D_{3h} | E | 2C_{3} (z) | 3C'_{2} | _{h} (xy) | 2S_{3} | 3_{v} | rotations |
functions |
functions |
---|---|---|---|---|---|---|---|---|---|
A'_{1} | +1 | +1 | +1 | +1 | +1 | +1 | - | x^{2}+y^{2}, z^{2} | x(x^{2}-3y^{2}) |
A'_{2} | +1 | +1 | -1 | +1 | +1 | -1 | R_{z} | - | y(3x^{2}-y^{2}) |
E' | +2 | -1 | 0 | +2 | -1 | 0 | (x, y) | (x^{2}-y^{2}, xy) | (xz^{2}, yz^{2}) [x(x^{2}+y^{2}), y(x^{2}+y^{2})] |
A''_{1} | +1 | +1 | +1 | -1 | -1 | -1 | - | - | - |
A''_{2} | +1 | +1 | -1 | -1 | -1 | +1 | z | - | z^{3}, z(x^{2}+y^{2}) |
E'' | +2 | -1 | 0 | -2 | +1 | 0 | (R_{x}, R_{y}) | (xz, yz) | [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 | 7 |
Subgroups
(Number of different orientations) |
C_{s} (2) , C_{2} , C_{3} , D_{3} , C_{2v} , C_{3v} , C_{3h} |
---|---|
Optical Isomerism (Chirality) | no |
Polar | no |
Borontrifluoride | Phosphoruspentafluoride | Ethane (eclipsed) |
---|---|---|
Cyclopropane | Ironpentacarbonyl | Borazine |
Prismane | Diironnonacarbonyl | Triphenylene |
Triptycene |
dipole (p) | E'+A''_{2} |
---|---|
quadrupole (d) | A'_{1}+E'+E'' |
octopole (f) | A'_{1}+A'_{2}+E'+A''_{2}+E'' |
hexadecapole (g) | A'_{1}+2E'+A''_{1}+A''_{2}+E'' |
32-pole (h) | A'_{1}+A'_{2}+2E'+A''_{2}+2E'' |
64-pole (i) | 2A'_{1}+A'_{2}+2E'+A''_{1}+A''_{2}+2E'' |
128-pole (j) | A'_{1}+A'_{2}+3E'+A''_{1}+2A''_{2}+2E'' |
256-pole(k) | 2A'_{1}+A'_{2}+3E'+A''_{1}+A''_{2}+3E'' |
512-pole (l) | 2A'_{1}+2A'_{2}+3E'+A''_{1}+2A''_{2}+3E'' |