# Dicyclic group

From Encyclopedia of Mathematics

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 |

**How to Cite This Entry:**

Dicyclic group.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Dicyclic_group&oldid=54642