A lower-bound for the number of conjugacy classes of $A_n$

We establish a sharp lower-bound for the number of conjugacy classes $k(A_n)$ in the alternating group $A_n$, for $n\ge 3$. Namely, we show that $k\left(A_n\right)\ge \frac{k\left(A_7\right)}{{\log }_2\mid A_7\mid }\cdot {\log }_2\mid A_n\mid$ with equality if, and only if, $n=7$. The observations leading towards this result were obtained through a genetic algorithm developed to search for groups having certain properties.