# This file was created automatically, do not edit!
#############################################################################
##
#W sporsolv.tst GAP 4 package CTblLib Thomas Breuer
##
## This file contains the GAP code of examples in the package
## documentation files.
##
## In order to run the tests, one starts GAP from the 'tst' subdirectory
## of the 'pkg/ctbllib' directory, and calls 'Test( "sporsolv.tst" );'.
##
gap> LoadPackage( "CTblLib", false );
true
gap> save:= SizeScreen();;
gap> SizeScreen( [ 72 ] );;
gap> START_TEST( "sporsolv.tst" );
##
gap> if IsBound( BrowseData ) then
> data:= BrowseData.defaults.dynamic.replayDefaults;
> oldinterval:= data.replayInterval;
> data.replayInterval:= 1;
> fi;
## doc2/sporsolv.xml (963-968)
gap> LoadPackage( "CTblLib", "1.2", false );
true
gap> LoadPackage( "TomLib", false );
true
## doc2/sporsolv.xml (977-979)
gap> MaxSolv:= rec();;
## doc2/sporsolv.xml (1015-1049)
gap> MaximalSolvableSubgroupInfoFromTom:= function( name )
> local tom, # table of marks for `name'
> n, # maximal order of a solvable subgroup
> maxsubs, # numbers of the classes of subgroups of order `n'
> orders, # list of orders of the classes of subgroups
> i, # loop over the classes of subgroups
> maxes, # list of positions of the classes of max. subgroups
> subs, # `SubsTom' value
> cont; # list of list of positions of max. subgroups
>
> tom:= TableOfMarks( name );
> if tom = fail then
> return false;
> fi;
> n:= 1;
> maxsubs:= [];
> orders:= OrdersTom( tom );
> for i in [ 1 .. Length( orders ) ] do
> if IsSolvableTom( tom, i ) then
> if orders[i] = n then
> Add( maxsubs, i );
> elif orders[i] > n then
> n:= orders[i];
> maxsubs:= [ i ];
> fi;
> fi;
> od;
> maxes:= MaximalSubgroupsTom( tom )[1];
> subs:= SubsTom( tom );
> cont:= List( maxsubs, j -> Filtered( maxes, i -> j in subs[i] ) );
>
> return [ name, n, List( cont, l -> orders{ l } ) ];
> end;;
## doc2/sporsolv.xml (1117-1153)
gap> SolvableSubgroupInfoFromCharacterTable:= function( tblM, minorder )
> local maxindex, # index of subgroups of order `minorder'
> N, # class positions describing a solvable normal subgroup
> fact, # character table of the factor by `N'
> classes, # class sizes in `fact'
> nsg, # list of class positions of normal subgroups
> i; # loop over the possible indices
>
> maxindex:= Int( Size( tblM ) / minorder );
> if maxindex = 0 then
> return false;
> elif IsSolvableCharacterTable( tblM ) then
> return [ tblM, maxindex, 1 ];
> elif maxindex < 5 then
> return false;
> fi;
>
> N:= [ 1 ];
> fact:= tblM;
> repeat
> fact:= fact / N;
