# Groups of order 4096

From Groupprops

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 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 . See also classification of finite abelian groups. |

Number of maximal class groups, i.e., groups of nilpotency class | 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.