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# Constructing Representations of Finite Simple Groups and Covers

Published:2006-02-01
Printed: Feb 2006
• Vahid Dabbaghian-Abdoly
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## Abstract

Let $G$ be a finite group and $\chi$ be an irreducible character of $G$. An efficient and simple method to construct representations of finite groups is applicable whenever $G$ has a subgroup $H$ such that $\chi_H$ has a linear constituent with multiplicity $1$. In this paper we show (with a few exceptions) that if $G$ is a simple group or a covering group of a simple group and $\chi$ is an irreducible character of $G$ of degree less than 32, then there exists a subgroup $H$ (often a Sylow subgroup) of $G$ such that $\chi_H$ has a linear constituent with multiplicity $1$.
 Keywords: group representations, simple groups, central covers, irreducible representations
 MSC Classifications: 20C40 - Computational methods 20C15 - Ordinary representations and characters

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