Spracherkennung für: .tbl vermutete Sprache: Unknown {[0] [0] [0]} [Methode: Schwerpunktbildung, einfache Gewichte, sechs Dimensionen]
#############################################################################
##
#W ctomaxi7.tbl GAP table library Thomas Breuer
##
## This file contains ordinary character tables of subgroups
## (which are neither ATLAS tables nor tables of Ostermann) of the
## Monster and the Babymonster.
##
#H ctbllib history
#H ---------------
#H $Log: ctomaxi7.tbl,v $
#H Revision 4.36 2012/04/23 16:16:14 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 4.35 2012/01/30 08:31:56 gap
#H removed #H entries from the headers
#H TB
#H
#H Revision 4.34 2011/09/28 13:21:44 gap
#H - removed revision entry and SET_TABLEFILENAME call,
#H - changed the construction of the table of C9Y3.3^5.U4(2)
#H (use `ConstructCentralProduct' not an explicit function)
#H TB
#H
#H Revision 4.33 2010/11/15 16:42:22 gap
#H added comments to various fusions to extensions of 2E6(2)
#H TB
#H
#H Revision 4.32 2010/05/05 13:20:06 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 4.31 2009/11/30 10:06:36 gap
#H added fusion 41:40 -> M
#H TB
#H
#H Revision 4.30 2009/07/29 14:00:25 gap
#H break a too long line
#H TB
#H
#H Revision 4.29 2009/06/15 15:45:18 gap
#H fixed a typo
#H TB
#H
#H Revision 4.28 2009/06/15 15:12:12 gap
#H added tables of 2E6(2)M3, 2E6(2)M4, 2E6(2)M5, 2E6(2)M7, 2E6(2)M8,
#H 2E6(2)M9, and corresponding fusions
#H TB
#H
#H Revision 4.27 2009/05/11 15:31:22 gap
#H added fusion 7^(1+4):(3x2.S7) -> M (determined using the table of MN7)
#H TB
#H
#H Revision 4.26 2009/04/27 08:25:41 gap
#H added fusion 5^(1+4).2^(1+4).A5.4 -> B
#H TB
#H
#H Revision 4.25 2009/04/22 12:39:05 gap
#H added missing maxes of He.2, ON.2, HN.2, Fi24, and B
#H TB
#H
#H Revision 4.24 2009/01/07 10:09:37 gap
#H identified 2.BM9 as 3.Fi24M3 and MN6A, added the corresp. fusions;
#H added (D10xHN).2 = MN5A
#H TB
#H
#H Revision 4.23 2007/07/03 08:44:42 gap
#H added table of (3^2:D8xU4(3).2^2).2 = BM14 (contributed by Eamonn)
#H TB
#H
#H Revision 4.22 2006/06/07 07:54:27 gap
#H unified ConstructMixed and ConstructMGA (for better programmatic access)
#H TB
#H
#H Revision 4.21 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 4.20 2004/03/26 09:47:58 gap
#H added fusion (2^2xF4(2)):2 -> F4(2).2
#H TB
#H
#H Revision 4.19 2003/11/14 08:39:17 gap
#H fixed the name of a new table
#H TB
#H
#H Revision 4.18 2003/11/10 08:05:19 gap
#H added tables of (2^2xF4(2)):2 and 2^2.(U3(3).2xS4)
#H TB
#H
#H Revision 4.17 2003/07/22 15:09:57 gap
#H added some maxes of B
#H TB
#H
#H Revision 4.16 2003/06/20 15:03:05 gap
#H added several fusions
#H TB
#H
#H Revision 4.15 2003/06/10 16:14:19 gap
#H added missing table automorphisms
#H TB
#H
#H Revision 4.14 2003/05/05 14:26:29 gap
#H added tables of 3^6.L4(3).D8 and BN3B (J. An had asked for them)
#H TB
#H
#H Revision 4.13 2003/04/07 17:13:08 gap
#H added table of 3^(3+6):(L3(3)xD8) (J. An was interested in it)
#H TB
#H
#H Revision 4.12 2003/03/31 16:33:22 gap
#H added fusions BN31 -> B, L2(31) -> B,
#H added some names and tables of maxes of 2.B,
#H added table of 2.(S3xFi22.2) < 2.B (J. An had asked for it)
#H TB
#H
#H Revision 4.11 2003/01/29 15:51:51 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 4.10 2002/10/22 12:44:11 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 4.9 2002/07/12 06:45:55 gap
#H further tidying up: removed `irredinfo' stuff, rearranged constructions
#H TB
#H
#H Revision 4.8 2002/07/08 16:06:56 gap
#H changed `construction' component from function (call) to list of function
#H name and arguments
#H TB
#H
#H Revision 4.7 2001/11/06 08:40:46 gap
#H adjustments that make it easier to use the data under GAP 3
#H TB
#H
#H Revision 4.6 2001/10/23 16:13:28 gap
#H changes to give GAP 3 easier access to some tables
#H TB
#H
#H Revision 4.5 2001/05/04 16:48:37 gap
#H first revision for ctbllib
#H
#H
#H tbl history (GAP 4)
#H -------------------
#H (Rev. 4.5 of ctbllib coincides with Rev. 4.4 of tbl in GAP 4)
#H
#H RCS file: /gap/CVS/GAP/4.0/tbl/ctomaxi7.tbl,v
#H Working file: ctomaxi7.tbl
#H head: 4.4
#H branch:
#H locks: strict
#H access list:
#H symbolic names:
#H GAP4R2: 4.3.0.8
#H GAP4R2PRE2: 4.3.0.6
#H GAP4R2PRE1: 4.3.0.4
#H GAP4R1: 4.3.0.2
#H keyword substitution: kv
#H total revisions: 4; selected revisions: 4
#H description:
#H ----------------------------
#H revision 4.4
#H date: 2001/03/12 16:48:29; author: gap; state: Exp; lines: +7480 -2
#H added tables of 2^24.Co1, 2^1+24.Co1, 2^1+24.2.Co1
#H (computed by Simon Norton)
#H
#H TB
#H ----------------------------
#H revision 4.3
#H date: 1999/07/23 13:47:18; author: gap; state: Exp; lines: +112 -2
#H added table of 9A centralizer in the Monster (computed by Simon Norton)
#H
#H TB
#H ----------------------------
#H revision 4.2
#H date: 1999/05/14 08:05:56; author: gap; state: Exp; lines: +4 -3
#H added the tables of some maxes of O8+(3)
#H (yes, these tables are not relevant for the release of GAP 4,
#H but Bob Guralnick had asked for them ...)
