Element structure of projective special linear group of degree three over a finite field

This article gives specific information, namely, element structure, about a family of groups, namely: projective special linear group of degree three.
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This article describes the element structure of the projective special linear group of degree three over a finite field.

We take $q$ as the number of elements in the field and $p$ as the underlying prime number, so $q$ is a power of $p$.

Conjugacy class structure

Here is the summary of formulas for the number of conjugacy classes:

Case	Number of conjugacy classes
$q$ is congruent to 0 or -1 mod 3	$q^2+q=q(q+1)$
$q$ is congruent to 1 mod 3	$(q^2+q+10)/3$