Spracherkennung für: .tst vermutete Sprache: Unknown {[0] [0] [0]} [Methode: Schwerpunktbildung, einfache Gewichte, sechs Dimensionen]
# This file was created automatically, do not edit!
#############################################################################
##
#W dntgap.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( "dntgap.tst" );'.
##
gap> LoadPackage( "CTblLib", false );
true
gap> save:= SizeScreen();;
gap> SizeScreen( [ 72 ] );;
gap> START_TEST( "dntgap.tst" );
##
gap> if IsBound( BrowseData ) then
> data:= BrowseData.defaults.dynamic.replayDefaults;
> oldinterval:= data.replayInterval;
> data.replayInterval:= 1;
> fi;
## doc2/dntgap.xml (46-55)
gap> LoadPackage( "AtlasRep", "1.5", false );
true
gap> LoadPackage( "cohomolo", "1.6", false );
true
gap> LoadPackage( "CTblLib", "1.2", false );
true
gap> LoadPackage( "TomLib", "1.2.1", false );
true
## doc2/dntgap.xml (70-94)
gap> p:= 2;; d:= 12;;
gap> t:= CharacterTable( "Sz(8)" ) mod p;
BrauerTable( "Sz(8)", 2 )
gap> irr:= Filtered( Irr( t ), x -> x[1] <= d );;
gap> Display( t, rec( chars:= irr, powermap:= false,
> centralizers:= false ) );
Sz(8)mod2
1a 5a 7a 7b 7c 13a 13b 13c
Y.1 1 1 1 1 1 1 1 1
Y.2 4 -1 A C B D F E
Y.3 4 -1 B A C E D F
Y.4 4 -1 C B A F E D
A = E(7)^2+E(7)^3+E(7)^4+E(7)^5
B = E(7)+E(7)^2+E(7)^5+E(7)^6
C = E(7)+E(7)^3+E(7)^4+E(7)^6
D = E(13)+E(13)^5+E(13)^8+E(13)^12
E = E(13)^4+E(13)^6+E(13)^7+E(13)^9
F = E(13)^2+E(13)^3+E(13)^10+E(13)^11
gap> List( irr, x -> SizeOfFieldOfDefinition( x, p ) );
[ 2, 8, 8, 8 ]
## doc2/dntgap.xml (105-117)
gap> info:= OneAtlasGeneratingSetInfo( "Sz(8)", Dimension, 4,
> Characteristic, p );
rec( charactername := "4a", constituents := [ 2 ], contents := "core",
dim := 4, groupname := "Sz(8)", id := "a",
identifier := [ "Sz(8)", [ "Sz8G1-f8r4aB0.m1", "Sz8G1-f8r4aB0.m2" ],
1, 8 ], repname := "Sz8G1-f8r4aB0", repnr := 17,
ring := GF(2^3), size := 29120, standardization := 1,
type := "matff" )
gap> gens_dim4:= AtlasGenerators( info ).generators;;
gap> b:= Basis( GF(8) );;
gap> gens_dim12:= List( gens_dim4, x -> BlownUpMatrix( b, x ) );;
## doc2/dntgap.xml (125-132)
gap> s:= AtlasGroup( "Sz(8)", IsPermGroup, true );;
gap> chr:= CHR( s, p, 0, gens_dim12 );;
gap> SizeScreen( [ 100 ] );;
gap> SecondCohomologyDimension( chr );
0
gap> SizeScreen( [ 72 ] );;
## doc2/dntgap.xml (159-171)
gap> mats:= List( [1 .. 3 ], x -> IdentityMat( d+1, GF(p) ) );;
gap> v:= mats[1][ d+1 ];;
gap> mats[1]{ [ 1 .. d ] }{ [ 1 .. d ] }:= gens_dim12[1];;
gap> mats[2]{ [ 1 .. d ] }{ [ 1 .. d ] }:= gens_dim12[2];;
