gives the number of finite groups of order n.


  • Integer mathematical function, suitable for both symbolic and numerical manipulation.
  • FiniteGroupCount automatically threads over lists.


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Basic Examples  (2)

Table of values:

Scope  (2)

Square-free number:

FiniteGroupCount threads element-wise over lists:

Applications  (2)

Density of 1 for groups with order less than :

The number of non-Abelian groups of order n:

Properties & Relations  (2)

FiniteGroupCount[p] takes the value 1 for all prime p:

FiniteGroupCount[p^2] takes the value 2 for all prime p:

FiniteGroupCount[p^3] takes the value 5 for all prime p:

FindSequenceFunction can recognize the FiniteGroupCount sequence:

Introduced in 2008