Dihedral Group is Non-Abelian.

Are all dihedral groups Non-Abelian?

Small dihedral groups

D₁ and D₂ are exceptional in that: D₁ and D₂ are the only abelian dihedral groups. Otherwise, D_n is non-abelian.

Is D4 abelian?

We see that D4 is not abelian; the Cayley table of an abelian group would be symmetric over the main diagonal. ... Higher order dihedral groups. The collection of symmetries of a regular n-gon forms the dihedral group Dn under composition.