> classes:= SizesConjugacyClasses( fact );
> nsg:= Difference( ClassPositionsOfNormalSubgroups( fact ), [ [ 1 ] ] );
> N:= First( nsg, x -> IsPrimePowerInt( Sum( classes{ x } ) ) );
> until N = fail;
>
> for i in Filtered( DivisorsInt( Size( fact ) ),
> d -> 5 <= d and d <= maxindex ) do
> if Length( PermChars( fact, rec( torso:= [ i ] ) ) ) > 0 then
> return [ tblM, maxindex, i ];
> fi;
> od;
>
> return false;
> end;;
## doc2/sporsolv.xml (1170-1194)
gap> solvinfo:= Filtered( List(
> AllCharacterTableNames( IsSporadicSimple, true,
> IsDuplicateTable, false ),
> MaximalSolvableSubgroupInfoFromTom ), x -> x <> false );;
gap> for entry in solvinfo do
> MaxSolv.( entry[1] ):= entry[2];
> od;
gap> for entry in solvinfo do
> Print( String( entry[1], 5 ), String( entry[2], 7 ),
> String( entry[3], 28 ), "\n" );
> od;
Co3 69984 [ [ 3849120, 699840 ] ]
HS 2000 [ [ 252000, 252000 ] ]
He 13824 [ [ 138240 ], [ 138240 ] ]
J1 168 [ [ 168 ] ]
J2 1152 [ [ 1152 ] ]
J3 1944 [ [ 1944 ] ]
M11 144 [ [ 144 ] ]
M12 432 [ [ 432 ], [ 432 ] ]
M22 576 [ [ 5760 ] ]
M23 1152 [ [ 40320, 5760 ] ]
M24 13824 [ [ 138240 ] ]
McL 11664 [ [ 3265920, 58320 ] ]
## doc2/sporsolv.xml (1285-1303)
gap> MaxSolv.( "HS.2" ):= 2 * MaxSolv.( "HS" );;
gap> n:= 2^(4+4) * ( 6 * 6 ) * 2; MaxSolv.( "He.2" ):= n;;
18432
gap> List( [ Size( CharacterTable( "S4(4).4" ) ),
> Factorial( 5 )^2 * 2,
> Size( CharacterTable( "2^2.L3(4).D12" ) ),
> 2^7 * Size( CharacterTable( "L3(2)" ) ) * 2,
> 7^2 * 2 * Size( CharacterTable( "L2(7)" ) ) * 2,
> 3 * Factorial( 7 ) * 2 ], i -> Int( i / n ) );
[ 212, 1, 52, 2, 1, 1 ]
gap> MaxSolv.( "J2.2" ):= 2 * MaxSolv.( "J2" );;
gap> MaxSolv.( "J3.2" ):= 2 * MaxSolv.( "J3" );;
gap> info:= MaximalSolvableSubgroupInfoFromTom( "M12.2" );
[ "M12.2", 432, [ [ 95040 ] ] ]
gap> MaxSolv.( "M12.2" ):= info[2];;
gap> MaxSolv.( "M22.2" ):= 2 * MaxSolv.( "M22" );;
gap> MaxSolv.( "McL.2" ):= 2 * MaxSolv.( "McL" );;
## doc2/sporsolv.xml (1328-1336)
gap> t:= CharacterTable( "Ru" );;
gap> mx:= List( Maxes( t ), CharacterTable );;
gap> n:= 49152;;
gap> info:= List( mx, x -> SolvableSubgroupInfoFromCharacterTable( x, n ) );;
gap> info:= Filtered( info, IsList );
[ [ CharacterTable( "2^3+8:L3(2)" ), 7, 7 ],
[ CharacterTable( "2.2^4+6:S5" ), 5, 5 ] ]
## doc2/sporsolv.xml (1367-1378)
gap> MaxSolv.( "Ru" ):= n;;
gap> s:= info[1][1];;
gap> cls:= SizesConjugacyClasses( s );;
gap> nsg:= Filtered( ClassPositionsOfNormalSubgroups( s ),
> x -> Sum( cls{ x } ) = 2^3 );
[ [ 1, 2 ] ]
gap> cls{ nsg[1] };
[ 1, 7 ]
gap> GetFusionMap( s, t ){ nsg[1] };
[ 1, 2 ]
