S_{6} | E | C_{3}(z) | (C_{3})^{2} | i | (S_{6})^{5} | S_{6} | rotations |
functions |
functions |
---|---|---|---|---|---|---|---|---|---|
A_{g} | +1 | +1 | +1 | +1 | +1 | +1 | R_{z} | x^{2}+y^{2}, z^{2} | - |
E_{g} | +1 +1 |
+ +^{*} |
+^{*} + |
+1 +1 |
+ +^{*} |
+^{*} + |
R_{x}+iR_{y} R_{x}-iR_{y} |
(x^{2}-y^{2}, xy) (xz, yz) | - |
A_{u} | +1 | +1 | +1 | -1 | -1 | -1 | z | - | z^{3}, y(3x^{2}-y^{2}), x(x^{2}-3y^{2}), z(x^{2}+y^{2}) |
E_{u} | +1 +1 |
+ +^{*} |
+^{*} + |
-1 -1 |
- -^{*} |
-^{*} - |
x+iy x-iy |
- | (xz^{2}, yz^{2}) [xyz, z(x^{2}-y^{2})] [x(x^{2}+y^{2}), y(x^{2}+y^{2})] |
Number of symmetry elements | h = 6 |
Number of irreducible representations | n = 6 |
Number of real irreducible representations | n = 4 |
Abelian group | yes |
Subgroups | C_{i} , C_{3} |
---|---|
Optical Isomerism (Chirality) | no |
dipole (p) | A_{u}+E_{u} |
---|---|
quadrupole (d) | A_{g}+2E_{g} |
octopole (f) | 3A_{u}+2E_{u} |
hexadecapole (g) | 3A_{g}+3E_{g} |
32-pole (h) | 3A_{u}+4E_{u} |
64-pole (i) | 5A_{g}+4E_{g} |
128-pole (j) | 5A_{u}+5E_{u} |
256-pole(k) | 5A_{g}+6E_{g} |
512-pole (l) | 7A_{u}+6E_{u} |