# Properties

 Label 6.2.1.d6 Name $$\mathrm{U}(1)[D_{6}]$$ Weight $6$ Degree $2$ Real dimension $1$ Components $12$ Contained in $$\mathrm{U}(2)$$ Identity Component $$\mathrm{U}(1)$$ Component group $$D_{6}$$

## Invariants

 Weight: $6$ Degree: $2$ $\mathbb{R}$-dimension: $1$ Components: $12$ Contained in: $\mathrm{U}(2)$ Rational: $\mathrm{False}$

## Identity Component

 Name: $\mathrm{U}(1)$ Index: $12$ $\mathbb{R}$-dimension: $1$ Description: $\left\{\begin{bmatrix}\alpha&0\\0&\bar\alpha\end{bmatrix}:\alpha\bar\alpha = 1,\ \alpha\in\mathbb{C}\right\}$

## Component Group

 Name: $D_{6}$ Order: $12$ Abelian: $\mathrm{False}$ Generators: $\left\{\begin{bmatrix} 0 & 1\\ -1 & 0\end{bmatrix}, \begin{bmatrix} 1 & 0 \\ 0 & \zeta_{6}\end{bmatrix}\right\}$

## Moment Statistics

$x$ $\mathrm{E}[x^{0}]$ $\mathrm{E}[x^{1}]$ $\mathrm{E}[x^{2}]$ $\mathrm{E}[x^{3}]$ $\mathrm{E}[x^{4}]$ $\mathrm{E}[x^{5}]$ $\mathrm{E}[x^{6}]$ $\mathrm{E}[x^{7}]$ $\mathrm{E}[x^{8}]$ $\mathrm{E}[x^{9}]$ $\mathrm{E}[x^{10}]$ $\mathrm{E}[x^{11}]$ $\mathrm{E}[x^{12}]$
$a_1$ $1$ $0$ $0$ $0$ $0$ $0$ $10$ $0$ $0$ $0$ $0$ $0$ $462$