$U\_n(\mathbb{F}\_p)$ is the group of upper triangular matrices of order n with diagonal entries 1 and other entries from $\mathbb{F}\_p$ (equipped with matrix multiplication). $$U\_n = \left \{\left ( \begin{matrix}
1 & &\* \\ 
 & 1 & \\ 
 0& & 1
\end{matrix}\right )\_n : \* \in \mathbb{F}\_p \right \}$$

I need to show that given any p-group $G$, it is isomorphic to a subgroup of $U\_n$ where $|G| = n$

One of the hints that I have been given is to see that there is an element in $\mathbb{F}\_p^n$ which is stabilised by all elements of $G$ when they are viewed as members of $GL\_n(\mathbb{F}\_p)$. I have proved this but I do not know how to proceed from here.