# Projective special linear group:PSL(2,17)

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## Contents

## Definition

This group is defined as the projective special linear group of degree two over field:F17.

## Arithmetic functions

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

order (number of elements, equivalently, cardinality or size of underlying set) | 2448 | groups with same order | As , odd: . See element structure of projective special linear group of degree two. |

exponent of a group | 1224 | groups with same order and exponent of a group | groups with same exponent of a group | As , odd: . See element structure of projective special linear group of degree two. |

### Arithmetic functions of a counting nature

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

number of conjugacy classes | 11 | As , odd: . See element structure of projective special linear group of degree two |

number of conjugacy classes of subgroups | 22 | |

number of subgroups | 2420 |

## Group properties

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

abelian group | No | |

nilpotent group | No | |

solvable group | No | |

simple group, simple non-abelian group | Yes | projective special linear group of degree two is simple (small exceptions exist) |

minimal simple group | Yes | See classification of finite minimal simple groups |

## GAP implementation

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

PSL(2,17) |
PSL |