Element structure of special affine group of degree two over a finite field

From Groupprops
Jump to: navigation, search

Contents

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

This article describes the element structure of SA(2,q), the special affine group of degree two over a finite field of size q, where q is a prime power. We denote by p the characteristic of the field, so p is a prime number. Thus, q = p^r for some positive integer r.

Summary

Item Value
order of the group q^2(q^3 - q) = q^3(q^2 - 1) = q^5 - q^3
number of conjugacy classes Case q even (e.g., q = 2,4,8,\dots): ?
Case q odd (e.g., q = 3,5,7,9,11,13,\dots): 2q + 4