,39,44,
45],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables"
]);
ALF("Isoclinic(2.A9.2)","2.O7(3)",[1,2,4,5,8,9,12,13,16,17,24,23,25,26,35,
44,47,48,56,57,60,73,80,81,3,5,20,24,28,36,38,43,39,40,50,51,61,67,79,78,
88,87],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);
MOT("2F4(2)'M7",
[
"7th maximal subgroup of 2F4(2)',\n",
"differs from 2F4(2)'M6 only by fusion map"
],
0,
0,
0,
0,
["ConstructPermuted",["A6.2^2"]]);
ALF("2F4(2)'M7","2F4(2)'",[1,3,4,7,8,3,5,9,2,13,14,7,12],[
"fusion A6.2^2 -> 2F4(2)' mapped under 2F4(2)'.2"
]);
MOT("3.A6",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5]"
],
[1080,1080,1080,24,24,24,9,9,12,12,12,15,15,15,15,15,15],
[,[1,3,2,1,3,2,7,8,4,6,5,15,17,16,12,14,13],[1,1,1,4,4,4,1,1,9,9,9,15,15,15,
12,12,12],,[1,3,2,4,6,5,7,8,9,11,10,1,3,2,1,3,2]],
0,
[(12,15)(13,16)(14,17),(7,8),( 2, 3)( 5, 6)(10,11)(13,14)(16,17)],
["ConstructProj",[["A6",[]],,["3.A6",[11,11,-1,-1,-1]]]]);
ARC("3.A6","maxes",["3xA5","3.A6M2","3^(1+2):4","3xSymm(4)","3.A6M5"]);
ALF("3.A6","A6",[1,1,1,2,2,2,3,4,5,5,5,6,6,6,7,7,7]);
ALF("3.A6","3.A6.2_1",[1,2,2,3,4,4,5,6,7,8,8,9,10,11,9,11,10],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("3.A6","3.A6.2_2",[1,2,2,3,4,4,5,5,6,7,7,8,9,9,10,11,11],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("3.A6","3.A6.2_3",[1,2,3,4,5,6,7,7,8,9,10,11,12,13,11,12,13]);
ALF("3.A6","3.A7",[1,2,3,4,5,6,8,7,9,10,11,12,13,14,12,13,14],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("3.A6","3.L3(4)",[1,2,3,4,5,6,7,7,8,9,10,17,18,19,20,21,22],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALN("3.A6",["3.L2(9)","3.S4(2)'","3.A1(9)","3.U2(9)","3.S2(9)","3.O3(9)",
"3.O4-(3)","3.C2(2)'","3.O5(2)'","3.A6.2_1M1"]);
MOT("3.A6.2^2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5]"
],
[4320,2160,96,48,18,48,24,30,15,48,16,6,40,8,10,24,12,24,24,24],
[,[1,2,1,2,5,3,4,8,9,1,3,5,1,6,8,3,4,6,7,7],[1,1,3,3,1,6,6,8,8,10,11,10,13,14,
15,16,16,18,18,18],,[1,2,3,4,5,6,7,1,2,10,11,12,13,14,13,16,17,18,19,20]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,
-1,-1,-1,-1,-1],[1,1,1,1,1,1,1,1,1,-1,-1,-1,1,1,1,-1,-1,-1,-1,-1],
[TENSOR,[2,3]],[10,10,2,2,1,-2,-2,0,0,2,2,-1,0,0,0,0,0,0,0,0],
[TENSOR,[5,3]],[16,16,0,0,-2,0,0,1,1,0,0,0,-4,0,1,0,0,0,0,0],
[TENSOR,[7,2]],[9,9,1,1,0,1,1,-1,-1,3,-1,0,-1,1,-1,1,1,-1,-1,-1],
[TENSOR,[9,2]],
[TENSOR,[9,3]],
[TENSOR,[9,4]],[20,20,-4,-4,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[12,-6,-4,2,0,4,
-2,2,-1,0,0,0,0,0,0,0,0,0,0,0],[12,-6,4,-2,0,0,0,2,-1,0,0,0,0,0,0,0,0,0,
-E(24)+E(24)^11+E(24)^17-E(24)^19,E(24)-E(24)^11-E(24)^17+E(24)^19],
[TENSOR,[15,2]],[18,-9,2,-1,0,2,-1,-2,1,0,0,0,0,0,0,2,-1,-2,1,1],
[TENSOR,[17,2]],[30,-15,-2,1,0,-2,1,0,0,0,0,0,0,0,0,2,-1,2,-1,-1],
[TENSOR,[19,2]]],
[(19,20)]);
ARC("3.A6.2^2","CAS",[rec(name:="3.a6.2^2",
permchars:=(),
permclasses:=(),
text:=[
"origin: CAS library,\n",
"maximal subgroup of sporadic simple Rudvalis group Ru,\n",
"source: received from S.Mattarei\n",
"test: 1.OR, JAMES, JAMES,n=3,\n",
"and restricted characters decompose properly.\n",
""])]);
ARC("3.A6.2^2","tomfusion",rec(name:="3.A6.2^2",map:=[1,5,2,17,6,8,39,14,
46,3,11,20,4,28,35,9,42,21,64,64],text:=[
"fusion map is unique"
]));
ALF("3.A6.2^2","Ru",[1,4,2,11,4,5,18,10,24,2,8,11,3,13,17,6,19,13,30,31],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("3.A6.2^2","J2.2",[1,4,2,9,5,6,15,7,16,17,18,20,3,12,13,18,23,21,27,
26],[
"fusion map is unique up to table autom.,\n",
"unique map that is compatible with Brauer tables"
]);
ALF("3.A6.2^2","A6.2^2",[1,1,2,2,3,4,4,5,5,6,7,8,9,10,11,12,12,13,13,13]);
ALF("3.A6.2^2","3.M22.2",[1,2,3,4,5,6,7,10,11,23,26,27,24,28,29,8,9,18,19,
19],[
"fusion map is unique"
]);
ALN("3.A6.2^2",["3.A6.V4","RuN3A","J2.2N3A"]);
MOT("3.A6.2_1",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5]"
],
[2160,1080,48,24,18,18,24,12,15,15,15,48,48,8,6,6],
[,[1,2,1,2,5,6,3,4,9,10,11,1,1,3,5,6],[1,1,3,3,1,1,7,7,9,9,9,12,13,14,12,
13],,[1,2,3,4,5,6,7,8,1,2,2,12,13,14,15,16]],
0,
[(10,11),( 5, 6)(12,13)(15,16)],
["ConstructMGA","3.A6","A6.2_1",[[8,11],[9,10],[12,13],[14,15],[16,17]],
()]);
ALF("3.A6.2_1","A6.2_1",[1,1,2,2,3,4,5,5,6,6,6,7,8,9,10,11]);
ALF("3.A6.2_1","3.A6.2^2",[1,2,3,4,5,5,6,7,8,9,9,10,10,11,12,12]);
ALF("3.A6.2_1","2^6:3.s6",[1,4,5,7,10,12,16,14,17,19,20,21,24,28,30,32],[
"fusion map is unique up to table automorphisms"
]);
ALF("3.A6.2_1","M24",[1,4,2,10,4,5,6,17,9,21,22,2,3,7,10,11],[
"fusion map is unique up to table automorphisms"
]);
ALN("3.A6.2_1",["3.S6"]);
MOT("3.A6.2_2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5]"
],
[2160,1080,48,24,9,24,12,30,15,30,15,20,8,8,10,10],
[,[1,2,1,2,5,3,4,10,11,8,9,1,6,6,10,8],[1,1,3,3,1,6,6,10,10,8,8,12,14,13,16,
15],,[1,2,3,4,5,6,7,1,2,1,2,12,14,13,12,12]],
0,
[(13,14),( 8,10)( 9,11)(15,16)],
["ConstructMGA","3.A6","A6.2_2",[[8,9],[10,11],[12,13],[14,15],[16,17]],
()]);
ARC("3.A6.2_2","CAS",[rec(name:="3.pgl(2,9)",
permchars:=( 3, 9, 8, 7, 4, 5, 6)(12,13),
permclasses:=( 5, 6, 7, 8, 9,10,11,12)(15,16),
text:=[
"maximal subgroup of sporadic simple Janko group j2\n",
"test:1.OR,JAMES,JAMES,n=3,\n",
"and restricted characters decompose properly.\n",
""])]);
ARC("3.A6.2_2","tomfusion",rec(name:="3.PGL2(9)",map:=[1,4,2,11,5,7,22,9,
25,9,25,3,14,14,19,19],text:=[
"fusion map is unique"
]));
ALF("3.A6.2_2","A6.2_2",[1,1,2,2,3,4,4,5,5,6,6,7,8,9,10,11]);
ALF("3.A6.2_2","3.A6.2^2",[1,2,3,4,5,6,7,8,9,8,9,13,14,14,15,15]);
ALF("3.A6.2_2","J2",[1,4,2,11,5,6,19,7,20,8,21,3,14,14,15,16],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALN("3.A6.2_2",["3.pgl(2,9)","J2N3A"]);
MOT("3.A6.2_3",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5]"
],
[2160,2160,2160,48,48,48,9,24,24,24,15,15,15,12,12,12,24,24,24,24,24,24],
[,[1,3,2,1,3,2,7,4,6,5,11,13,12,4,6,5,8,10,9,8,10,9],[1,1,1,4,4,4,1,8,8,8,11,
11,11,14,14,14,17,17,17,20,20,20],,[1,3,2,4,6,5,7,8,10,9,1,3,2,14,16,15,20,22,
21,17,19,18]],
0,
[(17,20)(18,21)(19,22),( 2, 3)( 5, 6)( 9,10)(12,13)(15,16)(18,19)(21,22)],
["ConstructProj",[["A6.2_3",[]],,["3.A6.2_3",[-1,17,-1,-1]]]]);
ALF("3.A6.2_3","A6.2_3",[1,1,1,2,2,2,3,4,4,4,5,5,5,6,6,6,7,7,7,8,8,8]);
ALF("3.A6.2_3","3.A6.2^2",[1,2,2,3,4,4,5,6,7,7,8,9,9,16,17,17,18,19,20,18,
20,19],[
"fusion map is unique up to table autom.,\n",
"unique map that is compatible with Brauer tables"
]);
ALF("3.A6.2_3","3.M22",[1,2,3,4,5,6,7,8,9,10,14,15,16,11,12,13,26,27,28,
26,27,28],[
"fusion map determined up to table aut. by compatibility\n",
"with factors"
]);
ALF("3.A6.2_3","3.U3(5)",[1,3,2,4,6,5,7,8,10,9,14,16,15,8,10,9,32,34,33,
35,37,36],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);
MOT("3.A7",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[7560,7560,7560,72,72,72,36,9,12,12,12,15,15,15,36,36,36,21,21,21,21,21,21],
[,[1,3,2,1,3,2,7,8,4,6,5,12,14,13,7,7,7,18,20,19,21,23,22],[1,1,1,4,4,4,1,1,9,
9,9,12,12,12,4,4,4,21,21,21,18,18,18],,[1,3,2,4,6,5,7,8,9,11,10,1,3,2,15,17,
16,21,23,22,18,20,19],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,1,2,3,1,2,
3]],
0,
[(18,21)(19,22)(20,23),( 2, 3)( 5, 6)(10,11)(13,14)(16,17)(19,20)(22,23)],
["ConstructProj",[["A7",[]],,["3.A7",[-1,-1,-1,-1,-1,-13,-13]]]]);
ARC("3.A7","maxes",["3.A6","3xL3(2)","3xL3(2)","3xA5.2","3.(A4x3):2"]);
ALF("3.A7","A7",[1,1,1,2,2,2,3,4,5,5,5,6,6,6,7,7,7,8,8,8,9,9,9]);
ALF("3.A7","3.A7.2",[1,2,2,3,4,4,5,6,7,8,8,9,10,10,11,12,12,13,14,15,13,
15,14],[
"fusion map is unique up to table autom.,\n",
"unique map that is compatible with Brauer tables"
]);
ALF("3.A7","3.M22",[1,2,3,4,5,6,7,7,11,12,13,14,15,16,17,18,19,20,21,22,
23,24,25],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("3.A7","3.U3(5)",[1,2,3,4,5,6,7,7,8,9,10,14,15,16,23,24,25,26,27,28,
29,30,31],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);
ALF("3.A7","3.Suz",[1,2,3,7,8,9,16,16,26,27,28,32,33,34,47,47,47,48,49,50,
48,49,50],[
"fusion map of the maximal subgroup 3.A7 determined up to table aut."
]);
ALF("3.A7","3.ON",[1,2,3,4,5,6,7,7,11,12,13,14,15,16,17,17,17,21,22,23,21,
22,23],[
"fusion map determined by Brauer tables"
]);
MOT("3.A7.2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[15120,7560,144,72,72,18,24,12,30,15,72,36,21,21,21,240,48,24,12,6,10,12],
[,[1,2,1,2,5,6,3,4,9,10,5,5,13,15,14,1,1,3,5,6,9,11],[1,1,3,3,1,1,7,7,9,9,3,3,
13,13,13,16,17,18,16,17,21,18],,[1,2,3,4,5,6,7,8,1,2,11,12,13,14,15,16,17,18,
19,20,16,22],,[1,2,3,4,5,6,7,8,9,10,11,12,1,2,2,16,17,18,19,20,21,22]],
0,
[(14,15)],
["ConstructMGA","3.A7","A7.2",
[[10,11],[12,13],[14,15],[16,17],[18,19],[20,23],[21,22]],()]);
ARC("3.A7.2","CAS",[rec(name:="3.s7",
permchars:=( 5,11,10, 9, 8, 7, 6)(17,18)(21,22),
permclasses:=(),
text:=[
" test:= 1. o.r., sym 2 decompose correctly\n",
""])]);
ARC("3.A7.2","tomfusion",rec(name:="3.S7",map:=[1,5,3,19,6,7,12,56,15,66,
17,20,29,79,79,2,4,10,25,27,41,55],text:=[
"fusion map is unique"
]));
ALF("3.A7.2","A7.2",[1,1,2,2,3,4,5,5,6,6,7,7,8,8,8,9,10,11,12,13,14,15]);
ALF("3.A7.2","He",[1,4,2,10,4,5,6,19,9,25,10,10,14,28,29,2,3,6,10,11,18,
19],[
"fusion is unique up to table automorphisms,\n",
"unique map that is compatible with Brauer tables,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("3.A7.2","3.Suz.2",[1,2,5,6,11,11,18,19,22,23,31,31,32,33,33,77,76,79,
83,82,91,94],[
"fusion map is unique"
]);
ALF("3.A7.2","3.s7x2",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,
21,22],[
"fusion map is unique up to table aut."
