def get_exchange_group_info(self, symprec=1e-2, angle_tolerance=5.0):
        """
        Returns the information on the symmetry of the Hamiltonian
        describing the exchange energy of the system, taking into
        account relative direction of magnetic moments but not their
        absolute direction.

        This is not strictly accurate (e.g. some/many atoms will
        have zero magnetic moments), but defining symmetry this
        way is a useful way of keeping track of distinct magnetic
        orderings within pymatgen.

        :param symprec: same as SpacegroupAnalyzer
        :param angle_tolerance: same as SpacegroupAnalyzer
        :return: spacegroup_symbol, international_number
        """

        structure = self.get_structure_with_spin()

        return structure.get_space_group_info(
            symprec=symprec, angle_tolerance=angle_tolerance
        )