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Properties

Label 7.8-3.0.2-2-2-2-4-4.5
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: $4, 4, 4, 4, 5, 5$

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.

7.8-3.0.2-2-2-2-4-4.5.1

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

7.8-3.0.2-2-2-2-4-4.5.2
  (1,5) (2,6) (3,8) (4,7)
  (1,5) (2,6) (3,8) (4,7)
  (1,5) (2,6) (3,8) (4,7)
  (1,6) (2,5) (3,7) (4,8)
  (1,7,2,8) (3,6,4,5)
  (1,7,2,8) (3,6,4,5)

7.8-3.0.2-2-2-2-4-4.5.3
  (1,5) (2,6) (3,8) (4,7)
  (1,5) (2,6) (3,8) (4,7)
  (1,6) (2,5) (3,7) (4,8)
  (1,5) (2,6) (3,8) (4,7)
  (1,7,2,8) (3,6,4,5)
  (1,7,2,8) (3,6,4,5)

7.8-3.0.2-2-2-2-4-4.5.4
  (1,5) (2,6) (3,8) (4,7)
  (1,5) (2,6) (3,8) (4,7)
  (1,6) (2,5) (3,7) (4,8)
  (1,6) (2,5) (3,7) (4,8)
  (1,7,2,8) (3,6,4,5)
  (1,8,2,7) (3,5,4,6)

7.8-3.0.2-2-2-2-4-4.5.5
  (1,5) (2,6) (3,8) (4,7)
  (1,6) (2,5) (3,7) (4,8)
  (1,5) (2,6) (3,8) (4,7)
  (1,5) (2,6) (3,8) (4,7)
  (1,7,2,8) (3,6,4,5)
  (1,7,2,8) (3,6,4,5)

7.8-3.0.2-2-2-2-4-4.5.6
  (1,5) (2,6) (3,8) (4,7)
  (1,6) (2,5) (3,7) (4,8)
  (1,5) (2,6) (3,8) (4,7)
  (1,6) (2,5) (3,7) (4,8)
  (1,7,2,8) (3,6,4,5)
  (1,8,2,7) (3,5,4,6)

7.8-3.0.2-2-2-2-4-4.5.7
  (1,5) (2,6) (3,8) (4,7)
  (1,6) (2,5) (3,7) (4,8)
  (1,6) (2,5) (3,7) (4,8)
  (1,5) (2,6) (3,8) (4,7)
  (1,7,2,8) (3,6,4,5)
  (1,8,2,7) (3,5,4,6)

7.8-3.0.2-2-2-2-4-4.5.8
  (1,5) (2,6) (3,8) (4,7)
  (1,6) (2,5) (3,7) (4,8)
  (1,6) (2,5) (3,7) (4,8)
  (1,6) (2,5) (3,7) (4,8)
  (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.

  7.8-3.0.2-2-2-2-4-4.5.1

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