This document is provided by the Chemical Portal www.webqc.org C_{6} point group |
Abelian, 4(6) irreducible representations |
Subgroups: C_{2}, C_{3} |
E | C_{6} | C_{3} | C_{2} | (C_{3})^{2} | (C_{6})^{5} | linear, rotations | quadratic | |
---|---|---|---|---|---|---|---|---|
A | 1 | 1 | 1 | 1 | 1 | 1 | z, R_{z} | x^{2}+y^{2}, z^{2} |
B | 1 | -1 | 1 | -1 | 1 | -1 | ||
E_{1} | 1 1 |
e e^{*} |
-e^{*} -e |
-1 -1 |
-e -e^{*} |
e^{*} e |
x+iy; R_{x}+iR_{y} x-iy; R_{x}-iR_{y} |
(xz, yz) |
E_{2} | 1 1 |
-e^{*} -e |
-e -e^{*} |
1 1 |
-e^{*} -e |
-e -e^{*} |
(x^{2}-y^{2}, xy) |
A_{} | B_{} | E_{1} | E_{2} | |
---|---|---|---|---|
A_{} | A_{} | B_{} | E_{1} | E_{2} |
B_{} | B_{} | A_{} | E_{2} | E_{1} |
E_{1} | E_{1} | E_{2} | 2A_{}+E_{2} | 2B_{}+E_{1} |
E_{2} | E_{2} | E_{1} | 2B_{}+E_{1} | 2A_{}+E_{2} |