Properties

Label 1.4.4.2.1a
  
Name \(N(G_{1,3})\)
Weight 1
Degree 4
Real dimension 4
Components 2
Contained in \(\mathrm{USp}(4)\)
Identity Component \(\mathrm{U}(1)\times\mathrm{SU}(2)\)
Component group \(C_2\)

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Invariants

Weight:$1$
Degree:$4$
$\mathbb{R}$-dimension:$4$
Components:$2$
Contained in:$\mathrm{USp}(4)$
Rational:$\mathrm{True}$

Identity Component

Name:$\mathrm{U}(1)\times\mathrm{SU}(2)$
Index:$2$
$\mathbb{R}$-dimension:$4$
Description:$\left\{\begin{bmatrix}A&0\\0&B\end{bmatrix}: A\in \mathrm{U}(1),\ B\in\mathrm{SU}(2)\right\}$

Component Group

Name:$C_2$
Order:$2$
Abelian:$\mathrm{True}$

Subgroups and Supergroups

Maximal Subgroups:$G_{1,3}$
Minimal Supergroups:

Moment Statistics

$x$ $\mathrm{E}[x^{0}]$ $\mathrm{E}[x^{1}]$ $\mathrm{E}[x^{2}]$ $\mathrm{E}[x^{3}]$ $\mathrm{E}[x^{4}]$ $\mathrm{E}[x^{5}]$ $\mathrm{E}[x^{6}]$ $\mathrm{E}[x^{7}]$ $\mathrm{E}[x^{8}]$ $\mathrm{E}[x^{9}]$ $\mathrm{E}[x^{10}]$ $\mathrm{E}[x^{11}]$ $\mathrm{E}[x^{12}]$
$a_1$ $1$ $0$ $2$ $0$ $11$ $0$ $90$ $0$ $889$ $0$ $9723$ $0$ $113322$
$a_2$ $1$ $2$ $5$ $14$ $46$ $172$ $714$ $3180$ $14858$ $71732$ $354676$ $1786072$ $9127672$

Event Probabilities

$\mathrm{P}[a_2=2]=\frac{1}{2}$