# Mathieu group

From Groupprops

## The list

There are eight isomorphism classes of Mathieu groups, given by their degrees. The *degree* of a Mathieu group is the smallest size set on which it has a faithful permutation representation, which is precisely the representation of interest:

Degree | Mathieu group | Order of group | Prime factorization of order | Number of conjugacy classes | Sporadic simple? | Simple? | Almost simple? | Alternative descriptions |
---|---|---|---|---|---|---|---|---|

9 | Mathieu group:M9 | 72 | 6 | No | No | No | projective special unitary group | |

10 | Mathieu group:M10 | 720 | 8 | No | No | Yes | ? | |

11 | Mathieu group:M11 | 7920 | 10 | Yes | Yes | Yes | -- | |

12 | Mathieu group:M12 | 95040 | 15 | Yes | Yes | Yes | -- | |

21 | Mathieu group:M21 | 20160 | 10 | No | Yes | Yes | projective special linear group | |

22 | Mathieu group:M22 | 443520 | 12 | Yes | Yes | Yes | -- | |

23 | Mathieu group:M23 | 10200960 | 17 | Yes | Yes | Yes | -- | |

24 | Mathieu group:M24 | 244823040 | 26 | Yes | Yes | Yes | -- |