# Linear representation theory of projective general linear group of degree two over a finite field

From Groupprops

This article describes the linear representation theory of the general linear group of degree two over a finite field. The order (size) of the field is , and the characteristic prime is . is a power of .

See also linear representation theory of special linear group of degree two, linear representation theory of projective general linear group of degree two, and linear representation theory of general linear group of degree two.

## Particular cases

Group | Order of the group | Number of irreducible representations | Linear representation theory page | ||
---|---|---|---|---|---|

symmetric group:S3 | 2 | 2 | 6 | 3 | linear representation theory of symmetric group:S3 |

symmetric group:S4 | 3 | 3 | 24 | 5 | linear representation theory of symmetric group:S4 |

alternating group:A5 | 2 | 4 | 60 | 5 | linear representation theory of alternating group:A5 |

symmetric group:S5 | 5 | 5 | 120 | 7 | linear representation theory of symmetric group:S5 |

projective general linear group:PGL(2,7) | 7 | 7 | 336 | 9 | linear representation theory of projective general linear group:PGL(2,7) |

special linear group:SL(2,8) | 2 | 8 | 504 | 9 | linear representation theory of special linear group:SL(2,8) |

projective general linear group:PGL(2,9) | 3 | 9 | 720 | 11 | linear representation theory of projective general linear group:PGL(2,9) |