Invariants
Weight: | $0$ |
Degree: | $1$ |
$\mathbb{R}$-dimension: | $0$ |
Components: | $40$ |
Contained in: | $\mathrm{O}(1)$ |
Rational: | yes |
Identity component
Name: | $\mathrm{SO}(1)$ |
$\mathbb{R}$-dimension: | $0$ |
Description: | $\textsf{trivial}$ |
Component group
Name: | $C_{40}$ |
Order: | $40$ |
Abelian: | yes |
Generators: | $\begin{bmatrix}\zeta_{40}\end{bmatrix}$ |
Subgroups and supergroups
Maximal subgroups: | $\mu(20)$, $\mu(8)$ |
Minimal supergroups: | $\mu(80)$, $\mu(120)$, $\mu(200)$, $\cdots$ |
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
$\mathrm{Pr}[a_1=1]=1/40$ |