Quelle ctblcons.tst
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# This file was created automatically, do not edit!
#############################################################################
##
#W ctblcons.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( "ctblcons.tst" );'.
##
gap> LoadPackage( "CTblLib", false );
true
gap> save:= SizeScreen();;
gap> SizeScreen( [ 72 ] );;
gap> START_TEST( "ctblcons.tst" );
##
gap> if IsBound( BrowseData ) then
> data:= BrowseData.defaults.dynamic.replayDefaults;
> oldinterval:= data.replayInterval;
> data.replayInterval:= 1;
> fi;
## doc2/ctblcons.xml ( 45- 48)
gap> LoadPackage( "ctbllib", " 1. 1. 4", false );
true
## doc2/ctblcons.xml ( 172- 187)
gap> RepresentativesCharacterTables:= function( list )
> local reps, entry, r;
>
> reps:= [];
> for entry in list do
> if ForAll( reps, r -> ( IsCharacterTable( r ) and
> TransformingPermutationsCharacterTables( entry, r ) = fail )
> or ( IsRecord( r ) and TransformingPermutationsCharacterTables(
> entry.table, r.table ) = fail ) ) then
> Add( reps, entry );
> fi;
> od;
> return reps;
> end;;
## doc2/ctblcons.xml ( 513- 526)
gap> t:= CharacterTable( " 3.L3( 4). 3" );
CharacterTable( " 3.L3( 4). 3" )
gap> iso1:= CharacterTableIsoclinic( t );
CharacterTable( "Isoclinic( 3.L3( 4). 3, 1)" )
gap> iso2:= CharacterTableIsoclinic( t, rec( k:= 2 ) );
CharacterTable( "Isoclinic( 3.L3( 4). 3, 2)" )
gap> TransformingPermutationsCharacterTables( t, iso1 );
fail
gap> TransformingPermutationsCharacterTables( t, iso2 );
fail
gap> TransformingPermutationsCharacterTables( iso1, iso2 );
fail
## doc2/ctblcons.xml ( 535- 539)
gap> IsRecord( TransformingPermutationsCharacterTables( t,
> CharacterTable( GL( 3, 4 ) ) ) );
true
## doc2/ctblcons.xml ( 567- 582)
gap> t:= CharacterTable( " 2.A6. 2_ 1" );
CharacterTable( " 2.A6. 2_ 1" )
gap> TransformingPermutationsCharacterTables( t,
> CharacterTableIsoclinic( t ) );
rec( columns := ( 4, 6)( 5, 7)( 11, 12)( 14, 16)( 15, 17),
group := Group([ ( 16, 17), ( 14, 15) ]),
rows := ( 3, 5)( 4, 6)( 10, 11)( 12, 15, 13, 14) )
gap> t:= CharacterTable( " 2.L2( 25). 2_ 2" );
CharacterTable( " 2.L2( 25). 2_ 2" )
gap> TransformingPermutationsCharacterTables( t,
> CharacterTableIsoclinic( t ) );
rec( columns := ( 7, 9)( 8, 10)( 20, 21)( 23, 24)( 25, 27)( 26, 28),
group := <permutation group with 4 generators>,
rows := ( 3, 5)( 4, 6)( 14, 15)( 16, 17)( 19, 22, 20, 21) )
## doc2/ctblcons.xml ( 609- 628)
gap> tbls:= [];;
gap> for m in [ " 4_ 1", " 4_ 2" ] do
> for a in [ " 2_ 1", " 2_ 2", " 2_ 3" ] do
> Add( tbls, CharacterTable( Concatenation( m, ".L3( 4).", a ) ) );
> od;
> od;
gap> tbls;
[ CharacterTable( " 4_ 1.L3( 4). 2_ 1" ), CharacterTable( " 4_ 1.L3( 4). 2_ 2" )
, CharacterTable( " 4_ 1.L3( 4). 2_ 3" ),
CharacterTable( " 4_ 2.L3( 4). 2_ 1" ), CharacterTable( " 4_ 2.L3( 4). 2_ 2" )
, CharacterTable( " 4_ 2.L3( 4). 2_ 3" ) ]
gap> case1:= Filtered( tbls, t -> Size( ClassPositionsOfCentre( t ) ) = 2 );
[ CharacterTable( " 4_ 1.L3( 4). 2_ 1" ), CharacterTable( " 4_ 1.L3( 4). 2_ 2" )
, CharacterTable( " 4_ 2.L3( 4). 2_ 1" ),
CharacterTable( " 4_ 2.L3( 4). 2_ 3" ) ]
gap> case2:= Filtered( tbls, t -> Size( ClassPositionsOfCentre( t ) ) = 4 );
[ CharacterTable( " 4_ 1.L3( 4). 2_ 3" ),
CharacterTable( " 4_ 2.L3( 4). 2_ 2" ) ]
## doc2/ctblcons.xml ( 640- 647)
gap> isos1:= List( case1, CharacterTableIsoclinic );;
gap> List( [ 1 .. 4 ], i -> Irr( case1[i] ) = Irr( isos1[i] ) );
[ true, true, true, true ]
gap> List( [ 1 .. 4 ],
> i -> TransformingPermutationsCharacterTables( case1[i], isos1[i] ) );
[ fail, fail, fail, fail ]
## doc2/ctblcons.xml ( 656- 673)
gap> isos2:= List( case2, CharacterTableIsoclinic );;
gap> List( [ 1, 2 ],
> i -> TransformingPermutationsCharacterTables( case2[i], isos2[i] ) );
[ rec( columns := ( 26, 27, 28, 29)( 30, 31, 32, 33)( 38, 39, 40, 41)( 42, 43, 44, 45)
, group := <permutation group with 5 generators>,
rows := ( 16, 17)( 18, 19)( 20, 21)( 22, 23)( 28, 29)( 32, 33)( 36, 37)( 40,
41) ),
rec( columns := ( 28, 29, 30, 31)( 32, 33)( 34, 35, 36, 37)( 38, 39, 40, 41)( 42,
43, 44, 45)( 46, 47, 48, 49), group := <permutation group with
3 generators>, rows := ( 15, 16)( 17, 18)( 20, 21)( 22, 23)( 24, 25)( 26,
27)( 28, 29)( 34, 35)( 38, 39)( 42, 43)( 46, 47) ) ]
gap> isos3:= List( case2, t -> CharacterTableIsoclinic( t,
> ClassPositionsOfCentre( t ) ) );;
gap> List( [ 1, 2 ],
> i -> TransformingPermutationsCharacterTables( case2[i], isos3[i] ) );
[ fail, fail ]
## doc2/ctblcons.xml ( 2049- 2074)
gap> tblMG:= CharacterTable( "Cyclic", 3 );;
gap> tblG:= CharacterTable( "Cyclic", 1 );;
gap> tblGA:= CharacterTable( "Cyclic", 2 );;
gap> StoreFusion( tblMG, [ 1, 1, 1 ], tblG );
gap> StoreFusion( tblG, [ 1 ], tblGA );
gap> elms:= Elements( AutomorphismsOfTable( tblMG ) );
[ (), ( 2, 3) ]
gap> orbs:= [ [ 1 ], [ 2, 3 ] ];;
gap> new:= PossibleCharacterTablesOfTypeMGA( tblMG, tblG, tblGA, orbs,
> "S3" );
[ rec( MGfusMGA := [ 1, 2, 2 ], table := CharacterTable( "S3" ) ) ]
gap> Display( new[ 1].table );
S3
2 1 . 1
3 1 1 .
1a 3a 2a
2P 1a 3a 1a
3P 1a 1a 2a
X. 1 1 1 1
X. 2 1 1 - 1
X. 3 2 - 1 .
## doc2/ctblcons.xml ( 2087- 2104)
gap> tblMG:= CharacterTable( "Cyclic", 4 );;
gap> tblG:= CharacterTable( "Cyclic", 2 );;
gap> tblGA:= CharacterTable( " 2^ 2" );;
gap> OrdersClassRepresentatives( tblMG );
[ 1, 4, 2, 4 ]
gap> StoreFusion( tblMG, [ 1, 2, 1, 2 ], tblG );
gap> StoreFusion( tblG, [ 1, 2 ], tblGA );
gap> elms:= Elements( AutomorphismsOfTable( tblMG ) );
[ (), ( 2, 4) ]
gap> orbs:= Orbits( Group( elms[ 2] ), [ 1 .. 4 ] );;
gap> new:= PossibleCharacterTablesOfTypeMGA( tblMG, tblG, tblGA, orbs,
> "order8" );
[ rec( MGfusMGA := [ 1, 2, 3, 2 ],
table := CharacterTable( "order8" ) ),
rec( MGfusMGA := [ 1, 2, 3, 2 ],
table := CharacterTable( "order8" ) ) ]
## doc2/ctblcons.xml ( 2113- 2129)
gap> List( new, x -> OrdersClassRepresentatives( x.table ) );
[ [ 1, 4, 2, 2, 2 ], [ 1, 4, 2, 4, 4 ] ]
gap> Display( new[ 1].table );
order8
2 3 2 3 2 2
1a 4a 2a 2b 2c
2P 1a 2a 1a 1a 1a
X. 1 1 1 1 1 1
X. 2 1 1 1 - 1 - 1
X. 3 1 - 1 1 1 - 1
X. 4 1 - 1 1 - 1 1
X. 5 2 . - 2 . .
## doc2/ctblcons.xml ( 2229- 2254)
gap> tblMG:= CharacterTable( " 7: 3" ) * CharacterTable( "A5" );;
gap> nsg:= ClassPositionsOfNormalSubgroups( tblMG );
[ [ 1 ], [ 1, 6 .. 11 ], [ 1 .. 5 ], [ 1, 6 .. 21 ], [ 1 .. 15 ],
[ 1 .. 25 ] ]
gap> List( nsg, x -> Sum( SizesConjugacyClasses( tblMG ){ x } ) );
[ 1, 7, 60, 21, 420, 1260 ]
gap> tblG:= tblMG / nsg[ 2];;
gap> tblGA:= CharacterTable( "Cyclic", 3 ) * CharacterTable( "A5. 2" );;
gap> GfusGA:= PossibleClassFusions( tblG, tblGA );
[ [ 1, 2, 3, 4, 4, 8, 9, 10, 11, 11, 15, 16, 17, 18, 18 ],
[ 1, 2, 3, 4, 4, 15, 16, 17, 18, 18, 8, 9, 10, 11, 11 ] ]
gap> reps:= RepresentativesFusions( Group(()), GfusGA, tblGA );
[ [ 1, 2, 3, 4, 4, 8, 9, 10, 11, 11, 15, 16, 17, 18, 18 ] ]
gap> StoreFusion( tblG, reps[ 1], tblGA );
gap> acts:= PossibleActionsForTypeMGA( tblMG, tblG, tblGA );
[ [ [ 1 ], [ 2 ], [ 3 ], [ 4, 5 ], [ 6, 11 ], [ 7, 12 ], [ 8, 13 ],
[ 9, 15 ], [ 10, 14 ], [ 16 ], [ 17 ], [ 18 ], [ 19, 20 ],
[ 21 ], [ 22 ], [ 23 ], [ 24, 25 ] ] ]
gap> poss:= PossibleCharacterTablesOfTypeMGA( tblMG, tblG, tblGA,
> acts[ 1], "A12N7" );
[ rec(
MGfusMGA := [ 1, 2, 3, 4, 4, 5, 6, 7, 8, 9, 5, 6, 7, 9, 8, 10,
11, 12, 13, 13, 14, 15, 16, 17, 17 ],
table := CharacterTable( "A12N7" ) ) ]
## doc2/ctblcons.xml ( 2263- 2268)
gap> g:= AlternatingGroup( 12 );;
gap> IsRecord( TransformingPermutationsCharacterTables( poss[ 1].table,
> CharacterTable( Normalizer( g, SylowSubgroup( g, 7 ) ) ) ) );
true
## doc2/ctblcons.xml ( 2280- 2290)
gap> tblh1:= CharacterTable( " 7: 3" );;
gap> tblg1:= CharacterTable( " 7: 6" );;
gap> tblh2:= CharacterTable( "A5" );;
gap> tblg2:= CharacterTable( "A5. 2" );;
gap> subdir:= CharacterTableOfIndexTwoSubdirectProduct( tblh1, tblg1,
> tblh2, tblg2, "( 7: 3xA5). 2" );;
gap> IsRecord( TransformingPermutationsCharacterTables( poss[ 1].table,
> subdir.table ) );
true
## doc2/ctblcons.xml ( 2326- 2376)
gap> listMGA:= [
> [ " 3.A6", "A6", "A6. 2_ 1", " 3.A6. 2_ 1" ],
> [ " 3.A6", "A6", "A6. 2_ 2", " 3.A6. 2_ 2" ],
> [ " 6.A6", " 2.A6", " 2.A6. 2_ 1", " 6.A6. 2_ 1" ],
> [ " 6.A6", " 2.A6", " 2.A6. 2_ 2", " 6.A6. 2_ 2" ],
> [ " 3.A7", "A7", "A7. 2", " 3.A7. 2" ],
> [ " 6.A7", " 2.A7", " 2.A7. 2", " 6.A7. 2" ],
> [ " 3.L3( 4)", "L3( 4)", "L3( 4). 2_ 2", " 3.L3( 4). 2_ 2" ],
> [ " 3.L3( 4)", "L3( 4)", "L3( 4). 2_ 3", " 3.L3( 4). 2_ 3" ],
> [ " 6.L3( 4)", " 2.L3( 4)", " 2.L3( 4). 2_ 2", " 6.L3( 4). 2_ 2" ],
> [ " 6.L3( 4)", " 2.L3( 4)", " 2.L3( 4). 2_ 3", " 6.L3( 4). 2_ 3" ],
> [ " 12_ 1.L3( 4)", " 4_ 1.L3( 4)", " 4_ 1.L3( 4). 2_ 2", " 12_ 1.L3( 4). 2_ 2" ],
> [ " 12_ 1.L3( 4)", " 4_ 1.L3( 4)", " 4_ 1.L3( 4). 2_ 3", " 12_ 1.L3( 4). 2_ 3" ],
> [ " 12_ 2.L3( 4)", " 4_ 2.L3( 4)", " 4_ 2.L3( 4). 2_ 2", " 12_ 2.L3( 4). 2_ 2" ],
> [ " 12_ 2.L3( 4)", " 4_ 2.L3( 4)", " 4_ 2.L3( 4). 2_ 3", " 12_ 2.L3( 4). 2_ 3" ],
> [ " 3.U3( 5)", "U3( 5)", "U3( 5). 2", " 3.U3( 5). 2" ],
> [ " 3.M22", "M22", "M22. 2", " 3.M22. 2" ],
> [ " 6.M22", " 2.M22", " 2.M22. 2", " 6.M22. 2" ],
> [ " 12.M22", " 4.M22", " 4.M22. 2", " 12.M22. 2" ],
> [ " 3.L3( 7)", "L3( 7)", "L3( 7). 2", " 3.L3( 7). 2" ],
> [ " 3_ 1.U4( 3)", "U4( 3)", "U4( 3). 2_ 1", " 3_ 1.U4( 3). 2_ 1" ],
> [ " 3_ 1.U4( 3)", "U4( 3)", "U4( 3). 2_ 2'", " 3_ 1.U4( 3). 2_ 2'" ],
> [ " 3_ 2.U4( 3)", "U4( 3)", "U4( 3). 2_ 1", " 3_ 2.U4( 3). 2_ 1" ],
> [ " 3_ 2.U4( 3)", "U4( 3)", "U4( 3). 2_ 3'", " 3_ 2.U4( 3). 2_ 3'" ],
> [ " 6_ 1.U4( 3)", " 2.U4( 3)", " 2.U4( 3). 2_ 1", " 6_ 1.U4( 3). 2_ 1" ],
> [ " 6_ 1.U4( 3)", " 2.U4( 3)", " 2.U4( 3). 2_ 2'", " 6_ 1.U4( 3). 2_ 2'" ],
> [ " 6_ 2.U4( 3)", " 2.U4( 3)", " 2.U4( 3). 2_ 1", " 6_ 2.U4( 3). 2_ 1" ],
> [ " 6_ 2.U4( 3)", " 2.U4( 3)", " 2.U4( 3). 2_ 3'", " 6_ 2.U4( 3). 2_ 3'" ],
> [ " 12_ 1.U4( 3)", " 4.U4( 3)", " 4.U4( 3). 2_ 1", " 12_ 1.U4( 3). 2_ 1" ],
> [ " 12_ 2.U4( 3)", " 4.U4( 3)", " 4.U4( 3). 2_ 1", " 12_ 2.U4( 3). 2_ 1" ],
> [ " 3.G2( 3)", "G2( 3)", "G2( 3). 2", " 3.G2( 3). 2" ],
> [ " 3.U3( 8)", "U3( 8)", "U3( 8). 2", " 3.U3( 8). 2" ],
> [ " 3.U3( 8). 3_ 1", "U3( 8). 3_ 1", "U3( 8). 6", " 3.U3( 8). 6" ],
> [ " 3.J3", "J3", "J3. 2", " 3.J3. 2" ],
> [ " 3.U3( 11)", "U3( 11)", "U3( 11). 2", " 3.U3( 11). 2" ],
> [ " 3.McL", "McL", "McL. 2", " 3.McL. 2" ],
> [ " 3.O7( 3)", "O7( 3)", "O7( 3). 2", " 3.O7( 3). 2" ],
> [ " 6.O7( 3)", " 2.O7( 3)", " 2.O7( 3). 2", " 6.O7( 3). 2" ],
> [ " 3.U6( 2)", "U6( 2)", "U6( 2). 2", " 3.U6( 2). 2" ],
> [ " 6.U6( 2)", " 2.U6( 2)", " 2.U6( 2). 2", " 6.U6( 2). 2" ],
> [ " 3.Suz", "Suz", "Suz. 2", " 3.Suz. 2" ],
> [ " 6.Suz", " 2.Suz", " 2.Suz. 2", " 6.Suz. 2" ],
> [ " 3.ON", "ON", "ON. 2", " 3.ON. 2" ],
> [ " 3.Fi22", "Fi22", "Fi22. 2", " 3.Fi22. 2" ],
> [ " 6.Fi22", " 2.Fi22", " 2.Fi22. 2", " 6.Fi22. 2" ],
> [ " 3. 2E6( 2)", " 2E6( 2)", " 2E6( 2). 2", " 3. 2E6( 2). 2" ],
> [ " 6. 2E6( 2)", " 2. 2E6( 2)", " 2. 2E6( 2). 2", " 6. 2E6( 2). 2" ],
> [ " 3.F3+", "F3+", "F3+. 2", " 3.F3+. 2" ],
> ];;
## doc2/ctblcons.xml ( 2402- 2409)
gap> Append( listMGA, [
> [ "( 2^ 2x3).L3( 4)", " 2^ 2.L3( 4)", " 2^ 2.L3( 4). 2_ 2", "( 2^ 2x3).L3( 4). 2_ 2" ],
> [ "( 2^ 2x3).L3( 4)", " 2^ 2.L3( 4)", " 2^ 2.L3( 4). 2_ 3", "( 2^ 2x3).L3( 4). 2_ 3" ],
> [ "( 2^ 2x3).U6( 2)", " 2^ 2.U6( 2)", " 2^ 2.U6( 2). 2", "( 2^ 2x3).U6( 2). 2" ],
> [ "( 2^ 2x3). 2E6( 2)", " 2^ 2. 2E6( 2)", " 2^ 2. 2E6( 2). 2", "( 2^ 2x3). 2E6( 2). 2" ],
> ] );
## doc2/ctblcons.xml ( 2420- 2440)
gap> Append( listMGA, [
> [ " 3.A6. 2_ 3", "A6. 2_ 3", "A6. 2^ 2", " 3.A6. 2^ 2" ],
> [ " 3.L3( 4). 2_ 1", "L3( 4). 2_ 1", "L3( 4). 2^ 2", " 3.L3( 4). 2^ 2" ],
> [ " 3_ 1.U4( 3). 2_ 2", "U4( 3). 2_ 2", "U4( 3).( 2^ 2)_{ 122}",
> " 3_ 1.U4( 3).( 2^ 2)_{ 122}" ],
> [ " 3_ 2.U4( 3). 2_ 3", "U4( 3). 2_ 3", "U4( 3).( 2^ 2)_{ 133}",
> " 3_ 2.U4( 3).( 2^ 2)_{ 133}" ],
> [ " 3^ 2.U4( 3). 2_ 3'", " 3_ 2.U4( 3). 2_ 3'", " 3_ 2.U4( 3).( 2^ 2)_{ 133}",
> " 3^ 2.U4( 3).( 2^ 2)_{ 133}" ],
> [ " 2^ 2.L3( 4)", "L3( 4)", "L3( 4). 3", " 2^ 2.L3( 4). 3" ],
> [ "( 2^ 2x3).L3( 4)", " 3.L3( 4)", " 3.L3( 4). 3", "( 2^ 2x3).L3( 4). 3" ],
> [ " 2^ 2.L3( 4). 2_ 1", "L3( 4). 2_ 1", "L3( 4). 6", " 2^ 2.L3( 4). 6" ],
> [ " 2^ 2.Sz( 8)", "Sz( 8)", "Sz( 8). 3", " 2^ 2.Sz( 8). 3" ],
> [ " 2^ 2.U6( 2)", "U6( 2)", "U6( 2). 3", " 2^ 2.U6( 2). 3" ],
> [ "( 2^ 2x3).U6( 2)", " 3.U6( 2)", " 3.U6( 2). 3", "( 2^ 2x3).U6( 2). 3" ],
> [ " 2^ 2.O8+( 2)", "O8+( 2)", "O8+( 2). 3", " 2^ 2.O8+( 2). 3" ],
> [ " 2^ 2.O8+( 3)", "O8+( 3)", "O8+( 3). 3", " 2^ 2.O8+( 3). 3" ],
> [ " 2^ 2. 2E6( 2)", " 2E6( 2)", " 2E6( 2). 3", " 2^ 2. 2E6( 2). 3" ],
> ] );
## doc2/ctblcons.xml ( 2480- 2515)
gap> ConstructOrdinaryMGATable:= function( tblMG, tblG, tblGA, name, lib )
> local acts, poss, trans;
>
> acts:= PossibleActionsForTypeMGA( tblMG, tblG, tblGA );
> poss:= Concatenation( List( acts, pi ->
> PossibleCharacterTablesOfTypeMGA( tblMG, tblG, tblGA, pi,
> name ) ) );
> poss:= RepresentativesCharacterTables( poss );
> if Length( poss ) = 1 then
> # Compare the computed table with the library table.
> if not IsCharacterTable( lib ) then
> List( poss, x -> AutomorphismsOfTable( x.table ) );
> Print( "#I no library table for ", name, "\n" );
> else
> trans:= TransformingPermutationsCharacterTables( poss[ 1].table,
> lib );
> if not IsRecord( trans ) then
> Print( "#E computed table and library table for ", name,
> " differ\n" );
> fi;
> # Compare the computed fusion with the stored one.