]);
ALN("3.A7.2",["3.s7","HeN3A"]);
MOT("Isoclinic(2.A6x2)",
[
"central product of 2.A6 with a cyclic group of order 4,\n",
"subgroup of 4.A6.2_3"
],
0,
0,
0,
[(19,23)(20,24)(21,25)(22,26),(15,17)(16,18),(7,11)(8,12)(9,13)(10,14),(2,4)(8
,10)(12,14)(15,17)(20,22)(24,26)],
["ConstructIsoclinic",[["2.A6"],["Cyclic",2]]]);
ALF("Isoclinic(2.A6x2)","4.A6.2_3",[1,3,2,3,4,5,6,8,7,9,6,9,7,8,10,11,10,
12,13,15,14,16,13,16,14,15]);
MOT("4.A6.2_3",
[
"origin: ATLAS of finite groups"
],
[2880,2880,1440,32,32,36,36,36,36,16,32,32,20,20,20,20,8,8,16,16,16,16],
[,[1,1,2,2,1,6,6,7,7,4,4,4,13,13,14,14,5,5,11,11,12,12],[1,2,3,4,5,1,2,3,3,10,
11,12,13,14,15,16,18,17,20,19,22,21],,[1,2,3,4,5,6,7,8,9,10,12,11,1,2,3,3,17,
18,21,22,19,20]],
0,
[(15,16),( 8, 9),(17,18)(19,20)(21,22),(11,12)(17,18)(19,22)(20,21)],
["ConstructMGA","Isoclinic(2.A6x2)","(2xA6).2_3",[[15,18],[16,17],
[19,22],[20,21],[23,26],[24,25]],()]);
ALF("4.A6.2_3","(2xA6).2_3",[1,1,2,3,4,5,5,6,6,7,8,8,9,9,10,10,11,12,13,
14,15,16]);
ALF("4.A6.2_3","A6.2_3",[1,1,1,2,2,3,3,3,3,4,4,4,5,5,5,5,6,6,7,7,8,8]);
MOT("6.A6",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5]"
],
[2160,2160,2160,2160,2160,2160,24,24,24,18,18,18,18,24,24,24,24,24,24,30,30,
30,30,30,30,30,30,30,30,30,30],
[,[1,3,5,1,3,5,4,6,2,10,10,12,12,7,9,8,7,9,8,26,28,30,26,28,30,20,22,24,20,22,
24],[1,4,1,4,1,4,7,7,7,1,4,1,4,17,14,17,14,17,14,26,29,26,29,26,29,20,23,20,
23,20,23],,[1,6,5,4,3,2,7,9,8,10,11,12,13,17,16,15,14,19,18,1,6,5,4,3,2,1,6,5,
4,3,2]],
0,
[(20,26)(21,27)(22,28)(23,29)(24,30)(25,31),(14,17)(15,18)(16,19),(10,12)
(11,13),( 2, 6)( 3, 5)( 8, 9)(15,19)(16,18)(21,25)(22,24)(27,31)(28,30)],
["ConstructProj",[["A6",[]],["2.A6",[]],["3.A6",[11,11,-1,-1,-1]],,,["6.A6",
[17,17,11,11]]]]);
ARC("6.A6","maxes",["3x2.A5","6.A6M2","6.A6M3","3x2.Symm(4)","6.A6M5"]);
ALF("6.A6","A6",[1,1,1,1,1,1,2,2,2,3,3,4,4,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,
7,7,7]);
ALF("6.A6","2.A6",[1,2,1,2,1,2,3,3,3,4,5,6,7,8,9,8,9,8,9,10,11,10,11,10,
11,12,13,12,13,12,13]);
ALF("6.A6","3.A6",[1,2,3,1,2,3,4,5,6,7,7,8,8,9,10,11,9,10,11,12,13,14,12,
13,14,15,16,17,15,16,17]);
ALF("6.A6","6.A6.2_1",[1,2,3,4,3,2,5,6,6,7,8,9,10,11,12,12,11,13,13,14,15,
16,17,18,19,14,19,18,17,16,15],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALF("6.A6","6.A6.2_2",[1,2,3,4,3,2,5,6,6,7,8,7,8,9,10,11,12,11,10,13,14,
15,16,15,14,17,18,19,20,19,18],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables and factors"
]);
ALF("6.A6","6.A7",[1,2,3,4,5,6,7,8,9,12,13,10,11,14,15,16,17,18,19,20,21,
22,23,24,25,20,21,22,23,24,25],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
ALN("6.A6",["6.L2(9)","6.S4(2)'","6.A1(9)","6.U2(9)","6.S2(9)","6.O3(9)",
"6.O4-(3)","6.C2(2)'","6.O5(2)'","6.A6.2_1M1"]);
MOT("6.A6.2_1",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5]"
],
[4320,2160,2160,4320,48,24,36,36,36,36,24,24,24,30,30,30,30,30,30,48,48,8,12,
12,12,12],
[,[1,3,3,1,4,2,7,7,9,9,5,6,6,14,18,16,14,18,16,1,4,5,7,7,10,10],[1,4,1,4,5,5,
1,4,1,4,11,11,11,14,17,14,17,14,17,20,21,22,20,20,21,21],,[1,2,3,4,5,6,7,8,9,
10,11,12,13,1,2,3,4,3,2,20,21,22,24,23,26,25]],
0,
[(25,26),(23,24),(15,19)(16,18),(12,13),(12,13)(25,26),(12,13)(15,19)(16,18)
(23,24)(25,26)],
["ConstructMGA","6.A6","2.A6.2_1",[[14,17],[15,16],[18,19],[20,21],[22,23],
[24,27],[25,26],[28,31],[29,30]],()]);
ALF("6.A6.2_1","A6.2_1",[1,1,1,1,2,2,3,3,4,4,5,5,5,6,6,6,6,6,6,7,8,9,10,
10,11,11]);
ALF("6.A6.2_1","2.A6.2_1",[1,2,1,2,3,3,4,5,6,7,8,8,8,9,10,9,10,9,10,11,12,
13,14,15,16,17]);
ALF("6.A6.2_1","3.A6.2_1",[1,2,2,1,3,4,5,5,6,6,7,8,8,9,10,11,9,10,11,12,
13,14,15,15,16,16]);
ALN("6.A6.2_1",["6.S6"]);
MOT("6.A6.2_2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5]"
],
[4320,2160,2160,4320,48,24,18,18,48,24,24,48,60,30,30,60,60,30,30,60,20,16,16,
16,16,20,20,20,20],
[,[1,3,3,1,4,2,7,7,5,6,6,5,17,19,19,17,13,15,15,13,4,9,9,12,12,20,20,16,16],[
1,4,1,4,5,5,1,4,12,9,12,9,17,20,17,20,13,16,13,16,21,25,24,22,23,28,29,27,
26],,[1,2,3,4,5,6,7,8,12,11,10,9,1,2,3,4,1,2,3,4,21,24,25,23,22,21,21,21,21]],
0,
[(26,27)(28,29),(22,23)(24,25),(13,17)(14,18)(15,19)(16,20)(26,28,27,29),
( 9,12)(10,11)(22,24,23,25),( 9,12)(10,11)(22,24,23,25)(26,27)(28,29),(13,17)
(14,18)(15,19)(16,20)(26,29,27,28)],
["ConstructMGA","6.A6","2.A6.2_2",[[14,15],[16,17],[18,19],[20,21],[22,23],
[24,25],[26,27],[28,29],[30,31]],()]);
ALF("6.A6.2_2","A6.2_2",[1,1,1,1,2,2,3,3,4,4,4,4,5,5,5,5,6,6,6,6,7,8,8,9,
9,10,10,11,11]);
ALF("6.A6.2_2","2.A6.2_2",[1,2,1,2,3,3,4,5,6,7,6,7,8,9,8,9,10,11,10,11,12,
13,14,15,16,17,18,19,20]);
ALF("6.A6.2_2","3.A6.2_2",[1,2,2,1,3,4,5,5,6,7,7,6,8,9,9,8,10,11,11,10,12,
13,13,14,14,15,15,16,16]);
MOT("Isoclinic(6.A6.2_2)",
[
"isoclinic group of the 6.A6.2_2 given in the ATLAS"
],
0,
0,
0,
[(13,17)(14,18)(15,19)(16,20)(26,28,27,29),(9,12)(10,11)(22,24,23,25)],
["ConstructIsoclinic",[["6.A6.2_2"]]]);
ALF("Isoclinic(6.A6.2_2)","3.A6.2_2",[1,2,2,1,3,4,5,5,6,7,7,6,8,9,9,8,10,
11,11,10,12,13,13,14,14,15,15,16,16]);
MOT("6.A7",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[15120,15120,15120,15120,15120,15120,72,72,72,72,72,18,18,24,24,24,24,24,24,
30,30,30,30,30,30,36,36,36,42,42,42,42,42,42,42,42,42,42,42,42],
[,[1,3,5,1,3,5,4,6,2,10,10,12,12,7,9,8,7,9,8,20,22,24,20,22,24,11,11,11,29,31,
33,29,31,33,35,37,39,35,37,39],[1,4,1,4,1,4,7,7,7,1,4,1,4,17,14,17,14,17,14,
20,23,20,23,20,23,7,7,7,35,38,35,38,35,38,29,32,29,32,29,32],,[1,6,5,4,3,2,7,
9,8,10,11,12,13,17,16,15,14,19,18,1,6,5,4,3,2,26,28,27,35,40,39,38,37,36,29,
34,33,32,31,30],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,
24,25,26,27,28,1,2,3,4,5,6,1,2,3,4,5,6]],
0,
[(29,35)(30,36)(31,37)(32,38)(33,39)(34,40),(14,17)(15,18)(16,19),( 2, 6)
( 3, 5)( 8, 9)(15,19)(16,18)(21,25)(22,24)(27,28)(30,34)(31,33)(36,40)
(37,39)],
["ConstructProj",[["A7",[]],["2.A7",[]],["3.A7",[-1,-1,-1,-1,-1,-13,-13]],,,
["6.A7",[17,17,-13,-13,-1]]]]);
ARC("6.A7","maxes",["6.A6","3x2.L3(2)","3x2.L3(2)","3xIsoclinic(2.A5.2)",
"6.(A4x3).2"]);
ALF("6.A7","A7",[1,1,1,1,1,1,2,2,2,3,3,4,4,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,
8,8,8,8,8,8,9,9,9,9,9,9]);
ALF("6.A7","2.A7",[1,2,1,2,1,2,3,3,3,4,5,6,7,8,9,8,9,8,9,10,11,10,11,10,
11,12,12,12,13,14,13,14,13,14,15,16,15,16,15,16]);
ALF("6.A7","3.A7",[1,2,3,1,2,3,4,5,6,7,7,8,8,9,10,11,9,10,11,12,13,14,12,
13,14,15,16,17,18,19,20,18,19,20,21,22,23,21,22,23]);
ALF("6.A7","6.A7.2",[1,2,3,4,3,2,5,6,6,7,8,9,10,11,12,12,11,13,13,14,15,
16,17,16,15,18,19,19,20,21,22,23,24,25,20,25,24,23,22,21],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables"
]);
ALF("6.A7","6.Suz",[1,2,3,4,5,6,13,14,15,28,29,28,29,42,43,44,42,43,44,51,
52,53,54,55,56,81,81,81,82,83,84,85,86,87,82,83,84,85,86,87],[
"fusion map is unique up to table autom.,\n",
"representative compatible with factors"
]);
MOT("6.A7.2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[30240,15120,15120,30240,144,72,144,144,36,36,24,24,24,60,30,30,60,72,36,42,
42,42,42,42,42,240,48,24,12,12,12,20,20,24,24],
[,[1,3,3,1,4,2,7,7,9,9,5,6,6,14,16,16,14,8,8,20,22,24,20,22,24,1,4,5,7,10,10,
14,14,18,18],[1,4,1,4,5,5,1,4,1,4,11,11,11,14,17,14,17,5,5,20,23,20,23,20,23,
26,27,28,26,27,27,33,32,28,28],,[1,2,3,4,5,6,7,8,9,10,11,12,13,1,2,3,4,18,19,
20,21,22,23,24,25,26,27,28,29,31,30,26,26,34,35],,[1,2,3,4,5,6,7,8,9,10,11,12,
13,14,15,16,17,18,19,1,2,3,4,3,2,26,27,28,29,31,30,33,32,35,34]],
0,
[(34,35),(32,33),(30,31),(30,31)(34,35),(21,25)(22,24),(12,13)(30,31),(12,13)
(21,25)(22,24)(30,31)(34,35),(12,13)],
["ConstructMGA","6.A7","2.A7.2",[[17,18],[19,20],[21,22],[23,24],[25,26],
[27,30],[28,29],[31,34],[32,33],[35,38],[36,37],[39,40]],()]);
ALF("6.A7.2","A7.2",[1,1,1,1,2,2,3,3,4,4,5,5,5,6,6,6,6,7,7,8,8,8,8,8,8,9,
10,11,12,13,13,14,14,15,15]);
ALF("6.A7.2","2.A7.2",[1,2,1,2,3,3,4,5,6,7,8,8,8,9,10,9,10,11,11,12,13,12,
13,12,13,14,15,16,17,18,19,20,21,22,23]);
ALF("6.A7.2","3.A7.2",[1,2,2,1,3,4,5,5,6,6,7,8,8,9,10,10,9,11,12,13,14,15,
13,14,15,16,17,18,19,20,20,21,21,22,22]);
ALN("6.A7.2",["6.S7"]);
MOT("Isoclinic(6.A7.2)",
[
"isoclinic group of the 6.A7.2 given in the ATLAS"
],
0,
0,
0,
[(34,35),(32,33),(30,31),(21,25)(22,24),(12,13)],
["ConstructIsoclinic",[["6.A7.2"]]]);
ALF("Isoclinic(6.A7.2)","A7.2",[1,1,1,1,2,2,3,3,4,4,5,5,5,6,6,6,6,7,7,8,8,
8,8,8,8,9,10,11,12,13,13,14,14,15,15]);
ALF("Isoclinic(6.A7.2)","3.A7.2",[1,2,2,1,3,4,5,5,6,6,7,8,8,9,10,10,9,11,
12,13,14,15,13,14,15,16,17,18,19,20,20,21,21,22,22]);
MOT("A10",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[1814400,2880,384,7560,216,81,96,96,32,300,25,72,72,12,21,8,9,9,20,12,12,15,
21,21],
[,[1,1,1,4,5,6,2,2,3,10,11,4,5,5,15,9,17,18,10,12,13,22,24,23],[1,2,3,1,1,1,7,
8,9,10,11,2,2,3,15,16,6,6,19,8,7,10,15,15],,[1,2,3,4,5,6,7,8,9,1,1,12,13,14,
15,16,17,18,2,20,21,4,23,24],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,1,16,17,18,19,
20,21,22,4,4]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[9,5,1,6,3,0,-1,3,1,4,-1,2,
-1,1,2,-1,0,0,0,0,-1,1,-1,-1],[35,11,3,14,2,-1,3,3,-1,5,0,2,2,0,0,1,-1,-1,1,0,
0,-1,0,0],[36,8,-4,15,3,0,-2,2,0,6,1,-1,-1,-1,1,0,0,0,-2,-1,1,0,1,1],[42,6,2,
0,3,-3,-4,0,2,-3,2,0,3,-1,0,0,0,0,1,0,-1,0,0,0],[75,15,3,15,0,3,-3,1,-1,0,0,3,
0,0,-2,-1,0,0,0,1,0,0,1,1],[84,0,-4,21,3,3,2,-2,0,4,-1,-3,3,-1,0,0,0,0,0,1,-1,
1,0,0],[90,14,2,6,3,0,4,0,2,-5,0,2,-1,-1,-1,0,0,0,-1,0,1,1,-1,-1],[126,-14,6,
21,6,0,0,-4,-2,1,1,1,-2,0,0,0,0,0,1,-1,0,1,0,0],[160,16,0,34,-2,-2,0,0,0,5,0,
-2,-2,0,-1,0,1,1,1,0,0,-1,-1,-1],[210,6,-6,-21,0,3,0,-4,2,5,0,3,0,0,0,0,0,0,1,
-1,0,-1,0,0],[224,-16,0,14,2,-1,0,0,0,-1,-1,2,2,0,0,0,2,-1,-1,0,0,-1,0,0],[
224,-16,0,14,2,-1,0,0,0,-1,-1,2,2,0,0,0,-1,2,-1,0,0,-1,0,0],[225,5,9,15,-6,0,
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ARC("A10","CAS",[rec(name:="a10",
permchars:=(20,21),
permclasses:=(7,8),
text:=[
" names:= a10\n",
" order: 2^7.3^4.5^2.7 = 1814400\n",
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" comments: alternating group\n",
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""])]);
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ARC("A10","isSimple",true);
ARC("A10","extInfo",["2","2"]);
ARC("A10","tomfusion",rec(name:="A10",map:=[1,2,3,4,5,6,15,14,16,17,18,25,26,
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text:=[
"fusion map is unique up to table autom."
]));
ALF("A10","A10.2",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,17,18,19,20,
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ALF("A10","A11",[1,2,3,4,5,6,9,7,8,10,11,13,14,15,17,18,19,19,20,24,25,27,
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"fusion map is unique up to table autom."
]);
ALF("A10","O9(3)",[1,3,5,7,13,15,20,19,23,24,25,37,54,65,68,73,87,88,92,
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]);
MOT("A10.2",
[
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],
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[]);
ARC("A10.2","CAS",[rec(name:="s10",
permchars:=(23,35,34,33,32,31,30,29,28,27,26,25,24)(36,42,41,40,39,38,37),
permclasses:=(7,8),
text:=[
" names:= s10\n",
" order: 2^8.3^4.5^2.7 = 3628800\n",
" number of classes: 42\n",
" source: cambridge atlas\n",
" comments: symmetric group\n",
" test: orth, min, sym[3]\n",
""])]);
ARC("A10.2","ClassParameters",[[1,[1,1,1,1,1,1,1,1,1,1]],[1,[2,2,1,1,1,1,1,1]
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ARC("A10.2","CharacterParameters",[[1,[10]],[1,[1,1,1,1,1,1,1,1,1,1]],[1,[9,1]
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ARC("A10.2","maxes",["A10","A9.2","S8x2","S7xS3","s5wrs2","S6xS4","s2wrs5",
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ARC("A10.2","tomfusion",rec(name:="S10",map:=[1,3,6,7,8,9,30,31,32,35,36,53,
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157,211,212,221,406,533],text:=[
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]));
ALF("A10.2","A11.2",[1,2,3,4,5,6,9,7,8,10,11,13,14,15,17,18,19,20,23,24,
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"fusion map is unique"
]);
ALF("A10.2","A12",[1,2,4,5,6,8,11,9,10,13,14,15,17,19,22,23,25,28,32,35,
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]);
ALF("A10.2","Fi22",[1,3,4,5,7,8,10,13,12,14,14,18,23,24,26,30,33,35,46,47,
52,60,2,3,4,10,13,12,15,22,20,19,23,25,30,34,35,41,47,51,59,65],[
"fusion map is unique"
]);
ALF("A10.2","S8(2)",[1,4,7,8,10,11,17,19,23,24,25,28,37,41,42,48,50,53,62,
65,69,77,2,5,6,13,20,23,26,39,32,33,38,40,48,51,54,57,61,68,76,80],[
"fusion map is unique"
]);
ALN("A10.2",["S10"]);
MOT("A11",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11]"
],
[19958400,20160,1152,60480,1080,162,480,96,96,1800,25,576,288,72,36,18,84,8,9,
40,11,11,48,24,12,28,45,45,20,21,21],
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[(30,31),(21,22)]);
ARC("A11","CAS",[rec(name:="a11",
permchars:=(18,19),
permclasses:=(),
text:=[
" names:= a11\n",
" order: 2^7.3^4.5^2.7.11 = 19958400\n",
" number of classes: 31\n",
" source: cambridge atlas\n",
" comments: alternating group\n",
" test: orth, min, sym[3]\n",
""])]);
ARC("A11","CharacterParameters",[[1,[1,1,1,1,1,1,1,1,1,1,1]],[1,[2,1,1,1,1,1,
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],[1,[4,1,1,1,1,1,1,1]],[1,[[6,1,1,1,1,1],'+']],[1,[[6,1,1,1,1,1],'-']],[1,[2,
2,2,2,2,1]],[1,[2,2,2,2,1,1,1]],[1,[5,1,1,1,1,1,1]],[1,[3,2,1,1,1,1,1,1]],[1,
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1,1,1,1]],[1,[[4,3,3,1],'+']],[1,[[4,3,3,1],'-']],[1,[3,3,3,1,1]],[1,[3,2,2,2,
1,1]],[1,[4,4,1,1,1]],[1,[5,2,1,1,1,1]],[1,[3,3,2,1,1,1]],[1,[3,3,2,2,1]],[1,
[4,3,1,1,1,1]],[1,[4,2,2,2,1]],[1,[4,2,2,1,1,1]],[1,[4,3,2,2]],[1,[5,2,2,1,1]
],[1,[4,3,2,1,1]]]);
ARC("A11","ClassParameters",[[1,[1,1,1,1,1,1,1,1,1,1,1]],[1,[2,2,1,1,1,1,1,1,
1]],[1,[2,2,2,2,1,1,1]],[1,[3,1,1,1,1,1,1,1,1]],[1,[3,3,1,1,1,1,1]],[1,[3,3,3,
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],[1,[6,3,2]],[1,[7,1,1,1,1]],[1,[8,2,1]],[1,[9,1,1]],[1,[5,2,2,1,1]],[1,[[
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ARC("A11","projectives",["2.A11",[[16,0,0,-8,4,-2,0,0,0,-4,1,0,0,0,0,0,2,0,1,
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ARC("A11","maxes",["A10","A9.2","(A8x3).2","(A7xA4):2","(A6xA5):2","M11",
"M11"]);
ARC("A11","isSimple",true);
ARC("A11","extInfo",["2","2"]);
ARC("A11","tomfusion",rec(name:="A11",map:=[1,2,3,4,5,6,14,15,16,17,18,26,27,
28,29,30,31,53,58,62,63,63,94,95,96,97,99,100,155,159,159],text:=[
"fusion map is unique"
]));
ALF("A11","A11.2",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,
21,22,23,24,25,26,27,28,29,29]);
ALF("A11","A12",[1,2,4,5,6,8,9,10,11,13,14,16,15,17,19,21,22,23,25,28,30,
31,34,32,35,36,37,38,39,40,40],[
"fusion map is unique up to table autom."