gap> mats[3][ d+1 ][1]:= Z(p)^0;;
gap> grp:= Group( mats );;
gap> g:= Image( IsomorphismPermGroup( grp ) );;
gap> Size( g );
119275520
gap> NrConjugacyClasses( g );
41
## doc2/dntgap.xml (195-205)
gap> iso:= IsomorphismTypeInfoFiniteSimpleGroup( s );
rec( name := "2B(2,8) = 2C(2,8) = Sz(8)", parameter := 8,
series := "2B", shortname := "Sz(8)" )
gap> names:= AllCharacterTableNames( Size, 2^12 * Size( s ) );;
gap> cand:= List( names, CharacterTable );;
gap> cand:= Filtered( cand,
> t -> ForAny( ClassPositionsOfMinimalNormalSubgroups( t ),
> n -> IsomorphismTypeInfoFiniteSimpleGroup( t / n ) = iso ) );
[ CharacterTable( "2^12:Sz(8)" ) ]
## doc2/dntgap.xml (214-219)
gap> t:= cand[1];;
gap> rationals:= Filtered( Irr( t ), x -> IsSubset( Integers, x ) );;
gap> Collected( List( rationals, x -> x[1] ) );
[ [ 1, 1 ], [ 64, 1 ], [ 91, 1 ], [ 455, 8 ], [ 3640, 8 ] ]
## doc2/dntgap.xml (234-253)
gap> p:= 2;; d:= 10;;
gap> t:= CharacterTable( "M22" ) mod p;
BrauerTable( "M22", 2 )
gap> irr:= Filtered( Irr( t ), x -> x[1] <= d );;
gap> Display( t, rec( chars:= irr, powermap:= false,
> centralizers:= false ) );
M22mod2
1a 3a 5a 7a 7b 11a 11b
Y.1 1 1 1 1 1 1 1
Y.2 10 1 . A /A -1 -1
Y.3 10 1 . /A A -1 -1
A = E(7)+E(7)^2+E(7)^4
= (-1+Sqrt(-7))/2 = b7
gap> List( irr, x -> SizeOfFieldOfDefinition( x, p ) );
[ 2, 2, 2 ]
## doc2/dntgap.xml (264-280)
gap> info:= AllAtlasGeneratingSetInfos( "M22", Dimension, d,
> Characteristic, p );
[ rec( charactername := "10a", constituents := [ 2 ],
contents := "core", dim := 10, groupname := "M22", id := "a",
identifier :=
[ "M22", [ "M22G1-f2r10aB0.m1", "M22G1-f2r10aB0.m2" ], 1, 2 ],
repname := "M22G1-f2r10aB0", repnr := 13, ring := GF(2),
size := 443520, standardization := 1, type := "matff" ),
rec( charactername := "10b", constituents := [ 3 ],
contents := "core", dim := 10, groupname := "M22", id := "b",
identifier :=
[ "M22", [ "M22G1-f2r10bB0.m1", "M22G1-f2r10bB0.m2" ], 1, 2 ],
repname := "M22G1-f2r10bB0", repnr := 14, ring := GF(2),
size := 443520, standardization := 1, type := "matff" ) ]
gap> gens:= List( info, r -> AtlasGenerators( r ).generators );;
## doc2/dntgap.xml (289-299)
gap> s:= AtlasGroup( "M22", IsPermGroup, true );;
gap> chr:= CHR( s, p, 0, gens[1] );;
gap> SizeScreen( [ 100 ] );;
gap> SecondCohomologyDimension( chr );
0
gap> chr:= CHR( s, p, 0, gens[2] );;
gap> SecondCohomologyDimension( chr );
0
gap> SizeScreen( [ 72 ] );;
## doc2/dntgap.xml (314-333)
gap> gens_1:= gens[1];;
gap> mats:= List( [1 .. 3 ], x -> IdentityMat( d+1, GF(p) ) );;
gap> v:= mats[1][ d+1 ];;
gap> mats[1]{ [ 1 .. d ] }{ [ 1 .. d ] }:= gens_1[1];;
gap> mats[2]{ [ 1 .. d ] }{ [ 1 .. d ] }:= gens_1[2];;
gap> mats[3][ d+1 ][1]:= Z(p)^0;;
gap> grp_1:= Group( mats );;
gap> Size( grp_1 );
454164480
gap> gens_2:= gens[1];;
gap> mats:= List( [1 .. 3 ], x -> IdentityMat( d+1, GF(p) ) );;
gap> v:= mats[1][ d+1 ];;
gap> mats[1]{ [ 1 .. d ] }{ [ 1 .. d ] }:= gens_2[1];;
gap> mats[2]{ [ 1 .. d ] }{ [ 1 .. d ] }:= gens_2[2];;
gap> mats[3][ d+1 ][1]:= Z(p)^0;;
gap> grp_2:= Group( mats );;
gap> Size( grp_2 );
454164480
## doc2/dntgap.xml (343-354)
gap> iso:= IsomorphismTypeInfoFiniteSimpleGroup( s );
rec( name := "M(22)", series := "Spor", shortname := "M22" )
gap> names:= AllCharacterTableNames( Size, 2^10 * Size( s ) );;
gap> cand:= List( names, CharacterTable );;
gap> cand:= Filtered( cand,
> t -> ForAny( ClassPositionsOfMinimalNormalSubgroups( t ),
> n -> IsomorphismTypeInfoFiniteSimpleGroup( t / n ) = iso ) );
[ CharacterTable( "2^10:M22'" ), CharacterTable( "2^10:m22" ) ]
gap> List( cand, NrConjugacyClasses );
[ 47, 43 ]
## doc2/dntgap.xml (363-379)
gap> t:= cand[1];;
gap> rationals:= Filtered( Irr( t ), x -> IsSubset( Integers, x ) );;
gap> Collected( List( rationals, x -> x[1] ) );
[ [ 1, 1 ], [ 21, 1 ], [ 22, 1 ], [ 55, 1 ], [ 99, 1 ], [ 154, 1 ],
[ 210, 1 ], [ 231, 3 ], [ 385, 1 ], [ 440, 1 ], [ 770, 5 ],
[ 924, 2 ], [ 1155, 2 ], [ 1386, 1 ], [ 1408, 1 ], [ 3080, 2 ],
[ 3465, 4 ], [ 4620, 2 ], [ 6930, 3 ], [ 9240, 1 ] ]
gap> t:= cand[2];;
gap> rationals:= Filtered( Irr( t ), x -> IsSubset( Integers, x ) );;
gap> Collected( List( rationals, x -> x[1] ) );
[ [ 1, 1 ], [ 21, 1 ], [ 55, 1 ], [ 77, 1 ], [ 99, 1 ], [ 154, 1 ],
[ 210, 1 ], [ 231, 1 ], [ 330, 1 ], [ 385, 3 ], [ 616, 2 ],
[ 693, 1 ], [ 770, 1 ], [ 1155, 2 ], [ 1980, 1 ], [ 2310, 4 ],
[ 2640, 1 ], [ 3465, 2 ], [ 4620, 1 ], [ 5544, 2 ], [ 6160, 1 ],
[ 6930, 2 ], [ 9856, 1 ] ]
## doc2/dntgap.xml (396-419)
gap> p:= 2;; d:= 12;;
gap> t:= CharacterTable( "J2" ) mod p;
BrauerTable( "J2", 2 )
gap> irr:= Filtered( Irr( t ), x -> x[1] <= d );;
gap> Display( t, rec( chars:= irr, powermap:= false,
> centralizers:= false ) );
J2mod2
1a 3a 3b 5a 5b 5c 5d 7a 15a 15b
Y.1 1 1 1 1 1 1 1 1 1 1
Y.2 6 -3 . A *A B *B -1 C *C
Y.3 6 -3 . *A A *B B -1 *C C
A = -2*E(5)-2*E(5)^4
= 1-Sqrt(5) = 1-r5
B = E(5)+2*E(5)^2+2*E(5)^3+E(5)^4
= (-3-Sqrt(5))/2 = -2-b5
C = E(5)+E(5)^4
= (-1+Sqrt(5))/2 = b5
gap> List( irr, x -> SizeOfFieldOfDefinition( x, p ) );
[ 2, 4, 4 ]
## doc2/dntgap.xml (430-441)
gap> info:= OneAtlasGeneratingSetInfo( "J2", Dimension, 6,
> Characteristic, p );
