# Properties

 Label 1.4.4.2.1a Name $$N(G_{1,3})$$ Weight 1 Degree 4 Real dimension 4 Components 2 Contained in $$\mathrm{USp}(4)$$ Identity Component $$\mathrm{U}(1)\times\mathrm{SU}(2)$$ Component group $$C_2$$

## Invariants

 Weight: $1$ Degree: $4$ $\mathbb{R}$-dimension: $4$ Components: $2$ Contained in: $\mathrm{USp}(4)$ Rational: $\mathrm{True}$

## Identity Component

 Name: $\mathrm{U}(1)\times\mathrm{SU}(2)$ Index: $2$ $\mathbb{R}$-dimension: $4$ Description: $\left\{\begin{bmatrix}A&0\\0&B\end{bmatrix}: A\in \mathrm{U}(1),\ B\in\mathrm{SU}(2)\right\}$

## Component Group

 Name: $C_2$ Order: $2$ Abelian: $\mathrm{True}$

## Moment Statistics

$x$ $\mathrm{E}[x^{0}]$ $\mathrm{E}[x^{1}]$ $\mathrm{E}[x^{2}]$ $\mathrm{E}[x^{3}]$ $\mathrm{E}[x^{4}]$ $\mathrm{E}[x^{5}]$ $\mathrm{E}[x^{6}]$ $\mathrm{E}[x^{7}]$ $\mathrm{E}[x^{8}]$ $\mathrm{E}[x^{9}]$ $\mathrm{E}[x^{10}]$ $\mathrm{E}[x^{11}]$ $\mathrm{E}[x^{12}]$
$a_1$ $1$ $0$ $2$ $0$ $11$ $0$ $90$ $0$ $889$ $0$ $9723$ $0$ $113322$
$a_2$ $1$ $2$ $5$ $14$ $46$ $172$ $714$ $3180$ $14858$ $71732$ $354676$ $1786072$ $9127672$

## Event Probabilities

 $\mathrm{P}[a_2=2]=\frac{1}{2}$