Number of nilpotent groups equals product of number of groups of order each maximal prime power divisor
From Groupprops
Statement
Suppose is a natural number with prime factorization:
where are distinct primes and
are natural numbers.
Then the number of nilpotent groups of order is the product of the number of groups of order
for all
:
(Number of groups of order )
(Number of groups of order
)
(Number of groups of order
)