]);
MOT("A11.2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11],\n",
"constructions: Aut(A11)"
],
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ARC("A11.2","CAS",[rec(name:="s11",
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text:=[
" names:= s11\n",
" order: 2^8.3^4.5^2.7.11 = 39916800\n",
" number of classes: 56\n",
" source: cambridge atlas\n",
" comments: symmetric group\n",
" test: orth, min, sym[3]\n",
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ARC("A12","CAS",[rec(name:="a12",
permchars:=(12,13),
permclasses:=(17,18,19),
text:=[
" names:= a11\n",
" order: 2^7.3^4.5^2.7.11 = 19958400\n",
" number of classes: 31\n",
" source: cambridge atlas\n",
" comments: alternating group\n",
" test: orth, min, sym[3]\n",
""])]);
ARC("A12","CharacterParameters",[[1,[1,1,1,1,1,1,1,1,1,1,1,1]],[1,[2,1,1,1,1,
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ARC("A12","ClassParameters",[[1,[1,1,1,1,1,1,1,1,1,1,1,1]],[1,[2,2,1,1,1,1,1,
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ARC("A12","maxes",["A11","A10.2","(A9x3):2","(A6xA6):2^2","(A8xA4):2",
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ARC("A12","isSimple",true);
ARC("A12","extInfo",["2","2"]);
ARC("A12","tomfusion",rec(name:="A12",map:=[1,2,3,4,5,6,7,8,22,23,24,25,26,27,
38,39,40,41,42,43,44,45,114,113,125,126,126,131,132,133,133,183,182,184,185,
187,188,189,387,391,530,717,717],text:=[
"fusion map is unique"
]));
ALF("A12","A12.2",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,
22,23,24,25,26,26,27,28,29,29,30,31,32,33,34,35,36,37,38,39,40,40]);
ALF("A12","HN",[1,2,2,3,4,4,4,5,7,6,7,6,9,13,14,15,14,14,15,14,16,17,19,
19,20,20,20,22,26,29,29,30,30,31,30,33,34,34,41,44,48,51,52],[
"fusion map is unique up to table automorphisms"
]);
ALF("A12","A13",[1,2,4,3,5,6,8,7,9,10,11,12,13,14,15,16,19,20,17,22,21,23,
24,25,26,27,28,30,31,32,32,33,36,35,37,41,42,43,47,48,52,55,54],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables"
]);
ALF("A12","O10-(2)",[1,3,4,5,6,9,10,11,15,19,18,19,21,22,27,33,40,37,44,
41,45,46,51,51,56,54,55,58,59,60,61,69,78,77,83,84,85,88,100,101,106,114,
115],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables"
]);
ALN("A12",["O10-(2)M7"]);
MOT("A12.2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11],\n",
"constructions: Aut(A12)"
],
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text:=[
" names:= s12\n",
" order: 2^10.3^5.5^2.7.11 = 479001600\n",
" number of classes: 77\n",
" source: cambridge atlas\n",
" comments: symmetric group\n",
" test: orth, min, sym[3]\n",
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ARC("A12.2","tomfusion",rec(name:="S12",map:=[1,3,4,6,8,9,10,11,45,47,49,51,
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ALF("A12.2","A13.2",[1,2,4,3,5,6,8,7,9,10,11,12,13,14,15,16,19,20,17,22,
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ALF("A12.2","A14",[1,2,4,3,5,6,8,7,9,10,12,14,15,16,17,19,21,23,18,26,24,
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ALF("A12.2","Fi23",[1,3,3,4,5,7,7,8,11,10,11,10,13,13,16,22,24,24,25,24,
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ALF("A12.2","HN.2",[1,2,2,3,4,4,4,5,7,6,7,6,9,12,13,14,13,13,14,13,15,16,
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"fusion map is unique"
]);
ALN("A12.2",["A14M2","S12"]);
MOT("A13",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11,13]"
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ARC("A13","maxes",["A12","A11.2","(A10x3):2","(A9xA4):2","(A8xA5):2",
"(A7xA6):2","L3(3)","L3(3)","13:6"]);
ALF("A13","A13.2",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,
22,23,24,25,26,27,27,28,29,30,31,32,33,34,35,36,37,38,38,39,40,41,42,43,
44,45,46,47,48,49,50,51,52,52]);
ALF("A13","A14",[1,2,3,4,5,6,7,8,9,10,12,14,15,16,17,19,18,22,21,23,24,26,
27,29,31,32,33,33,35,34,37,38,39,42,41,44,40,46,48,49,50,51,53,54,55,57,
56,59,60,61,63,64,65,68,68],[
"fusion map is unique up to table automorphisms"
]);
ALN("A13",["A14M1"]);
MOT("A13.2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11,13],\n",
"constructions: Aut(A13)"
],
[6227020800,2903040,46080,46080,10886400,90720,3888,1944,40320,3840,1152,256,
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22,576,576,192,144,144,72,13,112,1800,180,150,72,160,80,126,126,48,56,120,60,
35,79833600,241920,23040,1451520,3840,1536,384,384,241920,30240,11520,4320,
3456,864,648,432,288,144,108,960,64,7200,480,100,60,8640,648,432,192,192,48,
12,336,336,36,480,160,22,48,56,180,180,60,30,36,40,42,42,60],
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4,5,6,5,6,5,6,7,7,6,7,8,10,10,13,13,14,14,15,18,19,15,16,19,22,23,23,26,29,29,
31,34,39,40,41,41,42,43,44,46,47,50],[1,2,3,4,1,1,1,1,9,10,11,12,13,14,2,3,3,
2,2,4,3,4,23,24,25,7,7,28,29,30,31,9,11,10,9,11,11,38,39,13,13,14,18,44,45,23,
23,24,49,29,28,52,53,54,55,56,57,58,59,60,53,54,55,53,54,54,53,54,55,55,54,72,
73,74,75,76,77,56,56,56,57,59,58,60,85,86,67,88,89,90,72,92,74,74,75,77,79,98,
85,86,88],,[1,2,3,4,5,6,7,8,9,10,11,12,1,1,15,16,17,18,19,20,21,22,23,24,25,
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54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,53,54,53,55,78,79,
80,81,82,83,84,85,86,87,56,57,90,91,92,61,64,62,63,97,72,99,100,78],,[1,2,3,4,
5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,1,24,25,26,27,28,29,30,31,32,
33,34,35,36,37,38,2,40,41,42,43,44,45,5,6,48,9,50,51,13,53,54,55,56,57,58,59,
60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,53,
54,87,88,89,90,91,56,93,94,95,96,97,98,61,62,101],,,,[1,2,3,4,5,6,7,8,9,10,11,
12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,1,32,33,34,35,36,37,
38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,
64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,
53,91,92,93,94,95,96,97,98,99,100,101],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,
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68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,
94,95,96,97,98,99,100,101]],
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62,61,60,59)(75,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77),
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text:=[
" names:= s13\n",
" order: 2^10.3^5.5^2.7.11.13 = 6227020800\n",
" number of classes: 101\n",
" source: cambridge atlas\n",
" comments: symmetric group\n",
" test: orth, min, sym[3]\n",
""])]);
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ALN("A13.2",["S13","A14.2M2"]);
MOT("A14",
[
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" names:= a14\n",
" order: 2^10.3^5.5^2.7^2.11.13 = 43589145600\n",
" number of classes: 72\n",
" source: stockhofe [aachen] from table of s14 (kerber,bayreuth)\n",
" comments: alternating group\n",
" test: orth, min\n",
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0,
0,
0,
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ALN("A14",["A14.2M1"]);
MOT("A5",
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[60,4,3,5,5],
[,[1,1,3,5,4],[1,2,1,5,4],,[1,2,3,1,1]],
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ARC("A5","CAS",[rec(name:="a5",
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permclasses:=(),
text:=[
" names: a5; psl(2,4),psu(2,4),psp(2,4),o(3,4),\n",
" a1(4), 2a1(4), c1(4), b1(4), (lie-not.)\n",
" psl(2,5),psu(2,5),psp(2,5),o(3,5),\n",
" a1(5), 2a1(5), c1(5), b1(5) (lie-not.)\n",
" order: 2^2.3.5 = 60\n",
" number of classes: 5\n",
" source: generated by dixon-algorithm aachen (1982)\n",
" comments: alternating group, catalogue nr.60.13\n",
" test: orth, min, sym(3)\n",
"maximal subgroup of sporadic Janko group j2\n",
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""])]);
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ARC("A5","tomfusion",rec(name:="A5",map:=[1,2,3,5,5],text:=[
"fusion map is unique"
]));
ALF("A5","A5.2",[1,2,3,4,4]);
ALF("A5","A6",[1,2,3,6,7],[
"fusion map is unique up to table automorphisms"
],"tom:21");
ALF("A5","L2(11)",[1,2,3,4,5],[
"fusion map is unique up to table automorphisms"
]);
ALF("A5","L2(16)",[1,2,3,4,5],[
"fusion map is unique up to table autom."
]);
ALF("A5","L2(19)",[1,2,3,4,5],[
"fusion map is unique up to table autom."
]);
ALF("A5","L2(29)",[1,2,3,4,5],[
"fusion map is unique up to table autom."
]);
ALF("A5","L2(31)",[1,2,3,5,6],[
"fusion map is unique up to table autom."
]);
ALF("A5","L2(109)",[1,30,21,41,52],[
"fusion map is unique up to table autom."
]);
ALF("A5","L2(125)",[1,34,55,2,3],[
"fusion map is unique up to table autom."
]);
ALF("A5","2^4:A5",[1,3,7,8,9],[
"fusion map is unique up to table autom."
]);
ALF("A5","J2",[1,3,5,9,10],[
"the maximal A5 in J2 contains elements of 2B and 3B (see ATLAS);\n",
"together with that, the fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("A5","S6(3)",[1,3,10,14,14],[
"fusion map is unique (use structure constants)"
]);
ALF("A5","P1/G1/L1/V1/ext2",[1,4,7,11,12],[
"fusion map is unique up to table autom."
]);
ALN("A5",["L2(4)","L2(5)","A1(4)","A1(5)","U2(4)","U2(5)","S2(4)","S2(5)",
"O3(4)","O3(5)","O4-(2)"]);
MOT("A6M2",
[
"2nd maximal subgroup of A6,\n",
"differs from A6M1 only by fusion map"
],
0,
0,
0,
0,
["ConstructPermuted",["A5"]]);
ALF("A6M2","A6",[1,2,4,7,6],[
"fusion A5 -> A6 mapped under A6.2_3"
]);
MOT("A5.2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5],\n",
"constructions: Aut(A5)"
],
[120,8,6,5,12,4,6],
[,[1,1,3,4,1,2,3],[1,2,1,4,5,6,5],,[1,2,3,1,5,6,7]],
[[1,1,1,1,1,1,1],[1,1,1,1,-1,-1,-1],[6,-2,0,1,0,0,0],[4,0,1,-1,2,0,-1],
[TENSOR,[4,2]],[5,1,-1,0,1,-1,1],
[TENSOR,[6,2]]],
[]);
ARC("A5.2","CAS",[rec(name:="s5",
permchars:=(3,7,6,5,4),
permclasses:=(),
text:=[
"names: s5; o-[2,4],\n",
"2d2[2] [lie-not.]\n",
"order: 2^3.3.5 = 120\n",
"number of classes: 7\n",
"source: generated by dixon-algorithm aachen [1982]\n",
"comments: symmetric group\n",
"test: orth, min, sym[3]\n",
""])]);
ARC("A5.2","projectives",["2.A5.2",[[4,0,-2,-1,0,0,0],[4,0,1,-1,0,0,
E(3)-E(3)^2],[6,0,0,1,0,E(8)+E(8)^3,0]],]);
ARC("A5.2","ClassParameters",[[1,[1,1,1,1,1]],[1,[2,2,1]],[1,[3,1,1]],[1,[5]],
[1,[2,1,1,1]],[1,[4,1]],[1,[3,2]]]);
ARC("A5.2","CharacterParameters",[[1,[5]],[1,[1,1,1,1,1]],[1,[3,1,1]],[1,[4,1]
],[1,[2,1,1,1]],[1,[3,2]],[1,[2,2,1]]]);
ARC("A5.2","tomfusion",rec(name:="S5",map:=[1,3,4,8,2,6,11],text:=[
"fusion map is unique"
]));
ARC("A5.2","maxes",["A5","s4","5:4","S3x2"]);
ALF("A5.2","A6.2_1",[1,2,3,6,7,9,10],[
"fusion map is unique up to table automorphisms"
],"tom:54");
ALF("A5.2","A7",[1,2,3,6,2,5,7],[
"fusion map is unique"
]);
ALF("A5.2","L2(25)",[1,2,3,5,2,4,7],[
"fusion map is unique up to table autom."
],"tom:34");
ALF("A5.2","L3(4).2_1",[1,2,3,7,9,10,11],[
"fusion map is unique"
]);
ALF("A5.2","L3(5)",[1,2,3,8,2,6,9],[
"fusion map is unique"
]);
ALF("A5.2","M11",[1,2,3,5,2,4,6],[
"fusion map is unique, equal to that on the CAS table"
]);
ALF("A5.2","Th",[1,2,4,8,2,7,11],[
"fusion map is unique (use structure constants)"
]);
ALF("A5.2","M12.2",[1,2,5,7,13,15,16],[
"determined as the unique fusion of the maximal subgroup (novelty),\n",
"contains 2A and 3B elements"
]);
ALF("A5.2","J2.2",[1,3,5,8,17,19,20],[
"fusion of maximal subgroup S5, determined as the unique one with 2B image"
]);
ALF("A5.2","mo62",[1,4,7,10,11,17,15],[
"fusion map is unique"
]);
ALF("A5.2","2^4:s5",[1,3,6,7,8,10,12],[
"fusion map is unique"
]);
ALF("A5.2","3^4:S5",[1,8,14,20,21,31,34],[
"fusion map is unique"
]);
ALN("A5.2",["S5"]);
MOT("A6.2_1M3",
[
"3rd maximal subgroup of A6.2_1,\n",
"differs from A6.2_1M2 only by fusion map"
],
0,
0,
0,
0,
["ConstructPermuted",["A5.2"]]);
ALF("A6.2_1M3","A6.2_1",[1,2,4,6,8,9,11],[
"fusion A5.2 -> A6.2_1 mapped under A6.2^2"
]);
MOT("A6",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5]"
],
[360,8,9,9,4,5,5],
[,[1,1,3,4,2,7,6],[1,2,1,1,5,7,6],,[1,2,3,4,5,1,1]],
[[1,1,1,1,1,1,1],[5,1,2,-1,-1,0,0],[5,1,-1,2,-1,0,0],[8,0,-1,-1,0,
-E(5)-E(5)^4,-E(5)^2-E(5)^3],
[GALOIS,[4,2]],[9,1,0,0,1,-1,-1],[10,-2,1,1,0,0,0]],
[(6,7),(3,4)]);
ARC("A6","CAS",[rec(name:="a6",
permchars:=(4,5),
permclasses:=(),
text:=[
" names:= a6; psl[2,9],psu[2,9],psp[2,9],o[3,9],o-[4,3],\n",
" a1[9], 2a1[9], c1[9], b1[9], 2d2[3], [lie-not.]\n",
" psp[4,2]',o[5,2]',\n",
" c2[2]', b2[2]' [lie-not.]\n",
" order: 2^3.3^2.5 = 360\n",
" number of classes: 7\n",
" source: cambridge atlas\n",
" comments: alternating group\n",
" test: orth, min, sym[3]\n",
""])]);
ARC("A6","CharacterParameters",[[1,[1,1,1,1,1,1]],[1,[2,1,1,1,1]],[1,[2,2,2]],
[1,[[3,2,1],'+']],[1,[[3,2,1],'-']],[1,[2,2,1,1]],[1,[3,1,1,1]]]);
ARC("A6","ClassParameters",[[1,[1,1,1,1,1,1]],[1,[2,2,1,1]],[1,[3,3]],
[1,[3,1,1,1]],[1,[4,2]],[1,[[5,1],'+']],[1,[[5,1],'-']]]);
ARC("A6","projectives",["2.A6",[[4,0,-2,1,0,-1,-1],[4,0,1,-2,0,-1,-1],[8,0,-1,
-1,0,-E(5)-E(5)^4,-E(5)^2-E(5)^3],
[GALOIS,[3,2]],[10,0,1,1,E(8)-E(8)^3,0,0],
[GALOIS,[5,3]]],"3.A6",[[3,-1,0,0,1,-E(5)-E(5)^4,-E(5)^2-E(5)^3],
[GALOIS,[1,2]],[6,2,0,0,0,1,1],[9,1,0,0,1,-1,-1],[15,-1,0,0,-1,0,0]],"6.A6",[[
6,0,0,0,E(8)-E(8)^3,1,1],
[GALOIS,[1,3]],[12,0,0,0,0,E(5)+E(5)^4,E(5)^2+E(5)^3],
[GALOIS,[3,2]]],]);
ARC("A6","maxes",["A5","A6M2","3^2:4","s4","A6M5"]);
ARC("A6","isSimple",true);
ARC("A6","extInfo",["6","2^2"]);
ARC("A6","tomfusion",rec(name:="A6",map:=[1,2,4,3,6,5,5],text:=[
"fusion map is unique up to table autom.,\n",
"compatible with class parameters"
]));
ALF("A6","A6.2_1",[1,2,3,4,5,6,6]);
ALF("A6","A6.2_2",[1,2,3,3,4,5,6]);
ALF("A6","A6.2_3",[1,2,3,3,4,5,5]);
ALF("A6","A7",[1,2,4,3,5,6,6],[
"fusion map is unique up to table autom.,\n",
"unique map that is compatible with 2^4:a6 -> 2^4:a7"
]);
ALF("A6","L3(4)",[1,2,3,3,4,7,8],[
"fusion map is unique up to table autom."
],"tom:92");
ALF("A6","S4(5)",[1,3,4,5,7,12,13],[
"fusion map is unique up to table autom."
]);
ALF("A6","U3(11)",[1,2,3,3,6,7,8],[
"fusion map is unique up to table autom."
]);
ALF("A6","2^4:a6",[1,3,6,8,9,11,12],[
"fusion map is unique up to table autom."
