Character table for point group C3
=exp(2
i/3)=exp(2i/3)| C3 | E | C3 | (C3)2 | rotations |
functions |
functions |
|---|---|---|---|---|---|---|
| A | +1 | +1 | +1 | z, Rz | x2+y2, z2 | z3, y(3x2-y2), x(x2-3y2), z(x2+y2) |
| E | +1 +1 |
+ + * |
+* + |
x+iy; Rx+iRy x-iy; Rx-iRy |
(x2-y2, xy) (yz, xz) | (xz2, yz2) [xyz, z(x2-y2)] [x(x2+y2), y(x2+y2)] |
| Number of symmetry elements | h = 3 |
| Number of irreducible representations | n = 3 |
| Number of real irreducible representations | n = 2 |
| Abelian group | yes |
| Optical Isomerism (Chirality) | yes |
| Polar | yes |
| 1,1,1-Trichloroethane (rotated) | Triphenylmethane |
|---|
| dipole (p) | A+E |
|---|---|
| quadrupole (d) | A+2E |
| octopole (f) | 3A+2E |
| hexadecapole (g) | 3A+3E |
| 32-pole (h) | 3A+4E |
| 64-pole (i) | 5A+4E |
| 128-pole (j) | 5A+5E |
| 256-pole(k) | 5A+6E |
| 512-pole (l) | 7A+6E |
