D_{7h} | E | 2C_{7} | 2(C_{7})^{2} | 2(C_{7})^{3} | 7C'_{2} | _{h} | 2S_{7} | 2(S_{7})^{5} | 2(S_{7})^{3} | 7_{v} | rotations |
functions |
functions |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
A'_{1} | +1 | +1 | +1 | +1 | +1 | +1 | +1 | +1 | +1 | +1 | - | x^{2}+y^{2}, z^{2} | - |
A'_{2} | +1 | +1 | +1 | +1 | -1 | +1 | +1 | +1 | +1 | -1 | R_{z} | - | - |
E'_{1} | +2 | +2cos(2/7) | +2cos(4/7) | +2cos(6/7) | 0 | +2 | +2cos(2/7) | +2cos(4/7) | +2cos(6/7) | 0 | (x, y) | - | (xz^{2}, yz^{2}) [x(x^{2}+y^{2}), y(x^{2}+y^{2})] |
E'_{2} | +2 | +2cos(4/7) | +2cos(6/7) | +2cos(2/7) | 0 | +2 | +2cos(4/7) | +2cos(6/7) | +2cos(2/7) | 0 | - | (x^{2}-y^{2}, xy) | - |
E'_{3} | +2 | +2cos(6/7) | +2cos(2/7) | +2cos(4/7) | 0 | +2 | +2cos(6/7) | +2cos(2/7) | +2cos(4/7) | 0 | - | - | [y(3x^{2}-y^{2}), x(x^{2}-3y^{2})] |
A''_{1} | +1 | +1 | +1 | +1 | +1 | -1 | -1 | -1 | -1 | -1 | - | - | - |
A''_{2} | +1 | +1 | +1 | +1 | -1 | -1 | -1 | -1 | -1 | +1 | z | - | z^{3}, z(x^{2}+y^{2}) |
E''_{1} | +2 | +2cos(2/7) | +2cos(4/7) | +2cos(6/7) | 0 | -2 | -2cos(2/7) | -2cos(4/7) | -2cos(6/7) | 0 | (R_{x}, R_{y}) | (xz, yz) | - |
E''_{2} | +2 | +2cos(4/7) | +2cos(6/7) | +2cos(2/7) | 0 | -2 | -2cos(4/7) | -2cos(6/7) | -2cos(2/7) | 0 | - | - | [xyz, z(x^{2}-y^{2})] |
E''_{3} | +2 | +2cos(6/7) | +2cos(2/7) | +2cos(4/7) | 0 | -2 | -2cos(6/7) | -2cos(2/7) | -2cos(4/7) | 0 | - | - | - |
Number of symmetry elements | h = 28 |
Number of irreducible representations | n = 10 |
Abelian group | no |
Subgroups | C_{s} , C_{2} , C_{7} , D_{7} , C_{2v} , C_{7v} , C_{7h} |
---|---|
Optical Isomerism (Chirality) | no |
dipole (p) | E'_{1}+A''_{2} |
---|---|
quadrupole (d) | A'_{1}+E'_{2}+E''_{1} |
octopole (f) | E'_{1}+E'_{3}+A''_{2}+E''_{2} |
hexadecapole (g) | A'_{1}+E'_{2}+E'_{3}+E''_{1}+E''_{3} |
32-pole (h) | E'_{1}+E'_{2}+E'_{3}+A''_{2}+E''_{2}+E''_{3} |
64-pole (i) | A'_{1}+E'_{1}+E'_{2}+E'_{3}+E''_{1}+E''_{2}+E''_{3} |
128-pole (j) | A'_{1}+A'_{2}+E'_{1}+E'_{2}+E'_{3}+A''_{2}+E''_{1}+E''_{2}+E''_{3} |
256-pole(k) | A'_{1}+2E'_{1}+E'_{2}+E'_{3}+A''_{1}+A''_{2}+E''_{1}+E''_{2}+E''_{3} |
512-pole (l) | A'_{1}+A'_{2}+E'_{1}+2E'_{2}+E'_{3}+A''_{2}+2E''_{1}+E''_{2}+E''_{3} |