# Dihedral and dicyclic groups are isoclinic

From Groupprops

## Statement

Suppose is an integer. Then, the following two groups are isoclinic groups:

- The dicyclic group of degree and order .
- The dihedral group of degree and order .

Further, if is odd, the nboth of these are also isoclinic to the dihedral group of degree and order .

## Particular cases

dicyclic group of degree , order | dihedral group of degree , order | If is odd, dihedral group of degree , order | |||
---|---|---|---|---|---|

2 | 4 | 8 | quaternion group | dihedral group:D8 | -- |

3 | 6 | 12 | dicyclic group:Dic12 | dihedral group:D12 | symmetric group:S3 |

4 | 8 | 16 | generalized quaternion group:Q16 | dihedral group:D16 | -- |

5 | 10 | 20 | dicyclic group:Dic20 | dihedral group:D20 | dihedral group:D10 |