48.15 CharTableFactorGroup

CharTableFactorGroup( tbl, classes_of_normal_subgroup )

returns the table of the factor group of tbl with respect to a particular normal subgroup: If the list of irreducibles stored in tbl.irreducibles is complete, this normal subgroup is the normal closure of classes_of_normal_subgroup; otherwise it is the intersection of kernels of those irreducibles stored on tbl which contain classes_of_normal_subgroups in their kernel --that may cause strange results.

    gap> s4:= CharTable( "Symmetric", 4 );;
    gap> PrintCharTable( CharTableFactorGroup( s4, [ 3 ] ) );
    rec( size := 6, identifier := "S4/[ 3 ]", order :=
    6, name := "S4/[ 3 ]", centralizers := [ 6, 2, 3 ], powermap :=
    [ , [ 1, 1, 3 ], [ 1, 2, 1 ] ], fusions := [  ], fusionsource :=
    [ "S4" ], irreducibles := [ [ 1, -1, 1 ], [ 2, 0, -1 ], [ 1, 1, 1 ]
     ], orders := [ 1, 2, 3 ], classes :=
    [ 1, 3, 2 ], operations := CharTableOps )
    gap> s4.fusions;
    [ rec(
          map := [ 1, 2, 1, 3, 2 ],
          type := "factor",
          name := "S4/[ 3 ]" ) ]

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