I | E | 12C_{5} | 12(C_{5})^{2} | 20C_{3} | 15C_{2} | rotations |
functions |
functions |
---|---|---|---|---|---|---|---|---|
A | +1 | +1 | +1 | +1 | +1 | - | x^{2}+y^{2}+z^{2} | - |
T_{1} | +3 | -2cos(4/5) | -2cos(2/5) | 0 | -1 | (x, y, z) (R_{x}, R_{y}, R_{z}) | - | [x(z^{2}+y^{2}), y(z^{2}+x^{2}), z(x^{2}+y^{2})] |
T_{2} | +3 | -2cos(2/5) | -2cos(4/5) | 0 | -1 | - | - | [x^{3}, y^{3}, z^{3}] |
G | +4 | -1 | -1 | +1 | 0 | - | - | [x(z^{2}-y^{2}), y(z^{2}-x^{2}), z(x^{2}-y^{2}), xyz] |
H | +5 | 0 | 0 | -1 | +1 | - | [2z^{2}-x^{2}-y^{2}, x^{2}-y^{2}, xy, xz, yz] | - |
Number of symmetry elements | h = 60 |
Number of irreducible representations | n = 5 |
Abelian group | no |
Number of subgroups | 7 |
Subgroups | C_{2} , C_{3} , C_{5} , D_{2} , D_{3} , D_{5} , T |
---|---|
Optical Isomerism (Chirality) | yes |
Polar | no |
dipole (p) | T_{1} |
---|---|
quadrupole (d) | H |
octopole (f) | T_{2}+G |
hexadecapole (g) | G+H |
32-pole (h) | T_{1}+T_{2}+H |
64-pole (i) | A+T_{1}+G+H |
128-pole (j) | T_{1}+T_{2}+G+H |
256-pole(k) | T_{2}+G+2H |
512-pole (l) | T_{1}+T_{2}+2G+H |