## Character table for point group Oh

 Oh E 8C3 6C2 6C4 3C2 =(C4)2 i 6S4 8S6 3h 6d linear functions,rotations quadraticfunctions cubicfunctions A1g +1 +1 +1 +1 +1 +1 +1 +1 +1 +1 - x2+y2+z2 - A2g +1 +1 -1 -1 +1 +1 -1 +1 +1 -1 - - - Eg +2 -1 0 0 +2 +2 0 -1 +2 0 - (2z2-x2-y2, x2-y2) - T1g +3 0 -1 +1 -1 +3 +1 0 -1 -1 (Rx, Ry, Rz) - - T2g +3 0 +1 -1 -1 +3 -1 0 -1 +1 - (xz, yz, xy) - A1u +1 +1 +1 +1 +1 -1 -1 -1 -1 -1 - - - A2u +1 +1 -1 -1 +1 -1 +1 -1 -1 +1 - - xyz Eu +2 -1 0 0 +2 -2 0 +1 -2 0 - - - T1u +3 0 -1 +1 -1 -3 -1 0 +1 +1 (x, y, z) - (x3, y3, z3) [x(z2+y2), y(z2+x2), z(x2+y2)] T2u +3 0 +1 -1 -1 -3 +1 0 +1 -1 - - [x(z2-y2), y(z2-x2), z(x2-y2)]

 Cs (2) , Ci , C2 (2) , C3 , C4 , D2 (2) , D3 , D4 , C2v (3) , C3v , C4v , C2h (2) , C4h , D2h (2) , D4h , D2d (2) , D3d , S4 , S6 , T , Th , Td , O Number of symmetry elements h = 48 Number of irreducible representations n = 10 Abelian group no Number of subgroups 31 Number of distinct subgroups 23 Subgroups (Number of different orientations) Optical Isomerism (Chirality) no Polar no

## Reduction formula for point group Oh

Type of representation

general 3N vib

E 8C3 6C2 6C4 3C2 =(C4)2 i 6S4 8S6 3h 6d

## Multipoles

dipole (p) T1u Eg+T2g A2u+T1u+T2u A1g+Eg+T1g+T2g Eu+2T1u+T2u A1g+A2g+Eg+T1g+2T2g A2u+Eu+2T1u+2T2u A1g+2Eg+2T1g+2T2g A1u+A2u+Eu+3T1u+2T2u