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FiniteGroupCount

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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)Summary of the most common use cases

Table of values:

In[1]:=1
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https://wolfram.com/xid/0btng7gz7umq-cjbcm
Out[1]=1
In[1]:=1
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https://wolfram.com/xid/0btng7gz7umq-lar3jb
Out[1]=1

Scope  (2)Survey of the scope of standard use cases

Square-free number:

In[1]:=1
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https://wolfram.com/xid/0btng7gz7umq-crzdgo
Out[1]=1

FiniteGroupCount threads element-wise over lists:

In[1]:=1
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https://wolfram.com/xid/0btng7gz7umq-isgnks
Out[1]=1

Applications  (2)Sample problems that can be solved with this function

Density of 1 for groups with order less than :

In[1]:=1
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https://wolfram.com/xid/0btng7gz7umq-mwa33m
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0btng7gz7umq-b702t4
Out[2]=2

The number of non-Abelian groups of order n:

In[1]:=1
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https://wolfram.com/xid/0btng7gz7umq-em2hot
Out[1]=1

Properties & Relations  (2)Properties of the function, and connections to other functions

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

In[1]:=1
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https://wolfram.com/xid/0btng7gz7umq-e8dnsj
Out[1]=1

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

In[2]:=2
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https://wolfram.com/xid/0btng7gz7umq-bw1b2
Out[2]=2

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

In[3]:=3
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https://wolfram.com/xid/0btng7gz7umq-p76dd
Out[3]=3

FindSequenceFunction can recognize the FiniteGroupCount sequence:

In[1]:=1
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https://wolfram.com/xid/0btng7gz7umq-hj2mn6
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0btng7gz7umq-5okec
Out[2]=2
Wolfram Research (2008), FiniteGroupCount, Wolfram Language function, https://reference.wolfram.com/language/ref/FiniteGroupCount.html.
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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.

✖
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.

✖
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

✖
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: 01-May-2025 ]}

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@misc{reference.wolfram_2025_finitegroupcount, author="Wolfram Research", title="{FiniteGroupCount}", year="2008", howpublished="\url{https://reference.wolfram.com/language/ref/FiniteGroupCount.html}", note=[Accessed: 01-May-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: 01-May-2025 ]}

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@online{reference.wolfram_2025_finitegroupcount, organization={Wolfram Research}, title={FiniteGroupCount}, year={2008}, url={https://reference.wolfram.com/language/ref/FiniteGroupCount.html}, note=[Accessed: 01-May-2025 ]}