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FiniteGroupCount[n]

gives the number of finite groups of order n.

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Basic Examples  
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Applications  
Properties & Relations  
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FiniteGroupCount

FiniteGroupCount[n]

gives the number of finite groups of order n.

Details

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

Examples

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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:

Wolfram Research (2008), FiniteGroupCount, Wolfram Language function, https://reference.wolfram.com/language/ref/FiniteGroupCount.html.

Text

Wolfram Research (2008), FiniteGroupCount, Wolfram Language function, https://reference.wolfram.com/language/ref/FiniteGroupCount.html.

CMS

Wolfram Language. 2008. "FiniteGroupCount." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/FiniteGroupCount.html.

APA

Wolfram Language. (2008). FiniteGroupCount. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/FiniteGroupCount.html

BibTeX

@misc{reference.wolfram_2025_finitegroupcount, author="Wolfram Research", title="{FiniteGroupCount}", year="2008", howpublished="\url{https://reference.wolfram.com/language/ref/FiniteGroupCount.html}", note=[Accessed: 13-August-2025]}

BibLaTeX

@online{reference.wolfram_2025_finitegroupcount, organization={Wolfram Research}, title={FiniteGroupCount}, year={2008}, url={https://reference.wolfram.com/language/ref/FiniteGroupCount.html}, note=[Accessed: 13-August-2025]}