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Mathematica > Mathematics and Algorithms > Discrete Mathematics > Combinatorial Functions >

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FiniteGroupCount

FiniteGroupCount[n]
gives the number of finite groups of order n.

Integer mathematical function, suitable for both symbolic and numerical manipulation.

Table of values:

Square-free number:

FiniteGroupCount threads element-wise over lists:

Density of 1 for groups with order less than 10⁴:

The number of non-abelian groups of order n:

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

FiniteGroupCount[p²] takes the value 2 for all prime p:

FiniteGroupCount[p³] takes the value 5 for all prime p: