Character table for point group C3h
=exp(2
i/3)=exp(2i/3)| C3h | E | C3(z) | (C3)2 |  h |
S3 | (S3)5 | rotations |
functions |
functions |
|---|---|---|---|---|---|---|---|---|---|
| A' | +1 | +1 | +1 | +1 | +1 | +1 | Rz | x2+y2, z2 | y(3x2-y2), x(x2-3y2) |
| E' | +1 +1 |
+ + * |
+* + |
+1 +1 |
+ + * |
+* + |
x+iy x-iy |
(x2-y2, xy) | (xz2, yz2) [x(x2+y2), y(x2+y2)] |
| A'' | +1 | +1 | +1 | -1 | -1 | -1 | z | - | z3, z(x2+y2) |
| E'' | +1 +1 |
+ + * |
+* + |
-1 -1 |
- - * |
-* - |
Rx+iRy Rx-iRy |
(xz, yz) | [xyz, z(x2-y2)] |
| Number of symmetry elements | h = 6 |
| Number of irreducible representations | n = 6 |
| Number of real irreducible representations | n = 4 |
| Abelian group | yes |
| Number of subgroups | 2 |
| Subgroups | Cs , C3 |
|---|---|
| Optical Isomerism (Chirality) | no |
| Polar | no |
| Boric Acid | 1,3,5-Trihydroxybenzene | Tricyclo[3.3.3.0(1,5)]undecane |
|---|---|---|
| Bicyclo[3.3.3]undecane |
| dipole (p) | E'+A'' |
|---|---|
| quadrupole (d) | A'+E'+E'' |
| octopole (f) | 2A'+E'+A''+E'' |
| hexadecapole (g) | A'+2E'+2A''+E'' |
| 32-pole (h) | 2A'+2E'+A''+2E'' |
| 64-pole (i) | 3A'+2E'+2A''+2E'' |
| 128-pole (j) | 2A'+3E'+3A''+2E'' |
| 256-pole(k) | 3A'+3E'+2A''+3E'' |
| 512-pole (l) | 4A'+3E'+3A''+3E'' |