> if OnTuples( poss[ 1].MGfusMGA, trans.columns )
> <> GetFusionMap( tblMG, lib ) then
> Print( "#E computed and stored fusion for ", name,
> " differ\n" );
> fi;
> fi;
> elif Length( poss ) = 0 then
> Print( "#E no solution for ", name, "\n" );
> else
> Print( "#E ", Length( poss ), " possibilities for ", name, "\n" );
> fi;
> return poss;
> end;;
## doc2/ctblcons.xml ( 2532- 2564)
gap> ConstructModularMGATables:= function( tblMG, tblGA, ordtblMGA )
> local name, poss, p, modtblMG, modtblGA, modtblMGA, modlib, trans;
>
> name:= Identifier( ordtblMGA );
> poss:= [];
> for p in PrimeDivisors( Size( ordtblMGA ) ) do
> modtblMG := tblMG mod p;
> modtblGA := tblGA mod p;
> if ForAll( [ modtblMG, modtblGA ], IsCharacterTable ) then
> modtblMGA:= BrauerTableOfTypeMGA( modtblMG, modtblGA, ordtblMGA );
> Add( poss, modtblMGA );
> modlib:= ordtblMGA mod p;
> if IsCharacterTable( modlib ) then
> trans:= TransformingPermutationsCharacterTables( modtblMGA.table,
> modlib );
> if not IsRecord( trans ) then
> Print( "#E computed table and library table for ", name,
> " mod ", p, " differ\n" );
> fi;
> else
> AutomorphismsOfTable( modtblMGA.table );
> Print( "#I no library table for ", name, " mod ", p, "\n" );
> fi;
> else
> Print( "#I not all input tables for ", name, " mod ", p,
> " available\n" );
> fi;
> od;
>
> return poss;
> end;;
## doc2/ctblcons.xml ( 2576- 2637)
gap> for input in listMGA do
> tblMG := CharacterTable( input[ 1] );
> tblG := CharacterTable( input[ 2] );
> tblGA := CharacterTable( input[ 3] );
> name := Concatenation( "new", input[ 4] );
> lib := CharacterTable( input[ 4] );
> poss:= ConstructOrdinaryMGATable( tblMG, tblG, tblGA, name, lib );
> if 1 <> Length( poss ) then
> Print( "#I ", Length( poss ), " possibilities for ", name, "\n" );
> elif lib = fail then
> Print( "#I no library table for ", input[ 4], "\n" );
> else
> ConstructModularMGATables( tblMG, tblGA, lib );
> fi;
> od;
#I not all input tables for 3. 2E6( 2). 2 mod 2 available
#I not all input tables for 3. 2E6( 2). 2 mod 3 available
#I not all input tables for 3. 2E6( 2). 2 mod 5 available
#I not all input tables for 3. 2E6( 2). 2 mod 7 available
#I not all input tables for 3. 2E6( 2). 2 mod 11 available
#I not all input tables for 3. 2E6( 2). 2 mod 13 available
#I not all input tables for 3. 2E6( 2). 2 mod 17 available
#I not all input tables for 3. 2E6( 2). 2 mod 19 available
#I not all input tables for 6. 2E6( 2). 2 mod 2 available
#I not all input tables for 6. 2E6( 2). 2 mod 3 available
#I not all input tables for 6. 2E6( 2). 2 mod 5 available
#I not all input tables for 6. 2E6( 2). 2 mod 7 available
#I not all input tables for 6. 2E6( 2). 2 mod 11 available
#I not all input tables for 6. 2E6( 2). 2 mod 13 available
#I not all input tables for 6. 2E6( 2). 2 mod 17 available
#I not all input tables for 6. 2E6( 2). 2 mod 19 available
#I not all input tables for 3.F3+. 2 mod 2 available
#I not all input tables for 3.F3+. 2 mod 3 available
#I not all input tables for 3.F3+. 2 mod 5 available
#I not all input tables for 3.F3+. 2 mod 7 available
#I not all input tables for 3.F3+. 2 mod 13 available
#I not all input tables for 3.F3+. 2 mod 17 available
#I not all input tables for 3.F3+. 2 mod 29 available
#I not all input tables for ( 2^ 2x3). 2E6( 2). 2 mod 2 available
#I not all input tables for ( 2^ 2x3). 2E6( 2). 2 mod 3 available
#I not all input tables for ( 2^ 2x3). 2E6( 2). 2 mod 5 available
#I not all input tables for ( 2^ 2x3). 2E6( 2). 2 mod 7 available
#I not all input tables for ( 2^ 2x3). 2E6( 2). 2 mod 11 available
#I not all input tables for ( 2^ 2x3). 2E6( 2). 2 mod 13 available
#I not all input tables for ( 2^ 2x3). 2E6( 2). 2 mod 17 available
#I not all input tables for ( 2^ 2x3). 2E6( 2). 2 mod 19 available
#I not all input tables for 3^ 2.U4( 3).( 2^ 2)_{ 133} mod 2 available
#I not all input tables for 3^ 2.U4( 3).( 2^ 2)_{ 133} mod 5 available
#I not all input tables for 3^ 2.U4( 3).( 2^ 2)_{ 133} mod 7 available
#I not all input tables for 2^ 2.O8+( 3). 3 mod 5 available
#I not all input tables for 2^ 2.O8+( 3). 3 mod 7 available
#I not all input tables for 2^ 2.O8+( 3). 3 mod 13 available
#I not all input tables for 2^ 2. 2E6( 2). 3 mod 2 available
#I not all input tables for 2^ 2. 2E6( 2). 3 mod 3 available
#I not all input tables for 2^ 2. 2E6( 2). 3 mod 5 available
#I not all input tables for 2^ 2. 2E6( 2). 3 mod 7 available
#I not all input tables for 2^ 2. 2E6( 2). 3 mod 11 available
#I not all input tables for 2^ 2. 2E6( 2). 3 mod 13 available
#I not all input tables for 2^ 2. 2E6( 2). 3 mod 17 available
#I not all input tables for 2^ 2. 2E6( 2). 3 mod 19 available
## doc2/ctblcons.xml ( 2669- 2678)
gap> listMGA2:= [
> [ " 4_ 1.L3( 4)", " 2.L3( 4)", " 2.L3( 4). 2_ 1", " 4_ 1.L3( 4). 2_ 1" ],
> [ " 4_ 1.L3( 4)", " 2.L3( 4)", " 2.L3( 4). 2_ 2", " 4_ 1.L3( 4). 2_ 2" ],
> [ " 4_ 2.L3( 4)", " 2.L3( 4)", " 2.L3( 4). 2_ 1", " 4_ 2.L3( 4). 2_ 1" ],
> [ " 4.M22", " 2.M22", " 2.M22. 2", " 4.M22. 2" ],
> [ " 4.U4( 3)", " 2.U4( 3)", " 2.U4( 3). 2_ 2", " 4.U4( 3). 2_ 2" ],
> [ " 4.U4( 3)", " 2.U4( 3)", " 2.U4( 3). 2_ 3", " 4.U4( 3). 2_ 3" ],
> ];;
## doc2/ctblcons.xml ( 2697- 2706)
gap> Append( listMGA2, [
> [ " 2^ 2.L3( 4)", " 2.L3( 4)", " 2.L3( 4). 2_ 2", " 2^ 2.L3( 4). 2_ 2" ],
> [ " 2^ 2.L3( 4)", " 2.L3( 4)", " 2.L3( 4). 2_ 3", " 2^ 2.L3( 4). 2_ 3" ],
> [ " 2^ 2.L3( 4). 2_ 1", " 2.L3( 4). 2_ 1", " 2.L3( 4).( 2^ 2)_{ 123}", " 2^ 2.L3( 4). 2^ 2" ],
> [ " 2^ 2.O8+( 2)", " 2.O8+( 2)", " 2.O8+( 2). 2", " 2^ 2.O8+( 2). 2" ],
> [ " 2^ 2.U6( 2)", " 2.U6( 2)", " 2.U6( 2). 2", " 2^ 2.U6( 2). 2" ],
> [ " 2^ 2. 2E6( 2)", " 2. 2E6( 2)", " 2. 2E6( 2). 2", " 2^ 2. 2E6( 2). 2" ],
> ] );
## doc2/ctblcons.xml ( 2719- 2724)
gap> Append( listMGA2, [
> [ " 12_ 1.L3( 4)", " 6.L3( 4)", " 6.L3( 4). 2_ 1", " 12_ 1.L3( 4). 2_ 1" ],
> [ " 12_ 2.L3( 4)", " 6.L3( 4)", " 6.L3( 4). 2_ 1", " 12_ 2.L3( 4). 2_ 1" ],
> ] );
## doc2/ctblcons.xml ( 2743- 2750)
gap> Append( listMGA2, [
> [ " 12.M22", " 6.M22", " 6.M22. 2", " 12.M22. 2" ],
> [ " 12_ 1.L3( 4)", " 6.L3( 4)", " 6.L3( 4). 2_ 2", " 12_ 1.L3( 4). 2_ 2" ],
> [ " 12_ 1.U4( 3)", " 6_ 1.U4( 3)", " 6_ 1.U4( 3). 2_ 2", " 12_ 1.U4( 3). 2_ 2" ],
> [ " 12_ 2.U4( 3)", " 6_ 2.U4( 3)", " 6_ 2.U4( 3). 2_ 3", " 12_ 2.U4( 3). 2_ 3" ],
> ] );
## doc2/ctblcons.xml ( 2761- 2768)
gap> Append( listMGA2, [
> [ "( 2^ 2x3).L3( 4)", " 6.L3( 4)", " 6.L3( 4). 2_ 2", "( 2^ 2x3).L3( 4). 2_ 2" ],
> [ "( 2^ 2x3).L3( 4)", " 6.L3( 4)", " 6.L3( 4). 2_ 3", "( 2^ 2x3).L3( 4). 2_ 3" ],
> [ "( 2^ 2x3).U6( 2)", " 6.U6( 2)", " 6.U6( 2). 2", "( 2^ 2x3).U6( 2). 2" ],
> [ "( 2^ 2x3). 2E6( 2)", " 6. 2E6( 2)", " 6. 2E6( 2). 2", "( 2^ 2x3). 2E6( 2). 2" ],
> ] );
## doc2/ctblcons.xml ( 2776- 2835)
gap> for input in listMGA2 do
> tblMG := CharacterTable( input[ 1] );
> tblG := CharacterTable( input[ 2] );
> tblGA := CharacterTable( input[ 3] );
> name := Concatenation( "new", input[ 4] );
> lib := CharacterTable( input[ 4] );
> poss:= ConstructOrdinaryMGATable( tblMG, tblG, tblGA, name, lib );
> if Length( poss ) = 2 then
> iso:= CharacterTableIsoclinic( poss[ 1].table );
> if IsRecord( TransformingPermutationsCharacterTables( poss[ 2].table,
> iso ) ) then
> Unbind( poss[ 2] );
> fi;
> elif Length( poss ) = 1 then
> Print( "#I unique up to permutation equivalence: ", name, "\n" );
> fi;
> if 1 <> Length( poss ) then
> Print( "#I ", Length( poss ), " possibilities for ", name, "\n" );
> elif lib = fail then
> Print( "#I no library table for ", input[ 4], "\n" );
> else
> ConstructModularMGATables( tblMG, tblGA, lib );
> fi;
> od;
#E 2 possibilities for new4_1.L3( 4). 2_ 1
#E 2 possibilities for new4_1.L3( 4). 2_ 2
#E 2 possibilities for new4_2.L3( 4). 2_ 1
#E 2 possibilities for new4.M22. 2
#E 2 possibilities for new4.U4( 3). 2_ 2
#E 2 possibilities for new4.U4( 3). 2_ 3
#I unique up to permutation equivalence: new2^ 2.L3( 4). 2_ 2
#I unique up to permutation equivalence: new2^ 2.L3( 4). 2_ 3
#I unique up to permutation equivalence: new2^ 2.L3( 4). 2^ 2
#I unique up to permutation equivalence: new2^ 2.O8+( 2). 2
#I unique up to permutation equivalence: new2^ 2.U6( 2). 2
#I unique up to permutation equivalence: new2^ 2. 2E6( 2). 2
#I not all input tables for 2^ 2. 2E6( 2). 2 mod 2 available
#I not all input tables for 2^ 2. 2E6( 2). 2 mod 3 available
#I not all input tables for 2^ 2. 2E6( 2). 2 mod 5 available
#I not all input tables for 2^ 2. 2E6( 2). 2 mod 7 available
#E 2 possibilities for new12_1.L3( 4). 2_ 1
#E 2 possibilities for new12_2.L3( 4). 2_ 1
#E 2 possibilities for new12.M22. 2
#E 2 possibilities for new12_1.L3( 4). 2_ 2
#E 2 possibilities for new12_1.U4( 3). 2_ 2
#E 2 possibilities for new12_2.U4( 3). 2_ 3
#I unique up to permutation equivalence: new( 2^ 2x3).L3( 4). 2_ 2
#I unique up to permutation equivalence: new( 2^ 2x3).L3( 4). 2_ 3
#I unique up to permutation equivalence: new( 2^ 2x3).U6( 2). 2
#I unique up to permutation equivalence: new( 2^ 2x3). 2E6( 2). 2
#I not all input tables for ( 2^ 2x3). 2E6( 2). 2 mod 2 available
#I not all input tables for ( 2^ 2x3). 2E6( 2). 2 mod 3 available
#I not all input tables for ( 2^ 2x3). 2E6( 2). 2 mod 5 available
#I not all input tables for ( 2^ 2x3). 2E6( 2). 2 mod 7 available
#I not all input tables for ( 2^ 2x3). 2E6( 2). 2 mod 11 available
#I not all input tables for ( 2^ 2x3). 2E6( 2). 2 mod 13 available
#I not all input tables for ( 2^ 2x3). 2E6( 2). 2 mod 17 available
#I not all input tables for ( 2^ 2x3). 2E6( 2). 2 mod 19 available
## doc2/ctblcons.xml ( 2857- 2881)
gap> tblMG := CharacterTable( " 4_ 2.L3( 4)" );;
gap> tblG := CharacterTable( " 2.L3( 4)" );;
gap> tblGA := CharacterTable( " 2.L3( 4). 2_ 3" );;
gap> name := "new4_2.L3( 4). 2_ 3";;
gap> lib := CharacterTable( " 4_ 2.L3( 4). 2_ 3" );;
gap> poss := ConstructOrdinaryMGATable( tblMG, tblG, tblGA, name, lib );
#E 4 possibilities for new4_2.L3( 4). 2_ 3
[ rec(
MGfusMGA := [ 1, 2, 3, 2, 4, 5, 6, 7, 8, 7, 9, 10, 11, 10, 12,
12, 13, 14, 15, 14, 16, 17, 18, 17, 19, 20, 21, 22, 19, 22,
21, 20 ], table := CharacterTable( "new4_2.L3( 4). 2_ 3" ) ),
rec(
MGfusMGA := [ 1, 2, 3, 2, 4, 5, 6, 7, 8, 7, 9, 10, 11, 10, 12,
12, 13, 14, 15, 14, 16, 17, 18, 17, 19, 20, 21, 22, 19, 22,
21, 20 ], table := CharacterTable( "new4_2.L3( 4). 2_ 3" ) ),
rec(
MGfusMGA := [ 1, 2, 3, 2, 4, 5, 6, 7, 8, 7, 9, 10, 11, 10, 12,
12, 13, 14, 15, 14, 16, 17, 18, 17, 19, 20, 21, 22, 19, 22,
21, 20 ], table := CharacterTable( "new4_2.L3( 4). 2_ 3" ) ),
rec(
MGfusMGA := [ 1, 2, 3, 2, 4, 5, 6, 7, 8, 7, 9, 10, 11, 10, 12,
12, 13, 14, 15, 14, 16, 17, 18, 17, 19, 20, 21, 22, 19, 22,
21, 20 ], table := CharacterTable( "new4_2.L3( 4). 2_ 3" ) ) ]
## doc2/ctblcons.xml ( 2901- 2908)
gap> IsRecord( TransformingPermutationsCharacterTables( poss[ 1].table,
> CharacterTableIsoclinic( poss[ 4].table ) ) );
true
gap> IsRecord( TransformingPermutationsCharacterTables( poss[ 2].table,
> CharacterTableIsoclinic( poss[ 3].table ) ) );
true
## doc2/ctblcons.xml ( 2919- 2929)
gap> List( poss, x -> PowerMap( x.table, 2 ) );
[ [ 1, 3, 1, 1, 3, 6, 8, 6, 4, 4, 4, 5, 16, 18, 16, 13, 15, 13, 19,
21, 19, 21, 1, 1, 6, 6, 9, 9, 11, 11, 16, 16, 13, 13 ],
[ 1, 3, 1, 1, 3, 6, 8, 6, 4, 4, 4, 5, 16, 18, 16, 13, 15, 13, 19,
21, 19, 21, 1, 1, 6, 6, 11, 11, 9, 9, 16, 16, 13, 13 ],
[ 1, 3, 1, 1, 3, 6, 8, 6, 4, 4, 4, 5, 16, 18, 16, 13, 15, 13, 19,
21, 19, 21, 3, 3, 8, 8, 9, 9, 11, 11, 18, 18, 15, 15 ],
[ 1, 3, 1, 1, 3, 6, 8, 6, 4, 4, 4, 5, 16, 18, 16, 13, 15, 13, 19,
21, 19, 21, 3, 3, 8, 8, 11, 11, 9, 9, 18, 18, 15, 15 ] ]
## doc2/ctblcons.xml ( 2946- 2956)
gap> PossiblePowerMaps( poss[ 1].table, 2 );
[ [ 1, 3, 1, 1, 3, 6, 8, 6, 4, 4, 4, 5, 16, 18, 16, 13, 15, 13, 19,
21, 19, 21, 1, 1, 6, 6, 11, 11, 9, 9, 16, 16, 13, 13 ],
[ 1, 3, 1, 1, 3, 6, 8, 6, 4, 4, 4, 5, 16, 18, 16, 13, 15, 13, 19,
21, 19, 21, 1, 1, 6, 6, 9, 9, 11, 11, 16, 16, 13, 13 ] ]
gap> t:= CharacterTable( " 4.U4( 3)" );;
gap> List( [ "L3( 4)", " 2.L3( 4)", " 4_ 1.L3( 4)", " 4_ 2.L3( 4)" ], name ->
> Length( PossibleClassFusions( CharacterTable( name ), t ) ) );
[ 0, 0, 0, 4 ]
## doc2/ctblcons.xml ( 2969- 2973)
gap> t2:= CharacterTable( " 4.U4( 3). 2_ 3" );;
gap> List( poss, x -> Length( PossibleClassFusions( x.table, t2 ) ) );
[ 0, 16, 0, 0 ]
## doc2/ctblcons.xml ( 3010- 3015)
gap> IsRecord( TransformingPermutationsCharacterTables( poss[ 2].table,
> lib ) );
true
gap> ConstructModularMGATables( tblMG, tblGA, lib );;
## doc2/ctblcons.xml ( 3026- 3049)
gap> tblMG := CharacterTable( " 12_ 2.L3( 4)" );;
gap> tblG := CharacterTable( " 6.L3( 4)" );;
gap> tblGA := CharacterTable( " 6.L3( 4). 2_ 3" );;
gap> name := "new12_2.L3( 4). 2_ 3";;
gap> lib := CharacterTable( " 12_ 2.L3( 4). 2_ 3" );;
gap> poss := ConstructOrdinaryMGATable( tblMG, tblG, tblGA, name, lib );;
#E 4 possibilities for new12_2.L3( 4). 2_ 3
gap> Length( poss );
4
gap> nsg:= ClassPositionsOfNormalSubgroups( poss[ 1].table );
[ [ 1 ], [ 1, 5 ], [ 1, 7 ], [ 1, 4 .. 7 ], [ 1, 3 .. 7 ],
[ 1 .. 7 ], [ 1 .. 50 ], [ 1 .. 62 ] ]
gap> List( nsg, x -> Sum( SizesConjugacyClasses( poss[ 1].table ){ x } ) );
[ 1, 3, 2, 4, 6, 12, 241920, 483840 ]
gap> factlib:= CharacterTable( " 4_ 2.L3( 4). 2_ 3" );;
gap> List( poss, x -> IsRecord( TransformingPermutationsCharacterTables(
> x.table / [ 1, 5 ], factlib ) ) );
[ false, true, false, false ]
gap> IsRecord( TransformingPermutationsCharacterTables( poss[ 2].table,
> lib ) );
true
gap> ConstructModularMGATables( tblMG, tblGA, lib );;
## doc2/ctblcons.xml ( 3075- 3084)
gap> tblMG := CharacterTable( " 12_ 1.U4( 3)" );;
gap> tblG := CharacterTable( " 2.U4( 3)" );;
gap> tblGA := CharacterTable( " 2.U4( 3). 2_ 2'" );;
gap> name := "new12_1.U4( 3). 2_ 2'";;
gap> lib := CharacterTable( " 12_ 1.U4( 3). 2_ 2'" );;
gap> poss := ConstructOrdinaryMGATable( tblMG, tblG, tblGA, name, lib );;
#E 2 possibilities for new12_1.U4( 3). 2_ 2'
gap> ConstructModularMGATables( tblMG, tblGA, lib );;
## doc2/ctblcons.xml ( 3096- 3103)
gap> Irr( poss[ 1].table ) = Irr( poss[ 2].table );
true
gap> iso:= CharacterTableIsoclinic( poss[ 1].table );;
gap> TransformingPermutationsCharacterTables( iso, poss[ 2].table );
rec( columns := (), group := <permutation group with 5 generators>,
rows := () )
## doc2/ctblcons.xml ( 3113- 3126)
gap> tblMG := CharacterTable( " 12_ 2.U4( 3)" );;
gap> tblG := CharacterTable( " 2.U4( 3)" );;
gap> tblGA := CharacterTable( " 2.U4( 3). 2_ 3'" );;
gap> name := "new12_2.U4( 3). 2_ 3'";;
gap> lib := CharacterTable( " 12_ 2.U4( 3). 2_ 3'" );;
gap> poss := ConstructOrdinaryMGATable( tblMG, tblG, tblGA, name, lib );;
#E 2 possibilities for new12_2.U4( 3). 2_ 3'
gap> ConstructModularMGATables( tblMG, tblGA, lib );;
gap> iso:= CharacterTableIsoclinic( poss[ 1].table );;
gap> TransformingPermutationsCharacterTables( iso, poss[ 2].table );
rec( columns := (), group := <permutation group with 8 generators>,
rows := () )
## doc2/ctblcons.xml ( 3177- 3205)
gap> s:= SU( 3, 8);;
gap> gens:= GeneratorsOfGroup( s );;
gap> imgs1:= List( gens, m -> List( m, v -> List( v, x -> x^ 4 ) ) );;
gap> imgs2:= List( gens, m -> List( m, v -> List( v, x -> x^ 16 ) ) );;
gap> f:= GF( 64);;
gap> mats:= List( gens, m -> IdentityMat( 9, f ) );;
gap> for i in [ 1 .. Length( gens ) ] do
> mats[i]{ [ 1 .. 3 ] }{ [ 1 .. 3 ] }:= gens[i];
> mats[i]{ [ 4 .. 6 ] }{ [ 4 .. 6 ] }:= imgs1[i];
> mats[i]{ [ 7 .. 9 ] }{ [ 7 .. 9 ] }:= imgs2[i];
> od;
gap> fieldaut:= NullMat( 9, 9, f );;
gap> fieldaut{ [ 4 .. 6 ] }{ [ 1 .. 3 ] }:= IdentityMat( 3, f );;
gap> fieldaut{ [ 7 .. 9 ] }{ [ 4 .. 6 ] }:= IdentityMat( 3, f );;
gap> fieldaut{ [ 1 .. 3 ] }{ [ 7 .. 9 ] }:= IdentityMat( 3, f );;
gap> v:= [ 1, 0, 0, 1, 0, 0, 1, 0, 0 ] * One( f );;
gap> g:= Group( Concatenation( mats, [ fieldaut ] ) );;
gap> orb:= Orbit( g, v );;
gap> Length( orb );
32319
gap> act:= Action( g, orb );;
gap> Size( act ) = 3 * Size( s );
true
gap> sm:= SmallerDegreePermutationRepresentation( act );;
gap> NrMovedPoints( Image( sm ) );
4617
gap> g:= Image( sm );;
## doc2/ctblcons.xml ( 3221- 3243)
gap> c:= CyclicGroup( IsPermGroup, 9 );;
gap> dp:= DirectProduct( g, c );;
gap> u:= Image( Embedding( dp, 1 ) );;
gap> c:= Image( Embedding( dp, 2 ) );;
gap> c3:= c. 1^ 3;
( 4618, 4621, 4624)( 4619, 4622, 4625)( 4620, 4623, 4626)
gap> z:= Centre( u );;
gap> Size( z ); Length( GeneratorsOfGroup( z ) );
3
1
gap> diag:= Subgroup( dp, [ c3 * z. 1 ] );;
gap> orb:= Orbit( dp, [ 1, 4618 ], OnPairs );;
gap> Length( orb );
41553
gap> orb:= Set( orb );;
gap> orbs:= List( OrbitsDomain( diag, orb, OnSets ), Set );;
gap> Length( orbs );
13851
gap> cp:= Action( dp, orbs, OnSetsSets );;
gap> Size( cp );
148925952
## doc2/ctblcons.xml ( 3254- 3265)
gap> der:= DerivedSubgroup( cp );;
gap> Index( cp, der );
9
gap> inter:= IntermediateSubgroups( cp, der ).subgroups;;
gap> z:= Centre( cp );;
gap> Size( z );
9
gap> inter:= Filtered( inter, x -> not IsSubset( x, z ) );;
gap> List( inter, Size );
[ 49641984, 49641984, 49641984 ]
## doc2/ctblcons.xml ( 3273- 3278)
gap> IsomorphismGroups( inter[ 1], inter[ 2] ) <> fail;
true
gap> IsomorphismGroups( inter[ 1], inter[ 3] ) <> fail;
true
## doc2/ctblcons.xml ( 3294- 3302)
gap> t1:= CharacterTable( " 3.U3( 8). 3_ 1" );;
gap> t2:= CharacterTableIsoclinic( t1, rec( k:= 1 ) );;
gap> t3:= CharacterTableIsoclinic( t1, rec( k:= 2 ) );;
gap> TransformingPermutationsCharacterTables( t1, t2 ) <> fail;
true
gap> TransformingPermutationsCharacterTables( t1, t3 ) <> fail;
true
## doc2/ctblcons.xml ( 3398- 3423)
gap> f42:= CharacterTable( "F4( 2)" );;
gap> v4:= CharacterTable( " 2^ 2" );;
gap> dp:= v4 * f42;
CharacterTable( "V4xF4( 2)" )
gap> b:= CharacterTable( "B" );;
gap> f42fusb:= PossibleClassFusions( f42, b );;
gap> Length( f42fusb );
1
gap> f42fusdp:= GetFusionMap( f42, dp );;
gap> comp:= CompositionMaps( f42fusb[ 1], InverseMap( f42fusdp ) );
[ 1, 3, 3, 3, 5, 6, 6, 7, 9, 9, 9, 9, 14, 14, 13, 13, 10, 14, 14, 12,
14, 17, 15, 18, 22, 22, 22, 22, 26, 26, 22, 22, 27, 27, 28, 31, 31,
39, 39, 36, 36, 33, 33, 39, 39, 35, 41, 42, 47, 47, 49, 49, 49, 58,
58, 56, 56, 66, 66, 66, 66, 58, 58, 66, 66, 69, 69, 60, 72, 72, 75,
79, 79, 81, 81, 85, 86, 83, 83, 91, 91, 94, 94, 104, 104, 109, 109,
116, 116, 114, 114, 132, 132, 140, 140 ]
gap> v4fusdp:= GetFusionMap( v4, dp );
[ 1, 96 .. 286 ]
gap> comp[ v4fusdp[ 2] ]:= 4;;
gap> dpfusb:= PossibleClassFusions( dp, b, rec( fusionmap:= comp ) );;
gap> Length( dpfusb );
4
gap> Set( dpfusb, x -> x{ v4fusdp } );
[ [ 1, 4, 2, 2 ] ]
## doc2/ctblcons.xml ( 3440- 3451)
gap> tblG:= dp / v4fusdp{ [ 1, 2 ] };;
gap> tblMG:= dp;;
gap> c2:= CharacterTable( "Cyclic", 2 );;
gap> tblGA:= c2 * CharacterTable( "F4( 2). 2" );
CharacterTable( "C2xF4( 2). 2" )
gap> GfusGA:= PossibleClassFusions( tblG, tblGA );;
gap> Length( GfusGA );
4
gap> Length( RepresentativesFusions( tblG, GfusGA, tblGA ) );
1
## doc2/ctblcons.xml ( 3468- 3472)
gap> Length( RepresentativesFusions( Group( () ), GfusGA, tblGA ) );
1
gap> StoreFusion( tblG, GfusGA[ 1], tblGA );
## doc2/ctblcons.xml ( 3477- 3486)
gap> elms:= PossibleActionsForTypeMGA( tblMG, tblG, tblGA );;
gap> Length( elms );
1
gap> poss:= PossibleCharacterTablesOfTypeMGA( tblMG, tblG, tblGA, elms[ 1],
> "( 2^ 2xF4( 2)): 2" );;
gap> Length( poss );
1
gap> tblMGA:= poss[ 1].table;;
## doc2/ctblcons.xml ( 3498- 3502)
gap> IsRecord( TransformingPermutationsCharacterTables( tblMGA,
> CharacterTable( "( 2^ 2xF4( 2)): 2" ) ) );
true
## doc2/ctblcons.xml ( 3565- 3573)
gap> s3:= CharacterTable( "Dihedral", 6 );;
gap> fi222:= CharacterTable( "Fi22. 2" );;
gap> tblMbar:= s3 * fi222;;
gap> b:= CharacterTable( "B" );;
gap> Mbarfusb:= PossibleClassFusions( tblMbar, b );;
gap> Length( Mbarfusb );
1
## doc2/ctblcons.xml ( 3584- 3588)
gap> 2b:= CharacterTable( " 2.B" );;
gap> PossibleClassFusions( CharacterTable( "Fi22" ), 2b );
[ ]
## doc2/ctblcons.xml ( 3607- 3612)
gap> c3:= CharacterTable( "Cyclic", 3 );;
gap> 2fi222:= CharacterTable( " 2.Fi22. 2" );;
gap> PossibleClassFusions( c3 * CharacterTableIsoclinic( 2fi222 ), 2b );
[ ]
## doc2/ctblcons.xml ( 3621- 3631)
gap> s3inMbar:= GetFusionMap( s3, tblMbar );
[ 1, 113 .. 225 ]
gap> s3inb:= Mbarfusb[ 1]{ s3inMbar };
[ 1, 6, 2 ]
gap> 2bfusb:= GetFusionMap( 2b, b );;
gap> 2s3in2B:= InverseMap( 2bfusb ){ s3inb };
[ [ 1, 2 ], [ 8, 9 ], 3 ]
gap> CompositionMaps( OrdersClassRepresentatives( 2b ), 2s3in2B );
[ [ 1, 2 ], [ 3, 6 ], 2 ]
## doc2/ctblcons.xml ( 3650- 3653)
gap> PossibleClassFusions( s3 * 2fi222, 2b );
[ ]
## doc2/ctblcons.xml ( 3759- 3781)
gap> c2:= CharacterTable( "Cyclic", 2 );;
gap> 2fi22:= CharacterTable( " 2.Fi22" );;
gap> tblNmodY:= c2 * 2fi22;;
gap> centre:= GetFusionMap( 2fi22, tblNmodY ){
> ClassPositionsOfCentre( 2fi22 ) };
[ 1, 2 ]
gap> tblNmod6:= tblNmodY / centre;;
gap> tblMmod6:= c2 * fi222;;
gap> fus:= PossibleClassFusions( tblNmod6, tblMmod6 );;
gap> Length( fus );
1
gap> StoreFusion( tblNmod6, fus[ 1], tblMmod6 );
gap> elms:= PossibleActionsForTypeMGA( tblNmodY, tblNmod6, tblMmod6 );;
gap> Length( elms );
1
gap> poss:= PossibleCharacterTablesOfTypeMGA( tblNmodY, tblNmod6, tblMmod6,
> elms[ 1], " 2^ 2.Fi22. 2" );;
gap> Length( poss );
1
gap> tblMmodY:= poss[ 1].table;
CharacterTable( " 2^ 2.Fi22. 2" )
## doc2/ctblcons.xml ( 3792- 3811)
gap> tblU:= c3 * 2fi222;;
gap> tblUmodY:= tblU / GetFusionMap( c3, tblU );;
gap> fus:= PossibleClassFusions( tblUmodY, tblMmodY );;
gap> Length( RepresentativesFusions( Group( () ), fus, tblMmodY ) );
1
gap> StoreFusion( tblUmodY, fus[ 1], tblMmodY );
gap> elms:= PossibleActionsForTypeMGA( tblU, tblUmodY, tblMmodY );;
gap> Length( elms );
1
gap> poss:= PossibleCharacterTablesOfTypeMGA( tblU, tblUmodY, tblMmodY,
> elms[ 1], "(S3x2.Fi22). 2" );;
gap> Length( poss );
1
gap> tblM:= poss[ 1].table;
CharacterTable( "(S3x2.Fi22). 2" )
gap> mfus2b:= PossibleClassFusions( tblM, 2b );;
gap> Length( RepresentativesFusions( tblM, mfus2b, 2b ) );
1
## doc2/ctblcons.xml ( 3821- 3824)
gap> Irr( tblM / ClassPositionsOfCentre( tblM ) ) = Irr( tblMbar );
true
## doc2/ctblcons.xml ( 3833- 3837)
gap> IsRecord( TransformingPermutationsCharacterTables( tblM,
> CharacterTable( "(S3x2.Fi22). 2" ) ) );
true
## doc2/ctblcons.xml ( 3939- 3947)
gap> fi24:= CharacterTable( "Fi24" );;
gap> t:= CharacterTable( " 2^ 2.Fi22. 2" );;
gap> fus:= PossibleClassFusions( t, fi24 );;
gap> Length( fus );
4
gap> Length( RepresentativesFusions( t, fus, fi24 ) );
1
## doc2/ctblcons.xml ( 3976- 3986)
gap> t:= CharacterTable( "(S3x2.Fi22). 2" );;
gap> 3fi24:= CharacterTable( " 3.Fi24" );;
gap> fus:= PossibleClassFusions( t, 3fi24 );;
gap> Length( fus );
16
gap> Length( RepresentativesFusions( t, fus, 3fi24 ) );
1
gap> GetFusionMap( t, 3fi24 ) in fus;
true
## doc2/ctblcons.xml ( 3995- 4013)
gap> m:= CharacterTable( "M" );;
gap> tfusm:= PossibleClassFusions( t, m );;
gap> Length( tfusm );
4
gap> Length( RepresentativesFusions( t, tfusm, m ) );
1
gap> nsg:= Filtered( ClassPositionsOfNormalSubgroups( t ),
> x -> Sum( SizesConjugacyClasses( t ){ x } ) = 6 );
[ [ 1, 2, 142, 143 ] ]
gap> Set( tfusm, x -> x{ nsg[ 1] } );
[ [ 1, 2, 4, 13 ] ]
gap> OrdersClassRepresentatives( t ){ nsg[ 1] };
[ 1, 2, 3, 6 ]
gap> PowerMap( m, - 1 )[ 13];
13
gap> Size( t ) = 2 * SizesCentralizers( m )[ 13];
true
## doc2/ctblcons.xml ( 4096- 4102)
gap> 2Fi22:= CharacterTable( " 2.Fi22" );;
gap> ClassPositionsOfCentre( 2Fi22 );
[ 1, 2 ]
gap> 2 in PowerMap( 2Fi22, 2 );
false
## doc2/ctblcons.xml ( 4114- 4122)
gap> PossibleClassFusions( CharacterTable( "U4( 3)" ), 2Fi22 );
[ ]
gap> tblU:= CharacterTable( " 2.U4( 3). 2_ 2" );;
gap> iso:= CharacterTableIsoclinic( tblU );
CharacterTable( "Isoclinic( 2.U4( 3). 2_ 2)" )
gap> PossibleClassFusions( iso, 2Fi22 );
[ ]
## doc2/ctblcons.xml ( 4148- 4153)
gap> derpos:= ClassPositionsOfDerivedSubgroup( tblU );;
gap> outer:= Difference( [ 1 .. NrConjugacyClasses( tblU ) ], derpos );;
gap> 2 in OrdersClassRepresentatives( tblU ){ outer };
true
## doc2/ctblcons.xml ( 4169- 4177)
gap> tblM:= CharacterTable( "Dihedral", 6 ) * tblU;;