#H
#H TB
#H ----------------------------
#H revision 4.1
#H date: 1997/11/25 15:45:22; author: gap; state: Exp;
#H first attempt to link the library of character tables and the
#H library of tables of marks
#H TB
#H ==========================================================================
##
MOT("3^5.U4(2)",
[
"nonsplit extension of 3^5 with U4(2),\n",
"central quotient of the derived subgroup of the 9A centralizer\n",
"in the Monster,\n",
"constructed by Simon Norton, July 1997"
],
[6298560,87480,78732,69984,1728,864,2592,432,324,216,5832,729,5832,729,324,
162,162,243,243,243,144,144,144,24,12,15,15,15,72,72,36,36,18,36,18,27,27,27,
27,27,27,36,36,36,36,36,36],
[,[1,2,3,4,1,4,1,4,3,2,13,14,11,12,15,16,17,18,19,20,5,6,6,7,10,26,27,28,13,
11,15,15,17,15,16,39,40,41,36,37,38,30,30,30,29,29,29],[1,1,1,1,5,5,7,7,7,7,1,
1,1,1,1,3,1,3,3,3,21,21,21,24,24,26,26,26,5,5,5,5,5,7,9,12,12,12,14,14,14,21,
21,21,21,21,21],,[1,2,3,4,5,6,7,8,9,10,13,14,11,12,15,16,17,18,19,20,21,23,22,
24,25,1,2,2,30,29,32,31,33,34,35,39,40,41,36,37,38,45,46,47,42,43,44]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1],[5,5,5,5,-3,-3,1,1,1,1,E(3)-2*E(3)^2,E(3)-2*E(3)^2,
-2*E(3)+E(3)^2,-2*E(3)+E(3)^2,-1,-1,2,2,2,2,1,1,1,-1,-1,0,0,0,E(3)+2*E(3)^2,
2*E(3)+E(3)^2,E(3)-E(3)^2,-E(3)+E(3)^2,0,1,1,-E(3),-E(3),-E(3),-E(3)^2,
-E(3)^2,-E(3)^2,E(3),E(3),E(3),E(3)^2,E(3)^2,E(3)^2],
[GALOIS,[2,2]],[6,6,6,6,-2,-2,2,2,2,2,-3,-3,-3,-3,3,3,0,0,0,0,2,2,2,0,0,1,1,1,
1,1,1,1,-2,-1,-1,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1],[10,10,10,10,2,2,-2,-2,-2,-2,
5*E(3)+2*E(3)^2,5*E(3)+2*E(3)^2,2*E(3)+5*E(3)^2,2*E(3)+5*E(3)^2,1,1,1,1,1,1,2,
2,2,0,0,0,0,0,E(3)-2*E(3)^2,-2*E(3)+E(3)^2,-1,-1,-1,1,1,E(3)^2,E(3)^2,E(3)^2,
E(3),E(3),E(3),-E(3),-E(3),-E(3),-E(3)^2,-E(3)^2,-E(3)^2],
[GALOIS,[5,2]],[15,15,15,15,-1,-1,-1,-1,-1,-1,6,6,6,6,3,3,0,0,0,0,3,3,3,-1,-1,
0,0,0,2,2,-1,-1,2,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0],[15,15,15,15,7,7,3,3,3,3,-3,
-3,-3,-3,0,0,3,3,3,3,-1,-1,-1,1,1,0,0,0,1,1,-2,-2,1,0,0,0,0,0,0,0,0,-1,-1,-1,
-1,-1,-1],[20,20,20,20,4,4,4,4,4,4,2,2,2,2,5,5,-1,-1,-1,-1,0,0,0,0,0,0,0,0,-2,
-2,1,1,1,1,1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0],[24,24,24,24,8,8,0,0,0,0,6,6,6,6,
0,0,3,3,3,3,0,0,0,0,0,-1,-1,-1,2,2,2,2,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[30,30,
30,30,-10,-10,2,2,2,2,3,3,3,3,3,3,3,3,3,3,-2,-2,-2,0,0,0,0,0,-1,-1,-1,-1,-1,
-1,-1,0,0,0,0,0,0,1,1,1,1,1,1],[30,30,30,30,6,6,2,2,2,2,6*E(3)-3*E(3)^2,
6*E(3)-3*E(3)^2,-3*E(3)+6*E(3)^2,-3*E(3)+6*E(3)^2,-3,-3,0,0,0,0,2,2,2,0,0,0,0,
0,2*E(3)+E(3)^2,E(3)+2*E(3)^2,-E(3)+E(3)^2,E(3)-E(3)^2,0,-1,-1,0,0,0,0,0,0,
-E(3)^2,-E(3)^2,-E(3)^2,-E(3),-E(3),-E(3)],
[GALOIS,[12,2]],[40,40,40,40,-8,-8,0,0,0,0,2*E(3)+8*E(3)^2,2*E(3)+8*E(3)^2,
8*E(3)+2*E(3)^2,8*E(3)+2*E(3)^2,-2,-2,1,1,1,1,0,0,0,0,0,0,0,0,-2*E(3),
-2*E(3)^2,-2*E(3),-2*E(3)^2,1,0,0,E(3)^2,E(3)^2,E(3)^2,E(3),E(3),E(3),0,0,0,0,
0,0],
[GALOIS,[14,2]],[45,45,45,45,-3,-3,-3,-3,-3,-3,-9*E(3),-9*E(3),-9*E(3)^2,
-9*E(3)^2,0,0,0,0,0,0,1,1,1,1,1,0,0,0,3*E(3),3*E(3)^2,0,0,0,0,0,0,0,0,0,0,0,
E(3),E(3),E(3),E(3)^2,E(3)^2,E(3)^2],
[GALOIS,[16,2]],[60,60,60,60,-4,-4,4,4,4,4,6,6,6,6,-3,-3,-3,-3,-3,-3,0,0,0,0,
0,0,0,0,2,2,-1,-1,-1,1,1,0,0,0,0,0,0,0,0,0,0,0,0],[64,64,64,64,0,0,0,0,0,0,-8,
-8,-8,-8,4,4,-2,-2,-2,-2,0,0,0,0,0,-1,-1,-1,0,0,0,0,0,0,0,1,1,1,1,1,1,0,0,0,0,
0,0],[81,81,81,81,9,9,-3,-3,-3,-3,0,0,0,0,0,0,0,0,0,0,-3,-3,-3,-1,-1,1,1,1,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[216,27,-27,0,0,0,-12,0,-3,3,0,0,0,0,0,0,
0,0,0,0,0,0,0,2,-1,1,-E(15)^7-E(15)^11-E(15)^13-E(15)^14,