],"tom:132");
ALF("A6","3^4:A6",[1,5,9,10,19,20,21],[
"fusion map is unique up to table automorphisms"
]);
ALN("A6",["L2(9)","S4(2)'","A1(9)","U2(9)","S2(9)","O3(9)","O4-(3)",
"C2(2)'","O5(2)'"]);
MOT("A6.2^2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5],\n",
"constructions: Aut(A6), PGammaL(2,9)"
],
[1440,32,18,16,10,48,16,6,40,8,10,8,8],
[,[1,1,3,2,5,1,2,3,1,4,5,2,4],[1,2,1,4,5,6,7,6,9,10,11,12,13],,[1,2,3,4,1,6,7,
8,9,10,9,12,13]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1],[1,1,1,1,1,-1,
-1,-1,1,1,1,-1,-1],
[TENSOR,[2,3]],[10,2,1,-2,0,2,2,-1,0,0,0,0,0],
[TENSOR,[5,3]],[16,0,-2,0,1,0,0,0,4,0,-1,0,0],
[TENSOR,[7,2]],[9,1,0,1,-1,3,-1,0,-1,1,-1,1,-1],
[TENSOR,[9,2]],
[TENSOR,[9,3]],
[TENSOR,[9,4]],[20,-4,2,0,0,0,0,0,0,0,0,0,0]],
[]);
ARC("A6.2^2","CAS",[rec(name:="m10.2",
permchars:=( 2, 3, 4)( 5, 9)( 6,10, 7,11, 8,12),
permclasses:=( 6, 8,11,13, 7,10,12),
text:=[
"names: m10.2, s6.2\n",
"order: 2^5.3^2.5 = 1,440\n",
"number of classes: 13\n",
"source/origin: pahlings,h. [1984]\n",
"comments: m10.2 is maximal subgroup of m12\n",
"test: orth.1, min, sym(3) '\n",
"maximal subgroup of sporadic simple Rudvalis group Ru,\n",
"test: Restricted characters from ru decompose properly.\n",
""])]);
ARC("A6.2^2","tomfusion",rec(name:="A6.2^2",map:=[1,4,5,8,13,2,9,16,3,20,29,
12,19],text:=[
"fusion map is unique"
]));
ALF("A6.2^2","A10.2",[1,3,6,9,11,25,28,34,24,35,37,9,16],[
"fusion map is unique"
]);
ALF("A6.2^2","L3(4).2^2",[1,2,3,4,6,13,14,15,18,20,22,9,11],[
"fusion map is unique"
]);
ALF("A6.2^2","M12",[1,3,4,7,8,3,6,10,2,12,13,7,12],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
],"tom:144");
ALF("A6.2^2","M22.2",[1,2,3,4,6,12,15,16,13,17,18,5,10],[
"uniquely determined by the fact that M10 lies inside M22"
]);
ALF("A6.2^2","Ru",[1,2,4,8,10,2,8,11,3,15,17,8,15],[
"fusion determined by the facts that the maximal A6.2^2 contains 5B\n",
"elements and no 4A-C elements (checked using structure constants),\n",
"the map is equal to that on the CAS table"
]);
ALF("A6.2^2","U3(5).2",[1,2,3,4,6,12,13,14,12,15,16,4,10],[
"fusion map is unique"
]);
ALF("A6.2^2","U4(3).2_1",[1,2,6,7,9,19,22,26,20,27,28,8,15],[
"fusion map is unique"
]);
ALF("A6.2^2","U4(3).2_3",[1,2,5,6,8,16,17,18,16,19,22,7,12],[
"determined as extension from A6.2_3 < U4(3)"
]);
ALF("A6.2^2","2F4(2)'",[1,3,4,7,8,3,5,9,2,12,14,7,13],[
"fusion map is unique up to table automorphisms"
],"tom:421");
ALN("A6.2^2",["A6.V4","S6.2","m10.2"]);
MOT("U4(3).2_3M10",
0,
0,
0,
0,
0,
["ConstructPermuted",["A6.2^2"]]);
ALF("U4(3).2_3M10","U4(3).2_3",[1,2,4,7,8,2,7,10,16,21,22,17,21],[
"determined as novelty extending S6 < U4(2) < U4(3)"
]);
MOT("A6.2_1",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5]"
],
[720,16,18,18,8,5,48,48,8,6,6],
[,[1,1,3,4,2,6,1,1,2,3,4],[1,2,1,1,5,6,7,8,9,7,8],,[1,2,3,4,5,1,7,8,9,10,11]],
[[1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,-1,-1,-1,-1,-1],[5,1,2,-1,-1,0,3,-1,1,0,
-1],
[TENSOR,[3,2]],[5,1,-1,2,-1,0,-1,3,1,-1,0],
[TENSOR,[5,2]],[16,0,-2,-2,0,1,0,0,0,0,0],[9,1,0,0,1,-1,3,3,-1,0,0],
[TENSOR,[8,2]],[10,-2,1,1,0,0,2,-2,0,-1,1],
[TENSOR,[10,2]]],
[( 3, 4)( 7, 8)(10,11)]);
ARC("A6.2_1","CAS",[rec(name:="s6",
permchars:=( 5, 6)( 7,11,10, 9, 8),
permclasses:=(),
text:=[
" names:= s6\n",
" order: 2^4.3^2.5 = 720\n",
" number of classes: 11\n",
" source: cambridge atlas\n",
" comments: symmetric group\n",
" test: orth, min, sym[3]\n",
""])]);
ARC("A6.2_1","ClassParameters",[[1,[1,1,1,1,1,1]],[1,[2,2,1,1]],[1,[3,3]],[1,
[3,1,1,1]],[1,[4,2]],[1,[5,1]],[1,[2,2,2]],[1,[2,1,1,1,1]],[1,[4,1,1]],
[1,[6]],[1,[3,2,1]]]);
ARC("A6.2_1","CharacterParameters",[[1,[6]],[1,[1,1,1,1,1,1]],[1,[2,2,2]],[1,
[3,3]],[1,[5,1]],[1,[2,1,1,1,1]],[1,[3,2,1]],[1,[4,2]],[1,[2,2,1,1]],[1,[3,1,
1,1]],[1,[4,1,1]]]);
ARC("A6.2_1","projectives",["2.A6.2_1",[[4,0,-2,1,0,-1,0,0,0,0,
-E(12)^7+E(12)^11],[4,0,1,-2,0,-1,0,0,0,E(3)-E(3)^2,0],[16,0,-2,-2,0,1,0,0,0,
0,0],[20,0,2,2,0,0,0,0,0,0,0]],]);
ARC("A6.2_1","tomfusion",rec(name:="S6",map:=[1,4,6,5,9,14,3,2,11,17,20],
text:=[
"fusion map is unique up to table autom.,\n",
"compatible with class parameters"
],
perm:=(5,6)));
ARC("A6.2_1","maxes",["A6","A5.2","A6.2_1M3","s3wrs2","2xSymm(4)","s2wrs3"]);
ALF("A6.2_1","A6.2^2",[1,2,3,3,4,5,6,6,7,8,8]);
ALF("A6.2_1","A7.2",[1,2,4,3,5,6,10,9,11,13,12],[
"fusion map is unique up to table automorphisms"
]);
ALF("A6.2_1","A8",[1,3,5,4,7,8,2,3,7,10,9],[
"fusion map is unique up to table autom."
]);
ALF("A6.2_1","L3(4).2_2",[1,2,3,3,4,6,9,9,10,11,11],[
"fusion map is unique"
]);
ALF("A6.2_1","S4(4)",[1,4,5,6,8,13,2,3,8,14,15],[
"fusion map is unique up to table autom."
]);
ALF("A6.2_1","U4(2)",[1,3,7,6,9,10,2,3,9,15,16],[
"fusion map is unique up to table autom."
]);
ALN("A6.2_1",["S6","S4(2)","O5(2)"]);
MOT("A6.2_2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5],\n",
"constructions: PGL(2,9), PGU(2,9)"
],
[720,16,9,8,10,10,20,8,8,10,10],
[,[1,1,3,2,6,5,1,4,4,6,5],[1,2,1,4,6,5,7,9,8,11,10],,[1,2,3,4,1,1,7,9,8,7,7]],
[[1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,-1,-1,-1,-1,-1],[10,2,1,-2,0,0,0,0,0,0,
0],[8,0,-1,0,-E(5)-E(5)^4,-E(5)^2-E(5)^3,2,0,0,E(5)+E(5)^4,E(5)^2+E(5)^3],
[TENSOR,[4,2]],
[GALOIS,[4,2]],
[TENSOR,[6,2]],[9,1,0,1,-1,-1,-1,1,1,-1,-1],
[TENSOR,[8,2]],[10,-2,1,0,0,0,0,E(8)-E(8)^3,-E(8)+E(8)^3,0,0],
[TENSOR,[10,2]]],
[(8,9),( 5, 6)(10,11)]);
ARC("A6.2_2","CAS",[rec(name:="pgl(2,9)",
permchars:=(3,9,8,7,4,5,6),
permclasses:=(10,11),
text:=[
" names:= pgl[2,9]\n",
" order: 2^4.3^2.5 = 720\n",
" number of classes: 11\n",
" source: cambridge atlas\n",
" comments: projective linear group\n",
" test: orth, min, sym[3]\n",
""])]);
ARC("A6.2_2","projectives",["2.A6.2_2",[[8,0,-1,0,-2,-2,0,0,0,0,0],[8,0,-1,0,
-E(5)-E(5)^4,-E(5)^2-E(5)^3,0,0,0,E(20)-E(20)^9,-E(20)^13+E(20)^17],
[GALOIS,[2,7]],[10,0,1,E(8)-E(8)^3,0,0,0,E(16)-E(16)^7,-E(16)^3+E(16)^5,0,0],
[GALOIS,[4,3]]],]);
ARC("A6.2_2","tomfusion",rec(name:="A6.2_2",map:=[1,3,4,6,8,8,2,12,12,15,
15],text:=[
"fusion map is unique"
]));
ALF("A6.2_2","A6.2^2",[1,2,3,4,5,5,9,10,10,11,11]);
ALF("A6.2_2","L3(4).2_3",[1,2,3,4,6,7,9,11,11,13,14],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables"
]);
ALF("A6.2_2","L3(9)",[1,2,4,7,8,9,2,19,20,23,24],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables"
]);
ALF("A6.2_2","L4(3)",[1,3,7,9,11,11,2,17,17,20,20],[
"fusion map is unique"
]);
ALF("A6.2_2","U3(9)",[1,2,4,5,10,11,2,14,13,19,20],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables"
]);
ALF("A6.2_2","ON.2",[1,2,3,5,6,6,26,30,30,31,32],[
"fusion determined using that the A6 type subgroup contains 4B elements\n",
"of ON (which follows from the fusion of the A7 type subgroups of ON)"
]);
ALN("A6.2_2",["pgl(2,9)"]);
MOT("A6.2_3",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5]"
],
[720,16,9,8,5,4,8,8],
[,[1,1,3,2,5,2,4,4],[1,2,1,4,5,6,7,8],,[1,2,3,4,1,6,8,7]],
[[1,1,1,1,1,1,1,1],[1,1,1,1,1,-1,-1,-1],[10,2,1,-2,0,0,0,0],[16,0,-2,0,1,0,0,
0],[9,1,0,1,-1,1,-1,-1],
[TENSOR,[5,2]],[10,-2,1,0,0,0,E(8)+E(8)^3,-E(8)-E(8)^3],
[TENSOR,[7,2]]],
[(7,8)]);
ARC("A6.2_3","CAS",[rec(name:="m10",
permchars:=(3,5)(4,8,7,6),
permclasses:=(),
text:=[
"names: m10\n",
"order: 2^4.3^2.5 = 720\n",
"number of classes: 8\n",
"source: cambridge atlas\n",
"comments: point stabilizer of mathieu-group m11\n",
"test: orth, min, sym[3]\n",
""])]);
ARC("A6.2_3","projectives",["3.A6.2_3",[[6,-2,0,2,1,0,0,0],[6,2,0,0,1,0,
E(8)+E(8)^3,-E(8)-E(8)^3],[9,1,0,1,-1,1,-1,-1],[15,-1,0,-1,0,1,1,
1]],"(2xA6).2_3",[[1,1,1,1,1,E(4),E(4),E(4)],[10,2,1,-2,0,0,0,0],[16,0,-2,0,1,
0,0,0],[9,1,0,1,-1,E(4),-E(4),-E(4)],[10,-2,1,0,0,0,-E(8)+E(8)^3,
E(8)-E(8)^3]],]);
ARC("A6.2_3","tomfusion",rec(name:="A6.2_3",map:=[1,2,3,5,7,6,9,9],text:=[
"fusion map is unique"
]));
ARC("A6.2_3","maxes",["A6","3^2:Q8","5:4","M11N2"]);
ALF("A6.2_3","A6.2^2",[1,2,3,4,5,12,13,13]);
ALF("A6.2_3","A10",[1,3,6,9,11,9,16,16],[
"fusion map is unique"
]);
ALF("A6.2_3","L3(4).2_1",[1,2,3,4,7,10,12,12],[
"fusion map is unique up to table autom."
],"tom:146");
ALF("A6.2_3","M11",[1,2,3,4,5,4,7,8],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("A6.2_3","M22",[1,2,3,4,6,5,10,10],[
"maximal A6.2_3 determined by permutation character (see ATLAS)"
]);
ALF("A6.2_3","Th",[1,2,4,7,8,7,14,14],[
"fusion map is unique (use structure constants)"
]);
ALF("A6.2_3","U3(5)",[1,2,3,4,6,4,12,13],[
"fusion map is unique up to table autom."
],"tom:75");
ALF("A6.2_3","U4(3)",[1,2,6,7,9,8,15,15],[
"fusion map is unique"
]);
ALF("A6.2_3","3^4:m10",[1,4,7,12,13,14,17,18],[
"fusion map is unique up to table automorphisms"
]);
ALN("A6.2_3",["M10"]);
MOT("A7",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[2520,24,36,9,4,5,12,7,7],
[,[1,1,3,4,2,6,3,8,9],[1,2,1,1,5,6,2,9,8],,[1,2,3,4,5,1,7,9,8],,[1,2,3,4,5,6,
7,1,1]],
[[1,1,1,1,1,1,1,1,1],[6,2,3,0,0,1,-1,-1,-1],[10,-2,1,1,0,0,1,
E(7)+E(7)^2+E(7)^4,E(7)^3+E(7)^5+E(7)^6],
[GALOIS,[3,3]],[14,2,2,-1,0,-1,2,0,0],[14,2,-1,2,0,-1,-1,0,0],[15,-1,3,0,-1,0,
-1,1,1],[21,1,-3,0,-1,1,1,0,0],[35,-1,-1,-1,1,0,-1,0,0]],
[(8,9)]);
ARC("A7","CAS",[rec(name:="a7",
permchars:=(),
permclasses:=(),
text:=[
"names: a7\n",
"order: 2^3.3^2.5.7 = 2520\n",
"number of classes: 9\n",
"source: cambridge atlas\n",
"comments: alternating group\n",
"test: orth, min, sym[3]\n",
""])]);
ARC("A7","CharacterParameters",[[1,[1,1,1,1,1,1,1]],[1,[2,1,1,1,1,1]],[1,[[4,
1,1,1],'+']],[1,[[4,1,1,1],'-']],[1,[2,2,1,1,1]],[1,[2,2,2,1]],[1,[3,1,1,1,1]
],[1,[3,2,2]],[1,[3,2,1,1]]]);
ARC("A7","ClassParameters",[[1,[1,1,1,1,1,1,1]],[1,[2,2,1,1,1]],[1,[3,1,1,1,
1]],[1,[3,3,1]],[1,[4,2,1]],[1,[5,1,1]],[1,[3,2,2]],[1,[[7],'+']],[1,[[7],'-']
]]);
ARC("A7","projectives",["2.A7",[[4,0,-2,1,0,-1,0,-E(7)-E(7)^2-E(7)^4,
-E(7)^3-E(7)^5-E(7)^6],
[GALOIS,[1,3]],[14,0,2,-1,E(8)-E(8)^3,-1,0,0,0],
[GALOIS,[3,3]],[20,0,-4,-1,0,0,0,-1,-1],[20,0,2,2,0,0,0,-1,-1],[36,0,0,0,0,1,
0,1,1]],"3.A7",[[6,2,0,0,0,1,2,-1,-1],[15,-1,0,0,-1,0,2,1,1],[15,3,0,0,1,0,0,
1,1],[21,1,0,0,-1,1,-2,0,0],[21,-3,0,0,1,1,0,0,0],[24,0,0,0,0,-1,0,
E(7)+E(7)^2+E(7)^4,E(7)^3+E(7)^5+E(7)^6],
[GALOIS,[6,3]]],"6.A7",[[6,0,0,0,E(8)-E(8)^3,1,0,-1,-1],
[GALOIS,[1,3]],[24,0,0,0,0,-1,0,E(7)+E(7)^2+E(7)^4,E(7)^3+E(7)^5+E(7)^6],
[GALOIS,[3,3]],[36,0,0,0,0,1,0,1,1]],]);
ARC("A7","isSimple",true);
ARC("A7","extInfo",["6","2"]);
ARC("A7","maxes",["A6","L3(2)","L3(2)","A5.2","(A4x3):2"]);
ARC("A7","tomfusion",rec(name:="A7",map:=[1,2,3,4,7,8,9,12,12],text:=[
"fusion map is unique"
]));
ALF("A7","A7.2",[1,2,3,4,5,6,7,8,8]);
ALF("A7","A8",[1,3,4,5,7,8,9,11,12],[
"fusion map is unique up to table autom."
]);
ALF("A7","M22",[1,2,3,3,5,6,7,8,9],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("A7","Suz",[1,3,6,6,10,12,17,18,18],[
"fusion map is unique (use structure constants)"
]);
ALF("A7","ON",[1,2,3,3,5,6,7,9,9],[
"fusion map uniquely determined by Brauer tables"
]);
ALF("A7","U3(5)",[1,2,3,3,4,6,9,10,11],[
"fusion map is unique up to table autom."
],"tom:79");
ALF("A7","U4(3)",[1,2,4,6,8,9,11,13,14],[
"fusion map is unique up to table autom."
],"tom:365");
ALF("A7","2^4:a7",[1,3,5,6,8,10,11,12,14],[
"fusion map is unique up to table autom."
