Element structure of general linear group over a finite field

This article gives specific information, namely, element structure, about a family of groups, namely: general linear group.
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This article describes the element structure of the general linear group of finite degree over a finite field, i.e., a group of the form $GL(n,\mathbb {F} _{q})$, also denoted $GL(n,q)$, defined as the general linear group of degree $n$ over the (unique up to isomorphism) field of size $q$.

This builds on conjugacy class size formula in general linear group over a finite field.

Particular cases

Particular cases by degree

Value of degree $n$	Element structure of general linear group $GL(n,q)$	order of group	degree as a polynomial in $q$ (= $n^{2}$)	number of conjugacy classes	degree as a polynomial in $q$ (= $n$)
1	the general linear group is a cyclic group of size $q-1$, given by the multiplicative group of $\mathbb {F} _{q}$ -- see multiplicative group of a finite field is cyclic	$q-1$	1	$q-1$	1
2	element structure of general linear group of degree two over a finite field	$(q^{2}-1)(q^{2}-q)$	4	$q^{2}-1$	2
3	element structure of general linear group of degree three over a finite field	$(q^{3}-1)(q^{3}-q)(q^{3}-q^{2})$	9	$q^{3}-q$	3