-E(15)-E(15)^2-E(15)^4-E(15)^8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[21,7]],[432,54,-54,0,0,0,24,0,6,-6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,
-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[648,81,-81,0,0,0,12,0,3,-3,0,0,
0,0,0,0,0,0,0,0,0,0,0,2,-1,-2,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[
1080,135,-135,0,0,0,-12,0,-3,3,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,1,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0],[80,-10,-1,8,0,0,8,-4,-1,2,8,-1,8,-1,2,-1,2,5,-4,
-4,0,0,0,0,0,0,0,0,0,0,0,0,0,2,-1,2,-1,-1,2,-1,-1,0,0,0,0,0,0],[80,-10,-1,8,0,
0,8,-4,-1,2,8,-1,8,-1,2,-1,2,-4,5,-4,0,0,0,0,0,0,0,0,0,0,0,0,0,2,-1,-1,2,-1,
-1,2,-1,0,0,0,0,0,0],[80,-10,-1,8,0,0,8,-4,-1,2,8,-1,8,-1,2,-1,2,-4,-4,5,0,0,
0,0,0,0,0,0,0,0,0,0,0,2,-1,-1,-1,2,-1,-1,2,0,0,0,0,0,0],[240,-30,-3,24,0,0,-8,
4,1,-2,24,-3,24,-3,6,-3,6,-3,-3,-3,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,1,0,0,0,0,0,0,
0,0,0,0,0,0],[320,-40,-4,32,0,0,0,0,0,0,16*E(3)-8*E(3)^2,-2*E(3)+E(3)^2,
-8*E(3)+16*E(3)^2,E(3)-2*E(3)^2,-4,2,2,5,-4,-4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
2*E(3)^2,-E(3)^2,-E(3)^2,2*E(3),-E(3),-E(3),0,0,0,0,0,0],[320,-40,-4,32,0,0,0,
0,0,0,16*E(3)-8*E(3)^2,-2*E(3)+E(3)^2,-8*E(3)+16*E(3)^2,E(3)-2*E(3)^2,-4,2,2,
-4,5,-4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-E(3)^2,2*E(3)^2,-E(3)^2,-E(3),2*E(3),
-E(3),0,0,0,0,0,0],[320,-40,-4,32,0,0,0,0,0,0,16*E(3)-8*E(3)^2,-2*E(3)+E(3)^2,
-8*E(3)+16*E(3)^2,E(3)-2*E(3)^2,-4,2,2,-4,-4,5,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
-E(3)^2,-E(3)^2,2*E(3)^2,-E(3),-E(3),2*E(3),0,0,0,0,0,0],
[GALOIS,[30,2]],
[GALOIS,[31,2]],
[GALOIS,[32,2]],[480,-60,-6,48,0,0,-16,8,2,-4,-24,3,-24,3,6,-3,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,2,-1,0,0,0,0,0,0,0,0,0,0,0,0],[480,-60,-6,48,0,0,16,-8,-2,
4,-24,3,-24,3,6,-3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,1,0,0,0,0,0,0,0,0,0,0,
0,0],[960,-120,-12,96,0,0,0,0,0,0,24,-3,24,-3,0,0,-6,3,3,3,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[270,0,27,-27,6,-3,18,9,-9,0,0,0,0,0,0,0,
0,0,0,0,6,-3,-3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[270,0,27,
-27,6,-3,-6,-3,3,0,0,0,0,0,0,0,0,0,0,0,2,3*E(3)-E(3)^2,-E(3)+3*E(3)^2,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,2*E(3),2*E(3)^2,2,2*E(3)^2,2*E(3)],[270,0,27,
-27,6,-3,-6,-3,3,0,0,0,0,0,0,0,0,0,0,0,2,3*E(3)-E(3)^2,-E(3)+3*E(3)^2,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,2*E(3)^2,2,2*E(3),2*E(3),2,2*E(3)^2],[270,0,27,
-27,6,-3,-6,-3,3,0,0,0,0,0,0,0,0,0,0,0,2,3*E(3)-E(3)^2,-E(3)+3*E(3)^2,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,2*E(3),2*E(3)^2,2,2*E(3)^2,2*E(3),2],
[GALOIS,[40,2]],
[GALOIS,[41,2]],
[GALOIS,[42,2]],[810,0,81,-81,18,-9,6,3,-3,0,0,0,0,0,0,0,0,0,0,0,-6,3,3,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[1080,0,108,-108,-24,12,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]],
[(27,28),(19,20)(37,38)(40,41),(18,19)(36,37)(39,40),(11,13)(12,14)(22,23)(27,
28)(29,30)(31,32)(36,39)(37,40)(38,41)(42,45)(43,46)(44,47),(42,43,44)(45,46,
47),(22,23)(43,44)(46,47)]);
ARC("3^5.U4(2)","projectives",["3.3^5.U4(2)",[[27,9,0,0,3,0,7,4,-2,1,0,0,0,0,
3,-3,0,0,0,0,3,0,0,1,1,2,-1,-1,0,0,E(3)-E(3)^2,-E(3)+E(3)^2,0,1,1,0,0,0,0,0,0,
0,0,0,0,0,0],[81,27,0,0,9,0,-3,0,6,3,0,0,0,0,0,0,0,0,0,0,-3,0,0,-1,-1,1,
-E(15)^7-E(15)^11-E(15)^13-E(15)^14,-E(15)-E(15)^2-E(15)^4-E(15)^8,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[2,7]],[108,36,0,0,12,0,4,4,4,4,0,0,0,0,3,-3,0,0,0,0,0,0,0,0,0,-2,1,1,
0,0,E(3)-E(3)^2,-E(3)+E(3)^2,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0],
[135,45,0,0,15,0,11,8,2,5,0,0,0,0,-3,3,0,0,0,0,3,0,0,1,1,0,0,0,
