| Oh | E | 8C3 | 6C2 | 6C4 | 3C2(=C4²) | i | 6S4 | 8S6 | 3σh | 6σd | 线性 / 转动linear, rotations | 二次quadratic |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| A1g | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | x²+y²+z² | |
| A2g | 1 | 1 | −1 | −1 | 1 | 1 | −1 | 1 | 1 | −1 | ||
| Eg | 2 | −1 | 0 | 0 | 2 | 2 | 0 | −1 | 2 | 0 | (2z²−x²−y², x²−y²) | |
| T1g | 3 | 0 | −1 | 1 | −1 | 3 | 1 | 0 | −1 | −1 | (Rx, Ry, Rz) | |
| T2g | 3 | 0 | 1 | −1 | −1 | 3 | −1 | 0 | −1 | 1 | (xy, xz, yz) | |
| A1u | 1 | 1 | 1 | 1 | 1 | −1 | −1 | −1 | −1 | −1 | ||
| A2u | 1 | 1 | −1 | −1 | 1 | −1 | 1 | −1 | −1 | 1 | ||
| Eu | 2 | −1 | 0 | 0 | 2 | −2 | 0 | 1 | −2 | 0 | ||
| T1u | 3 | 0 | −1 | 1 | −1 | −3 | −1 | 0 | 1 | 1 | (x, y, z) | |
| T2u | 3 | 0 | 1 | −1 | −1 | −3 | 1 | 0 | 1 | −1 |
| 阶 hOrder h | 48 |
|---|---|
| 类数Classes | 10 |
| 所属族Family | 立方 Cubic |
| 代表分子Examples | SF₆, [Co(NH₃)₆]³⁺, 立方烷, NaCl 晶体中的 Na⁺ 格位SF₆, [Co(NH₃)₆]³⁺, cubane, the Na⁺ site in NaCl |
约化可约表示Reduce a representation
输入可约表示在各类上的特征标，按约化公式 \(n_i = \frac{1}{h}\sum_R g_R\,\chi(R)\,\chi_i(R)^{*}\) 求出各不可约表示出现的次数。
Enter the characters of a reducible representation; the reduction formula gives how many times each irreducible representation occurs.