Computing characters of groups with central subgroups

The so-called Burnside-Dixon-Schneider (BDS) method, currently used as the default method of computing character tables in GAP for groups which are not solvable, is often inefficient in dealing with groups with large centres. If G is a finite group with centre Z and lambda a linear character of Z, then we describe a method of computing the set Irr(G, lambda) of irreducible characters x of G whose restriction chi(Z) is a multiple of A. This modification of the BDS method involves only [Irr(G, lambda)] conjugacy classes of G and so is relatively fast. A generalization of the method can be applied to computation of small sets of characters of groups with a solvable normal subgroup.