Properties

Label 1.4.3.4.1a
  
Name \(E_4\)
Weight 1
Degree 4
Real dimension 3
Components 4
Contained in \(\mathrm{USp}(4)\)
Identity Component \(\mathrm{SU}(2)_2\)
Component group \(C_4\)

Learn more about

Invariants

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

Identity Component

Name:$\mathrm{SU}(2)_2$
Index:$4$
$\mathbb{R}$-dimension:$3$
Description:$\left\{\begin{bmatrix}A&0\\0&\bar{A}\end{bmatrix}: A\in \mathrm{SU}(2)\right\}$

Component Group

Name:$C_4$
Order:$4$
Abelian:$\mathrm{True}$

Subgroups and Supergroups

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

Moment Statistics

$x$ $\mathrm{E}[x^{0}]$ $\mathrm{E}[x^{1}]$ $\mathrm{E}[x^{2}]$ $\mathrm{E}[x^{3}]$ $\mathrm{E}[x^{4}]$ $\mathrm{E}[x^{5}]$ $\mathrm{E}[x^{6}]$ $\mathrm{E}[x^{7}]$ $\mathrm{E}[x^{8}]$ $\mathrm{E}[x^{9}]$ $\mathrm{E}[x^{10}]$ $\mathrm{E}[x^{11}]$ $\mathrm{E}[x^{12}]$
$a_1$ $1$ $0$ $2$ $0$ $12$ $0$ $100$ $0$ $1008$ $0$ $11424$ $0$ $139392$
$a_2$ $1$ $1$ $4$ $11$ $46$ $182$ $824$ $3817$ $18582$ $92678$ $473368$ $2458326$ $12947532$

Event Probabilities

$\mathrm{P}[a_1=0]=\frac{1}{4}$