| S4 | E | S4 | C2 | (S4)3 | rotations |
functions |
functions |
|---|---|---|---|---|---|---|---|
| A | +1 | +1 | +1 | +1 | Rz | x2+y2, z2 | xyz, z(x2-y2) |
| B | +1 | -1 | +1 | -1 | z | x2-y2, xy | z3, z(x2+y2) |
| E | +1 +1 |
+i -i |
-1 -1 |
-i +i |
x+iy; Rx+iRy x-iy; Rx-iRy |
(xz, yz) | (xz2, yz2) (xy2, x2y) (x3, y3) |
| Number of symmetry elements | h = 4 |
| Number of irreducible representations | n = 4 |
| Number of real irreducible representations | n = 3 |
| Abelian group | yes |
| Number of subgroups | 1 |
| Subgroup | C2 |
|---|---|
| Optical Isomerism (Chirality) | no |
| Polar | no |
| 1,3,5,7-Tetrachlorocyclooctatetraene | Tetrachloroneopentane | Tetraphenylmethane |
|---|
| dipole (p) | B+E |
|---|---|
| quadrupole (d) | A+2B+E |
| octopole (f) | 2A+B+2E |
| hexadecapole (g) | 3A+2B+2E |
| 32-pole (h) | 2A+3B+3E |
| 64-pole (i) | 3A+4B+3E |
| 128-pole (j) | 4A+3B+4E |
| 256-pole(k) | 5A+4B+4E |
| 512-pole (l) | 4A+5B+5E |