Properties

Genus \(5\)
Small Group \(C_2^4:C_5\)
Signature \([ 0; 2, 5, 5 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 5
Group name: $C_2^4:C_5$
Group identifier: [80,49]
Signature: $[ 0; 2, 5, 5 ]$
Conjugacy classes for this refined passport: 2, 6, 7

The full automorphism group for this family is $C_2^4:D_5$ with signature $[ 0; 2, 4, 5 ]$.

Jacobian variety group algebra decomposition:$E^{5}$
Corresponding character(s): 6

Other Data

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

5.80-49.0.2-5-5.2.1

  (1,2) (3,4) (5,6) (7,8) (9,10) (11,12) (13,14) (15,16) (17,18) (19,20) (21,22) (23,24) (25,26) (27,28) (29,30) (31,32) (33,34) (35,36) (37,38) (39,40) (41,42) (43,44) (45,46) (47,48) (49,50) (51,52) (53,54) (55,56) (57,58) (59,60) (61,62) (63,64) (65,66) (67,68) (69,70) (71,72) (73,74) (75,76) (77,78) (79,80)
  (1,33,65,17,49) (2,43,73,32,61) (3,40,68,30,60) (4,46,76,19,56) (5,47,71,26,54) (6,37,79,23,58) (7,42,70,21,63) (8,36,78,28,51) (9,48,77,18,59) (10,38,69,31,55) (11,41,80,29,50) (12,35,72,20,62) (13,34,75,25,64) (14,44,67,24,52) (15,39,74,22,53) (16,45,66,27,57)
  (1,50,30,67,43) (2,62,19,75,33) (3,59,17,66,46) (4,55,32,74,40) (5,53,21,69,37) (6,57,28,77,47) (7,64,26,72,36) (8,52,23,80,42) (9,60,29,79,38) (10,56,20,71,48) (11,49,18,78,35) (12,61,31,70,41) (13,63,22,73,44) (14,51,27,65,34) (15,54,25,76,45) (16,58,24,68,39)