Family Information
| Genus: | $6$ |
| Quotient genus: | $0$ |
| Group name: | $C_3:C_4$ |
| Group identifier: | $[12,1]$ |
| Signature: | $[ 0; 3, 3, 4, 4 ]$ |
| Conjugacy classes for this refined passport: | $3, 3, 4, 5$ |
The full automorphism group for this family is $C_3:D_4$ with signature $[ 0; 2, 2, 3, 4 ]$.
| Jacobian variety group algebra decomposition: | $A_{4}\times E^{2}$ |
| Corresponding character(s): | $5, 6$ |
Generating vector(s)
Displaying 2 of 2 generating vectors for this refined passport.
6.12-1.0.3-3-4-4.1.1
| (1,2,3) (4,5,6) (7,8,9) (10,11,12) | |
| (1,2,3) (4,5,6) (7,8,9) (10,11,12) | |
| (1,7,4,10) (2,9,5,12) (3,8,6,11) | |
| (1,11,4,8) (2,10,5,7) (3,12,6,9) |
6.12-1.0.3-3-4-4.1.2
| (1,2,3) (4,5,6) (7,8,9) (10,11,12) | |
| (1,3,2) (4,6,5) (7,9,8) (10,12,11) | |
| (1,7,4,10) (2,9,5,12) (3,8,6,11) | |
| (1,10,4,7) (2,12,5,9) (3,11,6,8) |
Displaying the unique representative of this refined passport up to braid equivalence.
6.12-1.0.3-3-4-4.1.1
| (1,2,3) (4,5,6) (7,8,9) (10,11,12) | |
| (1,2,3) (4,5,6) (7,8,9) (10,11,12) | |
| (1,7,4,10) (2,9,5,12) (3,8,6,11) | |
| (1,11,4,8) (2,10,5,7) (3,12,6,9) |