GAP Manual: 50.5. KernelChar

KernelChar( char )

returns the set of classes which form the kernel of the character char, i.e. the set of positions i with char[i] = char[1].

For a factor fusion map fus, KernelChar( fus ) is the kernel of the epimorphism.

    gap> s4:= CharTable( "Symmetric", 4 );;
    gap> s4.irreducibles;
    [ [ 1, -1, 1, 1, -1 ], [ 3, -1, -1, 0, 1 ], [ 2, 0, 2, -1, 0 ],
      [ 3, 1, -1, 0, -1 ], [ 1, 1, 1, 1, 1 ] ]
    gap> List( last, KernelChar );
    [ [ 1, 3, 4 ], [ 1 ], [ 1, 3 ], [ 1 ], [ 1, 2, 3, 4, 5 ] ]