gap> fus:= PossibleClassFusions( tblM, 2Fi22 );;
gap> Length( RepresentativesFusions( tblM, fus, 2Fi22 ) );
1
gap> IsRecord( TransformingPermutationsCharacterTables( tblM,
> CharacterTable( " 2.Fi22M8" ) ) );
true
## doc2/ctblcons.xml ( 4275- 4278)
gap> c2:= CharacterTable( "Cyclic", 2 );;
gap> tblC:= CharacterTableIsoclinic( CharacterTable( " 2.HS" ) * c2 );;
## doc2/ctblcons.xml ( 4287- 4292)
gap> ord2:= Filtered( ClassPositionsOfNormalSubgroups( tblC ),
> x -> Length( x ) = 2 );
[ [ 1, 3 ] ]
gap> tblCbar:= tblC / ord2[ 1];;
## doc2/ctblcons.xml ( 4302- 4309)
gap> tblNbar:= CharacterTable( "HS. 2" ) * c2;;
gap> fus:= PossibleClassFusions( tblCbar, tblNbar );
[ [ 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, 29, 30, 31, 32,
33, 34, 35, 36, 35, 36, 37, 38, 39, 40, 41, 42, 41, 42 ] ]
gap> StoreFusion( tblCbar, fus[ 1], tblNbar );
## doc2/ctblcons.xml ( 4318- 4340)
gap> elms:= PossibleActionsForTypeMGA( tblC, tblCbar, tblNbar );
[ [ [ 1 ], [ 2, 4 ], [ 3 ], [ 5 ], [ 6, 8 ], [ 7 ], [ 9 ], [ 10 ],
[ 11 ], [ 12, 14 ], [ 13 ], [ 15 ], [ 16, 18 ], [ 17 ], [ 19 ],
[ 20 ], [ 21 ], [ 22 ], [ 23 ], [ 24, 26 ], [ 25 ], [ 27 ],
[ 28, 30 ], [ 29 ], [ 31 ], [ 32, 34 ], [ 33 ], [ 35 ],
[ 36, 38 ], [ 37 ], [ 39 ], [ 40, 42 ], [ 41 ], [ 43 ],
[ 44, 46 ], [ 45 ], [ 47 ], [ 48, 50 ], [ 49 ], [ 51, 53 ],
[ 52, 54 ], [ 55 ], [ 56, 58 ], [ 57 ], [ 59 ], [ 60 ],
[ 61, 65 ], [ 62, 68 ], [ 63, 67 ], [ 64, 66 ], [ 69 ],
[ 70, 72 ], [ 71 ], [ 73 ], [ 74, 76 ], [ 75 ], [ 77, 81 ],
[ 78, 84 ], [ 79, 83 ], [ 80, 82 ] ],
[ [ 1 ], [ 2, 4 ], [ 3 ], [ 5 ], [ 6, 8 ], [ 7 ], [ 9 ], [ 10 ],
[ 11 ], [ 12, 14 ], [ 13 ], [ 15, 17 ], [ 16 ], [ 18 ], [ 19 ],
[ 20 ], [ 21 ], [ 22 ], [ 23 ], [ 24, 26 ], [ 25 ], [ 27 ],
[ 28, 30 ], [ 29 ], [ 31 ], [ 32, 34 ], [ 33 ], [ 35, 37 ],
[ 36 ], [ 38 ], [ 39 ], [ 40, 42 ], [ 41 ], [ 43 ], [ 44, 46 ],
[ 45 ], [ 47, 49 ], [ 48 ], [ 50 ], [ 51, 53 ], [ 52, 54 ],
[ 55 ], [ 56, 58 ], [ 57 ], [ 59 ], [ 60 ], [ 61, 65 ],
[ 62, 68 ], [ 63, 67 ], [ 64, 66 ], [ 69, 71 ], [ 70 ], [ 72 ],
[ 73 ], [ 74, 76 ], [ 75 ], [ 77, 83 ], [ 78, 82 ], [ 79, 81 ],
[ 80, 84 ] ] ]
## doc2/ctblcons.xml ( 4348- 4353)
gap> poss:= List( elms, pi -> PossibleCharacterTablesOfTypeMGA(
> tblC, tblCbar, tblNbar, pi, " 4.HS. 2" ) );;
gap> List( poss, Length );
[ 0, 2 ]
## doc2/ctblcons.xml ( 4376- 4389)
gap> result:= poss[ 2];;
gap> hn2:= CharacterTable( "HN. 2" );;
gap> possfus:= List( result, r -> PossibleClassFusions( r.table, hn2 ) );;
gap> List( possfus, Length );
[ 32, 0 ]
gap> RepresentativesFusions( result[ 1].table, possfus[ 1], hn2 );
[ [ 1, 46, 2, 2, 47, 3, 7, 45, 4, 58, 13, 6, 46, 47, 6, 47, 7, 48,
10, 62, 20, 9, 63, 21, 12, 64, 24, 27, 49, 50, 13, 59, 14, 16,
70, 30, 18, 53, 52, 17, 54, 20, 65, 22, 36, 56, 26, 76, 39, 77,
28, 59, 58, 31, 78, 41, 34, 62, 35, 65, 2, 45, 3, 45, 6, 48, 7,
47, 17, 54, 13, 49, 13, 50, 14, 50, 18, 53, 18, 52, 21, 56, 25,
57, 27, 59, 30, 60, 44, 72, 34, 66, 35, 66, 41, 71 ] ]
## doc2/ctblcons.xml ( 4404- 4409)
gap> libtbl:= CharacterTable( " 4.HS. 2" );;
gap> IsRecord( TransformingPermutationsCharacterTables( result[ 1].table,
> libtbl ) );
true
## doc2/ctblcons.xml ( 4427- 4434)
gap> StoreFusion( tblC, result[ 1].MGfusMGA, result[ 1].table );
gap> ForAll( PrimeDivisors( Size( result[ 1].table ) ),
> p -> IsRecord( TransformingPermutationsCharacterTables(
> BrauerTableOfTypeMGA( tblC mod p, tblNbar mod p,
> result[ 1].table ).table, libtbl mod p ) ) );
true
## doc2/ctblcons.xml ( 4571- 4601)
gap> c2:= CharacterTable( "Cyclic", 2 );;
gap> 2a6:= CharacterTable( " 2.A6" );;
gap> tblC:= CharacterTableIsoclinic( 2a6 * c2 );;
gap> ord2:= Filtered( ClassPositionsOfNormalSubgroups( tblC ),
> x -> Length( x ) = 2 );
[ [ 1, 3 ] ]
gap> tblG:= tblC / ord2[ 1];;
gap> tblNbar:= CharacterTableIsoclinic( CharacterTable( "A6. 2_ 3" ) * c2 );;
gap> fus:= PossibleClassFusions( tblG, tblNbar );
[ [ 1, 2, 3, 4, 5, 6, 5, 6, 7, 8, 9, 10, 9, 10 ] ]
gap> StoreFusion( tblG, fus[ 1], tblNbar );
gap> elms:= PossibleActionsForTypeMGA( tblC, tblG, tblNbar );
[ [ [ 1 ], [ 2 ], [ 3 ], [ 4 ], [ 5 ], [ 6 ], [ 7, 11 ], [ 8, 12 ],
[ 9, 13 ], [ 10, 14 ], [ 15, 17 ], [ 16, 18 ], [ 19, 23 ],
[ 20, 24 ], [ 21, 25 ], [ 22, 26 ] ],
[ [ 1 ], [ 2, 4 ], [ 3 ], [ 5 ], [ 6 ], [ 7, 11 ], [ 8, 14 ],
[ 9, 13 ], [ 10, 12 ], [ 15 ], [ 16, 18 ], [ 17 ], [ 19, 23 ],
[ 20, 26 ], [ 21, 25 ], [ 22, 24 ] ],
[ [ 1 ], [ 2, 4 ], [ 3 ], [ 5 ], [ 6 ], [ 7, 11 ], [ 8, 14 ],
[ 9, 13 ], [ 10, 12 ], [ 15, 17 ], [ 16 ], [ 18 ], [ 19, 23 ],
[ 20, 26 ], [ 21, 25 ], [ 22, 24 ] ] ]
gap> poss:= List( elms, pi -> PossibleCharacterTablesOfTypeMGA(
> tblC, tblG, tblNbar, pi, " 4.A6. 2_ 3" ) );
[ [ ], [ ],
[
rec(
MGfusMGA := [ 1, 2, 3, 2, 4, 5, 6, 7, 8, 9, 6, 9, 8, 7, 10,
11, 10, 12, 13, 14, 15, 16, 13, 16, 15, 14 ],
table := CharacterTable( " 4.A6. 2_ 3" ) ) ] ]
## doc2/ctblcons.xml ( 4611- 4616)
gap> t:= poss[ 3][ 1].table;;
gap> IsRecord( TransformingPermutationsCharacterTables( t,
> CharacterTable( " 4.A6. 2_ 3" ) ) );
true
## doc2/ctblcons.xml ( 4645- 4664)
gap> g:= GammaL( 2, 9);;
gap> phi:= IsomorphismPermGroup( g );;
gap> img:= Image( phi );;
gap> der:= DerivedSubgroup( img );;
gap> derder:= DerivedSubgroup( der );;
gap> Index( img, derder );
16
gap> inter:= Filtered( IntermediateSubgroups( img, derder ).subgroups,
> s -> Size( s ) = 4 * Size( derder ) and
> IsCyclic( CommutatorFactorGroup( s ) ) and
> Size( Centre( s ) ) = 2 );;
gap> Length( inter );
2
gap> ForAll( inter, x -> IsConjugate( img, inter[ 1], x ) );
true
gap> IsRecord( TransformingPermutationsCharacterTables( t,
> CharacterTable( inter[ 1] ) ) );
true
## doc2/ctblcons.xml ( 4752- 4779)
gap> tblC:= 2a6 * c2;;
gap> z:= GetFusionMap( 2a6, tblC ){ ClassPositionsOfCentre( 2a6 ) };
[ 1, 3 ]
gap> tblG:= tblC / z;;
gap> tblNbar:= CharacterTableIsoclinic( CharacterTable( "A6. 2_ 3" ) * c2 );;
gap> fus:= PossibleClassFusions( tblG, tblNbar );
[ [ 1, 2, 3, 4, 5, 6, 5, 6, 7, 8, 9, 10, 9, 10 ] ]
gap> StoreFusion( tblG, fus[ 1], tblNbar );
gap> elms:= PossibleActionsForTypeMGA( tblC, tblG, tblNbar );
[ [ [ 1 ], [ 2 ], [ 3 ], [ 4 ], [ 5 ], [ 6 ], [ 7, 11 ], [ 8, 12 ],
[ 9, 13 ], [ 10, 14 ], [ 15, 17 ], [ 16, 18 ], [ 19, 23 ],
[ 20, 24 ], [ 21, 25 ], [ 22, 26 ] ],
[ [ 1 ], [ 2, 4 ], [ 3 ], [ 5 ], [ 6 ], [ 7, 11 ], [ 8, 14 ],
[ 9, 13 ], [ 10, 12 ], [ 15 ], [ 16, 18 ], [ 17 ], [ 19, 23 ],
[ 20, 26 ], [ 21, 25 ], [ 22, 24 ] ],
[ [ 1 ], [ 2, 4 ], [ 3 ], [ 5 ], [ 6 ], [ 7, 11 ], [ 8, 14 ],
[ 9, 13 ], [ 10, 12 ], [ 15, 17 ], [ 16 ], [ 18 ], [ 19, 23 ],
[ 20, 26 ], [ 21, 25 ], [ 22, 24 ] ] ]
gap> poss:= List( elms, pi -> PossibleCharacterTablesOfTypeMGA(
> tblC, tblG, tblNbar, pi, " 2^ 2.A6. 2_ 3" ) );
[ [ ], [ ],
[
rec(
MGfusMGA := [ 1, 2, 3, 2, 4, 5, 6, 7, 8, 9, 6, 9, 8, 7, 10,
11, 10, 12, 13, 14, 15, 16, 13, 16, 15, 14 ],
table := CharacterTable( " 2^ 2.A6. 2_ 3" ) ) ] ]
## doc2/ctblcons.xml ( 4878- 4931)
gap> c2:= CharacterTable( "Cyclic", 2 );;
gap> tblC:= CharacterTableIsoclinic( CharacterTable( " 6.A6" ) * c2 );;
gap> ord2:= Filtered( ClassPositionsOfNormalSubgroups( tblC ),
> x -> Length( x ) = 2 );
[ [ 1, 7 ] ]
gap> tblG:= tblC / ord2[ 1];;
gap> tblNbar:= CharacterTableIsoclinic( CharacterTable( " 3.A6. 2_ 3" ) * c2 );;
gap> fus:= PossibleClassFusions( tblG, tblNbar );
[ [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 13, 14, 15, 16,
17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 21, 22, 23, 24, 25, 26 ]
,
[ 1, 2, 5, 6, 3, 4, 7, 8, 11, 12, 9, 10, 13, 14, 13, 14, 15, 16,
19, 20, 17, 18, 21, 22, 25, 26, 23, 24, 21, 22, 25, 26, 23, 24
] ]
gap> rep:= RepresentativesFusions( Group( () ), fus, tblNbar );
[ [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 13, 14, 15, 16,
17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 21, 22, 23, 24, 25, 26
] ]
gap> StoreFusion( tblG, rep[ 1], tblNbar );
gap> elms:= PossibleActionsForTypeMGA( tblC, tblG, tblNbar );
[ [ [ 1 ], [ 2 ], [ 3 ], [ 4 ], [ 5 ], [ 6 ], [ 7 ], [ 8 ], [ 9 ],
[ 10 ], [ 11 ], [ 12 ], [ 13 ], [ 14 ], [ 15 ], [ 16 ], [ 17 ],
[ 18 ], [ 19, 23 ], [ 20, 24 ], [ 21, 25 ], [ 22, 26 ],
[ 27, 33 ], [ 28, 34 ], [ 29, 35 ], [ 30, 36 ], [ 31, 37 ],
[ 32, 38 ], [ 39, 51 ], [ 40, 52 ], [ 41, 53 ], [ 42, 54 ],
[ 43, 55 ], [ 44, 56 ], [ 45, 57 ], [ 46, 58 ], [ 47, 59 ],
[ 48, 60 ], [ 49, 61 ], [ 50, 62 ] ],
[ [ 1 ], [ 2, 8 ], [ 3 ], [ 4, 10 ], [ 5 ], [ 6, 12 ], [ 7 ],
[ 9 ], [ 11 ], [ 13 ], [ 14 ], [ 15 ], [ 16 ], [ 17 ], [ 18 ],
[ 19, 23 ], [ 20, 26 ], [ 21, 25 ], [ 22, 24 ], [ 27 ],
[ 28, 34 ], [ 29 ], [ 30, 36 ], [ 31 ], [ 32, 38 ], [ 33 ],
[ 35 ], [ 37 ], [ 39, 51 ], [ 40, 58 ], [ 41, 53 ], [ 42, 60 ],
[ 43, 55 ], [ 44, 62 ], [ 45, 57 ], [ 46, 52 ], [ 47, 59 ],
[ 48, 54 ], [ 49, 61 ], [ 50, 56 ] ],
[ [ 1 ], [ 2, 8 ], [ 3 ], [ 4, 10 ], [ 5 ], [ 6, 12 ], [ 7 ],
[ 9 ], [ 11 ], [ 13 ], [ 14 ], [ 15 ], [ 16 ], [ 17 ], [ 18 ],
[ 19, 23 ], [ 20, 26 ], [ 21, 25 ], [ 22, 24 ], [ 27, 33 ],
[ 28 ], [ 29, 35 ], [ 30 ], [ 31, 37 ], [ 32 ], [ 34 ], [ 36 ],
[ 38 ], [ 39, 51 ], [ 40, 58 ], [ 41, 53 ], [ 42, 60 ],
[ 43, 55 ], [ 44, 62 ], [ 45, 57 ], [ 46, 52 ], [ 47, 59 ],
[ 48, 54 ], [ 49, 61 ], [ 50, 56 ] ] ]
gap> poss:= List( elms, pi -> PossibleCharacterTablesOfTypeMGA(
> tblC, tblG, tblNbar, pi, " 12.A6. 2_ 3" ) );
[ [ ], [ ],
[
rec(
MGfusMGA := [ 1, 2, 3, 4, 5, 6, 7, 2, 8, 4, 9, 6, 10, 11, 12,
13, 14, 15, 16, 17, 18, 19, 16, 19, 18, 17, 20, 21, 22,
23, 24, 25, 20, 26, 22, 27, 24, 28, 29, 30, 31, 32, 33,
34, 35, 36, 37, 38, 39, 40, 29, 36, 31, 38, 33, 40, 35,
30, 37, 32, 39, 34 ],
table := CharacterTable( " 12.A6. 2_ 3" ) ) ] ]
## doc2/ctblcons.xml ( 4941- 4945)
gap> IsRecord( TransformingPermutationsCharacterTables( poss[ 3][ 1].table,
> CharacterTable( " 12.A6. 2_ 3" ) ) );
true
## doc2/ctblcons.xml ( 4955- 5006)
gap> c2:= CharacterTable( "Cyclic", 2 );;
gap> tblC:= CharacterTableIsoclinic( CharacterTable( " 2.L2( 25)" ) * c2 );;
gap> ord2:= Filtered( ClassPositionsOfNormalSubgroups( tblC ),
> x -> Length( x ) = 2 );
[ [ 1, 3 ] ]
gap> tblG:= tblC / ord2[ 1];;
gap> tblNbar:= CharacterTableIsoclinic( CharacterTable( "L2( 25). 2_ 3" ) * c2 );;
gap> fus:= PossibleClassFusions( tblG, tblNbar );
[ [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 9, 10, 11, 12, 13, 14, 13, 14, 15,
16, 15, 16, 17, 18, 17, 18, 19, 20, 19, 20 ],
[ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 9, 10, 11, 12, 13, 14, 13, 14, 17,
18, 17, 18, 19, 20, 19, 20, 15, 16, 15, 16 ],
[ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 9, 10, 11, 12, 13, 14, 13, 14, 19,
20, 19, 20, 15, 16, 15, 16, 17, 18, 17, 18 ] ]
gap> rep:= RepresentativesFusions( Group( () ), fus, tblNbar );
[ [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 9, 10, 11, 12, 13, 14, 13, 14, 15,
16, 15, 16, 17, 18, 17, 18, 19, 20, 19, 20 ] ]
gap> StoreFusion( tblG, rep[ 1], tblNbar );
gap> elms:= PossibleActionsForTypeMGA( tblC, tblG, tblNbar );
[ [ [ 1 ], [ 2 ], [ 3 ], [ 4 ], [ 5 ], [ 6 ], [ 7 ], [ 8 ], [ 9 ],
[ 10 ], [ 11, 13 ], [ 12, 14 ], [ 15, 19 ], [ 16, 20 ],
[ 17, 21 ], [ 18, 22 ], [ 23, 25 ], [ 24, 26 ], [ 27, 33 ],
[ 28, 34 ], [ 29, 31 ], [ 30, 32 ], [ 35, 39 ], [ 36, 40 ],
[ 37, 41 ], [ 38, 42 ], [ 43, 47 ], [ 44, 48 ], [ 45, 49 ],
[ 46, 50 ], [ 51, 55 ], [ 52, 56 ], [ 53, 57 ], [ 54, 58 ] ],
[ [ 1 ], [ 2, 4 ], [ 3 ], [ 5 ], [ 6 ], [ 7 ], [ 8, 10 ], [ 9 ],
[ 11 ], [ 12, 14 ], [ 13 ], [ 15, 19 ], [ 16, 22 ], [ 17, 21 ],
[ 18, 20 ], [ 23, 25 ], [ 24 ], [ 26 ], [ 27, 31 ], [ 28, 34 ],
[ 29, 33 ], [ 30, 32 ], [ 35, 39 ], [ 36, 42 ], [ 37, 41 ],
[ 38, 40 ], [ 43, 47 ], [ 44, 50 ], [ 45, 49 ], [ 46, 48 ],
[ 51, 55 ], [ 52, 58 ], [ 53, 57 ], [ 54, 56 ] ],
[ [ 1 ], [ 2, 4 ], [ 3 ], [ 5 ], [ 6 ], [ 7 ], [ 8, 10 ], [ 9 ],
[ 11, 13 ], [ 12 ], [ 14 ], [ 15, 19 ], [ 16, 22 ], [ 17, 21 ],
[ 18, 20 ], [ 23, 25 ], [ 24 ], [ 26 ], [ 27, 33 ], [ 28, 32 ],
[ 29, 31 ], [ 30, 34 ], [ 35, 39 ], [ 36, 42 ], [ 37, 41 ],
[ 38, 40 ], [ 43, 47 ], [ 44, 50 ], [ 45, 49 ], [ 46, 48 ],
[ 51, 55 ], [ 52, 58 ], [ 53, 57 ], [ 54, 56 ] ] ]
gap> poss:= List( elms, pi -> PossibleCharacterTablesOfTypeMGA(
> tblC, tblG, tblNbar, pi, " 4.L2( 25). 2_ 3" ) );
[ [ ], [ ],
[
rec(
MGfusMGA := [ 1, 2, 3, 2, 4, 5, 6, 7, 8, 7, 9, 10, 9, 11, 12,
13, 14, 15, 12, 15, 14, 13, 16, 17, 16, 18, 19, 20, 21,
22, 21, 20, 19, 22, 23, 24, 25, 26, 23, 26, 25, 24, 27,
28, 29, 30, 27, 30, 29, 28, 31, 32, 33, 34, 31, 34, 33,
32 ], table := CharacterTable( " 4.L2( 25). 2_ 3" ) ) ] ]
gap> IsRecord( TransformingPermutationsCharacterTables( poss[ 3][ 1].table,
> CharacterTable( " 4.L2( 25). 2_ 3" ) ) );
true
## doc2/ctblcons.xml ( 5019- 5032)
gap> g:= GammaL( 2, 25);;
gap> phi:= IsomorphismPermGroup( g );;
gap> img:= Image( phi );;
gap> der:= DerivedSubgroup( img );;
gap> derder:= DerivedSubgroup( der );;
gap> Index( img, derder );
48
gap> inter:= Filtered( IntermediateSubgroups( img, derder ).subgroups,
> s -> Size( s ) = 4 * Size( derder ) and
> IsCyclic( CommutatorFactorGroup( s ) ) and
> Size( Centre( s ) ) = 2 );
[ ]
## doc2/ctblcons.xml ( 5048- 5065)
gap> c:= Centralizer( img, derder );;
gap> Size( c ); IsCyclic( c );
24
true
gap> cgen:= MinimalGeneratingSet( c );;
gap> four:= cgen[ 1]^ 6;;
gap> s:= ClosureGroup( derder, four );;
gap> LoadPackage( "GrpConst", false );
true
gap> filt:= Filtered( CyclicExtensions( s, 2 ),
> x -> Size( Centre( x ) ) = 2 and
> IsCyclic( CommutatorFactorGroup( x ) ) );;
gap> Length( filt );
2
gap> IsomorphismGroups( filt[ 1], filt[ 2] ) <> fail;
true
## doc2/ctblcons.xml ( 5073- 5077)
gap> TransformingPermutationsCharacterTables( CharacterTable( filt[ 1] ),
> CharacterTable( " 4.L2( 25). 2_ 3" ) ) <> fail;
true
## doc2/ctblcons.xml ( 5115- 5136)
gap> c2:= CharacterTable( "Cyclic", 2 );;
gap> 2l:= CharacterTable( " 2.L2( 49)" );;
gap> tblC:= CharacterTableIsoclinic( 2l * c2 );;
gap> ord2:= Filtered( ClassPositionsOfNormalSubgroups( tblC ),
> x -> Length( x ) = 2 );
[ [ 1, 3 ] ]
gap> tblG:= tblC / ord2[ 1];;
gap> tblNbar:= CharacterTableIsoclinic(
> CharacterTable( "L2( 49). 2_ 3" ) * c2 );;
gap> fus:= PossibleClassFusions( tblG, tblNbar );;
gap> Length( fus );
10
gap> StoreFusion( tblG, fus[ 1], tblNbar );
gap> elms:= PossibleActionsForTypeMGA( tblC, tblG, tblNbar );;
gap> poss:= List( elms, pi -> PossibleCharacterTablesOfTypeMGA(
> tblC, tblG, tblNbar, pi, " 4.L2( 49). 2_ 3" ) );;
gap> List( poss, Length );
[ 0, 0, 1 ]
gap> t:= poss[ 3][ 1].table;
CharacterTable( " 4.L2( 49). 2_ 3" )
## doc2/ctblcons.xml ( 5149- 5165)
gap> g:= GammaL( 2, 49);;
gap> phi:= IsomorphismPermGroup( g );;
gap> img:= Image( phi );;
gap> der:= DerivedSubgroup( img );;
gap> derder:= DerivedSubgroup( der );;
gap> Index( img, derder );
96
gap> inter:= Filtered( IntermediateSubgroups( img, derder ).subgroups,
> s -> Size( s ) = 4 * Size( derder ) and
> IsCyclic( CommutatorFactorGroup( s ) ) and
> Size( Centre( s ) ) = 2 );;
gap> Length( inter );
4
gap> ForAll( inter, x -> IsConjugate( img, inter[ 1], x ) );
true
## doc2/ctblcons.xml ( 5174- 5181)
gap> TransformingPermutationsCharacterTables( t,
> CharacterTable( inter[ 1] ) ) <> fail;
true
gap> TransformingPermutationsCharacterTables( t,
> CharacterTable( " 4.L2( 49). 2_ 3" ) ) <> fail;
true
## doc2/ctblcons.xml ( 5195- 5220)
gap> c2:= CharacterTable( "Cyclic", 2 );;
gap> 2l:= CharacterTable( " 2.L2( 81)" );;
gap> tblC:= CharacterTableIsoclinic( 2l * c2 );;
gap> ord2:= Filtered( ClassPositionsOfNormalSubgroups( tblC ),
> x -> Length( x ) = 2 );
[ [ 1, 3 ] ]
gap> tblG:= tblC / ord2[ 1];;
gap> tblNbar:= CharacterTableIsoclinic(
> CharacterTable( "L2( 81). 2_ 3" ) * c2 );;
gap> fus:= PossibleClassFusions( tblG, tblNbar );;
gap> Length( fus );
40
gap> fusreps:= RepresentativesFusions( tblG, fus, tblNbar );;
gap> Length( fusreps );
1
gap> StoreFusion( tblG, fusreps[ 1], tblNbar );
gap> elms:= PossibleActionsForTypeMGA( tblC, tblG, tblNbar );;
gap> poss:= List( elms, pi -> PossibleCharacterTablesOfTypeMGA(
> tblC, tblG, tblNbar, pi, " 4.L2( 81). 2_ 3" ) );;
gap> List( poss, Length );
[ 0, 0, 1 ]
gap> TransformingPermutationsCharacterTables( poss[ 3][ 1].table,
> CharacterTable( " 4.L2( 81). 2_ 3" ) ) <> fail;
true
## doc2/ctblcons.xml ( 5230- 5248)
gap> g:= GammaL( 2, 81);;
gap> phi:= IsomorphismPermGroup( g );;
gap> img:= Image( phi );;
gap> der:= DerivedSubgroup( img );;
gap> derder:= DerivedSubgroup( der );;
gap> Index( img, derder );
320
gap> inter:= Filtered( IntermediateSubgroups( img, derder ).subgroups,
> s -> Size( s ) = 4 * Size( derder ) and
> IsCyclic( CommutatorFactorGroup( s ) ) and
> Size( Centre( s ) ) = 2 );;
gap> ForAll( inter, x -> IsConjugate( img, inter[ 1], x ) );
true
gap> NrConjugacyClasses( inter[ 1] );
52
gap> NrConjugacyClasses( CharacterTable( " 4.L2( 81). 2_ 3" ) );
112
## doc2/ctblcons.xml ( 5257- 5264)
gap> t:= CharacterTable( " 2.L2( 81). 4_ 1" );;
gap> NrConjugacyClasses( t );
52
gap> TransformingPermutationsCharacterTables( t,
> CharacterTable( inter[ 1] ) ) <> fail;
true
## doc2/ctblcons.xml ( 5275- 5295)
gap> c:= Centralizer( img, derder );;
gap> Size( c ); IsCyclic( c );
80
true
gap> cgen:= MinimalGeneratingSet( c );;
gap> four:= cgen[ 1]^ 20;;
gap> s:= ClosureGroup( derder, four );;
gap> LoadPackage( "GrpConst", false );
true
gap> filt:= Filtered( CyclicExtensions( s, 2 ),
> x -> Size( Centre( x ) ) = 2 and
> IsCyclic( CommutatorFactorGroup( x ) ) );;
gap> Length( filt );
2
gap> IsomorphismGroups( filt[ 1], filt[ 2] ) <> fail;
true
gap> TransformingPermutationsCharacterTables( CharacterTable( filt[ 1] ),
> CharacterTable( " 4.L2( 81). 2_ 3" ) ) <> fail;
true
## doc2/ctblcons.xml ( 5834- 5855)
gap> s:= CharacterTable( "U3( 8)" );;
gap> s3:= CharacterTable( "U3( 8). 3_ 3" );;
gap> poss:= PossibleClassFusions( s, s3 );;
gap> Length( poss );
4
gap> Length( RepresentativesFusions( s, poss, s3 ) );
1
gap> smod2:= s mod 2;;
gap> s3mod2:= s3 mod 2;;
gap> good:= [];; modmap:= 0;;
gap> for map in poss do
> modmap:= CompositionMaps( InverseMap( GetFusionMap( s3mod2, s3 ) ),
> CompositionMaps( map, GetFusionMap( smod2, s ) ) );
> rest:= List( Irr( s3mod2 ), x -> x{ modmap } );
> if not fail in Decomposition( Irr( smod2 ), rest, "nonnegative" ) then
> Add( good, map );
> fi;
> od;
gap> Length( good );
2
## doc2/ctblcons.xml ( 5865- 5871)
gap> good[ 2] = CompositionMaps( PowerMap( s3, - 1 ), good[ 1] );
true
gap> GetFusionMap( s, s3 ) in good;
true
gap> sfuss3:= GetFusionMap( s, s3 );;
## doc2/ctblcons.xml ( 5903- 5931)
gap> c3:= CharacterTable( "Cyclic", 3 );;
gap> tblG:= s * c3;;
gap> dp:= s3 * c3;;
gap> tblGA1:= CharacterTableIsoclinic( dp, rec( k:= 1 ) );;
gap> tblGA2:= CharacterTableIsoclinic( dp, rec( k:= 2 ) );;
gap> good:= [];;
gap> tblGmod2:= tblG mod 2;;
gap> for tblGA in [ tblGA1, tblGA2 ] do
> tblGAmod2:= tblGA mod 2;
> for map in PossibleClassFusions( tblG, tblGA ) do
> modmap:= CompositionMaps(
> InverseMap( GetFusionMap( tblGAmod2, tblGA ) ),
> CompositionMaps( map, GetFusionMap( tblGmod2, tblG ) ) );
> rest:= List( Irr( tblGAmod2 ), x -> x{ modmap } );
> if not fail in Decomposition( Irr( tblGmod2 ), rest,
> "nonnegative" ) and
> CompositionMaps( GetFusionMap( tblGA, s3 ), map ) =
> CompositionMaps( sfuss3, GetFusionMap( tblG, s ) ) then
> Add( good, [ tblGA, map ] );
> fi;
> od;
> od;
gap> List( good, x -> x[ 1] );
[ CharacterTable( "Isoclinic(U3( 8). 3_ 3xC3, 1)" ),
CharacterTable( "Isoclinic(U3( 8). 3_ 3xC3, 1)" ),
CharacterTable( "Isoclinic(U3( 8). 3_ 3xC3, 2)" ),
CharacterTable( "Isoclinic(U3( 8). 3_ 3xC3, 2)" ) ]
## doc2/ctblcons.xml ( 5944- 5948)
gap> 3s:= CharacterTable( " 3.U3( 8)" );;
gap> dp:= 3s * c3;;
gap> tblMG:= CharacterTableIsoclinic( dp );;
## doc2/ctblcons.xml ( 5959- 5972)
gap> GetFusionMap( tblMG, tblG );
fail
gap> cen:= ClassPositionsOfCentre( tblMG );
[ 1, 2, 3, 4, 5, 6, 7, 8, 9 ]
gap> OrdersClassRepresentatives( tblMG ){ cen };
[ 1, 9, 9, 3, 9, 9, 3, 9, 9 ]
gap> facttbl:= tblMG / [ 1, 4, 7 ];;
gap> tr:= TransformingPermutationsCharacterTables( facttbl, tblG );;
gap> tr.rows; tr.columns;
()
()
gap> StoreFusion( tblMG, GetFusionMap( tblMG, facttbl ), tblG );
## doc2/ctblcons.xml ( 5982- 5998)
gap> posstbls:= [];;
gap> for pair in good do
> tblGA:= pair[ 1];
> GfusGA:= pair[ 2];
> tblG:= s * c3;
> StoreFusion( tblG, GfusGA, tblGA );
> for pi in PossibleActionsForTypeMGA( tblMG, tblG, tblGA ) do
> for cand in PossibleCharacterTablesOfTypeMGA(
> tblMG, tblG, tblGA, pi, "test" ) do
> Add( posstbls, [ tblGA, cand ] );
> od;
> od;
> od;
gap> Length( posstbls );
32
## doc2/ctblcons.xml ( 6007- 6030)
gap> compatible:= [];; r:= 0;; modr:= 0;;
gap> for pair in posstbls do
> tblGA:= pair[ 1];
> r:= pair[ 2];
> comp:= ComputedClassFusions( tblMG );
> pos:= PositionProperty( comp, x -> x.name = Identifier( r.table ) );
> if pos = fail then
> StoreFusion( tblMG, r.MGfusMGA, r.table );
> else
> comp[ pos ]:= ShallowCopy( comp[ pos ] );
> comp[ pos ].map:= r.MGfusMGA;
> fi;
> Unbind( ComputedBrauerTables( tblMG )[ 2] );
> modr:= BrauerTableOfTypeMGA( tblMG mod 2, tblGA mod 2, r.table );
> rest:= List( Irr( modr.table ), x -> x{ modr.MGfusMGA } );
> dec:= Decomposition( Irr( tblMG mod 2 ), rest, "nonnegative" );
> if not fail in dec then
> Add( compatible, pair );
> fi;
> od;
gap> Length( compatible );
8
## doc2/ctblcons.xml ( 6038- 6048)
gap> tbls:= [];;
gap> for pair in compatible do
> if ForAll( tbls, t -> TransformingPermutationsCharacterTables(
> t, pair[ 2].table ) = fail ) then
> Add( tbls, pair[ 2].table );
> fi;
> od;
gap> Length( tbls );
2
## doc2/ctblcons.xml ( 6061- 6074)
gap> Set( OrdersClassRepresentatives( tbls[ 1] ) );
[ 1, 2, 3, 4, 6, 7, 9, 12, 18, 19, 21, 27, 36, 54, 57, 63, 171 ]
gap> Set( OrdersClassRepresentatives( tbls[ 2] ) );
[ 1, 2, 3, 4, 6, 7, 9, 12, 18, 19, 21, 27, 36, 57, 63, 171 ]
gap> pos171:= Positions( OrdersClassRepresentatives( tbls[ 1] ), 171 );;
gap> pow4:= PowerMap( tbls[ 1], 4 );;
gap> ForAny( [ 1 .. Length( pos171 ) ],
> i -> pos171[i] = pow4[ pos171[i] ] );
false
gap> pos171:= Positions( OrdersClassRepresentatives( tbls[ 2] ), 171 );;
gap> PowerMap( tbls[ 2], 4 ){ pos171 } = pos171;
true
## doc2/ctblcons.xml ( 6083- 6100)
gap> gu:= GU( 3, 8);;
gap> orbs:= OrbitsDomain( gu, Elements( GF( 64)^ 3 ) );;
gap> List( orbs, Length );
[ 1, 32319, 32832, 32832, 32832, 32832, 32832, 32832, 32832 ]
gap> orb:= SortedList( First( orbs, x -> Length( x ) = 32319 ) );;
gap> actgu:= Action( gu, orb, OnRight );;
gap> Size( actgu ) = Size( gu );
true
gap> cen:= Centre( actgu );;
gap> Size( cen );
9
gap> u:= ClosureGroup( DerivedSubgroup( actgu ), cen );;
gap> aut:= v -> List( v, x -> x^ 4 );;
gap> pi:= PermList( List( orb, v -> PositionSorted( orb, aut( v ) ) ) );;
gap> outer:= First( GeneratorsOfGroup( actgu ), x -> not x in u );;
gap> g:= ClosureGroup( u, pi * outer );;
## doc2/ctblcons.xml ( 6109- 6120)
gap> g:= Group( SmallGeneratingSet( g ) );;
gap> allbl:= AllBlocks( g );;
gap> List( allbl, Length );
[ 3, 21, 63, 9, 7 ]
gap> orb:= Orbit( g, First( allbl, x -> Length( x ) = 7 ), OnSets );;
gap> act:= Action( g, orb, OnSets );;
gap> Size( act ) = Size( g );
true
gap> NrMovedPoints( act );
4617
## doc2/ctblcons.xml ( 6129- 6133)
gap> repeat x:= PseudoRandom( act ); until Order( x ) = 171;
gap> IsConjugate( act, x, x^ 4 );
true
## doc2/ctblcons.xml ( 6144- 6148)
gap> lib:= CharacterTable( " 9.U3( 8). 3_ 3" );;
gap> IsRecord( TransformingPermutationsCharacterTables( tbls[ 2], lib ) );
true
## doc2/ctblcons.xml ( 6190- 6202)
gap> tblMG := CharacterTable( " 3.A6" );;
gap> tblG := CharacterTable( "A6" );;
gap> tblGA := CharacterTable( "A6. 2_ 3" );;
gap> elms:= PossibleActionsForTypeMGA( tblMG, tblG, tblGA );
[ [ [ 1 ], [ 2, 3 ], [ 4 ], [ 5, 6 ], [ 7, 8 ], [ 9 ], [ 10, 11 ],
[ 12, 15 ], [ 13, 17 ], [ 14, 16 ] ] ]
gap> poss:= PossibleCharacterTablesOfTypeMGA(
> tblMG, tblG, tblGA, elms[ 1], "pseudo" );
[ rec(
MGfusMGA := [ 1, 2, 2, 3, 4, 4, 5, 5, 6, 7, 7, 8, 9, 10, 8, 10,
9 ], table := CharacterTable( "pseudo" ) ) ]
## doc2/ctblcons.xml ( 6232- 6278)
gap> pseudo:= poss[ 1].table;
CharacterTable( "pseudo" )
gap> Display( pseudo );
pseudo
2 4 3 4 3 . 3 2 . . . 2 3 3
3 3 3 1 1 2 1 1 1 1 1 . . .
