Properties

Label 1.4.4.1.1a
  
Name \(G_{1,3}\)
Weight 1
Degree 4
Real dimension 4
Components 1
Contained in \(\mathrm{USp}(4)\)
Identity Component \(\mathrm{U}(1)\times\mathrm{SU}(2)\)
Component group \(C_1\)

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Invariants

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

Identity Component

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

Subgroups and Supergroups

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

Moment Statistics

$x$ $\mathrm{E}[x^{0}]$ $\mathrm{E}[x^{1}]$ $\mathrm{E}[x^{2}]$ $\mathrm{E}[x^{3}]$ $\mathrm{E}[x^{4}]$ $\mathrm{E}[x^{5}]$ $\mathrm{E}[x^{6}]$ $\mathrm{E}[x^{7}]$ $\mathrm{E}[x^{8}]$ $\mathrm{E}[x^{9}]$ $\mathrm{E}[x^{10}]$ $\mathrm{E}[x^{11}]$ $\mathrm{E}[x^{12}]$
$a_1$ $1$ $0$ $3$ $0$ $20$ $0$ $175$ $0$ $1764$ $0$ $19404$ $0$ $226512$
$a_2$ $1$ $2$ $6$ $20$ $76$ $312$ $1364$ $6232$ $29460$ $142952$ $708328$ $3570096$ $18251248$