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

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## Contents

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]