]);
ALF("A7","2^6:A7",[1,5,11,16,21,24,28,31,32],[
"fusion map is unique up to table automorphisms"
]);
MOT("A7.2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7],\n",
"constructions: Aut(A7)"
],
[5040,48,72,18,8,10,24,7,240,48,24,12,6,10,12],
[,[1,1,3,4,2,6,3,8,1,1,2,3,4,6,7],[1,2,1,1,5,6,2,8,9,10,11,9,10,14,11],,[1,2,
3,4,5,1,7,8,9,10,11,12,13,9,15],,[1,2,3,4,5,6,7,1,9,10,11,12,13,14,15]],
[[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],[6,2,
3,0,0,1,-1,-1,4,0,2,1,0,-1,-1],
[TENSOR,[3,2]],[20,-4,2,2,0,0,2,-1,0,0,0,0,0,0,0],[14,2,2,-1,0,-1,2,0,6,2,0,0,
-1,1,0],
[TENSOR,[6,2]],[14,2,-1,2,0,-1,-1,0,4,0,-2,1,0,-1,1],
[TENSOR,[8,2]],[15,-1,3,0,-1,0,-1,1,5,-3,1,-1,0,0,1],
[TENSOR,[10,2]],[21,1,-3,0,-1,1,1,0,1,-3,-1,1,0,1,-1],
[TENSOR,[12,2]],[35,-1,-1,-1,1,0,-1,0,5,1,-1,-1,1,0,-1],
[TENSOR,[14,2]]],
[]);
ARC("A7.2","CAS",[rec(name:="s7",
permchars:=( 5,11,10, 9, 8, 7, 6),
permclasses:=(),
text:=[
" names:= s7\n",
" order: 2^4.3^2.5.7 = 5040\n",
" number of classes: 15\n",
" source: cambridge atlas\n",
" comments: symmetric group\n",
" test: orth, min, sym[3]\n",
""])]);
ARC("A7.2","ClassParameters",[[1,[1,1,1,1,1,1,1]],[1,[2,2,1,1,1]],[1,[3,1,1,1,
1]],[1,[3,3,1]],[1,[4,2,1]],[1,[5,1,1]],[1,[3,2,2]],[1,[7]],[1,[2,1,1,1,1,1]],
[1,[2,2,2,1]],[1,[4,1,1,1]],[1,[3,2,1,1]],[1,[6,1]],[1,[5,2]],[1,[4,3]]]);
ARC("A7.2","CharacterParameters",[[1,[7]],[1,[1,1,1,1,1,1,1]],[1,[6,1]],[1,[2,
1,1,1,1,1]],[1,[4,1,1,1]],[1,[5,2]],[1,[2,2,1,1,1]],[1,[4,3]],[1,[2,2,2,1]],
[1,[5,1,1]],[1,[3,1,1,1,1]],[1,[3,3,1]],[1,[3,2,2]],[1,[4,2,1]],[1,[3,2,1,1]]
]);
ARC("A7.2","projectives",["2.A7.2",[[8,0,-4,2,0,-2,0,1,0,0,0,0,0,0,0],[28,0,4,
-2,0,-2,0,0,0,0,0,0,0,0,0],[20,0,-4,-1,0,0,0,-1,0,0,0,0,-E(12)^7+E(12)^11,0,
0],[20,0,2,2,0,0,0,-1,0,0,0,0,0,0,E(24)-E(24)^11-E(24)^17+E(24)^19],[36,0,0,0,
0,1,0,1,0,0,0,0,0,E(5)-E(5)^2-E(5)^3+E(5)^4,0]],]);
ARC("A7.2","tomfusion",rec(name:="S7",map:=[1,3,5,6,11,14,16,23,2,4,9,19,
21,34,41],text:=[
"fusion map is unique"
]));
ARC("A7.2","maxes",["A7","A6.2_1","2xS5","S4xS3","7:6"]);
ALF("A7.2","A8.2",[1,3,4,5,7,8,9,11,13,14,15,17,19,21,22],[
"fusion map is unique"
]);
ALF("A7.2","A9",[1,2,4,6,7,9,10,12,2,3,7,10,11,15,16],[
"fusion map is unique"
]);
ALF("A7.2","Suz.2",[1,3,6,6,10,12,16,17,39,38,41,45,44,53,56],[
"fusion map is unique"
]);
ALF("A7.2","U3(5).2",[1,2,3,3,4,6,8,9,12,12,13,14,14,16,17],[
"fusion map is unique"
]);
ALN("A7.2",["S7"]);
MOT("A8",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[20160,192,96,180,18,16,8,15,12,6,7,7,15,15],
[,[1,1,1,4,5,2,3,8,4,5,11,12,13,14],[1,2,3,1,1,6,7,8,3,2,12,11,8,8],,[1,2,3,4,
5,6,7,1,9,10,12,11,4,4],,[1,2,3,4,5,6,7,8,9,10,1,1,14,13]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1],[7,-1,3,4,1,-1,1,2,0,-1,0,0,-1,-1],[14,6,2,-1,
2,2,0,-1,-1,0,0,0,-1,-1],[20,4,4,5,-1,0,0,0,1,1,-1,-1,0,0],[21,-3,1,6,0,1,-1,
1,-2,0,0,0,1,1],[21,-3,1,-3,0,1,-1,1,1,0,0,0,-E(15)^7-E(15)^11-E(15)^13
-E(15)^14,-E(15)-E(15)^2-E(15)^4-E(15)^8],
[GALOIS,[6,7]],[28,-4,4,1,1,0,0,-2,1,-1,0,0,1,1],[35,3,-5,5,2,-1,-1,0,1,0,0,0,
0,0],[45,-3,-3,0,0,1,1,0,0,0,E(7)+E(7)^2+E(7)^4,E(7)^3+E(7)^5+E(7)^6,0,0],
[GALOIS,[10,3]],[56,8,0,-4,-1,0,0,1,0,-1,0,0,1,1],[64,0,0,4,-2,0,0,-1,0,0,1,1,
-1,-1],[70,-2,2,-5,1,-2,0,0,-1,1,0,0,0,0]],
[(13,14),(11,12)]);
ARC("A8","CAS",[rec(name:="a8",
permchars:=(),
permclasses:=(),
text:=[
"names: a8; psl[4,2],gl[4,2],pgl[4,2],sl[4,2],o+[6,2],\n",
"a3[2], d3[2] [lie-not.]\n",
"order: 2^6.3^2.5.7 = 20160\n",
"number of classes: 14\n",
"source: cambridge atlas\n",
"comments: alternating group\n",
"test: orth, min, sym[3], restricted characters of m23 and ru.\n",
""])]);
ARC("A8","CharacterParameters",[[1,[1,1,1,1,1,1,1,1]],[1,[2,1,1,1,1,1,1]],[1,
[2,2,2,2]],[1,[2,2,1,1,1,1]],[1,[3,1,1,1,1,1]],[1,[[3,3,2],'+']],[1,[[3,3,2],
'-']],[1,[2,2,2,1,1]],[1,[4,1,1,1,1]],[1,[[4,2,1,1],'+']],[1,[[4,2,1,1],'-']],
[1,[3,3,1,1]],[1,[3,2,1,1,1]],[1,[3,2,2,1]]]);
ARC("A8","ClassParameters",[[1,[1,1,1,1,1,1,1,1]],[1,[2,2,2,2]],[1,[2,2,1,1,1,
1]],[1,[3,1,1,1,1,1]],[1,[3,3,1,1]],[1,[4,4]],[1,[4,2,1,1]],[1,[5,1,1,1]],[1,
[3,2,2,1]],[1,[6,2]],[1,[[7,1],'+']],[1,[[7,1],'-']],[1,[[5,3],'+']],[1,[[5,
3],'-']]]);
ARC("A8","projectives",["2.A8",[[8,0,0,-4,2,0,0,-2,0,0,1,1,1,1],[24,0,0,-6,0,
0,0,-1,0,0,E(7)+E(7)^2+E(7)^4,E(7)^3+E(7)^5+E(7)^6,-1,-1],
[GALOIS,[2,3]],[48,0,0,6,0,0,0,-2,0,0,-1,-1,1,1],[56,0,0,-4,-1,0,0,1,0,
E(3)-E(3)^2,0,0,1,1],
[GALOIS,[5,2]],[56,0,0,2,2,0,0,1,0,0,0,0,-E(15)^7-E(15)^11-E(15)^13-E(15)^14,
-E(15)-E(15)^2-E(15)^4-E(15)^8],
[GALOIS,[7,7]],[64,0,0,4,-2,0,0,-1,0,0,1,1,-1,-1]],]);
ARC("A8","maxes",["A7","2^3:sl(3,2)","2^3:sl(3,2)","A6.2_1","2^4:(S3xS3)",
"(A5x3):2"]);
ARC("A8","isSimple",true);
ARC("A8","extInfo",["2","2"]);
ARC("A8","tomfusion",rec(name:="A8",map:=[1,2,3,4,5,12,13,14,17,18,20,20,
48,48],text:=[
"fusion map is unique"
]));
ALF("A8","A8.2",[1,2,3,4,5,6,7,8,9,10,11,11,12,12]);
ALF("A8","A9",[1,3,2,4,6,8,7,9,10,11,12,12,17,18],[
"fusion map is unique up to table autom."
]);
ALF("A8","M23",[1,2,2,3,3,4,4,5,6,6,7,8,15,14],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("A8","Ru",[1,2,2,4,4,7,8,10,11,11,12,12,24,24],[
"fusion map is unique, equal to that on the CAS table"
]);
ALF("A8","2^4:a8",[1,3,5,7,8,11,14,16,17,18,20,22,24,25],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables"
]);
ALF("A8","2^6:A8",[1,4,9,14,17,21,25,29,31,34,38,39,40,41],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables"
]);
ALF("A8","P31/G1/L1/V1/ext3",[1,16,21,51,72,87,89,107,118,136,139,142,145,
148],[
"fusion map is unique up to table automorphisms"
]);
ALN("A8",["sl42","L4(2)"]);
MOT("A8.2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7],\n",
"constructions: Aut(A8)"
],
[40320,384,192,360,36,32,16,30,24,12,7,15,1440,96,96,32,36,36,12,8,10,12],
[,[1,1,1,4,5,2,3,8,4,5,11,12,1,1,3,3,4,5,5,6,8,9],[1,2,3,1,1,6,7,8,3,2,11,8,
13,14,15,16,13,13,14,20,21,15],,[1,2,3,4,5,6,7,1,9,10,11,4,13,14,15,16,17,18,
19,20,13,22],,[1,2,3,4,5,6,7,8,9,10,1,12,13,14,15,16,17,18,19,20,21,22]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,-1],[7,-1,3,4,1,-1,1,2,0,-1,0,-1,5,1,3,-1,2,-1,1,-1,0,0],
[TENSOR,[3,2]],[14,6,2,-1,2,2,0,-1,-1,0,0,-1,4,0,-2,2,1,-2,0,0,-1,1],
[TENSOR,[5,2]],[20,4,4,5,-1,0,0,0,1,1,-1,0,10,2,2,2,1,1,-1,0,0,-1],
[TENSOR,[7,2]],[21,-3,1,6,0,1,-1,1,-2,0,0,1,9,-3,3,-1,0,0,0,1,-1,0],
[TENSOR,[9,2]],[42,-6,2,-6,0,2,-2,2,2,0,0,-1,0,0,0,0,0,0,0,0,0,0],[28,-4,4,1,
1,0,0,-2,1,-1,0,1,10,2,-2,-2,1,1,-1,0,0,1],
[TENSOR,[12,2]],[35,3,-5,5,2,-1,-1,0,1,0,0,0,5,-3,1,1,-1,2,0,-1,0,1],
[TENSOR,[14,2]],[90,-6,-6,0,0,2,2,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0],[56,8,0,-4,
-1,0,0,1,0,-1,0,1,4,4,0,0,-2,1,1,0,-1,0],
[TENSOR,[17,2]],[64,0,0,4,-2,0,0,-1,0,0,1,-1,16,0,0,0,-2,-2,0,0,1,0],
[TENSOR,[19,2]],[70,-2,2,-5,1,-2,0,0,-1,1,0,0,10,-2,-4,0,1,1,1,0,0,-1],
[TENSOR,[21,2]]],
[]);
ARC("A8.2","CAS",[rec(name:="s8",
permchars:=(11,15,14,13,12)(16,22,21,20,19,18,17),
permclasses:=(),
text:=[
"names: s8\n",
"order: 2^7.3^2.5.7 = 40320\n",
"number of classes: 22\n",
"source: cambridge atlas\n",
"comments: symmetric group\n",
"test: orth, min, sym[3] and restricted characters decompose properly\n",
""])]);
ARC("A8.2","ClassParameters",[[1,[1,1,1,1,1,1,1,1]],[1,[2,2,2,2]],[1,[2,2,1,1,
1,1]],[1,[3,1,1,1,1,1]],[1,[3,3,1,1]],[1,[4,4]],[1,[4,2,1,1]],[1,[5,1,1,1]],
[1,[3,2,2,1]],[1,[6,2]],[1,[7,1]],[1,[5,3]],[1,[2,1,1,1,1,1,1]],[1,[2,2,2,1,1]
],[1,[4,1,1,1,1]],[1,[4,2,2]],[1,[3,2,1,1,1]],[1,[3,3,2]],[1,[6,1,1]],[1,[8]],
[1,[5,2,1]],[1,[4,3,1]]]);
ARC("A8.2","CharacterParameters",[[1,[8]],[1,[1,1,1,1,1,1,1,1]],[1,[7,1]],[1,
[2,1,1,1,1,1,1]],[1,[4,4]],[1,[2,2,2,2]],[1,[6,2]],[1,[2,2,1,1,1,1]],[1,[6,1,
1]],[1,[3,1,1,1,1,1]],[1,[3,3,2]],[1,[5,3]],[1,[2,2,2,1,1]],[1,[5,1,1,1]],[1,
[4,1,1,1,1]],[1,[4,2,1,1]],[1,[4,2,2]],[1,[3,3,1,1]],[1,[5,2,1]],[1,[3,2,1,1,
1]],[1,[4,3,1]],[1,[3,2,2,1]]]);
ARC("A8.2","projectives",["2.A8.2",[[8,0,0,-4,2,0,0,-2,0,0,1,1,0,0,0,0,0,0,0,
2*E(4),0,0],[48,0,0,-12,0,0,0,-2,0,0,-1,-2,0,0,0,0,0,0,0,0,0,0],[48,0,0,6,0,0,
0,-2,0,0,-1,1,0,0,0,0,0,0,0,0,0,E(24)-E(24)^11-E(24)^17+E(24)^19],[112,0,0,-8,
-2,0,0,2,0,0,0,2,0,0,0,0,0,0,0,0,0,0],[112,0,0,4,4,0,0,2,0,0,0,-1,0,0,0,0,0,0,
0,0,0,0],[64,0,0,4,-2,0,0,-1,0,0,1,-1,0,0,0,0,0,0,0,0,E(5)-E(5)^2-E(5)^3
+E(5)^4,0]],]);
ARC("A8.2","maxes",["A8","A7.2","S6x2","mo61","S5xS3","s2wrs4","L3(2).2"]);
ARC("A8.2","tomfusion",rec(name:="S8",map:=[1,3,4,6,7,18,20,23,30,35,36,95,2,
5,11,15,29,26,32,68,73,81],text:=[
"fusion map is unique"
]));
ALF("A8.2","A10",[1,3,2,4,5,9,8,10,12,14,15,22,2,3,8,7,12,13,14,16,19,20],[
"fusion map is unique"
]);
ALF("A8.2","A9.2",[1,3,2,4,6,8,7,9,10,11,12,16,17,18,19,20,21,23,24,26,27,
28],[
"fusion map is unique"
]);
ALF("A8.2","HS",[1,2,2,4,4,6,7,9,12,12,13,22,3,3,5,6,11,11,11,14,18,21],[
"fusion map is unique, equal to that on the CAS table"
]);
ALF("A8.2","S6(2)",[1,3,4,6,8,12,13,14,18,20,22,30,2,5,11,10,15,19,21,24,
26,28],[
"fusion map is unique"
]);
ALF("A8.2","2^6:S8",[1,4,8,13,16,19,22,26,28,31,34,35,36,40,44,47,51,55,
57,59,61,63],[
"fusion map is unique up to table automorphisms"
]);
ALF("A8.2","2^8:S8",[1,11,14,16,20,26,28,30,31,33,38,39,41,45,47,48,51,53,
56,60,61,62],[
"fusion map is unique"
]);
ALN("A8.2",["S8"]);
MOT("A9",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[181440,480,192,1080,81,54,24,16,60,24,6,7,9,9,20,12,15,15],
[,[1,1,1,4,5,6,2,3,9,4,6,12,13,14,9,10,17,18],[1,2,3,1,1,1,7,8,9,2,3,12,5,5,
15,7,9,9],,[1,2,3,4,5,6,7,8,1,10,11,12,13,14,2,16,4,4],,[1,2,3,4,5,6,7,8,9,10,
11,1,13,14,15,16,18,17]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[8,4,0,5,-1,2,2,0,3,1,0,1,-1,-1,-1,-1,
0,0],[21,1,-3,-3,3,0,-1,1,1,1,0,0,0,0,1,-1,-E(15)^7-E(15)^11-E(15)^13-E(15)^14
,-E(15)-E(15)^2-E(15)^4-E(15)^8],
[GALOIS,[3,7]],[27,7,3,9,0,0,1,-1,2,1,0,-1,0,0,2,1,-1,-1],[28,4,-4,10,1,1,0,0,
3,-2,-1,0,1,1,-1,0,0,0],[35,-5,3,5,-1,2,-1,-1,0,1,0,0,2,-1,0,-1,0,0],[35,-5,3,
5,-1,2,-1,-1,0,1,0,0,-1,2,0,-1,0,0],[42,6,2,0,-3,3,0,2,-3,0,-1,0,0,0,1,0,0,
0],[48,8,0,6,3,0,0,0,-2,2,0,-1,0,0,-2,0,1,1],[56,-4,0,11,2,2,-2,0,1,-1,0,0,-1,
-1,1,1,1,1],[84,4,4,-6,3,3,0,0,-1,-2,1,0,0,0,-1,0,-1,-1],[105,5,1,15,-3,-3,-1,
1,0,-1,1,0,0,0,0,-1,0,0],[120,0,8,0,3,-3,0,0,0,0,-1,1,0,0,0,0,0,0],[162,6,-6,
0,0,0,0,-2,-3,0,0,1,0,0,1,0,0,0],[168,4,0,-15,-3,0,-2,0,3,1,0,0,0,0,-1,1,0,
0],[189,-11,-3,9,0,0,1,1,-1,1,0,0,0,0,-1,1,-1,-1],[216,-4,0,-9,0,0,2,0,1,-1,0,
-1,0,0,1,-1,1,1]],
[(17,18),(13,14)]);
ARC("A9","CAS",[rec(name:="a9",
permchars:=(),
permclasses:=(),
text:=[
" names:= a9\n",
" order: 2^6.3^4.5.7 = 181440\n",
" number of classes: 18\n",
" source: cambridge atlas\n",
" comments: alternating group\n",
" test: orth, min, sym[3]\n",
""])]);
ARC("A9","CharacterParameters",[[1,[1,1,1,1,1,1,1,1,1]],[1,[2,1,1,1,1,1,1,1]],
[1,[[3,3,3],'+']],[1,[[3,3,3],'-']],[1,[2,2,1,1,1,1,1]],[1,[3,1,1,1,1,1,1]],
[1,[[5,1,1,1,1],'-']],[1,[[5,1,1,1,1],'+']],[1,[2,2,2,2,1]],[1,[2,2,2,1,1,1]],
[1,[4,1,1,1,1,1]],[1,[3,2,2,2]],[1,[3,2,1,1,1,1]],[1,[3,3,1,1,1]],[1,[3,2,2,1,
1]],[1,[3,3,2,1]],[1,[4,2,1,1,1]],[1,[4,2,2,1]]]);
ARC("A9","ClassParameters",[[1,[1,1,1,1,1,1,1,1,1]],[1,[2,2,1,1,1,1,1]],[1,[2,
2,2,2,1]],[1,[3,1,1,1,1,1,1]],[1,[3,3,3]],[1,[3,3,1,1,1]],[1,[4,2,1,1,1]],[1,
[4,4,1]],[1,[5,1,1,1,1]],[1,[3,2,2,1,1]],[1,[6,2,1]],[1,[7,1,1]],[1,[[9],'+']
],[1,[[9],'-']],[1,[5,2,2]],[1,[4,3,2]],[1,[[5,3,1],'+']],[1,[[5,3,1],'-']]]);
ARC("A9","projectives",["2.A9",[[8,0,0,-4,-1,2,0,0,-2,0,0,1,2,-1,0,0,1,1],[8,
0,0,-4,-1,2,0,0,-2,0,0,1,-1,2,0,0,1,1],[48,0,0,6,3,0,0,0,-2,0,0,-1,0,0,0,
E(24)+E(24)^11-E(24)^17-E(24)^19,1,1],
[GALOIS,[3,13]],[56,0,0,-16,2,2,0,0,-4,0,0,0,-1,-1,0,0,-1,-1],[112,0,0,4,4,4,
0,0,2,0,0,0,1,1,0,0,-1,-1],[120,0,0,0,3,-3,0,0,0,0,E(3)-E(3)^2,1,0,0,0,0,0,0],
[GALOIS,[7,2]],[160,0,0,-20,-2,-2,0,0,0,0,0,-1,1,1,0,0,0,0],[168,0,0,12,-3,0,
0,0,-2,0,0,0,0,0,0,0,-E(15)^7-E(15)^11-E(15)^13-E(15)^14,
-E(15)-E(15)^2-E(15)^4-E(15)^8],
[GALOIS,[10,7]],[224,0,0,-4,-1,2,0,0,4,0,0,0,-1,-1,0,0,1,1]],]);
ARC("A9","maxes",["A8","A7.2","(3xA6).2_1","L2(8).3","A9M5","(A4xA5):2",
"3^3.S4","3^2:2A4"]);
ARC("A9","isSimple",true);
ARC("A9","extInfo",["2","2"]);
ARC("A9","tomfusion",rec(name:="A9",map:=[1,2,3,4,5,6,12,14,15,18,22,23,43,44,
46,60,63,63],text:=[
"fusion map is unique up to table autom."
