Let $m$ and $n$ be positive integers and $p$ a prime number. Let $G \subseteq \mathrm{GL}_{m}(\mathbb{F}_{p})$ be a subgroup of order $p^{n}$. Let $U \subseteq \mathrm{GL}_{m}(\mathbb{F}_{p})$ be the subgroup that consists of all the matrices with 1's on the diagonal and 0's below the diagonal. Show that there exists $A \in \mathrm{GL}_{m}(\mathbb{F}_{p})$ such that $AGA^{-1} \subseteq U$.