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

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This article describes an open problem in the following area of/related to group theory: p-groups


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.