General linear group:GL(2,5): Difference between revisions
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==Definition== | ==Definition== | ||
The group, denoted <math>GL(2,5)</math> or <math>GL_2(5)</math>, is defined as the [[defining ingredient::general linear group of degree two]] over the field of five elements. | The group, denoted <math>GL(2,5)</math> or <math>GL_2(5)</math>, is defined as the [[defining ingredient::general linear group of degree two]] over the field of five elements. It is a [[groups of order 480|group of order 480]]. | ||
==Arithmetic functions== | |||
{| class="sortable" border="1" | |||
! Function !! Value !! Explanation | |||
|- | |||
| [[order of a group|order]] || 480 || <math>5^2 - 1</math> options for first row, <math>5^2 - 5</math> options for second row.<br>See [[order formulas for linear groups of degree two]] | |||
|- | |||
| [[number of conjugacy classes]] || 24 || There are <math>5(5-1)</math> conjugacy classes of semisimple matrices and <math>5 - 1</math> conjugacy classes of matrices with repeated eigenvalues. | |||
|} | |||
==GAP implementation== | ==GAP implementation== | ||
Latest revision as of 21:04, 27 December 2023
This article is about a particular group, i.e., a group unique upto isomorphism. View specific information (such as linear representation theory, subgroup structure) about this group
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Definition
The group, denoted or , 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 | options for first row, options for second row. See order formulas for linear groups of degree two |
| number of conjugacy classes | 24 | There are conjugacy classes of semisimple matrices and conjugacy classes of matrices with repeated eigenvalues. |
GAP implementation
Group ID
This group has ID among the groups of order . 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)