Invariants
| Weight: | $0$ |
| Degree: | $1$ |
| $\mathbb{R}$-dimension: | $0$ |
| Components: | $45$ |
| Contained in: | $\mathrm{U}(1)$ |
| Rational: | $\mathrm{False}$ |
Identity Component
| Name: | $\mathrm{SO}(1)$ |
| Index: | $45$ |
| $\mathbb{R}$-dimension: | $0$ |
| Description: | $\mathrm{trivial}$ |
Component Group
| Name: | $C_{45}$ |
| Order: | $45$ |
| Abelian: | $\mathrm{True}$ |
| Generators: | $\left[\zeta_{45}\right]$ |
Subgroups and Supergroups
| Maximal Subgroups: | $\mu(15)$, $\mu(9)$ |
| Minimal Supergroups: | $\mu(90)$, $\mu(135)$, $\mu(225)$, $\ldots$ |
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
| $\mathrm{P}[a_1=1]=\frac{1}{45}$ |