The Oh point groupOh carries 48 symmetry operations in 10 classes, around a principal axis of order 4. A character table of the group therefore has 10 columns and as many irreducible representations.It contains an improper operation, so no molecule in it is chiral. No direction is left invariant, so a molecule in it has no permanent dipole. It contains the inversion, so its vibrations and its electronic states divide into g and u, and no vibration is both infrared and Raman active.In Hermann-Mauguin notation it is m-3m, written in full as 4/m -3 2/m, and it is one of the crystal classes of the cubic system. A diffraction pattern from a crystal in it shows the Laue symmetry m-3m.

Sulfur hexafluoride (SF6): A regular octahedron: three C4, four C3, and an inversion centre.

Cubane (C8H8): Eight carbons at the corners of a cube, each hydrogen on a body diagonal.

The 10 conjugacy classes of Oh, in the order a character table prints them.

Class

Operations in it

8C3

6C2

6C4

3C2(=C4²)

6S4

8S6

3σh

6σd

Molecular point groups with their operations and character tables, the 230 space groups with a cell builder, and the 17 wallpaper and 7 frieze groups drawn live. The tool needs JavaScript, and WebGL2 for the 3D views; these are the pages it offers: