Properties

 Label 0.1.37 Name $$\mu(37)$$ Weight $0$ Degree $1$ Real dimension $0$ Components $37$ Contained in $$\mathrm{U}(1)$$ Identity Component $$\mathrm{SO}(1)$$ Component group $$C_{37}$$

Invariants

 Weight: $0$ Degree: $1$ $\mathbb{R}$-dimension: $0$ Components: $37$ Contained in: $\mathrm{U}(1)$ Rational: $\mathrm{False}$

Identity Component

 Name: $\mathrm{SO}(1)$ Index: $37$ $\mathbb{R}$-dimension: $0$ Description: $\mathrm{trivial}$

Component Group

 Name: $C_{37}$ Order: $37$ Abelian: $\mathrm{True}$ Generators: $\left[\zeta_{37}\right]$

Subgroups and Supergroups

 Maximal Subgroups: $\mu(1)$ Minimal Supergroups: $\mu(74)$, $\mu(111)$, $\mu(185)$, $\ldots$

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

 $\mathrm{P}[a_1=1]=\frac{1}{37}$