# Projective special linear group:PSL(3,4)

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## Contents

## Definition

This group is a finite group defined in the following equivalent ways:

- As the projective special linear group of degree three over the field of four elements.
- As the Mathieu group of degree .

It is a member of the smallest pair of distinct isomorphism classes of finite simple non-abelian groups that have the same order; the other member of the pair being alternating group:A8, which is also . See there are at most two finite simple groups of any order for more information.

## Arithmetic functions

Want to compare and contrast arithmetic function values with other groups of the same order? Check out groups of order 20160#Arithmetic functions

### Basic arithmetic functions

Function | Value | Similar groups | Explanation |
---|---|---|---|

order (number of elements, equivalently, cardinality or size of underlying set) | 20160 | groups with same order | As : |

### Arithmetic functions of a counting nature

Function | Value | Similar groups | Explanation |
---|---|---|---|

number of conjugacy classes | 10 | groups with same order and number of conjugacy classes | groups with same number of conjugacy classes | As (case is 1 mod 3): See element structure of projective special linear group of degree three over a finite field for more information |

## GAP implementation

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

PSL(3,4) |
PSL |

MathieuGroup(21) |
MathieuGroup |