Character table for point group S6
=exp(2
i/3)=exp(2i/3)| S6 | E | C3(z) | (C3)2 | i | (S6)5 | S6 | rotations |
functions |
functions |
|---|---|---|---|---|---|---|---|---|---|
| Ag | +1 | +1 | +1 | +1 | +1 | +1 | Rz | x2+y2, z2 | - |
| Eg | +1 +1 |
+ + * |
+* + |
+1 +1 |
+ + * |
+* + |
Rx+iRy Rx-iRy |
(x2-y2, xy) (xz, yz) | - |
| Au | +1 | +1 | +1 | -1 | -1 | -1 | z | - | z3, y(3x2-y2), x(x2-3y2), z(x2+y2) |
| Eu | +1 +1 |
+ + * |
+* + |
-1 -1 |
- - * |
-* - |
x+iy x-iy |
- | (xz2, yz2) [xyz, z(x2-y2)] [x(x2+y2), y(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 | Ci , C3 |
|---|---|
| Optical Isomerism (Chirality) | no |
| Polar | no |
| dipole (p) | Au+Eu |
|---|---|
| quadrupole (d) | Ag+2Eg |
| octopole (f) | 3Au+2Eu |
| hexadecapole (g) | 3Ag+3Eg |
| 32-pole (h) | 3Au+4Eu |
| 64-pole (i) | 5Ag+4Eg |
| 128-pole (j) | 5Au+5Eu |
| 256-pole(k) | 5Ag+6Eg |
| 512-pole (l) | 7Au+6Eu |
