Computing characters of groups with central subgroups

Abstract

AbstractThe 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 $\mathrm{Irr} (G, \lambda )$ of irreducible characters $\chi $ of $G$ whose restriction ${\chi }_{Z} $ is a multiple of $\lambda $. This modification of the BDS method involves only $\vert \mathrm{Irr} (G, \lambda )\vert $ 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.Supplementary materials are available with this article.