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For any positive integer $k$ coprime to $p$, and any positive integers $n,m$ there is a bijection between conjugacy classes of elements of order $k$ in ${\rm GL}_{n}(\mathbb{Z}/p^{m}\mathbb{Z})$ and conjugacy classes of elements of order $k$ in ${\rm GL}_{n}(\mathbb{Z}/p\mathbb{Z}).$ This is because ${\rm GL}_{n}(\mathbb{Z}/p^{m}\mathbb{Z})$ has a normal $p$-subgroup $U$ such that${\rm GL}_{n}(\mathbb{Z}/p^{m}\mathbb{Z})/U \cong {\rm GL}_{n}(\mathbb{Z}/p\mathbb{Z})$. ( It is also necessary to invoke the Schur-Zassenhaus Theorem).