T | E | 4C_{3} | 4(C_{3})^{2} | 3C_{2} | rotations |
functions |
functions |
---|---|---|---|---|---|---|---|
A | +1 | +1 | +1 | +1 | - | x^{2}+y^{2}+z^{2} | xyz |
E | +1 +1 |
+ +^{*} |
+^{*} + |
+1 +1 |
- | (x^{2}-y^{2}, 2z^{2}-x^{2}-y^{2}) | - |
T | +3 | 0 | 0 | -1 | (x, y, z) (R_{x}, R_{y}, R_{z}) | (xy, xz, yz) | (x^{3}, y^{3}, z^{3}) (xy^{2}, x^{2}z, yz^{2}) (xz^{2}, x^{2}y, y^{2}z) |
Number of symmetry elements | h = 12 |
Number of irreducible representations | n = 4 |
Number of real irreducible representations | n = 3 |
Abelian group | no |
Subgroups | C_{2} , C_{3} , D_{2} |
---|---|
Optical Isomerism (Chirality) | yes |
dipole (p) | T |
---|---|
quadrupole (d) | E+T |
octopole (f) | A+2T |
hexadecapole (g) | A+E+2T |
32-pole (h) | E+3T |
64-pole (i) | 2A+E+3T |
128-pole (j) | A+E+4T |
256-pole(k) | A+2E+4T |
512-pole (l) | 2A+E+5T |