Element structure of general affine group of degree one over a finite field
This article gives specific information, namely, element structure, about a family of groups, namely: general affine group of degree one.
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This article describes the element structure of the general affine group of degree one over a finite field. We denote the field size by the letter and the characteristic of the field by the letter . Note that is a prime power with underlying prime .
|number of conjugacy classes|| |
equals number of irreducible representations, see also linear representation theory of general affine group of degree one over a finite field
|conjugacy class size statistics||size 1 (1 class), size (1 class), size ( classes)|
Conjugacy class structure
All the elements of this group are of the form:
|Nature of conjugacy class||Size of conjugacy class||Number of such conjugacy classes||Total number of elements|
|(conjugacy class is independent of choice of )||1|
|(conjugacy class is determined completely by choice of and is independent of choice of ; in other words, each conjugacy class is a coset of the subgroup of translations)|