## doc2/sporsolv.xml (1392-1403)
gap> t:= CharacterTable( "Suz" );;
gap> mx:= List( Maxes( t ), CharacterTable );;
gap> n:= 139968;;
gap> info:= List( mx, x -> SolvableSubgroupInfoFromCharacterTable( x, n ) );;
gap> info:= Filtered( info, IsList );
[ [ CharacterTable( "G2(4)" ), 1797, 416 ],
[ CharacterTable( "3_2.U4(3).2_3'" ), 140, 72 ],
[ CharacterTable( "3^5:M11" ), 13, 11 ],
[ CharacterTable( "2^4+6:3a6" ), 7, 6 ],
[ CharacterTable( "3^2+4:2(2^2xa4)2" ), 1, 1 ] ]
## doc2/sporsolv.xml (1434-1437)
gap> MaxSolv.( "Suz" ):= n;;
gap> MaxSolv.( "Suz.2" ):= 2 * n;;
## doc2/sporsolv.xml (1451-1460)
gap> t:= CharacterTable( "ON" );;
gap> mx:= List( Maxes( t ), CharacterTable );;
gap> n:= 25920;;
gap> info:= List( mx, x -> SolvableSubgroupInfoFromCharacterTable( x, n ) );;
gap> info:= Filtered( info, IsList );
[ [ CharacterTable( "L3(7).2" ), 144, 114 ],
[ CharacterTable( "ONM2" ), 144, 114 ],
[ CharacterTable( "3^4:2^(1+4)D10" ), 1, 1 ] ]
## doc2/sporsolv.xml (1485-1488)
gap> MaxSolv.( "ON" ):= n;;
gap> MaxSolv.( "ON.2" ):= 2 * n;;
## doc2/sporsolv.xml (1501-1514)
gap> t:= CharacterTable( "Co2" );;
gap> mx:= List( Maxes( t ), CharacterTable );;
gap> n:= 2359296;;
gap> info:= List( mx, x -> SolvableSubgroupInfoFromCharacterTable( x, n ) );;
gap> info:= Filtered( info, IsList );
[ [ CharacterTable( "U6(2).2" ), 7796, 672 ],
[ CharacterTable( "2^10:m22:2" ), 385, 22 ],
[ CharacterTable( "McL" ), 380, 275 ],
[ CharacterTable( "2^1+8:s6f2" ), 315, 28 ],
[ CharacterTable( "2^1+4+6.a8" ), 17, 8 ],
[ CharacterTable( "U4(3).D8" ), 11, 8 ],
[ CharacterTable( "2^(4+10)(S5xS3)" ), 5, 5 ] ]
## doc2/sporsolv.xml (1536-1547)
gap> s:= info[7][1];
CharacterTable( "2^(4+10)(S5xS3)" )
gap> cls:= SizesConjugacyClasses( s );;
gap> nsg:= Filtered( ClassPositionsOfNormalSubgroups( s ),
> x -> Sum( cls{ x } ) = 2^4 );
[ [ 1 .. 3 ] ]
gap> cls{ nsg[1] };
[ 1, 5, 10 ]
gap> GetFusionMap( s, t ){ nsg[1] };
[ 1, 2, 3 ]
## doc2/sporsolv.xml (1580-1582)
gap> MaxSolv.( "Co2" ):= n;;
## doc2/sporsolv.xml (1597-1609)
gap> t:= CharacterTable( "Fi22" );;
gap> mx:= List( Maxes( t ), CharacterTable );;
gap> n:= 5038848;;
gap> info:= List( mx, x -> SolvableSubgroupInfoFromCharacterTable( x, n ) );;
gap> info:= Filtered( info, IsList );
[ [ CharacterTable( "2.U6(2)" ), 3650, 672 ],
[ CharacterTable( "O7(3)" ), 910, 351 ],
[ CharacterTable( "Fi22M3" ), 910, 351 ],
[ CharacterTable( "O8+(2).3.2" ), 207, 6 ],
[ CharacterTable( "2^10:m22" ), 90, 22 ],
[ CharacterTable( "3^(1+6):2^(3+4):3^2:2" ), 1, 1 ] ]
## doc2/sporsolv.xml (1642-1645)
gap> MaxSolv.( "Fi22" ):= n;;
gap> MaxSolv.( "Fi22.2" ):= 2 * n;;
