Invariants
| Weight: | $0$ |
| Degree: | $1$ |
| $\mathbb{R}$-dimension: | $0$ |
| Components: | $54$ |
| Contained in: | $\mathrm{U}(1)$ |
| Rational: | no |
Identity component
| Name: | $\mathrm{SO}(1)$ |
| $\mathbb{R}$-dimension: | $0$ |
| Description: | $\textsf{trivial}$ |
Component group
| Name: | $C_{54}$ |
| Order: | $54$ |
| Abelian: | yes |
| Generators: | $\left[\zeta_{54}\right]$ |
Subgroups and supergroups
| Maximal subgroups: | $\mu(27)$, $\mu(18)$ |
| Minimal supergroups: | $\mu(108)$, $\mu(162)$, $\mu(270)$, $\ldots$ |
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
| $\mathrm{Pr}[a_1=1]=\frac{1}{54}$ |