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Properties

Label 1.2.3.c293223628800
  
Name \(\mathrm{SU}(2)[C_{293223628800}]\)
Weight 1
Degree 2
Real dimension 3
Components 293223628800
Contained in \(\mathrm{U}(2)\)
Identity Component \(\mathrm{SU}(2)\)
Component group \(C_{293223628800}\)

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Invariants

Weight:$1$
Degree:$2$
$\mathbb{R}$-dimension:$3$
Components:$293223628800$
Contained in:$\mathrm{U}(2)$
Rational:$\mathrm{False}$

Identity Component

Name:$\mathrm{SU}(2)$
Index:$293223628800$
$\mathbb{R}$-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:$C_{293223628800}$
Order:$293223628800$
Abelian:$\mathrm{True}$
Generators:$\begin{bmatrix} 1 & 0 \\ 0 & \zeta_{293223628800}\end{bmatrix}$

Subgroups and Supergroups

Maximal Subgroups:$\mathrm{SU}(2)[C_{146611814400}]$, $\mathrm{SU}(2)[C_{97741209600}]$, $\mathrm{SU}(2)[C_{58644725760}]$, $\mathrm{SU}(2)[C_{597196800}]$
Minimal Supergroups:$\mathrm{SU}(2)[C_{586447257600}]$, $\mathrm{SU}(2)[C_{879670886400}]$, $\mathrm{SU}(2)[C_{1466118144000}]$, $\ldots$

Moment Statistics

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