Computation of the character tables of certain group extensions

Abstract

The work done in this mini-thesis deals mainly with different methods of calculating character tables of split extensions of finite groups. Three of the six character tables that are calculated are done with the use of Fischer matrices. In this work, the method of Fischer is applied on groups of the form N.G where N is an elementary abelian group. In fact, only one of the six groups of which the character tables are calculated is not of this form and so Fischer matrices could easily have been used to calculate five of the character tables. The aim of the work done here however is to exhibit a variety of methods to calculate the character tables of split extensions. In Chapter One a review of basic definitions and results on group extensions and a description of a method for finding the conjugacy tables of group extensions is given. An example of the application of this method is also given. Chapter two deals with basic concepts and results on representation and character theory as well as the application of some of these results in calculating the character tables of some group extensions. In Chapter Three we discuss Fischer matrices and how it is used to calculate the character tables of group extensions of the form N.G where N is an elementary abelian group.