# Properties

 Label 0.1.53 Name $$\mu(53)$$ Weight $0$ Degree $1$ Real dimension $0$ Components $53$ Contained in $$\mathrm{O}(1)$$ Identity component $$\mathrm{SO}(1)$$ Component group $$C_{53}$$

## Invariants

 Weight: $0$ Degree: $1$ $\mathbb{R}$-dimension: $0$ Components: $53$ Contained in: $\mathrm{O}(1)$ Rational: yes

## Identity component

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

## Component group

 Name: $C_{53}$ Order: $53$ Abelian: yes Generators: $\begin{bmatrix}\zeta_{53}\end{bmatrix}$

## Subgroups and supergroups

 Maximal subgroups: $\mu(1)$ Minimal supergroups: $\mu(106)$, $\mu(159)$, $\mu(265)$, $\cdots$

## 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

 $\mathrm{Pr}[a_1=1]=1/53$