Properties

Genus \(10\)
Quotient Genus \(0\)
Group \(He_3:C_2\)
Signature \([ 0; 3, 6, 6 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 10
Quotient Genus: 0
Group name: $He_3:C_2$
Group identifier: [54,5]
Signature: $[ 0; 3, 6, 6 ]$
Conjugacy classes for this refined passport: 6, 9, 10

The full automorphism group for this family is $C_3.S_3\wr C_2$ with signature $[ 0; 2, 4, 6 ]$.

Jacobian variety group algebra decomposition:$A_{2}^{2}\times E^{6}$
Corresponding character(s): 8, 10

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

10.54-5.0.3-6-6.1.1

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