# Higman-Sims group

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## Contents

## Definition

This group, denoted *HS*, and termed the **Higman-Sims group**, is one of the sporadic simple groups and was discovered by Higman and Sims. It has order:

## Arithmetic functions

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

order (number of elements, equivalently, cardinality or size of underlying set) | 44352000 | groups with same order |

### Arithmetic functions of a counting nature

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

number of conjugacy classes | 24 |

## Group properties

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

abelian group | No | |

nilpotent group | No | |

solvable group | No | |

simple group, simple non-abelian group | Yes |