Groups of order 1024
From Groupprops
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 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 ![]() |
Number of maximal class groups, i.e., groups of nilpotency class ![]() |
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.