Family Information
| Genus: | $5$ |
| Quotient genus: | $0$ |
| Group name: | $D_6$ |
| Group identifier: | $[12,4]$ |
| Signature: | $[ 0; 2, 2, 2, 2, 3 ]$ |
| Conjugacy classes for this refined passport: | $3, 3, 4, 4, 5$ |
| Jacobian variety group algebra decomposition: | $E\times E^{2}\times E^{2}$ |
| Corresponding character(s): | $2, 5, 6$ |
Other Data
| Hyperelliptic curve(s): | no |
| Cyclic trigonal curve(s): | no |
Generating vector(s)
Displaying 9 of 9 generating vectors for this refined passport.
5.12-4.0.2-2-2-2-3.3.1
| (1,7) (2,9) (3,8) (4,10) (5,12) (6,11) | |
| (1,7) (2,9) (3,8) (4,10) (5,12) (6,11) | |
| (1,10) (2,12) (3,11) (4,7) (5,9) (6,8) | |
| (1,12) (2,11) (3,10) (4,9) (5,8) (6,7) | |
| (1,2,3) (4,5,6) (7,8,9) (10,11,12) |
5.12-4.0.2-2-2-2-3.3.2
| (1,7) (2,9) (3,8) (4,10) (5,12) (6,11) | |
| (1,7) (2,9) (3,8) (4,10) (5,12) (6,11) | |
| (1,12) (2,11) (3,10) (4,9) (5,8) (6,7) | |
| (1,10) (2,12) (3,11) (4,7) (5,9) (6,8) | |
| (1,3,2) (4,6,5) (7,9,8) (10,12,11) |
5.12-4.0.2-2-2-2-3.3.3
| (1,7) (2,9) (3,8) (4,10) (5,12) (6,11) | |
| (1,7) (2,9) (3,8) (4,10) (5,12) (6,11) | |
| (1,12) (2,11) (3,10) (4,9) (5,8) (6,7) | |
| (1,11) (2,10) (3,12) (4,8) (5,7) (6,9) | |
| (1,2,3) (4,5,6) (7,8,9) (10,11,12) |
5.12-4.0.2-2-2-2-3.3.4
| (1,7) (2,9) (3,8) (4,10) (5,12) (6,11) | |
| (1,9) (2,8) (3,7) (4,12) (5,11) (6,10) | |
| (1,10) (2,12) (3,11) (4,7) (5,9) (6,8) | |
| (1,10) (2,12) (3,11) (4,7) (5,9) (6,8) | |
| (1,2,3) (4,5,6) (7,8,9) (10,11,12) |
5.12-4.0.2-2-2-2-3.3.5
| (1,7) (2,9) (3,8) (4,10) (5,12) (6,11) | |
| (1,9) (2,8) (3,7) (4,12) (5,11) (6,10) | |
| (1,10) (2,12) (3,11) (4,7) (5,9) (6,8) | |
| (1,12) (2,11) (3,10) (4,9) (5,8) (6,7) | |
| (1,3,2) (4,6,5) (7,9,8) (10,12,11) |
5.12-4.0.2-2-2-2-3.3.6
| (1,7) (2,9) (3,8) (4,10) (5,12) (6,11) | |
| (1,9) (2,8) (3,7) (4,12) (5,11) (6,10) | |
| (1,12) (2,11) (3,10) (4,9) (5,8) (6,7) | |
| (1,12) (2,11) (3,10) (4,9) (5,8) (6,7) | |
| (1,2,3) (4,5,6) (7,8,9) (10,11,12) |
5.12-4.0.2-2-2-2-3.3.7
| (1,7) (2,9) (3,8) (4,10) (5,12) (6,11) | |
| (1,9) (2,8) (3,7) (4,12) (5,11) (6,10) | |
| (1,12) (2,11) (3,10) (4,9) (5,8) (6,7) | |
| (1,11) (2,10) (3,12) (4,8) (5,7) (6,9) | |
| (1,3,2) (4,6,5) (7,9,8) (10,12,11) |
5.12-4.0.2-2-2-2-3.3.8
| (1,7) (2,9) (3,8) (4,10) (5,12) (6,11) | |
| (1,9) (2,8) (3,7) (4,12) (5,11) (6,10) | |
| (1,11) (2,10) (3,12) (4,8) (5,7) (6,9) | |
| (1,10) (2,12) (3,11) (4,7) (5,9) (6,8) | |
| (1,3,2) (4,6,5) (7,9,8) (10,12,11) |
5.12-4.0.2-2-2-2-3.3.9
| (1,7) (2,9) (3,8) (4,10) (5,12) (6,11) | |
| (1,9) (2,8) (3,7) (4,12) (5,11) (6,10) | |
| (1,11) (2,10) (3,12) (4,8) (5,7) (6,9) | |
| (1,11) (2,10) (3,12) (4,8) (5,7) (6,9) | |
| (1,2,3) (4,5,6) (7,8,9) (10,11,12) |
Displaying the unique representative of this refined passport up to braid equivalence.
5.12-4.0.2-2-2-2-3.3.1
| (1,7) (2,9) (3,8) (4,10) (5,12) (6,11) | |
| (1,7) (2,9) (3,8) (4,10) (5,12) (6,11) | |
| (1,10) (2,12) (3,11) (4,7) (5,9) (6,8) | |
| (1,12) (2,11) (3,10) (4,9) (5,8) (6,7) | |
| (1,2,3) (4,5,6) (7,8,9) (10,11,12) |