h (xy)vrotations
functions
functions
| D3h | E | 2C3 (z) | 3C'2 | h (xy) |
2S3 | 3v |
rotations |
functions |
functions |
|---|---|---|---|---|---|---|---|---|---|
| A'1 | +1 | +1 | +1 | +1 | +1 | +1 | - | x2+y2, z2 | x(x2-3y2) |
| A'2 | +1 | +1 | -1 | +1 | +1 | -1 | Rz | - | y(3x2-y2) |
| E' | +2 | -1 | 0 | +2 | -1 | 0 | (x, y) | (x2-y2, xy) | (xz2, yz2) [x(x2+y2), y(x2+y2)] |
| A''1 | +1 | +1 | +1 | -1 | -1 | -1 | - | - | - |
| A''2 | +1 | +1 | -1 | -1 | -1 | +1 | z | - | z3, z(x2+y2) |
| E'' | +2 | -1 | 0 | -2 | +1 | 0 | (Rx, Ry) | (xz, yz) | [xyz, z(x2-y2)] |
| Number of symmetry elements | h = 12 |
| Number of irreducible representations | n = 6 |
| Abelian group | no |
| Number of subgroups | 8 |
| Number of distinct subgroups | 7 |
| Subgroups
(Number of different orientations) |
Cs (2) , C2 , C3 , D3 , C2v , C3v , C3h |
|---|---|
| Optical Isomerism (Chirality) | no |
| Polar | no |
| Borontrifluoride | Phosphoruspentafluoride | Ethane (eclipsed) |
|---|---|---|
| Cyclopropane | Ironpentacarbonyl | Borazine |
| Prismane | Diironnonacarbonyl | Triphenylene |
| Triptycene | Fullerene C74 |
| dipole (p) | E'+A''2 |
|---|---|
| quadrupole (d) | A'1+E'+E'' |
| octopole (f) | A'1+A'2+E'+A''2+E'' |
| hexadecapole (g) | A'1+2E'+A''1+A''2+E'' |
| 32-pole (h) | A'1+A'2+2E'+A''2+2E'' |
| 64-pole (i) | 2A'1+A'2+2E'+A''1+A''2+2E'' |
| 128-pole (j) | A'1+A'2+3E'+A''1+2A''2+2E'' |
| 256-pole(k) | 2A'1+A'2+3E'+A''1+A''2+3E'' |
| 512-pole (l) | 2A'1+2A'2+3E'+A''1+2A''2+3E'' |
