\begin{definition}[Definition:Dicyclic Group]
For even $n$, the '''dicyclic group''' $\Dic n$ of order $4 n$ is the group having the presentation:
:$\Dic n = \gen {a, b: a^{2 n} = e, b^2 = a^n, b^{-1} a b = a^{-1} }$
\end{definition}