FiniteGroupCount [n]
gives the number of finite groups of order n.
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
open all close allBasic 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:
See Also
Related Guides
History
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: 16-November-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: 16-November-2025]}