One refined passport of genus 4 with automorphism group S3S_3

• Label: 4.6-1.1.2-2.1
• Genus: $4$
• Quotient genus: $1$
• Group: $S_3$
• Signature: $[ 1; 2, 2 ]$
• Generating Vectors: $23$

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: