# Properties

 Label 1.6.E.6.1a Name $$E_{s,t}$$ Weight $1$ Degree $6$ Real dimension $9$ Components $6$ Contained in $$\mathrm{USp}(6)$$ Identity component $$\mathrm{SU}(2)^3$$ Component group $$S_3$$

## Invariants

 Weight: $1$ Degree: $6$ $\mathbb{R}$-dimension: $9$ Components: $6$ 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: $S_3$ Order: $6$ Abelian: no Generators: $\begin{bmatrix}0 & 0 & 0 & 0 & 1 & 0 \\0 & 0 & 0 & 0 & 0 & 1 \\1 & 0 & 0 & 0 &0 & 0 \\0 & 1 & 0 & 0 & 0 & 0 \\0 & 0 & 1 & 0 & 0 & 0 \\0 & 0 & 0 & 1 & 0 & 0 \\\end{bmatrix}, \begin{bmatrix}1 & 0 & 0 & 0 & 0 & 0 \\0 & 1 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 1 & 0 \\0 & 0 & 0 & 0 & 0 & 1 \\0 & 0 & 1 & 0 & 0 & 0 \\0 & 0 & 0 & 1 & 0 & 0 \\\end{bmatrix}$

## Moment sequences

$x$ $\mathrm{E}[x^{0}]$ $\mathrm{E}[x^{1}]$ $\mathrm{E}[x^{2}]$ $\mathrm{E}[x^{3}]$ $\mathrm{E}[x^{4}]$ $\mathrm{E}[x^{5}]$ $\mathrm{E}[x^{6}]$ $\mathrm{E}[x^{7}]$ $\mathrm{E}[x^{8}]$ $\mathrm{E}[x^{9}]$ $\mathrm{E}[x^{10}]$ $\mathrm{E}[x^{11}]$ $\mathrm{E}[x^{12}]$
$a_1$ $1$ $0$ $1$ $0$ $5$ $0$ $50$ $0$ $714$ $0$ $12222$ $0$ $233904$
$a_2$ $1$ $1$ $3$ $12$ $65$ $436$ $3377$ $28792$ $262817$ $2526496$ $25309505$ $262280932$ $2796539990$
$a_3$ $1$ $0$ $3$ $0$ $124$ $0$ $12275$ $0$ $1705536$ $0$ $289716588$ $0$ $56419337172$