Character table for point group Th
=exp(2
i/3)=exp(2i/3)| Th | E | 4C3 | 4(C3)2 | 3C2 | i | 4(S6)5 | 4S6 | 3 h |
rotations |
functions |
functions |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Ag | +1 | +1 | +1 | +1 | +1 | +1 | +1 | +1 | - | x2+y2+z2 | - |
| Eg | +1 +1 |
+ + * |
+* + |
+1 +1 |
+1 +1 |
+ + * |
+* + |
+1 +1 |
- | (x2-y2, 2z2-x2-y2) | - |
| Tg | +3 | 0 | 0 | -1 | +3 | 0 | 0 | -1 | (Rx, Ry, Rz) | (xy, xz, yz) | - |
| Au | +1 | +1 | +1 | +1 | -1 | -1 | -1 | -1 | - | - | xyz |
| Eu | +1 +1 |
+ + * |
+* + |
+1 +1 |
-1 -1 |
- - * |
-* - |
-1 -1 |
- | - | - |
| Tu | +3 | 0 | 0 | -1 | -3 | 0 | 0 | +1 | (x, y, z) | - | (x3, y3, z3) (xy2, x2z, yz2) (xz2, x2y, y2z) |
| Number of symmetry elements | h = 24 |
| Number of irreducible representations | n = 8 |
| Number of real irreducible representations | n = 6 |
| Abelian group | no |
| Number of subgroups | 10 |
| Subgroups | Cs , Ci , C2 , C3 , D2 , C2v , C2h , D2h , S6 , T |
|---|---|
| Optical Isomerism (Chirality) | no |
| Polar | no |
| [Mg(H2O)6]2+-Ion | Bromofullerene C60Br24 |
|---|
| dipole (p) | Tu |
|---|---|
| quadrupole (d) | Eg+Tg |
| octopole (f) | Au+2Tu |
| hexadecapole (g) | Ag+Eg+2Tg |
| 32-pole (h) | Eu+3Tu |
| 64-pole (i) | 2Ag+Eg+3Tg |
| 128-pole (j) | Au+Eu+4Tu |
| 256-pole(k) | Ag+2Eg+4Tg |
| 512-pole (l) | 2Au+Eu+5Tu |
