# Conjecture that the automorphism group of a non-cyclic group of prime power order is always bigger

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Let $p$ be a prime and $G$ be a non-cyclic $p$-group; in other words, $G$ is a group of prime power order. The conjecture states that the order of the automorphism group $\operatorname{Aut}(G)$ is at least equal to the order of $G$.