The task is to Find all the natural numbers such that $Z_n$ is isomorphic to the dihedral group $D_n$.
I am pretty sure that for $n>2$ there is no such isomorphism because $Z_n$ has $n$ elements, while $D_n$ has $2n$ elements.
But for $n=1$ and $n=2$ however I think there is an isomorphism because here the reflections act the same as the rotations.
Any help here?