## Character table for point group D6d

(x axis coincident with C'2 axis)
 D6d E 2S12 2C6 2S4 2C3 2(S12)5 C2 6C'2 6d linear functions,rotations quadraticfunctions cubicfunctions A1 +1 +1 +1 +1 +1 +1 +1 +1 +1 - x2+y2, z2 - A2 +1 +1 +1 +1 +1 +1 +1 -1 -1 Rz - - B1 +1 -1 +1 -1 +1 -1 +1 +1 -1 - - - B2 +1 -1 +1 -1 +1 -1 +1 -1 +1 z - z3, z(x2+y2) E1 +2 +(3)½ +1 0 -1 -(3)½ -2 0 0 (x, y) - (xz2, yz2) [x(x2+y2), y(x2+y2)] E2 +2 +1 -1 -2 -1 +1 +2 0 0 - (x2-y2, xy) - E3 +2 0 -2 0 +2 0 -2 0 0 - - [y(3x2-y2), x(x2-3y2)] E4 +2 -1 -1 +2 -1 -1 +2 0 0 - - [xyz, z(x2-y2)] E5 +2 -(3)½ +1 0 -1 +(3)½ -2 0 0 (Rx, Ry) (xz, yz) -

 Cs , C2 (2) , C3 , C6 , D2 , D3 , D6 , C2v , C3v , C6v , D2d , S4 , S12 Number of symmetry elements h = 24 Number of irreducible representations n = 9 Abelian group no Number of subgroups 14 Number of distinct subgroups 13 Subgroups (Number of different orientations) Optical Isomerism (Chirality) no Polar no

## Reduction formula for point group D6d

Type of representation

general 3N vib

E 2S12 2C6 2S4 2C3 2(S12)5 C2 6C'2 6d

## Multipoles

dipole (p) B2+E1 A1+E2+E5 B2+E1+E3+E4 A1+E2+E3+E4+E5 B2+E1+E2+E3+E4+E5 A1+B1+B2+E1+E2+E3+E4+E5 A1+A2+B2+E1+E2+E3+E4+2E5 A1+B1+B2+2E1+E2+E3+2E4+E5 A1+A2+B2+E1+2E2+2E3+E4+2E5