Invariants
| Weight: | $1$ |
| Degree: | $4$ |
| $\mathbb{R}$-dimension: | $1$ |
| Components: | $12$ |
| Contained in: | $\mathrm{USp}(4)$ |
| Rational: | $\mathrm{True}$ |
Identity Component
| Name: | $\mathrm{U}(1)_2$ |
| Index: | $12$ |
| $\mathbb{R}$-dimension: | $1$ |
| Description: | $\left\{\begin{bmatrix}\mathrm{diag}_2(\alpha)&0\\0&\mathrm{diag}_2(\bar\alpha)\end{bmatrix}: \alpha\bar\alpha = 1,\ \alpha\in\mathbb{C}\right\},\ \mathrm{diag}_2(\alpha):=\begin{bmatrix}\alpha&0\\0&\alpha\end{bmatrix}$ |
Component Group
| Name: | $D_6$ |
| Order: | $12$ |
| Abelian: | $\mathrm{False}$ |
Subgroups and Supergroups
| Maximal Subgroups: | $D_2$, $D_3$, $C_6$ |
| Minimal Supergroups: | $J(D_6)$ |
Moment Statistics
| $x$ | $\mathrm{E}[x^{0}]$ | $\mathrm{E}[x^{1}]$ | $\mathrm{E}[x^{2}]$ | $\mathrm{E}[x^{3}]$ | $\mathrm{E}[x^{4}]$ | $\mathrm{E}[x^{5}]$ | $\mathrm{E}[x^{6}]$ | $\mathrm{E}[x^{7}]$ | $\mathrm{E}[x^{8}]$ | $\mathrm{E}[x^{9}]$ | $\mathrm{E}[x^{10}]$ | $\mathrm{E}[x^{11}]$ | $\mathrm{E}[x^{12}]$ |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| $a_1$ | $1$ | $0$ | $2$ | $0$ | $18$ | $0$ | $200$ | $0$ | $2450$ | $0$ | $31752$ | $0$ | $427812$ |
| $a_2$ | $1$ | $1$ | $5$ | $16$ | $77$ | $356$ | $1803$ | $9262$ | $48933$ | $262372$ | $1427255$ | $7850822$ | $43608271$ |
Event Probabilities
| $\mathrm{P}[a_1=0]=\frac{7}{12}$ |