Several authors have proposed approximation hierarchies for Copositive Programming. These hierarchies converge to the optimal value, but they grow exponentially in size and quickly become unsolvable. We show that if the original problem has symmetry, this symmetry can be used to reduce the size of each level of the hierarchy, which allows to solve higher levels of the hierarchy. As a result of our approach we are able to compute new best-bounds for the crossing number of the complete bipartite graph $K_{7,n}$.