Groups of order 6561

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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 6561 = 3^8 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 unknown
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