Questions on the group-theoretic functionality of Mathematica.

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Does “FiniteRingData” or something like that exists?

I want to find a function like FiniteGroupData but for finite rings. Does something like that exists?
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Can Mathematica rewrite irreps given in Dynkin Coeffs in tensor form?

Apparently, it is possible to do Young Tableaux calculations with mathematica (see the Susyno and LieART packages). A natural follow up question is then, given that one has decomposed a direct product ...
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Group theory - symmetry inequivalent sqaure matrices with PBC

I would like to obtain the symmetry inequivalent possible occupations of indistinguishable objects in a square lattice with periodic boundary conditions. Examples: 1 object in a 4 by 4 square ...