0,0,-E(3)+E(3)^2,E(3)-E(3)^2,0,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0],
[135,45,0,0,-9,0,7,4,-2,1,0,0,0,0,6,-6,0,0,0,0,3,0,0,-1,-1,0,0,
0,0,0,0,0,0,-2,-2,0,0,0,0,0,0,0,0,0,0,0,0],[135,45,0,0,-9,0,7,4,-2,1,0,0,0,0,
-3,3,0,0,0,0,3,0,0,-1,-1,0,0,0,0,0,3,3,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0],[135,45,
0,0,-9,0,7,4,-2,1,0,0,0,0,-3,3,0,0,0,0,3,0,0,-1,-1,0,0,0,0,0,-3,-3,0,1,1,0,0,
0,0,0,0,0,0,0,0,0,0],[270,90,0,0,6,0,-14,-8,4,-2,0,0,0,0,3,-3,0,0,0,0,6,0,0,0,
0,0,0,0,0,0,-E(3)+E(3)^2,E(3)-E(3)^2,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0],
[270,90,0,0,6,0,10,4,-8,-2,0,0,0,0,3,-3,0,0,0,0,-6,0,0,0,0,0,
0,0,0,0,-E(3)+E(3)^2,E(3)-E(3)^2,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0],
[405,135,0,0,-27,0,-3,0,6,3,0,0,0,0,0,0,0,0,0,0,-3,0,0,1,1,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[540,180,0,0,12,0,-4,-4,-4,-4,0,0,
0,0,-3,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,E(3)-E(3)^2,-E(3)+E(3)^2,0,-1,-1,0,0,0,0,
0,0,0,0,0,0,0,0],
[216,-9,0,0,0,0,20,-4,2,-1,0,0,0,0,6,3,0,0,0,0,0,0,0,2,-1,1,1,
1,0,0,0,0,0,2,-1,0,0,0,0,0,0,0,0,0,0,0,0],[216,-9,0,0,0,0,4,4,4,-5,0,0,0,0,6,
3,0,0,0,0,0,0,0,-2,1,1,1,1,0,0,0,0,0,-2,1,0,0,0,0,0,0,0,0,0,0,0,0],[864,-36,0,
0,0,0,16,-8,-2,4,0,0,0,0,6,3,0,0,0,0,0,0,0,0,0,-1,-1,-1,0,0,0,0,0,-2,1,0,0,0,
0,0,0,0,0,0,0,0,0],[864,-36,0,0,0,0,-16,8,2,-4,0,0,0,0,6,3,0,0,0,0,0,0,0,0,0,
-1,-1,-1,0,0,0,0,0,2,-1,0,0,0,0,0,0,0,0,0,0,0,0],[1080,-45,0,0,0,0,4,4,4,-5,0,
0,0,0,-6,-3,0,0,0,0,0,0,0,2,-1,0,0,0,0,0,0,0,0,-2,1,0,0,0,0,0,0,0,0,0,0,0,0],[
1080,-45,0,0,0,0,20,-4,2,-1,0,0,0,0,-6,-3,0,0,0,0,0,0,0,-2,1,0,0,0,0,0,0,0,0,
2,-1,0,0,0,0,0,0,0,0,0,0,0,0],[1296,-54,0,0,0,0,-24,0,-6,6,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]],]);
ALF("3^5.U4(2)","U4(2)",[1,1,1,1,2,2,3,3,3,3,4,4,5,5,6,6,7,7,7,7,8,8,8,9,
9,10,10,10,11,12,13,14,15,16,16,17,17,17,18,18,18,19,19,19,20,20,20]);
MOT("3.3^5.U4(2)",
[
"derived subgroup of the 9A centralizer in the Monster,\n",
"constructed by Simon Norton, July 1997"
],
[18895680,18895680,18895680,262440,262440,262440,78732,69984,5184,5184,5184,
864,7776,7776,7776,1296,1296,1296,972,972,972,648,648,648,5832,729,5832,729,
972,972,972,486,486,486,162,243,243,243,432,432,432,144,144,72,72,72,36,36,36,
45,45,45,45,45,45,45,45,45,72,72,108,108,108,108,108,108,18,108,108,108,54,54,
54,27,27,27,27,27,27,36,36,36,36,36,36],
[,[1,3,2,4,6,5,7,8,1,3,2,8,1,3,2,8,8,8,7,7,7,4,6,5,27,28,25,26,29,31,30,32,34,
33,35,36,37,38,9,11,10,12,12,13,15,14,22,24,23,50,52,51,53,55,54,56,58,57,27,
25,29,31,30,29,31,30,35,29,31,30,32,34,33,77,78,79,74,75,76,60,60,60,59,59,
59],[1,1,1,1,1,1,1,1,9,9,9,9,13,13,13,13,13,13,13,13,13,13,13,13,3,3,2,2,1,1,
1,7,7,7,1,7,7,7,39,39,39,39,39,44,44,44,44,44,44,50,50,50,50,50,50,50,50,50,
11,10,9,9,9,9,9,9,9,13,13,13,19,19,19,26,26,26,28,28,28,41,41,41,40,40,40],,[
1,3,2,4,6,5,7,8,9,11,10,12,13,15,14,16,18,17,19,21,20,22,24,23,27,28,25,26,29,
31,30,32,34,33,35,36,37,38,39,41,40,43,42,44,46,45,47,49,48,1,3,2,4,6,5,4,6,5,
60,59,64,66,65,61,63,62,67,68,70,69,71,73,72,77,78,79,74,75,76,83,84,85,80,81,
82]],
0,
[(53,56)(54,57)(55,58),(37,38)(75,76)(78,79),(36,37)(74,75)(77,78),(2,3)(5,6)
(10,11)(14,15)(17,18)(20,21)(23,24)(25,27)(26,28)(30,31)(33,34)(40,41)(42,43)
(45,46)(48,49)(51,52)(53,56)(54,58)(55,57)(59,60)(61,64)(62,66)(63,65)(69,70)
(72,73)(74,77)(75,78)(76,79)(80,83)(81,84)(82,85),(80,81,82)(83,84,85),(42,43)
(81,82)(84,85)],
["ConstructProj",[["3^5.U4(2)",[]],,["3.3^5.U4(2)",[-1,-1,-1,-1,-1,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1]]]]);
ALF("3.3^5.U4(2)","3^5.U4(2)",[1,1,1,2,2,2,3,4,5,5,5,6,7,7,7,8,8,8,9,9,9,
