Family Information
| Genus: | $6$ |
| Quotient genus: | $0$ |
| Group name: | $A_4$ |
| Group identifier: | $[12,3]$ |
| Signature: | $[ 0; 2, 2, 2, 3, 3 ]$ |
| Conjugacy classes for this refined passport: | $2, 2, 2, 3, 4$ |
| Jacobian variety group algebra decomposition: | $A_{2}^{3}$ |
| Corresponding character(s): | $4$ |
Other Data
| Hyperelliptic curve(s): | no |
| Cyclic trigonal curve(s): | no |
Generating vector(s)
Displaying 9 of 9 generating vectors for this refined passport.
6.12-3.0.2-2-2-3-3.1.1
| (1,2) (3,4) (5,6) (7,8) (9,10) (11,12) | |
| (1,2) (3,4) (5,6) (7,8) (9,10) (11,12) | |
| (1,2) (3,4) (5,6) (7,8) (9,10) (11,12) | |
| (1,5,9) (2,8,11) (3,6,12) (4,7,10) | |
| (1,10,8) (2,12,5) (3,11,7) (4,9,6) |
6.12-3.0.2-2-2-3-3.1.2
| (1,2) (3,4) (5,6) (7,8) (9,10) (11,12) | |
| (1,2) (3,4) (5,6) (7,8) (9,10) (11,12) | |
| (1,4) (2,3) (5,8) (6,7) (9,12) (10,11) | |
| (1,5,9) (2,8,11) (3,6,12) (4,7,10) | |
| (1,12,7) (2,10,6) (3,9,8) (4,11,5) |
6.12-3.0.2-2-2-3-3.1.3
| (1,2) (3,4) (5,6) (7,8) (9,10) (11,12) | |
| (1,2) (3,4) (5,6) (7,8) (9,10) (11,12) | |
| (1,3) (2,4) (5,7) (6,8) (9,11) (10,12) | |
| (1,5,9) (2,8,11) (3,6,12) (4,7,10) | |
| (1,11,6) (2,9,7) (3,10,5) (4,12,8) |
6.12-3.0.2-2-2-3-3.1.4
| (1,2) (3,4) (5,6) (7,8) (9,10) (11,12) | |
| (1,4) (2,3) (5,8) (6,7) (9,12) (10,11) | |
| (1,2) (3,4) (5,6) (7,8) (9,10) (11,12) | |
| (1,5,9) (2,8,11) (3,6,12) (4,7,10) | |
| (1,12,7) (2,10,6) (3,9,8) (4,11,5) |
6.12-3.0.2-2-2-3-3.1.5
| (1,2) (3,4) (5,6) (7,8) (9,10) (11,12) | |
| (1,4) (2,3) (5,8) (6,7) (9,12) (10,11) | |
| (1,4) (2,3) (5,8) (6,7) (9,12) (10,11) | |
| (1,5,9) (2,8,11) (3,6,12) (4,7,10) | |
| (1,10,8) (2,12,5) (3,11,7) (4,9,6) |
6.12-3.0.2-2-2-3-3.1.6
| (1,2) (3,4) (5,6) (7,8) (9,10) (11,12) | |
| (1,4) (2,3) (5,8) (6,7) (9,12) (10,11) | |
| (1,3) (2,4) (5,7) (6,8) (9,11) (10,12) | |
| (1,5,9) (2,8,11) (3,6,12) (4,7,10) | |
| (1,9,5) (2,11,8) (3,12,6) (4,10,7) |
6.12-3.0.2-2-2-3-3.1.7
| (1,2) (3,4) (5,6) (7,8) (9,10) (11,12) | |
| (1,3) (2,4) (5,7) (6,8) (9,11) (10,12) | |
| (1,2) (3,4) (5,6) (7,8) (9,10) (11,12) | |
| (1,5,9) (2,8,11) (3,6,12) (4,7,10) | |
| (1,11,6) (2,9,7) (3,10,5) (4,12,8) |
6.12-3.0.2-2-2-3-3.1.8
| (1,2) (3,4) (5,6) (7,8) (9,10) (11,12) | |
| (1,3) (2,4) (5,7) (6,8) (9,11) (10,12) | |
| (1,4) (2,3) (5,8) (6,7) (9,12) (10,11) | |
| (1,5,9) (2,8,11) (3,6,12) (4,7,10) | |
| (1,9,5) (2,11,8) (3,12,6) (4,10,7) |
6.12-3.0.2-2-2-3-3.1.9
| (1,2) (3,4) (5,6) (7,8) (9,10) (11,12) | |
| (1,3) (2,4) (5,7) (6,8) (9,11) (10,12) | |
| (1,3) (2,4) (5,7) (6,8) (9,11) (10,12) | |
| (1,5,9) (2,8,11) (3,6,12) (4,7,10) | |
| (1,10,8) (2,12,5) (3,11,7) (4,9,6) |
Displaying the unique representative of this refined passport up to braid equivalence.
6.12-3.0.2-2-2-3-3.1.1
| (1,2) (3,4) (5,6) (7,8) (9,10) (11,12) | |
| (1,2) (3,4) (5,6) (7,8) (9,10) (11,12) | |
| (1,2) (3,4) (5,6) (7,8) (9,10) (11,12) | |
| (1,5,9) (2,8,11) (3,6,12) (4,7,10) | |
| (1,10,8) (2,12,5) (3,11,7) (4,9,6) |