Let $p$ be a prime number, and let $\mathbb{F}_{p}$ be a finite field of order $p$. Let $U_{n}$ denote the unitriangular group of $n\times n$ upper triangular matrices with ones on the diagonal, over $\mathbb{F}_{p}$. Are there groups such as their automorphism group is $U_{n}$?.
Any example or reference will be helpful. Thank you all.