# Moufang loops of order 32

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 32.

See pages on algebraic structures of order 32|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 | Total for Moufang loops |
---|---|---|---|

Total number up to isomorphism | 51 | 71 | 122 |

Number up to isomorphism that are commutative | 7 | 0 | 7 |

Number up to isomorphism that have nilpotency class exactly two | 26 | 54 | 80 |

Number up to isomorphism that have nilpotency class exactly three | 15 | 17 | 32 |

Number up to isomorphism that have nilpotency class exactly four | 3 | 0 | 3 |

To understand these in a broader context, see Moufang loops of order 2^n | Moufang loops of prime-fifth order

This article concentrates on the Moufang loops of order 32 that are not groups. For a discussion of the groups, see groups of order 32.