rec( charactername := "6a", constituents := [ 2 ], contents := "core",
dim := 6, groupname := "J2", id := "a",
identifier := [ "J2", [ "J2G1-f4r6aB0.m1", "J2G1-f4r6aB0.m2" ], 1,
4 ], repname := "J2G1-f4r6aB0", repnr := 16, ring := GF(2^2),
size := 604800, standardization := 1, type := "matff" )
gap> gens_dim6:= AtlasGenerators( info ).generators;;
gap> b:= Basis( GF(4) );;
gap> gens_dim12:= List( gens_dim6, x -> BlownUpMatrix( b, x ) );;
## doc2/dntgap.xml (449-456)
gap> s:= AtlasGroup( "J2", IsPermGroup, true );;
gap> chr:= CHR( s, p, 0, gens_dim12 );;
gap> SizeScreen( [ 100 ] );;
gap> SecondCohomologyDimension( chr );
0
gap> SizeScreen( [ 72 ] );;
## doc2/dntgap.xml (469-479)
gap> mats:= List( [ 1 .. 3 ], x -> IdentityMat( d+1, GF(p) ) );;
gap> v:= mats[1][ d+1 ];;
gap> mats[1]{ [ 1 .. d ] }{ [ 1 .. d ] }:= gens_dim12[1];;
gap> mats[2]{ [ 1 .. d ] }{ [ 1 .. d ] }:= gens_dim12[2];;
gap> mats[3][ d+1 ][1]:= Z(p)^0;;
gap> grp:= Group( mats );;
gap> g:= Image( IsomorphismPermGroup( grp ) );;
gap> Size( g );
2477260800
## doc2/dntgap.xml (489-499)
gap> iso:= IsomorphismTypeInfoFiniteSimpleGroup( s );
rec( name := "HJ = J(2) = F(5-)", series := "Spor", shortname := "J2"
)
gap> names:= AllCharacterTableNames( Size, 2^12 * Size( s ) );;
gap> cand:= List( names, CharacterTable );;
gap> cand:= Filtered( cand,
> t -> ForAny( ClassPositionsOfMinimalNormalSubgroups( t ),
> n -> IsomorphismTypeInfoFiniteSimpleGroup( t / n ) = iso ) );
[ CharacterTable( "2^12:J2" ) ]
## doc2/dntgap.xml (508-516)
gap> t:= cand[1];;
gap> rationals:= Filtered( Irr( t ), x -> IsSubset( Integers, x ) );;
gap> Collected( List( rationals, x -> x[1] ) );
[ [ 1, 1 ], [ 36, 1 ], [ 63, 1 ], [ 90, 1 ], [ 126, 1 ], [ 160, 1 ],
[ 175, 1 ], [ 225, 1 ], [ 288, 1 ], [ 300, 1 ], [ 336, 1 ],
[ 1575, 2 ], [ 2520, 4 ], [ 3150, 1 ], [ 4725, 6 ], [ 9450, 1 ],
[ 10080, 4 ], [ 12600, 4 ], [ 18900, 2 ] ]
## doc2/dntgap.xml (531-544)
gap> p:= 5;; d:= 14;;
gap> t:= CharacterTable( "J2" ) mod p;
BrauerTable( "J2", 5 )
gap> irr:= Filtered( Irr( t ), x -> x[1] <= d );;
gap> Display( t, rec( chars:= irr, powermap:= false,
> centralizers:= false ) );
J2mod5
1a 2a 2b 3a 3b 4a 6a 6b 7a 8a 12a
Y.1 1 1 1 1 1 1 1 1 1 1 1
Y.2 14 -2 2 5 -1 2 1 -1 . . -1
## doc2/dntgap.xml (576-613)
gap> orbits_from_tom:= function( tom, matgens, q )
> local slp, fixed, idmat, i, rest, decomp, nonzeropos;
>
> slp:= StraightLineProgramsTom( tom );
> fixed:= [];
> idmat:= matgens[1]^0;
> for i in [ 1 .. Length( slp ) ] do
> if IsList( slp[i] ) then
> # Each subgroup generator has a program of its own.
