On the group pseudo-algebra of finite groups

Let G be a finite group. The group pseudo-algebra of G is defined as the multi-set C(G)=\(d,mG(d)) d∈ Cod(G)\, where mG(d) is the number of irreducible characters of with codegree d∈ Cod(G). We show that there exist two finite p-groups with distinct orders that have the same group pseudo-algebra, providing an answer to Question 3.2 in {Moreto2023}. In addition, we also discuss under what hypothesis two p-groups with the same group pseudo-algebra will be isomorphic.