Family Information
| Genus: | $12$ |
| Quotient genus: | $0$ |
| Group name: | $D_{18}$ |
| Group identifier: | $[36,4]$ |
| Signature: | $[ 0; 2, 2, 3, 18 ]$ |
| Conjugacy classes for this refined passport: | $3, 4, 5, 12$ |
| Jacobian variety group algebra decomposition: | $A_{3}^{2}\times A_{3}^{2}$ |
| Corresponding character(s): | $7, 8$ |
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) (25,26,27) (28,29,30) (31,32,33) (34,35,36) |
Generating vector(s)
Displaying 2 of 2 generating vectors for this refined passport.
12.36-4.0.2-2-3-18.3.1
| (1,19) (2,21) (3,20) (4,26) (5,25) (6,27) (7,23) (8,22) (9,24) (10,28) (11,30) (12,29) (13,35) (14,34) (15,36) (16,32) (17,31) (18,33) | |
| (1,36) (2,35) (3,34) (4,33) (5,32) (6,31) (7,30) (8,29) (9,28) (10,27) (11,26) (12,25) (13,24) (14,23) (15,22) (16,21) (17,20) (18,19) | |
| (1,2,3) (4,5,6) (7,8,9) (10,11,12) (13,14,15) (16,17,18) (19,20,21) (22,23,24) (25,26,27) (28,29,30) (31,32,33) (34,35,36) | |
| (1,14,9,12,4,17,2,15,7,10,5,18,3,13,8,11,6,16) (19,32,27,30,22,35,20,33,25,28,23,36,21,31,26,29,24,34) |
12.36-4.0.2-2-3-18.3.2
| (1,19) (2,21) (3,20) (4,26) (5,25) (6,27) (7,23) (8,22) (9,24) (10,28) (11,30) (12,29) (13,35) (14,34) (15,36) (16,32) (17,31) (18,33) | |
| (1,35) (2,34) (3,36) (4,32) (5,31) (6,33) (7,29) (8,28) (9,30) (10,26) (11,25) (12,27) (13,23) (14,22) (15,24) (16,20) (17,19) (18,21) | |
| (1,3,2) (4,6,5) (7,9,8) (10,12,11) (13,15,14) (16,18,17) (19,21,20) (22,24,23) (25,27,26) (28,30,29) (31,33,32) (34,36,35) | |
| (1,14,9,12,4,17,2,15,7,10,5,18,3,13,8,11,6,16) (19,32,27,30,22,35,20,33,25,28,23,36,21,31,26,29,24,34) |