Family Information
| Genus: | $7$ |
| Quotient genus: | $0$ |
| Group name: | $C_3:C_4$ |
| Group identifier: | $[12,1]$ |
| Signature: | $[ 0; 4, 4, 4, 4 ]$ |
| Conjugacy classes for this refined passport: | $4, 4, 4, 4$ |
The full automorphism group for this family is $S_3\times D_4$ with signature $[ 0; 2, 2, 2, 4 ]$.
| Jacobian variety group algebra decomposition: | $E\times A_{2}\times A_{4}$ |
| Corresponding character(s): | $2, 3, 5$ |
Generating vector(s)
Displaying 4 of 4 generating vectors for this refined passport.
7.12-1.0.4-4-4-4.1.1
| (1,7,4,10) (2,9,5,12) (3,8,6,11) | |
| (1,7,4,10) (2,9,5,12) (3,8,6,11) | |
| (1,9,4,12) (2,8,5,11) (3,7,6,10) | |
| (1,9,4,12) (2,8,5,11) (3,7,6,10) |
7.12-1.0.4-4-4-4.1.2
| (1,7,4,10) (2,9,5,12) (3,8,6,11) | |
| (1,9,4,12) (2,8,5,11) (3,7,6,10) | |
| (1,7,4,10) (2,9,5,12) (3,8,6,11) | |
| (1,8,4,11) (2,7,5,10) (3,9,6,12) |
7.12-1.0.4-4-4-4.1.3
| (1,7,4,10) (2,9,5,12) (3,8,6,11) | |
| (1,9,4,12) (2,8,5,11) (3,7,6,10) | |
| (1,9,4,12) (2,8,5,11) (3,7,6,10) | |
| (1,7,4,10) (2,9,5,12) (3,8,6,11) |
7.12-1.0.4-4-4-4.1.4
| (1,7,4,10) (2,9,5,12) (3,8,6,11) | |
| (1,9,4,12) (2,8,5,11) (3,7,6,10) | |
| (1,8,4,11) (2,7,5,10) (3,9,6,12) | |
| (1,9,4,12) (2,8,5,11) (3,7,6,10) |
Displaying the unique representative of this refined passport up to braid equivalence.
7.12-1.0.4-4-4-4.1.1
| (1,7,4,10) (2,9,5,12) (3,8,6,11) | |
| (1,7,4,10) (2,9,5,12) (3,8,6,11) | |
| (1,9,4,12) (2,8,5,11) (3,7,6,10) | |
| (1,9,4,12) (2,8,5,11) (3,7,6,10) |