# Groups of order 6561

From Groupprops

## Contents |

This article gives information about, and links to more details on, groups of order 6561

See pages on algebraic structures of order 6561| See pages on groups of a particular order

## Statistics at a glance

To understand these in a broader context, see groups of order 3^n | groups of prime-eighth order

Since is a prime power, and prime power order implies nilpotent, all groups of this order are nilpotent groups.

Quantity | Value | Explanation |
---|---|---|

Total number of groups up to isomorphism | unknown | |

Number of abelian groups | 22 | equal to the number of unordered integer partitions of 8. See classification of finite abelian groups |

Number of groups of nilpotency class exactly two |
unknown | |

Number of groups of nilpotency class exactly three |
unknown | |

Number of groups of nilpotency class exactly four |
unknown | |

Number of groups of nilpotency class exactly five |
unknown | |

Number of groups of nilpotency class exactly six |
unknown | |

Number of groups of nilpotency class exactly seven, i.e., maximal class groups |
unknown |