Properties

Genus \(4\)
Quotient Genus \(1\)
Group \(S_3\)
Signature \([ 1; 2, 2 ]\)
Generating Vectors \(23\)

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Family Information

Genus: 4
Quotient Genus: 1
Group name: $S_3$
Group identifier: [6,1]
Signature: $[ 1; 2, 2 ]$
Conjugacy classes for this refined passport: 2, 2

The full automorphism group for this family is $D_6$ with signature $[ 0; 2, 2, 2, 2, 2 ]$.

Jacobian variety group algebra decomposition:$E\times E\times E^{2}$
Corresponding character(s): 1, 2, 3

Generating Vector(s)

Displaying 20 of 23 generating vectors for this refined passport.

4.6-1.1.2-2.1.1

  (1,2,3) (4,5,6)
  Id(G)
  (1,4) (2,6) (3,5)
  (1,4) (2,6) (3,5)

4.6-1.1.2-2.1.2
  (1,3,2) (4,6,5)
  Id(G)
  (1,4) (2,6) (3,5)
  (1,4) (2,6) (3,5)

4.6-1.1.2-2.1.3
  (1,6) (2,5) (3,4)
  Id(G)
  (1,4) (2,6) (3,5)
  (1,4) (2,6) (3,5)

4.6-1.1.2-2.1.4
  (1,5) (2,4) (3,6)
  Id(G)
  (1,4) (2,6) (3,5)
  (1,4) (2,6) (3,5)

4.6-1.1.2-2.1.5
  Id(G)
  (1,2,3) (4,5,6)
  (1,4) (2,6) (3,5)
  (1,4) (2,6) (3,5)

4.6-1.1.2-2.1.6
  (1,2,3) (4,5,6)
  (1,2,3) (4,5,6)
  (1,4) (2,6) (3,5)
  (1,4) (2,6) (3,5)

4.6-1.1.2-2.1.7
  (1,3,2) (4,6,5)
  (1,2,3) (4,5,6)
  (1,4) (2,6) (3,5)
  (1,4) (2,6) (3,5)

4.6-1.1.2-2.1.8
  Id(G)
  (1,3,2) (4,6,5)
  (1,4) (2,6) (3,5)
  (1,4) (2,6) (3,5)

4.6-1.1.2-2.1.9
  (1,2,3) (4,5,6)
  (1,3,2) (4,6,5)
  (1,4) (2,6) (3,5)
  (1,4) (2,6) (3,5)

4.6-1.1.2-2.1.10
  (1,3,2) (4,6,5)
  (1,3,2) (4,6,5)
  (1,4) (2,6) (3,5)
  (1,4) (2,6) (3,5)

4.6-1.1.2-2.1.11
  Id(G)
  (1,6) (2,5) (3,4)
  (1,4) (2,6) (3,5)
  (1,4) (2,6) (3,5)

4.6-1.1.2-2.1.12
  (1,6) (2,5) (3,4)
  (1,6) (2,5) (3,4)
  (1,4) (2,6) (3,5)
  (1,4) (2,6) (3,5)

4.6-1.1.2-2.1.13
  Id(G)
  (1,5) (2,4) (3,6)
  (1,4) (2,6) (3,5)
  (1,4) (2,6) (3,5)

4.6-1.1.2-2.1.14
  (1,5) (2,4) (3,6)
  (1,5) (2,4) (3,6)
  (1,4) (2,6) (3,5)
  (1,4) (2,6) (3,5)

4.6-1.1.2-2.1.15
  (1,2,3) (4,5,6)
  (1,4) (2,6) (3,5)
  (1,4) (2,6) (3,5)
  (1,6) (2,5) (3,4)

4.6-1.1.2-2.1.16
  (1,5) (2,4) (3,6)
  (1,4) (2,6) (3,5)
  (1,4) (2,6) (3,5)
  (1,6) (2,5) (3,4)

4.6-1.1.2-2.1.17
  (1,4) (2,6) (3,5)
  (1,3,2) (4,6,5)
  (1,4) (2,6) (3,5)
  (1,6) (2,5) (3,4)

4.6-1.1.2-2.1.18
  (1,6) (2,5) (3,4)
  (1,3,2) (4,6,5)
  (1,4) (2,6) (3,5)
  (1,6) (2,5) (3,4)

4.6-1.1.2-2.1.19
  (1,5) (2,4) (3,6)
  (1,3,2) (4,6,5)
  (1,4) (2,6) (3,5)
  (1,6) (2,5) (3,4)

4.6-1.1.2-2.1.20
  (1,2,3) (4,5,6)
  (1,6) (2,5) (3,4)
  (1,4) (2,6) (3,5)
  (1,6) (2,5) (3,4)

Display number of generating vectors: