Element structure of general affine group of degree one over a finite field

This article gives specific information, namely, element structure, about a family of groups, namely: general affine group of degree one.
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This article describes the element structure of the general affine group of degree one over a finite field. We denote the field size by the letter $q$ and the characteristic of the field by the letter $p$. Note that $q$ is a prime power with underlying prime $p$.

Summary

Item	Value
number of conjugacy classes	$q$ equals number of irreducible representations, see also linear representation theory of general affine group of degree one over a finite field
order	$q(q - 1)$
exponent	$p(q - 1)$
conjugacy class size statistics	size 1 (1 class), size $q - 1$ (1 class), size $q$ ($q - 2$ classes)

Conjugacy class structure

All the elements of this group are of the form:

$x \mapsto ax + v, a \in \mathbb{F}_q^\ast, v \in \mathbb{F}_q$

Nature of conjugacy class	Size of conjugacy class	Number of such conjugacy classes	Total number of elements
$a = 1, v = 0$	1	1	1
$a = 1, v \ne 0$ (conjugacy class is independent of choice of $v$)	$q - 1$	1	$q - 1$
$a \ne 1$ (conjugacy class is determined completely by choice of $a$ and is independent of choice of $v$; in other words, each conjugacy class is a coset of the subgroup of translations)	$q$	$q - 2$	$q(q - 2)$
Total (--)	--	$q$	$q(q - 1)$