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

This article gives specific information, namely, linear representation theory, about a family of groups, namely: unitriangular matrix group of degree four.
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This article describes the linear representation theory of the unitriangular matrix group of degree four over a finite field of size $q$, where $q$ is a prime power $p^{r}$ with underlying prime $p$. $p$ is the characteristic of the field.

Summary

Item	Value
number of conjugacy classes (equals number of irreducible representations over a splitting field)	$2q^{3}+q^{2}-2q$. 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 $q^{3}$ times), $q$ (occurs $q^{3}-q$ times), $q^{2}$ (occurs $q^{2}-q$ times)
sum of squares of degrees of irreducible representations	$q^{6}$ (equals order of the group) see sum of squares of degrees of irreducible representations equals order of group
lcm of degrees of irreducible representations	$q^{2}$