5 1 1 . . . . . 1 1 1 . . .
1a 3a 2a 6a 3b 4a 12a 5a 15a 15b 4b 8a 8b
2P 1a 3a 1a 3a 3b 2a 6a 5a 15a 15b 2a 4a 4a
3P 1a 1a 2a 2a 1a 4a 4a 5a 5a 5a 4b 8a 8b
5P 1a 3a 2a 6a 3b 4a 12a 1a 3a 3a 4b 8b 8a
X. 1 1 1 1 1 1 1 1 1 1 1 1 1 1
X. 2 1 1 1 1 1 1 1 1 1 1 - 1 - 1 - 1
X. 3 10 10 2 2 1 - 2 - 2 . . . . . .
X. 4 16 16 . . - 2 . . 1 1 1 . . .
X. 5 9 9 1 1 . 1 1 - 1 - 1 - 1 1 - 1 - 1
X. 6 9 9 1 1 . 1 1 - 1 - 1 - 1 - 1 1 1
X. 7 10 10 - 2 - 2 1 . . . . . . B -B
X. 8 10 10 - 2 - 2 1 . . . . . . -B B
X. 9 6 - 3 - 2 1 . 2 - 1 1 A /A . . .
X. 10 6 - 3 - 2 1 . 2 - 1 1 /A A . . .
X. 11 12 - 6 4 - 2 . . . 2 - 1 - 1 . . .
X. 12 18 - 9 2 - 1 . 2 - 1 - 2 1 1 . . .
X. 13 30 - 15 - 2 1 . - 2 1 . . . . . .
A = -E( 15)-E( 15)^ 2-E( 15)^ 4-E( 15)^ 8
= (- 1-Sqrt(- 15))/ 2 = - 1-b15
B = E( 8)+E( 8)^ 3
= Sqrt(- 2) = i2
gap> IsInternallyConsistent( pseudo );
true
gap> irr:= Irr( pseudo );;
gap> test:= Concatenation( List( [ 2 .. 5 ],
> n -> Symmetrizations( pseudo, irr, n ) ) );;
gap> Append( test, Set( Tensored( irr, irr ) ) );
gap> fail in Decomposition( irr, test, "nonnegative" );
false
gap> if ForAny( Tuples( [ 1 .. NrConjugacyClasses( pseudo ) ], 3 ),
> t -> not ClassMultiplicationCoefficient( pseudo, t[ 1], t[ 2], t[ 3] )
> in NonnegativeIntegers ) then
> Error( "contradiction" );
> fi;
## doc2/ctblcons.xml ( 6315- 6325)
gap> tblMG := CharacterTable( " 3.L3( 4)" );;
gap> tblG := CharacterTable( "L3( 4)" );;
gap> tblGA := CharacterTable( "L3( 4). 2_ 1" );;
gap> elms:= PossibleActionsForTypeMGA( tblMG, tblG, tblGA );
[ [ [ 1 ], [ 2, 3 ], [ 4 ], [ 5, 6 ], [ 7 ], [ 8 ], [ 9, 10 ],
[ 11 ], [ 12, 13 ], [ 14 ], [ 15, 16 ], [ 17, 20 ], [ 18, 22 ],
[ 19, 21 ], [ 23, 26 ], [ 24, 28 ], [ 25, 27 ] ] ]
gap> PossibleCharacterTablesOfTypeMGA( tblMG, tblG, tblGA, elms[ 1], "?" );
[ ]
## doc2/ctblcons.xml ( 6337- 6347)
gap> tblG := CharacterTable( "U4( 3)" );;
gap> tblMG := CharacterTable( " 3_ 1.U4( 3)" );;
gap> tblGA := CharacterTable( "U4( 3). 2_ 2" );;
gap> PossibleActionsForTypeMGA( tblMG, tblG, tblGA );
[ ]
gap> tblMG:= CharacterTable( " 3_ 2.U4( 3)" );;
gap> tblGA:= CharacterTable( "U4( 3). 2_ 3" );;
gap> PossibleActionsForTypeMGA( tblMG, tblG, tblGA );
[ ]
## doc2/ctblcons.xml ( 6497- 6549)
gap> FindExtraordinaryCase:= function( tblMGA )
> local result, der, nsg, tblMGAclasses, orders, tblMG,
> tblMGfustblMGA, tblMGclasses, pos, M, Mimg, tblMGAfustblGA, tblGA,
> outer, inv, filt, other, primes, p;
> result:= [];
> der:= ClassPositionsOfDerivedSubgroup( tblMGA );
> nsg:= ClassPositionsOfNormalSubgroups( tblMGA );
> tblMGAclasses:= SizesConjugacyClasses( tblMGA );
> orders:= OrdersClassRepresentatives( tblMGA );
> if Length( der ) < NrConjugacyClasses( tblMGA ) then
> # Look for tables of normal subgroups of the form $M.G$.
> for tblMG in Filtered( List( NamesOfFusionSources( tblMGA ),
> CharacterTable ), x -> x <> fail ) do
> tblMGfustblMGA:= GetFusionMap( tblMG, tblMGA );
> tblMGclasses:= SizesConjugacyClasses( tblMG );
> pos:= Position( nsg, Set( tblMGfustblMGA ) );
> if pos <> fail and
> Size( tblMG ) = Sum( tblMGAclasses{ nsg[ pos ] } ) then
> # Look for normal subgroups of the form $M$.
> for M in Difference( ClassPositionsOfNormalSubgroups( tblMG ),
> [ [ 1 ], [ 1 .. NrConjugacyClasses( tblMG ) ] ] ) do
> Mimg:= Set( tblMGfustblMGA{ M } );
> if Sum( tblMGAclasses{ Mimg } ) = Sum( tblMGclasses{ M } ) then
> tblMGAfustblGA:= First( ComputedClassFusions( tblMGA ),
> r -> ClassPositionsOfKernel( r.map ) = Mimg );
> if tblMGAfustblGA <> fail then
> tblGA:= CharacterTable( tblMGAfustblGA.name );
> tblMGAfustblGA:= tblMGAfustblGA.map;
> outer:= Difference( [ 1 .. NrConjugacyClasses( tblGA ) ],
> CompositionMaps( tblMGAfustblGA, tblMGfustblMGA ) );
> inv:= InverseMap( tblMGAfustblGA ){ outer };
> filt:= Flat( Filtered( inv, IsList ) );
> if not IsEmpty( filt ) then
> other:= Filtered( inv, IsInt );
> primes:= Filtered( PrimeDivisors( Size( tblMGA ) ),
> p -> ForAll( orders{ filt }, x -> x mod p = 0 )
> and ForAny( orders{ other }, x -> x mod p <> 0 ) );
> for p in primes do
> Add( result, [ Identifier( tblMG ),
> Identifier( tblMGA ),
> Identifier( tblGA ), p ] );
> od;
> fi;
> fi;
> fi;
> od;
> fi;
> od;
> fi;
> return result;
> end;;
## doc2/ctblcons.xml ( 6557- 6594)
gap> cases:= [];;
gap> for name in AllCharacterTableNames( IsDuplicateTable, false ) do
> Append( cases, FindExtraordinaryCase( CharacterTable( name ) ) );
> od;
gap> for i in Set( cases ) do
> Print( i, "\n" );
> od;
[ " 2.A6", " 2.A6. 2_ 1", "A6. 2_ 1", 3 ]
[ " 2.Fi22", " 2.Fi22. 2", "Fi22. 2", 3 ]
[ " 2.L2( 25)", " 2.L2( 25). 2_ 2", "L2( 25). 2_ 2", 5 ]
[ " 2.L2( 49)", " 2.L2( 49). 2_ 2", "L2( 49). 2_ 2", 7 ]
[ " 2.L2( 81)", " 2.L2( 81). 2_ 1", "L2( 81). 2_ 1", 3 ]
[ " 2.L2( 81)", " 2.L2( 81). 4_ 1", "L2( 81). 4_ 1", 3 ]
[ " 2.L2( 81). 2_ 1", " 2.L2( 81). 4_ 1", "L2( 81). 4_ 1", 3 ]
[ " 2.L4( 3)", " 2.L4( 3). 2_ 2", "L4( 3). 2_ 2", 3 ]
[ " 2.L4( 3)", " 2.L4( 3). 2_ 3", "L4( 3). 2_ 3", 3 ]
[ " 2.S3", " 2.D12", "S3x2", 3 ]
[ " 2.U4( 3). 2_ 1", " 2.U4( 3).( 2^ 2)_{ 12* 2*}", "U4( 3).( 2^ 2)_{ 122}", 3 ]
[ " 2.U4( 3). 2_ 1", " 2.U4( 3).( 2^ 2)_{ 122}", "U4( 3).( 2^ 2)_{ 122}", 3 ]
[ " 2.U4( 3). 2_ 1", " 2.U4( 3).( 2^ 2)_{ 13* 3*}", "U4( 3).( 2^ 2)_{ 133}", 3 ]
[ " 2.U4( 3). 2_ 1", " 2.U4( 3).( 2^ 2)_{ 133}", "U4( 3).( 2^ 2)_{ 133}", 3 ]
[ " 3.U3( 8)", " 3.U3( 8). 3_ 1", "U3( 8). 3_ 1", 2 ]
[ " 3.U3( 8)", " 3.U3( 8). 6", "U3( 8). 6", 2 ]
[ " 3.U3( 8)", " 3.U3( 8). 6", "U3( 8). 6", 3 ]
[ " 3.U3( 8). 2", " 3.U3( 8). 6", "U3( 8). 6", 2 ]
[ " 3^ 2: 8", " 2.A8N3", "s3wrs2", 3 ]
[ " 5^( 1+ 2): 8: 4", " 2.HS. 2N5", "HS. 2N5", 5 ]
[ " 6.A6", " 6.A6. 2_ 1", " 3.A6. 2_ 1", 3 ]
[ " 6.A6", " 6.A6. 2_ 1", "A6. 2_ 1", 3 ]
[ " 6.Fi22", " 6.Fi22. 2", " 3.Fi22. 2", 3 ]
[ " 6.Fi22", " 6.Fi22. 2", "Fi22. 2", 3 ]
[ "Isoclinic( 2.U4( 3). 2_ 1)", " 2.U4( 3).( 2^ 2)_{ 1* 2* 2}",
"U4( 3).( 2^ 2)_{ 122}", 3 ]
[ "Isoclinic( 2.U4( 3). 2_ 1)", " 2.U4( 3).( 2^ 2)_{ 1* 3* 3}",
"U4( 3).( 2^ 2)_{ 133}", 3 ]
[ "bd10", " 2.D20", "D20", 5 ]
## doc2/ctblcons.xml ( 6604- 6626)
gap> Display( CharacterTable( " 2.A6. 2_ 1" ) mod 3 );
2.A6. 2_ 1mod3
2 5 5 4 3 1 1 4 4 3
3 2 2 . . . . 1 1 .
5 1 1 . . 1 1 . . .
1a 2a 4a 8a 5a 10a 2b 4b 8b
2P 1a 1a 2a 4a 5a 5a 1a 2a 4a
3P 1a 2a 4a 8a 5a 10a 2b 4b 8b
5P 1a 2a 4a 8a 1a 2a 2b 4b 8b
X. 1 1 1 1 1 1 1 1 1 1
X. 2 1 1 1 1 1 1 - 1 - 1 - 1
X. 3 6 6 - 2 2 1 1 . . .
X. 4 4 4 . - 2 - 1 - 1 2 - 2 .
X. 5 4 4 . - 2 - 1 - 1 - 2 2 .
X. 6 9 9 1 1 - 1 - 1 3 3 - 1
X. 7 9 9 1 1 - 1 - 1 - 3 - 3 1
X. 8 4 - 4 . . - 1 1 . . .
X. 9 12 - 12 . . 2 - 2 . . .
## doc2/ctblcons.xml ( 6646- 6674)
gap> for input in cases do
> p:= input[ 4];
> modtblMG:= CharacterTable( input[ 1] ) mod p;
> ordtblMGA:= CharacterTable( input[ 2] );
> modtblGA:= CharacterTable( input[ 3] ) mod p;
> name:= Concatenation( Identifier( ordtblMGA ), " mod ", String(p) );
> if ForAll( [ modtblMG, modtblGA ], IsCharacterTable ) then
> poss:= BrauerTableOfTypeMGA( modtblMG, modtblGA, ordtblMGA );
> modlib:= ordtblMGA mod p;
> if IsCharacterTable( modlib ) then
> trans:= TransformingPermutationsCharacterTables( poss.table,
> modlib );
> if not IsRecord( trans ) then
> Print( "#E computed table and library table for ", name,
> " differ\n" );
> fi;
> else
> Print( "#I no library table for ", name, "\n" );
> fi;
> else
> Print( "#I not all input tables for ", name, " available\n" );
> fi;
> od;
#I not all input tables for 2.L2( 49). 2_ 2 mod 7 available
#I not all input tables for 2.L2( 81). 2_ 1 mod 3 available
#I not all input tables for 2.L2( 81). 4_ 1 mod 3 available
#I not all input tables for 2.L2( 81). 4_ 1 mod 3 available
## doc2/ctblcons.xml ( 6710- 6742)
gap> c2:= CharacterTable( "Cyclic", 2 );;
gap> t:= c2 * c2;;
gap> tC:= CharacterTable( "Dihedral", 8 );;
gap> tK:= CharacterTable( "Alternating", 4 );;
gap> tfustC:= PossibleClassFusions( t, tC );
[ [ 1, 3, 4, 4 ], [ 1, 3, 5, 5 ], [ 1, 4, 3, 4 ], [ 1, 4, 4, 3 ],
[ 1, 5, 3, 5 ], [ 1, 5, 5, 3 ] ]
gap> StoreFusion( t, tfustC[ 1], tC );
gap> tfustK:= PossibleClassFusions( t, tK );
[ [ 1, 2, 2, 2 ] ]
gap> StoreFusion( t, tfustK[ 1], tK );
gap> elms:= PossibleActionsForTypeGS3( t, tC, tK );
[ ( 3, 4) ]
gap> new:= CharacterTableOfTypeGS3( t, tC, tK, elms[ 1], "S4" );
rec( table := CharacterTable( "S4" ),
tblCfustblKC := [ 1, 4, 2, 2, 5 ], tblKfustblKC := [ 1, 2, 3, 3 ] )
gap> Display( new.table );
S4
2 3 3 . 2 2
3 1 . 1 . .
1a 2a 3a 4a 2b
2P 1a 1a 3a 2a 1a
3P 1a 2a 1a 4a 2b
X. 1 1 1 1 1 1
X. 2 1 1 1 - 1 - 1
X. 3 3 - 1 . 1 - 1
X. 4 3 - 1 . - 1 1
X. 5 2 2 - 1 . .
## doc2/ctblcons.xml ( 6762- 6798)
gap> t:= CharacterTable( "Cyclic", 2 );;
gap> tC:= CharacterTable( "Cyclic", 6 );;
gap> tK:= CharacterTable( "Quaternionic", 8 );;
gap> tfustC:= PossibleClassFusions( t, tC );
[ [ 1, 4 ] ]
gap> StoreFusion( t, tfustC[ 1], tC );
gap> tfustK:= PossibleClassFusions( t, tK );
[ [ 1, 3 ] ]
gap> StoreFusion( t, tfustK[ 1], tK );
gap> elms:= PossibleActionsForTypeGS3( t, tC, tK );
[ ( 2, 5, 4) ]
gap> new:= CharacterTableOfTypeGS3( t, tC, tK, elms[ 1], "SL( 2, 3)" );
rec( table := CharacterTable( "SL( 2, 3)" ),
tblCfustblKC := [ 1, 4, 5, 3, 6, 7 ],
tblKfustblKC := [ 1, 2, 3, 2, 2 ] )
gap> Display( new.table );
SL( 2, 3)
