# Properties

 Label 1.6.N.36.11a Name $$C(6,2)$$ Weight $1$ Degree $6$ Real dimension $1$ Components $36$ Contained in $$\mathrm{USp}(6)$$ Identity component $$\mathrm{U}(1)_3$$ Component group $$C_3\times A_4$$

## Invariants

 Weight: $1$ Degree: $6$ $\mathbb{R}$-dimension: $1$ Components: $36$ Contained in: $\mathrm{USp}(6)$ Rational: yes

## Identity component

 Name: $\mathrm{U}(1)_3$ $\mathbb{R}$-dimension: $1$ Description: $\left\{\begin{bmatrix}\alpha I_3&0,\\ 0&\bar \alpha I_3\end{bmatrix}: \alpha\bar\alpha=1,\ \alpha\in\mathbb{C}\right\}$ Symplectic form: $\begin{bmatrix} 0 & I_3\\ -I_3 & 0\end{bmatrix}$ Hodge circle: $u\mapsto \mathrm{diag}(u,u, u, \bar u, \bar u, \bar u)$

## Component group

 Name: $C_3\times A_4$ Order: $36$ Abelian: no Generators: $\begin{bmatrix}\zeta_{6}^{1} & 0 & 0 & 0 & 0 & 0 \\0 & 1 & 0 & 0 & 0 & 0 \\0 &0 & \zeta_{6}^{5} & 0 & 0 & 0 \\0 & 0 & 0 & \zeta_{6}^{5} & 0 & 0 \\0 & 0 & 0 & 0 & 1 & 0 \\0 & 0 & 0 & 0 & 0 & \zeta_{6}^{1} \\\end{bmatrix}, \begin{bmatrix}\zeta_{3}^{2} & 0 & 0 & 0 & 0 & 0 \\0 & \zeta_{6}^{1} & 0 & 0 & 0 & 0 \\0 & 0 & \zeta_{6}^{1} & 0 & 0 & 0 \\0 & 0 & 0 & \zeta_{3}^{1} & 0 & 0 \\0 & 0 & 0 & 0 & \zeta_{6}^{5} & 0 \\0 & 0 & 0 & 0 & 0 & \zeta_{6}^{5} \\\end{bmatrix}, \begin{bmatrix}0 & 0 & 1 & 0 & 0 & 0 \\1 & 0 & 0& 0 & 0 & 0 \\0 & 1 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 0 & 1 \\0 & 0 & 0 & 1 & 0 & 0 \\0 & 0 & 0 & 0 & 1 & 0 \\\end{bmatrix}$

## Subgroups and supergroups

 Maximal subgroups: $C(2,2)$${}^{\times 3}, A(6,2), C(3,1) Minimal supergroups: J(C(6,2)), J_s(C(6,2)), D(6,2), C(6,6)$${}^{\times 3}$

## Moment sequences

$x$ $\mathrm{E}[x^{0}]$ $\mathrm{E}[x^{1}]$ $\mathrm{E}[x^{2}]$ $\mathrm{E}[x^{3}]$ $\mathrm{E}[x^{4}]$ $\mathrm{E}[x^{5}]$ $\mathrm{E}[x^{6}]$ $\mathrm{E}[x^{7}]$ $\mathrm{E}[x^{8}]$ $\mathrm{E}[x^{9}]$ $\mathrm{E}[x^{10}]$ $\mathrm{E}[x^{11}]$ $\mathrm{E}[x^{12}]$
$a_1$ $1$ $0$ $2$ $0$ $30$ $0$ $620$ $0$ $15750$ $0$ $456372$ $0$ $14271180$
$a_2$ $1$ $1$ $7$ $61$ $627$ $7241$ $90645$ $1196091$ $16316571$ $227280577$ $3208501497$ $45698791271$ $654946598509$
$a_3$ $1$ $0$ $12$ $0$ $1724$ $0$ $462700$ $0$ $151838316$ $0$ $53592239472$ $0$ $19508674639124$