| O | E | 8C3 | 6C'2 | 6C4 | 3C2 =(C4)2 | rotations |
functions |
functions |
|---|---|---|---|---|---|---|---|---|
| A1 | +1 | +1 | +1 | +1 | +1 | - | x2+y2+z2 | - |
| A2 | +1 | +1 | -1 | -1 | +1 | - | - | xyz |
| E | +2 | -1 | 0 | 0 | +2 | - | (x2-y2, 2z2-x2-y2) | - |
| T1 | +3 | 0 | -1 | +1 | -1 | (x, y, z) (Rx, Ry, Rz) | - | (x3, y3, z3) [x(z2+y2), y(z2+x2), z(x2+y2)] |
| T2 | +3 | 0 | +1 | -1 | -1 | - | (xy, xz, yz) | [x(z2-y2), y(z2-x2), z(x2-y2)] |
| Number of symmetry elements | h = 24 |
| Number of irreducible representations | n = 5 |
| Abelian group | no |
| Number of subgroups | 9 |
| Number of distinct subgroups | 7 |
| Subgroups
(Number of different orientations) |
C2 (2) , C3 , C4 , D2 (2) , D3 , D4 , T |
|---|---|
| Optical Isomerism (Chirality) | yes |
| Polar | no |
| Octamethylsilsesquioxane (rotated) | Dodecaethyleneoctamine |
|---|
| dipole (p) | T1 |
|---|---|
| quadrupole (d) | E+T2 |
| octopole (f) | A2+T1+T2 |
| hexadecapole (g) | A1+E+T1+T2 |
| 32-pole (h) | E+2T1+T2 |
| 64-pole (i) | A1+A2+E+T1+2T2 |
| 128-pole (j) | A2+E+2T1+2T2 |
| 256-pole(k) | A1+2E+2T1+2T2 |
| 512-pole (l) | A1+A2+E+3T1+2T2 |