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