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 inecient in dealing with groups with large centres. If G is a nite group with centre Z and a linear character of Z, then we describe a method of computing the set Irr(G; ) of irreducible characters of G whose restriction Z is a multiple of . This modication of the BDS method involves only jIrr(G; )j 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.