| D6h | E | 2C6 | 2C3 | C2 | 3C2′ | 3C2″ | i | 2S3 | 2S6 | σh | 3σd | 3σv | 线性 / 转动linear, rotations | 二次quadratic |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| A1g | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | x²+y², z² | |
| A2g | 1 | 1 | 1 | 1 | −1 | −1 | 1 | 1 | 1 | 1 | −1 | −1 | Rz | |
| B1g | 1 | −1 | 1 | −1 | 1 | −1 | 1 | −1 | 1 | −1 | 1 | −1 | ||
| B2g | 1 | −1 | 1 | −1 | −1 | 1 | 1 | −1 | 1 | −1 | −1 | 1 | ||
| E1g | 2 | 1 | −1 | −2 | 0 | 0 | 2 | 1 | −1 | −2 | 0 | 0 | (Rx, Ry) | (xz, yz) |
| E2g | 2 | −1 | −1 | 2 | 0 | 0 | 2 | −1 | −1 | 2 | 0 | 0 | (x²−y², xy) | |
| A1u | 1 | 1 | 1 | 1 | 1 | 1 | −1 | −1 | −1 | −1 | −1 | −1 | ||
| A2u | 1 | 1 | 1 | 1 | −1 | −1 | −1 | −1 | −1 | −1 | 1 | 1 | z | |
| B1u | 1 | −1 | 1 | −1 | 1 | −1 | −1 | 1 | −1 | 1 | −1 | 1 | ||
| B2u | 1 | −1 | 1 | −1 | −1 | 1 | −1 | 1 | −1 | 1 | 1 | −1 | ||
| E1u | 2 | 1 | −1 | −2 | 0 | 0 | −2 | −1 | 1 | 2 | 0 | 0 | (x, y) | |
| E2u | 2 | −1 | −1 | 2 | 0 | 0 | −2 | 1 | 1 | −2 | 0 | 0 |
| 阶 hOrder h | 24 |
|---|---|
| 类数Classes | 12 |
| 所属族Family | Dnh |
| 代表分子Examples | 苯, 二苯铬 Cr(C₆H₆)₂（重叠式）, 晕苯benzene, eclipsed Cr(C₆H₆)₂, coronene |
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.