If G is a finite cyclic group of order n, what is the group Aut(G)? Aut(Aut(G))?
The Attempt at a Solution
Aut(G) is given by the automorphisms that send a generator to a power k < n where (k,n) = 1 with order p(n) where p is Euler's function.
I'm having trouble visualizing or describing Aut(Aut(G)) as automorphisms of automorphisms. Is Aut(G) isomorphic to a cyclic group of order p(n)?