# Properties

 Label 1.4.3.8.3a Name $$J(E_4)$$ Weight 1 Degree 4 Real dimension 3 Components 8 Contained in $$\mathrm{USp}(4)$$ Identity Component $$\mathrm{SU}(2)_2$$ Component group $$D_4$$

## Invariants

 Weight: $1$ Degree: $4$ $\mathbb{R}$-dimension: $3$ Components: $8$ Contained in: $\mathrm{USp}(4)$ Rational: $\mathrm{True}$

## Identity Component

 Name: $\mathrm{SU}(2)_2$ Index: $8$ $\mathbb{R}$-dimension: $3$ Description: $\left\{\begin{bmatrix}A&0\\0&\bar{A}\end{bmatrix}: A\in \mathrm{SU}(2)\right\}$

## Component Group

 Name: $D_4$ Order: $8$ Abelian: $\mathrm{False}$

## Moment Statistics

$x$ $\mathrm{E}[x^{0}]$ $\mathrm{E}[x^{1}]$ $\mathrm{E}[x^{2}]$ $\mathrm{E}[x^{3}]$ $\mathrm{E}[x^{4}]$ $\mathrm{E}[x^{5}]$ $\mathrm{E}[x^{6}]$ $\mathrm{E}[x^{7}]$ $\mathrm{E}[x^{8}]$ $\mathrm{E}[x^{9}]$ $\mathrm{E}[x^{10}]$ $\mathrm{E}[x^{11}]$ $\mathrm{E}[x^{12}]$
$a_1$ $1$ $0$ $1$ $0$ $6$ $0$ $50$ $0$ $504$ $0$ $5712$ $0$ $69696$
$a_2$ $1$ $1$ $3$ $7$ $26$ $96$ $422$ $1926$ $9326$ $46402$ $236810$ $1229394$ $6474228$

## Event Probabilities

 $\mathrm{P}[a_1=0]=\frac{5}{8}$