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 ] ]
GAP 3.4.4