# Properties

 Label 1.6.H.8.2a Name $$H_{c,at}$$ Weight $1$ Degree $6$ Real dimension $3$ Components $8$ Contained in $$\mathrm{USp}(6)$$ Identity component $$\mathrm{U}(1)^3$$ Component group $$C_2\times C_4$$

## Invariants

 Weight: $1$ Degree: $6$ $\mathbb{R}$-dimension: $3$ Components: $8$ Contained in: $\mathrm{USp}(6)$ Rational: yes

## Identity component

 Name: $\mathrm{U}(1)^3$ $\mathbb{R}$-dimension: $3$ Description: $\left\{\begin{bmatrix}A&0&0\\0&B&0\\0&0&C\end{bmatrix}: A,B,C\in\mathrm{U}(1)\subseteq\mathrm{SU}(2)\right\}$ 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: $C_2\times C_4$ Order: $8$ Abelian: yes Generators: $\begin{bmatrix}1 & 0 & 0 & 0 & 0 & 0 \\0 & 1 & 0 & 0 & 0 & 0 \\0 & 0 & 1 & 0 &0 & 0 \\0 & 0 & 0 & 1 & 0 & 0 \\0 & 0 & 0 & 0 & 0 & 1 \\0 & 0 & 0 & 0 & -1 & 0 \\\end{bmatrix}, \begin{bmatrix}0 & 0 & 0 & 1 & 0 & 0 \\0 & 0 & -1 & 0 & 0 & 0 \\1 & 0 & 0 & 0 & 0 & 0 \\0 & 1 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 1 & 0 \\0 & 0 & 0 & 0 & 0 & 1 \\\end{bmatrix}$

## Moment sequences

$x$ $\mathrm{E}[x^{0}]$ $\mathrm{E}[x^{1}]$ $\mathrm{E}[x^{2}]$ $\mathrm{E}[x^{3}]$ $\mathrm{E}[x^{4}]$ $\mathrm{E}[x^{5}]$ $\mathrm{E}[x^{6}]$ $\mathrm{E}[x^{7}]$ $\mathrm{E}[x^{8}]$ $\mathrm{E}[x^{9}]$ $\mathrm{E}[x^{10}]$ $\mathrm{E}[x^{11}]$ $\mathrm{E}[x^{12}]$
$a_1$ $1$ $0$ $2$ $0$ $18$ $0$ $290$ $0$ $6230$ $0$ $154602$ $0$ $4169088$
$a_2$ $1$ $2$ $7$ $38$ $293$ $2822$ $30805$ $360740$ $4408633$ $55434098$ $711476627$ $9275791010$ $122452588967$
$a_3$ $1$ $0$ $7$ $0$ $699$ $0$ $142000$ $0$ $36822555$ $0$ $10613578752$ $0$ $3250344268248$