Dicyclic group

2020 Mathematics Subject Classification: Primary: 20F05 [MSN][ZBL]

A finite group of order $4n$, obtained as the extension of the cyclic group of order $2$ by a cyclic group of order $2n$. It has the presentation $\langle n,2,2 \rangle$ and group presentation $$A^n = B^2 = (AB)^2 \ .$$ It may be realised as a subgroup of the unit quaternions.

The dicyclic group $n=2$ is the quaternion group of order $8$.

References

[a1]	H.S.M. Coxeter, "Regular complex polytopes" , Cambridge Univ. Press (1974) ISBN 0-521-20125-X Zbl 0732.51002