# Properties

 Label 1.4.3.2.1b Name $$J(E_1)$$ Weight $1$ Degree $4$ Real dimension $3$ Components $2$ Contained in $$\mathrm{USp}(4)$$ Identity Component $$\mathrm{SU}(2)_2$$ Component group $$C_2$$

## Invariants

 Weight: $1$ Degree: $4$ $\mathbb{R}$-dimension: $3$ Components: $2$ Contained in: $\mathrm{USp}(4)$ Rational: $\mathrm{True}$

## Identity Component

 Name: $\mathrm{SU}(2)_2$ Index: $2$ $\mathbb{R}$-dimension: $3$ Description: $\left\{\begin{bmatrix}A&0\\0&\bar{A}\end{bmatrix}: A\in \mathrm{SU}(2)\right\}$

## Component Group

 Name: $C_2$ Order: $2$ Abelian: $\mathrm{True}$

## Moment Statistics

$x$ $\mathrm{E}[x^{0}]$ $\mathrm{E}[x^{1}]$ $\mathrm{E}[x^{2}]$ $\mathrm{E}[x^{3}]$ $\mathrm{E}[x^{4}]$ $\mathrm{E}[x^{5}]$ $\mathrm{E}[x^{6}]$ $\mathrm{E}[x^{7}]$ $\mathrm{E}[x^{8}]$ $\mathrm{E}[x^{9}]$ $\mathrm{E}[x^{10}]$ $\mathrm{E}[x^{11}]$ $\mathrm{E}[x^{12}]$
$a_1$ $1$ $0$ $2$ $0$ $16$ $0$ $160$ $0$ $1792$ $0$ $21504$ $0$ $270336$
$a_2$ $1$ $2$ $6$ $20$ $78$ $332$ $1516$ $7240$ $35734$ $180620$ $929940$ $4858328$ $25687052$

## Event Probabilities

 $\mathrm{P}[a_1=0]=\frac{1}{2}$