Element structure of general semilinear group of degree two over a finite field

This article gives specific information, namely, element structure, about a family of groups, namely: general semilinear group of degree two.
View element structure of group families | View other specific information about general semilinear group of degree two

This article describes the element structure of the general semilinear group of degree two over a finite field of size $q=p^{r}$, where $p$ is the characteristic of the field. The Galois group of the extension $\mathbb {F} _{q}/\mathbb {F} _{p}$ is a cyclic group of order $r$, generated by the $p$-power map (the Frobenius automorphism). Note that $r=\log _{p}q$

Summary

Item	Value
order of the group	$r(q^{2}-1)(q^{2}-q)$
number of conjugacy classes	PLACEHOLDER FOR INFORMATION TO BE FILLED IN: [SHOW MORE] One of the people editing this page intended to fill in this information at a later stage, but hasn't gotten around to doing it yet. If you see this placeholder for a long time, file an error report at the error reporting page.