Properties

Label 0.1.528
  
Name \(\mu(528)\)
Weight $0$
Degree $1$
Real dimension $0$
Components $528$
Contained in \(\mathrm{U}(1)\)
Identity component \(\mathrm{SO}(1)\)
Component group \(C_{528}\)

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Invariants

Weight:$0$
Degree:$1$
$\mathbb{R}$-dimension:$0$
Components:$528$
Contained in:$\mathrm{U}(1)$
Rational:no

Identity component

Name:$\mathrm{SO}(1)$
$\mathbb{R}$-dimension:$0$
Description:$\textsf{trivial}$

Component group

Name:$C_{528}$
Order:$528$
Abelian:yes
Generators:$\left[\zeta_{528}\right]$

Subgroups and supergroups

Maximal subgroups:$\mu(264)$, $\mu(176)$, $\mu(48)$
Minimal supergroups:$\mu(1056)$, $\mu(1584)$, $\mu(2640)$, $\ldots$

Moment sequences

$x$ $\mathrm{E}[x^{0}]$ $\mathrm{E}[x^{1}]$ $\mathrm{E}[x^{2}]$ $\mathrm{E}[x^{3}]$ $\mathrm{E}[x^{4}]$ $\mathrm{E}[x^{5}]$ $\mathrm{E}[x^{6}]$ $\mathrm{E}[x^{7}]$ $\mathrm{E}[x^{8}]$ $\mathrm{E}[x^{9}]$ $\mathrm{E}[x^{10}]$ $\mathrm{E}[x^{11}]$ $\mathrm{E}[x^{12}]$
$a_1$ $1$ $0$ $0$ $0$ $0$ $0$ $0$ $0$ $0$ $0$ $0$ $0$ $0$

Event probabilities

[['\\mathrm{Pr}[a_1=1]=\\frac{1}{528}', '\\mathrm{Pr}[a_1=-1]=\\frac{1}{528}']]