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I started using Mathematica and want to do some computation involving Characters of the symmetric group. In maple, I used to use the package combinat. The link is below https://www.maplesoft.com/support/help/maple/view.aspx?path=combinat

Which have partition function, Character of the symmetric group and things? I wonder what would be an equivalent package for Mathematica? I am sure it should exist but could not find it for now.

What I am particularly looking is to work with the symmetric group $S_n$. Conjugancy classes of $S_n$ are given by partition, so I want to evaluate the Char on some conjugancy class. In maple it is

Char([],[]) [] represent partition for integer n.

So I want to ask the community.

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    $\begingroup$ This guide might be helpful. But the built-in group-theoretic capabilities are indeed somewhat limited. $\endgroup$
    – Henrik Schumacher
    Aug 21, 2018 at 10:54
  • $\begingroup$ Maybe it is also possible to call Gap from Mathematica; check this link. This "package" was written for Mathematica 2, though. Quite unlikely that it will work with modern versions. $\endgroup$
    – Henrik Schumacher
    Aug 21, 2018 at 10:58
  • $\begingroup$ You can get character tables of the symmetric groups using FiniteGroupData[{"SymmetricGroup", 6}, "CharacterTable"] for example. The table is sorted following IntegerPartitions[6]. $\endgroup$
    – jose
    Aug 21, 2018 at 21:38

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