I was reading articles and books on automorphism group. It is always an interesting question to decide when the automorphism group is a $p$-group.
In this regard my question is
Let $\gamma(H)$ be the last non-trivial term of lower-central series of a finite $p$-group $H$. Suppose automorphism group of $G/\gamma(H)$ is a $p$-group. Then prove or disprove that the automorphism group of $H$ be a $p$-group
Sorry for not showing much effort from my side, I will appreciate any help.
Thanks in advance.