Let $D_n$ be the dihedral group of order $2n$. Show that all irreducible representations have vector space dimension $1$ or $2$, and describe them up to isomorphism.
Any hints how to even start?
Each irreducible representation of $D_n$ is spanned by at most $[G:H]$ independent vectors for every abelian subgroup $H<D_n$
Let $H=<r> \subset D_n$.
$H$ is clearly abelian and $[G:H]=2$, hence the result.
if $|H|=n$ is even, there are 4 irreducible representations of dimension 1 and $n/2 - 1$ irreducible representations of dimension 2.