Properties

Label 1.4.3.6.2a
  
Name \(E_6\)
Weight 1
Degree 4
Real dimension 3
Components 6
Contained in \(\mathrm{USp}(4)\)
Identity Component \(\mathrm{SU}(2)_2\)
Component group \(C_6\)

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Invariants

Weight:$1$
Degree:$4$
$\mathbb{R}$-dimension:$3$
Components:$6$
Contained in:$\mathrm{USp}(4)$
Rational:$\mathrm{True}$

Identity Component

Name:$\mathrm{SU}(2)_2$
Index:$6$
$\mathbb{R}$-dimension:$3$
Description:$\left\{\begin{bmatrix}A&0\\0&\bar{A}\end{bmatrix}: A\in \mathrm{SU}(2)\right\}$

Component Group

Name:$C_6$
Order:$6$
Abelian:$\mathrm{True}$

Subgroups and Supergroups

Maximal Subgroups:$E_2$, $E_3$
Minimal Supergroups:$J(E_6)$

Moment Statistics

$x$ $\mathrm{E}[x^{0}]$ $\mathrm{E}[x^{1}]$ $\mathrm{E}[x^{2}]$ $\mathrm{E}[x^{3}]$ $\mathrm{E}[x^{4}]$ $\mathrm{E}[x^{5}]$ $\mathrm{E}[x^{6}]$ $\mathrm{E}[x^{7}]$ $\mathrm{E}[x^{8}]$ $\mathrm{E}[x^{9}]$ $\mathrm{E}[x^{10}]$ $\mathrm{E}[x^{11}]$ $\mathrm{E}[x^{12}]$
$a_1$ $1$ $0$ $2$ $0$ $12$ $0$ $100$ $0$ $980$ $0$ $10584$ $0$ $122232$
$a_2$ $1$ $1$ $4$ $11$ $44$ $172$ $754$ $3397$ $16020$ $77516$ $384578$ $1944626$ $9997970$

Event Probabilities

$\mathrm{P}[a_1=0]=\frac{1}{6}$