10,10,10,11,12,13,14,15,15,15,16,16,16,17,18,19,20,21,21,21,22,23,24,24,
24,25,25,25,26,26,26,27,27,27,28,28,28,29,30,31,31,31,32,32,32,33,34,34,
34,35,35,35,36,37,38,39,40,41,42,43,44,45,46,47]);
ALF("3.3^5.U4(2)","U4(2)",[1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,
3,4,4,5,5,6,6,6,6,6,6,7,7,7,7,8,8,8,8,8,9,9,9,9,9,9,10,10,10,10,10,10,10,
10,10,11,12,13,13,13,14,14,14,15,16,16,16,16,16,16,17,17,17,18,18,18,19,
19,19,20,20,20]);
MOT("C9Y3.3^5.U4(2)",
[
"9A centralizer in the sporadic simple Monster group M,\n",
"central product of a cyclic group of order 9 with 3.3^5.U4(2),\n",
"constructed by Simon Norton, July 1997"
],
0,
0,
0,
[( 37, 38)( 75, 76)( 78, 79)(122,123)(160,161)(163,164)(207,208)(245,246)(248,
249),( 36, 38, 37)( 74, 76, 75)( 77, 79, 78)(121,123,122)(159,161,160)(162,
164,163)(206,208,207)(244,246,245)(247,249,248),( 42, 43)( 81, 82)( 84, 85)
(127,128)(166,167)(169,170)(212,213)(251,252)(254,255),( 80, 81, 82)( 83, 84,
85)(165,166,167)(168,169,170)(250,251,252)(253,254,255),( 86, 87, 88)( 89,
90, 91)( 94, 95, 96)( 98, 99,100)(101,102,103)(104,105,106)(107,108,109)(114,
115,116)(117,118,119)(124,125,126)(129,130,131)(132,133,134)(135,136,137)(138,
139,140)(141,142,143)(146,147,148)(149,150,151)(153,154,155)(156,157,158)(171,
173,172)(174,176,175)(179,181,180)(183,185,184)(186,188,187)(189,191,190)(192,
194,193)(199,201,200)(202,204,203)(209,211,210)(214,216,215)(217,219,218)(220,
222,221)(223,225,224)(226,228,227)(231,233,232)(234,236,235)(238,240,239)(241,
243,242),( 53, 56)( 54, 57)( 55, 58)(138,141)(139,142)(140,143)(223,226)(224,
227)(225,228),( 2, 3)( 5, 6)( 10, 11)( 14, 15)( 17, 18)( 20, 21)( 23, 24)
( 25, 27)( 26, 28)( 30, 31)( 33, 34)( 40, 41)( 45, 46)( 48, 49)( 51, 52)( 54,
55)( 57, 58)( 59, 60)( 61, 64)( 62, 66)( 63, 65)( 69, 70)( 72, 73)( 74, 77)
( 75, 78)( 76, 79)( 80, 83)( 81, 85)( 82, 84)( 86,171, 88,172, 87,173)( 89,
174, 91,175, 90,176)( 92,177)( 93,178)( 94,179, 96,180, 95,181)( 97,182)( 98,
183,100,184, 99,185)(101,186,103,187,102,188)(104,189,106,190,105,191)(107,
192,109,193,108,194)(110,197)(111,198)(112,195)(113,196)(114,199,116,200,115,
201)(117,202,119,203,118,204)(120,205)(121,206)(122,207)(123,208)(124,209,126,
210,125,211)(127,212)(128,213)(129,214,131,215,130,216)(132,217,134,218,133,
219)(135,220,137,221,136,222)(138,223,140,224,139,225)(141,226,143,227,142,
228)(144,230)(145,229)(146,234,148,235,147,236)(149,231,151,232,150,233)(152,
237)(153,238,155,239,154,240)(156,241,158,242,157,243)(159,247)(160,248)(161,
249)(162,244)(163,245)(164,246)(165,253)(166,255)(167,254)(168,250)(169,252)
(170,251)],
["ConstructCentralProduct",[["Cyclic",9],["3.3^5.U4(2)"]],[1,257,513],(),
(48,49,51,55,63,79,157,228,239,52,57,67,133,134,136,140,148,164,242,58,69,137,
142,152,218,219,221,225,233,249,72,143,154,222,227,237)(50,53,59,71,141,150,
168,250,74,147,162,238)(54,61,75,149,166,246,66,85,169,252,78,155,224,231,245,
64,81,161,236,255,84,167,248,70,139,146,160,234,251,76,151,170,254,82,163,240)
(56,65,83,165,244,62,77,153,220,223,229,241)(60,73,145,158,230,243)(68,135,
138,144,156,226,235,253,80,159,232,247)]);
ALF("C9Y3.3^5.U4(2)","U4(2)",[1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,
3,3,4,4,5,5,6,6,6,6,6,6,7,7,7,7,8,8,8,8,8,9,9,9,9,9,9,10,10,10,10,10,10,
10,10,10,11,12,13,13,13,14,14,14,15,16,16,16,16,16,16,17,17,17,18,18,18,
19,19,19,20,20,20,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,4,4,5,5,
6,6,6,6,6,6,7,7,7,7,8,8,8,8,8,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,11,
12,13,13,13,14,14,14,15,16,16,16,16,16,16,17,17,17,18,18,18,19,19,19,20,
