What is the number of automorphisms (including identity) for permutation group $S_3$ on 3 letters?
I believe the answer for this is 6. As we can write the group elements as below
Can we generalize that for any $S_n$ onto $n$ the number of automorphisms will be $n!$ Also I cannot find this anywhere in my text, can we have a permutation $S_n$ onto $m$ where $n\neq m$? (for eg: is it possible to have a permutation group say $S_5$ on say 2 elements?)