# Properties

 Label 1.4.1.16.11a Name $$J(D_4)$$ Weight 1 Degree 4 Real dimension 1 Components 16 Contained in $$\mathrm{USp}(4)$$ Identity Component $$\mathrm{U}(1)_2$$ Component group $$C_2\times D_4$$

## Invariants

 Weight: $1$ Degree: $4$ $\mathbb{R}$-dimension: $1$ Components: $16$ Contained in: $\mathrm{USp}(4)$ Rational: $\mathrm{True}$

## Identity Component

 Name: $\mathrm{U}(1)_2$ Index: $16$ $\mathbb{R}$-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: $C_2\times D_4$ Order: $16$ Abelian: $\mathrm{False}$

## Moment Statistics

$x$ $\mathrm{E}[x^{0}]$ $\mathrm{E}[x^{1}]$ $\mathrm{E}[x^{2}]$ $\mathrm{E}[x^{3}]$ $\mathrm{E}[x^{4}]$ $\mathrm{E}[x^{5}]$ $\mathrm{E}[x^{6}]$ $\mathrm{E}[x^{7}]$ $\mathrm{E}[x^{8}]$ $\mathrm{E}[x^{9}]$ $\mathrm{E}[x^{10}]$ $\mathrm{E}[x^{11}]$ $\mathrm{E}[x^{12}]$
$a_1$ $1$ $0$ $1$ $0$ $9$ $0$ $100$ $0$ $1260$ $0$ $17136$ $0$ $243936$
$a_2$ $1$ $1$ $4$ $10$ $45$ $191$ $973$ $5048$ $27443$ $151579$ $850659$ $4818848$ $27506262$

## Event Probabilities

 $\mathrm{P}[a_1=0]=\frac{13}{16}$ $\mathrm{P}[a_2=-2]=\frac{1}{16}$ $\mathrm{P}[a_2=0]=\frac{2}{16}$ $\mathrm{P}[a_2=2]=\frac{5}{16}$