20,20,1,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,4,4,5,5,6,6,6,6,6,6,
7,7,7,7,8,8,8,8,8,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,11,12,13,13,13,
14,14,14,15,16,16,16,16,16,16,17,17,17,18,18,18,19,19,19,20,20,20]);
ALN("C9Y3.3^5.U4(2)",["MC9A"]);
MOT("2^24.Co1",
[
"central factor group of the maximal subgroup 2^(1+24).Co1 of the Monster,\n",
"constructed by Simon Norton, Dec. 2000"
],
[69755919563168164085760000,709767191322427392000,8412055600858398720,
8317584273309696000,5844591496396800,48704929136640,43293270343680,
2705829396480,190253629440,180388626432,8244323942400,2013265920,1594506608640
,1594506608640,6039797760,2013265920,1610612736,778567680,1345036492800,
240789749760,637009920,141557760,119439360,806215680,29859840,22394880,
139345920,1161216,1032192,95126814720,792723456,704643072,301989888,100663296,
12582912,8388608,1572864,754974720,125829120,75497472,50331648,23592960,
6291456,2097152,1572864,75497472,12582912,8388608,1572864,1572864,524288,
3096576,49152,983040,983040,81920,65536,65536,49152,3024000,9216000,153600,
122880,76800,240000,48000,24000,9953280,483840,9953280,368640,276480,9953280,
368640,276480,5308416,884736,589824,147456,55296,49152,248832,82944,20736,
221184,221184,18432,12288,6912,23040,1536,9216,9216,1536,1152,17640,75264,
10752,10752,3584,2688,1474560,98304,98304,98304,16384,12288,98304,32768,8192,
32768,32768,16384,8192,4096,49152,49152,16384,16384,12288,12288,4096,4096,2048
,12288,4096,1024,1944,1944,648,7776,1296,864,9600,1200,19200,1280,9600,1920,
960,9600,1920,960,2560,2560,1280,640,320,1056,352,352,352,176,138240,9216,4608
,10368,3456,27648,4608,3072,864,9216,3072,768,4608,4608,1536,1536,576,4608,
4608,2304,768,768,4608,1536,768,768,1152,384,288,96,192,192,96,156,168,896,896
,896,896,448,448,448,448,224,5400,900,180,1440,480,480,480,240,120,120,120,120
,256,256,128,256,256,128,216,216,72,216,72,480,160,160,80,80,80,80,80,252,63,
84,84,84,84,88,88,88,88,92,92,92,92,92,92,92,92,576,192,576,192,96,192,192,96,
96,96,96,96,52,112,112,112,112,28,120,60,60,120,120,120,120,120,120,120,120,33
,35,36,39,39,40,84,60],
[,[1,1,1,1,1,1,1,3,2,3,1,3,3,1,2,3,3,4,19,20,20,20,20,24,24,24,27,27,27,5,6,7,
5,7,6,7,10,7,5,5,7,6,10,10,8,5,7,7,8,10,10,11,12,13,14,15,17,17,16,60,61,61,61
,61,65,65,65,19,19,20,22,21,24,24,24,20,20,20,22,21,22,24,24,25,22,20,21,22,23
,27,29,29,27,29,28,96,97,97,97,97,97,30,32,30,32,32,31,33,34,35,33,34,34,35,36
,41,38,38,41,40,39,44,44,43,46,48,51,128,129,129,131,131,131,60,60,61,63,61,63
,62,65,65,65,63,61,63,62,64,149,149,149,149,149,68,68,68,82,83,76,77,78,69,76,
78,81,74,73,74,73,75,78,76,77,79,81,76,78,79,81,82,83,90,91,92,93,94,187,96,97
,97,97,97,98,99,98,99,100,198,199,200,201,201,201,201,201,206,206,206,206,108,
109,110,111,112,114,128,129,129,131,133,134,144,145,147,142,141,143,143,229,
230,231,231,231,231,150,149,152,151,239,239,239,239,243,243,243,243,154,155,
159,161,156,159,161,160,168,166,167,169,187,189,190,191,192,188,198,199,200,
201,202,203,204,206,206,206,206,276,277,216,279,280,221,229,265],[1,2,3,4,5,6,
7,8,9,10,11,12,13,14,15,16,17,18,1,1,2,3,4,1,2,4,1,4,3,30,31,32,33,34,35,36,37
,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
,64,65,66,67,5,11,5,8,9,5,7,6,5,6,7,8,9,10,5,6,9,13,14,15,17,18,11,12,13,14,16
,18,96,97,99,98,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,
115,116,117,118,119,120,121,122,123,124,125,126,127,24,24,26,24,26,25,134,135,
136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,30,33,
46,30,31,30,31,32,52,33,34,37,38,40,41,39,42,38,40,42,45,43,46,47,49,50,33,35,
