| D3d | E | 2C3 | 3C2 | i | 2S6 | 3σd | 线性 / 转动linear, rotations | 二次quadratic |
|---|---|---|---|---|---|---|---|---|
| A1g | 1 | 1 | 1 | 1 | 1 | 1 | x²+y², z² | |
| A2g | 1 | 1 | −1 | 1 | 1 | −1 | Rz | |
| Eg | 2 | −1 | 0 | 2 | −1 | 0 | (Rx, Ry) | (x²−y², xy), (xz, yz) |
| A1u | 1 | 1 | 1 | −1 | −1 | −1 | ||
| A2u | 1 | 1 | −1 | −1 | −1 | 1 | z | |
| Eu | 2 | −1 | 0 | −2 | 1 | 0 | (x, y) |
| 阶 hOrder h | 12 |
|---|---|
| 类数Classes | 6 |
| 所属族Family | Dnd |
| 代表分子Examples | 乙烷（交叉式）, 环己烷（椅式）, [Mn₂(CO)₁₀]ethane (staggered), cyclohexane (chair), [Mn₂(CO)₁₀] |
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.