# Linear representation theory of unitriangular matrix group of degree five over a finite field

From Groupprops

## Contents |

This article gives specific information, namely, linear representation theory, about a family of groups, namely: unitriangular matrix group of degree five. This article restricts attention to the case where the underlying ring is a finite field.

View linear representation theory of group families | View other specific information about unitriangular matrix group of degree five | View other specific information about group families for rings of the type finite field

This article describes the linear representation theory of the unitriangular matrix group of degree five over a finite field of size , where is a prime power with underlying prime . is the characteristic of the field.

## Related information

- Linear representation theory of unitriangular matrix group over a finite field
- Linear representation theory of unitriangular matrix group of degree three over a finite field
- Linear representation theory of unitriangular matrix group of degree four over a finite field

## Summary

Item | Value |
---|---|

number of conjugacy classes (equals number of irreducible representations over a splitting field) | . See number of irreducible representations equals number of conjugacy classes, element structure of unitriangular matrix group of degree four over a finite field |

degrees of irreducible representations | 1 (occurs times) (occurs times) (occurs times) (occurs times) (occurs times) |

sum of squares of degrees of irreducible representations | (equals order of the group) see sum of squares of degrees of irreducible representations equals order of group |

lcm of degrees of irreducible representations |