The **dihedral group** is the set of symmetries of a regular $n$-gon under 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.

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- Last edited by John Jones on 2019-05-23 19:46:47

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