# Properties

 Label 1.4.3.6.1a Name $$J(E_3)$$ Weight 1 Degree 4 Real dimension 3 Components 6 Contained in $$\mathrm{USp}(4)$$ Identity Component $$\mathrm{SU}(2)_2$$ Component group $$S_3$$

## Invariants

 Weight: $1$ Degree: $4$ $\mathbb{R}$-dimension: $3$ Components: $6$ Contained in: $\mathrm{USp}(4)$ Rational: $\mathrm{True}$

## Identity Component

 Name: $\mathrm{SU}(2)_2$ Index: $6$ $\mathbb{R}$-dimension: $3$ Description: $\left\{\begin{bmatrix}A&0\\0&\bar{A}\end{bmatrix}: A\in \mathrm{SU}(2)\right\}$

## Component Group

 Name: $S_3$ Order: $6$ Abelian: $\mathrm{False}$

## Moment Statistics

$x$ $\mathrm{E}[x^{0}]$ $\mathrm{E}[x^{1}]$ $\mathrm{E}[x^{2}]$ $\mathrm{E}[x^{3}]$ $\mathrm{E}[x^{4}]$ $\mathrm{E}[x^{5}]$ $\mathrm{E}[x^{6}]$ $\mathrm{E}[x^{7}]$ $\mathrm{E}[x^{8}]$ $\mathrm{E}[x^{9}]$ $\mathrm{E}[x^{10}]$ $\mathrm{E}[x^{11}]$ $\mathrm{E}[x^{12}]$
$a_1$ $1$ $0$ $1$ $0$ $6$ $0$ $55$ $0$ $602$ $0$ $7182$ $0$ $90156$
$a_2$ $1$ $1$ $3$ $8$ $29$ $116$ $517$ $2437$ $11965$ $60326$ $310265$ $1620125$ $8564063$

## Event Probabilities

 $\mathrm{P}[a_1=0]=\frac{3}{6}$