Suppose that W is an irreducible FqG-module of dimension n (d 2 < n < d 3) and that H is given as G = ⟨X⟩ acting irreducibly on W where X is a set of n × n matrices with entries in F = Fq. In this paper, we present a Las Vegas algorithm that constructs a representation of G of dimension d. We consider the twisted tensor products of the modules of high weights λ1, λ2, λ d−2 , λ d−1 , 2λ1, 2λ d−1 .
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