The D∞h point groupD∞h is one of the two linear point groups: its principal axis is of infinite order, so it carries infinitely many symmetry operations in 6 classes.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.

Carbon dioxide (CO2): Linear and the same from both ends, so it has an inversion centre.

Ethyne (C2H2): Linear and centrosymmetric: the classic mutual-exclusion example.

The 6 conjugacy classes of D∞h, in the order a character table prints them.

Class

Operations in it

2C∞

∞σv

infinitely many

2S∞

∞C2

infinitely many

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: