# Properties

 Label 1.4.3.6.2a Name $E_6$ Weight 1 Degree 4 Real dimension 3 Components 6 Contained in $\mathrm{USp}(4)$ Identity Component $\mathrm{SU}(2)_2$ Component group $C_6$

# Learn more about

## 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: $C_6$ Order: $6$ Abelian: $\mathrm{True}$

## Moment Statistics

$x$ $\mathrm{E}[x^{0}]$ $\mathrm{E}[x^{1}]$ $\mathrm{E}[x^{2}]$ $\mathrm{E}[x^{3}]$ $\mathrm{E}[x^{4}]$ $\mathrm{E}[x^{5}]$ $\mathrm{E}[x^{6}]$ $\mathrm{E}[x^{7}]$ $\mathrm{E}[x^{8}]$ $\mathrm{E}[x^{9}]$ $\mathrm{E}[x^{10}]$ $\mathrm{E}[x^{11}]$ $\mathrm{E}[x^{12}]$
$a_1$ $1$ $0$ $2$ $0$ $12$ $0$ $100$ $0$ $980$ $0$ $10584$ $0$ $122232$
$a_2$ $1$ $1$ $4$ $11$ $44$ $172$ $754$ $3397$ $16020$ $77516$ $384578$ $1944626$ $9997970$

## Event Probabilities

 $\mathrm{P}[a_1=0]=\frac{1}{6}$