The characteristically simple Beauville group conjecture

A characteristically simple group is a finite group isomorphic to $H^k$, where $H$ is finite simple and $k$ is a positive integer. The characteristically simple Beauville group conjecture. For every finite characteristically simple group $G$, $G$ is Beauville if and only if $G$ is 2-generated and is not isomorphic to the alternating group $A_5$. The source reports verification for several families and computationally for all such groups of order at most $10^{30}$, while leaving the general statement unresolved.