Family Information
| Genus: | $5$ |
| Quotient genus: | $0$ |
| Group name: | $D_6$ |
| Group identifier: | $[12,4]$ |
| Signature: | $[ 0; 2, 2, 6, 6 ]$ |
| Conjugacy classes for this refined passport: | $3, 3, 6, 6$ |
The full automorphism group for this family is $C_2\times D_6$ with signature $[ 0; 2, 2, 2, 6 ]$.
| Jacobian variety group algebra decomposition: | $E\times E^{2}\times E^{2}$ |
| Corresponding character(s): | $3, 5, 6$ |
Generating vector(s)
Displaying 2 of 2 generating vectors for this refined passport.
5.12-4.0.2-2-6-6.1.1
| (1,7) (2,9) (3,8) (4,10) (5,12) (6,11) | |
| (1,7) (2,9) (3,8) (4,10) (5,12) (6,11) | |
| (1,5,3,4,2,6) (7,11,9,10,8,12) | |
| (1,6,2,4,3,5) (7,12,8,10,9,11) |
5.12-4.0.2-2-6-6.1.2
| (1,7) (2,9) (3,8) (4,10) (5,12) (6,11) | |
| (1,9) (2,8) (3,7) (4,12) (5,11) (6,10) | |
| (1,6,2,4,3,5) (7,12,8,10,9,11) | |
| (1,6,2,4,3,5) (7,12,8,10,9,11) |
Displaying the unique representative of this refined passport up to braid equivalence.
5.12-4.0.2-2-6-6.1.1
| (1,7) (2,9) (3,8) (4,10) (5,12) (6,11) | |
| (1,7) (2,9) (3,8) (4,10) (5,12) (6,11) | |
| (1,5,3,4,2,6) (7,11,9,10,8,12) | |
| (1,6,2,4,3,5) (7,12,8,10,9,11) |