Let $N$ be a normal $p$-subgroup of finite centerless group $G$ such that $G/N\cong A_{5}$. Is it possible $G/N\cong \leq $Aut$(Z(N))$?
Normal p-subgroup of finite group
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group-theory
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0Background, origin of problem, ideas, insights, self work...? – 2012-10-22
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0Is this really the question you want? Every finite group is a subgroup of Aut(Z(N)) for some p-group N. – 2012-10-22
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0What does $\cong\le$ mean? – 2012-10-22
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0@DerekHolt "isomorphic to a subgroup" perhaps? – 2012-10-22
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0@DerekHolt: Isomorphic to a subgroup. This question related to my former question. – 2012-10-23
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0The answer is yes. It is not only possible, it is certain! Use the action by conjugation. – 2012-10-23