# Properties

 Label 1.4.1.12.4d Name $D_{6,2}$ Weight 1 Degree 4 Real dimension 1 Components 12 Contained in $\mathrm{USp}(4)$ Identity Component $\mathrm{U}(1)_2$ Component group $D_6$

## Invariants

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

## Identity Component

 Name: $\mathrm{U}(1)_2$ Index: $12$ $\mathbb{R}$-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: $D_6$ Order: $12$ Abelian: $\mathrm{False}$

## Moment Statistics

$x$ $\mathrm{E}[x^{0}]$ $\mathrm{E}[x^{1}]$ $\mathrm{E}[x^{2}]$ $\mathrm{E}[x^{3}]$ $\mathrm{E}[x^{4}]$ $\mathrm{E}[x^{5}]$ $\mathrm{E}[x^{6}]$ $\mathrm{E}[x^{7}]$ $\mathrm{E}[x^{8}]$ $\mathrm{E}[x^{9}]$ $\mathrm{E}[x^{10}]$ $\mathrm{E}[x^{11}]$ $\mathrm{E}[x^{12}]$
$a_1$ $1$ $0$ $2$ $0$ $18$ $0$ $200$ $0$ $2450$ $0$ $31752$ $0$ $427812$
$a_2$ $1$ $2$ $6$ $20$ $82$ $372$ $1825$ $9326$ $49026$ $262628$ $1427641$ $7851846$ $43609857$

## Event Probabilities

 $\mathrm{P}[a_1=0]=\frac{7}{12}$ $\mathrm{P}[a_2=2]=\frac{6}{12}$