  Let $G$ be a finite group. The group pseudo-algebra of $G$ is defined as the
multi-set $C(G)=\{(d,m_G(d))\mid d\in{\rm Cod}(G)\},$ where $m_G(d)$ is the
number of irreducible characters of with codegree $d\in {\rm Cod}(G)$. 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 \cite{Moreto2023}.
In addition, we also discuss under what hypothesis two $p$-groups with the same
group pseudo-algebra will be isomorphic.
