  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 ${\rm
GL}_n(q)$. The size of $X(n,q)$ is a polynomial in $q$. In this note it is
shown that generically this polynomial has degree $n^2(1-a^{-1}) - \epsilon_r$
and leading coefficient $m_r$, where $\epsilon_r$ and $m_r$ are constants
depending only on $r := n \mod a$. We also present an algorithm for explicitly
determining these constants.
