Properties

Label 0.1.285
  
Name \(\mu(285)\)
Weight $0$
Degree $1$
Real dimension $0$
Components $285$
Contained in \(\mathrm{O}(1)\)
Identity component \(\mathrm{SO}(1)\)
Component group \(C_{285}\)

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Invariants

Weight:$0$
Degree:$1$
$\mathbb{R}$-dimension:$0$
Components:$285$
Contained in:$\mathrm{O}(1)$
Rational:yes

Identity component

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

Component group

Name:$C_{285}$
Order:$285$
Abelian:yes
Generators:$\begin{bmatrix}\zeta_{285}\end{bmatrix}$

Subgroups and supergroups

Maximal subgroups:$\mu(95)$, $\mu(57)$, $\mu(15)$
Minimal supergroups:$\mu(570)$, $\mu(855)$, $\mu(1425)$, $\cdots$

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

$\mathrm{Pr}[a_1=1]=1/285$