> rest:= List( slp[i],
> prg -> ResultOfStraightLineProgram( prg, gens ) );
> else
> # The subgroup generators are computed with one common program.
> rest:= ResultOfStraightLineProgram( slp[i], gens );
> fi;
> if IsEmpty( rest ) then
> # The subgroup is trivial.
> fixed[i]:= q^Length( idmat );
> else
> # Compute the intersection of fixed spaces of the transposed
> # matrices, since we act on Irr(N) not on N.
> fixed[i]:= q^Length( NullspaceMat( TransposedMat( Concatenation(
> List( rest, x -> x - idmat ) ) ) ) );
> fi;
> od;
>
> decomp:= DecomposedFixedPointVector( tom, fixed );
> nonzeropos:= Filtered( [ 1 .. Length( decomp ) ],
> i -> decomp[i] <> 0 );
>
> return rec( fixed:= fixed,
> decomp:= decomp,
> nonzeropos:= nonzeropos,
> staborders:= OrdersTom( tom ){ nonzeropos },
> );
> end;;
## doc2/dntgap.xml (627-637)
gap> tom:= TableOfMarks( "J2" );
TableOfMarks( "J2" )
gap> StandardGeneratorsInfo( tom );
[ rec( ATLAS := true,
description := "|z|=10, z^5=a, |b|=3, |C(b)|=36, |ab|=7",
generators := "a, b",
script :=
[ [ 1, 10, 5 ], [ 2, 3 ], [ [ 2, 1 ], [ "|C(",, ")|" ], 36 ],
[ 1, 1, 2, 1, 7 ] ], standardization := 1 ) ]
## doc2/dntgap.xml (646-659)
gap> info:= OneAtlasGeneratingSetInfo( "J2", Dimension, d, Ring, GF(p) );
rec( charactername := "14a", constituents := [ 2 ],
contents := "core", dim := 14, givenRing := GF(5),
groupname := "J2", id := "",
identifier := [ "J2", [ "J2G1-f5r14B0.m1", "J2G1-f5r14B0.m2" ], 1,
5 ], repname := "J2G1-f5r14B0", repnr := 19, ring := GF(5),
size := 604800, standardization := 1, type := "matff" )
gap> gens:= AtlasGenerators( info ).generators;;
gap> map:= GroupGeneralMappingByImages( UnderlyingGroup( tom ),
> Group( gens ), GeneratorsOfGroup( UnderlyingGroup( tom ) ), gens );;
gap> IsGroupHomomorphism( map );
true
## doc2/dntgap.xml (667-693)
gap> orbits_from_tom( tom, gens, p );
rec(
decomp := [ 8600, 0, 2512, 359, 10, 0, 0, 212, 5, 0, 0, 4, 0, 240,
16, 10, 0, 0, 0, 0, 10, 0, 0, 0, 0, 2, 0, 0, 36, 0, 0, 0, 26,
0, 0, 0, 0, 0, 0, 0, 20, 0, 10, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 10, 0, 0, 5, 0, 0, 0, 26, 0, 10, 0, 0, 0, 0, 10, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 2, 0,
0, 0, 0, 2, 4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 4, 0, 0, 0, 4, 0, 0, 1 ],
fixed := [ 6103515625, 15625, 390625, 390625, 625, 25, 3125, 3125,
