Groups of order 2048

This article gives information about, and links to more details on, groups of order 2048
See pages on algebraic structures of order 2048 | See pages on groups of a particular order

The number of groups of this order up to isomorphism is, as of time of the last revision of this article, unknown. This may change in the future with improved computing power. If the number of groups of this order up to isomorphism has been found and this page has not been updated in a while since then, please consider reporting an error.

Statistics at a glance

Since $2048=2^{11}$ is a prime power, and prime power order implies nilpotent, all groups of this order are nilpotent groups.

Quantity	Value	Explanation
Number of groups up to isomorphism	unknown, but very large (strictly exceeds 1774274116992170)
Number of abelian groups up to isomorphism	56	Equals the number of unordered integer partitions of $11$. See also classification of finite abelian groups.
Number of maximal class groups, i.e., groups of nilpotency class $11-1=10$	3	The dihedral group, semidihedral group, and generalized quaternion group

GAP implementation

Unfortunately, GAP's SmallGroup library is not available for this order, because the groups have not yet been classified. However individual groups of this order can be constructed with GAP using their presentations or using other means of constructing groups.