Family Information
| Genus: | $6$ |
| Quotient genus: | $0$ |
| Group name: | $C_3:D_4$ |
| Group identifier: | $[24,8]$ |
| Signature: | $[ 0; 2, 2, 3, 4 ]$ |
| Conjugacy classes for this refined passport: | $3, 4, 5, 6$ |
| Jacobian variety group algebra decomposition: | $E^{2}\times A_{2}^{2}$ |
| Corresponding character(s): | $5, 8$ |
Other Data
| Hyperelliptic curve(s): | no |
| Cyclic trigonal curve(s): | yes |
| Trigonal automorphism: | (1,2,3) (4,5,6) (7,8,9) (10,11,12) (13,14,15) (16,17,18) (19,20,21) (22,23,24) |
Generating vector(s)
Displaying 2 of 2 generating vectors for this refined passport.
6.24-8.0.2-2-3-4.1.1
| (1,7) (2,8) (3,9) (4,10) (5,11) (6,12) (13,19) (14,20) (15,21) (16,22) (17,23) (18,24) | |
| (1,13) (2,15) (3,14) (4,16) (5,18) (6,17) (7,22) (8,24) (9,23) (10,19) (11,21) (12,20) | |
| (1,2,3) (4,5,6) (7,8,9) (10,11,12) (13,14,15) (16,17,18) (19,20,21) (22,23,24) | |
| (1,20,4,23) (2,19,5,22) (3,21,6,24) (7,17,10,14) (8,16,11,13) (9,18,12,15) |
6.24-8.0.2-2-3-4.1.2
| (1,7) (2,8) (3,9) (4,10) (5,11) (6,12) (13,19) (14,20) (15,21) (16,22) (17,23) (18,24) | |
| (1,13) (2,15) (3,14) (4,16) (5,18) (6,17) (7,22) (8,24) (9,23) (10,19) (11,21) (12,20) | |
| (1,3,2) (4,6,5) (7,9,8) (10,12,11) (13,15,14) (16,18,17) (19,21,20) (22,24,23) | |
| (1,21,4,24) (2,20,5,23) (3,19,6,22) (7,18,10,15) (8,17,11,14) (9,16,12,13) |
Displaying the unique representative of this refined passport up to braid equivalence.
6.24-8.0.2-2-3-4.1.1
| (1,7) (2,8) (3,9) (4,10) (5,11) (6,12) (13,19) (14,20) (15,21) (16,22) (17,23) (18,24) | |
| (1,13) (2,15) (3,14) (4,16) (5,18) (6,17) (7,22) (8,24) (9,23) (10,19) (11,21) (12,20) | |
| (1,2,3) (4,5,6) (7,8,9) (10,11,12) (13,14,15) (16,17,18) (19,20,21) (22,23,24) | |
| (1,20,4,23) (2,19,5,22) (3,21,6,24) (7,17,10,14) (8,16,11,13) (9,18,12,15) |