Invariants
| Weight: | $1$ |
| Degree: | $4$ |
| $\mathbb{R}$-dimension: | $1$ |
| Components: | $24$ |
| Contained in: | $\mathrm{USp}(4)$ |
| Rational: | $\mathrm{True}$ |
Identity Component
| Name: | $\mathrm{U}(1)_2$ |
| Index: | $24$ |
| $\mathbb{R}$-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: | $C_2^2\times S_3$ |
| Order: | $24$ |
| Abelian: | $\mathrm{False}$ |
Subgroups and Supergroups
| Maximal Subgroups: | $J(D_2)$, $D_6$, $J(D_3)$, $D_{6,1}$, $D_{6,2}$, $J(C_6)$ |
| Minimal Supergroups: |
Moment Statistics
| $x$ | $\mathrm{E}[x^{0}]$ | $\mathrm{E}[x^{1}]$ | $\mathrm{E}[x^{2}]$ | $\mathrm{E}[x^{3}]$ | $\mathrm{E}[x^{4}]$ | $\mathrm{E}[x^{5}]$ | $\mathrm{E}[x^{6}]$ | $\mathrm{E}[x^{7}]$ | $\mathrm{E}[x^{8}]$ | $\mathrm{E}[x^{9}]$ | $\mathrm{E}[x^{10}]$ | $\mathrm{E}[x^{11}]$ | $\mathrm{E}[x^{12}]$ |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| $a_1$ | $1$ | $0$ | $1$ | $0$ | $9$ | $0$ | $100$ | $0$ | $1225$ | $0$ | $15876$ | $0$ | $213906$ |
| $a_2$ | $1$ | $1$ | $4$ | $10$ | $44$ | $186$ | $923$ | $4663$ | $24552$ | $131314$ | $713969$ | $3925923$ | $21805501$ |
Event Probabilities
| $\mathrm{P}[a_1=0]=\frac{19}{24}$ | |||
| $\mathrm{P}[a_2=-2]=\frac{1}{24}$ | $\mathrm{P}[a_2=-1]=\frac{2}{24}$ | $\mathrm{P}[a_2=1]=\frac{2}{24}$ | $\mathrm{P}[a_2=2]=\frac{7}{24}$ |