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Let G be a finite group and Χ an irreducible character of G. A simple method for constructing a representation affording Χ can be used whenever G has a subgroup H such that ΧH has a linear constituent with multiplicity 1. In this paper we show that (with a few exceptions) if G is a simple group or a covering group of a simple group and Χ is an irreducible character of G of degree between 32 and 100, then such a subgroup exists.

Constructing representations of higher degrees of finite simple groups and covers