Properties

Label 1.4.1.2.1a
  
Name \(C_2\)
Weight 1
Degree 4
Real dimension 1
Components 2
Contained in \(\mathrm{USp}(4)\)
Identity Component \(\mathrm{U}(1)_2\)
Component group \(C_2\)

Learn more about

Invariants

Weight:$1$
Degree:$4$
$\mathbb{R}$-dimension:$1$
Components:$2$
Contained in:$\mathrm{USp}(4)$
Rational:$\mathrm{True}$

Identity Component

Name:$\mathrm{U}(1)_2$
Index:$2$
$\mathbb{R}$-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:$C_2$
Order:$2$
Abelian:$\mathrm{True}$

Subgroups and Supergroups

Maximal Subgroups:$C_1$
Minimal Supergroups:$C_4$, $C_{4,1}$, $D_2$, $J(C_2)$, $D_{2,1}$, $D_3$, $C_6$

Moment Statistics

$x$ $\mathrm{E}[x^{0}]$ $\mathrm{E}[x^{1}]$ $\mathrm{E}[x^{2}]$ $\mathrm{E}[x^{3}]$ $\mathrm{E}[x^{4}]$ $\mathrm{E}[x^{5}]$ $\mathrm{E}[x^{6}]$ $\mathrm{E}[x^{7}]$ $\mathrm{E}[x^{8}]$ $\mathrm{E}[x^{9}]$ $\mathrm{E}[x^{10}]$ $\mathrm{E}[x^{11}]$ $\mathrm{E}[x^{12}]$
$a_1$ $1$ $0$ $4$ $0$ $48$ $0$ $640$ $0$ $8960$ $0$ $129024$ $0$ $1892352$
$a_2$ $1$ $2$ $10$ $44$ $230$ $1212$ $6628$ $36696$ $205766$ $1162988$ $6616940$ $37841256$ $217331804$

Event Probabilities

$\mathrm{P}[a_1=0]=\frac{1}{2}$