625, 625, 625, 625, 5, 3125, 125, 625, 25, 25, 125, 5, 125, 25,
125, 25, 25, 25, 5, 125, 125, 125, 25, 25, 3125, 1, 1, 5, 5,
25, 5, 25, 125, 5, 25, 25, 25, 25, 25, 25, 5, 25, 25, 5, 25, 5,
5, 5, 5, 25, 25, 1, 125, 1, 5, 5, 125, 1, 25, 5, 25, 1, 5, 25,
5, 5, 25, 25, 5, 5, 5, 1, 5, 5, 1, 1, 1, 5, 1, 25, 25, 25, 1,
5, 25, 5, 5, 1, 1, 125, 5, 5, 5, 25, 5, 5, 5, 1, 1, 5, 5, 1, 5,
1, 5, 1, 1, 25, 5, 5, 1, 1, 1, 1, 5, 1, 1, 25, 1, 1, 5, 1, 1,
5, 1, 5, 1, 1, 5, 1, 5, 1, 1, 1, 5, 1, 1, 1 ],
nonzeropos := [ 1, 3, 4, 5, 8, 9, 12, 14, 15, 16, 21, 26, 29, 33,
41, 43, 44, 58, 61, 65, 67, 72, 89, 93, 98, 99, 105, 116, 126,
139, 143, 146 ],
staborders := [ 1, 2, 3, 3, 4, 4, 5, 6, 6, 6, 8, 9, 10, 12, 12, 12,
14, 20, 24, 24, 24, 30, 48, 50, 60, 60, 72, 120, 192, 600,
1920, 604800 ] )
## doc2/dntgap.xml (715-742)
gap> p:= 2;; d:= 28;;
gap> t:= CharacterTable( "J2" ) mod p;
BrauerTable( "J2", 2 )
gap> irr:= Filtered( Irr( t ), x -> x[1] <= d );;
gap> Display( t, rec( chars:= irr, powermap:= false,
> centralizers:= false ) );
J2mod2
1a 3a 3b 5a 5b 5c 5d 7a 15a 15b
Y.1 1 1 1 1 1 1 1 1 1 1
Y.2 6 -3 . A *A C *C -1 D *D
Y.3 6 -3 . *A A *C C -1 *D D
Y.4 14 5 -1 B *B -C -*C . . .
Y.5 14 5 -1 *B B -*C -C . . .
A = -2*E(5)-2*E(5)^4
= 1-Sqrt(5) = 1-r5
B = -3*E(5)-3*E(5)^4
= (3-3*Sqrt(5))/2 = -3b5
C = E(5)+2*E(5)^2+2*E(5)^3+E(5)^4
= (-3-Sqrt(5))/2 = -2-b5
D = E(5)+E(5)^4
= (-1+Sqrt(5))/2 = b5
gap> List( irr, x -> SizeOfFieldOfDefinition( x, p ) );
[ 2, 4, 4, 4, 4 ]
## doc2/dntgap.xml (750-780)
gap> tom:= TableOfMarks( "J2" );;
gap> info:= OneAtlasGeneratingSetInfo( "J2", Dimension, 14, Ring, GF(4) );;
gap> gens:= List( AtlasGenerators( info ).generators,
> x -> BlownUpMat( Basis(GF(4)), x ) );;
gap> orbits_from_tom( tom, gens, p );
rec(
decomp := [ 235, 33, 282, 38, 0, 0, 6, 31, 36, 0, 0, 0, 3, 66, 9,
0, 0, 0, 0, 0, 0, 2, 18, 0, 0, 1, 0, 0, 15, 0, 0, 0, 6, 0, 0,
0, 0, 0, 0, 0, 12, 0, 0, 5, 0, 1, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 3, 1, 3, 0, 9, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0,
0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
3, 0, 0, 0, 0, 0, 3, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0,
0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 3, 0,
0, 0, 3, 0, 0, 1 ],
fixed := [ 268435456, 65536, 65536, 65536, 256, 1024, 4096, 1024,
