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

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

This article gives the element structure of the general affine group of degree two over a finite field. Similar structure works over an infinite field or a field of infinite characteristic, with suitable modification. For more on that, see element structure of general affine group of degree two over a field.

The discussion here builds upon the discussion of element structure of general linear group of degree two over a finite field.

Summary

Item Value
order q^2(q^2 - 1)(q^2 - q) = q^3(q + 1)(q - 1)^2
exponent  ?
number of conjugacy classes q^2 + q - 1

Particular cases

q (field size) p (underlying prime, field characteristic) general affine group GL(2,q) order of the group (= q^2(q^2 - 1)(q^2 - q)) number of conjugacy classes (= q^2 + q - 1) element structure page
2 2 symmetric group:S4 24 5 element structure of symmetric group:S4
3 3 general affine group:GA(2,3) 432 11 element structure of general affine group:GA(2,3)
4 2 general affine group:GA(2,4) 2880 19
5 5 general affine group:GA(2,5) 12000 29