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Atomorphism Automorphism group in theof a simple group

Let $G$ be a simple group of order $p^{2}-1$ where $p$ is Mersenne prime.

I am looking for get a contradiction when $p\mid |Aut(G)|$. Does anyone knows how we can get a contradiction? Thanks.

Atomorphism group in the simple group

Let $G$ be simple group of order $p^{2}-1$ where $p$ is Mersenne prime.

I am looking for get a contradiction when $p\mid |Aut(G)|$. Does anyone knows how we can get a contradiction? Thanks.

Automorphism group of a simple group

Let $G$ be a simple group of order $p^{2}-1$ where $p$ is Mersenne prime.

I am looking for a contradiction when $p\mid |Aut(G)|$. Does anyone knows how we can get a contradiction? Thanks.

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Atomorphism group in the simple group

Let $G$ be simple group of order $p^{2}-1$ where $p$ is Mersenne prime.

I am looking for get a contradiction when $p\mid |Aut(G)|$. Does anyone knows how we can get a contradiction? Thanks.