52,53,54,55,59,187,188,189,190,192,191,194,193,196,195,197,60,61,60,61,62,63,
63,64,65,67,66,66,210,211,212,213,214,215,82,82,83,82,84,221,222,223,224,225,
226,227,228,96,96,97,101,99,98,235,236,237,238,239,240,241,242,243,244,245,246
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136,135,138,140,139,139,141,143,142,142,149,277,157,187,187,281,188,221],,[1,2
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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,
57,58,59,1,1,2,3,4,1,2,4,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85
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128,129,130,131,132,133,5,11,11,12,5,8,9,5,7,6,13,14,16,15,18,149,150,151,152,
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,
192,191,194,193,196,195,197,19,19,27,20,21,22,22,23,24,26,25,25,210,211,212,
213,214,215,216,217,218,219,220,30,54,55,56,38,39,42,42,229,230,231,232,234,
233,235,236,237,238,243,244,245,246,239,240,241,242,247,248,249,250,251,252,
253,254,255,256,257,258,259,260,261,263,262,264,68,69,90,70,72,71,71,73,75,74,
74,276,96,278,279,280,102,282,154],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17
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156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,
175,176,177,178,179,180,181,182,183,184,185,186,187,11,5,6,7,7,8,8,10,10,9,198
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218,219,220,221,222,223,224,225,226,227,228,19,20,27,28,29,29,235,236,238,237,
243,244,245,246,239,240,241,242,247,248,249,250,251,252,253,254,255,256,257,
258,259,30,31,32,32,52,265,266,267,268,269,271,270,272,273,275,274,276,60,278,
280,279,281,69,283],,,,[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,
119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,
138,139,140,141,142,143,144,145,146,147,148,1,3,4,4,2,154,155,156,157,158,159,
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,
198,199,200,201,202,204,203,205,206,207,209,208,210,211,212,213,214,215,216,
217,218,219,220,221,222,223,224,225,226,228,227,229,230,231,232,233,234,13,14,
18,18,243,244,245,246,239,240,241,242,247,248,249,250,251,252,253,254,255,256,
257,258,259,260,261,262,263,264,265,266,267,268,269,271,270,272,273,275,274,19
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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,
97,99,98,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,
117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,
136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,152,151,153,154,
155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,
174,175,176,177,178,179,180,181,182,183,184,185,186,1,188,189,190,192,191,194,
193,196,195,197,198,199,200,201,202,204,203,205,206,207,209,208,210,211,212,
213,214,215,216,217,218,219,220,221,222,223,224,225,226,228,227,229,230,231,
232,234,233,235,236,238,237,239,240,241,242,243,244,245,246,247,248,249,250,
251,252,253,254,255,256,257,258,11,260,261,263,262,264,265,266,267,268,269,271
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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
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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,
224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,1,2,4,3,1,2,4,3,
247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,
266,267,268,269,270,271,272,273,274,275,276,277,278,280,279,281,282,283]],
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53,53,53,54,54,54,54,55,55,56,56,57,57,57,58,59,60,60,60,60,60,60,60,60,
60,61,62,63,64,64,64,64,64,65,65,65,65,66,66,66,67,67,67,68,69,69,70,70,
71,72,72,72,73,73,73,73,74,75,76,76,76,76,77,77,77,77,78,78,78,78,79,79,
