Order of Automorphism Group of Dihedral Group

Theorem
Let $D_n$ denote the dihedral group of order $n$.

Let $\Aut {D_n}$ denote the automorphism group of $D_n$.

Then:
 * $\order {\Aut {D_n} } = n \cdot \map \phi n$

where:
 * $\order {\, \cdot \,}$ denotes the order of a group
 * $\map \phi n$ is the Euler $\phi$ function.