The former group can be seen as the group of unitriangular $3 \times 3$-matrices over the field with $p$ elements: $$G = \\left\{ \begin{pmatrix} 1 & * & * \\\\ 0 & 1 & * \\\\ 0 & 0 & 1 \end{pmatrix} \\right\} \leq SL(3,p)$$ The automorphism groups of such groups have been studied (in a much larger generality); see for instance the paper "The automorphism group of the group of unitriangular matrices over a field" by Ayan Mahalanobis (http://arxiv.org/abs/1012.5534v1).

The former group can be seen as the group of unitriangular $3 \times 3$-matrices over the field with $p$ elements: $$G = \left\{ \begin{pmatrix} 1 & * & * \\ 0 & 1 & * \\ 0 & 0 & 1 \end{pmatrix} \right\} \leq SL(3,p)$$ The automorphism groups of such groups have been studied (in a much larger generality); see for instance the paper "The automorphism group of the group of unitriangular matrices over a field" by Ayan Mahalanobis (http://arxiv.org/abs/1012.5534v1).