Optimal factor group for nonsymmorphic space groups

The construction of the irreducible representations of single and double nonsymmorphic space groups is discussed. The proof is given that for any symmetry element where the nonsymmorphism plays a role there is a finite group of lowest order such that its irreducible representations engender all the allowable representations of the little group. For most high symmetry elements the order of this optimal factor group is only twice the order of the corresponding point group of the wave vector. The computational advantages of using this group instead of other known factor groups are stressed.