# 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:

$\order {\Aut {D_n} } = 2 \map \phi n$

where:

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