Family Information
| Genus: | $4$ |
| Quotient genus: | $1$ |
| Group name: | $S_3$ |
| Group identifier: | $[6,1]$ |
| Signature: | $[ 1; 2, 2 ]$ |
| Conjugacy classes for this refined passport: | $2, 2$ |
The full automorphism group for this family is $D_6$ with signature $[ 0; 2, 2, 2, 2, 2 ]$.
| Jacobian variety group algebra decomposition: | $E\times E\times E^{2}$ |
| Corresponding character(s): | $1, 2, 3$ |
Generating vector(s)
Displaying 20 of 23 generating vectors for this refined passport.
4.6-1.1.2-2.1.1
| (1,2,3) (4,5,6) | |
| Id(G) | |
| (1,4) (2,6) (3,5) | |
| (1,4) (2,6) (3,5) |
4.6-1.1.2-2.1.2
| (1,3,2) (4,6,5) | |
| Id(G) | |
| (1,4) (2,6) (3,5) | |
| (1,4) (2,6) (3,5) |
4.6-1.1.2-2.1.3
| (1,6) (2,5) (3,4) | |
| Id(G) | |
| (1,4) (2,6) (3,5) | |
| (1,4) (2,6) (3,5) |
4.6-1.1.2-2.1.4
| (1,5) (2,4) (3,6) | |
| Id(G) | |
| (1,4) (2,6) (3,5) | |
| (1,4) (2,6) (3,5) |
4.6-1.1.2-2.1.5
| Id(G) | |
| (1,2,3) (4,5,6) | |
| (1,4) (2,6) (3,5) | |
| (1,4) (2,6) (3,5) |
4.6-1.1.2-2.1.6
| (1,2,3) (4,5,6) | |
| (1,2,3) (4,5,6) | |
| (1,4) (2,6) (3,5) | |
| (1,4) (2,6) (3,5) |
4.6-1.1.2-2.1.7
| (1,3,2) (4,6,5) | |
| (1,2,3) (4,5,6) | |
| (1,4) (2,6) (3,5) | |
| (1,4) (2,6) (3,5) |
4.6-1.1.2-2.1.8
| Id(G) | |
| (1,3,2) (4,6,5) | |
| (1,4) (2,6) (3,5) | |
| (1,4) (2,6) (3,5) |
4.6-1.1.2-2.1.9
| (1,2,3) (4,5,6) | |
| (1,3,2) (4,6,5) | |
| (1,4) (2,6) (3,5) | |
| (1,4) (2,6) (3,5) |
4.6-1.1.2-2.1.10
| (1,3,2) (4,6,5) | |
| (1,3,2) (4,6,5) | |
| (1,4) (2,6) (3,5) | |
| (1,4) (2,6) (3,5) |
4.6-1.1.2-2.1.11
| Id(G) | |
| (1,6) (2,5) (3,4) | |
| (1,4) (2,6) (3,5) | |
| (1,4) (2,6) (3,5) |
4.6-1.1.2-2.1.12
| (1,6) (2,5) (3,4) | |
| (1,6) (2,5) (3,4) | |
| (1,4) (2,6) (3,5) | |
| (1,4) (2,6) (3,5) |
4.6-1.1.2-2.1.13
| Id(G) | |
| (1,5) (2,4) (3,6) | |
| (1,4) (2,6) (3,5) | |
| (1,4) (2,6) (3,5) |
4.6-1.1.2-2.1.14
| (1,5) (2,4) (3,6) | |
| (1,5) (2,4) (3,6) | |
| (1,4) (2,6) (3,5) | |
| (1,4) (2,6) (3,5) |
4.6-1.1.2-2.1.15
| (1,2,3) (4,5,6) | |
| (1,4) (2,6) (3,5) | |
| (1,4) (2,6) (3,5) | |
| (1,6) (2,5) (3,4) |
4.6-1.1.2-2.1.16
| (1,5) (2,4) (3,6) | |
| (1,4) (2,6) (3,5) | |
| (1,4) (2,6) (3,5) | |
| (1,6) (2,5) (3,4) |
4.6-1.1.2-2.1.17
| (1,4) (2,6) (3,5) | |
| (1,3,2) (4,6,5) | |
| (1,4) (2,6) (3,5) | |
| (1,6) (2,5) (3,4) |
4.6-1.1.2-2.1.18
| (1,6) (2,5) (3,4) | |
| (1,3,2) (4,6,5) | |
| (1,4) (2,6) (3,5) | |
| (1,6) (2,5) (3,4) |
4.6-1.1.2-2.1.19
| (1,5) (2,4) (3,6) | |
| (1,3,2) (4,6,5) | |
| (1,4) (2,6) (3,5) | |
| (1,6) (2,5) (3,4) |
4.6-1.1.2-2.1.20
| (1,2,3) (4,5,6) | |
| (1,6) (2,5) (3,4) | |
| (1,4) (2,6) (3,5) | |
| (1,6) (2,5) (3,4) |