1024, 256, 256, 256, 64, 1024, 64, 256, 16, 16, 64, 64, 64,
256, 256, 64, 16, 16, 64, 64, 64, 64, 16, 16, 1024, 4, 4, 4, 4,
16, 16, 16, 64, 16, 16, 16, 16, 64, 16, 16, 16, 64, 16, 16, 16,
16, 4, 16, 16, 16, 16, 1, 64, 4, 16, 4, 64, 4, 16, 4, 16, 1, 4,
16, 4, 4, 16, 16, 4, 4, 16, 1, 4, 16, 1, 1, 1, 16, 4, 16, 16,
16, 1, 4, 16, 4, 4, 1, 4, 64, 4, 4, 4, 16, 4, 4, 4, 1, 1, 4,
16, 1, 4, 1, 4, 1, 4, 16, 4, 4, 1, 1, 1, 1, 4, 1, 1, 16, 1, 1,
4, 1, 4, 4, 1, 4, 1, 1, 4, 1, 4, 1, 1, 1, 4, 1, 1, 1 ],
nonzeropos := [ 1, 2, 3, 4, 7, 8, 9, 13, 14, 15, 22, 23, 26, 29,
33, 41, 44, 46, 50, 61, 62, 63, 65, 72, 82, 93, 99, 105, 109,
116, 126, 131, 139, 143, 146 ],
staborders := [ 1, 2, 2, 3, 4, 4, 4, 6, 6, 6, 8, 8, 9, 10, 12, 12,
14, 16, 16, 24, 24, 24, 24, 30, 40, 50, 60, 72, 96, 120, 192,
240, 600, 1920, 604800 ] )
## doc2/dntgap.xml (801-830)
gap> p:= 2;; d:= 26;;
gap> t:= CharacterTable( "3D4(2)" ) mod p;
BrauerTable( "3D4(2)", 2 )
gap> irr:= Filtered( Irr( t ), x -> x[1] <= d );;
gap> Display( t, rec( chars:= irr, powermap:= false,
> centralizers:= false ) );
3D4(2)mod2
1a 3a 3b 7a 7b 7c 7d 9a 9b 9c 13a 13b 13c 21a 21b 21c
Y.1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
Y.2 8 2 -1 A C B 1 D F E G I H J L K
Y.3 8 2 -1 B A C 1 E D F H G I K J L
Y.4 8 2 -1 C B A 1 F E D I H G L K J
Y.5 26 -1 -1 5 5 5 -2 2 2 2 . . . -1 -1 -1
A = 3*E(7)^2+E(7)^3+E(7)^4+3*E(7)^5
B = 3*E(7)+E(7)^2+E(7)^5+3*E(7)^6
C = E(7)+3*E(7)^3+3*E(7)^4+E(7)^6
D = -E(9)^2+E(9)^3-2*E(9)^4-2*E(9)^5+E(9)^6-E(9)^7
E = -E(9)^2+E(9)^3+E(9)^4+E(9)^5+E(9)^6-E(9)^7
F = 2*E(9)^2+E(9)^3+E(9)^4+E(9)^5+E(9)^6+2*E(9)^7
G = E(13)+E(13)^2+E(13)^3+E(13)^5+E(13)^8+E(13)^10+E(13)^11+E(13)^12
H = E(13)+E(13)^4+E(13)^5+E(13)^6+E(13)^7+E(13)^8+E(13)^9+E(13)^12
I = E(13)^2+E(13)^3+E(13)^4+E(13)^6+E(13)^7+E(13)^9+E(13)^10+E(13)^11
J = E(7)^3+E(7)^4
K = E(7)^2+E(7)^5
L = E(7)+E(7)^6
## doc2/dntgap.xml (838-853)
gap> tom:= TableOfMarks( "3D4(2)" );
TableOfMarks( "3D4(2)" )
gap> StandardGeneratorsInfo( tom );
[ rec( ATLAS := true,
description := "|z|=8, z^4=a, |b|=9, |ab|=13, |abb|=8",
generators := "a, b",
script := [ [ 1, 8, 4 ], [ 2, 9 ], [ 1, 1, 2, 1, 13 ],
[ 1, 1, 2, 1, 2, 1, 8 ] ], standardization := 1 ) ]
gap> info:= OneAtlasGeneratingSetInfo( "3D4(2)", Dimension, 26, Ring, GF(2) );;
gap> gens:= AtlasGenerators( info ).generators;;