## doc2/sporsolv.xml (1659-1667)
gap> t:= CharacterTable( "HN" );;
gap> mx:= List( Maxes( t ), CharacterTable );;
gap> n:= 2000000;;
gap> info:= List( mx, x -> SolvableSubgroupInfoFromCharacterTable( x, n ) );;
gap> info:= Filtered( info, IsList );
[ [ CharacterTable( "A12" ), 119, 12 ],
[ CharacterTable( "5^(1+4):2^(1+4).5.4" ), 1, 1 ] ]
## doc2/sporsolv.xml (1690-1693)
gap> MaxSolv.( "HN" ):= n;;
gap> MaxSolv.( "HN.2" ):= 2 * n;;
## doc2/sporsolv.xml (1707-1718)
gap> t:= CharacterTable( "Ly" );;
gap> mx:= List( Maxes( t ), CharacterTable );;
gap> n:= 900000;;
gap> info:= List( mx, x -> SolvableSubgroupInfoFromCharacterTable( x, n ) );;
gap> info:= Filtered( info, IsList );
[ [ CharacterTable( "G2(5)" ), 6510, 3906 ],
[ CharacterTable( "3.McL.2" ), 5987, 275 ],
[ CharacterTable( "5^3.psl(3,5)" ), 51, 31 ],
[ CharacterTable( "2.A11" ), 44, 11 ],
[ CharacterTable( "5^(1+4):4S6" ), 10, 6 ] ]
## doc2/sporsolv.xml (1744-1746)
gap> MaxSolv.( "Ly" ):= n;;
## doc2/sporsolv.xml (1761-1772)
gap> t:= CharacterTable( "Th" );;
gap> mx:= List( Maxes( t ), CharacterTable );;
gap> n:= 944784;;
gap> info:= List( mx, x -> SolvableSubgroupInfoFromCharacterTable( x, n ) );;
gap> info:= Filtered( info, IsList );
[ [ CharacterTable( "2^5.psl(5,2)" ), 338, 31 ],
[ CharacterTable( "2^1+8.a9" ), 98, 9 ],
[ CharacterTable( "U3(8).6" ), 35, 6 ],
[ CharacterTable( "ThN3B" ), 1, 1 ],
[ CharacterTable( "ThM7" ), 1, 1 ] ]
## doc2/sporsolv.xml (1795-1797)
gap> MaxSolv.( "Th" ):= n;;
## doc2/sporsolv.xml (1812-1821)
gap> t:= CharacterTable( "Fi23" );;
gap> mx:= List( Maxes( t ), CharacterTable );;
gap> n:= 3265173504;;
gap> info:= List( mx, x -> SolvableSubgroupInfoFromCharacterTable( x, n ) );;
gap> info:= Filtered( info, IsList );
[ [ CharacterTable( "2.Fi22" ), 39545, 3510 ],
[ CharacterTable( "O8+(3).3.2" ), 9100, 6 ],
[ CharacterTable( "3^(1+8).2^(1+6).3^(1+2).2S4" ), 1, 1 ] ]
## doc2/sporsolv.xml (1841-1843)
gap> MaxSolv.( "Fi23" ):= n;;
## doc2/sporsolv.xml (1858-1872)
gap> t:= CharacterTable( "Co1" );;
gap> mx:= List( Maxes( t ), CharacterTable );;
gap> n:= 84934656;;
gap> info:= List( mx, x -> SolvableSubgroupInfoFromCharacterTable( x, n ) );;
gap> info:= Filtered( info, IsList );
[ [ CharacterTable( "Co2" ), 498093, 2300 ],
[ CharacterTable( "3.Suz.2" ), 31672, 1782 ],
[ CharacterTable( "2^11:M24" ), 5903, 24 ],
[ CharacterTable( "Co3" ), 5837, 276 ],
[ CharacterTable( "2^(1+8)+.O8+(2)" ), 1050, 120 ],
[ CharacterTable( "U6(2).3.2" ), 649, 6 ],
[ CharacterTable( "2^(2+12):(A8xS3)" ), 23, 8 ],
[ CharacterTable( "2^(4+12).(S3x3S6)" ), 10, 6 ] ]
