Properties

 Label 1.4.1.24.14a Name $$J(D_6)$$ Weight 1 Degree 4 Real dimension 1 Components 24 Contained in $$\mathrm{USp}(4)$$ Identity Component $$\mathrm{U}(1)_2$$ Component group $$C_2^2\times S_3$$

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: $\mathrm{False}$

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

 $\mathrm{P}[a_1=0]=\frac{19}{24}$ $\mathrm{P}[a_2=-2]=\frac{1}{24}$ $\mathrm{P}[a_2=-1]=\frac{2}{24}$ $\mathrm{P}[a_2=1]=\frac{2}{24}$ $\mathrm{P}[a_2=2]=\frac{7}{24}$