Invariants
| Weight: | $3$ |
| Degree: | $2$ |
| $\mathbb{R}$-dimension: | $3$ |
| Components: | $703125$ |
| Contained in: | $\mathrm{U}(2)$ |
| Rational: | $\mathrm{False}$ |
Identity Component
| Name: | $\mathrm{SU}(2)$ |
| Index: | $703125$ |
| $\mathbb{R}$-dimension: | $3$ |
| Description: | $\left\{\begin{bmatrix}\alpha&\beta\\-\bar\beta&\bar\alpha\end{bmatrix}:\alpha\bar\alpha+\beta\bar\beta = 1,\ \alpha,\beta\in\mathbb{C}\right\}$ |
Component Group
| Name: | $C_{703125}$ |
| Order: | $703125$ |
| Abelian: | $\mathrm{True}$ |
| Generators: | $\begin{bmatrix} 1 & 0 \\ 0 & \zeta_{703125}\end{bmatrix}$ |
Subgroups and Supergroups
| Maximal Subgroups: | $\mathrm{SU}(2)[C_{234375}]$, $\mathrm{SU}(2)[C_{140625}]$ |
| Minimal Supergroups: | $\mathrm{SU}(2)[C_{1406250}]$, $\mathrm{SU}(2)[C_{2109375}]$, $\mathrm{SU}(2)[C_{3515625}]$, $\ldots$ |
Moment Statistics
| $x$ | $\mathrm{E}[x^{0}]$ | $\mathrm{E}[x^{1}]$ | $\mathrm{E}[x^{2}]$ | $\mathrm{E}[x^{3}]$ | $\mathrm{E}[x^{4}]$ | $\mathrm{E}[x^{5}]$ | $\mathrm{E}[x^{6}]$ | $\mathrm{E}[x^{7}]$ | $\mathrm{E}[x^{8}]$ | $\mathrm{E}[x^{9}]$ | $\mathrm{E}[x^{10}]$ | $\mathrm{E}[x^{11}]$ | $\mathrm{E}[x^{12}]$ |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| $a_1$ | $1$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ |