Groups of order 4096

From Groupprops
Jump to: navigation, search
This article gives information about, and links to more details on, groups of order 4096
See pages on algebraic structures of order 4096| See pages on groups of a particular order

Statistics at a glance

Since 4096 = 2^{12} 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 (insert order of magnitude estimate)
Number of abelian groups up to isomorphism 77 Equals the number of unordered integer partitions of 12. See also classification of finite abelian groups.
Number of maximal class groups, i.e., groups of nilpotency class 12 - 1 = 11 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.