Properties

 Label 1.6.G.4.1a Name $$F_{ac}\times \mathrm{SU}(2)$$ Weight $1$ Degree $6$ Real dimension $5$ Components $4$ Contained in $$\mathrm{USp}(6)$$ Identity component $$\mathrm{U}(1)^2\times\mathrm{SU}(2)$$ Component group $$C_4$$

Invariants

 Weight: $1$ Degree: $6$ $\mathbb{R}$-dimension: $5$ Components: $4$ Contained in: $\mathrm{USp}(6)$ Rational: yes

Identity component

 Name: $\mathrm{U}(1)^2\times\mathrm{SU}(2)$ $\mathbb{R}$-dimension: $5$ Description: $\left\{\begin{bmatrix}A&0&0\\0&B&0\\0&0&C\end{bmatrix}: A,B\in\mathrm{U}(1)\subseteq\mathrm{SU}(2),C\in\mathrm{SU}(2)\right\}$ 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: $C_4$ Order: $4$ Abelian: yes Generators: $\begin{bmatrix}0 & 0 & 0 & 1 & 0 & 0 \\0 & 0 & -1 & 0 & 0 & 0 \\-1 & 0 & 0 & 0& 0 & 0 \\0 & -1 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 1 & 0 \\0 & 0 & 0 & 0 & 0 & 1\\\end{bmatrix}$

Moment sequences

$x$ $\mathrm{E}[x^{0}]$ $\mathrm{E}[x^{1}]$ $\mathrm{E}[x^{2}]$ $\mathrm{E}[x^{3}]$ $\mathrm{E}[x^{4}]$ $\mathrm{E}[x^{5}]$ $\mathrm{E}[x^{6}]$ $\mathrm{E}[x^{7}]$ $\mathrm{E}[x^{8}]$ $\mathrm{E}[x^{9}]$ $\mathrm{E}[x^{10}]$ $\mathrm{E}[x^{11}]$ $\mathrm{E}[x^{12}]$
$a_1$ $1$ $0$ $2$ $0$ $17$ $0$ $270$ $0$ $5439$ $0$ $123123$ $0$ $3001284$
$a_2$ $1$ $2$ $7$ $38$ $284$ $2567$ $25820$ $276845$ $3098618$ $35803781$ $424226048$ $5130820433$ $63130916975$
$a_3$ $1$ $0$ $7$ $0$ $658$ $0$ $111760$ $0$ $23819390$ $0$ $5769914640$ $0$ $1520601479760$