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Sébastien Palcoux, <a href="https://mathoverflow.net/q/466864/34538">Is a prime factor the rank of an integral MTC's an upper bound for the prime factors of its FPdim bounded by the rank?</a>, MathOverflow.

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These reformulations are demonstrated explained in the linked MathOverflow postposts.

Sébastien Palcoux, <a href="https://mathoverflow.net/q/466864/34538">Is a prime factor an integral MTC's FPdim bounded by the rank?</a>, MathOverflow.

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The number of conjugacy classes of pairs of commuting elements in a finite group G is the cardinal cardinality of the set {c(a,b) | a,b in G and ab=ba} where c(a,b) = {(gag^(-1),gbg^(-1)) | g in G}.

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These reformulation reformulations are demonstrated in the linked MathOverflow post.

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The number of conjugacy classes of pairs of commuting elements in a finite group G equals is the number cardinal of conjugacy classes within the centralizers of class representatives of G. This reformulation, demonstrated set {c(a,b) | a,b in the linked MathOverflow post, was employed G and ab=ba} where c(a,b) = {(gag^(-1),gbg^(-1)) | g in the sequence-generating programG}.

It is equal to the number of conjugacy classes within the centralizers of class representatives of G.

This reformulation was employed in the sequence-generating program.

It is also equal to the rank of the modular fusion category Z(Rep(G)), the Drinfeld center of Rep(G).

These reformulation are demonstrated in the linked MathOverflow post.

A.Davydov, Bogomolov multiplier, double class-preserving automorphisms, and modular invariants for orbifolds. J. Math. Phys. 55 (2014), no. 9, 092305, 13 pp.

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