Properties

Label 0.1.13250
  
Name \(\mu(13250)\)
Weight $0$
Degree $1$
Real dimension $0$
Components $13250$
Contained in \(\mathrm{O}(1)\)
Identity component \(\mathrm{SO}(1)\)
Component group \(C_{13250}\)

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Invariants

Weight:$0$
Degree:$1$
$\mathbb{R}$-dimension:$0$
Components:$13250$
Contained in:$\mathrm{O}(1)$
Rational:yes

Identity component

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

Component group

Name:$C_{13250}$
Order:$13250$
Abelian:yes
Generators:$\begin{bmatrix}\zeta_{13250}\end{bmatrix}$

Subgroups and supergroups

Maximal subgroups:$\mu(6625)$, $\mu(2650)$, $\mu(250)$
Minimal supergroups:$\mu(26500)$, $\mu(39750)$, $\mu(66250)$, $\cdots$

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

$\mathrm{Pr}[a_1=1]=1/13250$