The question is to determine the group of automorphisms of S3 (the symmetric group of 3! elements). 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.