gap> map:= GroupGeneralMappingByImages( UnderlyingGroup( tom ),
> Group( gens ), GeneratorsOfGroup( UnderlyingGroup( tom ) ), gens );;
gap> IsGroupHomomorphism( map );
true
## doc2/dntgap.xml (861-867)
gap> orbsinfo:= orbits_from_tom( tom, gens, p );;
gap> orbsinfo.fixed[1];
67108864
gap> orbsinfo.decomp[1];
0
## doc2/dntgap.xml (878-890)
gap> orbsinfo.staborders;
[ 16, 16, 18, 42, 48, 52, 64, 72, 392, 1008, 1536, 3024, 3072, 3584,
258048, 211341312 ]
gap> orbsinfo.nonzeropos[3];
446
gap> orbsinfo.decomp[446];
1
gap> u:= RepresentativeTom( tom, 446 );
<permutation group of size 18 with 2 generators>
gap> IsDihedralGroup( u );
true
## doc2/dntgap.xml (904-912)
gap> cand:= Filtered( AllSmallGroups( 36 ),
> x -> Size( Centre( x ) ) = 2 and
> IsDihedralGroup( x / Centre( x ) ) );
[ <pc group of size 36 with 4 generators>,
<pc group of size 36 with 4 generators> ]
gap> List( cand, StructureDescription );
[ "C9 : C4", "D36" ]
## doc2/dntgap.xml (929-950)
gap> Display( CharacterTable( "Dihedral", 18 ) );
Dihedral(18)
2 1 . . . . 1
3 2 2 2 2 2 .
1a 9a 9b 3a 9c 2a
2P 1a 9b 9c 3a 9a 1a
3P 1a 3a 3a 1a 3a 2a
X.1 1 1 1 1 1 1
X.2 1 1 1 1 1 -1
X.3 2 A B -1 C .
X.4 2 B C -1 A .
X.5 2 -1 -1 2 -1 .
X.6 2 C A -1 B .
A = -E(9)^2-E(9)^4-E(9)^5-E(9)^7
B = E(9)^2+E(9)^7
C = E(9)^4+E(9)^5
## doc2/dntgap.xml (970-988)
gap> p:= 3;; d:= 25;;
gap> t:= CharacterTable( "3D4(2)" ) mod p;
BrauerTable( "3D4(2)", 3 )
gap> irr:= Filtered( Irr( t ), x -> x[1] <= d );;
gap> Display( t, rec( chars:= irr, powermap:= false,
> centralizers:= false ) );
3D4(2)mod3
1a 2a 2b 4a 4b 4c 7a 7b 7c 7d 8a 8b 13a 13b 13c 14a 14b 14c 28a
Y.1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
Y.2 25 -7 1 5 -3 1 4 4 4 -3 -1 -1 -1 -1 -1 . . . -2
28b 28c
Y.1 1 1
Y.2 -2 -2
## doc2/dntgap.xml (996-1005)
gap> tom:= TableOfMarks( "3D4(2)" );;
gap> info:= OneAtlasGeneratingSetInfo( "3D4(2)", Dimension, d, Ring, GF(p) );;
gap> gens:= AtlasGenerators( info ).generators;;
gap> orbsinfo:= orbits_from_tom( tom, gens, p );;
gap> orbsinfo.fixed[1];
847288609443
gap> orbsinfo.decomp[1];
3551
##
gap> if IsBound( BrowseData ) then
> data:= BrowseData.defaults.dynamic.replayDefaults;
> data.replayInterval:= oldinterval;
> fi;
##
gap> STOP_TEST( "dntgap.tst" );
gap> SizeScreen( save );;
#############################################################################
##
#E
