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Definition
Let be a natural number. The number of groups of order is defined as the number of isomorphism classes of groups whose order is .
This is a finite number and is bounded by for obvious reasons. The function is not strictly increasing in and depends heavily on the nature of the prime factorization of .
Initial valuesThe ID of the sequence of these numbers in the Online Encyclopedia of Integer Sequences is A000001 Numbers up till 100
Small powers of small primes
(For general formulas, see the next section).
Numbers Groups And Codes PdfPowers of 2:[SHOW MORE]Numbers Groups And Codes Solution Manual 2016FactsNumbers Groups And Codes Solution Manual FreeBasic facts
Asymptotic facts and conjectures
PropertiesSupermultiplicativity
If with and relatively prime, the number of groups of order is bounded from below by the product of the number of groups of orders and respectively. This is because we can take direct products for every pair of a group of order and a group of order .
Numbers Groups And Codes Solution Manual Download
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