Talk at South Regional Algebra Conference, University of South Alabama, March 19 2017. Abstract:The Smith and critical groups of a graph are interesting invariants. The Smith group of a graph is the abelian group whose cyclic decomposition is given by the Smith normal form of the adjacency matrix of the graph. The critical group is the finite part of the abelian group whose cyclic decomposition is given by the Smith normal form of the Laplacian matrix of a graph. An active line of research has been to calculate the Smith and critical groups of families of strongly regular graphs. In this presentation, we shall find the elementary divisors of the strongly regular graph associated with the rank 3 permutation action of the symplectic group. This is joint work with Peter Sin. pdf