Generalized cluster algebras that are Krull domains can have any finitely generated abelian group as their class group, including finite ones with torsion.
[GLS13] Christof Geiss, Bernard Leclerc, and Jan Schr¨ oer
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Every finitely generated abelian group is the class group of a generalized cluster algebra
Generalized cluster algebras that are Krull domains can have any finitely generated abelian group as their class group, including finite ones with torsion.