Groups of order 1024

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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.