2 3 2 3 1 1 1 1
3 1 . 1 1 1 1 1
1a 4a 2a 6a 3a 3b 6b
2P 1a 2a 1a 3a 3b 3a 3b
3P 1a 4a 2a 2a 1a 1a 2a
X. 1 1 1 1 1 1 1 1
X. 2 1 1 1 A /A A /A
X. 3 1 1 1 /A A /A A
X. 4 3 - 1 3 . . . .
X. 5 2 . - 2 /A -A -/A A
X. 6 2 . - 2 1 - 1 - 1 1
X. 7 2 . - 2 A -/A -A /A
A = E( 3)
= (- 1+Sqrt(- 3))/ 2 = b3
## doc2/ctblcons.xml ( 6819- 6844)
gap> listGS3:= [
> [ "U3( 5)", "U3( 5). 2", "U3( 5). 3", "U3( 5).S3" ],
> [ " 3.U3( 5)", " 3.U3( 5). 2", " 3.U3( 5). 3", " 3.U3( 5).S3" ],
> [ "L3( 4)", "L3( 4). 2_ 2", "L3( 4). 3", "L3( 4). 3. 2_ 2" ],
> [ "L3( 4)", "L3( 4). 2_ 3", "L3( 4). 3", "L3( 4). 3. 2_ 3" ],
> [ " 3.L3( 4)", " 3.L3( 4). 2_ 2", " 3.L3( 4). 3", " 3.L3( 4). 3. 2_ 2" ],
> [ " 3.L3( 4)", " 3.L3( 4). 2_ 3", " 3.L3( 4). 3", " 3.L3( 4). 3. 2_ 3" ],
> [ " 2^ 2.L3( 4)", " 2^ 2.L3( 4). 2_ 2"," 2^ 2.L3( 4). 3", " 2^ 2.L3( 4). 3. 2_ 2" ],
> [ " 2^ 2.L3( 4)", " 2^ 2.L3( 4). 2_ 3"," 2^ 2.L3( 4). 3", " 2^ 2.L3( 4). 3. 2_ 3" ],
> [ "U6( 2)", "U6( 2). 2", "U6( 2). 3", "U6( 2). 3. 2" ],
> [ " 3.U6( 2)", " 3.U6( 2). 2", " 3.U6( 2). 3", " 3.U6( 2). 3. 2" ],
> [ " 2^ 2.U6( 2)", " 2^ 2.U6( 2). 2", " 2^ 2.U6( 2). 3", " 2^ 2.U6( 2). 3. 2" ],
> [ "O8+( 2)", "O8+( 2). 2", "O8+( 2). 3", "O8+( 2). 3. 2" ],
> [ " 2^ 2.O8+( 2)", " 2^ 2.O8+( 2). 2", " 2^ 2.O8+( 2). 3", " 2^ 2.O8+( 2). 3. 2" ],
> [ "L3( 7)", "L3( 7). 2", "L3( 7). 3", "L3( 7).S3" ],
> [ " 3.L3( 7)", " 3.L3( 7). 2", " 3.L3( 7). 3", " 3.L3( 7).S3" ],
> [ "U3( 8)", "U3( 8). 2", "U3( 8). 3_ 2", "U3( 8).S3" ],
> [ " 3.U3( 8)", " 3.U3( 8). 2", " 3.U3( 8). 3_ 2", " 3.U3( 8).S3" ],
> [ "U3( 11)", "U3( 11). 2", "U3( 11). 3", "U3( 11).S3" ],
> [ " 3.U3( 11)", " 3.U3( 11). 2", " 3.U3( 11). 3", " 3.U3( 11).S3" ],
> [ "O8+( 3)", "O8+( 3). 2_ 2", "O8+( 3). 3", "O8+( 3).S3" ],
> [ " 2E6( 2)", " 2E6( 2). 2", " 2E6( 2). 3", " 2E6( 2).S3" ],
> [ " 2^ 2. 2E6( 2)", " 2^ 2. 2E6( 2). 2", " 2^ 2. 2E6( 2). 3", " 2^ 2. 2E6( 2).S3" ],
> ];;
## doc2/ctblcons.xml ( 6866- 6873)
gap> Append( listGS3, [
> [ "L3( 4). 2_ 1", "L3( 4). 2^ 2", "L3( 4). 6", "L3( 4).D12" ],
> [ " 2^ 2.L3( 4). 2_ 1", " 2^ 2.L3( 4). 2^ 2", " 2^ 2.L3( 4). 6", " 2^ 2.L3( 4).D12" ],
> [ "U3( 8). 3_ 1", "U3( 8). 6", "U3( 8). 3^ 2", "U3( 8).(S3x3)" ],
> [ "O8+( 3).( 2^ 2)_{ 111}", "O8+( 3).D8", "O8+( 3).A4", "O8+( 3).S4" ],
> ] );
## doc2/ctblcons.xml ( 6898- 6947)
gap> ProcessGS3Example:= function( t, tC, tK, identifier, pi )
> local tF, lib, trans, p, tmodp, tCmodp, tKmodp, modtF;
>
> tF:= CharacterTableOfTypeGS3( t, tC, tK, pi,
> Concatenation( identifier, "new" ) );
> lib:= CharacterTable( identifier );
> if lib <> fail then
> trans:= TransformingPermutationsCharacterTables( tF.table, lib );
> if not IsRecord( trans ) then
> Print( "#E computed table and library table for `", identifier,
> "' differ\n" );
> fi;
> else
> Print( "#I no library table for `", identifier, "'\n" );
> fi;
> StoreFusion( tC, tF.tblCfustblKC, tF.table );
> StoreFusion( tK, tF.tblKfustblKC, tF.table );
> for p in PrimeDivisors( Size( t ) ) do
> tmodp := t mod p;
> tCmodp:= tC mod p;
> tKmodp:= tK mod p;
> if IsCharacterTable( tmodp ) and
> IsCharacterTable( tCmodp ) and
> IsCharacterTable( tKmodp ) then
> modtF:= CharacterTableOfTypeGS3( tmodp, tCmodp, tKmodp,
> tF.table,
> Concatenation( identifier, "mod", String( p ) ) );
> if Length( Irr( modtF.table ) ) <>
> Length( Irr( modtF.table )[ 1] ) then
> Print( "#E nonsquare result table for `",
> identifier, " mod ", p, "'\n" );
> elif lib <> fail and IsCharacterTable( lib mod p ) then
> trans:= TransformingPermutationsCharacterTables( modtF.table,
> lib mod p );
> if not IsRecord( trans ) then
> Print( "#E computed table and library table for `",
> identifier, " mod ", p, "' differ\n" );
> fi;
> else
> Print( "#I no library table for `", identifier, " mod ",
> p, "'\n" );
> fi;
> else
> Print( "#I not all inputs available for `", identifier,
> " mod ", p, "'\n" );
> fi;
> od;
> end;;
## doc2/ctblcons.xml ( 6955- 6989)
gap> for input in listGS3 do
> t := CharacterTable( input[ 1] );
> tC:= CharacterTable( input[ 2] );
> tK:= CharacterTable( input[ 3] );
> identifier:= input[ 4];
> elms:= PossibleActionsForTypeGS3( t, tC, tK );
> if Length( elms ) = 1 then
> ProcessGS3Example( t, tC, tK, identifier, elms[ 1] );
> else
> Print( "#I ", Length( elms ), " actions possible for `",
> identifier, "'\n" );
> fi;
> od;
#I not all inputs available for `O8+( 3).S3 mod 3'
#I not all inputs available for ` 2E6( 2).S3 mod 2'
#I not all inputs available for ` 2E6( 2).S3 mod 3'
#I not all inputs available for ` 2E6( 2).S3 mod 5'
#I not all inputs available for ` 2E6( 2).S3 mod 7'
#I not all inputs available for ` 2E6( 2).S3 mod 11'
#I not all inputs available for ` 2E6( 2).S3 mod 13'
#I not all inputs available for ` 2E6( 2).S3 mod 17'
#I not all inputs available for ` 2E6( 2).S3 mod 19'
#I not all inputs available for ` 2^ 2. 2E6( 2).S3 mod 2'
#I not all inputs available for ` 2^ 2. 2E6( 2).S3 mod 3'
#I not all inputs available for ` 2^ 2. 2E6( 2).S3 mod 5'
#I not all inputs available for ` 2^ 2. 2E6( 2).S3 mod 7'
#I not all inputs available for ` 2^ 2. 2E6( 2).S3 mod 11'
#I not all inputs available for ` 2^ 2. 2E6( 2).S3 mod 13'
#I not all inputs available for ` 2^ 2. 2E6( 2).S3 mod 17'
#I not all inputs available for ` 2^ 2. 2E6( 2).S3 mod 19'
#I not all inputs available for `U3( 8).(S3x3) mod 2'
#I not all inputs available for `U3( 8).(S3x3) mod 19'
#I not all inputs available for `O8+( 3).S4 mod 3'
## doc2/ctblcons.xml ( 7001- 7022)
gap> input:= [ "O8+( 3)", "O8+( 3). 3", "O8+( 3).( 2^ 2)_{ 111}", "O8+( 3).A4" ];;
gap> t := CharacterTable( input[ 1] );;
gap> tC:= CharacterTable( input[ 2] );;
gap> tK:= CharacterTable( input[ 3] );;
gap> identifier:= input[ 4];;
gap> elms:= PossibleActionsForTypeGS3( t, tC, tK );;
gap> Length( elms );
4
gap> differ:= MovedPoints( Group( List( elms, x -> x / elms[ 1] ) ) );;
gap> List( elms, x -> RestrictedPerm( x, differ ) );
[ ( 118, 216, 169)( 119, 217, 170)( 120, 218, 167)( 121, 219, 168),
( 118, 216, 170)( 119, 217, 169)( 120, 219, 168)( 121, 218, 167),
( 118, 217, 169)( 119, 216, 170)( 120, 218, 168)( 121, 219, 167),
( 118, 217, 170)( 119, 216, 169)( 120, 219, 167)( 121, 218, 168) ]
gap> poss:= List( elms, pi -> CharacterTableOfTypeGS3( t, tC, tK, pi,
> Concatenation( identifier, "new" ) ) );;
gap> lib:= CharacterTable( identifier );;
gap> ForAll( poss, r -> IsRecord(
> TransformingPermutationsCharacterTables( r.table, lib ) ) );
true
## doc2/ctblcons.xml ( 7031- 7034)
gap> ProcessGS3Example( t, tC, tK, identifier, elms[ 1] );
#I not all inputs available for `O8+( 3).A4 mod 3'
## doc2/ctblcons.xml ( 7089- 7098)
gap> tblG:= CharacterTable( "A6" );;
gap> tblsG2:= List( [ "A6. 2_ 1", "A6. 2_ 2", "A6. 2_ 3" ], CharacterTable );;
gap> List( tblsG2, NrConjugacyClasses );
[ 11, 11, 8 ]
gap> possact:= List( tblsG2, x -> Filtered( Elements(
> AutomorphismsOfTable( x ) ), y -> Order( y ) <= 2 ) );
[ [ (), ( 3, 4)( 7, 8)( 10, 11) ],
[ (), ( 8, 9), ( 5, 6)( 10, 11), ( 5, 6)( 8, 9)( 10, 11) ], [ (), ( 7, 8) ] ]
## doc2/ctblcons.xml ( 7118- 7122)
gap> List( tblsG2, x -> GetFusionMap( tblG, x ) );
[ [ 1, 2, 3, 4, 5, 6, 6 ], [ 1, 2, 3, 3, 4, 5, 6 ],
[ 1, 2, 3, 3, 4, 5, 5 ] ]
## doc2/ctblcons.xml ( 7134- 7137)
gap> acts:= PossibleActionsForTypeGV4( tblG, tblsG2 );
[ [ ( 3, 4)( 7, 8)( 10, 11), ( 5, 6)( 8, 9)( 10, 11), ( 7, 8) ] ]
## doc2/ctblcons.xml ( 7148- 7159)
gap> poss:= PossibleCharacterTablesOfTypeGV4( tblG, tblsG2, acts[ 1],
> "A6. 2^ 2" );
[ rec(
G2fusGV4 := [ [ 1, 2, 3, 3, 4, 5, 6, 6, 7, 8, 8 ],
[ 1, 2, 3, 4, 5, 5, 9, 10, 10, 11, 11 ],
[ 1, 2, 3, 4, 5, 12, 13, 13 ] ],
table := CharacterTable( "A6. 2^ 2" ) ) ]
gap> IsRecord( TransformingPermutationsCharacterTables( poss[ 1].table,
> CharacterTable( "A6. 2^ 2" ) ) );
true
## doc2/ctblcons.xml ( 7169- 7177)
gap> PossibleCharacterTablesOfTypeGV4( tblG mod 3,
> List( tblsG2, t -> t mod 3 ), poss[ 1].table );
[ rec(
G2fusGV4 :=
[ [ 1, 2, 3, 4, 5, 5, 6 ], [ 1, 2, 3, 4, 4, 7, 8, 8, 9, 9 ],
[ 1, 2, 3, 4, 10, 11, 11 ] ],
table := BrauerTable( "A6. 2^ 2", 3 ) ) ]
## doc2/ctblcons.xml ( 7208- 7232)
gap> listGV4:= [
> [ "A6", "A6. 2_ 1", "A6. 2_ 2", "A6. 2_ 3", "A6. 2^ 2" ],
> [ " 3.A6", " 3.A6. 2_ 1", " 3.A6. 2_ 2", " 3.A6. 2_ 3", " 3.A6. 2^ 2" ],
> [ "L2( 25)", "L2( 25). 2_ 1", "L2( 25). 2_ 2", "L2( 25). 2_ 3", "L2( 25). 2^ 2" ],
> [ "L3( 4)", "L3( 4). 2_ 1", "L3( 4). 2_ 2", "L3( 4). 2_ 3", "L3( 4). 2^ 2" ],
> [ " 2^ 2.L3( 4)", " 2^ 2.L3( 4). 2_ 1", " 2^ 2.L3( 4). 2_ 2", " 2^ 2.L3( 4). 2_ 3",
> " 2^ 2.L3( 4). 2^ 2" ],
> [ " 3.L3( 4)", " 3.L3( 4). 2_ 1", " 3.L3( 4). 2_ 2", " 3.L3( 4). 2_ 3", " 3.L3( 4). 2^ 2" ],
> [ "U4( 3)", "U4( 3). 2_ 1", "U4( 3). 2_ 2", "U4( 3). 2_ 2'",
> "U4( 3).( 2^ 2)_{ 122}" ],
> [ "U4( 3)", "U4( 3). 2_ 1", "U4( 3). 2_ 3", "U4( 3). 2_ 3'",
> "U4( 3).( 2^ 2)_{ 133}" ],
> [ " 3_ 1.U4( 3)", " 3_ 1.U4( 3). 2_ 1", " 3_ 1.U4( 3). 2_ 2", " 3_ 1.U4( 3). 2_ 2'",
> " 3_ 1.U4( 3).( 2^ 2)_{ 122}" ],
> [ " 3_ 2.U4( 3)", " 3_ 2.U4( 3). 2_ 1", " 3_ 2.U4( 3). 2_ 3", " 3_ 2.U4( 3). 2_ 3'",
> " 3_ 2.U4( 3).( 2^ 2)_{ 133}" ],
> [ "L2( 49)", "L2( 49). 2_ 1", "L2( 49). 2_ 2", "L2( 49). 2_ 3", "L2( 49). 2^ 2" ],
> [ "L2( 81)", "L2( 81). 2_ 1", "L2( 81). 2_ 2", "L2( 81). 2_ 3", "L2( 81). 2^ 2" ],
> [ "L3( 9)", "L3( 9). 2_ 1", "L3( 9). 2_ 2", "L3( 9). 2_ 3", "L3( 9). 2^ 2" ],
> [ "O8+( 3)", "O8+( 3). 2_ 1", "O8+( 3). 2_ 2", "O8+( 3). 2_ 2'",
> "O8+( 3).( 2^ 2)_{ 122}" ],
> [ "O8-( 3)", "O8-( 3). 2_ 1", "O8-( 3). 2_ 2", "O8-( 3). 2_ 3", "O8-( 3). 2^ 2" ],
> ];;
## doc2/ctblcons.xml ( 7260- 7272)
gap> Append( listGV4, [
> [ "L3( 4). 3", "L3( 4). 6", "L3( 4). 3. 2_ 2", "L3( 4). 3. 2_ 3", "L3( 4).D12" ],
> [ " 2^ 2.L3( 4). 3", " 2^ 2.L3( 4). 6", " 2^ 2.L3( 4). 3. 2_ 2", " 2^ 2.L3( 4). 3. 2_ 3",
> " 2^ 2.L3( 4).D12" ],
> [ "U4( 3). 2_ 1", "U4( 3). 4", "U4( 3).( 2^ 2)_{ 122}", "U4( 3).( 2^ 2)_{ 133}",
> "U4( 3).D8" ],
> [ "O8+( 3). 2_ 1", "O8+( 3).( 2^ 2)_{ 111}", "O8+( 3).( 2^ 2)_{ 122}", "O8+( 3). 4",
> "O8+( 3).D8" ],
> [ "L4( 4)", "L4( 4). 2_ 1", "L4( 4). 2_ 2", "L4( 4). 2_ 3", "L4( 4). 2^ 2" ],
> [ "U4( 5)", "U4( 5). 2_ 1", "U4( 5). 2_ 2", "U4( 5). 2_ 3", "U4( 5). 2^ 2" ],
> ] );
## doc2/ctblcons.xml ( 7298- 7341)
gap> ConstructOrdinaryGV4Table:= function( tblG, tblsG2, name, lib )
> local acts, nam, poss, reps, i, trans;
>
> # Compute the possible actions for the ordinary tables.
> acts:= PossibleActionsForTypeGV4( tblG, tblsG2 );
> # Compute the possible ordinary tables for the given actions.
> nam:= Concatenation( "new", name );
> poss:= Concatenation( List( acts, triple ->
> PossibleCharacterTablesOfTypeGV4( tblG, tblsG2, triple, nam ) ) );
> # Test the possibilities for permutation equivalence.
> reps:= RepresentativesCharacterTables( poss );
> if 1 < Length( reps ) then
> Print( "#I ", name, ": ", Length( reps ),
> " equivalence classes\n" );
> elif Length( reps ) = 0 then
> Print( "#E ", name, ": no solution\n" );
> else
> # Compare the computed table with the library table.
> if not IsCharacterTable( lib ) then
> Print( "#I no library table for ", name, "\n" );
> PrintToLib( name, poss[ 1].table );
> for i in [ 1 .. 3 ] do
> Print( LibraryFusion( tblsG2[i],
> rec( name:= name, map:= poss[ 1].G2fusGV4[i] ) ) );
> od;
> else
> trans:= TransformingPermutationsCharacterTables( poss[ 1].table,
> lib );
> if not IsRecord( trans ) then
> Print( "#E computed table and library table for ", name,
> " differ\n" );
> fi;
> # Compare the computed fusions with the stored ones.
> if List( poss[ 1].G2fusGV4, x -> OnTuples( x, trans.columns ) )
> <> List( tblsG2, x -> GetFusionMap( x, lib ) ) then
> Print( "#E computed and stored fusions for ", name,
> " differ\n" );
> fi;
> fi;
> fi;
> return poss;
> end;;
## doc2/ctblcons.xml ( 7366- 7454)
gap> ConstructModularGV4Tables:= function( tblG, tblsG2, ordposs,
> ordlibtblGV4 )
> local name, modposs, primes, checkordinary, i, record, p, tmodp,
> t2modp, poss, modlib, trans, reps;
>
> if not IsCharacterTable( ordlibtblGV4 ) then
> Print( "#I no ordinary library table ...\n" );
> return [];
> fi;
> name:= Identifier( ordlibtblGV4 );
> modposs:= List( ordposs, x -> [] );
> primes:= ShallowCopy( PrimeDivisors( Size( tblG ) ) );
> ordposs:= ShallowCopy( ordposs );
> checkordinary:= false;
> for i in [ 1 .. Length( ordposs ) ] do
> record:= ordposs[i];
> for p in primes do
> tmodp := tblG mod p;
> t2modp:= List( tblsG2, t2 -> t2 mod p );
> if IsCharacterTable( tmodp ) and
> ForAll( t2modp, IsCharacterTable ) then
> poss:= PossibleCharacterTablesOfTypeGV4( tmodp, t2modp,
> record.table, record.G2fusGV4 );
> poss:= RepresentativesCharacterTables( poss );
> if Length( poss ) = 0 then
> Print( "#I excluded cand. ", i, " (out of ",
> Length( ordposs ), ") for ", name, " by ", p,
> "-mod. table\n" );
> Unbind( ordposs[i] );
> Unbind( modposs[i] );
> checkordinary:= true;
> break;
> elif Length( poss ) = 1 then
> # Compare the computed table with the library table.
> modlib:= ordlibtblGV4 mod p;
> if IsCharacterTable( modlib ) then
> trans:= TransformingPermutationsCharacterTables(
> poss[ 1].table, modlib );
> if not IsRecord( trans ) then
> Print( "#E computed table and library table for ",
> name, " mod ", p, " differ\n" );
> fi;
> else
> Print( "#I no library table for ",
> name, " mod ", p, "\n" );
> PrintToLib( name, poss[ 1].table );
> fi;
> else
> Print( "#I ", name, " mod ", p, ": ", Length( poss ),
> " equivalence classes\n" );
> fi;
> Add( modposs[i], poss );
> elif i = 1 then
> Print( "#I not all input tables for ", name, " mod ", p,
> " available\n" );
> primes:= Difference( primes, [ p ] );
> fi;
> od;
> od;
> if checkordinary then
> # Test whether the ordinary table is admissible.
> ordposs:= Compacted( ordposs );
> modposs:= Compacted( modposs );
> reps:= RepresentativesCharacterTables( ordposs );
> if 1 < Length( reps ) then
> Print( "#I ", name, ": ", Length( reps ),
> " equivalence classes (ord. table)\n" );
> elif Length( reps ) = 0 then
> Print( "#E ", name, ": no solution (ord. table)\n" );
> else
> # Compare the computed table with the library table.
> trans:= TransformingPermutationsCharacterTables(
> ordposs[ 1].table, ordlibtblGV4 );
> if not IsRecord( trans ) then
> Print( "#E computed table and library table for ", name,
> " differ\n" );
> fi;
> # Compare the computed fusions with the stored ones.
> if List( ordposs[ 1].G2fusGV4, x -> OnTuples( x, trans.columns ) )
> <> List( tblsG2, x -> GetFusionMap( x, ordlibtblGV4 ) ) then
> Print( "#E computed and stored fusions for ", name,
> " differ\n" );
> fi;
> fi;
> fi;
> return rec( ordinary:= ordposs, modular:= modposs );
> end;;
## doc2/ctblcons.xml ( 7462- 7497)
gap> for input in listGV4 do
> tblG := CharacterTable( input[ 1] );
> tblsG2 := List( input{ [ 2 .. 4 ] }, CharacterTable );
> lib := CharacterTable( input[ 5] );
> poss := ConstructOrdinaryGV4Table( tblG, tblsG2, input[ 5], lib );
> ConstructModularGV4Tables( tblG, tblsG2, poss, lib );
> od;
#I excluded cand. 2 (out of 2) for L3( 4). 2^ 2 by 3-mod. table
#I excluded cand. 2 (out of 8) for 2^ 2.L3( 4). 2^ 2 by 7-mod. table
#I excluded cand. 3 (out of 8) for 2^ 2.L3( 4). 2^ 2 by 5-mod. table
#I excluded cand. 4 (out of 8) for 2^ 2.L3( 4). 2^ 2 by 5-mod. table
#I excluded cand. 5 (out of 8) for 2^ 2.L3( 4). 2^ 2 by 5-mod. table
#I excluded cand. 6 (out of 8) for 2^ 2.L3( 4). 2^ 2 by 5-mod. table
#I excluded cand. 7 (out of 8) for 2^ 2.L3( 4). 2^ 2 by 7-mod. table
#I excluded cand. 2 (out of 2) for 3.L3( 4). 2^ 2 by 3-mod. table
#I excluded cand. 2 (out of 2) for L3( 9). 2^ 2 by 7-mod. table
#I not all input tables for O8+( 3).( 2^ 2)_{ 122} mod 3 available
#I not all input tables for O8-( 3). 2^ 2 mod 3 available
#I not all input tables for O8-( 3). 2^ 2 mod 5 available
#I not all input tables for O8-( 3). 2^ 2 mod 7 available
#I not all input tables for O8-( 3). 2^ 2 mod 13 available
#I not all input tables for O8-( 3). 2^ 2 mod 41 available
#I excluded cand. 2 (out of 2) for L3( 4).D12 by 3-mod. table
#I excluded cand. 2 (out of 2) for 2^ 2.L3( 4).D12 by 7-mod. table
#I not all input tables for O8+( 3).D8 mod 3 available
#I not all input tables for L4( 4). 2^ 2 mod 3 available
#I not all input tables for L4( 4). 2^ 2 mod 5 available
#I not all input tables for L4( 4). 2^ 2 mod 7 available
#I not all input tables for L4( 4). 2^ 2 mod 17 available
#I not all input tables for U4( 5). 2^ 2 mod 2 available
#I not all input tables for U4( 5). 2^ 2 mod 3 available
#I not all input tables for U4( 5). 2^ 2 mod 5 available
#I not all input tables for U4( 5). 2^ 2 mod 7 available
#I not all input tables for U4( 5). 2^ 2 mod 13 available
## doc2/ctblcons.xml ( 7527- 7535)
gap> tblG:= CharacterTable( "S4( 9)" );;
gap> tblsG2:= List( [ "S4( 9). 2_ 1", "S4( 9). 2_ 2", "S4( 9). 2_ 3" ],
> CharacterTable );;
gap> lib:= CharacterTable( "S4( 9). 2^ 2" );;
gap> poss:= ConstructOrdinaryGV4Table( tblG, tblsG2, "newS4( 9). 2^ 2", lib );;
#I newS4( 9). 2^ 2: 2 equivalence classes
gap> poss:= RepresentativesCharacterTables( poss );;
## doc2/ctblcons.xml ( 7546- 7557)
gap> order80:= PositionsProperty( OrdersClassRepresentatives( tblsG2[ 2] ),
> x -> x = 80 );
[ 98, 99, 100, 101, 102, 103, 104, 105 ]
gap> List( poss, r -> r.G2fusGV4[ 2]{ order80 } );
[ [ 77, 77, 78, 79, 80, 78, 79, 80 ],
[ 77, 78, 79, 79, 77, 80, 80, 78 ] ]
gap> PowerMap( tblsG2[ 2], 3 ){ order80 };
[ 99, 98, 103, 104, 105, 100, 101, 102 ]
gap> PowerMap( tblsG2[ 2], 13 ){ order80 };
[ 102, 105, 101, 100, 98, 104, 103, 99 ]
## doc2/ctblcons.xml ( 7573- 7576)
gap> List( tblsG2, x -> 80 in OrdersClassRepresentatives( x ) );
[ false, true, false ]
## doc2/ctblcons.xml ( 7586- 7590)
gap> tbl:= poss[ 1].table;;
gap> IsRecord( TransformingPermutationsCharacterTables( tbl, lib ) );
true
## doc2/ctblcons.xml ( 7621- 7706)
gap> names:= List( [ 1 .. 3 ],
> i -> Concatenation( " 2.L3( 4). 2_", String( i ) ) );;
gap> tbls:= List( names, CharacterTable );
[ CharacterTable( " 2.L3( 4). 2_ 1" ), CharacterTable( " 2.L3( 4). 2_ 2" ),
CharacterTable( " 2.L3( 4). 2_ 3" ) ]
gap> isos:= List( names, nam -> CharacterTable( Concatenation( nam, "*" ) ) );
[ CharacterTable( "Isoclinic( 2.L3( 4). 2_ 1)" ),
CharacterTable( "Isoclinic( 2.L3( 4). 2_ 2)" ),
CharacterTable( "Isoclinic( 2.L3( 4). 2_ 3)" ) ]
gap> inputs:= [
> [ tbls[ 1], tbls[ 2], tbls[ 3], " 2.L3( 4).( 2^ 2)_{ 123}" ],
> [ tbls[ 1], isos[ 2], tbls[ 3], " 2.L3( 4).( 2^ 2)_{ 12* 3}" ],
> [ tbls[ 1], tbls[ 2], isos[ 3], " 2.L3( 4).( 2^ 2)_{ 123*}" ],
> [ tbls[ 1], isos[ 2], isos[ 3], " 2.L3( 4).( 2^ 2)_{ 12* 3*}" ],
> [ isos[ 1], tbls[ 2], tbls[ 3], " 2.L3( 4).( 2^ 2)_{ 1* 23}" ],
> [ isos[ 1], isos[ 2], tbls[ 3], " 2.L3( 4).( 2^ 2)_{ 1* 2* 3}" ],
> [ isos[ 1], tbls[ 2], isos[ 3], " 2.L3( 4).( 2^ 2)_{ 1* 23*}" ],
> [ isos[ 1], isos[ 2], isos[ 3], " 2.L3( 4).( 2^ 2)_{ 1* 2* 3*}" ] ];;
gap> tblG:= CharacterTable( " 2.L3( 4)" );;
gap> result:= [];;
gap> for input in inputs do
> tblsG2:= input{ [ 1 .. 3 ] };
> lib:= CharacterTable( input[ 4] );
> poss:= ConstructOrdinaryGV4Table( tblG, tblsG2, input[ 4], lib );
> ConstructModularGV4Tables( tblG, tblsG2, poss, lib );
> Append( result, RepresentativesCharacterTables( poss ) );
> od;
#I excluded cand. 2 (out of 8) for 2.L3( 4).( 2^ 2)_{ 123} by
5-mod. table
#I excluded cand. 3 (out of 8) for 2.L3( 4).( 2^ 2)_{ 123} by
5-mod. table
#I excluded cand. 4 (out of 8) for 2.L3( 4).( 2^ 2)_{ 123} by
7-mod. table
#I excluded cand. 5 (out of 8) for 2.L3( 4).( 2^ 2)_{ 123} by
7-mod. table
#I excluded cand. 6 (out of 8) for 2.L3( 4).( 2^ 2)_{ 123} by
5-mod. table
#I excluded cand. 7 (out of 8) for 2.L3( 4).( 2^ 2)_{ 123} by
5-mod. table
#I excluded cand. 2 (out of 8) for 2.L3( 4).( 2^ 2)_{ 12* 3*} by
5-mod. table
#I excluded cand. 3 (out of 8) for 2.L3( 4).( 2^ 2)_{ 12* 3*} by
5-mod. table
#I excluded cand. 4 (out of 8) for 2.L3( 4).( 2^ 2)_{ 12* 3*} by
7-mod. table
#I excluded cand. 5 (out of 8) for 2.L3( 4).( 2^ 2)_{ 12* 3*} by
7-mod. table
#I excluded cand. 6 (out of 8) for 2.L3( 4).( 2^ 2)_{ 12* 3*} by
5-mod. table
#I excluded cand. 7 (out of 8) for 2.L3( 4).( 2^ 2)_{ 12* 3*} by
5-mod. table
#I excluded cand. 2 (out of 8) for 2.L3( 4).( 2^ 2)_{ 1* 2* 3} by
5-mod. table
#I excluded cand. 3 (out of 8) for 2.L3( 4).( 2^ 2)_{ 1* 2* 3} by
5-mod. table
#I excluded cand. 4 (out of 8) for 2.L3( 4).( 2^ 2)_{ 1* 2* 3} by
7-mod. table
#I excluded cand. 5 (out of 8) for 2.L3( 4).( 2^ 2)_{ 1* 2* 3} by
7-mod. table
#I excluded cand. 6 (out of 8) for 2.L3( 4).( 2^ 2)_{ 1* 2* 3} by
5-mod. table
#I excluded cand. 7 (out of 8) for 2.L3( 4).( 2^ 2)_{ 1* 2* 3} by
5-mod. table
#I excluded cand. 2 (out of 8) for 2.L3( 4).( 2^ 2)_{ 1* 23*} by
5-mod. table
#I excluded cand. 3 (out of 8) for 2.L3( 4).( 2^ 2)_{ 1* 23*} by
5-mod. table
#I excluded cand. 4 (out of 8) for 2.L3( 4).( 2^ 2)_{ 1* 23*} by
7-mod. table
#I excluded cand. 5 (out of 8) for 2.L3( 4).( 2^ 2)_{ 1* 23*} by
