# Properties

 Label 1.6.E.3.1a Name $$E_{s}$$ Weight $1$ Degree $6$ Real dimension $9$ Components $3$ Contained in $$\mathrm{USp}(6)$$ Identity component $$\mathrm{SU}(2)^3$$ Component group $$C_3$$

## Invariants

 Weight: $1$ Degree: $6$ $\mathbb{R}$-dimension: $9$ Components: $3$ Contained in: $\mathrm{USp}(6)$ Rational: yes

## Identity component

 Name: $\mathrm{SU}(2)^3$ $\mathbb{R}$-dimension: $9$ Description: $\left\{\begin{bmatrix}A&0&0\\0&B&0\\0&0&C\end{bmatrix}: A,B,C\in\mathrm{SU}(2)\right\}$ Symplectic form: $\begin{bmatrix}J_2&0&0\\0&J_2&0\\0&0&J_2\end{bmatrix},\ J_2:=\begin{bmatrix}0&1\\-1&0\end{bmatrix}$ Hodge circle: $u\mapsto\mathrm{diag}(u,\bar u, u, \bar u, u, \bar u)$

## Component group

 Name: $C_3$ Order: $3$ Abelian: yes Generators: $\begin{bmatrix}0 & 0 & 0 & 0 & 1 & 0 \\0 & 0 & 0 & 0 & 0 & 1 \\1 & 0 & 0 & 0 &0 & 0 \\0 & 1 & 0 & 0 & 0 & 0 \\0 & 0 & 1 & 0 & 0 & 0 \\0 & 0 & 0 & 1 & 0 & 0 \\\end{bmatrix}$

## Moment sequences

$x$ $\mathrm{E}[x^{0}]$ $\mathrm{E}[x^{1}]$ $\mathrm{E}[x^{2}]$ $\mathrm{E}[x^{3}]$ $\mathrm{E}[x^{4}]$ $\mathrm{E}[x^{5}]$ $\mathrm{E}[x^{6}]$ $\mathrm{E}[x^{7}]$ $\mathrm{E}[x^{8}]$ $\mathrm{E}[x^{9}]$ $\mathrm{E}[x^{10}]$ $\mathrm{E}[x^{11}]$ $\mathrm{E}[x^{12}]$
$a_1$ $1$ $0$ $1$ $0$ $8$ $0$ $95$ $0$ $1414$ $0$ $24402$ $0$ $467676$
$a_2$ $1$ $1$ $4$ $20$ $121$ $851$ $6703$ $57457$ $525311$ $5052157$ $50616822$ $524556066$ $5593064469$
$a_3$ $1$ $0$ $5$ $0$ $244$ $0$ $24525$ $0$ $3410876$ $0$ $579431412$ $0$ $112838656920$