| C3h | E | C3 | C3² | σh | S3 | S3⁵ | 线性 / 转动linear, rotations | 二次quadratic |
|---|---|---|---|---|---|---|---|---|
| A′ | 1 | 1 | 1 | 1 | 1 | 1 | Rz | x²+y², z² |
| E′ | 12 | ε−1 | ε*−1 | 12 | ε−1 | ε*−1 | (x, y) | (x²−y², xy) |
| ↳ 共轭conj. | 1 | ε* | ε | 1 | ε* | ε | ||
| A″ | 1 | 1 | 1 | −1 | −1 | −1 | z | |
| E″ | 12 | ε−1 | ε*−1 | −1−2 | −ε1 | −ε*1 | (Rx, Ry) | (xz, yz) |
| ↳ 共轭conj. | 1 | ε* | ε | −1 | −ε* | −ε |
\(\varepsilon = \exp(2\pi i/3)\)，\(\varepsilon^{*}\) 为其复共轭。合并后每对复共轭不可约表示相加成一个二维实表示（物理上简并）。; \(\varepsilon^{*}\) is its complex conjugate. Merging adds each conjugate pair into one two-dimensional real representation (physically degenerate).
| 阶 hOrder h | 6 |
|---|---|
| 类数Classes | 6 |
| 所属族Family | Cnh |
| 代表分子Examples | B(OH)₃（平面）, 间苯三酚B(OH)₃ (planar), phloroglucinol |
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.