Element structure of general affine group of degree one 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 one.
View element structure of group families | View other specific information about general affine group of degree one
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
.
Summary
Item | Value |
---|---|
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 |
order | ![]() |
exponent | ![]() |
conjugacy class size statistics | size 1 (1 class), size ![]() ![]() ![]() |
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 |
---|---|---|---|
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1 | 1 | 1 |
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1 | ![]() |
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Total (--) | -- | ![]() |
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