Suppose that $G$ is a non-abelian simple group and $r$ is a prime number such that $r$ not divide $|G|$. It is a question for me that whether $r$ can divide |Aut($G$)|?
Prime divisor in the Automorphism group
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group-theory
finite-groups
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1Some more examples: $\text{PSL}_2(128)$ for $r=7$, $\text{PSL}_2(243)$ for $r=5$, $\text{PSL}_3(32)$ for $r=5$. – 2012-12-25