# Properties

 Label 1.4.3.4.1a Name $$E_4$$ Weight $1$ Degree $4$ Real dimension $3$ Components $4$ Contained in $$\mathrm{USp}(4)$$ Identity Component $$\mathrm{SU}(2)_2$$ Component group $$C_4$$

## Invariants

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

## Identity Component

 Name: $\mathrm{SU}(2)_2$ Index: $4$ $\mathbb{R}$-dimension: $3$ Description: $\left\{\begin{bmatrix}A&0\\0&\bar{A}\end{bmatrix}: A\in \mathrm{SU}(2)\right\}$

## Component Group

 Name: $C_4$ Order: $4$ Abelian: $\mathrm{True}$

## Moment Statistics

$x$ $\mathrm{E}[x^{0}]$ $\mathrm{E}[x^{1}]$ $\mathrm{E}[x^{2}]$ $\mathrm{E}[x^{3}]$ $\mathrm{E}[x^{4}]$ $\mathrm{E}[x^{5}]$ $\mathrm{E}[x^{6}]$ $\mathrm{E}[x^{7}]$ $\mathrm{E}[x^{8}]$ $\mathrm{E}[x^{9}]$ $\mathrm{E}[x^{10}]$ $\mathrm{E}[x^{11}]$ $\mathrm{E}[x^{12}]$
$a_1$ $1$ $0$ $2$ $0$ $12$ $0$ $100$ $0$ $1008$ $0$ $11424$ $0$ $139392$
$a_2$ $1$ $1$ $4$ $11$ $46$ $182$ $824$ $3817$ $18582$ $92678$ $473368$ $2458326$ $12947532$

## Event Probabilities

 $\mathrm{P}[a_1=0]=\frac{1}{4}$