Invariants
Weight: | $0$ |
Degree: | $1$ |
$\mathbb{R}$-dimension: | $0$ |
Components: | $54$ |
Contained in: | $\mathrm{U}(1)$ |
Rational: | $\mathrm{False}$ |
Identity Component
Name: | $\mathrm{SO}(1)$ |
Index: | $54$ |
$\mathbb{R}$-dimension: | $0$ |
Description: | $\mathrm{trivial}$ |
Component Group
Name: | $C_{54}$ |
Order: | $54$ |
Abelian: | $\mathrm{True}$ |
Generators: | $\left[\zeta_{54}\right]$ |
Subgroups and Supergroups
Maximal Subgroups: | $\mu(27)$, $\mu(18)$ |
Minimal Supergroups: | $\mu(108)$, $\mu(162)$, $\mu(270)$, $\ldots$ |
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
$\mathrm{P}[a_1=1]=\frac{1}{54}$ |
$\mathrm{P}[a_1=-1]=\frac{1}{54}$ |