Family Information
| Genus: | $4$ |
| Quotient genus: | $0$ |
| Group name: | $S_4$ |
| Group identifier: | $[24,12]$ |
| Signature: | $[ 0; 2, 2, 2, 4 ]$ |
| Conjugacy classes for this refined passport: | $3, 3, 3, 5$ |
| Jacobian variety group algebra decomposition: | $E\times E^{3}$ |
| Corresponding character(s): | $2, 4$ |
Other Data
| Hyperelliptic curve(s): | no |
| Cyclic trigonal curve(s): | no |
Generating vector(s)
Displaying 4 of 4 generating vectors for this refined passport.
4.24-12.0.2-2-2-4.1.1
| (1,13) (2,15) (3,14) (4,16) (5,21) (6,23) (7,22) (8,24) (9,17) (10,19) (11,18) (12,20) | |
| (1,16) (2,14) (3,15) (4,13) (5,24) (6,22) (7,23) (8,21) (9,20) (10,18) (11,19) (12,17) | |
| (1,21) (2,24) (3,23) (4,22) (5,17) (6,20) (7,19) (8,18) (9,13) (10,16) (11,15) (12,14) | |
| (1,24,3,22) (2,21,4,23) (5,20,7,18) (6,17,8,19) (9,16,11,14) (10,13,12,15) |
4.24-12.0.2-2-2-4.1.2
| (1,13) (2,15) (3,14) (4,16) (5,21) (6,23) (7,22) (8,24) (9,17) (10,19) (11,18) (12,20) | |
| (1,21) (2,24) (3,23) (4,22) (5,17) (6,20) (7,19) (8,18) (9,13) (10,16) (11,15) (12,14) | |
| (1,16) (2,14) (3,15) (4,13) (5,24) (6,22) (7,23) (8,21) (9,20) (10,18) (11,19) (12,17) | |
| (1,19,2,20) (3,18,4,17) (5,15,6,16) (7,14,8,13) (9,23,10,24) (11,22,12,21) |
4.24-12.0.2-2-2-4.1.3
| (1,13) (2,15) (3,14) (4,16) (5,21) (6,23) (7,22) (8,24) (9,17) (10,19) (11,18) (12,20) | |
| (1,21) (2,24) (3,23) (4,22) (5,17) (6,20) (7,19) (8,18) (9,13) (10,16) (11,15) (12,14) | |
| (1,23) (2,22) (3,21) (4,24) (5,19) (6,18) (7,17) (8,20) (9,15) (10,14) (11,13) (12,16) | |
| (1,14,4,15) (2,16,3,13) (5,22,8,23) (6,24,7,21) (9,18,12,19) (10,20,11,17) |
4.24-12.0.2-2-2-4.1.4
| (1,13) (2,15) (3,14) (4,16) (5,21) (6,23) (7,22) (8,24) (9,17) (10,19) (11,18) (12,20) | |
| (1,21) (2,24) (3,23) (4,22) (5,17) (6,20) (7,19) (8,18) (9,13) (10,16) (11,15) (12,14) | |
| (1,18) (2,17) (3,19) (4,20) (5,14) (6,13) (7,15) (8,16) (9,22) (10,21) (11,23) (12,24) | |
| (1,24,3,22) (2,21,4,23) (5,20,7,18) (6,17,8,19) (9,16,11,14) (10,13,12,15) |
Displaying the unique representative of this refined passport up to braid equivalence.
4.24-12.0.2-2-2-4.1.1
| (1,13) (2,15) (3,14) (4,16) (5,21) (6,23) (7,22) (8,24) (9,17) (10,19) (11,18) (12,20) | |
| (1,16) (2,14) (3,15) (4,13) (5,24) (6,22) (7,23) (8,21) (9,20) (10,18) (11,19) (12,17) | |
| (1,21) (2,24) (3,23) (4,22) (5,17) (6,20) (7,19) (8,18) (9,13) (10,16) (11,15) (12,14) | |
| (1,24,3,22) (2,21,4,23) (5,20,7,18) (6,17,8,19) (9,16,11,14) (10,13,12,15) |