]));
ALF("A9","A9.2",[1,2,3,4,5,6,7,8,9,10,11,12,13,13,14,15,16,16]);
ALF("A9","A10",[1,2,3,4,6,5,8,9,10,12,14,15,17,18,19,20,22,22],[
"fusion map is unique up to table autom."
]);
ALF("A9","O8+(2)",[1,3,6,7,10,11,14,17,18,24,34,35,39,40,41,48,51,51],[
"fusion map is unique up to table autom."
],"tom:11163");
ALF("A9","2^8.A9",[1,6,16,20,28,29,35,43,46,53,61,65,68,69,71,73,79,81],[
"fusion map is unique up to table automorphisms"
]);
MOT("A9.2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7],\n",
"constructions: Aut(A9)"
],
[362880,960,384,2160,162,108,48,32,120,48,12,14,9,40,24,15,10080,288,480,32,
144,144,36,36,18,8,20,24,14,20],
[,[1,1,1,4,5,6,2,3,9,4,6,12,13,9,10,16,1,1,2,2,4,4,6,6,5,8,9,10,12,14],[1,2,3,
1,1,1,7,8,9,2,3,12,5,14,7,9,17,18,19,20,17,18,17,18,18,26,27,19,29,30],,[1,2,
3,4,5,6,7,8,1,10,11,12,13,2,15,4,17,18,19,20,21,22,23,24,25,26,17,28,29,19],,[
1,2,3,4,5,6,7,8,9,10,11,1,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,17,
30]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[8,4,0,5,-1,2,2,
0,3,1,0,1,-1,-1,-1,0,6,2,4,0,3,-1,0,2,-1,0,1,1,-1,-1],
[TENSOR,[3,2]],[42,2,-6,-6,6,0,-2,2,2,2,0,0,0,2,-2,-1,0,0,0,0,0,0,0,0,0,0,0,0,
0,0],[27,7,3,9,0,0,1,-1,2,1,0,-1,0,2,1,-1,15,3,5,1,3,3,0,0,0,-1,0,-1,1,0],
[TENSOR,[6,2]],[28,4,-4,10,1,1,0,0,3,-2,-1,0,1,-1,0,0,14,-2,6,-2,2,-2,-1,1,1,
0,-1,0,0,1],
[TENSOR,[8,2]],[70,-10,6,10,-2,4,-2,-2,0,2,0,0,1,0,-2,0,0,0,0,0,0,0,0,0,0,0,0,
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1],
[TENSOR,[11,2]],[48,8,0,6,3,0,0,0,-2,2,0,-1,0,-2,0,1,20,4,0,0,2,-2,2,-2,1,0,0,
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[TENSOR,[13,2]],[56,-4,0,11,2,2,-2,0,1,-1,0,0,-1,1,1,1,14,-6,4,0,-1,3,2,0,0,0,
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[TENSOR,[15,2]],[84,4,4,-6,3,3,0,0,-1,-2,1,0,0,-1,0,-1,14,-2,-6,2,2,-2,-1,1,1,
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[TENSOR,[17,2]],[105,5,1,15,-3,-3,-1,1,0,-1,1,0,0,0,-1,0,35,-1,5,1,-1,-1,-1,
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[TENSOR,[21,2]],[162,6,-6,0,0,0,0,-2,-3,0,0,1,0,1,0,0,36,0,-6,-2,0,0,0,0,0,0,
1,0,1,-1],
[TENSOR,[23,2]],[168,4,0,-15,-3,0,-2,0,3,1,0,0,0,-1,1,0,14,2,-4,0,-1,-1,2,2,
-1,0,-1,-1,0,1],
[TENSOR,[25,2]],[189,-11,-3,9,0,0,1,1,-1,1,0,0,0,-1,1,-1,21,-3,1,1,-3,-3,0,0,
0,-1,1,1,0,1],
[TENSOR,[27,2]],[216,-4,0,-9,0,0,2,0,1,-1,0,-1,0,1,-1,1,6,-6,-4,0,3,3,0,0,0,0,
1,-1,-1,1],
[TENSOR,[29,2]]],
[]);
ARC("A9.2","CAS",[rec(name:="s9",
permchars:=( 5,11, 9, 8, 7, 6)(10,16,15,14,13,12),
permclasses:=(23,24),
text:=[
" names:= s9\n",
" order: 2^7.3^4.5.7 = 362880\n",
" number of classes: 30\n",
" source: cambridge atlas\n",
" comments: symmetric group\n",
" test: orth, min, sym[3]\n",
""])]);
ARC("A9.2","ClassParameters",[[1,[1,1,1,1,1,1,1,1,1]],[1,[2,2,1,1,1,1,1]],[1,
[2,2,2,2,1]],[1,[3,1,1,1,1,1,1]],[1,[3,3,3]],[1,[3,3,1,1,1]],[1,[4,2,1,1,1]],
[1,[4,4,1]],[1,[5,1,1,1,1]],[1,[3,2,2,1,1]],[1,[6,2,1]],[1,[7,1,1]],[1,[9]],
[1,[5,2,2]],[1,[4,3,2]],[1,[5,3,1]],[1,[2,1,1,1,1,1,1,1]],[1,[2,2,2,1,1,1]],
[1,[4,1,1,1,1,1]],[1,[4,2,2,1]],[1,[3,2,1,1,1,1]],[1,[3,2,2,2]],[1,[3,3,2,1]],
[1,[6,1,1,1]],[1,[6,3]],[1,[8,1]],[1,[5,2,1,1]],[1,[4,3,1,1]],[1,[7,2]],[1,[5,
4]]]);
ARC("A9.2","CharacterParameters",[[1,[9]],[1,[1,1,1,1,1,1,1,1,1]],[1,[8,1]],
[1,[2,1,1,1,1,1,1,1]],[1,[3,3,3]],[1,[7,2]],[1,[2,2,1,1,1,1,1]],[1,[7,1,1]],
[1,[3,1,1,1,1,1,1]],[1,[5,1,1,1,1]],[1,[5,4]],[1,[2,2,2,2,1]],[1,[6,3]],[1,[2,
2,2,1,1,1]],[1,[6,1,1,1]],[1,[4,1,1,1,1,1]],[1,[4,4,1]],[1,[3,2,2,2]],[1,[6,2,
1]],[1,[3,2,1,1,1,1]],[1,[5,2,2]],[1,[3,3,1,1,1]],[1,[5,3,1]],[1,[3,2,2,1,1]],
[1,[4,3,2]],[1,[3,3,2,1]],[1,[5,2,1,1]],[1,[4,2,1,1,1]],[1,[4,3,1,1]],[1,[4,2,
2,1]]]);
ARC("A9.2","projectives",["2.A9.2",[[16,0,0,-8,-2,4,0,0,-4,0,0,2,1,0,0,2,0,0,
0,0,0,0,0,0,0,0,0,0,0,0],[96,0,0,12,6,0,0,0,-4,0,0,-2,0,0,0,2,0,0,0,0,0,0,0,0,
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E(40)^7+E(40)^13-E(40)^21+E(40)^23-E(40)^29-E(40)^31+E(40)^37-E(40)^39],[240,
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-2,0,0,0,0,0,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,E(7)+E(7)^2-E(7)^3+E(7)^4
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0,0,0,0],[224,0,0,-4,-1,2,0,0,4,0,0,0,-1,0,0,1,0,0,0,0,0,0,0,0,3*E(4),0,0,0,0,
0]],]);
ARC("A9.2","tomfusion",rec(name:="S9",map:=[1,3,4,6,7,8,15,22,24,32,41,42,80,
82,97,123,2,5,11,21,28,27,35,34,37,71,84,94,121,178],text:=[
"fusion map is unique"
]));
ARC("A9.2","maxes",["A9","A8.2","S7x2","S3xS6","S5xS4","s3wrs3","3^2.2.S4"]);
ALF("A9.2","A10.2",[1,2,3,4,6,5,8,9,10,12,14,15,17,18,19,21,23,25,26,27,
29,31,32,30,34,35,36,38,40,41],[
"fusion map is unique"
]);
ALF("A9.2","A11",[1,2,3,4,6,5,7,8,10,13,15,17,19,20,24,27,2,3,7,9,13,12,
14,15,16,18,20,24,26,29],[
"fusion map is unique"
]);
ALF("A9.2","O7(3)",[1,3,4,6,8,10,15,14,16,24,31,33,38,40,49,53,2,4,12,15,
18,25,27,30,28,35,41,45,52,58]);
ALN("A9.2",["S9"]);
MOT("M12M4",
[
"4th maximal subgroup of M12,\n",
"differs from M12M3 only by fusion map"
],
0,
0,
0,
0,
["ConstructPermuted",["A6.2^2"]]);
ALF("M12M4","M12",[1,3,4,6,8,3,7,10,2,11,13,6,11],[
"fusion A6.2^2 -> M12 mapped under M12.2"
]);
MOT("A14.2",
[
"origin: CAS library,\n",
" names:= s14\n",
" order: 2^11.3^5.5^2.7^2.11.13 = 87178291200\n",
" number of classes: 135\n",
" source: kerber [bayreuth]\n",
" comments: symmetric group\n",
" test: orth, min\n",
"tests: 1.o.r., pow[2,3,5,7,11,13],\n",
"constructions: Aut(A14)"
],
0,
0,
0,
[],
["ConstructPermuted",["Symmetric",14],
( 2, 70,117, 32, 39, 10, 80, 25, 74, 23, 8, 72, 18, 89, 26, 9, 5, 3)
( 4, 71, 81, 40, 77, 24, 85,108, 95, 58,126,101,135,113, 31,102, 66, 16,
82,109, 30, 11, 17, 21, 88,127,128, 57, 52, 35,103,134, 48, 15, 6, 73, 90,
93, 49, 97, 67,100, 62,118,114, 96,131, 65, 56,124, 99,122,129, 38,104,132,
110,120, 33,105, 28, 12, 83, 45, 43, 41, 14, 84, 46, 79, 91, 27, 75, 86,125,
37,106, 94,112,121,115,130,119, 54,123, 68, 36, 44,107, 29, 76, 87, 64, 69,
53, 50, 34, 42, 78, 92,111, 60,116, 61, 55, 63,133, 47, 13, 19, 20, 7)
( 51, 98, 59),
( 1, 2, 4, 10, 16, 42, 95, 96,120, 51,101, 84,126, 27, 52, 91, 30, 56,113,
68, 94, 86, 90, 49, 40,107, 59, 78,129, 11, 32, 99,100,116, 23, 62,133, 5,
18, 71, 26, 34,115, 43,111, 98,102, 82,134, 3, 6, 22, 77,128, 17, 65, 88,
76, 93, 92, 63,131, 9, 8, 14, 38, 89, 55,135)( 7, 24, 48, 20, 54,121, 41,
119, 45, 67,112, 53, 73, 97,106, 29, 83,118, 39, 58,132)( 12, 36,127, 31, 46,
79,124, 19, 50, 81,108, 72, 60, 87,114, 64,122, 35,103, 70, 47, 66, 74,109,
57,125, 33,117, 25)( 13, 44,123, 21, 85, 61,130, 15, 28, 69,104, 37,105)
( 80,110)]);
ARC("A14.2","projectives",["2.A14.2",[[64,0,0,0,-32,16,-8,4,0,0,0,0,0,0,-16,4,
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]);
ALF("A14.2","S12(2)",[1,4,8,10,11,12,14,16,21,35,28,32,50,48,51,53,56,70,
62,84,69,83,89,92,97,101,102,103,126,129,136,141,144,147,150,154,158,159,
164,212,187,181,219,201,203,234,251,253,256,259,262,261,264,284,295,299,
303,306,308,336,346,353,356,373,386,395,413,418,434,2,5,7,9,17,26,38,46,
44,49,54,61,60,58,67,75,73,78,71,77,85,95,96,100,117,135,139,145,149,157,
153,156,161,171,191,174,210,206,233,227,252,254,257,258,282,286,289,301,
297,310,330,341,350,354,360,369,361,372,378,401,408,411,416,429,459,462],[
"fusion map is unique"
]);
ALN("A14.2",["S14","S12(2)M13"]);
MOT("A15.2",
[
"origin: CAS library,\n",
" names:= s15\n",
" order: 2^11.3^6.5^3.7^2.11.13 = 1307674368000\n",
" number of classes: 176\n",
" source: kerber [bayreuth]\n",
" comments: symmetric group\n",
" test: orth, min\n",
"tests: 1.o.r., pow[2,3,5,7,11,13],\n",
"constructions: Aut(A15)"
],
0,
0,
0,
[],
["ConstructPermuted",["Symmetric",15],
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129,170,138,153, 39,128, 90,106,164,126, 82,162, 80, 42,131, 33, 13, 22,107,
89,112,140, 36,130, 86, 21, 7, 4, 92,115, 57, 40, 50, 51, 52, 99, 53, 15,
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49,134,118, 85,102,136,152,145, 74, 88, 26,111, 32, 97, 46, 14,105,163, 68,
61, 59, 41,133, 34,127,175,142, 73,173, 56,120,169,171, 55, 16)( 35, 45, 98,
135)( 71,148,143,167),
( 1, 2, 4, 10, 14, 53,122,166, 31, 70,161, 48,130, 71,175, 3, 6, 22, 88,
124,155, 64,163, 40,156, 50,134, 95,168, 29, 32, 90, 96,103,117,157, 25, 74,
176)( 5, 16, 24, 63,167, 23,100,172, 9, 8, 20, 72,150, 56, 43,110, 62,138,
113,106,153, 54, 66,173, 7, 26, 82,133, 60, 80,149, 67,152, 91,158, 27, 39,
112, 61, 68,140,107, 81,151, 75,121,123,143, 89,118,160, 46,144, 83,109,101,
164, 21, 55, 18, 65,148, 58,108, 79,146, 19, 84, 38,102,125, 73,169, 15, 37,
142, 87, 98,170, 11, 30, 49,165, 17, 45,114,119,147, 33, 78, 86, 59,116,105,
135, 93,145, 52,104,162, 44, 57, 76,139,111, 34, 47,136, 97,120,129, 77,127,
141,131, 36,132, 35, 92,171, 13, 51,128, 99,174)( 12, 41,154, 69, 94,159, 42,
126,115, 85, 28)]);
ALN("A15.2",["S15"]);
ARC("A15.2","projectives",["2.A15.2",[[128,0,0,0,-64,32,-16,-4,8,0,0,0,0,0,0,
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MOT("A15",
[
"origin: CAS library,\n",
" names:= a15\n",
" order: 2^10.3^6.5^3.7^2.11.13 = 653837184000\n",
" number of classes: 94\n",
" source: stockhofe [aachen] from table of s15 (kerber,bayreuth)\n",
" comments: alternating group\n",
" test: orth, min\n",
"tests: 1.o.r., pow[2,3,5,7,11,13]"
],
0,
0,
0,
[(93,94),(89,90),(82,83),(63,64)],
["ConstructPermuted",["Alternating",15],
( 6,19,45,21,50,46,26,51,53,80,39,91,55,29,16,10,23,11,24,14, 9)( 7,22,48,28,
15, 8,20,49,30,40,68,88,72,73,36,61,87,44,18,13,25,47,27,52,54,92,56,31,41,17,
12)(32,59,57)(33,78,65,84,43,62,71,35,79,38,67,94,64,76,75,86,69)(34,60,70)
(37,66,93,63,77)(81,85)(82,89)(83,90),
( 4, 5, 8,10, 7,15,20,39,59,57,23,53,64,90,19,45,60,61,43,58,41,82,65,88,66,
79,16,14,28, 6,11,17,24,35,49,89,63,74,91,34,25,40,83,62,37,76,84,51,69,75,85,
86,92,56, 9)(12,22,47,73,80,33,42,68,81,52,55,29,18,36,71,87,67,93)(13,27,21,
31,38,54,30,26,44,32,48,70,50,72,94)(46,77)]);
ARC("A15","ClassParameters",[[1,[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]],[1,[2,2,1,1,
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],[1,[6,2,2,2,1,1,1]],[1,[6,3,2,1,1,1,1]],[1,[6,3,2,2,2]],[1,[6,6,1,1,1]],[1,
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ARC("A15","isSimple",true);
ARC("A15","extInfo",["2","2"]);
ALF("A15","A15.2",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,
22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,
46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,63,64,65,66,67,68,
69,70,71,72,73,74,75,76,77,78,79,80,81,81,82,83,84,85,86,87,87,88,89,90,
90],[
"fusion map is unique"
]);
MOT("A16.2",
[
"origin: CAS library,\n",
" names:= s16\n",
" order: 2^15.3^6.5^3.7^2.11.13 = 20922789888000\n",
" number of classes: 231\n",
" source: kerber [bayreuth]\n",
" comments: symmetric group\n",
" test: orth, min\n",
"tests: 1.o.r., pow[2,3,5,7,11,13],\n",
"constructions: Aut(A16)"
],
0,
0,
0,
[],
["ConstructPermuted",["Symmetric",16],
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148, 87,224, 68,155,104,139, 70,156,227,106,143,216,103, 23, 8,122, 64, 17,
7, 5, 3)( 4,120, 63,171, 90,192,187, 45,170,195,213, 53,129,100, 84, 83,
190,186, 44, 57, 62,130,114,147,219,111, 34, 13,134, 35,127,209, 85,223,179,
152,228,183, 92, 20,140,181,107, 27, 9)( 6,121,177, 43,163, 39, 54, 15,136,
176,153,117,168, 42,166, 40,164,182,230, 78, 98, 77,206,210,193, 80,204,160,
218,221, 67, 48, 60,128,211,161,109, 32, 11,131,208,212,102,132, 33,124, 66,
154, 95,159,231,184,198,110,146, 88,225, 69, 49,165,149,200,188,185,222,178,
93,158,118, 65, 19, 26,142, 86,113, 36, 14, 24,138,180,215, 89, 82, 81,189,
79, 75, 96, 76, 74,205, 52, 16, 25, 30, 10)( 21, 29, 28,141, 71, 73, 97,207,
101)( 31,123,174, 91,112,144,108,135, 37,125,203, 51,126, 99,191, 46, 59,173,
196,105),
( 1, 2, 4, 10, 8, 28,110,218, 39, 94,200, 60,126,209, 75,160,123,189,101,
83,226, 13, 40,140,146,195,111,210, 70,124,180,127,215, 45,192,143,188, 68,
112,196,139,122,172,184, 87,220, 17, 24, 90,207, 93,175,137, 36, 96,198, 91,
141,133,159,109,183, 95,161,153,203, 58,181,164, 62,136, 79,190, 99,168,131,
66, 42, 154,157,178,176,193,119,199, 85,212, 29, 80,169, 97,219, 21, 88,208,
53,179, 81,100,155,149,145,174,151,225, 11, 14, 52,163, 64, 57,202, 35, 92,
98,135,147,211, 51,120,227, 9, 20, 86,231)( 3, 6, 22, 63,142,118,229, 5,
16, 50, 56,204, 73,194,115,186, 19, 71, 74,206, 77,224, 15, 61,173,166, 72,
144,213, 25,114,197, 89,187, 37, 65, 18, 44,177,162,105,138, 69,128,221, 33,
48,171,182,113,228, 7, 30, 67, 78,222, 23, 54,130,170,121,230)( 12, 32, 34,
76,167,117,214, 41,165, 38, 46,148,125,134,129,201, 27, 82,185, 49, 84,216,
47,158,191,103, 59,156,205, 55,152,223, 31)( 26,106,150,217, 43,116,132,107,
108,102)]);
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ALN("A16.2",["S16"]);
MOT("A16",
[
"origin: CAS library,\n",
" names:= a16\n",
" order: 2^14.3^6.5^3.7^2.11.13 = 10461394944000\n",
