Fix an arbitrary finite group A of order a, and let X(n, q) denote the set of homomorphisms from A to the finite general linear group GL n (q). The size of X(n, q) is a polynomial in q. In this note, it is shown that generically this polynomial has degree n 2(1 – a −1) − ε r and leading coefficient mr , where ε r and mr are constants depending only on r := n mod a. We also present an algorithm for explicitly determining these constants.
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