# Properties

 Label 1.4.3.12.4a Name $$J(E_6)$$ Weight 1 Degree 4 Real dimension 3 Components 12 Contained in $$\mathrm{USp}(4)$$ Identity Component $$\mathrm{SU}(2)_2$$ Component group $$D_6$$

# Learn more about

## Invariants

 Weight: $1$ Degree: $4$ $\mathbb{R}$-dimension: $3$ Components: $12$ Contained in: $\mathrm{USp}(4)$ Rational: $\mathrm{True}$

## Identity Component

 Name: $\mathrm{SU}(2)_2$ Index: $12$ $\mathbb{R}$-dimension: $3$ Description: $\left\{\begin{bmatrix}A&0\\0&\bar{A}\end{bmatrix}: A\in \mathrm{SU}(2)\right\}$

## Component Group

 Name: $D_6$ Order: $12$ Abelian: $\mathrm{False}$

## Moment Statistics

$x$ $\mathrm{E}[x^{0}]$ $\mathrm{E}[x^{1}]$ $\mathrm{E}[x^{2}]$ $\mathrm{E}[x^{3}]$ $\mathrm{E}[x^{4}]$ $\mathrm{E}[x^{5}]$ $\mathrm{E}[x^{6}]$ $\mathrm{E}[x^{7}]$ $\mathrm{E}[x^{8}]$ $\mathrm{E}[x^{9}]$ $\mathrm{E}[x^{10}]$ $\mathrm{E}[x^{11}]$ $\mathrm{E}[x^{12}]$
$a_1$ $1$ $0$ $1$ $0$ $6$ $0$ $50$ $0$ $490$ $0$ $5292$ $0$ $61116$
$a_2$ $1$ $1$ $3$ $7$ $25$ $91$ $387$ $1716$ $8045$ $38821$ $192415$ $972544$ $4999447$

## Event Probabilities

 $\mathrm{P}[a_1=0]=\frac{7}{12}$