# Semidihedral group

From Groupprops

## Definition

Let be a natural number greater than or equal to . The **semidihedral group** or **quasidihedral group** of order (and **degree** ), denoted , is defined by the following presentation:

(here, is the symbol for the identity element).

## Particular cases

Group | ||||
---|---|---|---|---|

4 | 16 | 3 | 8 | semidihedral group:SD16 |

5 | 32 | 4 | 16 | semidihedral group:SD32 |

6 | 64 | 5 | 32 | semidihedral group:SD64 |

7 | 128 | 6 | 64 | semidihedral group:SD128 |