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I got another question regarding semidirect products:

Construct all semidirect products of C3C3.

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    What is the automorphism group of $C_3$?2012-11-12

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The automorphism gorup of $C_3$ has only two elements as each automorphism must map a generator to a generator. Hence no automorphism has order thre, i.e. $C_3$ can act on itself only trivially. This makes the semidirect product a direct product.

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    Explicitly, the automorphism group of $C_3$ consists of the automorphism given by $x\mapsto x^2$ and the identity. These have order 2 and 1, respectively, hnence noe of them has order 3. In other words: An action of $C_3$ on itself is given by a homomorphism $C_3\to \operatorname{Aut}(C_3)\cong C_2$ and there is only the trivial homomorphism.2012-11-13