79,79,80,81,82,82,83,84,84,84,85,85,85,85,86,87,87,87,87,88,89,90,91,92,
92,92,92,93,93,93,93,94,95,96,97,98,99,100,101]);
MOT("2^1+24.Co1",
[
"maximal subgroup and 2B centralizer in the Monster,\n",
"constructed by Simon Norton, Dec. 2000"
],
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160,80,160,160,80,80,80,504,504,126,126,168,168,84,84,84,176,176,88,88,88,184,
184,92,92,92,184,184,92,92,92,576,384,384,576,192,96,192,192,96,192,192,96,96,
96,52,224,224,112,112,112,56,56,240,240,60,60,240,240,120,120,120,240,240,120,
120,120,66,66,70,70,72,72,78,78,78,78,80,80,84,120,120],
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145,122,123,125,135,136,137,140,141,313,314,315,316,318,317,319,320,157,158,
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44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,1,2,1,
2,3,4,5,2,1,3,5,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99
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7,13,13,14,7,6,10,11,7,6,9,8,15,16,18,17,20,175,176,177,178,179,180,181,182,
183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,
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26,27,29,28,31,30,30,250,251,252,253,254,255,256,257,258,259,260,261,262,263,
264,36,37,62,63,64,45,46,47,50,50,275,276,277,278,279,280,281,283,282,284,285,
286,287,288,294,295,296,297,298,289,290,291,292,293,299,300,301,302,303,304,
305,306,307,308,309,310,311,312,313,314,315,316,318,317,319,320,79,80,81,106,
83,82,85,84,84,87,86,89,88,88,335,336,112,113,339,340,341,342,343,344,120,120,
347,181,182],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,
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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,
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242,244,245,246,247,249,248,250,251,252,253,254,255,256,257,258,259,260,261,
262,263,264,265,266,267,268,269,270,271,272,273,274,21,22,23,24,32,33,34,35,35
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303,304,305,306,307,308,309,310,311,312,313,36,37,38,39,39,60,60,321,322,323,
324,325,326,327,329,328,330,331,332,334,333,335,336,68,69,339,340,343,344,341,
342,345,346,81,348,349],,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20
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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,
156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,1,
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299,300,301,302,303,304,305,306,307,308,309,310,311,312,13,314,315,316,318,317
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338,339,340,21,22,21,22,346,345,347,348,349],,,,,,,,,,[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
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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,
264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,
283,284,285,286,287,288,1,2,3,5,4,1,2,3,5,4,299,300,301,302,303,304,305,306,
307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,
326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,343,344,341,342,
345,346,347,348,349]],
0,
[(116,117)(226,227)(228,229)(230,231)(282,283)(317,318),(178,179)(287,288),
(242,243)(328,329),(248,249)(333,334),(273,274),(284,285),(319,320),
(341,343)(342,344),(345,346),(289,294)(290,295)(291,296)(292,297)(293,298)],
["ConstructProj",[["2^24.Co1",[]],["2^1+24.Co1",[]]]]);
ARC("2^1+24.Co1","projectives",["2^1+24.2.Co1",[[24,24,24,24,24,8,8,8,8,8,8,8,
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--> --------------------
--> maximum size reached
--> --------------------
