| D5h | E | 2C5 | 2C5² | 5C2 | σh | 2S5 | 2S5³ | 5σv | 线性 / 转动linear, rotations | 二次quadratic |
|---|---|---|---|---|---|---|---|---|---|---|
| A′1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | x²+y², z² | |
| A′2 | 1 | 1 | 1 | −1 | 1 | 1 | 1 | −1 | Rz | |
| E′1 | 2 | 2cos72° | 2cos144° | 0 | 2 | 2cos72° | 2cos144° | 0 | (x, y) | |
| E′2 | 2 | 2cos144° | 2cos72° | 0 | 2 | 2cos144° | 2cos72° | 0 | (x²−y², xy) | |
| A″1 | 1 | 1 | 1 | 1 | −1 | −1 | −1 | −1 | ||
| A″2 | 1 | 1 | 1 | −1 | −1 | −1 | −1 | 1 | z | |
| E″1 | 2 | 2cos72° | 2cos144° | 0 | −2 | −2cos72° | −2cos144° | 0 | (Rx, Ry) | (xz, yz) |
| E″2 | 2 | 2cos144° | 2cos72° | 0 | −2 | −2cos144° | −2cos72° | 0 |
| 阶 hOrder h | 20 |
|---|---|
| 类数Classes | 8 |
| 所属族Family | Dnh |
| 代表分子Examples | 重叠式二茂铁, IF₇, C₅H₅⁻eclipsed ferrocene, IF₇, C₅H₅⁻ |
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.