Groups of order 6561: Difference between revisions
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! Quantity !! Value !! Explanation | ! Quantity !! Value !! Explanation | ||
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| Total number of groups up to isomorphism || | | Total number of groups up to isomorphism || [[count::1396077]] || | ||
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| Number of [[abelian group]]s || 22 || equal to the number of [[unordered integer partitions]] of 8. See [[classification of finite abelian groups]] | | Number of [[abelian group]]s || 22 || equal to the number of [[unordered integer partitions]] of 8. See [[classification of finite abelian groups]] | ||
Latest revision as of 18:51, 10 December 2023
This article gives information about, and links to more details on, groups of order 6561
See pages on algebraic structures of order 6561 | See pages on groups of a particular order
Statistics at a glance
To understand these in a broader context, see groups of order 3^n | groups of prime-eighth order
Since is a prime power, and prime power order implies nilpotent, all groups of this order are nilpotent groups.
| Quantity | Value | Explanation |
|---|---|---|
| Total number of groups up to isomorphism | 1396077 | |
| Number of abelian groups | 22 | equal to the number of unordered integer partitions of 8. See classification of finite abelian groups |
| Number of groups of nilpotency class exactly two | unknown | |
| Number of groups of nilpotency class exactly three | unknown | |
| Number of groups of nilpotency class exactly four | unknown | |
| Number of groups of nilpotency class exactly five | unknown | |
| Number of groups of nilpotency class exactly six | unknown | |
| Number of groups of nilpotency class exactly seven, i.e., maximal class groups | unknown |