On the critical group of the missing Moore graph

We consider the critical group of a hypothetical Moore graph of diameter 2 and valency 57. Determining this group is equivalent to finding the Smith normal form of the Laplacian matrix of such a graph. We show that all of the Sylow p-subgroups of the critical group must be elementary abelian with the exception of p=5. We prove that the 5-rank of the Laplacian matrix determines the critical group up to two possibilities.