S_{10} | E | C_{5} | (C_{5})^{2} | (C_{5})^{3} | (C_{5})^{4} | i | (S_{10})^{7} | (S_{10})^{9} | S_{10} | (S_{10})^{3} | rotations |
functions |
functions |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
A_{g} | +1 | +1 | +1 | +1 | +1 | +1 | +1 | +1 | +1 | +1 | R_{z} | z^{2}, x^{2}+y^{2} | - |
E_{1g} | +1 +1 |
+ +^{*} | +^{2} +^{2*} | +^{2*} +^{2} | +^{*} + |
+1 +1 |
+ +^{*} |
+^{2} +^{2*} |
+^{2*} +^{2} |
+^{*} + |
R_{x}+iR_{y} R_{x}-iR_{y} |
(xz, yz) | - |
E_{2g} | +1 +1 |
+^{2} +^{2*} | +^{*} + | + +^{*} | +^{2*} +^{2} |
+1 +1 |
+^{2} +^{2*} |
+^{*} + |
+ +^{*} |
+^{2*} +^{2} |
- | (x^{2}-y^{2}, xy) | - |
A_{u} | +1 | +1 | +1 | +1 | +1 | -1 | -1 | -1 | -1 | -1 | z | - | z^{3}, z(x^{2}+y^{2}) |
E_{1u} | +1 +1 |
+ +^{*} | +^{2} +^{2*} | +^{2*} +^{2} | +^{*} + |
-1 -1 |
- -^{*} |
-^{2} -^{2*} |
-^{2*} -^{2} |
-^{*} - |
x+iy x-iy |
- | (xz^{2}, yz^{2}) [x(x^{2}+y^{2}), y(x^{2}+y^{2})] |
E_{2u} | +1 +1 |
+^{2} +^{2*} | +^{*} + | + +^{*} | +^{2*} +^{2} |
-1 -1 |
-^{2} -^{2*} |
-^{*} - |
- -^{*} |
-^{2*} -^{2} |
- | - | [xyz, z(x^{2}-y^{2})] [y(3x^{2}-y^{2}), x(x^{2}-3y^{2})] |
Number of symmetry elements | h = 10 |
Number of irreducible representations | n = 10 |
Number of real irreducible representations | n = 6 |
Abelian group | yes |
Number of subgroups | 2 |
Subgroups | C_{i} , C_{5} |
---|---|
Optical Isomerism (Chirality) | no |
dipole (p) | A_{u}+E_{1u} |
---|---|
quadrupole (d) | A_{g}+E_{1g}+E_{2g} |
octopole (f) | A_{u}+E_{1u}+2E_{2u} |
hexadecapole (g) | A_{g}+2E_{1g}+2E_{2g} |
32-pole (h) | 3A_{u}+2E_{1u}+2E_{2u} |
64-pole (i) | 3A_{g}+3E_{1g}+2E_{2g} |
128-pole (j) | 3A_{u}+3E_{1u}+3E_{2u} |
256-pole(k) | 3A_{g}+3E_{1g}+4E_{2g} |
512-pole (l) | 3A_{u}+4E_{1u}+4E_{2u} |