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 group representations, simple groups, central covers, irreducible representations

MSC Classifications:

20C40, 20C15 show english descriptions Computational methods
Ordinary representations and characters 20C40 - Computational methods
20C15 - Ordinary representations and characters

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