Alternating-group conjecture for diamond-shaped tableau groups

Let $G_\lambda$ be the group associated with a Young diagram $\lambda$, and let $\dim\lambda$ denote the dimension of the corresponding representation. Consider the diagrams $\lambda\in\{(4,2^2),(6,3),(4^2,1)\}$, for which the computed order of $G_\lambda$ is $(\dim\lambda)!/2$. Alternating-group conjecture. In these cases, $G_\lambda$ is isomorphic to the alternating group $A_{\dim\lambda}$. These cases arise among the computational results for diagrams with at most nine cells; the assertion is based on the computed group orders and remains stated as a conjecture in the source.