Groups of order 2^n

Number of groups of small orders

Exponent $n$	Value $2^{n}$	Number of groups of order $2^{n}$	Reason/Explanation/List
1	2	1	Only cyclic group:Z2; see [[equivalence of definitions of group of prime order
2	4	2	Only cyclic group:Z4 and Klein four-group; see also groups of order 4 and classification of groups of prime-square order
3	8	5	See groups of order 8; see classification of groups of prime-cube order
4	16	14	See groups of order 16
5	32	51	See groups of order 32
6	64	267	See groups of order 64
7	128	2328	See groups of order 128
8	256	56092	See groups of order 256
9	512	10494213	See groups of order 512
10	1024	49487365422	See groups of order 1024