Properties

Label 2.2.3.c6
  
Name \(\mathrm{SU}(2)[C_{6}]\)
Weight 2
Degree 2
Real dimension 3
Components 6
Contained in \(\mathrm{U}(2)\)
Identity Component \(\mathrm{SU}(2)\)
Component group \(C_{6}\)

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Invariants

Weight:$2$
Degree:$2$
$\mathbb{R}$-dimension:$3$
Components:$6$
Contained in:$\mathrm{U}(2)$
Rational:$\mathrm{False}$

Identity Component

Name:$\mathrm{SU}(2)$
Index:$6$
$\mathbb{R}$-dimension:$3$
Description:$\left\{\begin{bmatrix}\alpha&\beta\\-\bar\beta&\bar\alpha\end{bmatrix}:\alpha\bar\alpha+\beta\bar\beta = 1,\ \alpha,\beta\in\mathbb{C}\right\}$

Component Group

Name:$C_{6}$
Order:$6$
Abelian:$\mathrm{True}$
Generators:$\begin{bmatrix} 1 & 0 \\ 0 & \zeta_{6}\end{bmatrix}$

Subgroups and Supergroups

Maximal Subgroups:$\mathrm{SU}(2)[C_{3}]$, $\mathrm{SU}(2)[C_{2}]$
Minimal Supergroups:$\mathrm{SU}(2)[C_{12}]$, $\mathrm{SU}(2)[C_{18}]$, $\mathrm{SU}(2)[C_{30}]$, $\ldots$

Moment Statistics

$x$ $\mathrm{E}[x^{0}]$ $\mathrm{E}[x^{1}]$ $\mathrm{E}[x^{2}]$ $\mathrm{E}[x^{3}]$ $\mathrm{E}[x^{4}]$ $\mathrm{E}[x^{5}]$ $\mathrm{E}[x^{6}]$ $\mathrm{E}[x^{7}]$ $\mathrm{E}[x^{8}]$ $\mathrm{E}[x^{9}]$ $\mathrm{E}[x^{10}]$ $\mathrm{E}[x^{11}]$ $\mathrm{E}[x^{12}]$
$a_1$ $1$ $0$ $0$ $0$ $0$ $0$ $5$ $0$ $0$ $0$ $0$ $0$ $132$