Properties

Label 1.4.3.12.4a
  
Name \(J(E_6)\)
Weight 1
Degree 4
Real dimension 3
Components 12
Contained in \(\mathrm{USp}(4)\)
Identity Component \(\mathrm{SU}(2)_2\)
Component group \(D_6\)

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Invariants

Weight:$1$
Degree:$4$
$\mathbb{R}$-dimension:$3$
Components:$12$
Contained in:$\mathrm{USp}(4)$
Rational:$\mathrm{True}$

Identity Component

Name:$\mathrm{SU}(2)_2$
Index:$12$
$\mathbb{R}$-dimension:$3$
Description:$\left\{\begin{bmatrix}A&0\\0&\bar{A}\end{bmatrix}: A\in \mathrm{SU}(2)\right\}$

Component Group

Name:$D_6$
Order:$12$
Abelian:$\mathrm{False}$

Subgroups and Supergroups

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

Moment Statistics

$x$ $\mathrm{E}[x^{0}]$ $\mathrm{E}[x^{1}]$ $\mathrm{E}[x^{2}]$ $\mathrm{E}[x^{3}]$ $\mathrm{E}[x^{4}]$ $\mathrm{E}[x^{5}]$ $\mathrm{E}[x^{6}]$ $\mathrm{E}[x^{7}]$ $\mathrm{E}[x^{8}]$ $\mathrm{E}[x^{9}]$ $\mathrm{E}[x^{10}]$ $\mathrm{E}[x^{11}]$ $\mathrm{E}[x^{12}]$
$a_1$ $1$ $0$ $1$ $0$ $6$ $0$ $50$ $0$ $490$ $0$ $5292$ $0$ $61116$
$a_2$ $1$ $1$ $3$ $7$ $25$ $91$ $387$ $1716$ $8045$ $38821$ $192415$ $972544$ $4999447$

Event Probabilities

$\mathrm{P}[a_1=0]=\frac{7}{12}$