" number of classes: 123\n",
" source: stockhofe [aachen] from table of s16 (kerber,bayreuth)\n",
" comments: alternating group\n",
" test: orth, min\n",
"tests: 1.o.r., pow[2,3,5,7,11,13]"
],
0,
0,
0,
[(118,119),(113,114),(107,108),(78,79),(122,123)],
["ConstructPermuted",["Alternating",16],
( 4, 5)( 7, 22, 58, 34, 19, 13, 8, 24, 59, 36, 49, 50, 76, 89, 91, 41, 99,
46, 83,122, 78, 95, 93, 94,109, 86, 39, 97, 45,116, 67,117, 68, 33, 17, 10)
( 9, 25, 60, 55, 31, 61, 65,100, 81,105,119,107, 52, 85,111, 53, 21, 54, 23,
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123, 79,121, 72, 70)( 40, 74, 87)( 42, 75,110,103,112, 90, 92, 43, 82,120,
108,102,106, 51, 77, 88),
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77, 90,100, 74,103, 54, 70, 69, 59, 85,116, 64, 23, 31, 6, 11, 7, 15, 34,
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39, 50, 32, 17, 12, 16, 27, 44, 95, 67, 21, 47, 86,114, 18, 24, 48, 92, 94,
66, 9, 10)( 22, 35, 49, 45,102, 57,109, 71, 65)( 29, 43, 61, 93,108,122)
( 30, 37, 36, 51, 63, 76, 87,123)( 40, 75,111,106,113, 72)( 53, 96,105,117,
78,120, 82)( 55, 83, 99)( 80,101)]);
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],[1,[5,3,3,1,1,1,1,1]],[1,[5,3,3,3,1,1]],[1,[5,5,3,1,1,1]],[1,[5,5,3,3]],[1,
[[15,1],'+']],[1,[[15,1],'-']],[1,[9,2,2,1,1,1]],[1,[9,3,2,2]],[1,[5,4,2,1,1,
1,1,1]],[1,[5,4,4,1,1,1]],[1,[5,4,2,2,2,1]],[1,[5,5,4,2]],[1,[10,4,1,1]],[1,
[7,3,1,1,1,1,1,1]],[1,[7,3,3,3]],[1,[7,3,3,1,1,1]],[1,[11,2,2,1]],[1,[8,3,2,1,
1,1]],[1,[8,3,3,2]],[1,[8,6,1,1]],[1,[8,4,3,1]],[1,[7,4,2,1,1,1]],[1,[7,4,4,1]
],[1,[5,3,2,2,2,2]],[1,[5,3,2,2,1,1,1,1]],[1,[5,3,3,2,2,1]],[1,[6,5,2,1,1,1]],
[1,[6,5,3,2]],[1,[10,3,2,1]],[1,[10,6]],[1,[11,3,1,1]],[1,[7,5,1,1,1,1]],[1,
[9,4,2,1]],[1,[[13,3],'+']],[1,[[13,3],'-']],[1,[8,5,2,1]],[1,[7,3,2,2,1,1]],
[1,[7,6,2,1]],[1,[9,5,1,1]],[1,[[11,5],'+']],[1,[[11,5],'-']],[1,[5,4,4,3]],
[1,[5,4,3,2,1,1]],[1,[6,5,4,1]],[1,[[9,7],'+']],[1,[[9,7],'-']],[1,[7,5,2,2]],
[1,[7,4,3,2]],[1,[[7,5,3,1],'+']],[1,[[7,5,3,1],'-']]]);
ARC("A16","isSimple",true);
ARC("A16","extInfo",["2","2"]);
ALF("A16","A16.2",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,
22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,
46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,
70,71,72,73,74,75,76,77,78,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,
93,94,95,96,97,98,99,100,101,102,103,104,105,106,106,107,108,109,110,111,
111,112,113,114,115,115,116,117,118,118],[
"fusion map is unique"
]);
MOT("A17",
[
"origin: computed from generic table of alternating groups (reordered)"
],
0,
0,
0,
[(151,152),(143,144),(141,142),(132,133),(89,90)],
["ConstructPermuted",["Alternating",17],
( 4, 5)( 7, 22, 58, 86, 80, 34, 64, 29, 15, 27, 67, 36, 68, 37, 17, 33, 66,
31, 60, 87,101,155, 89,102, 41, 51,146, 75, 74, 73, 72, 69, 35, 18, 10)( 8,
24, 61, 99,129, 94,154, 88,136,150,112,134,124,131,152,133, 55,148, 77,120,
91,103,104, 42, 82, 39, 50, 97,153, 81, 38, 19, 11, 25, 62, 21, 14, 30, 16,
9, 26, 65, 32, 70, 59,121, 48, 84, 40, 52,147, 76,119, 92,113,135,100,138,
125,130,151,132, 54, 98,156, 90,137, 56, 20, 13)( 12, 28)( 23, 63)( 43,116,
145,144,143,139, 57, 53, 96,128,142,127,141,126,140,105, 44,117, 46,118, 47,
85, 79,149, 78,123, 49, 95,115,111,110, 45, 83,122, 93,114,109),
( 4, 5, 8, 19, 25, 46, 68,111,125,142, 35, 15, 33, 40, 45, 92, 50,110,129,
150, 95,143, 62,139,136,147,113,103,145, 88,120, 85, 91, 75, 38, 48, 96,114,
104,128,151, 83,127,115,121, 81, 77, 72, 58,106,100,149, 94,140, 65,126,108,
101,138, 80, 36, 27, 66, 70,105, 99,155, 17, 24, 29, 47, 59, 97,130,134,152,
21, 44, 89,124,133,154, 69,112,153, 39, 56, 60, 82,109,132,131, 71, 90,135,
146, 61,123, 98,156, 18, 10)( 6, 11, 7, 16, 32, 49,122, 52,116, 12, 14, 28,
43, 73, 9, 13, 22, 55, 30, 67, 76, 57, 87,144, 84,117, 31, 63,107, 54, 79,
51, 93,102,118, 53, 86,137,148,141, 20, 34)( 23, 41, 26, 64,119, 78, 74)]);
ARC("A17","isSimple",true);
ARC("A17","extInfo",["2","2"]);
ALF("A17","A17.2",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,
22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,
46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,
70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,89,90,91,92,
93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,
113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,
131,131,132,133,134,135,136,137,138,139,139,140,140,141,142,143,144,145,
146,147,147,148,149,150,151],[
"fusion map is unique"
]);
MOT("A17.2",
[
"origin: computed from generic table of symmetric groups (reordered),\n",
"constructions: Aut(A17)"
],
0,
0,
0,
[],
["ConstructPermuted",["Symmetric",17],
( 2,152,122,171,271,240,230, 46, 61,208,105,144,215,189,148,118, 21,173,272,
125, 32, 10, 6,154,145, 74,191,297, 89, 85, 83,253,193,128,181,113,120,165,
221,132, 37, 13,167,223,295,265, 56,158,184,293,277,140, 69,163,121, 23,174,
101,143, 73, 19,166, 79, 51,203, 42, 58,162,218,245,129, 36,157, 34,156,262,
238, 92,232,227,110,196,275,278,288,111, 86,254, 54,205, 44, 63,209,244,268,
57, 15,170,100,282,220,269,239, 49,210,106,235, 90,256, 55, 12, 22, 28, 27,
177,102, 95, 96,233, 91, 84,116, 98,142, 72, 17,168, 80, 82,115,236, 48, 62,
70,211,243,267,290,279,212,107, 20, 25,172,134,182,292, 81,251,147,252,291,
225,108,195,136, 59, 16, 26, 30,176,135, 35, 11,164, 40,160, 39, 14, 24, 8,
155,285,286, 78,194,273,287,247,294, 88,255,198,150,119,197,276,137,206,188,
289,131,179,112,258,123, 29, 9, 4,153,260,264,199, 41,200,224,133,183,149,
261, 99,284, 77, 52, 67,161,185,114, 87,117,283, 76,192,296,226,246,138, 71,
68, 18, 7, 5, 3)( 31, 33,175,274,126,169,222,270,104, 97,281,219,190,151,
259,263,146,216, 45,204,187,127)( 38,159)( 43,202,186,250, 93, 94,234,228,280,
75, 50, 65,213,242,130,180,249,231, 47,201,103,237,229,141,217,109, 53,207,
241,266,124,178,248,139,214)( 64, 66),
( 1, 2, 4, 10, 8, 34, 12, 28, 83,240,160,224,130,201, 82,203, 75, 73, 18,
20, 65,238,192,216,267, 33, 77,141,297)( 3, 6, 22,107,105, 249,108,191,265,
84,219,182,285, 21, 85,179,269, 58,197,204,135,227,128,254, 66,137,248,124,
167,165, 67,149,287, 29, 91,147,157,126,101,264, 92, 97,246,140,280, 42, 81,
151,283, 46,133,284, 40, 87,276, 64,223,228, 86,262,142,289, 27,129,272, 72,
113,252, 25, 89,234,138,292, 13, 41, 49,229, 78,145,281, 48,185,233,118,146,
194,158,200,132,286, 17, 45,181,250,106,112,290, 15, 63,199, 98,296)( 5, 16,
61,232, 74, 43,143,277, 52,217,261,110,244,184,206,156,154,257,102,221,239,
178,163, 76,111,236,120, 24, 55, 57,171,211,214,164, 36, 51,183,295)( 7, 32,
95,274, 54,155,237,188,271, 56,117,176,235,104,242,202, 38, 93,193, 94,268,
35, 30,131,215,253, 37, 71,177,220,166,121, 59,187,172,270, 68,207,134,256,
96,213,148,260,114,241,152,293, 9, 26,125,159,212,245, 90,258,150,243,170,
119,136,139,288, 19, 47,115,226,180,291, 11, 14, 53,169,127,189,273, 80, 69,
209,247,174,230, 44,175,279, 23, 79, 99,294)( 31,123,153,208,210,190,275, 70,
195,218,231, 39,109,251, 60,161,198,122,103,278)( 50,205,162,168,173,259,116,
263, 88,225,144,255,100,282)( 62,266)(186,222,196)]);
ARC("A17.2","projectives",["2.A17.2",[[256,0,0,0,0,-128,64,-32,16,-8,0,0,0,0,0
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-2*E(60)^7-2*E(60)^11+2*E(60)^19+2*E(60)^23+2*E(60)^31-2*E(60)^43+2*E(60)^47
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,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]],]);
ALN("A17.2",["S17"]);
MOT("A18",
[
"computed using generic character table for alternating groups"
],
0,
0,
0,
[(191,192),(187,188),(175,176),(109,110),(112,113)],
["ConstructPermuted",["Alternating",18],
( 7, 25, 69,107,168,123,172,156,162,186, 93,183, 91,149,115,193,100, 90,146,
54,147, 55,105,126, 99, 44, 22, 14, 8, 27, 74, 26, 73,106,169,125, 47, 62,
122,171, 67,104, 98, 43, 21, 12, 33, 17, 9, 29, 80, 41, 20, 10)
( 11, 28, 72, 24, 15, 34, 18, 38, 83, 84, 77, 32, 13, 30, 79, 40, 19)
( 16, 35, 71,121,160,176,157,174, 68,150, 56,118,197,110,128, 48,101,153, 57,
120,200,113,194,143,137,136,135, 52,148,114,142,133,134, 50,145,178,158,196,
109,170,185, 94,184, 92,152, 58,179,173,167,155,163, 59,180,177,189,139,165,
66, 63,181,191,187, 95,151,116,159,175,130, 49,144,138, 53,103, 97, 45, 60,
182,192,188, 96, 36, 82, 70,124,195,108,127,129, 51,102, 46, 61,119,198,111,
140,199,112,141,166,154,161,117,190,164, 64, 23)( 31, 75)( 37, 76)
( 39, 81, 42, 85, 78)( 86, 89),
(4,5,8,19,10,11)(6,12,7,16,33,81,148,171,185,187,
162,200,35,62,29,78,147,145,50,112,195,70,165,168,190,109,174,18,31,51,95,
137,108,152,193,71,154,172,77,126,115,189,161,176,64,94,116,196,101,170,
151,181,120,188,160,158,183,173,130,143,103,175,40,26,28,66,121,182,163,
199,34,61,91,72,135,144,68,84,82,85,9,17,37,32,75,119,186,90,83,92,38)(13,
14,21,36,65,118,132,192,44,57,107,110,164,197,102,146,106,49,97,111,
138)(15,27,47,45,43,58,136,184,141,79,117,122,167,155,180,63,60,113,198,
23,55,133,179,100,177,93,73,169,150,123,87,41,39)(20,24,54,127,153,157,
139,30,67,89,76,80,131,191)(22,46,25,42,48,69,134,159,194,99,149,156,74,
129,125,53,105,124,88,56,104,140,52,59,128,166,86)(96,142,98)(114,178)]);
ARC("A18","isSimple",true);
ARC("A18","extInfo",["2","2"]);
ALF("A18","A18.2",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,
22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,
46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,
70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,
94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,109,110,111,111,
112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,
130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,
148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,
166,167,168,169,170,171,172,173,173,174,175,176,177,178,179,180,181,182,
183,184,184,185,186,187,187,188,189,190,191,192,193,194,195],[
"fusion map is unique"
]);
MOT("A18.2",
[
"origin: computed from generic table of symmetric groups (reordered),\n",
"constructions: Aut(A18)"
],
0,
0,
0,
[],
["ConstructPermuted",["Symmetric",18],
( 2,196,277,164,272,344,307,172, 88,246, 99,324,327,336,338,339,370,162,259,
309,191, 45, 15, 27,218,318, 59,268,313,115,360,278,345,155, 40,202, 97,323,
251,239,352,174,276,194,237,348,156,235,195, 44,205,284,357, 91, 62, 13, 25,
30, 35, 11, 6,199,236,158,232,384,111,358,280,314,295,291,112,176,322, 66,
18,216,317,371,372,356,265, 52,256,129,104,145, 31, 9, 5, 3)
( 4,197, 90,248,320, 64, 17, 29,228,368,316,379,108,298, 58, 79, 20,213,168,
89, 61, 75, 81, 85, 22,220,373,184,180,329,121,178,332,182,333,304,343,128,
63,203,283,315,183,335, 67,207,347,185,364,281,135,122,362,279,131,148,221,
189, 36,226,188,149,215,349,355,187,334,254, 49, 73,271, 53, 72, 76,206,124,
23, 33, 38,201,282,136,303,342,306,160,230,369,137,363, 93,321,252, 51, 74,
83, 21, 28, 34,224,140,253,240,353,377,354,367, 96,143, 26, 8,200, 46,255,
308,376,287, 54,264,241,170,275,378,141,106,297,292,290,289, 55, 80,266,242,
190,233,193, 43, 16,219,139, 24,222,374,286,382,288,244, 47, 69,262,310,173,
273,163, 84,209,350,171,270,243,385,296,114,177,144,217,138,119,301,341, 68,
71,269,134,300, 57,258,130,330,305,161, 70, 82,267,133,331,123,302,159, 42,
204, 98,102,103,328,153,231,192,234,381,109,118,117,359, 92,101,326,337,154,
225,319,247,127,250, 48,257,311,383,110,299,293,113,361, 94,142,212,351,380,
340,165, 77, 19, 7)( 10,198,151,229,186,181,150, 32,223,375,100,146,227,157,
41, 14,214,126, 65,208,167,274,346,366, 95,325,152, 39, 12,211,125,249,238,
169, 87, 60,263, 50,260,132,107,116,179,147, 37)( 56,261,312,294)
( 78,210,166)( 86,245,285,175),
( 1, 2, 3, 5, 15, 53,198,175,176,168,382, 8, 37, 63,116,376, 20, 47, 85,
17, 69,258,297,219,364, 68,164,372, 42, 92, 71,294,139,205,192,240,323,103,
332,199, 64,180,352, 93,142, 25, 79,222,366, 32,146,188,228,329,155,344, 95,
264,309,226,253,207,229,373, 24,104,270,283,159,342, 76,156,369, 50,212,357,
60,214,319, 46, 49,186,287, 82,166,334,149, 96,274,331,181,383, 6, 23,106,
94,220,358, 72,260,335,187,238,299,267,345,101,322,145,154,235,321,123,224,
327,185,377, 28,128,239,311,147,194,339, 70,312,163,348,115,361, 86, 43,112,
374, 18, 61,174,347,117,233,285,183,360, 78,284,141,167,384, 4, 9, 33,158,
326,209,328,165,302,281,232,381, 10, 21, 67,170,351, 91,140,234,333, 99,288,
80,252,190,250, 83,177,296,269,243,127,315,111,266,293,169,378, 16, 65,225,
362, 56,196,271,261,277,263,191,303,291,137,317, 62, 57,202,124,102,282,257,
307,189,150,200, 35,120,359, 58,262,255,136,305,259,273,325,201, 75,227,206,
122,316,105,237,193,301,179,354, 66,231,370, 52,114,338,107,208,308,265,349,
109,330,221,385)( 7, 31, 98,184,343, 97,210,251,138,160,204,216,172,379, 12,
13, 27, 90,162,268,375, 30,130,365, 54,244,133,304,289, 45, 81,286,131,367,
26, 55,256,241,295,230,314,153,298,236,215,278,121,346,143, 59,246,171,318,
