Properties

Genus \(15\)
Quotient Genus \(0\)
Group \(C_2.S_4\)
Signature \([ 0; 6, 8, 8 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 15
Quotient Genus: 0
Group name: $C_2.S_4$
Group identifier: [48,28]
Signature: $[ 0; 6, 8, 8 ]$
Conjugacy classes for this refined passport: 6, 7, 7

The full automorphism group for this family is $(C_2.S_4):C_2$ with signature $[ 0; 2, 8, 12 ]$.

Jacobian variety group algebra decomposition:$A_{4}\times E^{3}\times A_{4}^{2}$
Corresponding character(s): 4, 7, 8

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

15.48-28.0.6-8-8.1.1

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