Properties

Genus \(8\)
Small Group \(S_3\times D_5\)
Signature \([ 0; 2, 6, 10 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 8
Group name: $S_3\times D_5$
Group identifier: [60,8]
Signature: $[ 0; 2, 6, 10 ]$
Conjugacy classes for this refined passport: 4, 8, 9

Jacobian variety group algebra decomposition:$A_{2}^{4}$
Corresponding character(s): 11

Other Data

Hyperelliptic curve(s):No
Cyclic trigonal curve(s):Yes
Trigonal automorphism: (1,6,11) (2,7,12) (3,8,13) (4,9,14) (5,10,15) (16,21,26) (17,22,27) (18,23,28) (19,24,29) (20,25,30) (31,36,41) (32,37,42) (33,38,43) (34,39,44) (35,40,45) (46,51,56) (47,52,57) (48,53,58) (49,54,59) (50,55,60)

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

8.60-8.0.2-6-10.1.1

  (1,46) (2,50) (3,49) (4,48) (5,47) (6,56) (7,60) (8,59) (9,58) (10,57) (11,51) (12,55) (13,54) (14,53) (15,52) (16,31) (17,35) (18,34) (19,33) (20,32) (21,41) (22,45) (23,44) (24,43) (25,42) (26,36) (27,40) (28,39) (29,38) (30,37)
  (1,40,11,35,6,45) (2,39,12,34,7,44) (3,38,13,33,8,43) (4,37,14,32,9,42) (5,36,15,31,10,41) (16,55,26,50,21,60) (17,54,27,49,22,59) (18,53,28,48,23,58) (19,52,29,47,24,57) (20,51,30,46,25,56)
  (1,22,3,24,5,21,2,23,4,25) (6,17,8,19,10,16,7,18,9,20) (11,27,13,29,15,26,12,28,14,30) (31,52,33,54,35,51,32,53,34,55) (36,47,38,49,40,46,37,48,39,50) (41,57,43,59,45,56,42,58,44,60)