## doc2/sporsolv.xml (1905-1907)
gap> MaxSolv.( "Co1" ):= n;;
## doc2/sporsolv.xml (1922-1932)
gap> t:= CharacterTable( "J4" );;
gap> mx:= List( Maxes( t ), CharacterTable );;
gap> n:= 28311552;;
gap> info:= List( mx, x -> SolvableSubgroupInfoFromCharacterTable( x, n ) );;
gap> info:= Filtered( info, IsList );
[ [ CharacterTable( "mx1j4" ), 17710, 24 ],
[ CharacterTable( "c2aj4" ), 770, 22 ],
[ CharacterTable( "2^10:L5(2)" ), 361, 31 ],
[ CharacterTable( "J4M4" ), 23, 5 ] ]
## doc2/sporsolv.xml (1961-1972)
gap> s:= info[1][1];
CharacterTable( "mx1j4" )
gap> cls:= SizesConjugacyClasses( s );;
gap> nsg:= Filtered( ClassPositionsOfNormalSubgroups( s ),
> x -> Sum( cls{ x } ) = 2^11 );
[ [ 1 .. 3 ] ]
gap> cls{ nsg[1] };
[ 1, 276, 1771 ]
gap> GetFusionMap( s, t ){ nsg[1] };
[ 1, 3, 2 ]
## doc2/sporsolv.xml (1998-2000)
gap> MaxSolv.( "J4" ):= n;;
## doc2/sporsolv.xml (2015-2027)
gap> t:= CharacterTable( "Fi24'" );;
gap> mx:= List( Maxes( t ), CharacterTable );;
gap> n:= 29386561536;;
gap> info:= List( mx, x -> SolvableSubgroupInfoFromCharacterTable( x, n ) );;
gap> info:= Filtered( info, IsList );
[ [ CharacterTable( "Fi23" ), 139161244, 31671 ],
[ CharacterTable( "2.Fi22.2" ), 8787, 3510 ],
[ CharacterTable( "(3xO8+(3):3):2" ), 3033, 6 ],
[ CharacterTable( "O10-(2)" ), 851, 495 ],
[ CharacterTable( "3^(1+10):U5(2):2" ), 165, 165 ],
[ CharacterTable( "2^2.U6(2).3.2" ), 7, 6 ] ]
## doc2/sporsolv.xml (2059-2062)
gap> MaxSolv.( "Fi24'" ):= n;;
gap> MaxSolv.( "Fi24'.2" ):= 2 * n;;
## doc2/sporsolv.xml (2085-2091)
gap> n:= 29686813949952;;
gap> n = 2^(2+10+20) * 2^4 * 3^2 * 8 * 6;
true
gap> n = 2^(2+10+20) * MaxSolv.( "M22.2" ) * 6;
true
## doc2/sporsolv.xml (2129-2140)
gap> b:= CharacterTable( "B" );;
gap> mx:= List( Maxes( b ), CharacterTable );;
gap> Filtered( mx, x -> Size( x ) >= n );
[ CharacterTable( "2.2E6(2).2" ), CharacterTable( "2^(1+22).Co2" ),
CharacterTable( "Fi23" ), CharacterTable( "2^(9+16).S8(2)" ),
CharacterTable( "Th" ), CharacterTable( "(2^2xF4(2)):2" ),
CharacterTable( "2^(2+10+20).(M22.2xS3)" ),
CharacterTable( "[2^30].L5(2)" ), CharacterTable( "S3xFi22.2" ),
CharacterTable( "[2^35].(S5xL3(2))" ), CharacterTable( "HN.2" ),
CharacterTable( "O8+(3).S4" ) ]
## doc2/sporsolv.xml (2151-2158)
gap> List( [ 2^(1+22) * MaxSolv.( "Co2" ),
> MaxSolv.( "Fi23" ),
> MaxSolv.( "Th" ),
> 6 * MaxSolv.( "Fi22.2" ),
> MaxSolv.( "HN.2" ) ], i -> Int( i / n ) );
[ 0, 0, 0, 0, 0 ]
## doc2/sporsolv.xml (2168-2178)
gap> List( [ Size( CharacterTable( "2.2E6(2).2" ) ),
> 2^(9+16) * Size( CharacterTable( "S8(2)" ) ),
