| D4d | E | 2S8 | 2C4 | 2S8³ | C2 | 4C2′ | 4σd | 线性 / 转动linear, rotations | 二次quadratic |
|---|---|---|---|---|---|---|---|---|---|
| A1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | x²+y², z² | |
| A2 | 1 | 1 | 1 | 1 | 1 | −1 | −1 | Rz | |
| B1 | 1 | −1 | 1 | −1 | 1 | 1 | −1 | ||
| B2 | 1 | −1 | 1 | −1 | 1 | −1 | 1 | z | |
| E1 | 2 | √2 | 0 | −√2 | −2 | 0 | 0 | (x, y) | |
| E2 | 2 | 0 | −2 | 0 | 2 | 0 | 0 | (x²−y², xy) | |
| E3 | 2 | −√2 | 0 | √2 | −2 | 0 | 0 | (Rx, Ry) | (xz, yz) |
| 阶 hOrder h | 16 |
|---|---|
| 类数Classes | 7 |
| 所属族Family | Dnd |
| 代表分子Examples | S₈（冠状）, Mn₂(CO)₁₀, [XeF₈]²⁻S₈ (crown), Mn₂(CO)₁₀, [XeF₈]²⁻ |
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.