C_{6} | E | C_{6} | C_{3} | C_{2} | (C_{3})^{2} | (C_{6})^{5} | rotations |
functions |
functions |
---|---|---|---|---|---|---|---|---|---|
A | +1 | +1 | +1 | +1 | +1 | +1 | z, R_{z} | x^{2}+y^{2}, z^{2} | z^{3}, z(x^{2}+y^{2}) |
B | +1 | -1 | +1 | -1 | +1 | -1 | - | - | y(3x^{2}-y^{2}), x(x^{2}-3y^{2}) |
E_{1} | +1 +1 |
+ +^{*} |
-^{*} - |
-1 -1 |
- -^{*} |
+^{*} + |
x+iy; R_{x}+iR_{y} x-iy; R_{x}-iR_{y} |
(xz, yz) | (xz^{2}, yz^{2}) [x(x^{2}+y^{2}), y(x^{2}+y^{2})] |
E_{2} | +1 +1 |
-^{*} - |
- -^{*} |
+1 +1 |
-^{*} - |
- -^{*} |
- | (x^{2}-y^{2}, xy) | [xyz, z(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 |
Number of subgroups | 2 |
Subgroups | C_{2} , C_{3} |
---|---|
Optical Isomerism (Chirality) | yes |
dipole (p) | A+E_{1} |
---|---|
quadrupole (d) | A+E_{1}+E_{2} |
octopole (f) | A+2B+E_{1}+E_{2} |
hexadecapole (g) | A+2B+E_{1}+2E_{2} |
32-pole (h) | A+2B+2E_{1}+2E_{2} |
64-pole (i) | 3A+2B+2E_{1}+2E_{2} |
128-pole (j) | 3A+2B+3E_{1}+2E_{2} |
256-pole(k) | 3A+2B+3E_{1}+3E_{2} |
512-pole (l) | 3A+4B+3E_{1}+3E_{2} |