# Properties

 Label 1.4.3.4.2a Name $J(E_2)$ Weight 1 Degree 4 Real dimension 3 Components 4 Contained in $\mathrm{USp}(4)$ Identity Component $\mathrm{SU}(2)_2$ Component group $C_2^2$

## 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: $C_2^2$ Order: $4$ Abelian: $\mathrm{True}$

## Moment Statistics

$x$ $\mathrm{E}[x^{0}]$ $\mathrm{E}[x^{1}]$ $\mathrm{E}[x^{2}]$ $\mathrm{E}[x^{3}]$ $\mathrm{E}[x^{4}]$ $\mathrm{E}[x^{5}]$ $\mathrm{E}[x^{6}]$ $\mathrm{E}[x^{7}]$ $\mathrm{E}[x^{8}]$ $\mathrm{E}[x^{9}]$ $\mathrm{E}[x^{10}]$ $\mathrm{E}[x^{11}]$ $\mathrm{E}[x^{12}]$
$a_1$ $1$ $0$ $1$ $0$ $8$ $0$ $80$ $0$ $896$ $0$ $10752$ $0$ $135168$
$a_2$ $1$ $1$ $4$ $10$ $42$ $166$ $768$ $3620$ $17902$ $90310$ $465096$ $2429164$ $12843988$

## Event Probabilities

 $\mathrm{P}[a_1=0]=\frac{3}{4}$