Groups of prime-fourth order
This article is about the groups of prime-fourth order for an odd prime number, i.e., the groups of order where is an odd prime. The special case is somewhat different -- see groups of order 16 for a summary of information on these groups.
Among the odd primes , the case is slightly different from the other primes.
Statistics at a glance
|Quantity||Value case||Value case||Value case||Explanation|
|Total number of groups||14||15||15||See classification of groups of order 16, classification of groups of prime-fourth order for odd prime|
|Number of abelian groups||5||5||5||See classification of finite abelian groups and structure theorem for finitely generated abelian groups.. In this case, the number of unordered integer partitions of 4 equals 5.|
|Number of groups of nilpotency class exactly two||6||6||6|
|Number of groups of nilpotency class exactly three||3||4||4|
|Prime||Number of groups||Information on groups of order|
|2||16||14||groups of order 16 -- behaves quite differently from the others.|
|3||81||15||groups of order 81 -- behaves somewhat differently from the others.|
|5||625||15||groups of order 625|
|7||2401||15||groups of order 2401|
|11||14641||15||groups of order 14641|