When additional n-two-fold axes perpendicular to … are present, but no mirror planes, then the … groups are generated. Addition of a … plane to the rotation symmetry elements of a … group generates the … groups. Similar to the … groups an … symmetry axis is also produced (if n is even an inversion center will be present). The product … (where C2 is associated with n …C2 axes in the … group) generates vertical mirror planes so that the … group also contains … planes (n odd) or …and … planes (n even). If in addition to the elements of a … group an … axis is present, then the … groups are obtained. The product … (C2 belngs to a C2 axis perpendicular to the n-fold axis) yields the operation … so that an additional n dihedral mirror planes are requied.