One refined passport of genus 12 with automorphism group $S_3\times D_7$

• Label: 12.84-8.0.2-6-14.3
• Genus: \(12\)
• Quotient genus: \(0\)
• Group: \(S_3\times D_7\)
• Signature: \([ 0; 2, 6, 14 ]\)
• Generating Vectors: \(1\)

Family Information

Genus:	$12$
Quotient genus:	$0$
Group name:	$S_3\times D_7$
Group identifier:	$[84,8]$
Signature:	$[ 0; 2, 6, 14 ]$

Conjugacy classes for this refined passport:

$4, 6, 12$

Jacobian variety group algebra decomposition:	$A_{3}^{4}$
Corresponding character(s):	$13$

Other Data

Hyperelliptic curve(s):	no
Cyclic trigonal curve(s):	yes
Trigonal automorphism:	(1,8,15) (2,9,16) (3,10,17) (4,11,18) (5,12,19) (6,13,20) (7,14,21) (22,29,36) (23,30,37) (24,31,38) (25,32,39) (26,33,40) (27,34,41) (28,35,42) (43,50,57) (44,51,58) (45,52,59) (46,53,60) (47,54,61) (48,55,62) (49,56,63) (64,71,78) (65,72,79) (66,73,80) (67,74,81) (68,75,82) (69,76,83) (70,77,84)

Generating vector(s)

Displaying the unique generating vector for this refined passport.

12.84-8.0.2-6-14.3.1

	(1,64) (2,70) (3,69) (4,68) (5,67) (6,66) (7,65) (8,78) (9,84) (10,83) (11,82) (12,81) (13,80) (14,79) (15,71) (16,77) (17,76) (18,75) (19,74) (20,73) (21,72) (22,43) (23,49) (24,48) (25,47) (26,46) (27,45) (28,44) (29,57) (30,63) (31,62) (32,61) (33,60) (34,59) (35,58) (36,50) (37,56) (38,55) (39,54) (40,53) (41,52) (42,51)
	(1,52,15,45,8,59) (2,51,16,44,9,58) (3,50,17,43,10,57) (4,56,18,49,11,63) (5,55,19,48,12,62) (6,54,20,47,13,61) (7,53,21,46,14,60) (22,73,36,66,29,80) (23,72,37,65,30,79) (24,71,38,64,31,78) (25,77,39,70,32,84) (26,76,40,69,33,83) (27,75,41,68,34,82) (28,74,42,67,35,81)
	(1,34,4,30,7,33,3,29,6,32,2,35,5,31) (8,27,11,23,14,26,10,22,13,25,9,28,12,24) (15,41,18,37,21,40,17,36,20,39,16,42,19,38) (43,76,46,72,49,75,45,71,48,74,44,77,47,73) (50,69,53,65,56,68,52,64,55,67,51,70,54,66) (57,83,60,79,63,82,59,78,62,81,58,84,61,80)