The Number of Conjugacy Classes and Irreducible Characters in a Finite Group

Remigius Okeke Aja,Everestus Obinwanne Eze,Uchenna Emmanuel Obasi

doi:10.34198/ejms.2119.181190

Abstract

In this paper, number of conjugacy classes and irreducible characters in a non-abelian group of order $2^6$ are investigated using cycle pattern of elements. Through the exploits of commutator and representation of elements as a product of disjoint cycles, the number of conjugacy classes is obtained which extends some results in literature.

Highlights

The concept of conjugacy classes and irreducible characters which started since the time of Burnside (1852-1927) and Frobenius (1849-1917), at the present time plays a more important role in the study of groups and their representations
Motivated by the above literature and on-going research in this direction, the objective of this paper is to find the number of conjugacy classes and irreducible characters in a finite group of non-abelian group of order 26
We consider a non-abelian group G = {x, y} with three subgroups p, q, r of G defined as p = (12), q = (13) (24) and r = (15) (26) (37) (48)

Summary

Introduction

The concept of conjugacy classes and irreducible characters which started since the time of Burnside (1852-1927) and Frobenius (1849-1917), at the present time plays a more important role in the study of groups and their representations. The important part of this group under discussion is the conjugacy classes of a non-abelian group of order sixty four (26 ). Conjugacy classes of finite group Sn can be represented using a cycle type which shows the partition of n as demonstrated in [3]. [4], [5] and [6] had worked on conjugacy classes of finite group with resounding results.

Objectives

Results

Conclusion