D_{6} | E | 2C_{6} (z) | 2C_{3} (z) | C_{2} (z) | 3C'_{2} | 3C''_{2} | rotations |
functions |
functions |
---|---|---|---|---|---|---|---|---|---|
A_{1} | +1 | +1 | +1 | +1 | +1 | +1 | - | x^{2}+y^{2}, z^{2} | - |
A_{2} | +1 | +1 | +1 | +1 | -1 | -1 | z, R_{z} | - | z^{3}, z(x^{2}+y^{2}) |
B_{1} | +1 | -1 | +1 | -1 | +1 | -1 | - | - | x(x^{2}-3y^{2}) |
B_{2} | +1 | -1 | +1 | -1 | -1 | +1 | - | - | y(3x^{2}-y^{2}) |
E_{1} | +2 | +1 | -1 | -2 | 0 | 0 | (x, y) (R_{x}, R_{y}) | (xz, yz) | (xz^{2}, yz^{2}) [x(x^{2}+y^{2}), y(x^{2}+y^{2})] |
E_{2} | +2 | -1 | -1 | +2 | 0 | 0 | - | (x^{2}-y^{2}, xy) | [xyz, z(x^{2}-y^{2})] |
Number of symmetry elements | h = 12 |
Number of irreducible representations | n = 6 |
Abelian group | no |
Number of subgroups | 8 |
Number of distinct subgroups | 5 |
Subgroups
(Number of different orientations) |
C_{2} (3) , C_{3} , C_{6} , D_{2} , D_{3} (2) |
---|---|
Optical Isomerism (Chirality) | yes |
Bis(benzene)chromium (rotated) |
dipole (p) | A_{2}+E_{1} |
---|---|
quadrupole (d) | A_{1}+E_{1}+E_{2} |
octopole (f) | A_{2}+B_{1}+B_{2}+E_{1}+E_{2} |
hexadecapole (g) | A_{1}+B_{1}+B_{2}+E_{1}+2E_{2} |
32-pole (h) | A_{2}+B_{1}+B_{2}+2E_{1}+2E_{2} |
64-pole (i) | 2A_{1}+A_{2}+B_{1}+B_{2}+2E_{1}+2E_{2} |
128-pole (j) | A_{1}+2A_{2}+B_{1}+B_{2}+3E_{1}+2E_{2} |
256-pole(k) | 2A_{1}+A_{2}+B_{1}+B_{2}+3E_{1}+3E_{2} |
512-pole (l) | A_{1}+2A_{2}+2B_{1}+2B_{2}+3E_{1}+3E_{2} |