7-mod. table
#I excluded cand. 6 (out of 8) for 2.L3( 4).( 2^ 2)_{ 1* 23*} by
5-mod. table
#I excluded cand. 7 (out of 8) for 2.L3( 4).( 2^ 2)_{ 1* 23*} by
5-mod. table
gap> result:= List( result, x -> x.table );
[ CharacterTable( "new2.L3( 4).( 2^ 2)_{ 123}" ),
CharacterTable( "new2.L3( 4).( 2^ 2)_{ 12* 3}" ),
CharacterTable( "new2.L3( 4).( 2^ 2)_{ 123*}" ),
CharacterTable( "new2.L3( 4).( 2^ 2)_{ 12* 3*}" ),
CharacterTable( "new2.L3( 4).( 2^ 2)_{ 1* 23}" ),
CharacterTable( "new2.L3( 4).( 2^ 2)_{ 1* 2* 3}" ),
CharacterTable( "new2.L3( 4).( 2^ 2)_{ 1* 23*}" ),
CharacterTable( "new2.L3( 4).( 2^ 2)_{ 1* 2* 3*}" ) ]
## doc2/ctblcons.xml ( 7720- 7737)
gap> List( result, NrConjugacyClasses );
[ 39, 33, 33, 39, 33, 39, 39, 33 ]
gap> t:= result[ 1];;
gap> nsg:= Filtered( ClassPositionsOfNormalSubgroups( t ),
> x -> Sum( SizesConjugacyClasses( t ){ x } ) = Size( t ) / 2 );;
gap> iso:= List( nsg, x -> CharacterTableIsoclinic( t, x ) );;
gap> List( iso, x -> PositionProperty( result, y ->
> TransformingPermutationsCharacterTables( x, y ) <> fail ) );
[ 4, 7, 6 ]
gap> t:= result[ 2];;
gap> nsg:= Filtered( ClassPositionsOfNormalSubgroups( t ),
> x -> Sum( SizesConjugacyClasses( t ){ x } ) = Size( t ) / 2 );;
gap> iso:= List( nsg, x -> CharacterTableIsoclinic( t, x ) );;
gap> List( iso, x -> PositionProperty( result, y ->
> TransformingPermutationsCharacterTables( x, y ) <> fail ) );
[ 3, 8, 5 ]
## doc2/ctblcons.xml ( 7758- 7768)
gap> l34:= CharacterTable( "L3( 4)" );;
gap> u:= CharacterTable( "U6( 2)" );;
gap> 2u:= CharacterTable( " 2.U6( 2)" );;
gap> cand:= PossibleClassFusions( l34, 2u );
[ [ 1, 5, 12, 16, 22, 22, 23, 23, 41, 41 ],
[ 1, 5, 12, 22, 16, 22, 23, 23, 41, 41 ],
[ 1, 5, 12, 22, 22, 16, 23, 23, 41, 41 ] ]
gap> OrdersClassRepresentatives( l34 );
[ 1, 2, 3, 4, 4, 4, 5, 5, 7, 7 ]
## doc2/ctblcons.xml ( 7784- 7793)
gap> GetFusionMap( 2u, u ){ [ 16, 22 ] };
[ 10, 14 ]
gap> ClassNames( u, "ATLAS" ){ [ 10, 14 ] };
[ " 4C", " 4G" ]
gap> GetFusionMap( u, CharacterTable( "U6( 2). 3" ) );
[ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 10, 10, 11, 12, 13, 14, 15, 16, 17,
18, 19, 20, 21, 22, 23, 24, 24, 24, 25, 26, 27, 28, 29, 30, 31, 32,
33, 34, 35, 36, 36, 36, 37, 38, 39, 40 ]
## doc2/ctblcons.xml ( 7808- 7813)
gap> 2u2:= CharacterTable( " 2.U6( 2). 2" );;
gap> fus:= List( result, x -> PossibleClassFusions( x, 2u2 ) );;
gap> List( fus, Length );
[ 4, 0, 0, 0, 0, 0, 0, 0 ]
## doc2/ctblcons.xml ( 7822- 7827)
gap> 2u2iso:= CharacterTableIsoclinic( 2u2 );;
gap> fus:= List( result, x -> PossibleClassFusions( x, 2u2iso ) );;
gap> List( fus, Length );
[ 0, 0, 0, 4, 0, 0, 0, 0 ]
## doc2/ctblcons.xml ( 7840- 7845)
gap> h2:= CharacterTable( "HS. 2" );;
gap> 2h2:= CharacterTable( " 2.HS. 2" );;
gap> PossibleClassFusions( l34, 2h2 );
[ ]
## doc2/ctblcons.xml ( 7859- 7867)
gap> fus:= List( result, x -> PossibleClassFusions( x, 2h2 ) );;
gap> List( fus, Length );
[ 0, 0, 0, 0, 4, 0, 0, 0 ]
gap> 2h2iso:= CharacterTableIsoclinic( 2h2 );;
gap> fus:= List( result, x -> PossibleClassFusions( x, 2h2iso ) );;
gap> List( fus, Length );
[ 0, 0, 0, 0, 0, 0, 0, 4 ]
## doc2/ctblcons.xml ( 7909- 7994)
gap> tbls:= List( [ " 1", " 2", " 3" ],
> i -> CharacterTable( Concatenation( " 6.L3( 4). 2_", i ) ) );
[ CharacterTable( " 6.L3( 4). 2_ 1" ), CharacterTable( " 6.L3( 4). 2_ 2" ),
CharacterTable( " 6.L3( 4). 2_ 3" ) ]
gap> isos:= List( [ " 1", " 2", " 3" ],
> i -> CharacterTable( Concatenation( " 6.L3( 4). 2_", i, "*" ) ) );
[ CharacterTable( "Isoclinic( 6.L3( 4). 2_ 1)" ),
CharacterTable( "Isoclinic( 6.L3( 4). 2_ 2)" ),
CharacterTable( "Isoclinic( 6.L3( 4). 2_ 3)" ) ]
gap> inputs:= [
> [ tbls[ 1], tbls[ 2], tbls[ 3], " 6.L3( 4).( 2^ 2)_{ 123}" ],
> [ tbls[ 1], isos[ 2], tbls[ 3], " 6.L3( 4).( 2^ 2)_{ 12* 3}" ],
> [ tbls[ 1], tbls[ 2], isos[ 3], " 6.L3( 4).( 2^ 2)_{ 123*}" ],
> [ tbls[ 1], isos[ 2], isos[ 3], " 6.L3( 4).( 2^ 2)_{ 12* 3*}" ],
> [ isos[ 1], tbls[ 2], tbls[ 3], " 6.L3( 4).( 2^ 2)_{ 1* 23}" ],
> [ isos[ 1], isos[ 2], tbls[ 3], " 6.L3( 4).( 2^ 2)_{ 1* 2* 3}" ],
> [ isos[ 1], tbls[ 2], isos[ 3], " 6.L3( 4).( 2^ 2)_{ 1* 23*}" ],
> [ isos[ 1], isos[ 2], isos[ 3], " 6.L3( 4).( 2^ 2)_{ 1* 2* 3*}" ] ];;
gap> tblG:= CharacterTable( " 6.L3( 4)" );;
gap> result:= [];;
gap> for input in inputs do
> tblsG2:= input{ [ 1 .. 3 ] };
> lib:= CharacterTable( input[ 4] );
> poss:= ConstructOrdinaryGV4Table( tblG, tblsG2, input[ 4], lib );
> ConstructModularGV4Tables( tblG, tblsG2, poss, lib );
> Append( result, RepresentativesCharacterTables( poss ) );
> od;
#I excluded cand. 2 (out of 8) for 6.L3( 4).( 2^ 2)_{ 123} by
5-mod. table
#I excluded cand. 3 (out of 8) for 6.L3( 4).( 2^ 2)_{ 123} by
5-mod. table
#I excluded cand. 4 (out of 8) for 6.L3( 4).( 2^ 2)_{ 123} by
7-mod. table
#I excluded cand. 5 (out of 8) for 6.L3( 4).( 2^ 2)_{ 123} by
7-mod. table
#I excluded cand. 6 (out of 8) for 6.L3( 4).( 2^ 2)_{ 123} by
5-mod. table
#I excluded cand. 7 (out of 8) for 6.L3( 4).( 2^ 2)_{ 123} by
5-mod. table
#I excluded cand. 2 (out of 8) for 6.L3( 4).( 2^ 2)_{ 12* 3*} by
5-mod. table
#I excluded cand. 3 (out of 8) for 6.L3( 4).( 2^ 2)_{ 12* 3*} by
5-mod. table
#I excluded cand. 4 (out of 8) for 6.L3( 4).( 2^ 2)_{ 12* 3*} by
7-mod. table
#I excluded cand. 5 (out of 8) for 6.L3( 4).( 2^ 2)_{ 12* 3*} by
7-mod. table
#I excluded cand. 6 (out of 8) for 6.L3( 4).( 2^ 2)_{ 12* 3*} by
5-mod. table
#I excluded cand. 7 (out of 8) for 6.L3( 4).( 2^ 2)_{ 12* 3*} by
5-mod. table
#I excluded cand. 2 (out of 8) for 6.L3( 4).( 2^ 2)_{ 1* 2* 3} by
5-mod. table
#I excluded cand. 3 (out of 8) for 6.L3( 4).( 2^ 2)_{ 1* 2* 3} by
5-mod. table
#I excluded cand. 4 (out of 8) for 6.L3( 4).( 2^ 2)_{ 1* 2* 3} by
7-mod. table
#I excluded cand. 5 (out of 8) for 6.L3( 4).( 2^ 2)_{ 1* 2* 3} by
7-mod. table
#I excluded cand. 6 (out of 8) for 6.L3( 4).( 2^ 2)_{ 1* 2* 3} by
5-mod. table
#I excluded cand. 7 (out of 8) for 6.L3( 4).( 2^ 2)_{ 1* 2* 3} by
5-mod. table
#I excluded cand. 2 (out of 8) for 6.L3( 4).( 2^ 2)_{ 1* 23*} by
5-mod. table
#I excluded cand. 3 (out of 8) for 6.L3( 4).( 2^ 2)_{ 1* 23*} by
5-mod. table
#I excluded cand. 4 (out of 8) for 6.L3( 4).( 2^ 2)_{ 1* 23*} by
7-mod. table
#I excluded cand. 5 (out of 8) for 6.L3( 4).( 2^ 2)_{ 1* 23*} by
7-mod. table
#I excluded cand. 6 (out of 8) for 6.L3( 4).( 2^ 2)_{ 1* 23*} by
5-mod. table
#I excluded cand. 7 (out of 8) for 6.L3( 4).( 2^ 2)_{ 1* 23*} by
5-mod. table
gap> result:= List( result, x -> x.table );
[ CharacterTable( "new6.L3( 4).( 2^ 2)_{ 123}" ),
CharacterTable( "new6.L3( 4).( 2^ 2)_{ 12* 3}" ),
CharacterTable( "new6.L3( 4).( 2^ 2)_{ 123*}" ),
CharacterTable( "new6.L3( 4).( 2^ 2)_{ 12* 3*}" ),
CharacterTable( "new6.L3( 4).( 2^ 2)_{ 1* 23}" ),
CharacterTable( "new6.L3( 4).( 2^ 2)_{ 1* 2* 3}" ),
CharacterTable( "new6.L3( 4).( 2^ 2)_{ 1* 23*}" ),
CharacterTable( "new6.L3( 4).( 2^ 2)_{ 1* 2* 3*}" ) ]
## doc2/ctblcons.xml ( 8004- 8021)
gap> List( result, NrConjugacyClasses );
[ 59, 53, 53, 59, 53, 59, 59, 53 ]
gap> t:= result[ 1];;
gap> nsg:= Filtered( ClassPositionsOfNormalSubgroups( t ),
> x -> Sum( SizesConjugacyClasses( t ){ x } ) = Size( t ) / 2 );;
gap> iso:= List( nsg, x -> CharacterTableIsoclinic( t, x ) );;
gap> List( iso, x -> PositionProperty( result, y ->
> TransformingPermutationsCharacterTables( x, y ) <> fail ) );
[ 7, 6, 4 ]
gap> t:= result[ 2];;
gap> nsg:= Filtered( ClassPositionsOfNormalSubgroups( t ),
> x -> Sum( SizesConjugacyClasses( t ){ x } ) = Size( t ) / 2 );;
gap> iso:= List( nsg, x -> CharacterTableIsoclinic( t, x ) );;
gap> List( iso, x -> PositionProperty( result, y ->
> TransformingPermutationsCharacterTables( x, y ) <> fail ) );
[ 8, 5, 3 ]
## doc2/ctblcons.xml ( 8044- 8049)
gap> 2l34:= CharacterTable( " 2.L3( 4)" );;
gap> 6u:= CharacterTable( " 6.U6( 2)" );;
gap> cand:= PossibleClassFusions( 2l34, 6u );
[ ]
## doc2/ctblcons.xml ( 8058- 8067)
gap> 6u2:= CharacterTable( " 6.U6( 2). 2" );;
gap> fus:= List( result, x -> PossibleClassFusions( x, 6u2 ) );;
gap> List( fus, Length );
[ 8, 0, 0, 0, 0, 0, 0, 0 ]
gap> 6u2iso:= CharacterTableIsoclinic( 6u2 );;
gap> fus:= List( result, x -> PossibleClassFusions( x, 6u2iso ) );;
gap> List( fus, Length );
[ 0, 0, 0, 8, 0, 0, 0, 0 ]
## doc2/ctblcons.xml ( 8081- 8087)
gap> 3l34:= CharacterTable( " 3.L3( 4)" );;
gap> g2:= CharacterTable( "G2( 4). 2" );;
gap> 2g2:= CharacterTable( " 2.G2( 4). 2" );;
gap> PossibleClassFusions( 3l34, 2g2 );
[ ]
## doc2/ctblcons.xml ( 8097- 8105)
gap> fus:= List( result, x -> PossibleClassFusions( x, 2g2 ) );;
gap> List( fus, Length );
[ 0, 0, 16, 0, 0, 0, 0, 0 ]
gap> 2g2iso:= CharacterTableIsoclinic( 2g2 );;
gap> fus:= List( result, x -> PossibleClassFusions( x, 2g2iso ) );;
gap> List( fus, Length );
[ 0, 0, 0, 0, 0, 0, 0, 16 ]
## doc2/ctblcons.xml ( 8113- 8162)
gap> names:= [ "L3( 4).( 2^ 2)_{ 123}", "L3( 4).( 2^ 2)_{ 12* 3}",
> "L3( 4).( 2^ 2)_{ 123*}", "L3( 4).( 2^ 2)_{ 12* 3*}" ];;
gap> inputs1:= List( names, nam -> [ " 6.L3( 4). 2_ 1", " 2.L3( 4). 2_ 1",
> Concatenation( " 2.", nam ), Concatenation( " 6.", nam ) ] );;
gap> names:= List( names, nam -> ReplacedString( nam, " 1", " 1*" ) );;
gap> inputs2:= List( names, nam -> [ " 6.L3( 4). 2_ 1*", " 2.L3( 4). 2_ 1*",
> Concatenation( " 2.", nam ), Concatenation( " 6.", nam ) ] );;
gap> inputs:= Concatenation( inputs1, inputs2 );
[ [ " 6.L3( 4). 2_ 1", " 2.L3( 4). 2_ 1", " 2.L3( 4).( 2^ 2)_{ 123}",
" 6.L3( 4).( 2^ 2)_{ 123}" ],
[ " 6.L3( 4). 2_ 1", " 2.L3( 4). 2_ 1", " 2.L3( 4).( 2^ 2)_{ 12* 3}",
" 6.L3( 4).( 2^ 2)_{ 12* 3}" ],
[ " 6.L3( 4). 2_ 1", " 2.L3( 4). 2_ 1", " 2.L3( 4).( 2^ 2)_{ 123*}",
" 6.L3( 4).( 2^ 2)_{ 123*}" ],
[ " 6.L3( 4). 2_ 1", " 2.L3( 4). 2_ 1", " 2.L3( 4).( 2^ 2)_{ 12* 3*}",
" 6.L3( 4).( 2^ 2)_{ 12* 3*}" ],
[ " 6.L3( 4). 2_ 1*", " 2.L3( 4). 2_ 1*", " 2.L3( 4).( 2^ 2)_{ 1* 23}",
" 6.L3( 4).( 2^ 2)_{ 1* 23}" ],
[ " 6.L3( 4). 2_ 1*", " 2.L3( 4). 2_ 1*", " 2.L3( 4).( 2^ 2)_{ 1* 2* 3}",
" 6.L3( 4).( 2^ 2)_{ 1* 2* 3}" ],
[ " 6.L3( 4). 2_ 1*", " 2.L3( 4). 2_ 1*", " 2.L3( 4).( 2^ 2)_{ 1* 23*}",
" 6.L3( 4).( 2^ 2)_{ 1* 23*}" ],
[ " 6.L3( 4). 2_ 1*", " 2.L3( 4). 2_ 1*", " 2.L3( 4).( 2^ 2)_{ 1* 2* 3*}",
" 6.L3( 4).( 2^ 2)_{ 1* 2* 3*}" ] ]
gap> result2:= [];;
gap> for input in inputs do
> tblMG := CharacterTable( input[ 1] );
> tblG := CharacterTable( input[ 2] );
> tblGA := CharacterTable( input[ 3] );
> name := Concatenation( "new", input[ 4] );
> lib := CharacterTable( input[ 4] );
> poss:= ConstructOrdinaryMGATable( tblMG, tblG, tblGA, name, lib );
> Append( result2, poss );
> od;
gap> result2:= List( result2, x -> x.table );
[ CharacterTable( "new6.L3( 4).( 2^ 2)_{ 123}" ),
CharacterTable( "new6.L3( 4).( 2^ 2)_{ 12* 3}" ),
CharacterTable( "new6.L3( 4).( 2^ 2)_{ 123*}" ),
CharacterTable( "new6.L3( 4).( 2^ 2)_{ 12* 3*}" ),
CharacterTable( "new6.L3( 4).( 2^ 2)_{ 1* 23}" ),
CharacterTable( "new6.L3( 4).( 2^ 2)_{ 1* 2* 3}" ),
CharacterTable( "new6.L3( 4).( 2^ 2)_{ 1* 23*}" ),
CharacterTable( "new6.L3( 4).( 2^ 2)_{ 1* 2* 3*}" ) ]
gap> trans:= List( [ 1 .. 8 ], i ->
> TransformingPermutationsCharacterTables( result[i],
> result2[i] ) );;
gap> ForAll( trans, IsRecord );
true
## doc2/ctblcons.xml ( 8202- 8230)
gap> tbls:= List( [ " 1", " 2", " 2'" ], i ->
> CharacterTable( Concatenation( " 2.U4( 3). 2_", i ) ) );;
gap> isos:= List( [ " 1", " 2", " 2'" ], i ->
> CharacterTable( Concatenation( "Isoclinic( 2.U4( 3). 2_", i, ")" ) ) );;
gap> inputs:= [
> [ tbls[ 1], tbls[ 2], tbls[ 3], " 2.U4( 3).( 2^ 2)_{ 122}" ],
> [ isos[ 1], tbls[ 2], tbls[ 3], " 2.U4( 3).( 2^ 2)_{ 1* 22}" ],
> [ tbls[ 1], isos[ 2], tbls[ 3], " 2.U4( 3).( 2^ 2)_{ 12* 2}" ],
> [ isos[ 1], isos[ 2], tbls[ 3], " 2.U4( 3).( 2^ 2)_{ 1* 2* 2}" ],
> [ tbls[ 1], isos[ 2], isos[ 3], " 2.U4( 3).( 2^ 2)_{ 12* 2*}" ],
> [ isos[ 1], isos[ 2], isos[ 3], " 2.U4( 3).( 2^ 2)_{ 1* 2* 2*}" ] ];;
gap> tblG:= CharacterTable( " 2.U4( 3)" );;
gap> result:= [];;
gap> for input in inputs do
> tblsG2:= input{ [ 1 .. 3 ] };
> lib:= CharacterTable( input[ 4] );
> poss:= ConstructOrdinaryGV4Table( tblG, tblsG2, input[ 4], lib );
> ConstructModularGV4Tables( tblG, tblsG2, poss, lib );
> Append( result, RepresentativesCharacterTables( poss ) );
> od;
gap> result:= List( result, x -> x.table );
[ CharacterTable( "new2.U4( 3).( 2^ 2)_{ 122}" ),
CharacterTable( "new2.U4( 3).( 2^ 2)_{ 1* 22}" ),
CharacterTable( "new2.U4( 3).( 2^ 2)_{ 12* 2}" ),
CharacterTable( "new2.U4( 3).( 2^ 2)_{ 1* 2* 2}" ),
CharacterTable( "new2.U4( 3).( 2^ 2)_{ 12* 2*}" ),
CharacterTable( "new2.U4( 3).( 2^ 2)_{ 1* 2* 2*}" ) ]
## doc2/ctblcons.xml ( 8244- 8261)
gap> List( result, NrConjugacyClasses );
[ 87, 102, 102, 87, 87, 102 ]
gap> t:= result[ 1];;
gap> nsg:= Filtered( ClassPositionsOfNormalSubgroups( t ),
> x -> Sum( SizesConjugacyClasses( t ){ x } ) = Size( t ) / 2 );;
gap> iso:= List( nsg, x -> CharacterTableIsoclinic( t, x ) );;
gap> List( iso, x -> PositionProperty( result, y ->
> TransformingPermutationsCharacterTables( x, y ) <> fail ) );
[ 4, 4, 5 ]
gap> t:= result[ 2];;
gap> nsg:= Filtered( ClassPositionsOfNormalSubgroups( t ),
> x -> Sum( SizesConjugacyClasses( t ){ x } ) = Size( t ) / 2 );;
gap> iso:= List( nsg, x -> CharacterTableIsoclinic( t, x ) );;
gap> List( iso, x -> PositionProperty( result, y ->
> TransformingPermutationsCharacterTables( x, y ) <> fail ) );
[ 3, 3, 6 ]
## doc2/ctblcons.xml ( 8279- 8284)
gap> u:= CharacterTable( "O8+( 3)" );;
gap> fus:= List( result, x -> PossibleClassFusions( x, u ) );;
gap> List( fus, Length );
[ 24, 0, 0, 0, 0, 0 ]
## doc2/ctblcons.xml ( 8293- 8298)
gap> u:= CharacterTable( "O7( 3). 2" );;
gap> fus:= List( result, x -> PossibleClassFusions( x, u ) );;
gap> List( fus, Length );
[ 0, 16, 0, 0, 0, 0 ]
## doc2/ctblcons.xml ( 8347- 8403)
gap> tbls:= List( [ " 1", " 3", " 3'" ],
> i -> CharacterTable( Concatenation( " 2.U4( 3). 2_", i ) ) );;
gap> isos:= List( [ " 1", " 3", " 3'" ], i ->
> CharacterTable( Concatenation( "Isoclinic( 2.U4( 3). 2_", i, ")" ) ) );;
gap> inputs:= [
> [ tbls[ 1], tbls[ 2], tbls[ 3], " 2.U4( 3).( 2^ 2)_{ 133}" ],
> [ isos[ 1], tbls[ 2], tbls[ 3], " 2.U4( 3).( 2^ 2)_{ 1* 33}" ],
> [ tbls[ 1], isos[ 2], tbls[ 3], " 2.U4( 3).( 2^ 2)_{ 13* 3}" ],
> [ isos[ 1], isos[ 2], tbls[ 3], " 2.U4( 3).( 2^ 2)_{ 1* 3* 3}" ],
> [ tbls[ 1], isos[ 2], isos[ 3], " 2.U4( 3).( 2^ 2)_{ 13* 3*}" ],
> [ isos[ 1], isos[ 2], isos[ 3], " 2.U4( 3).( 2^ 2)_{ 1* 3* 3*}" ] ];;
gap> tblG:= CharacterTable( " 2.U4( 3)" );;
gap> result:= [];;
gap> for input in inputs do
> tblsG2:= input{ [ 1 .. 3 ] };
> lib:= CharacterTable( input[ 4] );
> poss:= ConstructOrdinaryGV4Table( tblG, tblsG2, input[ 4], lib );
> ConstructModularGV4Tables( tblG, tblsG2, poss, lib );
> Append( result, RepresentativesCharacterTables( poss ) );
> od;
#I excluded cand. 2 (out of 4) for 2.U4( 3).( 2^ 2)_{ 1* 33} by
3-mod. table
#I excluded cand. 3 (out of 4) for 2.U4( 3).( 2^ 2)_{ 1* 33} by
3-mod. table
#I excluded cand. 2 (out of 4) for 2.U4( 3).( 2^ 2)_{ 13* 3} by
3-mod. table
#I excluded cand. 3 (out of 4) for 2.U4( 3).( 2^ 2)_{ 13* 3} by
3-mod. table
#I excluded cand. 2 (out of 4) for 2.U4( 3).( 2^ 2)_{ 1* 3* 3*} by
3-mod. table
#I excluded cand. 3 (out of 4) for 2.U4( 3).( 2^ 2)_{ 1* 3* 3*} by
3-mod. table
gap> result:= List( result, x -> x.table );
[ CharacterTable( "new2.U4( 3).( 2^ 2)_{ 133}" ),
CharacterTable( "new2.U4( 3).( 2^ 2)_{ 1* 33}" ),
CharacterTable( "new2.U4( 3).( 2^ 2)_{ 13* 3}" ),
CharacterTable( "new2.U4( 3).( 2^ 2)_{ 1* 3* 3}" ),
CharacterTable( "new2.U4( 3).( 2^ 2)_{ 13* 3*}" ),
CharacterTable( "new2.U4( 3).( 2^ 2)_{ 1* 3* 3*}" ) ]
gap> List( result, NrConjugacyClasses );
[ 69, 72, 72, 69, 69, 72 ]
gap> t:= result[ 1];;
gap> nsg:= Filtered( ClassPositionsOfNormalSubgroups( t ),
> x -> Sum( SizesConjugacyClasses( t ){ x } ) = Size( t ) / 2 );;
gap> iso:= List( nsg, x -> CharacterTableIsoclinic( t, x ) );;
gap> List( iso, x -> PositionProperty( result, y ->
> TransformingPermutationsCharacterTables( x, y ) <> fail ) );
[ 4, 4, 5 ]
gap> t:= result[ 2];;
gap> nsg:= Filtered( ClassPositionsOfNormalSubgroups( t ),
> x -> Sum( SizesConjugacyClasses( t ){ x } ) = Size( t ) / 2 );;
gap> iso:= List( nsg, x -> CharacterTableIsoclinic( t, x ) );;
gap> List( iso, x -> PositionProperty( result, y ->
> TransformingPermutationsCharacterTables( x, y ) <> fail ) );
[ 3, 3, 6 ]
## doc2/ctblcons.xml ( 8436- 8446)
gap> tbls:= List( [ " 1", " 2", " 3" ],
> i -> CharacterTable( Concatenation( " 4_ 1.L3( 4). 2_", i ) ) );
[ CharacterTable( " 4_ 1.L3( 4). 2_ 1" ), CharacterTable( " 4_ 1.L3( 4). 2_ 2" )
, CharacterTable( " 4_ 1.L3( 4). 2_ 3" ) ]
gap> isos:= List( [ " 1", " 2", " 3" ],
> i -> CharacterTable( Concatenation( " 4_ 1.L3( 4). 2_", i, "*" ) ) );
[ CharacterTable( "Isoclinic( 4_ 1.L3( 4). 2_ 1)" ),
CharacterTable( "Isoclinic( 4_ 1.L3( 4). 2_ 2)" ),
CharacterTable( " 4_ 1.L3( 4). 2_ 3*" ) ]
## doc2/ctblcons.xml ( 8457- 8463)
gap> List( tbls, ClassPositionsOfCentre );
[ [ 1, 3 ], [ 1, 3 ], [ 1, 2, 3, 4 ] ]
gap> IsRecord( TransformingPermutationsCharacterTables( tbls[ 3],
> CharacterTableIsoclinic( tbls[ 3] ) ) );
true
## doc2/ctblcons.xml ( 8472- 8564)
gap> inputs:= [
> [ tbls[ 1], tbls[ 2], tbls[ 3], " 4_ 1.L3( 4).( 2^ 2)_{ 123}" ],
> [ isos[ 1], tbls[ 2], tbls[ 3], " 4_ 1.L3( 4).( 2^ 2)_{ 1* 23}" ],
> [ tbls[ 1], isos[ 2], tbls[ 3], " 4_ 1.L3( 4).( 2^ 2)_{ 12* 3}" ],
> [ isos[ 1], isos[ 2], tbls[ 3], " 4_ 1.L3( 4).( 2^ 2)_{ 1* 2* 3}" ],
> [ tbls[ 1], tbls[ 2], isos[ 3], " 4_ 1.L3( 4).( 2^ 2)_{ 123*}" ],
> [ isos[ 1], tbls[ 2], isos[ 3], " 4_ 1.L3( 4).( 2^ 2)_{ 1* 23*}" ],
> [ tbls[ 1], isos[ 2], isos[ 3], " 4_ 1.L3( 4).( 2^ 2)_{ 12* 3*}" ],
> [ isos[ 1], isos[ 2], isos[ 3], " 4_ 1.L3( 4).( 2^ 2)_{ 1* 2* 3*}" ] ];;
gap> tblG:= CharacterTable( " 4_ 1.L3( 4)" );;
gap> result:= [];;
gap> for input in inputs do
> tblsG2:= input{ [ 1 .. 3 ] };
> lib:= CharacterTable( input[ 4] );
> poss:= ConstructOrdinaryGV4Table( tblG, tblsG2, input[ 4], lib );
> ConstructModularGV4Tables( tblG, tblsG2, poss, lib );
> Append( result, RepresentativesCharacterTables( poss ) );
> od;
#I excluded cand. 2 (out of 8) for 4_ 1.L3( 4).( 2^ 2)_{ 123} by
5-mod. table
#I excluded cand. 3 (out of 8) for 4_ 1.L3( 4).( 2^ 2)_{ 123} by
5-mod. table
#I excluded cand. 4 (out of 8) for 4_ 1.L3( 4).( 2^ 2)_{ 123} by
7-mod. table
#I excluded cand. 5 (out of 8) for 4_ 1.L3( 4).( 2^ 2)_{ 123} by
7-mod. table
#I excluded cand. 6 (out of 8) for 4_ 1.L3( 4).( 2^ 2)_{ 123} by
5-mod. table
#I excluded cand. 7 (out of 8) for 4_ 1.L3( 4).( 2^ 2)_{ 123} by
5-mod. table
#I excluded cand. 2 (out of 8) for 4_ 1.L3( 4).( 2^ 2)_{ 1* 23} by
5-mod. table
#I excluded cand. 3 (out of 8) for 4_ 1.L3( 4).( 2^ 2)_{ 1* 23} by
5-mod. table
#I excluded cand. 4 (out of 8) for 4_ 1.L3( 4).( 2^ 2)_{ 1* 23} by
7-mod. table
#I excluded cand. 5 (out of 8) for 4_ 1.L3( 4).( 2^ 2)_{ 1* 23} by
7-mod. table
#I excluded cand. 6 (out of 8) for 4_ 1.L3( 4).( 2^ 2)_{ 1* 23} by
5-mod. table
#I excluded cand. 7 (out of 8) for 4_ 1.L3( 4).( 2^ 2)_{ 1* 23} by
5-mod. table
#I excluded cand. 2 (out of 8) for 4_ 1.L3( 4).( 2^ 2)_{ 12* 3} by
5-mod. table
#I excluded cand. 3 (out of 8) for 4_ 1.L3( 4).( 2^ 2)_{ 12* 3} by
5-mod. table
#I excluded cand. 4 (out of 8) for 4_ 1.L3( 4).( 2^ 2)_{ 12* 3} by
7-mod. table
#I excluded cand. 5 (out of 8) for 4_ 1.L3( 4).( 2^ 2)_{ 12* 3} by
7-mod. table
#I excluded cand. 6 (out of 8) for 4_ 1.L3( 4).( 2^ 2)_{ 12* 3} by
5-mod. table
#I excluded cand. 7 (out of 8) for 4_ 1.L3( 4).( 2^ 2)_{ 12* 3} by
5-mod. table
#I excluded cand. 2 (out of 8) for 4_ 1.L3( 4).( 2^ 2)_{ 1* 2* 3} by
5-mod. table
#I excluded cand. 3 (out of 8) for 4_ 1.L3( 4).( 2^ 2)_{ 1* 2* 3} by
5-mod. table
#I excluded cand. 4 (out of 8) for 4_ 1.L3( 4).( 2^ 2)_{ 1* 2* 3} by
7-mod. table
#I excluded cand. 5 (out of 8) for 4_ 1.L3( 4).( 2^ 2)_{ 1* 2* 3} by
7-mod. table
#I excluded cand. 6 (out of 8) for 4_ 1.L3( 4).( 2^ 2)_{ 1* 2* 3} by
5-mod. table
#I excluded cand. 7 (out of 8) for 4_ 1.L3( 4).( 2^ 2)_{ 1* 2* 3} by
5-mod. table
gap> result:= List( result, x -> x.table );
[ CharacterTable( "new4_1.L3( 4).( 2^ 2)_{ 123}" ),
CharacterTable( "new4_1.L3( 4).( 2^ 2)_{ 1* 23}" ),
CharacterTable( "new4_1.L3( 4).( 2^ 2)_{ 12* 3}" ),
CharacterTable( "new4_1.L3( 4).( 2^ 2)_{ 1* 2* 3}" ),
CharacterTable( "new4_1.L3( 4).( 2^ 2)_{ 123*}" ),
CharacterTable( "new4_1.L3( 4).( 2^ 2)_{ 1* 23*}" ),
CharacterTable( "new4_1.L3( 4).( 2^ 2)_{ 12* 3*}" ),
CharacterTable( "new4_1.L3( 4).( 2^ 2)_{ 1* 2* 3*}" ) ]
gap> List( result, NrConjugacyClasses );
[ 48, 48, 48, 48, 42, 42, 42, 42 ]
gap> t:= result[ 1];;
gap> nsg:= Filtered( ClassPositionsOfNormalSubgroups( t ),
> x -> Sum( SizesConjugacyClasses( t ){ x } ) = Size( t ) / 2 );;
gap> iso:= List( nsg, x -> CharacterTableIsoclinic( t, x ) );;
gap> List( iso, x -> PositionProperty( result, y ->
> TransformingPermutationsCharacterTables( x, y ) <> fail ) );
