## Character table for point group D6h

(x axis coincident with C'2 axis)
 D6h E 2C6 (z) 2C3 C2 3C'2 3C''2 i 2S3 2S6 h (xy) 3d 3v linear functions,rotations quadraticfunctions cubicfunctions A1g +1 +1 +1 +1 +1 +1 +1 +1 +1 +1 +1 +1 - x2+y2, z2 - A2g +1 +1 +1 +1 -1 -1 +1 +1 +1 +1 -1 -1 Rz - - B1g +1 -1 +1 -1 +1 -1 +1 -1 +1 -1 +1 -1 - - - B2g +1 -1 +1 -1 -1 +1 +1 -1 +1 -1 -1 +1 - - - E1g +2 +1 -1 -2 0 0 +2 +1 -1 -2 0 0 (Rx, Ry) (xz, yz) - E2g +2 -1 -1 +2 0 0 +2 -1 -1 +2 0 0 - (x2-y2, xy) - A1u +1 +1 +1 +1 +1 +1 -1 -1 -1 -1 -1 -1 - - - A2u +1 +1 +1 +1 -1 -1 -1 -1 -1 -1 +1 +1 z - z3, z(x2+y2) B1u +1 -1 +1 -1 +1 -1 -1 +1 -1 +1 -1 +1 - - x(x2-3y2) B2u +1 -1 +1 -1 -1 +1 -1 +1 -1 +1 +1 -1 - - y(3x2-y2) E1u +2 +1 -1 -2 0 0 -2 -1 +1 +2 0 0 (x, y) - (xz2, yz2) [x(x2+y2), y(x2+y2)] E2u +2 -1 -1 +2 0 0 -2 +1 +1 -2 0 0 - - [xyz, z(x2-y2)]

 Cs (3) , Ci , C2 (3) , C3 , C6 , D2 , D3 (2) , D6 , C2v (3) , C3v (2) , C6v , C2h (3) , C3h , C6h , D2h , D3h (2) , D3d (2) , S6 Number of symmetry elements h = 24 Number of irreducible representations n = 12 Abelian group no Number of subgroups 30 Number of distinct subgroups 18 Subgroups (Number of different orientations) Optical Isomerism (Chirality) no Polar no

## Reduction formula for point group D6h

Type of representation

general 3N vib

E 2C6 (z) 2C3 C2 3C'2 3C''2 i 2S3 2S6 h (xy) 3d 3v

## Multipoles

dipole (p) A2u+E1u A1g+E1g+E2g A2u+B1u+B2u+E1u+E2u A1g+B1g+B2g+E1g+2E2g A2u+B1u+B2u+2E1u+2E2u 2A1g+A2g+B1g+B2g+2E1g+2E2g A1u+2A2u+B1u+B2u+3E1u+2E2u 2A1g+A2g+B1g+B2g+3E1g+3E2g A1u+2A2u+2B1u+2B2u+3E1u+3E2u