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

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 $$p$$.

Conjugacy class structure
All the elements of this group are of the form:

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