22, 88,108,290, 87, 77,242,247,197,248,119,355, 38, 11)( 14, 41, 73,320, 84,
161,144,100,336,129,276,313,213,353, 89,148,132,341, 40, 51,182,368, 44,110,
310,245,211,272,217,306,203,178,363, 74,249, 39, 29,152,324,125,218,371, 48,
134,279,195,223,356, 36,126,292,173,340, 34,118,254,151,280,275,337,113,380)
(135,350)(157,300)]);
ARC("A18.2","projectives",["2.A18.2",[[256,0,0,0,0,-128,64,-32,16,4,-8,0,0,0,0
,0,0,0,0,0,0,-64,16,-4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,32,4,0,0,0,0,
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ALN("A18.2",["S18"]);
MOT("A19",
[
"computed using generic character table for alternating groups"
],
0,
0,
0,
[(252,253),(240,241),(233,234),(231,232),(122,123),(131,132)],
["ConstructPermuted",["Alternating",19],(7,25,16,33,84,70,221,187,191,212,183,
128,204,176,218,149,207,137,244,112,181,127,145,205,177,57,172,159,156,55,170,
200,239,196,195,130,146,206,182,60,173,161,53,113,36,17,39,87,31,86,26,15,8,
28,78,119,180,126,203,71,222,211,143,251,124,144,189,194,213,184,61,117,49,22,
11)(9,30,77,175,217,150,51,65,219,186,62,133,242,233,103,100,96,85,120,50,64,
135,164,157,151,111,227,236,106,174,250,123,109,223,210,72,138,188,192,246,
167,198,231,102,97,91,41,80,140,247,121,108,179,59,116,48,88,38,76,115,45,21,
37,19,40,82,141,254,132,165,158,154,52,66,220,235,229,241,215,201,63,136,166,
58,171,152,148,245,209,228,240,197,230,95,75,69,139,237,107,178,160,153,190,
193,214,238,162,56,114,47,20,10,29,79,118,101,94,46,93,44,18)(12,27,74,68,134,
243,234,105,169,249,122,110,226,253,131,163,155,54,168,199,232,104,98,81,225,
252,125,202,67,224,216,73,23)(13,34,89,32,83,24,14,35)(42,92)(43,90)(129,147,
208,142,248,185),(4,5,8,18,39,66,130,250,27,31,82,161,176,201,222,177,229,94,
88,160,125,141,152,237,198,209,83,131,215,67,72,129,223,204,212,191,240,43,28,
46,61,106,143,113,155,230,174,136,200,171,148,225,153,145,189,251,44,37,71,
119,48,54,107,162,12,7,15,30,81,188,190,254,20,10,16,34,79,146,178,217,115,
211,194,185,207,235,233,213,17,41,6,11)(9,21,25,62,151,221,120,103,36,86,175,
124,147,159,168,99,76,179,195,247,122,192,248,123,199,90,156,236,110,154,169,
49,26,52,97,38,87,166,102,63,164,50,42,14,23,45,47,64,121,157,226,214,40,53,
112,205,253,19,29,68,32,60,133,144,165,77,183,73,117,172,180,228,210,149,245,
132,202,238,111,196,249,104,70,93,127,246,181,186,231,227,239,22,35,95)(24,59,
150,206,234,232,242,105,108,139,158,167,109,96)(33,51,69,58,128,243,118,140,
170,100,92,114,163)(55,80,197,208,219,91,138,244,74,84,85,135,241,75,134,216,
98,56,57,101,89,193,252,78,137,224,182,173,184,142)(65,126,220)(116,203,187,
218)]);
ARC("A19","isSimple",true);
ARC("A19","extInfo",["2","2"]);
ALF("A19","A19.2",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,
22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,
46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,
70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,
94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,
114,115,116,117,118,119,120,121,122,122,123,124,125,126,127,128,129,130,
130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,
148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,
166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,
184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,
202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,
220,221,222,223,224,225,226,227,228,229,229,230,230,231,232,233,234,235,
236,236,237,238,239,240,241,242,243,244,245,246,247,247,248],[
"fusion map is unique"
]);
MOT("A19.2",
[
"origin: computed from generic table of symmetric groups (reordered),\n",
"constructions: Aut(A19)"
],
0,
0,
0,
[],
["ConstructPermuted",["Symmetric",19],(2,249,434,442,462,387,193,99,65,323,
155,138,454,103,113,169,278,485,123,366,62,83,328,427,375,426,148,406,135,137,
219,410,457,458,227,292,489,362,357,126,217,225,290,240,110,397,71,260,471,
470,230,336,430,460,475,441,247,201,338,150,407,372,192,334,482,122,134,367,
422,199,97,64,84,258,163,120,131,452,343,386,361,127,451,104,395,67,319,56,
313,154,365,128,218,455,345,446,322,384,129,449,102,303,294,51,314,381,487,
124,133,132,450,341,159,139,220,179,42,12,264,238,108,399,400,174,282,465,194,
335,198,326,58,321,153,118,401,417,181,44,14,267,164,370,190,91,332,481,183,
46,16,271,463,160,24,34,276,248,143,304,54,79,80,331,197,94,88,325,298,440,
480,420,466,469,213,177,41,254,144,68,13,25,277,243,142,23,272,233,178,275,
488,421,234,416,141,136,368,189,333,244,431,231,101,66,89,93,263,472,349,216,
224,47,259,390,229,49,312,377,477,165,265,162,70,17,30,280,490,130,222,36,283,
432,185,287,437,484,352,158,223,285,439,214,221,414,311,378,241,348,486,444,
236,50,74,76,87,21,266,393,63,327,382,211,415,418,419,182,284,203,98,301,293,
205,167,269,392,235,291,474,351,299,394,302,52,78,82,90,330,428,147,115,404,
180,289,438,208,402,175,43,255,389,483,459,106,398,308,149,173,32,274,242,109,
114,116,171,279,246,433,461,107,168,31,39,37,10,252,145,306,55,315,380,478,
467,195,96,300,188,85,18,273,464,388,228,48,15,28,270,186,75,318,296,111,170,
38,281,187,317,53,320,297,146,69,256,161,309,379,212,412,310,152,409,226,45,
257,391,468,445,476,207,172,268,239,347,447,95,22,27,8,253,436,443,232,340,
157,453,344,245,200,337,429,184,288,206,408,140,369,425,374,191,81,92,20,7,4,
250,202,100,305,295,350,57,77,329,196,339,383,358,354,353,59,86,262,473,112,
405,411,373,424,73,261,237,346,215,456,105,166,26,35,40,11,6,251,435,209,403,
413,72,19,29,33,9,5,3)(60,324,156,371,423,479,121,364,359)(61,316,151,119,363)
(125,448,342,385,360,356,355)(176,286,204,396,307,376,210),(1,2,3,5,15,56,110,
300,129,432,189,448,95,17,78,266,476,46,118,270,213,451,137,434,151,428,107,
316,328,232,308,256,337,245,343,322,482,26,100,180,444,79,284,354,84,166,62,
293,105,211,488,6,21,45,90,304,206,430,197,342,356,205,331,371,392,101,174,
286,346,275,490)(4,9,37,138,466,81,365,311,291,366,281,334,340,391,106,278,
443,115,407,289,326,433,165,23,86,339,360,257,440,191,368,344,172,94,170,212,
478,22,65,244,236,33,98,108,269,226,369,404,277,461,34,154,327,313,413,279,
480,28,88,312,320,431,203,330,449,93,246,397,185,335,409,303,146,345,195,475,
53,220,394,51,134,417,181,418,221,273,455,135,460,36,168,150,400,237,75,260,
412,201,469,67,140,329,398,179,389,218,247,353,49,47,124,285,423,32,116,395,
85,262,486,10,31,159,295,264,447,77,355,152,452,113,301,39,128,464,61,208,363,
297,302,82,314,411,209,410,261,487,8,35,186,142,104,136,388,178,240,225,364,
372,427,143,222,162,283,214,420,125,271,384,319,441,133,280,376,227,459,66,
252,405,167,96,43,52,190,419,161,341,402,223,290,396,145,367,207,453,111,381,
298,267,429,131,416,157,438,99,148,435,219,336,386,299,239,192,481,20,19,54,
210,485,14,41,11,7,29,132,393,55,155,446,40,102,121,305,231,421,123,387,188,
403,241,228,401,276,470,57,198,358,163,307,144,323,437,199,472,24,114,317,204,
175,349,173,196,483,16,64,238,130,479,18,74,164,171,194,458,87,325,380,348,
259,378,374,318,351,156,450,97,72,250,456,89,375,288,465,73,230,362,332,445,
38,169,200,477,42,27,58,248,296,287,424,50,80,383,217,467,59,292,255,184,361,
338,229,390,160,242,176,357,216,454,109,187,272,463,69,112,399,147,310,385,
251,370,324,425,83,253,422,76,347,233,274,457,91,268,436,183,442,119,92,224,
377,352,117,333,474,48,103,68,60,258,462,63,321,415,249,414,235,141,294,177,
263,473,44,70,182,379,382,139,306,215,484,12,13,25,120,202,439,149,468,71,234,
254,243,126,426,127,471,30,158,408,309,350,122,373,265,406,193,489)(153,282,
315,359)]);
ALN("A19.2",["S19"]);
MOT("Isoclinic(6.A6x2)",
[
"central product of 6.A6 with a cyclic group of order 4,\n",
"subgroup of 12.A6.2_3"
],
[4320,4320,4320,4320,4320,4320,4320,4320,4320,4320,4320,4320,48,48,48,48,48,48
,36,36,36,36,36,36,36,36,48,48,48,48,48,48,48,48,48,48,48,48,60,60,60,60,60,60
,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60],
[,[1,7,5,11,9,3,1,7,5,11,9,3,7,1,11,5,3,9,19,21,19,21,23,25,23,25,13,13,17,17,
15,15,13,13,17,17,15,15,51,57,55,61,59,53,51,57,55,61,59,53,39,45,43,49,47,41,
39,45,43,49,47,41],[1,8,7,2,1,8,7,2,1,8,7,2,13,14,13,14,13,14,1,8,7,2,1,8,7,2,
33,28,27,34,33,28,27,34,33,28,27,34,51,58,57,52,51,58,57,52,51,58,57,52,39,46,
45,40,39,46,45,40,39,46,45,40],,[1,2,11,12,9,10,7,8,5,6,3,4,13,14,17,18,15,16,
19,20,21,22,23,24,25,26,33,34,31,32,29,30,27,28,37,38,35,36,1,2,11,12,9,10,7,8
,5,6,3,4,1,2,11,12,9,10,7,8,5,6,3,4]],
0,
[(39,51)(40,52)(41,53)(42,54)(43,55)(44,56)(45,57)(46,58)(47,59)(48,60)(49,61)
(50,62)
,(19,23)(20,24)(21,25)(22,26),(27,33)(28,34)(29,35)(30,36)(31,37)(32,38),
( 3,11)( 4,12)( 5, 9)( 6,10)(15,17)(16,18)(29,37)(30,38)(31,35)(32,36)(41,49)
(42,50)(43,47)(44,48)(53,61)(54,62)(55,59)(56,60),
( 2, 8)( 4,10)( 6,12)(20,22)(24,26)(28,34)(30,36)(32,38)(40,46)(42,48)(44,50)
(52,58)(54,60)(56,62)],
["ConstructIsoclinic",[["6.A6"],["Cyclic",2]]]);
ALF("Isoclinic(6.A6x2)","3.A6",[1,1,2,2,3,3,1,1,2,2,3,3,4,4,5,5,6,6,7,7,7,
7,8,8,8,8,9,9,10,10,11,11,9,9,10,10,11,11,12,12,13,13,14,14,12,12,13,13,
14,14,15,15,16,16,17,17,15,15,16,16,17,17]);
ALF("Isoclinic(6.A6x2)","12.A6.2_3",[1,7,5,8,2,9,4,7,3,8,6,9,10,13,11,14,
12,15,16,18,17,19,16,19,17,18,20,23,21,27,22,24,20,26,21,25,22,28,29,35,
33,39,30,36,32,38,31,37,34,40,29,38,33,37,30,40,32,35,31,39,34,36],[
"fusion map is unique up to table autom.,\n",
"compatible with Brauer tables"
]);
ALN("Isoclinic(6.A6x2)",["4Y6.A6"]);
MOT("Isoclinic(3.A6.2_3x2)",
[
"subdirect product of 3.A6.2_3 with a cyclic group of order 4,\n",
"factor group of 12.A6.2_3"
],
[4320,4320,4320,4320,4320,4320,96,96,96,96,96,96,18,18,48,48,48,48,48,48,30,30
,30,30,30,30,24,24,24,24,24,24,48,48,48,48,48,48,48,48,48,48,48,48],
[,[1,1,5,5,3,3,1,1,5,5,3,3,13,13,7,7,11,11,9,9,21,21,25,25,23,23,8,8,12,12,10,
10,16,16,20,20,18,18,16,16,20,20,18,18],[1,2,1,2,1,2,7,8,7,8,7,8,1,2,15,16,15,
16,15,16,21,22,21,22,21,22,28,27,28,27,28,27,34,33,34,33,34,33,40,39,40,39,40,
39],,[1,2,5,6,3,4,7,8,11,12,9,10,13,14,15,16,19,20,17,18,1,2,5,6,3,4,27,28,31,
32,29,30,39,40,43,44,41,42,33,34,37,38,35,36]],
0,
[(27,28)(29,30)(31,32)(33,34)(35,36)(37,38)(39,40)(41,42)(43,44),
(33,39)(34,40)(35,41)(36,42)(37,43)(38,44),
( 3, 5)( 4, 6)( 9,11)(10,12)(17,19)(18,20)(23,25)(24,26)(29,31)(30,32)(35,37)
(36,38)(41,43)(42,44)],
["ConstructIsoclinic",[["3.A6.2_3"],["Cyclic",2]]]);
ALF("Isoclinic(3.A6.2_3x2)","3.A6.2_3",[1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,
9,9,10,10,11,11,12,12,13,13,14,14,15,15,16,16,17,17,18,18,19,19,20,20,21,
21,22,22]);
ALF("Isoclinic(3.A6.2_3x2)","C4",[1,3,1,3,1,3,1,3,1,3,1,3,1,3,1,3,1,3,1,3,
1,3,1,3,1,3,2,4,2,4,2,4,2,4,2,4,2,4,2,4,2,4,2,4]);
MOT("12.A6.2_3",
[
"origin: ATLAS of finite groups"
],
[8640,8640,8640,8640,8640,8640,4320,4320,4320,96,96,96,96,96,96,36,36,36,36,48
,48,48,96,96,96,96,96,96,60,60,60,60,60,60,60,60,60,60,60,60,24,24,24,24,24,24
,48,48,48,48,48,48,48,48,48,48,48,48],
[,[1,3,2,1,2,3,4,6,5,4,6,5,1,2,3,16,16,17,17,10,12,11,10,11,12,10,12,11,29,31,
30,29,30,31,32,33,34,32,34,33,13,15,14,13,15,14,23,24,25,23,24,25,26,28,27,26,
28,27],[1,1,1,4,4,4,7,7,7,10,10,10,13,13,13,1,4,7,7,20,20,20,23,23,23,26,26,26
,29,29,29,32,32,32,35,35,35,38,38,38,44,44,44,41,41,41,50,50,50,47,47,47,56,56
,56,53,53,53],,[1,3,2,4,6,5,7,9,8,10,12,11,13,15,14,16,17,18,19,20,22,21,26,27
,28,23,24,25,1,3,2,4,6,5,7,8,9,7,9,8,41,43,42,44,46,45,53,55,54,56,58,57,47,49
,48,50,52,51]],
0,
[(35,38)(36,40)(37,39),(18,19),
(23,26)(24,28)(25,27)(41,44)(42,45)(43,46)(47,56)(48,57)(49,58)(50,53)(51,54)
(52,55),(23,26)(24,28)(25,27)(47,53)(48,54)(49,55)(50,56)(51,57)(52,58),
( 2, 3)( 5, 6)( 8, 9)(11,12)(14,15)(21,22)(23,26)(24,27)(25,28)(30,31)(33,34)
(36,37)(39,40)(41,44)(42,46)(43,45)(47,56)(48,58)(49,57)(50,53)(51,55)(52,54)
],
["ConstructMGA","Isoclinic(6.A6x2)","Isoclinic(3.A6.2_3x2)",[[15,18],[16,
17],[19,22],[20,21],[23,26],[24,25],[47,52],[48,51],[49,54],[50,53],[55,60],
[56,59],[57,62],[58,61]],(2,9,5,3)(4,10,13,7)(6,11)(8,12,14,15)(17,23,29,35,
41,47,19,25,31,37,43,49,21,27,33,39,45)(18,24,30,36,42,48,20,26,32,38,44,50,
22,28,34,40,46)]);
ALF("12.A6.2_3","Isoclinic(3.A6.2_3x2)",[1,5,3,1,3,5,2,4,6,7,9,11,8,10,
12,13,13,14,14,15,17,19,16,20,18,16,18,20,21,25,23,21,23,25,22,26,24,22,
24,26,27,29,31,28,30,32,33,35,37,34,36,38,39,41,43,40,42,44]);
ALF("12.A6.2_3","4.A6.2_3",[1,1,1,2,2,2,3,3,3,4,4,4,5,5,5,6,7,8,9,10,10,
10,11,11,11,12,12,12,13,13,13,14,14,14,15,15,15,16,16,16,17,17,17,18,18,
18,19,19,19,20,20,20,21,21,21,22,22,22]);
ALF("12.A6.2_3","3.A6.2_3",[1,3,2,1,2,3,1,2,3,4,5,6,4,5,6,7,7,7,7,8,9,10,
8,10,9,8,9,10,11,13,12,11,12,13,11,13,12,11,12,13,14,15,16,14,15,16,17,18,
19,17,18,19,20,21,22,20,21,22]);
ALF("12.A6.2_3","A6.2_3",[1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,4,4,4,4,4,
4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8]);
LIBTABLE.LOADSTATUS.ctoalter:="userloaded";
#############################################################################
##
#E
