# Moufang loops of order 81

This article gives information about, and links to more details on, algebraic structures of the type Moufang loop whose order (i.e., the size of the underlying set) is 81.

See pages on algebraic structures of order 81|See pages on Moufang loops of a particular order

## Statistics at a glance

Quantity | Value for groups | Value for Moufang loops that are not groups | Value for all Moufang loops |
---|---|---|---|

Total number up to isomorphism | 15 | 5 | 20 |

Number up to isomorphism that are commutative | 5 | 0 | 5 |

Number up to isomorphism that have nilpotency class exactly two |
6 | 5 | 11 |

Number up to isomorphism that have nilpotency class exactly three |
4 | 0 | 4 |

To understand these in a broader context, see Moufang loops of order 3^n | Moufang loops of prime-fourth order