Properties

Label 0.1.84
  
Name \(\mu(84)\)
Weight 0
Degree 1
Real dimension 0
Components 84
Contained in \(\mathrm{U}(1)\)
Identity Component \(\mathrm{SO}(1)\)
Component group \(C_{84}\)

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Invariants

Weight:$0$
Degree:$1$
$\mathbb{R}$-dimension:$0$
Components:$84$
Contained in:$\mathrm{U}(1)$
Rational:$\mathrm{False}$

Identity Component

Name:$\mathrm{SO}(1)$
Index:$84$
$\mathbb{R}$-dimension:$0$
Description:$\mathrm{trivial}$

Component Group

Name:$C_{84}$
Order:$84$
Abelian:$\mathrm{True}$
Generators:$\left[\zeta_{84}\right]$

Subgroups and Supergroups

Maximal Subgroups:$\mu(42)$, $\mu(28)$, $\mu(12)$
Minimal Supergroups:$\mu(168)$, $\mu(252)$, $\mu(420)$, $\ldots$

Moment Statistics

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

Event Probabilities

$\mathrm{P}[a_1=1]=\frac{1}{84}$
$\mathrm{P}[a_1=-1]=\frac{1}{84}$