Groups of order 2048: Difference between revisions
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! Quantity !! Value !! Explanation | ! Quantity !! Value !! Explanation | ||
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| Number of groups up to isomorphism || unknown, but very large (strictly exceeds 1774274116992170)<ref | | Number of groups up to isomorphism || unknown, but very large (strictly exceeds 1774274116992170)<ref>[https://www.math.auckland.ac.nz/~obrien/research/gnu.pdf | John H. Conway, Heiko Dietrich and E.A. O’Brien, Counting groups: gnus, moas and other exotica]</ref> || | ||
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| Number of [[abelian group]]s up to isomorphism || 56 || Equals the number of [[unordered integer partitions]] of <math>11</math>. See also [[classification of finite abelian groups]]. | | Number of [[abelian group]]s up to isomorphism || 56 || Equals the number of [[unordered integer partitions]] of <math>11</math>. See also [[classification of finite abelian groups]]. | ||
Revision as of 09:33, 5 June 2023
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
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 (strictly exceeds 1774274116992170)[1] | |
| Number of abelian groups up to isomorphism | 56 | 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.