# Mathieu group:M23

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## Contents

## Definition

This is the Mathieu group of degree 23, denoted , and is the subgroup of the symmetric group of degree 24 generated by the following permutations:

## Arithmetic functions

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

order (number of elements, equivalently, cardinality or size of underlying set) | 10200960 | groups with same order | |

exponent of a group | 212520 | groups with same order and exponent of a group | groups with same exponent of a group |

### Arithmetic functions of a counting nature

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

number of conjugacy classes | 17 |

## Group properties

Property | Satisfied? | Explanation |
---|---|---|

abelian group | No | |

nilpotent group | No | |

solvable group | No | |

simple group, simple non-abelian group | Yes | |

minimal simple group | No |

## GAP implementation

GAP's SmallGroup library is not available for this large order.

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

MathieuGroup(23) |
MathieuGroup |