# Properties

 Label 0.1.138 Name $$\mu(138)$$ Weight $0$ Degree $1$ Real dimension $0$ Components $138$ Contained in $$\mathrm{U}(1)$$ Identity component $$\mathrm{SO}(1)$$ Component group $$C_{138}$$

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## Invariants

 Weight: $0$ Degree: $1$ $\mathbb{R}$-dimension: $0$ Components: $138$ Contained in: $\mathrm{U}(1)$ Rational: no

## Identity component

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

## Component group

 Name: $C_{138}$ Order: $138$ Abelian: yes Generators: $\left[\zeta_{138}\right]$

## Subgroups and supergroups

 Maximal subgroups: $\mu(69)$, $\mu(46)$, $\mu(6)$ Minimal supergroups: $\mu(276)$, $\mu(414)$, $\mu(690)$, $\ldots$

## 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

 $\mathrm{Pr}[a_1=1]=\frac{1}{138}$