# Properties

 Label 0.1.160 Name $$\mu(160)$$ Weight 0 Degree 1 Real dimension 0 Components 160 Contained in $$\mathrm{U}(1)$$ Identity Component $$\mathrm{SO}(1)$$ Component group $$C_{160}$$

## Invariants

 Weight: $0$ Degree: $1$ $\mathbb{R}$-dimension: $0$ Components: $160$ Contained in: $\mathrm{U}(1)$ Rational: $\mathrm{False}$

## Identity Component

 Name: $\mathrm{SO}(1)$ Index: $160$ $\mathbb{R}$-dimension: $0$ Description: $\mathrm{trivial}$

## Component Group

 Name: $C_{160}$ Order: $160$ Abelian: $\mathrm{True}$ Generators: $\left[\zeta_{160}\right]$

## Subgroups and Supergroups

 Maximal Subgroups: $\mu(80)$, $\mu(32)$ Minimal Supergroups: $\mu(320)$, $\mu(480)$, $\mu(800)$, $\ldots$

## 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

 $\mathrm{P}[a_1=1]=\frac{1}{160}$ $\mathrm{P}[a_1=-1]=\frac{1}{160}$