drotations
functions
functions
| D3d | E | 2C3 | 3C'2 | i | 2S6 | 3d |
rotations |
functions |
functions |
|---|---|---|---|---|---|---|---|---|---|
| A1g | +1 | +1 | +1 | +1 | +1 | +1 | - | x2+y2, z2 | - |
| A2g | +1 | +1 | -1 | +1 | +1 | -1 | Rz | - | - |
| Eg | +2 | -1 | 0 | +2 | -1 | 0 | (Rx, Ry) | (x2-y2, xy) (xz, yz) | - |
| A1u | +1 | +1 | +1 | -1 | -1 | -1 | - | - | x(x2-3y2) |
| A2u | +1 | +1 | -1 | -1 | -1 | +1 | z | - | y(3x2-y2), z3, z(x2+y2) |
| Eu | +2 | -1 | 0 | -2 | +1 | 0 | (x, y) | - | (xz2, yz2) [xyz, z(x2-y2)] [x(x2+y2), y(x2+y2)] |
| Number of symmetry elements | h = 12 |
| Number of irreducible representations | n = 6 |
| Abelian group | no |
| Number of subgroups | 8 |
| Subgroups | Cs , Ci , C2 , C3 , D3 , C3v , C2h , S6 |
|---|---|
| Optical Isomerism (Chirality) | no |
| Polar | no |
| Sulfur S6 | Ethane (staggered) | Cyclohexane (chair) |
|---|---|---|
| Hexamethylbenzene |
| dipole (p) | A2u+Eu |
|---|---|
| quadrupole (d) | A1g+2Eg |
| octopole (f) | A1u+2A2u+2Eu |
| hexadecapole (g) | 2A1g+A2g+3Eg |
| 32-pole (h) | A1u+2A2u+4Eu |
| 64-pole (i) | 3A1g+2A2g+4Eg |
| 128-pole (j) | 2A1u+3A2u+5Eu |
| 256-pole(k) | 3A1g+2A2g+6Eg |
| 512-pole (l) | 3A1u+4A2u+6Eu |