[ 3, 2, 4 ]
gap> t:= result[ 5];;
gap> nsg:= Filtered( ClassPositionsOfNormalSubgroups( t ),
> x -> Sum( SizesConjugacyClasses( t ){ x } ) = Size( t ) / 2 );;
gap> iso:= List( nsg, x -> CharacterTableIsoclinic( t, x ) );;
gap> List( iso, x -> PositionProperty( result, y ->
> TransformingPermutationsCharacterTables( x, y ) <> fail ) );
[ 7, 6, 8 ]
## doc2/ctblcons.xml ( 8573- 8580)
gap> facts:= [ CharacterTable( " 2.L3( 4).( 2^ 2)_{ 123}" ),
> CharacterTable( " 2.L3( 4).( 2^ 2)_{ 123*}" ) ];;
gap> factresults:= List( result, t -> t / ClassPositionsOfCentre( t ) );;
gap> List( factresults, t -> PositionProperty( facts, f ->
> IsRecord( TransformingPermutationsCharacterTables( t, f ) ) ) );
[ 1, 1, 1, 1, 2, 2, 2, 2 ]
## doc2/ctblcons.xml ( 8592- 8607)
gap> test:= [ CharacterTable( " 4_ 1.L3( 4). 2_ 1" ),
> CharacterTable( " 4_ 1.L3( 4). 2_ 1*" ) ];;
gap> List( test, ClassPositionsOfCentre );
[ [ 1, 3 ], [ 1, 3 ] ]
gap> fact:= List( test, t -> t / ClassPositionsOfCentre( t ) );;
gap> IsRecord( TransformingPermutationsCharacterTables( fact[ 1], fact[ 2] ) );
true
gap> test:= [ CharacterTable( " 4_ 1.L3( 4). 2_ 2" ),
> CharacterTable( " 4_ 1.L3( 4). 2_ 2*" ) ];;
gap> List( test, ClassPositionsOfCentre );
[ [ 1, 3 ], [ 1, 3 ] ]
gap> fact:= List( test, t -> t / ClassPositionsOfCentre( t ) );;
gap> IsRecord( TransformingPermutationsCharacterTables( fact[ 1], fact[ 2] ) );
true
## doc2/ctblcons.xml ( 8617- 8674)
gap> names:= [ "L3( 4).( 2^ 2)_{ 123}", "L3( 4).( 2^ 2)_{ 1* 23}",
> "L3( 4).( 2^ 2)_{ 12* 3}", "L3( 4).( 2^ 2)_{ 1* 2* 3}" ];;
gap> inputs1:= List( names, nam -> [ " 4_ 1.L3( 4). 2_ 3", " 2.L3( 4). 2_ 3",
> Concatenation( " 2.", nam ), Concatenation( " 4_ 1.", nam ) ] );;
gap> names:= List( names, nam -> ReplacedString( nam, " 3}", " 3*}" ) );;
gap> inputs2:= List( names, nam -> [ " 4_ 1.L3( 4). 2_ 3*", " 2.L3( 4). 2_ 3*",
> Concatenation( " 2.", nam ), Concatenation( " 4_ 1.", nam ) ] );;
gap> inputs:= Concatenation( inputs1, inputs2 );
[ [ " 4_ 1.L3( 4). 2_ 3", " 2.L3( 4). 2_ 3", " 2.L3( 4).( 2^ 2)_{ 123}",
" 4_ 1.L3( 4).( 2^ 2)_{ 123}" ],
[ " 4_ 1.L3( 4). 2_ 3", " 2.L3( 4). 2_ 3", " 2.L3( 4).( 2^ 2)_{ 1* 23}",
" 4_ 1.L3( 4).( 2^ 2)_{ 1* 23}" ],
[ " 4_ 1.L3( 4). 2_ 3", " 2.L3( 4). 2_ 3", " 2.L3( 4).( 2^ 2)_{ 12* 3}",
" 4_ 1.L3( 4).( 2^ 2)_{ 12* 3}" ],
[ " 4_ 1.L3( 4). 2_ 3", " 2.L3( 4). 2_ 3", " 2.L3( 4).( 2^ 2)_{ 1* 2* 3}",
" 4_ 1.L3( 4).( 2^ 2)_{ 1* 2* 3}" ],
[ " 4_ 1.L3( 4). 2_ 3*", " 2.L3( 4). 2_ 3*", " 2.L3( 4).( 2^ 2)_{ 123*}",
" 4_ 1.L3( 4).( 2^ 2)_{ 123*}" ],
[ " 4_ 1.L3( 4). 2_ 3*", " 2.L3( 4). 2_ 3*", " 2.L3( 4).( 2^ 2)_{ 1* 23*}",
" 4_ 1.L3( 4).( 2^ 2)_{ 1* 23*}" ],
[ " 4_ 1.L3( 4). 2_ 3*", " 2.L3( 4). 2_ 3*", " 2.L3( 4).( 2^ 2)_{ 12* 3*}",
" 4_ 1.L3( 4).( 2^ 2)_{ 12* 3*}" ],
[ " 4_ 1.L3( 4). 2_ 3*", " 2.L3( 4). 2_ 3*", " 2.L3( 4).( 2^ 2)_{ 1* 2* 3*}",
" 4_ 1.L3( 4).( 2^ 2)_{ 1* 2* 3*}" ] ]
gap> result2:= [];;
gap> for input in inputs do
> tblMG := CharacterTable( input[ 1] );
> tblG := CharacterTable( input[ 2] );
> tblGA := CharacterTable( input[ 3] );
> name := Concatenation( "new", input[ 4] );
> lib := CharacterTable( input[ 4] );
> poss:= ConstructOrdinaryMGATable( tblMG, tblG, tblGA, name, lib );
> Append( result2, poss );
> od;
#E 4 possibilities for new4_1.L3( 4).( 2^ 2)_{ 123}
#E no solution for new4_1.L3( 4).( 2^ 2)_{ 1* 23}
#E no solution for new4_1.L3( 4).( 2^ 2)_{ 12* 3}
#E no solution for new4_1.L3( 4).( 2^ 2)_{ 1* 2* 3}
#E 4 possibilities for new4_1.L3( 4).( 2^ 2)_{ 123*}
#E no solution for new4_1.L3( 4).( 2^ 2)_{ 1* 23*}
#E no solution for new4_1.L3( 4).( 2^ 2)_{ 12* 3*}
#E no solution for new4_1.L3( 4).( 2^ 2)_{ 1* 2* 3*}
gap> Length( result2 );
8
gap> result2:= List( result2, x -> x.table );
[ CharacterTable( "new4_1.L3( 4).( 2^ 2)_{ 123}" ),
CharacterTable( "new4_1.L3( 4).( 2^ 2)_{ 123}" ),
CharacterTable( "new4_1.L3( 4).( 2^ 2)_{ 123}" ),
CharacterTable( "new4_1.L3( 4).( 2^ 2)_{ 123}" ),
CharacterTable( "new4_1.L3( 4).( 2^ 2)_{ 123*}" ),
CharacterTable( "new4_1.L3( 4).( 2^ 2)_{ 123*}" ),
CharacterTable( "new4_1.L3( 4).( 2^ 2)_{ 123*}" ),
CharacterTable( "new4_1.L3( 4).( 2^ 2)_{ 123*}" ) ]
gap> List( result, t1 -> PositionsProperty( result2, t2 -> IsRecord(
> TransformingPermutationsCharacterTables( t1, t2 ) ) ) );
[ [ 1 ], [ 4 ], [ 3 ], [ 2 ], [ 7 ], [ 6 ], [ 5 ], [ 8 ] ]
## doc2/ctblcons.xml ( 8693- 8703)
gap> tbls:= List( [ " 1", " 2", " 3" ],
> i -> CharacterTable( Concatenation( " 4_ 2.L3( 4). 2_", i ) ) );
[ CharacterTable( " 4_ 2.L3( 4). 2_ 1" ), CharacterTable( " 4_ 2.L3( 4). 2_ 2" )
, CharacterTable( " 4_ 2.L3( 4). 2_ 3" ) ]
gap> isos:= List( [ " 1", " 2", " 3" ],
> i -> CharacterTable( Concatenation( " 4_ 2.L3( 4). 2_", i, "*" ) ) );
[ CharacterTable( "Isoclinic( 4_ 2.L3( 4). 2_ 1)" ),
CharacterTable( " 4_ 2.L3( 4). 2_ 2*" ),
CharacterTable( "Isoclinic( 4_ 2.L3( 4). 2_ 3)" ) ]
## doc2/ctblcons.xml ( 8714- 8720)
gap> List( tbls, ClassPositionsOfCentre );
[ [ 1, 3 ], [ 1, 2, 3, 4 ], [ 1, 3 ] ]
gap> IsRecord( TransformingPermutationsCharacterTables( tbls[ 2],
> CharacterTableIsoclinic( tbls[ 2] ) ) );
true
## doc2/ctblcons.xml ( 8729- 8821)
gap> inputs:= [
> [ tbls[ 1], tbls[ 2], tbls[ 3], " 4_ 2.L3( 4).( 2^ 2)_{ 123}" ],
> [ isos[ 1], tbls[ 2], tbls[ 3], " 4_ 2.L3( 4).( 2^ 2)_{ 1* 23}" ],
> [ tbls[ 1], isos[ 2], tbls[ 3], " 4_ 2.L3( 4).( 2^ 2)_{ 12* 3}" ],
> [ tbls[ 1], tbls[ 2], isos[ 3], " 4_ 2.L3( 4).( 2^ 2)_{ 123*}" ],
> [ isos[ 1], isos[ 2], tbls[ 3], " 4_ 2.L3( 4).( 2^ 2)_{ 1* 2* 3}" ],
> [ isos[ 1], tbls[ 2], isos[ 3], " 4_ 2.L3( 4).( 2^ 2)_{ 1* 23*}" ],
> [ tbls[ 1], isos[ 2], isos[ 3], " 4_ 2.L3( 4).( 2^ 2)_{ 12* 3*}" ],
> [ isos[ 1], isos[ 2], isos[ 3], " 4_ 2.L3( 4).( 2^ 2)_{ 1* 2* 3*}" ] ];;
gap> tblG:= CharacterTable( " 4_ 2.L3( 4)" );;
gap> result:= [];;
gap> for input in inputs do
> tblsG2:= input{ [ 1 .. 3 ] };
> lib:= CharacterTable( input[ 4] );
> poss:= ConstructOrdinaryGV4Table( tblG, tblsG2, input[ 4], lib );
> ConstructModularGV4Tables( tblG, tblsG2, poss, lib );
> Append( result, RepresentativesCharacterTables( poss ) );
> od;
#I excluded cand. 2 (out of 8) for 4_ 2.L3( 4).( 2^ 2)_{ 123} by
5-mod. table
#I excluded cand. 3 (out of 8) for 4_ 2.L3( 4).( 2^ 2)_{ 123} by
5-mod. table
#I excluded cand. 4 (out of 8) for 4_ 2.L3( 4).( 2^ 2)_{ 123} by
7-mod. table
#I excluded cand. 5 (out of 8) for 4_ 2.L3( 4).( 2^ 2)_{ 123} by
7-mod. table
#I excluded cand. 6 (out of 8) for 4_ 2.L3( 4).( 2^ 2)_{ 123} by
5-mod. table
#I excluded cand. 7 (out of 8) for 4_ 2.L3( 4).( 2^ 2)_{ 123} by
5-mod. table
#I excluded cand. 2 (out of 8) for 4_ 2.L3( 4).( 2^ 2)_{ 1* 23} by
5-mod. table
#I excluded cand. 3 (out of 8) for 4_ 2.L3( 4).( 2^ 2)_{ 1* 23} by
5-mod. table
#I excluded cand. 4 (out of 8) for 4_ 2.L3( 4).( 2^ 2)_{ 1* 23} by
7-mod. table
#I excluded cand. 5 (out of 8) for 4_ 2.L3( 4).( 2^ 2)_{ 1* 23} by
7-mod. table
#I excluded cand. 6 (out of 8) for 4_ 2.L3( 4).( 2^ 2)_{ 1* 23} by
5-mod. table
#I excluded cand. 7 (out of 8) for 4_ 2.L3( 4).( 2^ 2)_{ 1* 23} by
5-mod. table
#I excluded cand. 2 (out of 8) for 4_ 2.L3( 4).( 2^ 2)_{ 123*} by
5-mod. table
#I excluded cand. 3 (out of 8) for 4_ 2.L3( 4).( 2^ 2)_{ 123*} by
5-mod. table
#I excluded cand. 4 (out of 8) for 4_ 2.L3( 4).( 2^ 2)_{ 123*} by
7-mod. table
#I excluded cand. 5 (out of 8) for 4_ 2.L3( 4).( 2^ 2)_{ 123*} by
7-mod. table
#I excluded cand. 6 (out of 8) for 4_ 2.L3( 4).( 2^ 2)_{ 123*} by
5-mod. table
#I excluded cand. 7 (out of 8) for 4_ 2.L3( 4).( 2^ 2)_{ 123*} by
5-mod. table
#I excluded cand. 2 (out of 8) for 4_ 2.L3( 4).( 2^ 2)_{ 1* 23*} by
5-mod. table
#I excluded cand. 3 (out of 8) for 4_ 2.L3( 4).( 2^ 2)_{ 1* 23*} by
5-mod. table
#I excluded cand. 4 (out of 8) for 4_ 2.L3( 4).( 2^ 2)_{ 1* 23*} by
7-mod. table
#I excluded cand. 5 (out of 8) for 4_ 2.L3( 4).( 2^ 2)_{ 1* 23*} by
7-mod. table
#I excluded cand. 6 (out of 8) for 4_ 2.L3( 4).( 2^ 2)_{ 1* 23*} by
5-mod. table
#I excluded cand. 7 (out of 8) for 4_ 2.L3( 4).( 2^ 2)_{ 1* 23*} by
5-mod. table
gap> result:= List( result, x -> x.table );
[ CharacterTable( "new4_2.L3( 4).( 2^ 2)_{ 123}" ),
CharacterTable( "new4_2.L3( 4).( 2^ 2)_{ 1* 23}" ),
CharacterTable( "new4_2.L3( 4).( 2^ 2)_{ 12* 3}" ),
CharacterTable( "new4_2.L3( 4).( 2^ 2)_{ 123*}" ),
CharacterTable( "new4_2.L3( 4).( 2^ 2)_{ 1* 2* 3}" ),
CharacterTable( "new4_2.L3( 4).( 2^ 2)_{ 1* 23*}" ),
CharacterTable( "new4_2.L3( 4).( 2^ 2)_{ 12* 3*}" ),
CharacterTable( "new4_2.L3( 4).( 2^ 2)_{ 1* 2* 3*}" ) ]
gap> List( result, NrConjugacyClasses );
[ 50, 50, 44, 50, 44, 50, 44, 44 ]
gap> t:= result[ 1];;
gap> nsg:= Filtered( ClassPositionsOfNormalSubgroups( t ),
> x -> Sum( SizesConjugacyClasses( t ){ x } ) = Size( t ) / 2 );;
gap> iso:= List( nsg, x -> CharacterTableIsoclinic( t, x ) );;
gap> List( iso, x -> PositionProperty( result, y ->
> TransformingPermutationsCharacterTables( x, y ) <> fail ) );
[ 4, 2, 6 ]
gap> t:= result[ 3];;
gap> nsg:= Filtered( ClassPositionsOfNormalSubgroups( t ),
> x -> Sum( SizesConjugacyClasses( t ){ x } ) = Size( t ) / 2 );;
gap> iso:= List( nsg, x -> CharacterTableIsoclinic( t, x ) );;
gap> List( iso, x -> PositionProperty( result, y ->
> TransformingPermutationsCharacterTables( x, y ) <> fail ) );
[ 7, 5, 8 ]
## doc2/ctblcons.xml ( 8830- 8837)
gap> facts:= [ CharacterTable( " 2.L3( 4).( 2^ 2)_{ 123}" ),
> CharacterTable( " 2.L3( 4).( 2^ 2)_{ 12* 3}" ) ];;
gap> factresults:= List( result, t -> t / ClassPositionsOfCentre( t ) );;
gap> List( factresults, t -> PositionProperty( facts, f ->
> IsRecord( TransformingPermutationsCharacterTables( t, f ) ) ) );
[ 1, 1, 2, 1, 2, 1, 2, 2 ]
## doc2/ctblcons.xml ( 8849- 8864)
gap> test:= [ CharacterTable( " 4_ 2.L3( 4). 2_ 1" ),
> CharacterTable( " 4_ 2.L3( 4). 2_ 1*" ) ];;
gap> List( test, ClassPositionsOfCentre );
[ [ 1, 3 ], [ 1, 3 ] ]
gap> fact:= List( test, t -> t / ClassPositionsOfCentre( t ) );;
gap> IsRecord( TransformingPermutationsCharacterTables( fact[ 1], fact[ 2] ) );
true
gap> test:= [ CharacterTable( " 4_ 2.L3( 4). 2_ 3" ),
> CharacterTable( " 4_ 2.L3( 4). 2_ 3*" ) ];;
gap> List( test, ClassPositionsOfCentre );
[ [ 1, 3 ], [ 1, 3 ] ]
gap> fact:= List( test, t -> t / ClassPositionsOfCentre( t ) );;
gap> IsRecord( TransformingPermutationsCharacterTables( fact[ 1], fact[ 2] ) );
true
## doc2/ctblcons.xml ( 8874- 8931)
gap> names:= [ "L3( 4).( 2^ 2)_{ 123}", "L3( 4).( 2^ 2)_{ 1* 23}",
> "L3( 4).( 2^ 2)_{ 123*}", "L3( 4).( 2^ 2)_{ 1* 23*}" ];;
gap> inputs1:= List( names, nam -> [ " 4_ 2.L3( 4). 2_ 2", " 2.L3( 4). 2_ 2",
> Concatenation( " 2.", nam ), Concatenation( " 4_ 2.", nam ) ] );;
gap> names:= List( names, nam -> ReplacedString( nam, " 23", " 2* 3" ) );;
gap> inputs2:= List( names, nam -> [ " 4_ 2.L3( 4). 2_ 2*", " 2.L3( 4). 2_ 2*",
> Concatenation( " 2.", nam ), Concatenation( " 4_ 2.", nam ) ] );;
gap> inputs:= Concatenation( inputs1, inputs2 );
[ [ " 4_ 2.L3( 4). 2_ 2", " 2.L3( 4). 2_ 2", " 2.L3( 4).( 2^ 2)_{ 123}",
" 4_ 2.L3( 4).( 2^ 2)_{ 123}" ],
[ " 4_ 2.L3( 4). 2_ 2", " 2.L3( 4). 2_ 2", " 2.L3( 4).( 2^ 2)_{ 1* 23}",
" 4_ 2.L3( 4).( 2^ 2)_{ 1* 23}" ],
[ " 4_ 2.L3( 4). 2_ 2", " 2.L3( 4). 2_ 2", " 2.L3( 4).( 2^ 2)_{ 123*}",
" 4_ 2.L3( 4).( 2^ 2)_{ 123*}" ],
[ " 4_ 2.L3( 4). 2_ 2", " 2.L3( 4). 2_ 2", " 2.L3( 4).( 2^ 2)_{ 1* 23*}",
" 4_ 2.L3( 4).( 2^ 2)_{ 1* 23*}" ],
[ " 4_ 2.L3( 4). 2_ 2*", " 2.L3( 4). 2_ 2*", " 2.L3( 4).( 2^ 2)_{ 12* 3}",
" 4_ 2.L3( 4).( 2^ 2)_{ 12* 3}" ],
[ " 4_ 2.L3( 4). 2_ 2*", " 2.L3( 4). 2_ 2*", " 2.L3( 4).( 2^ 2)_{ 1* 2* 3}",
" 4_ 2.L3( 4).( 2^ 2)_{ 1* 2* 3}" ],
[ " 4_ 2.L3( 4). 2_ 2*", " 2.L3( 4). 2_ 2*", " 2.L3( 4).( 2^ 2)_{ 12* 3*}",
" 4_ 2.L3( 4).( 2^ 2)_{ 12* 3*}" ],
[ " 4_ 2.L3( 4). 2_ 2*", " 2.L3( 4). 2_ 2*", " 2.L3( 4).( 2^ 2)_{ 1* 2* 3*}",
" 4_ 2.L3( 4).( 2^ 2)_{ 1* 2* 3*}" ] ]
gap> result2:= [];;
gap> for input in inputs do
> tblMG := CharacterTable( input[ 1] );
> tblG := CharacterTable( input[ 2] );
> tblGA := CharacterTable( input[ 3] );
> name := Concatenation( "new", input[ 4] );
> lib := CharacterTable( input[ 4] );
> poss:= ConstructOrdinaryMGATable( tblMG, tblG, tblGA, name, lib );
> Append( result2, poss );
> od;
#E 4 possibilities for new4_2.L3( 4).( 2^ 2)_{ 123}
#E no solution for new4_2.L3( 4).( 2^ 2)_{ 1* 23}
#E no solution for new4_2.L3( 4).( 2^ 2)_{ 123*}
#E no solution for new4_2.L3( 4).( 2^ 2)_{ 1* 23*}
#E 4 possibilities for new4_2.L3( 4).( 2^ 2)_{ 12* 3}
#E no solution for new4_2.L3( 4).( 2^ 2)_{ 1* 2* 3}
#E no solution for new4_2.L3( 4).( 2^ 2)_{ 12* 3*}
#E no solution for new4_2.L3( 4).( 2^ 2)_{ 1* 2* 3*}
gap> Length( result2 );
8
gap> result2:= List( result2, x -> x.table );
[ CharacterTable( "new4_2.L3( 4).( 2^ 2)_{ 123}" ),
CharacterTable( "new4_2.L3( 4).( 2^ 2)_{ 123}" ),
CharacterTable( "new4_2.L3( 4).( 2^ 2)_{ 123}" ),
CharacterTable( "new4_2.L3( 4).( 2^ 2)_{ 123}" ),
CharacterTable( "new4_2.L3( 4).( 2^ 2)_{ 12* 3}" ),
CharacterTable( "new4_2.L3( 4).( 2^ 2)_{ 12* 3}" ),
CharacterTable( "new4_2.L3( 4).( 2^ 2)_{ 12* 3}" ),
CharacterTable( "new4_2.L3( 4).( 2^ 2)_{ 12* 3}" ) ]
gap> List( result, t1 -> PositionsProperty( result2, t2 -> IsRecord(
> TransformingPermutationsCharacterTables( t1, t2 ) ) ) );
[ [ 1 ], [ 4 ], [ 7 ], [ 3 ], [ 6 ], [ 2 ], [ 5 ], [ 8 ] ]
## doc2/ctblcons.xml ( 8942- 8947)
gap> on2:= CharacterTable( "ON. 2" );;
gap> fus:= List( result, x -> PossibleClassFusions( x, on2 ) );;
gap> List( fus, Length );
[ 0, 0, 16, 0, 0, 0, 0, 0 ]
## doc2/ctblcons.xml ( 8986- 8998)
gap> input:= [ "L2( 81). 2_ 1", "L2( 81). 4_ 1", "L2( 81). 4_ 2", "L2( 81). 2^ 2",
> "L2( 81).( 2x4)" ];;
gap> tblG := CharacterTable( input[ 1] );;
gap> tblsG2 := List( input{ [ 2 .. 4 ] }, CharacterTable );;
gap> name := Concatenation( "new", input[ 5] );;
gap> lib := CharacterTable( input[ 5] );;
gap> poss := ConstructOrdinaryGV4Table( tblG, tblsG2, name, lib );;
#I newL2( 81).( 2x4): 2 equivalence classes
gap> reps:= RepresentativesCharacterTables( poss );;
gap> Length( reps );
2
## doc2/ctblcons.xml ( 9007- 9017)
gap> ord:= OrdersClassRepresentatives( reps[ 1].table );;
gap> ord = OrdersClassRepresentatives( reps[ 2].table );
true
gap> pos:= Position( ord, 80 );
33
gap> PowerMap( reps[ 1].table, 3 )[ pos ];
34
gap> PowerMap( reps[ 2].table, 3 )[ pos ];
33
## doc2/ctblcons.xml ( 9033- 9042)
gap> trans:= TransformingPermutationsCharacterTables( reps[ 2].table, lib );;
gap> IsRecord( trans );
true
gap> List( reps[ 2].G2fusGV4, x -> OnTuples( x, trans.columns ) )
> = List( tblsG2, x -> GetFusionMap( x, lib ) );
true
gap> ConstructModularGV4Tables( tblG, tblsG2, [ reps[ 2] ], lib );;
#I not all input tables for L2( 81).( 2x4) mod 41 available
## doc2/ctblcons.xml ( 9070- 9084)
gap> input:= [ "O8+( 3)", "O8+( 3). 2_ 1", "O8+( 3). 2_ 1'", "O8+( 3). 2_ 1''",
> "O8+( 3).( 2^ 2)_{ 111}" ];;
gap> tblG := CharacterTable( input[ 1] );;
gap> tblsG2 := List( input{ [ 2 .. 4 ] }, CharacterTable );;
gap> name := Concatenation( "new", input[ 5] );;
gap> lib := CharacterTable( input[ 5] );;
gap> poss := ConstructOrdinaryGV4Table( tblG, tblsG2, name, lib );;
#I newO8+( 3).( 2^ 2)_{ 111}: 2 equivalence classes
gap> Length( poss );
64
gap> reps:= RepresentativesCharacterTables( poss );;
gap> Length( reps );
2
## doc2/ctblcons.xml ( 9104- 9120)
gap> t:= reps[ 1].table;;
gap> ord7:= Filtered( [ 1 .. NrConjugacyClasses( t ) ],
> i -> OrdersClassRepresentatives( t )[i] = 7 );
[ 37 ]
gap> SizesCentralizers( t ){ ord7 };
[ 112 ]
gap> ord28:= Filtered( [ 1 .. NrConjugacyClasses( t ) ],
> i -> OrdersClassRepresentatives( t )[i] = 28 );
[ 112, 113, 114, 115, 161, 162, 163, 164, 210, 211, 212, 213 ]
gap> List( reps[ 1].G2fusGV4, x -> Intersection( ord28, x ) );
[ [ 112, 113, 114, 115 ], [ 161, 162, 163, 164 ],
[ 210, 211, 212, 213 ] ]
gap> sub:= CharacterTable( "Cyclic", 28 ) * CharacterTable( "Cyclic", 4 );;
gap> List( reps, x -> Length( PossibleClassFusions( sub, x.table ) ) );
[ 0, 96 ]
## doc2/ctblcons.xml ( 9132- 9139)
gap> trans:= TransformingPermutationsCharacterTables( reps[ 2].table, lib );;
gap> IsRecord( trans );
true
gap> List( reps[ 2].G2fusGV4, x -> OnTuples( x, trans.columns ) )
> = List( tblsG2, x -> GetFusionMap( x, lib ) );
true
## doc2/ctblcons.xml ( 9159- 9165)
gap> poss:= Filtered( poss,
> r -> TransformingPermutationsCharacterTables( r.table, lib )
> <> fail );;
gap> ConstructModularGV4Tables( tblG, tblsG2, poss, lib );;
#I not all input tables for O8+( 3).( 2^ 2)_{ 111} mod 3 available
## doc2/ctblcons.xml ( 9210- 9225)
gap> t:= CharacterTable( "Sz( 8)" );;
gap> 2t:= CharacterTable( " 2.Sz( 8)" );;
gap> aut:= AutomorphismsOfTable( t );;
gap> elms:= Set( Filtered( aut, x -> Order( x ) in [ 1, 3 ] ),
> SmallestGeneratorPerm );
[ (), ( 9, 10, 11), ( 6, 7, 8), ( 6, 7, 8)( 9, 10, 11), ( 6, 7, 8)( 9, 11, 10) ]
gap> poss:= List( elms,
> pi -> PossibleCharacterTablesOfTypeV4G( t, 2t, pi, " 2^ 2.Sz( 8)" ) );
[ [ CharacterTable( " 2^ 2.Sz( 8)" ) ], [ CharacterTable( " 2^ 2.Sz( 8)" ) ]
, [ CharacterTable( " 2^ 2.Sz( 8)" ) ],
[ CharacterTable( " 2^ 2.Sz( 8)" ) ],
[ CharacterTable( " 2^ 2.Sz( 8)" ) ] ]
gap> reps:= RepresentativesCharacterTables( Concatenation( poss ) );
[ CharacterTable( " 2^ 2.Sz( 8)" ) ]
## doc2/ctblcons.xml ( 9233- 9237)
gap> IsRecord( TransformingPermutationsCharacterTables( reps[ 1],
> CharacterTable( " 2^ 2.Sz( 8)" ) ) );
true
## doc2/ctblcons.xml ( 9251- 9261)
gap> GetFusionMap( poss[ 1][ 1], 2t, " 1" );
[ 1, 1, 2, 2, 3, 4, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12,
12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 17, 18, 18, 19, 19 ]
gap> GetFusionMap( poss[ 1][ 1], 2t, " 2" );
[ 1, 2, 1, 2, 3, 4, 5, 6, 7, 6, 7, 8, 9, 8, 9, 10, 11, 10, 11, 12,
13, 12, 13, 14, 15, 14, 15, 16, 17, 16, 17, 18, 19, 18, 19 ]
gap> GetFusionMap( poss[ 1][ 1], 2t, " 3" );
[ 1, 2, 2, 1, 3, 4, 5, 6, 7, 7, 6, 8, 9, 9, 8, 10, 11, 11, 10, 12,
13, 13, 12, 14, 15, 15, 14, 16, 17, 17, 16, 18, 19, 19, 18 ]
## doc2/ctblcons.xml ( 9275- 9278)
gap> PrimeDivisors( Size( t ) );
[ 2, 5, 7, 13 ]
## doc2/ctblcons.xml ( 9298- 9313)
gap> cand:= List( poss, l -> BrauerTableOfTypeV4G( l[ 1], 2t mod 5,
> ConstructionInfoCharacterTable( l[ 1] )[ 3] ) );
[ BrauerTable( " 2^ 2.Sz( 8)", 5 ), BrauerTable( " 2^ 2.Sz( 8)", 5 ),
BrauerTable( " 2^ 2.Sz( 8)", 5 ), BrauerTable( " 2^ 2.Sz( 8)", 5 ),
BrauerTable( " 2^ 2.Sz( 8)", 5 ) ]
gap> Length( RepresentativesCharacterTables( cand ) );
2
gap> List( cand, CTblLib.Test.TensorDecomposition );
[ false, true, false, true, true ]
gap> Length( RepresentativesCharacterTables( cand{ [ 2, 4, 5 ] } ) );
1
gap> IsRecord( TransformingPermutationsCharacterTables( cand[ 2],
> CharacterTable( " 2^ 2.Sz( 8)" ) mod 5 ) );
true
## doc2/ctblcons.xml ( 9327- 9338)
gap> cand:= List( poss, l -> BrauerTableOfTypeV4G( l[ 1], 2t mod 7,
> ConstructionInfoCharacterTable( l[ 1] )[ 3] ) );
[ BrauerTable( " 2^ 2.Sz( 8)", 7 ), BrauerTable( " 2^ 2.Sz( 8)", 7 ),
BrauerTable( " 2^ 2.Sz( 8)", 7 ), BrauerTable( " 2^ 2.Sz( 8)", 7 ),
BrauerTable( " 2^ 2.Sz( 8)", 7 ) ]
gap> Length( RepresentativesCharacterTables( cand ) );
1
gap> IsRecord( TransformingPermutationsCharacterTables( cand[ 1],
> CharacterTable( " 2^ 2.Sz( 8)" ) mod 7 ) );
true
## doc2/ctblcons.xml ( 9347- 9359)
gap> elms:= elms{ [ 2, 4, 5 ] };
[ ( 9, 10, 11), ( 6, 7, 8)( 9, 10, 11), ( 6, 7, 8)( 9, 11, 10) ]
gap> poss:= poss{ [ 2, 4, 5 ] };;
gap> cand:= List( poss, l -> BrauerTableOfTypeV4G( l[ 1], 2t mod 13,
> ConstructionInfoCharacterTable( l[ 1] )[ 3] ) );
[ BrauerTable( " 2^ 2.Sz( 8)", 13 ), BrauerTable( " 2^ 2.Sz( 8)", 13 ),
BrauerTable( " 2^ 2.Sz( 8)", 13 ) ]
gap> Length( RepresentativesCharacterTables( cand ) );
2
gap> List( cand, CTblLib.Test.TensorDecomposition );
[ true, true, true ]
## doc2/ctblcons.xml ( 9375- 9382)
gap> mod2:= CharacterTable( "Sz( 8)" ) mod 2;
BrauerTable( "Sz( 8)", 2 )
gap> AutomorphismsOfTable( mod2 );
Group([ ( 3, 4, 5)( 6, 7, 8) ])
gap> OrdersClassRepresentatives( mod2 );
[ 1, 5, 7, 7, 7, 13, 13, 13 ]
## doc2/ctblcons.xml ( 9391- 9397)
gap> Length( RepresentativesCharacterTables( cand{ [ 2, 3 ] } ) );
1
gap> IsRecord( TransformingPermutationsCharacterTables( cand[ 2],
> CharacterTable( " 2^ 2.Sz( 8)" ) mod 13 ) );
true
## doc2/ctblcons.xml ( 9458- 9470)
gap> listV4G:= [
> [ " 2^ 2.L3( 4)", " 2.L3( 4)", "L3( 4)" ],
> [ " 2^ 2.L3( 4). 2_ 1", " 2.L3( 4). 2_ 1", "L3( 4). 2_ 1" ],
> [ "( 2^ 2x3).L3( 4)", " 6.L3( 4)", " 3.L3( 4)" ],
> [ "( 2^ 2x3).L3( 4). 2_ 1", " 6.L3( 4). 2_ 1", " 3.L3( 4). 2_ 1" ],
> [ " 2^ 2.O8+( 2)", " 2.O8+( 2)", "O8+( 2)" ],
> [ " 2^ 2.U6( 2)", " 2.U6( 2)", "U6( 2)" ],
> [ "( 2^ 2x3).U6( 2)", " 6.U6( 2)", " 3.U6( 2)" ],
> [ " 2^ 2. 2E6( 2)", " 2. 2E6( 2)", " 2E6( 2)" ],
> [ "( 2^ 2x3). 2E6( 2)", " 6. 2E6( 2)", " 3. 2E6( 2)" ],
> ];;
## doc2/ctblcons.xml ( 9489- 9527)
gap> ConstructOrdinaryV4GTable:= function( tblG, tbl2G, name, lib )
> local ord3, nam, poss, reps, trans;
>
> # Compute the possible actions for the ordinary tables.
