What are the elements of dihedral group $\mathbb{D_6}$?

Question

I'm not really all that good with dihedral groups and can't find anything online that explicitly shows the elements of $\mathbb{D_6}$

Answer 1

$D_6\cong S_3$ and is the set of symmetries of an equilateral triangle. Three rotations and three reflections.

Equivalently, it's the set of permutations (bijections) of a three element set, say $\{1,2,3\}$.

Btw, it has the distinction of being the smallest non-abelian group.

Answer 2

@Chris is probably right. There is more about this group here:

If you are not sure look also to cycle graphs of dihedral groups. See there is $D_3$ (which could have name $D_6$) is isomorphic to $S_3$. And there is $D_6$ group symmetry of David star, which is $D_3 \times Z_2 $ which has 12 elements.