# Difference between revisions of "General linear group:GL(3,3)"

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| {{arithmetic function value order|11232}}order of a [[general linear group of degree three]] over a [[finite field]] with <math>q</math> elements is <math>(q^3 - 1)(q^3 - q)(q^3 - q^2)</math>. For <math>q = 3</math>, we get <math>(26)(24)(18) = 11232</math> | | {{arithmetic function value order|11232}}order of a [[general linear group of degree three]] over a [[finite field]] with <math>q</math> elements is <math>(q^3 - 1)(q^3 - q)(q^3 - q^2)</math>. For <math>q = 3</math>, we get <math>(26)(24)(18) = 11232</math> | ||

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− | | {{arithmetic function value exponent|312}} | + | | {{arithmetic function value given order|exponent of a group|11232|312}} |

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==GAP implementation=== | ==GAP implementation=== | ||

## Revision as of 02:51, 31 October 2010

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 groupView a complete list of particular groups (this is a very huge list!)[SHOW MORE]

## Definition

This group is defined as the general linear group of degree three over field:F3.

## Arithmetic functions

Function | Value | Explanation |
---|---|---|

order (number of elements, equivalently, cardinality or size of underlying set) | 11232 | groups with same orderorder of a general linear group of degree three over a finite field with elements is . For , we get |

exponent of a group | 11232 | groups with same order and exponent of a group | groups with same exponent of a group |

## GAP implementation=

Description | Functions used |
---|---|

GL(3,3) or GeneralLinearGroup(3,3) |
GAP:GL |