GAP Manual: 48.23. CharDegAgGroup

CharDegAgGroup( G [, q ] )

CharDegAgGroup computes the degrees of irreducible characters of the finite polycyclic group G over the algebraic closed field of characteristic q. The default value for q is zero. The degrees are returned as a list of pairs, the first entry denoting a degree, and the second denoting its multiplicity.

    gap> g:= SolvableGroup( 24, 15 );
    S4
    gap> CharDegAgGroup( g );
    [ [ 1, 2 ], [ 2, 1 ], [ 3, 2 ] ]    # two linear characters, one of
                                        # degree 2, two of degree 3
    gap> CharDegAgGroup( g, 3 );
    [ [ 1, 2 ], [ 3, 2 ] ]

The algorithm bases on Con90b. It works for all solvable groups.