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"
],
[711374856192000,711374856192000,49816166400,139345920,10321920,5529600,
523069747200,523069747200,1437004800,1437004800,13063680,13063680,466560,
466560,116640,116640,319334400,11612160,967680,92160,30720,12288,6144,4608,
4790016000,4790016000,504000,504000,3000,3000,87091200,4354560,829440,725760,
276480,62208,41472,34560,31104,25920,23040,15552,8640,1944,1728,1296,576,432,
50803200,50803200,1176,1176,80640,3840,2304,256,128,725760,725760,6480,6480,
648,648,1612800,230400,46080,2400,2400,480,100,15840,15840,967680,120960,
69120,46080,17280,13824,5184,3456,3456,2592,2304,1728,1536,1152,576,432,384,
144,72,48,624,624,40320,5376,28,10886400,10886400,129600,129600,19440,19440,
9720,9720,7200,7200,1800,1800,60,60,34,34,3456,1728,216,108,28800,3840,1920,
1280,400,240,211680,211680,6048,6048,2268,2268,588,588,176,1152,1152,288,288,
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,
2615348736000,1916006400,19353600,3870720,24908083200,11612160,322560,184320,
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,
2400,1500,480,100,43545600,362880,69120,15552,9216,7776,5760,5184,4608,4608,
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,
1296,864,384,384,384,192,192,52,20160,448,448,151200,21600,4320,4320,4320,
1620,720,600,540,540,480,300,240,180,60,60,864,288,216,216,960,320,5040,1008,
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],
[,[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,
9,7,10,8,11,9,10,12,11,9,14,14,15,12,13,13,16,49,49,51,51,18,21,18,21,23,58,
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,
16,18,18,18,21,22,25,26,27,25,27,28,29,28,29,31,34,31,39,31,42,34,39,33,33,34,
35,43,37,34,37,36,39,42,43,48,49,49,50,51,52,57,57,58,59,60,62,63,64,64,64,65,
67,66,67,67,71,72,75,79,81,75,85,85,81,81,93,95,95,96,98,101,99,100,101,104,
106,106,105,103,100,109,107,108,110,110,115,115,116,116,119,119,124,125,127,
126,126,129,129,131,131,132,139,139,142,143,145,148,143,145,145,149,149,153,
153,156,156,157,159,159,161,161,167,168,171,171,180,180,185,185,188,188],[1,2,
3,4,5,6,1,2,1,2,1,2,1,2,1,2,17,18,19,20,21,22,23,24,25,26,27,28,29,30,3,4,4,3,
6,4,4,6,3,4,5,3,6,4,6,4,5,6,49,50,51,52,53,54,55,56,57,11,12,11,12,11,12,64,
65,66,67,68,69,70,71,72,17,19,18,20,17,19,18,19,18,17,24,19,21,20,20,19,22,24,
24,23,93,94,95,96,97,25,26,25,26,25,26,25,26,27,28,27,28,29,30,112,113,36,39,
39,36,118,119,120,121,122,123,49,50,49,50,49,50,51,52,132,53,55,53,55,54,55,
139,140,141,142,64,66,64,66,65,67,65,66,68,69,71,72,71,72,157,158,159,160,79,
82,93,94,165,166,95,95,96,170,104,105,104,105,175,176,177,118,118,119,120,123,
128,129,185,140,141,157,158,190,191,192,193,194,195,196,197,198,199,200,201,
190,191,190,191,193,191,192,192,190,191,192,190,190,191,193,191,193,192,191,
192,193,193,224,225,226,227,228,229,230,231,232,233,234,235,236,237,194,194,
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,
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,
55,56,57,58,59,60,61,62,63,3,6,4,3,6,5,6,71,72,73,74,75,76,77,78,79,80,81,82,
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,
--> --------------------
--> maximum size reached
--> --------------------
