The question is to determine the group of automorphisms of S3 (the symmetric group of 3! elements).(adsbygoogle = window.adsbygoogle || []).push({});

I know Aut(S3)=Inn(S3) where Inn(S3) is the inner group of the automorphism group.

For a group G, Inn(G) is a conjugation group (I don't fully understand the definition from class and the book doesn't give one).

I also know that Inn(S3) is a subgroup of Aut(S3), so Inn(S3) is contained in

Aut(S3).

I'm not sure how to show the other way thought, that everything in Aut(S3) is in Inn(S3).

I talked to my professor, and he gave me the hint that Inn(S3) has only 6 automorphisms, so I should show there are no more than 6 automorphisms in

Aut(G). The problem is I'm not sure how to do this.

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# Homework Help: Group of automorphism of S3

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