Invariants
| Weight: | $2$ |
| Degree: | $2$ |
| $\mathbb{R}$-dimension: | $1$ |
| Components: | $163840$ |
| Contained in: | $\mathrm{U}(2)$ |
| Rational: | $\mathrm{False}$ |
Identity Component
| Name: | $\mathrm{U}(1)$ |
| Index: | $163840$ |
| $\mathbb{R}$-dimension: | $1$ |
| Description: | $\left\{\begin{bmatrix}\alpha&0\\0&\bar\alpha\end{bmatrix}:\alpha\bar\alpha = 1,\ \alpha\in\mathbb{C}\right\}$ |
Component Group
| Name: | $D_{81920}$ |
| Order: | $163840$ |
| Abelian: | $\mathrm{False}$ |
| Generators: | $\left\{\begin{bmatrix} 0 & 1\\ -1 & 0\end{bmatrix}, \begin{bmatrix} 1 & 0 \\ 0 & \zeta_{81920}\end{bmatrix}\right\}$ |
Subgroups and Supergroups
| Maximal Subgroups: | $\mathrm{U}(1)[D_{40960}]$, $\mathrm{U}(1)[D_{16384}]$ |
| Minimal Supergroups: | $\mathrm{U}(1)[D_{163840}]$, $\mathrm{U}(1)[D_{245760}]$, $\mathrm{U}(1)[D_{409600}]$, $\ldots$ |
Moment Statistics
| $x$ | $\mathrm{E}[x^{0}]$ | $\mathrm{E}[x^{1}]$ | $\mathrm{E}[x^{2}]$ | $\mathrm{E}[x^{3}]$ | $\mathrm{E}[x^{4}]$ | $\mathrm{E}[x^{5}]$ | $\mathrm{E}[x^{6}]$ | $\mathrm{E}[x^{7}]$ | $\mathrm{E}[x^{8}]$ | $\mathrm{E}[x^{9}]$ | $\mathrm{E}[x^{10}]$ | $\mathrm{E}[x^{11}]$ | $\mathrm{E}[x^{12}]$ |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| $a_1$ | $1$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ |