# Properties

 Label 1.4.1.12.4b Name $$J(D_3)$$ Weight 1 Degree 4 Real dimension 1 Components 12 Contained in $$\mathrm{USp}(4)$$ Identity Component $$\mathrm{U}(1)_2$$ Component group $$D_6$$

## 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: $\mathrm{False}$

## Moment Statistics

$x$ $\mathrm{E}[x^{0}]$ $\mathrm{E}[x^{1}]$ $\mathrm{E}[x^{2}]$ $\mathrm{E}[x^{3}]$ $\mathrm{E}[x^{4}]$ $\mathrm{E}[x^{5}]$ $\mathrm{E}[x^{6}]$ $\mathrm{E}[x^{7}]$ $\mathrm{E}[x^{8}]$ $\mathrm{E}[x^{9}]$ $\mathrm{E}[x^{10}]$ $\mathrm{E}[x^{11}]$ $\mathrm{E}[x^{12}]$
$a_1$ $1$ $0$ $1$ $0$ $9$ $0$ $110$ $0$ $1505$ $0$ $21546$ $0$ $315546$
$a_2$ $1$ $1$ $4$ $10$ $48$ $216$ $1153$ $6203$ $34576$ $194440$ $1104699$ $6311493$ $36235785$

## Event Probabilities

 $\mathrm{P}[a_1=0]=\frac{9}{12}$ $\mathrm{P}[a_2=-2]=\frac{1}{12}$ $\mathrm{P}[a_2=1]=\frac{2}{12}$ $\mathrm{P}[a_2=2]=\frac{3}{12}$