# Properties

 Label 1.6.F.4.2a Name $$F_{a,t}$$ Weight $1$ Degree $6$ Real dimension $7$ Components $4$ Contained in $$\mathrm{USp}(6)$$ Identity component $$\mathrm{U}(1)\times\mathrm{SU}(2)^2$$ Component group $$C_2^2$$

## Invariants

 Weight: $1$ Degree: $6$ $\mathbb{R}$-dimension: $7$ Components: $4$ Contained in: $\mathrm{USp}(6)$ Rational: yes

## Identity component

 Name: $\mathrm{U}(1)\times\mathrm{SU}(2)^2$ $\mathbb{R}$-dimension: $7$ Description: $\left\{\begin{bmatrix}A&0&0\\0&B&0\\0&0&C\end{bmatrix}: A\in\mathrm{U}(1)\subseteq\mathrm{SU}(2),B,C\in\mathrm{SU}(2)\right\}$ 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: $C_2^2$ Order: $4$ Abelian: yes Generators: $\begin{bmatrix}0 & 1 & 0 & 0 & 0 & 0 \\-1 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 1 & 0 & 0 & 0 \\0 & 0 & 0 & 1 & 0 & 0 \\0 & 0 & 0 & 0 & 1 & 0 \\0 & 0 & 0 & 0 & 0 & 1 \\\end{bmatrix}, \begin{bmatrix}1 & 0 & 0 & 0 & 0 & 0 \\0 & 1 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 1 & 0 \\0 & 0 & 0 & 0 & 0 & 1 \\0 & 0 & 1 & 0 & 0 & 0 \\0 & 0 & 0 & 1 & 0 & 0 \\\end{bmatrix}$

## Moment sequences

$x$ $\mathrm{E}[x^{0}]$ $\mathrm{E}[x^{1}]$ $\mathrm{E}[x^{2}]$ $\mathrm{E}[x^{3}]$ $\mathrm{E}[x^{4}]$ $\mathrm{E}[x^{5}]$ $\mathrm{E}[x^{6}]$ $\mathrm{E}[x^{7}]$ $\mathrm{E}[x^{8}]$ $\mathrm{E}[x^{9}]$ $\mathrm{E}[x^{10}]$ $\mathrm{E}[x^{11}]$ $\mathrm{E}[x^{12}]$
$a_1$ $1$ $0$ $2$ $0$ $14$ $0$ $165$ $0$ $2639$ $0$ $50253$ $0$ $1066659$
$a_2$ $1$ $2$ $7$ $32$ $191$ $1402$ $11905$ $111414$ $1114062$ $11681759$ $126982850$ $1420331497$ $16263790724$
$a_3$ $1$ $0$ $7$ $0$ $389$ $0$ $46510$ $0$ $7837347$ $0$ $1582522578$ $0$ $358153094508$