# Properties

 Label 1.4.1.6.2c Name $$C_{6,1}$$ Weight 1 Degree 4 Real dimension 1 Components 6 Contained in $$\mathrm{USp}(4)$$ Identity Component $$\mathrm{U}(1)_2$$ Component group $$C_6$$

## Invariants

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

## Identity Component

 Name: $\mathrm{U}(1)_2$ Index: $6$ $\mathbb{R}$-dimension: $1$ Description: $\left\{\begin{bmatrix}\mathrm{diag}_2(\alpha)&0\\0&\mathrm{diag}_2(\bar\alpha)\end{bmatrix}: \alpha\bar\alpha = 1,\ \alpha\in\mathbb{C}\right\},\ \mathrm{diag}_2(\alpha):=\begin{bmatrix}\alpha&0\\0&\alpha\end{bmatrix}$

## Component Group

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

## Moment Statistics

$x$ $\mathrm{E}[x^{0}]$ $\mathrm{E}[x^{1}]$ $\mathrm{E}[x^{2}]$ $\mathrm{E}[x^{3}]$ $\mathrm{E}[x^{4}]$ $\mathrm{E}[x^{5}]$ $\mathrm{E}[x^{6}]$ $\mathrm{E}[x^{7}]$ $\mathrm{E}[x^{8}]$ $\mathrm{E}[x^{9}]$ $\mathrm{E}[x^{10}]$ $\mathrm{E}[x^{11}]$ $\mathrm{E}[x^{12}]$
$a_1$ $1$ $0$ $2$ $0$ $18$ $0$ $220$ $0$ $3010$ $0$ $43092$ $0$ $631092$
$a_2$ $1$ $1$ $5$ $18$ $85$ $426$ $2264$ $12384$ $68989$ $388794$ $2208760$ $12622644$ $72469060$

## Event Probabilities

 $\mathrm{P}[a_1=0]=\frac{3}{6}$ $\mathrm{P}[a_2=-1]=\frac{2}{6}$ $\mathrm{P}[a_2=2]=\frac{1}{6}$