Properties

Label 1.4.6.2.1a
  
Name \(N(G_{3,3})\)
Weight 1
Degree 4
Real dimension 6
Components 2
Contained in \(\mathrm{USp}(4)\)
Identity Component \(\mathrm{SU}(2)\times\mathrm{SU}(2)\)
Component group \(C_2\)

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Invariants

Weight:$1$
Degree:$4$
$\mathbb{R}$-dimension:$6$
Components:$2$
Contained in:$\mathrm{USp}(4)$
Rational:$\mathrm{True}$

Identity Component

Name:$\mathrm{SU}(2)\times\mathrm{SU}(2)$
Index:$2$
$\mathbb{R}$-dimension:$6$
Description:$\left\{\begin{bmatrix}A&0\\0&B\end{bmatrix}: A,B\in\mathrm{SU}(2)\right\}$

Component Group

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

Subgroups and Supergroups

Maximal Subgroups:1.4.6.1a
Minimal Supergroups:

Moment Statistics

$x$ $\mathrm{E}[x^{0}]$ $\mathrm{E}[x^{1}]$ $\mathrm{E}[x^{2}]$ $\mathrm{E}[x^{3}]$ $\mathrm{E}[x^{4}]$ $\mathrm{E}[x^{5}]$ $\mathrm{E}[x^{6}]$ $\mathrm{E}[x^{7}]$ $\mathrm{E}[x^{8}]$ $\mathrm{E}[x^{9}]$ $\mathrm{E}[x^{10}]$ $\mathrm{E}[x^{11}]$ $\mathrm{E}[x^{12}]$
$a_1$ $1$ $0$ $1$ $0$ $5$ $0$ $35$ $0$ $294$ $0$ $2772$ $0$ $28314$
$a_2$ $1$ $1$ $3$ $7$ $23$ $76$ $287$ $1135$ $4769$ $20788$ $93695$ $433148$ $2046266$

Event Probabilities

$\mathrm{P}[a_1=0]=\frac{1}{2}$