Character tables of some groups of extension type

Abstract

The main aim of this mini-thesis is to give a description of some of the basic methods and techniques that have been developed to calculate the character tables of groups of extension type. We restrict our attention to split extensions G of the normal subgroup N of G by the subgroup G with the property that every irreducible character of N can be extended to an irreducible character of its inertia group in G. This is particularly true when N is abelian. We are therefore interested in this special case for which Bernd Fischer developed the theory of Fischer matrices based on the Clifford Theory, to calculate the character tables for both split and non-split extensions.