Invariants
| Weight: | $1$ |
| Degree: | $4$ |
| $\mathbb{R}$-dimension: | $3$ |
| Components: | $12$ |
| Contained in: | $\mathrm{USp}(4)$ |
| Rational: | $\mathrm{True}$ |
Identity Component
| Name: | $\mathrm{SU}(2)_2$ |
| Index: | $12$ |
| $\mathbb{R}$-dimension: | $3$ |
| Description: | $\left\{\begin{bmatrix}A&0\\0&\bar{A}\end{bmatrix}: A\in \mathrm{SU}(2)\right\}$ |
Component Group
| Name: | $D_6$ |
| Order: | $12$ |
| Abelian: | $\mathrm{False}$ |
Subgroups and Supergroups
| Maximal Subgroups: | $J(E_2)$, $J(E_3)$, $E_6$ |
| Minimal Supergroups: |
Moment Statistics
| $x$ | $\mathrm{E}[x^{0}]$ | $\mathrm{E}[x^{1}]$ | $\mathrm{E}[x^{2}]$ | $\mathrm{E}[x^{3}]$ | $\mathrm{E}[x^{4}]$ | $\mathrm{E}[x^{5}]$ | $\mathrm{E}[x^{6}]$ | $\mathrm{E}[x^{7}]$ | $\mathrm{E}[x^{8}]$ | $\mathrm{E}[x^{9}]$ | $\mathrm{E}[x^{10}]$ | $\mathrm{E}[x^{11}]$ | $\mathrm{E}[x^{12}]$ |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| $a_1$ | $1$ | $0$ | $1$ | $0$ | $6$ | $0$ | $50$ | $0$ | $490$ | $0$ | $5292$ | $0$ | $61116$ |
| $a_2$ | $1$ | $1$ | $3$ | $7$ | $25$ | $91$ | $387$ | $1716$ | $8045$ | $38821$ | $192415$ | $972544$ | $4999447$ |
Event Probabilities
| $\mathrm{P}[a_1=0]=\frac{7}{12}$ |