> 2^3 * Size( CharacterTable( "F4(2)" ) ),
> 2^(2+10+20) * Size( CharacterTable( "M22.2" ) ) * 6,
> 2^30 * Size( CharacterTable( "L5(2)" ) ),
> 2^35 * Factorial(5) * Size( CharacterTable( "L3(2)" ) ),
> Size( CharacterTable( "O8+(3)" ) ) * 24 ],
> i -> Int( i / n ) );
[ 10311982931, 53550, 892, 770, 361, 23, 4 ]
## doc2/sporsolv.xml (2241-2252)
gap> List( [ 2^(1+20) * Size( CharacterTable( "U6(2)" ) ),
> 2^(8+16) * Size( CharacterTable( "O8-(2)" ) ),
> Size( CharacterTable( "F4(2)" ) ),
> 2^(2+9+18) * Size( CharacterTable( "L3(4)" ) ) * 6,
> Size( CharacterTable( "Fi22" ) ),
> Size( CharacterTable( "O10-(2)" ) ),
> 2^(3+12+15) * 120 * Size( CharacterTable( "L3(2)" ) ),
> 6 * Size( CharacterTable( "U6(2)" ) ) ],
> i -> Int( i / ( n / 4 ) ) );
[ 2598, 446, 446, 8, 8, 3, 2, 0 ]
## doc2/sporsolv.xml (2273-2276)
gap> 2^(9+16+3+8) * 6 * 72 = n;
true
## doc2/sporsolv.xml (2287-2293)
gap> index:= Int( 2^(9+16) * Size( CharacterTable( "S8(2)" ) ) / n );
53550
gap> List( [ 120, 136, 255, 2295 ], i -> Int( index / i ) );
[ 446, 393, 210, 23 ]
gap> MaxSolv.( "B" ):= n;;
## doc2/sporsolv.xml (2334-2339)
gap> h:= mx[2];
CharacterTable( "2^(1+22).Co2" )
gap> pos:= Positions( GetFusionMap( h, b ), 3 );
[ 2, 4, 11, 20 ]
## doc2/sporsolv.xml (2350-2354)
gap> pos:= Filtered( Difference( pos, [ 2 ] ), i -> ForAny( pos,
> j -> NrPolyhedralSubgroups( h, 2, i, j ).number <> 0 ) );
[ 4, 11 ]
## doc2/sporsolv.xml (2363-2366)
gap> SizesConjugacyClasses( h ){ pos };
[ 93150, 7286400 ]
## doc2/sporsolv.xml (2374-2378)
gap> nr:= NrPolyhedralSubgroups( b, 3, 3, 3 );
rec( number := 14399283809600746875, type := "V4" )
gap> n0:= nr.number;;
## doc2/sporsolv.xml (2388-2393)
gap> cand:= List( pos, i -> Size( b ) / SizesCentralizers( h )[i] / 6 );
[ 181758140654146875, 14217525668946600000 ]
gap> Sum( cand ) = n0;
true
## doc2/sporsolv.xml (2402-2405)
gap> List( cand, x -> Size( b ) / x );
[ 22858846741463040, 292229574819840 ]
## doc2/sporsolv.xml (2420-2433)
gap> m:= mx[7];
CharacterTable( "2^(2+10+20).(M22.2xS3)" )
gap> Size( m );
22858846741463040
gap> nsg:= ClassPositionsOfMinimalNormalSubgroups( m );
[ [ 1, 2 ] ]
gap> SizesConjugacyClasses( m ){ nsg[1] };
[ 1, 3 ]
gap> GetFusionMap( m, b ){ nsg[1] };
[ 1, 3 ]
gap> List( cand, x -> Size( b ) / ( n * x ) );
[ 770, 315/32 ]
## doc2/sporsolv.xml (2451-2460)
gap> m:= mx[4];
CharacterTable( "2^(9+16).S8(2)" )
gap> nsg:= ClassPositionsOfMinimalNormalSubgroups( m );
[ [ 1, 2 ] ]
gap> SizesConjugacyClasses( m ){ nsg[1] };
[ 1, 255 ]
gap> GetFusionMap( m, b ){ nsg[1] };
[ 1, 3 ]
## doc2/sporsolv.xml (2473-2478)
gap> CharacterDegrees( CharacterTable( "S8(2)" ) mod 2 );
[ [ 1, 1 ], [ 8, 1 ], [ 16, 1 ], [ 26, 1 ], [ 48, 1 ], [ 128, 1 ],
[ 160, 1 ], [ 246, 1 ], [ 416, 1 ], [ 768, 1 ], [ 784, 1 ],
[ 2560, 1 ], [ 3936, 1 ], [ 4096, 1 ], [ 12544, 1 ], [ 65536, 1 ] ]
## doc2/sporsolv.xml (2500-2508)
gap> permg:= AtlasGroup( "S8(2)", NrMovedPoints, 5355 );
<permutation group of size 47377612800 with 2 generators>
gap> matg:= AtlasGroup( "S8(2)", Dimension, 8 );
<matrix group of size 47377612800 with 2 generators>
gap> hom:= GroupHomomorphismByImagesNC( matg, permg,
> GeneratorsOfGroup( matg ), GeneratorsOfGroup( permg ) );;
gap> max:= PreImages( hom, Stabilizer( permg, 1 ) );;
## doc2/sporsolv.xml (2519-2524)
gap> m:= GModuleByMats( GeneratorsOfGroup( max ), GF(2) );;
gap> comp:= MTX.CompositionFactors( m );;
gap> List( comp, r -> r.dimension );
[ 2, 4, 2 ]
## doc2/sporsolv.xml (2590-2593)
gap> n:= 2^25 * MaxSolv.( "Co1" );
2849934139195392
## doc2/sporsolv.xml (2603-2608)
gap> 2^(2+11+22) * MaxSolv.( "M24" ) * 6 = n;
true
gap> 2^39 * 24 * 3 * 72 = n;
true
## doc2/sporsolv.xml (2625-2636)
gap> cand:= [ "L2(13)", "Sz(8)", "U3(4)", "U3(8)" ];;
gap> List( cand, nam -> ExtensionInfoCharacterTable(
> CharacterTable( nam ) ) );
[ [ "2", "2" ], [ "2^2", "3" ], [ "", "4" ], [ "3", "(S3x3)" ] ]
gap> ll:= List( cand, x -> Size( CharacterTable( x ) ) );
[ 1092, 29120, 62400, 5515776 ]
gap> 18 * ll[4];
99283968
gap> 2^39 * 24 * 3 * 72;
2849934139195392
## doc2/sporsolv.xml (2688-2695)
gap> List( [ 2 * MaxSolv.( "B" ),
> 6 * MaxSolv.( "Fi24'" ),
> 3^13 * 2 * MaxSolv.( "Suz" ) * 2,
> 6 * MaxSolv.( "Th" ),
> 10 * MaxSolv.( "HN" ) * 2 ], i -> Int( i / n ) );
[ 0, 0, 0, 0, 0 ]
## doc2/sporsolv.xml (2707-2710)
gap> n / MaxSolv.( "B" );
96
## doc2/sporsolv.xml (2722-2725)
gap> Int( 3^8 * Size( CharacterTable( "O8-(3)" ) ) * 2 / n );
46
## doc2/sporsolv.xml (2738-2745)
gap> Int( 2^(10+16) * Size( CharacterTable( "O10+(2)" ) ) / n );
553350
gap> Int( 2^(5+10+20) * 6 * Size( CharacterTable( "L5(2)" ) ) / n );
723
gap> Int( 723 / 31 );
23
## doc2/sporsolv.xml (2767-2772)
gap> index:= Int( 2^(10+16) * Size( CharacterTable( "O10+(2)" ) ) / n );
553350
gap> List( [ 496, 527, 2295, 19840, 23715, 118575 ], i -> Int( index / i ) );
[ 1115, 1050, 241, 27, 23, 4 ]
## doc2/sporsolv.xml (2781-2783)
gap> MaxSolv.( "M" ):= n;;
## doc2/sporsolv.xml (2826-2835)
gap> m:= CharacterTable( "M" );;
gap> h:= CharacterTable( "2^1+24.Co1" );
CharacterTable( "2^1+24.Co1" )
gap> pos:= Positions( GetFusionMap( h, m ), 3 );
[ 2, 4, 7, 9, 16 ]
gap> pos:= Filtered( Difference( pos, [ 2 ] ), i -> ForAny( pos,
> j -> NrPolyhedralSubgroups( h, 2, i, j ).number <> 0 ) );
[ 4, 9, 16 ]
## doc2/sporsolv.xml (2844-2847)
gap> SizesConjugacyClasses( h ){ pos };
[ 16584750, 3222483264000, 87495303168000 ]
## doc2/sporsolv.xml (2856-2861)
gap> nr:= NrPolyhedralSubgroups( m, 3, 3, 3 );
rec( number := 87569110066985387357550925521828244921875,
type := "V4" )
gap> n0:= nr.number;;
## doc2/sporsolv.xml (2872-2879)
gap> cand:= List( pos, i -> Size( m ) / SizesCentralizers( h )[i] / 6 );
[ 16009115629875684006343550944921875,
3110635203347364905168577322802100000000,
84458458854522392576698341855475200000000 ]
gap> Sum( cand ) = n0;
true
## doc2/sporsolv.xml (2888-2891)
gap> List( cand, x -> Size( m ) / x );
[ 50472333605150392320, 259759622062080, 9567039651840 ]
## doc2/sporsolv.xml (2944-2971)
gap> g:= AtlasGroup( "2^(2+11+22).(M24xS3)" );
<permutation group of size 50472333605150392320 with 2 generators>
gap> NrMovedPoints( g );
294912
gap> bl:= Blocks( g, MovedPoints( g ) );;
gap> Length( bl );
147456
gap> hom1:= ActionHomomorphism( g, bl, OnSets );;
gap> act1:= Image( hom1 );;
gap> Size( g ) / Size( act1 );
8192
gap> bl2:= Blocks( act1, MovedPoints( act1 ) );;
gap> Length( bl2 );
72
gap> hom2:= ActionHomomorphism( act1, bl2, OnSets );;
gap> act2:= Image( hom2 );;
gap> Size( act2 );
1468938240
gap> Size( MathieuGroup( 24 ) ) * 6;
1468938240
gap> bl3:= AllBlocks( act2 );;
gap> List( bl3, Length );
[ 24, 3 ]
gap> bl3:= Orbit( act2, bl3[2], OnSets );;
gap> hom3:= ActionHomomorphism( act2, bl3, OnSets );;
gap> act3:= Image( hom3 );;
## doc2/sporsolv.xml (2984-2997)
gap> tom:= TableOfMarks( "M24" );;
gap> tomgroup:= UnderlyingGroup( tom );;
gap> iso:= IsomorphismGroups( act3, tomgroup );;
gap> pos:= Positions( OrdersTom( tom ), 13824 );
[ 1508 ]
gap> sub:= RepresentativeTom( tom, pos[1] );;
gap> pre:= PreImages( iso, sub );;
gap> pre:= PreImages( hom3, pre );;
gap> pre:= PreImages( hom2, pre );;
gap> pre:= PreImages( hom1, pre );;
gap> Size( pre ) = n;
true
## doc2/sporsolv.xml (3006-3010)
gap> pciso:= IsomorphismPcGroup( pre );;
gap> Size( Centre( Image( pciso ) ) );
1
## doc2/sporsolv.xml (3027-3031)
gap> Filtered( Set( RecNames( MaxSolv ) ),
> x -> MaxSolv.( x )^2 >= Size( CharacterTable( x ) ) );
[ "Fi23", "J2", "J2.2", "M11", "M12", "M22.2" ]
##
gap> if IsBound( BrowseData ) then
> data:= BrowseData.defaults.dynamic.replayDefaults;
> data.replayInterval:= oldinterval;
> fi;
##
gap> STOP_TEST( "sporsolv.tst" );
gap> SizeScreen( save );;
#############################################################################
##
#E
