# Janko group:J2

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## Contents

## Definition

This group, denoted , and also called the **Hall-Janko group** and sometimes denoted , is one of the Janko groups. Its existence was conjectured by Janko and it was constructed by Hall and Wales.

The order of the group is:

It is one of the sporadic simple groups.

## Arithmetic functions

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

order (number of elements, equivalently, cardinality or size of underlying set) | 604800 | groups with same order |

### Arithmetic functions of a counting nature

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

number of conjugacy classes | 21 | See element structure of Janko group:J2 |

## Group properties

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

abelian group | No | |

nilpotent group | No | |

solvable group | No | |

simple group, simple non-abelian group | Yes |

## GAP implementation

GAP does not have an implementation of this group as a group. However, the character table of the group can be accessed as a stored table using GAP's CharacterTable function, if the CtblLib package is loaded:

`CharacterTable("J2")`