# Properties

 Label 1.6.B.2.1a Name $$N(\mathrm{U}(3))$$ Weight $1$ Degree $6$ Real dimension $9$ Components $2$ Contained in $$\mathrm{USp}(6)$$ Identity component $$\mathrm{U}(3)$$ Component group $$C_2$$

## Invariants

 Weight: $1$ Degree: $6$ $\mathbb{R}$-dimension: $9$ Components: $2$ Contained in: $\mathrm{USp}(6)$ Rational: yes

## Identity component

 Name: $\mathrm{U}(3)$ $\mathbb{R}$-dimension: $9$ Description: $\left\{\begin{bmatrix}A&0\\0&\overline{A}\end{bmatrix}: A\in\mathrm{U}(3)\right\}$ 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: $C_2$ Order: $2$ Abelian: yes Generators: $\begin{bmatrix}0 & 0 & 0 & 1 & 0 & 0 \\0 & 0 & 0 & 0 & 1 & 0 \\0 & 0 & 0 & 0 &0 & 1 \\-1 & 0 & 0 & 0 & 0 & 0 \\0 & -1 & 0 & 0 & 0 & 0 \\0 & 0 & -1 & 0 & 0 & 0\\\end{bmatrix}$

## Moment sequences

$x$ $\mathrm{E}[x^{0}]$ $\mathrm{E}[x^{1}]$ $\mathrm{E}[x^{2}]$ $\mathrm{E}[x^{3}]$ $\mathrm{E}[x^{4}]$ $\mathrm{E}[x^{5}]$ $\mathrm{E}[x^{6}]$ $\mathrm{E}[x^{7}]$ $\mathrm{E}[x^{8}]$ $\mathrm{E}[x^{9}]$ $\mathrm{E}[x^{10}]$ $\mathrm{E}[x^{11}]$ $\mathrm{E}[x^{12}]$
$a_1$ $1$ $0$ $1$ $0$ $6$ $0$ $60$ $0$ $805$ $0$ $12978$ $0$ $237006$
$a_2$ $1$ $1$ $3$ $11$ $58$ $382$ $2922$ $24642$ $222728$ $2122232$ $21092807$ $217061737$ $2300105315$
$a_3$ $1$ $0$ $3$ $0$ $116$ $0$ $10630$ $0$ $1422428$ $0$ $236405736$ $0$ $45382171296$