Properties

Label 1.4.3.8.3a
  
Name \(J(E_4)\)
Weight 1
Degree 4
Real dimension 3
Components 8
Contained in \(\mathrm{USp}(4)\)
Identity Component \(\mathrm{SU}(2)_2\)
Component group \(D_4\)

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Invariants

Weight:$1$
Degree:$4$
$\mathbb{R}$-dimension:$3$
Components:$8$
Contained in:$\mathrm{USp}(4)$
Rational:$\mathrm{True}$

Identity Component

Name:$\mathrm{SU}(2)_2$
Index:$8$
$\mathbb{R}$-dimension:$3$
Description:$\left\{\begin{bmatrix}A&0\\0&\bar{A}\end{bmatrix}: A\in \mathrm{SU}(2)\right\}$

Component Group

Name:$D_4$
Order:$8$
Abelian:$\mathrm{False}$

Subgroups and Supergroups

Maximal Subgroups:$E_4$, $J(E_2)$
Minimal Supergroups:

Moment Statistics

$x$ $\mathrm{E}[x^{0}]$ $\mathrm{E}[x^{1}]$ $\mathrm{E}[x^{2}]$ $\mathrm{E}[x^{3}]$ $\mathrm{E}[x^{4}]$ $\mathrm{E}[x^{5}]$ $\mathrm{E}[x^{6}]$ $\mathrm{E}[x^{7}]$ $\mathrm{E}[x^{8}]$ $\mathrm{E}[x^{9}]$ $\mathrm{E}[x^{10}]$ $\mathrm{E}[x^{11}]$ $\mathrm{E}[x^{12}]$
$a_1$ $1$ $0$ $1$ $0$ $6$ $0$ $50$ $0$ $504$ $0$ $5712$ $0$ $69696$
$a_2$ $1$ $1$ $3$ $7$ $26$ $96$ $422$ $1926$ $9326$ $46402$ $236810$ $1229394$ $6474228$

Event Probabilities

$\mathrm{P}[a_1=0]=\frac{5}{8}$