The notion of symmetry groups is introduced and the representation of such groups is discussed. It is shown that the operator for the eigencurrents on a conducting body is invariant under the group of symmetry operations of the structure. The eigencurrents are shown to provide bases for the irreducible representations of the symmetry group. It is further proven that expansion of the current in terms of functions belonging to the irreducible representations of the symmetry group of the structure leads to block diagonalization of the matrix representations of the operator. Basis functions for bodies of revolution are discussed. Finally, perturbations are considered and it is argued that symmetry determines exactly the splitting of any degenerate resonances of the unperturbed conducting body. (Author).