Moufang loops of order 2^n

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Number of Moufang loops of small orders

Exponent n Value 2^n Number of groups of order 2^n Number of Moufang loops of order 2^n that are not groups Total number of Moufang loops of order 2^n Reason/explanation/list
0 1 1 0 1 only trivial group
1 2 1 0 1 only cyclic group:Z2
2 4 2 0 2 cyclic group:Z4 and Klein four-group. See groups of order 4, classification of groups of prime-square order.
3 8 5 0 5 See groups of order 8; see classification of groups of prime-cube order
4 16 14 5 19 See groups of order 16, Moufang loops of order 16
5 32 51 71 122 See groups of order 32, Moufang loops of order 32
6 64 267 4262 4529 See groups of order 64, Moufang loops of order 64

See also groups of order 2^n and nilpotent Lie rings of order 2^n for related information.