2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/76367Let $k(G)$ be the number of conjugacy classes of finite groups $G$ and $π_e(G)$ be the set of the orders of elements in $G$. Then there exists a non-negative integer $k$ such that $k(G)=|π_e(G)|+k$. We call such groups to be $co(k)$ groups. This paper classifies all finite $co(1)$ groups. They are isomorphic to one of the following groups: $A_5, L_2(7), S_5, Z_3, Z_4, S_4, A_4$, $D_{10}, Hol(Z_5)$, or $Z_3\rtimes Z_4$.15 pagesGroup Theory20D60, 20D05, 20D10text