# Classification of groups of order 2^n

This article gives information on the classification process for groups of order 2^n. All groups of order $2^n$ have been classified for $0 \le n \le 10$. The classification problem becomes more messy and huge as $n$ gets larger.

$n$ $2^n$ Number of groups of order $2^n$ Information on groups of order $2^n$ Information on classification
0 1 1 trivial group only --
1 2 1 cyclic group:Z2 only equivalence of definitions of group of prime order
2 4 2 groups of order 4 classification of groups of prime-square order
3 8 5 groups of order 8 classification of groups of prime-cube order, the case of $2^3$ differs somewhat from the case of $p^3$, $p$ odd
4 16 14 groups of order 16 classification of groups of order 16
5 32 51 groups of order 32 classification of groups of order 32
6 64 267 groups of order 64 classification of groups of order 64
7 128 2328 groups of order 128 classification of groups of order 128
8 256 56092 groups of order 256 classification of groups of order 256
9 512 10494213 groups of order 512 classification of groups of order 512
10 1024 49487365422 groups of order 1024 classification of groups of order 1024