Dihedral group (reviewed)

The dihedral group is the set of symmetries of a regular $n$-gon under the operation of composition. It consists of $n$ rotations and $n$ reflections, has order $2n$, and can be generated by one rotation of order $n$ and one reflection of order $2$. $$D_n = < g,h \mid g^n=h^2=1, hg=g^{-1}h > = \{e,g,g_2,...,g_{n-1},h,gh,...,g_{n-1}h\}.$$ It is the split extension $C_n\rtimes C_2$ with $C_2$ acting by $-1$. The non-split extension in this case is the dicyclic group.