Properties

Genus \(5\)
Small Group \(C_2^2.D_4\)
Signature \([ 0; 4, 4, 4 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 5
Group name: $C_2^2.D_4$
Group identifier: [32,6]
Signature: $[ 0; 4, 4, 4 ]$
Conjugacy classes for this refined passport: 7, 8, 10

The full automorphism group for this family is $C_2wrC_4$ with signature $[ 0; 2, 4, 8 ]$.

Jacobian variety group algebra decomposition:$E\times E^{4}$
Corresponding character(s): 6, 11

Other Data

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

5.32-6.0.4-4-4.1.1

  (1,11,2,12) (3,10,4,9) (5,15,6,16) (7,14,8,13) (17,27,18,28) (19,26,20,25) (21,31,22,32) (23,30,24,29)
  (1,17,3,19) (2,18,4,20) (5,22,7,24) (6,21,8,23) (9,29,11,31) (10,30,12,32) (13,26,15,28) (14,25,16,27)
  (1,25,7,31) (2,26,8,32) (3,28,5,30) (4,27,6,29) (9,21,15,19) (10,22,16,20) (11,24,13,18) (12,23,14,17)