Properties

Label 1.4.1.3.1a
  
Name \(C_3\)
Weight 1
Degree 4
Real dimension 1
Components 3
Contained in \(\mathrm{USp}(4)\)
Identity Component \(\mathrm{U}(1)_2\)
Component group \(C_3\)

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Invariants

Weight:$1$
Degree:$4$
$\mathbb{R}$-dimension:$1$
Components:$3$
Contained in:$\mathrm{USp}(4)$
Rational:$\mathrm{True}$

Identity Component

Name:$\mathrm{U}(1)_2$
Index:$3$
$\mathbb{R}$-dimension:$1$
Description:$\left\{\begin{bmatrix}\mathrm{diag}_2(\alpha)&0\\0&\mathrm{diag}_2(\bar\alpha)\end{bmatrix}: \alpha\bar\alpha = 1,\ \alpha\in\mathbb{C}\right\},\ \mathrm{diag}_2(\alpha):=\begin{bmatrix}\alpha&0\\0&\alpha\end{bmatrix}$

Component Group

Name:$C_3$
Order:$3$
Abelian:$\mathrm{True}$

Subgroups and Supergroups

Maximal Subgroups:$C_1$
Minimal Supergroups:$D_3$, $D_{3,2}$, $C_6$, $J(C_3)$, $C_{6,1}$, $T$

Moment Statistics

$x$ $\mathrm{E}[x^{0}]$ $\mathrm{E}[x^{1}]$ $\mathrm{E}[x^{2}]$ $\mathrm{E}[x^{3}]$ $\mathrm{E}[x^{4}]$ $\mathrm{E}[x^{5}]$ $\mathrm{E}[x^{6}]$ $\mathrm{E}[x^{7}]$ $\mathrm{E}[x^{8}]$ $\mathrm{E}[x^{9}]$ $\mathrm{E}[x^{10}]$ $\mathrm{E}[x^{11}]$ $\mathrm{E}[x^{12}]$
$a_1$ $1$ $0$ $4$ $0$ $36$ $0$ $440$ $0$ $6020$ $0$ $86184$ $0$ $1262184$
$a_2$ $1$ $2$ $8$ $34$ $164$ $842$ $4506$ $24726$ $137892$ $777418$ $4417178$ $25244606$ $144936754$