> ord3:= Set( Filtered( AutomorphismsOfTable( tblG ),
> x -> Order( x ) = 3 ),
> SmallestGeneratorPerm );
> if 1 < Length( ord3 ) then
> Print( "#I ", name,
> ": the action of the automorphism is not unique" );
> fi;
> # Compute the possible ordinary tables for the given actions.
> nam:= Concatenation( "new", name );
> poss:= Concatenation( List( ord3, pi ->
> PossibleCharacterTablesOfTypeV4G( tblG, tbl2G, pi, nam ) ) );
> # Test the possibilities for permutation equivalence.
> reps:= RepresentativesCharacterTables( poss );
> if 1 < Length( reps ) then
> Print( "#I ", name, ": ", Length( reps ),
> " equivalence classes\n" );
> elif Length( reps ) = 0 then
> Print( "#E ", name, ": no solution\n" );
> else
> # Compare the computed table with the library table.
> if not IsCharacterTable( lib ) then
> Print( "#I no library table for ", name, "\n" );
> PrintToLib( name, poss[ 1].table );
> else
> trans:= TransformingPermutationsCharacterTables( reps[ 1], lib );
> if not IsRecord( trans ) then
> Print( "#E computed table and library table for ", name,
> " differ\n" );
> fi;
> fi;
> fi;
> return poss;
> end;;
## doc2/ctblcons.xml ( 9542- 9631)
gap> ConstructModularV4GTables:= function( tblG, tbl2G, ordposs,
> ordlibtblV4G )
> local name, modposs, primes, checkordinary, i, p, tmodp, 2tmodp, aut,
> poss, modlib, trans, reps;
>
> if not IsCharacterTable( ordlibtblV4G ) then
> Print( "#I no ordinary library table ...\n" );
> return [];
> fi;
> name:= Identifier( ordlibtblV4G );
> modposs:= [];
> primes:= ShallowCopy( PrimeDivisors( Size( tblG ) ) );
> ordposs:= ShallowCopy( ordposs );
> checkordinary:= false;
> for i in [ 1 .. Length( ordposs ) ] do
> modposs[i]:= [];
> for p in primes do
> tmodp := tblG mod p;
> 2tmodp:= tbl2G mod p;
> if IsCharacterTable( tmodp ) and IsCharacterTable( 2tmodp ) then
> aut:= ConstructionInfoCharacterTable( ordposs[i] )[ 3];
> poss:= BrauerTableOfTypeV4G( ordposs[i], 2tmodp, aut );
> if CTblLib.Test.TensorDecomposition( poss, false ) = false then
> Print( "#I excluded cand. ", i, " (out of ",
> Length( ordposs ), ") for ", name, " by ", p,
> "-mod. table\n" );
> Unbind( ordposs[i] );
> Unbind( modposs[i] );
> checkordinary:= true;
> break;
> fi;
> Add( modposs[i], poss );
> else
> Print( "#I not all input tables for ", name, " mod ", p,
> " available\n" );
> primes:= Difference( primes, [ p ] );
> fi;
> od;
> if IsBound( modposs[i] ) then
> # Compare the computed Brauer tables with the library tables.
> for poss in modposs[i] do
> p:= UnderlyingCharacteristic( poss );
> modlib:= ordlibtblV4G mod p;
> if IsCharacterTable( modlib ) then
> trans:= TransformingPermutationsCharacterTables(
> poss, modlib );
> if not IsRecord( trans ) then
> Print( "#E computed table and library table for ",
> name, " mod ", p, " differ\n" );
> fi;
> else
> Print( "#I no library table for ",
> name, " mod ", p, "\n" );
> PrintToLib( name, poss );
> fi;
> od;
> fi;
> od;
> if checkordinary then
> # Test whether the ordinary table is admissible.
> ordposs:= Compacted( ordposs );
> modposs:= Compacted( modposs );
> reps:= RepresentativesCharacterTables( ordposs );
> if 1 < Length( reps ) then
> Print( "#I ", name, ": ", Length( reps ),
> " equivalence classes (ord. table)\n" );
> elif Length( reps ) = 0 then
> Print( "#E ", name, ": no solution (ord. table)\n" );
> else
> # Compare the computed table with the library table.
> trans:= TransformingPermutationsCharacterTables( reps[ 1],
> ordlibtblV4G );
> if not IsRecord( trans ) then
> Print( "#E computed table and library table for ", name,
> " differ\n" );
> fi;
> fi;
> fi;
> # Test the uniqueness of the Brauer tables.
> for poss in TransposedMat( modposs ) do
> reps:= RepresentativesCharacterTables( poss );
> if Length( reps ) <> 1 then
> Print( "#I ", name, ": ", Length( reps ), " candidates for the ",
> UnderlyingCharacteristic( reps[ 1] ), "-modular table\n" );
> fi;
> od;
> return rec( ordinary:= ordposs, modular:= modposs );
> end;;
## doc2/ctblcons.xml ( 9642- 9677)
gap> for input in listV4G do
> tblG := CharacterTable( input[ 3] );
> tbl2G := CharacterTable( input[ 2] );
> lib := CharacterTable( input[ 1] );
> poss := ConstructOrdinaryV4GTable( tblG, tbl2G, input[ 1], lib );
> ConstructModularV4GTables( tblG, tbl2G, poss, lib );
> od;
#I excluded cand. 1 (out of 16) for 2^ 2.L3( 4). 2_ 1 by 7-mod. table
#I excluded cand. 2 (out of 16) for 2^ 2.L3( 4). 2_ 1 by 7-mod. table
#I excluded cand. 7 (out of 16) for 2^ 2.L3( 4). 2_ 1 by 7-mod. table
#I excluded cand. 10 (out of 16) for 2^ 2.L3( 4). 2_ 1 by 7-mod. table
#I excluded cand. 15 (out of 16) for 2^ 2.L3( 4). 2_ 1 by 7-mod. table
#I excluded cand. 16 (out of 16) for 2^ 2.L3( 4). 2_ 1 by 7-mod. table
#I excluded cand. 1 (out of 16) for ( 2^ 2x3).L3( 4). 2_ 1 by 7-mod. table
#I excluded cand. 2 (out of 16) for ( 2^ 2x3).L3( 4). 2_ 1 by 7-mod. table
#I excluded cand. 7 (out of 16) for ( 2^ 2x3).L3( 4). 2_ 1 by 7-mod. table
#I excluded cand. 10 (out of 16) for ( 2^ 2x3).L3( 4). 2_ 1 by
7-mod. table
#I excluded cand. 15 (out of 16) for ( 2^ 2x3).L3( 4). 2_ 1 by
7-mod. table
#I excluded cand. 16 (out of 16) for ( 2^ 2x3).L3( 4). 2_ 1 by
7-mod. table
#I not all input tables for 2^ 2. 2E6( 2) mod 2 available
#I not all input tables for 2^ 2. 2E6( 2) mod 3 available
#I not all input tables for 2^ 2. 2E6( 2) mod 5 available
#I not all input tables for 2^ 2. 2E6( 2) mod 7 available
#I not all input tables for ( 2^ 2x3). 2E6( 2) mod 2 available
#I not all input tables for ( 2^ 2x3). 2E6( 2) mod 3 available
#I not all input tables for ( 2^ 2x3). 2E6( 2) mod 5 available
#I not all input tables for ( 2^ 2x3). 2E6( 2) mod 7 available
#I not all input tables for ( 2^ 2x3). 2E6( 2) mod 11 available
#I not all input tables for ( 2^ 2x3). 2E6( 2) mod 13 available
#I not all input tables for ( 2^ 2x3). 2E6( 2) mod 17 available
#I not all input tables for ( 2^ 2x3). 2E6( 2) mod 19 available
## doc2/ctblcons.xml ( 9708- 9716)
gap> entry:= [ " 2^ 2.O8+( 3)", " 2.O8+( 3)", "O8+( 3)" ];;
gap> tblG:= CharacterTable( entry[ 3] );;
gap> aut:= AutomorphismsOfTable( tblG );;
gap> ord3:= Set( Filtered( aut, x -> Order( x ) = 3 ),
> SmallestGeneratorPerm );;
gap> Length( ord3 );
4
## doc2/ctblcons.xml ( 9726- 9739)
gap> poss:= [];;
gap> tbl2G:= CharacterTable( entry[ 2] );
CharacterTable( " 2.O8+( 3)" )
gap> for pi in ord3 do
> Append( poss,
> PossibleCharacterTablesOfTypeV4G( tblG, tbl2G, pi, entry[ 1] ) );
> od;
gap> Length( poss );
32
gap> poss:= RepresentativesCharacterTables( poss );;
gap> Length( poss );
1
## doc2/ctblcons.xml ( 9747- 9752)
gap> lib:= CharacterTable( entry[ 1] );;
gap> if TransformingPermutationsCharacterTables( poss[ 1], lib ) = fail then
> Print( "#E differences for ", entry[ 1], "\n" );
> fi;
## doc2/ctblcons.xml ( 9979- 9991)
gap> tblG:= CharacterTable( " 2.L3( 4)" );;
gap> tbls2G:= List( [ " 4_ 1.L3( 4)", " 4_ 2.L3( 4)", " 2^ 2.L3( 4)"],
> CharacterTable );;
gap> poss:= PossibleCharacterTablesOfTypeV4G( tblG, tbls2G, "( 2x4).L3( 4)" );;
gap> Length( poss );
2
gap> reps:= RepresentativesCharacterTables( poss );
[ CharacterTable( "( 2x4).L3( 4)" ) ]
gap> lib:= CharacterTable( "( 2x4).L3( 4)" );;
gap> IsRecord( TransformingPermutationsCharacterTables( reps[ 1], lib ) );
true
## doc2/ctblcons.xml ( 10003- 10022)
gap> tblG:= tbls2G[ 3];
CharacterTable( " 2^ 2.L3( 4)" )
gap> tbl2G:= lib;
CharacterTable( "( 2x4).L3( 4)" )
gap> aut:= AutomorphismsOfTable( tblG );;
gap> ord3:= Set( Filtered( aut, x -> Order( x ) = 3 ),
> SmallestGeneratorPerm );
[ ( 2, 3, 4)( 6, 7, 8)( 10, 11, 12)( 13, 15, 17)( 14, 16, 18)( 20, 21, 22)( 24, 25, 26)( 28,
29, 30)( 32, 33, 34) ]
gap> pi:= ord3[ 1];;
gap> poss:= PossibleCharacterTablesOfTypeV4G( tblG, tbl2G, pi, " 4^ 2.L3( 4)" );;
gap> Length( poss );
4
gap> reps:= RepresentativesCharacterTables( poss );
[ CharacterTable( " 4^ 2.L3( 4)" ) ]
gap> lib:= CharacterTable( " 4^ 2.L3( 4)" );;
gap> IsRecord( TransformingPermutationsCharacterTables( reps[ 1], lib ) );
true
## doc2/ctblcons.xml ( 10036- 10069)
gap> tblG:= CharacterTable( " 6.L3( 4)" );;
gap> tbls2G:= List( [ " 12_ 1.L3( 4)", " 12_ 2.L3( 4)", "( 2^ 2x3).L3( 4)"],
> CharacterTable );;
gap> poss:= PossibleCharacterTablesOfTypeV4G( tblG, tbls2G, "( 2x12).L3( 4)" );;
gap> Length( poss );
2
gap> reps:= RepresentativesCharacterTables( poss );
[ CharacterTable( "( 2x12).L3( 4)" ) ]
gap> lib:= CharacterTable( "( 2x12).L3( 4)" );;
gap> IsRecord( TransformingPermutationsCharacterTables( reps[ 1], lib ) );
true
gap> tblG:= CharacterTable( "( 2^ 2x3).L3( 4)" );
CharacterTable( "( 2^ 2x3).L3( 4)" )
gap> tbl2G:= CharacterTable( "( 2x12).L3( 4)" );
CharacterTable( "( 2x12).L3( 4)" )
gap> aut:= AutomorphismsOfTable( tblG );;
gap> ord3:= Set( Filtered( aut, x -> Order( x ) = 3 ),
> SmallestGeneratorPerm );
[ ( 2, 7, 8)( 3, 4, 10)( 6, 11, 12)( 14, 19, 20)( 15, 16, 22)( 18, 23, 24)( 26, 27, 28)( 29,
35, 41)( 30, 37, 43)( 31, 39, 45)( 32, 36, 42)( 33, 38, 44)( 34, 40, 46)( 48, 53,
54)( 49, 50, 56)( 52, 57, 58)( 60, 65, 66)( 61, 62, 68)( 64, 69, 70)( 72, 77,
78)( 73, 74, 80)( 76, 81, 82)( 84, 89, 90)( 85, 86, 92)( 88, 93, 94) ]
gap> pi:= ord3[ 1];;
gap> poss:= PossibleCharacterTablesOfTypeV4G( tblG, tbl2G, pi,
> "( 4^ 2x3).L3( 4)" );;
gap> Length( poss );
4
gap> reps:= RepresentativesCharacterTables( poss );
[ CharacterTable( "( 4^ 2x3).L3( 4)" ) ]
gap> lib:= CharacterTable( "( 4^ 2x3).L3( 4)" );;
gap> IsRecord( TransformingPermutationsCharacterTables( reps[ 1], lib ) );
true
## doc2/ctblcons.xml ( 10101- 10141)
gap> for input in listMGA do
> ordtblMG := CharacterTable( input[ 1] );
> ordtblG := CharacterTable( input[ 2] );
> ordtblGA := CharacterTable( input[ 3] );
> ordtblMGA := CharacterTable( input[ 4] );
> p:= Size( ordtblGA ) / Size( ordtblG );
> if IsPrimeInt( p ) then
> modtblG:= ordtblG mod p;
> if modtblG <> fail then
> modtblGA := CharacterTableRegular( ordtblGA, p );
> SetIrr( modtblGA, IBrOfExtensionBySingularAutomorphism( modtblG,
> ordtblGA ) );
> modlibtblGA:= ordtblGA mod p;
> if modlibtblGA = fail then
> Print( "#E ", p, "-modular table of '", Identifier( ordtblGA ),
> "' is missing\n" );
> elif TransformingPermutationsCharacterTables( modtblGA,
> modlibtblGA ) = fail then
> Print( "#E computed table and library table for ", input[ 3],
> " mod ", p, " differ\n" );
> fi;
> fi;
> modtblMG:= ordtblMG mod p;
> if modtblMG <> fail then
> modtblMGA := CharacterTableRegular( ordtblMGA, p );
> SetIrr( modtblMGA, IBrOfExtensionBySingularAutomorphism( modtblMG,
> ordtblMGA ) );
> modlibtblMGA:= ordtblMGA mod p;
> if modlibtblMGA = fail then
> Print( "#E ", p, "-modular table of '", Identifier( ordtblMGA ),
> "' is missing\n" );
> elif TransformingPermutationsCharacterTables( modtblMGA,
> modlibtblMGA ) = fail then
> Print( "#E computed table and library table for ", input[ 4],
> " mod ", p, " differ\n" );
> fi;
> fi;
> fi;
> od;
## doc2/ctblcons.xml ( 10165- 10216)
gap> for input in listGS3 do
> modtblG:= CharacterTable( input[ 1] ) mod 2;
> if modtblG <> fail then
> ordtblG2 := CharacterTable( input[ 2] );
> modtblG2 := CharacterTableRegular( ordtblG2, 2 );
> SetIrr( modtblG2, IBrOfExtensionBySingularAutomorphism( modtblG,
> ordtblG2 ) );
> modlibtblG2:= ordtblG2 mod 2;
> if modlibtblG2 = fail then
> Print( "#E 2-modular table of '", Identifier( ordtblG2 ),
> "' is missing\n" );
> elif TransformingPermutationsCharacterTables( modtblG2,
> modlibtblG2 ) = fail then
> Print( "#E computed table and library table for ", input[ 2],
> " mod 2 differ\n" );
> fi;
> fi;
> modtblG:= CharacterTable( input[ 1] ) mod 3;
> if modtblG <> fail then
> ordtblG3 := CharacterTable( input[ 3] );
> modtblG3 := CharacterTableRegular( ordtblG3, 3 );
> SetIrr( modtblG3, IBrOfExtensionBySingularAutomorphism( modtblG,
> ordtblG3 ) );
> modlibtblG3:= ordtblG3 mod 3;
> if modlibtblG3 = fail then
> Print( "#E 3-modular table of '", Identifier( ordtblG3 ),
> "' is missing\n" );
> elif TransformingPermutationsCharacterTables( modtblG3,
> modlibtblG3 ) = fail then
> Print( "#E computed table and library table for ", input[ 3],
> " mod 3 differ\n" );
> fi;
> fi;
> modtblG3:= CharacterTable( input[ 3] ) mod 2;
> if modtblG3 <> fail then
> ordtblGS3 := CharacterTable( input[ 4] );
> modtblGS3 := CharacterTableRegular( ordtblGS3, 2 );
> SetIrr( modtblGS3, IBrOfExtensionBySingularAutomorphism( modtblG3,
> ordtblGS3 ) );
> modlibtblGS3:= ordtblGS3 mod 2;
> if modlibtblGS3 = fail then
> Print( "#E 2-modular table of '", Identifier( ordtblGS3 ),
> "' is missing\n" );
> elif TransformingPermutationsCharacterTables( modtblGS3,
> modlibtblGS3 ) = fail then
> Print( "#E computed table and library table for ", input[ 4],
> " mod 2 differ\n" );
> fi;
> fi;
> od;
## doc2/ctblcons.xml ( 10243- 10277)
gap> for input in listGV4 do
> modtblG:= CharacterTable( input[ 1] ) mod 2;
> if modtblG <> fail then
> ordtblsG2:= List( input{ [ 2 .. 4 ] }, CharacterTable );
> ordtblGV4:= CharacterTable( input[ 5] );
> for tblG2 in ordtblsG2 do
> modtblG2:= CharacterTableRegular( tblG2, 2 );
> SetIrr( modtblG2, IBrOfExtensionBySingularAutomorphism( modtblG,
> tblG2 ) );
> modlibtblG2:= tblG2 mod 2;
> if modlibtblG2 = fail then
> Print( "#E 2-modular table of '", Identifier( tblG2 ),
> "' is missing\n" );
> elif TransformingPermutationsCharacterTables( modtblG2,
> modlibtblG2 ) = fail then
> Print( "#E computed table and library table for ",
> Identifier( tblG2 ), " mod 2 differ\n" );
> fi;
> modtblGV4:= CharacterTableRegular( ordtblGV4, 2 );
> SetIrr( modtblGV4, IBrOfExtensionBySingularAutomorphism( modtblG2,
> ordtblGV4 ) );
> modlibtblGV4:= ordtblGV4 mod 2;
> if modlibtblGV4 = fail then
> Print( "#E 2-modular table of '", Identifier( ordtblGV4 ),
> "' is missing\n" );
> elif TransformingPermutationsCharacterTables( modtblGV4,
> ordtblGV4 mod 2 ) = fail then
> Print( "#E computed table and library table for ", input[ 5],
> " mod 2 differ\n" );
> fi;
> od;
> fi;
> od;
## doc2/ctblcons.xml ( 10294- 10312)
gap> ordtblG3:= CharacterTable( "U3( 8). 3^ 2" );;
gap> modlibtblG3:= ordtblG3 mod 3;
BrauerTable( "U3( 8). 3^ 2", 3 )
gap> for nam in [ "U3( 8). 3_ 1", "U3( 8). 3_ 2", "U3( 8). 3_ 3" ] do
> modtblG:= CharacterTable( nam ) mod 3;
> if modtblG = fail then
> Error( "no 3-modular table of ", nam );
> fi;
> modtblG3:= CharacterTableRegular( ordtblG3, 3 );
> SetIrr( modtblG3, IBrOfExtensionBySingularAutomorphism( modtblG,
> ordtblG3 ) );
> if TransformingPermutationsCharacterTables( modtblG3,
> modlibtblG3 ) = fail then
> Print( "#E computed table and library table for ",
> Identifier( ordtblG3 ), " mod 3 differ\n" );
> fi;
> od;
## doc2/ctblcons.xml ( 10326- 10330)
gap> rest:= RestrictedClassFunctions( Irr( ordtblG3 ), modlibtblG3 );;
gap> IsSubset( rest, Irr( modlibtblG3 ) );
true
## doc2/ctblcons.xml ( 10366- 10378)
gap> tblh1:= CharacterTable( "C3" );;
gap> tblg1:= CharacterTable( "S3" );;
gap> StoreFusion( tblh1, PossibleClassFusions( tblh1, tblg1 )[ 1], tblg1 );
gap> tblh2:= CharacterTable( "C5" );;
gap> tblg2:= CharacterTable( "D10" );;
gap> StoreFusion( tblh2, PossibleClassFusions( tblh2, tblg2 )[ 1], tblg2 );
gap> subdir:= CharacterTableOfIndexTwoSubdirectProduct( tblh1, tblg1,
> tblh2, tblg2, "D30" );;
gap> IsRecord( TransformingPermutationsCharacterTables( subdir.table,
> CharacterTable( "Dihedral", 30 ) ) );
true
## doc2/ctblcons.xml ( 10395- 10411)
gap> tblh1:= CharacterTable( "D10" );;
gap> tblg1:= CharacterTable( " 5: 4" );;
gap> tblh2:= CharacterTable( "HN" );;
gap> tblg2:= CharacterTable( "HN. 2" );;
gap> subdir:= CharacterTableOfIndexTwoSubdirectProduct( tblh1, tblg1,
> tblh2, tblg2, "(D10xHN). 2" );;
gap> IsRecord( TransformingPermutationsCharacterTables( subdir.table,
> CharacterTable( "(D10xHN). 2" ) ) );
true
gap> m:= CharacterTable( "M" );;
gap> fus:= PossibleClassFusions( subdir.table, m );;
gap> Length( fus );
16
gap> Length( RepresentativesFusions( subdir.table, fus, m ) );
1
## doc2/ctblcons.xml ( 10428- 10473)
gap> c2:= CharacterTable( "C2" );;
gap> hn:= CharacterTable( "HN" );;
gap> g:= c2 * hn;;
gap> d10:= CharacterTable( "D10" );;
gap> mg:= d10 * hn;;
gap> nsg:= ClassPositionsOfNormalSubgroups( mg );
[ [ 1 ], [ 1, 55 .. 109 ], [ 1, 55 .. 163 ], [ 1 .. 54 ],
[ 1 .. 162 ], [ 1 .. 216 ] ]
gap> SizesConjugacyClasses( mg ){ nsg[ 2] };
[ 1, 2, 2 ]
gap> g:= mg / nsg[ 2];
CharacterTable( "D10xHN/[ 1, 55, 109 ]" )
gap> help:= c2 * CharacterTable( "HN. 2" );
CharacterTable( "C2xHN. 2" )
gap> ga:= CharacterTableIsoclinic( help );
CharacterTable( "Isoclinic(C2xHN. 2)" )
gap> gfusga:= PossibleClassFusions( g, ga );
[ [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 11, 12, 13, 14, 15, 16, 17,
18, 19, 20, 21, 22, 23, 23, 24, 25, 25, 26, 27, 28, 29, 30, 31,
32, 32, 33, 33, 34, 35, 36, 37, 37, 38, 39, 40, 40, 41, 42, 42,
43, 43, 44, 44, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 89,
90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 101, 102,
103, 103, 104, 105, 106, 107, 108, 109, 110, 110, 111, 111,
112, 113, 114, 115, 115, 116, 117, 118, 118, 119, 120, 120,
121, 121, 122, 122 ],
[ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 11, 12, 13, 14, 15, 16, 17,
18, 19, 20, 21, 22, 23, 23, 24, 25, 25, 26, 27, 28, 29, 30, 31,
32, 32, 33, 33, 35, 34, 36, 37, 37, 38, 39, 40, 40, 41, 42, 42,
43, 43, 44, 44, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 89,
90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 101, 102,
103, 103, 104, 105, 106, 107, 108, 109, 110, 110, 111, 111,
113, 112, 114, 115, 115, 116, 117, 118, 118, 119, 120, 120,
121, 121, 122, 122 ] ]
gap> StoreFusion( g, gfusga[ 1], ga );
gap> acts:= PossibleActionsForTypeMGA( mg, g, ga );;
gap> Length( acts );
1
gap> poss:= PossibleCharacterTablesOfTypeMGA( mg, g, ga, acts[ 1],
> "(D10xHN). 2" );;
gap> Length( poss );
1
gap> IsRecord( TransformingPermutationsCharacterTables( poss[ 1].table,
> CharacterTable( "(D10xHN). 2" ) ) );
true
##
gap> if IsBound( BrowseData ) then
> data:= BrowseData.defaults.dynamic.replayDefaults;
> data.replayInterval:= oldinterval;
> fi;
##
gap> STOP_TEST( "ctblcons.tst" );
gap> SizeScreen( save );;
#############################################################################
##
#E
[Dauer der Verarbeitung: 0.164 Sekunden, vorverarbeitet 2026-06-17]
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2026-07-27
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