Properties

Genus \(10\)
Quotient Genus \(0\)
Group \(C_3^2\times S_3\)
Signature \([ 0; 3, 6, 6 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 10
Quotient Genus: 0
Group name: $C_3^2\times S_3$
Group identifier: [54,12]
Signature: $[ 0; 3, 6, 6 ]$
Conjugacy classes for this refined passport: 12, 22, 25

The full automorphism group for this family is $S_3^2:S_3$ with signature $[ 0; 2, 4, 6 ]$.

Jacobian variety group algebra decomposition:$E\times E\times E\times E\times A_{2}^{2}\times E^{2}$
Corresponding character(s): 4, 5, 7, 8, 20, 25

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

10.54-12.0.3-6-6.1.1

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