General linear group:GL(2,5)

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Definition

The group, denoted $GL(2,5)$ or $G{L}_2(5)$, is defined as the general linear group of degree two over the field of five elements. It is a group of order 480.

Arithmetic functions

Function	Value	Explanation
order	480	$5^2-1$ options for first row, $5^2-5$ options for second row. See order formulas for linear groups of degree two
number of conjugacy classes	24	There are $5(5-1)$ conjugacy classes of semisimple matrices and $5-1$ conjugacy classes of matrices with repeated eigenvalues.

GAP implementation

Group ID

This group has ID $218$ among the groups of order $480$. It can be defined using GAP's SmallGroup function:

SmallGroup(480,218)

Other definitions

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

GL(2,5)