# Orthogonal group of degree two and type -1

From Groupprops

## Definition

Consider the finite field with elements, an odd prime power. Suppose is an element of that is not a square. The orthogonal group or is defined as the orthogonal group for the symmetric bilinear form given by the matrix:

In other words, as a subgroup of the general linear group of degree two, it is defined as follows:

## Particular cases

Size of the field | Characteristic prime | Othogonal group |
---|---|---|

3 | 3 | dihedral group:D8 |

5 | 5 | dihedral group:D8 |

7 | 7 | dihedral group:D16 |