Groups of order 1024

This article gives information about, and links to more details on, groups of order 1024
See pages on algebraic structures of order 1024| See pages on groups of a particular order

Statistics at a glance

To understand these in a broader context, see
groups of order 2^n|groups of prime-tenth order

Since $1024 = 2^{10}$ is a prime power, and prime power order implies nilpotent, all groups of this order are nilpotent groups.

Quantity	Value	Greatest integer function of logarithm of value to base 2	Explanation
Number of groups up to isomorphism	49487365422	35
Number of abelian groups up to isomorphism	42	5	Equals the number of unordered integer partitions of $10$. See also classification of finite abelian groups.
Number of maximal class groups, i.e., groups of nilpotency class $10 - 1 = 9$	3	1	The dihedral group, semidihedral group, and generalized quaternion group; see classification of finite 2-groups of maximal class

GAP implementation

Unfortunately, GAP's SmallGroup library is not available for this order.