Properties

Label 1.4.3.3.1a
  
Name \(E_3\)
Weight 1
Degree 4
Real dimension 3
Components 3
Contained in \(\mathrm{USp}(4)\)
Identity Component \(\mathrm{SU}(2)_2\)
Component group \(C_3\)

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Invariants

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

Identity Component

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

Component Group

Name:$C_3$
Order:$3$
Abelian:$\mathrm{True}$

Subgroups and Supergroups

Maximal Subgroups:$E_1$
Minimal Supergroups:$J(E_3)$, $E_6$

Moment Statistics

$x$ $\mathrm{E}[x^{0}]$ $\mathrm{E}[x^{1}]$ $\mathrm{E}[x^{2}]$ $\mathrm{E}[x^{3}]$ $\mathrm{E}[x^{4}]$ $\mathrm{E}[x^{5}]$ $\mathrm{E}[x^{6}]$ $\mathrm{E}[x^{7}]$ $\mathrm{E}[x^{8}]$ $\mathrm{E}[x^{9}]$ $\mathrm{E}[x^{10}]$ $\mathrm{E}[x^{11}]$ $\mathrm{E}[x^{12}]$
$a_1$ $1$ $0$ $2$ $0$ $12$ $0$ $110$ $0$ $1204$ $0$ $14364$ $0$ $180312$
$a_2$ $1$ $1$ $4$ $13$ $52$ $222$ $1014$ $4839$ $23860$ $120526$ $620278$ $3239788$ $17127202$