# Difference between revisions of "Conjugacy class size formulas for linear groups of degree two"

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| [[general affine group of degree two]] || <math>GA(2,q)</math> or <math>AGL(2,q)</math> or <math>GA(2,\mathbb{F}_q)</math> or <math>AGL(2,\mathbb{F}_q)</math> || <matH>q^2 + q - 1</math> || <math>q^2 + q - 1</math> || 2 || [[element structure of general affine group of degree two over a finite field]] | | [[general affine group of degree two]] || <math>GA(2,q)</math> or <math>AGL(2,q)</math> or <math>GA(2,\mathbb{F}_q)</math> or <math>AGL(2,\mathbb{F}_q)</math> || <matH>q^2 + q - 1</math> || <math>q^2 + q - 1</math> || 2 || [[element structure of general affine group of degree two over a finite field]] | ||

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− | | [[special affine group of degree two]] || <math>SA(2,q)</math> or <math>ASL(2,q)</math> or <math>SA(2,\mathbb{F}_q)</math> or <math>ASL(2,\mathbb{F}_q)</math> || ? || <math>2q + 4</math> || [[element structure of special affine group of degree two over a finite field]] | + | | [[special affine group of degree two]] || <math>SA(2,q)</math> or <math>ASL(2,q)</math> or <math>SA(2,\mathbb{F}_q)</math> or <math>ASL(2,\mathbb{F}_q)</math> || ? || <math>2q + 4</math> || 1 || [[element structure of special affine group of degree two over a finite field]] |

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## Latest revision as of 23:40, 1 March 2012

This article gives formulas for the number of conjugacy classes as well as the sizes of individual conjugacy classes for the general linear group of degree two and some other related groups, both for a finite field of size and for some related rings.

## For a finite field of size

In the formulas below, the field size is . The characteristic of the field is a prime number . is a prime power with underlying prime . We let , so and is a nonnegative integer.