Properties

Label 1.4.2.4.1a
  
Name \(F_{ac}\)
Weight 1
Degree 4
Real dimension 2
Components 4
Contained in \(\mathrm{USp}(4)\)
Identity Component \(\mathrm{U}(1)\times\mathrm{U}(1)\)
Component group \(C_4\)

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Invariants

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

Identity Component

Name:$\mathrm{U}(1)\times\mathrm{U}(1)$
Index:$4$
$\mathbb{R}$-dimension:$2$
Description:$\left\{\begin{bmatrix}A&0\\0&B\end{bmatrix}: A,B\in \mathrm{U}(1)\right\}$

Component Group

Name:$C_4$
Order:$4$
Abelian:$\mathrm{True}$

Subgroups and Supergroups

Maximal Subgroups:$F_{ab}$
Minimal Supergroups:

Moment Statistics

$x$ $\mathrm{E}[x^{0}]$ $\mathrm{E}[x^{1}]$ $\mathrm{E}[x^{2}]$ $\mathrm{E}[x^{3}]$ $\mathrm{E}[x^{4}]$ $\mathrm{E}[x^{5}]$ $\mathrm{E}[x^{6}]$ $\mathrm{E}[x^{7}]$ $\mathrm{E}[x^{8}]$ $\mathrm{E}[x^{9}]$ $\mathrm{E}[x^{10}]$ $\mathrm{E}[x^{11}]$ $\mathrm{E}[x^{12}]$
$a_1$ $1$ $0$ $1$ $0$ $9$ $0$ $100$ $0$ $1225$ $0$ $15876$ $0$ $213444$
$a_2$ $1$ $1$ $3$ $10$ $41$ $186$ $912$ $4656$ $24425$ $130402$ $705368$ $3854016$ $21230420$

Event Probabilities

$\mathrm{P}[a_1=0]=\frac{3}{4}$
$\mathrm{P}[a_2=0]=\frac{2}{4}$ $\mathrm{P}[a_2=2]=\frac{1}{4}$