the group $\mathrm{C}_{2}$
- GAP SmallGroup id
- $[2, 1]$
- order
- $2$ (cyclic)
- structure
- $\mathrm{C}_{2}$
- presentation
- $\langle g_{1} \mid g_{1}^{2} \rangle$
character table
Columns are the conjugacy classes: order is the order of a class representative, size the number of elements in the class. Rows $\chi_i$ are the irreducible characters.
| order | 1 | 2 |
|---|---|---|
| size | 1 | 1 |
| $\chi_{ 1 }$ | $1$ | $1$ |
| $\chi_{ 2 }$ | $1$ | $-1$ |
hyperelliptic quotients
- dimension 2, representation $\operatorname{diag}(1, -1)$ with $q = 1$, $\operatorname{ord} \omega_X = 2$, moduli $2$
- dimension 3, representation $\operatorname{diag}(1, 1, -1)$ with $q = 2$, $\operatorname{ord} \omega_X = 2$, moduli $5$
- dimension 3, representation $\operatorname{diag}(1, -1, -1)$ with $q = 1$, $\operatorname{ord} \omega_X = 1$, moduli $5$
- dimension 4, representation $\operatorname{diag}(1, 1, 1, -1)$ with $q = 3$, $\operatorname{ord} \omega_X = 2$, moduli $10$
- dimension 4, representation $\operatorname{diag}(1, 1, -1, -1)$ with $q = 2$, $\operatorname{ord} \omega_X = 1$, moduli $8$
- dimension 4, representation $\operatorname{diag}(1, -1, -1, -1)$ with $q = 1$, $\operatorname{ord} \omega_X = 2$, moduli $10$