# Linear representation theory of unitriangular matrix group of degree three over a finite discrete valuation ring

From Groupprops

## Contents |

This article gives specific information, namely, linear representation theory, about a family of groups, namely: unitriangular matrix group of degree three.

View linear representation theory of group families | View other specific information about unitriangular matrix group of degree three

This article describes the linear representation theory of the unitriangular matrix group of degree three over a finite discrete valuation ring. It builds on the discussion at linear representation theory of unitriangular matrix group of degree three over a finite field.

We assume that the residue field has size and characteristic , with . We denote by the length of the discrete valuation ring. The size of the ring is thus and the order of the field is .

## Summary

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

degrees of irreducible representations over a splitting field (such as or ) | 1 (occurs times). For , occurs times. |

number of conjugacy classes equals number of irreducible representations over a splitting field | |

sum of squares of degrees of irreducible representations | |

maximum degree of irreducible representation |