CharTableNormalSubgroup( tbl, normal_subgroup )
returns the restriction of the character table tbl to the classes in
the list normal_subgroup.
This table is an approximation of the character table of this normal
subgroup. It has components order, identifier, centralizers,
orders, classes, powermap, irreducibles (contains the set of
those restrictions of irreducibles of tbl which are irreducible), and
fusions (contains the fusion in tbl).
In most cases, some classes of the normal subgroup must be split, see CharTableSplitClasses.
gap> s5:= CharTable( "A5.2" );;
gap> s3:= CharTable( "Symmetric", 3 );;
gap> SortCharactersCharTable( s3 );;
gap> s5xs3:= CharTableDirectProduct( s5, s3 );;
gap> nsg:= [ 1, 3, 4, 6, 7, 9, 10, 12, 14, 17, 20 ];;
gap> sub:= CharTableNormalSubgroup( s5xs3, nsg );;
#I CharTableNormalSubgroup: classes in [ 8 ] necessarily split
gap> PrintCharTable( sub );
rec( identifier := "Rest(A5.2xS3,[ 1, 3, 4, 6, 7, 9, 10, 12, 14, 17, 2\
0 ])", size :=
360, name := "Rest(A5.2xS3,[ 1, 3, 4, 6, 7, 9, 10, 12, 14, 17, 20 ])",\
order := 360, centralizers := [ 360, 180, 24, 12, 18, 9, 15, 15/2,
12, 4, 6 ], orders := [ 1, 3, 2, 6, 3, 3, 5, 15, 2, 4, 6
], powermap := [ , [ 1, 2, 1, 2, 5, 6, 7, 8, 1, 3, 5 ],
[ 1, 1, 3, 3, 1, 1, 7, 7, 9, 10, 9 ],,
[ 1, 2, 3, 4, 5, 6, 1, 2, 9, 10, 11 ] ], classes :=
[ 1, 2, 15, 30, 20, 40, 24, 48, 30, 90, 60
], operations := CharTableOps, irreducibles :=
[ [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ],
[ 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1 ],
[ 2, -1, 2, -1, 2, -1, 2, -1, 0, 0, 0 ],
[ 6, 6, -2, -2, 0, 0, 1, 1, 0, 0, 0 ],
[ 4, 4, 0, 0, 1, 1, -1, -1, 2, 0, -1 ],
[ 4, 4, 0, 0, 1, 1, -1, -1, -2, 0, 1 ],
[ 8, -4, 0, 0, 2, -1, -2, 1, 0, 0, 0 ],
[ 5, 5, 1, 1, -1, -1, 0, 0, 1, -1, 1 ],
[ 5, 5, 1, 1, -1, -1, 0, 0, -1, 1, -1 ],
[ 10, -5, 2, -1, -2, 1, 0, 0, 0, 0, 0 ] ], fusions := [ rec(
name := [ 'A', '5', '.', '2', 'x', 'S', '3' ],
map := [ 1, 3, 4, 6, 7, 9, 10, 12, 14, 17, 20 ] ) ] )
GAP 3.4.4