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Properties

Label 7.8-3.0.2-2-2-2-4-4.3
Genus \(7\)
Quotient genus \(0\)
Group \(D_4\)
Signature \([ 0; 2, 2, 2, 2, 4, 4 ]\)
Generating Vectors \(8\)

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Family Information

Genus: $7$
Quotient genus: $0$
Group name: $D_4$
Group identifier: $[8,3]$
Signature: $[ 0; 2, 2, 2, 2, 4, 4 ]$
Conjugacy classes for this refined passport: $3, 3, 3, 3, 5, 5$

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

Other Data

Hyperelliptic curve(s):no
Cyclic trigonal curve(s):no

Generating vector(s)

Displaying 8 of 8 generating vectors for this refined passport.

7.8-3.0.2-2-2-2-4-4.3.1

  (1,3) (2,4) (5,7) (6,8)
  (1,3) (2,4) (5,7) (6,8)
  (1,3) (2,4) (5,7) (6,8)
  (1,3) (2,4) (5,7) (6,8)
  (1,7,2,8) (3,6,4,5)
  (1,8,2,7) (3,5,4,6)

7.8-3.0.2-2-2-2-4-4.3.2
  (1,3) (2,4) (5,7) (6,8)
  (1,3) (2,4) (5,7) (6,8)
  (1,3) (2,4) (5,7) (6,8)
  (1,4) (2,3) (5,8) (6,7)
  (1,7,2,8) (3,6,4,5)
  (1,7,2,8) (3,6,4,5)

7.8-3.0.2-2-2-2-4-4.3.3
  (1,3) (2,4) (5,7) (6,8)
  (1,3) (2,4) (5,7) (6,8)
  (1,4) (2,3) (5,8) (6,7)
  (1,3) (2,4) (5,7) (6,8)
  (1,7,2,8) (3,6,4,5)
  (1,7,2,8) (3,6,4,5)

7.8-3.0.2-2-2-2-4-4.3.4
  (1,3) (2,4) (5,7) (6,8)
  (1,3) (2,4) (5,7) (6,8)
  (1,4) (2,3) (5,8) (6,7)
  (1,4) (2,3) (5,8) (6,7)
  (1,7,2,8) (3,6,4,5)
  (1,8,2,7) (3,5,4,6)

7.8-3.0.2-2-2-2-4-4.3.5
  (1,3) (2,4) (5,7) (6,8)
  (1,4) (2,3) (5,8) (6,7)
  (1,3) (2,4) (5,7) (6,8)
  (1,3) (2,4) (5,7) (6,8)
  (1,7,2,8) (3,6,4,5)
  (1,7,2,8) (3,6,4,5)

7.8-3.0.2-2-2-2-4-4.3.6
  (1,3) (2,4) (5,7) (6,8)
  (1,4) (2,3) (5,8) (6,7)
  (1,3) (2,4) (5,7) (6,8)
  (1,4) (2,3) (5,8) (6,7)
  (1,7,2,8) (3,6,4,5)
  (1,8,2,7) (3,5,4,6)

7.8-3.0.2-2-2-2-4-4.3.7
  (1,3) (2,4) (5,7) (6,8)
  (1,4) (2,3) (5,8) (6,7)
  (1,4) (2,3) (5,8) (6,7)
  (1,3) (2,4) (5,7) (6,8)
  (1,7,2,8) (3,6,4,5)
  (1,8,2,7) (3,5,4,6)

7.8-3.0.2-2-2-2-4-4.3.8
  (1,3) (2,4) (5,7) (6,8)
  (1,4) (2,3) (5,8) (6,7)
  (1,4) (2,3) (5,8) (6,7)
  (1,4) (2,3) (5,8) (6,7)
  (1,7,2,8) (3,6,4,5)
  (1,7,2,8) (3,6,4,5)

Display number of generating vectors:

Displaying the unique representative of this refined passport up to braid equivalence.

  7.8-3.0.2-2-2-2-4-4.3.1

  (1,3) (2,4) (5,7) (6,8)
  (1,3) (2,4) (5,7) (6,8)
  (1,3) (2,4) (5,7) (6,8)
  (1,3) (2,4) (5,7) (6,8)
  (1,7,2,8) (3,6,4,5)
  (1,8,2,7) (3,5,4,6)