Cyclic Automorphism Group

[StudentR]

I came accross a section of my notes that claimed the automorphism group of the cyclec groups C_2p where p=5,7,11 is cyclic,
that is Aut(C_2p) is cyclic for p = 5,7,11.
I wasn't able to see why this is so.
Is it just a fact or is there some sort of proof of the above...?
Thanks

[matt grime]

What is the automorphism group of the cyclic group? It sends a generator to a primitive power of itself. I.e. in C_m with generated g, any aut sends g to g^m for some m with (m,n)=1. You can work it out from there.