Constructing Representations of Finite Simple Groups and Covers
Printed: Feb 2006
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 $1$.
group representations, simple groups, central covers, irreducible representations
20C40 - Computational methods
20C15 - Ordinary representations and characters