General linear group:GL(2,7)

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Definition

The group, denoted $GL(2,7)$ or $G{L}_2(7)$, is defined as the general linear group of degree two over the field of seven elements. It is a group of order 2016.

Arithmetic functions

Function	Value	Explanation
order	2016	$7^2-1$ options for first row, $7^2-7$ options for second row. See order formulas for linear groups of degree two
number of conjugacy classes	48	There are $7(7-1)$ conjugacy classes of semisimple matrices and $7-1$ conjugacy classes of matrices with repeated eigenvalues.

GAP implementation

The group can be defined using GAP's GeneralLinearGroup function:

GL(2,7)