// Magma code for the lmfdb family of higher genus curves 12.96-7.0.2-4-48
// The results are stored in a list of records called 'data'

RecFormat:=recformat<group,gp_id, signature,gen_vectors,conj_classes,genus,dimension,r,g0, passport_label,gen_vect_label, is_hyperelliptic, hyp_involution, is_cyclic_trigonal,cyc_auto,full_auto, full_sign,topological_class,braid_class>;

data:=[];

// Create group as a permutation group, and generate data which is the same for all entries.
gp_id:=[96,7];
H:=SmallGroup(gp_id[1],gp_id[2]); n:=#H; LP:=[]; LG:=[g : g in H]; for i in [1..n] do x:=LG[i]; Tx:=[LG[j]*x : j in [1..n]]; permL:=[]; for j in [1..n] do for k in [1..n] do if Tx[j] eq LG[k] then permL[j]:=k;  break; end if; end for; end for; Append(~LP,permL); end for; G:=PermutationGroup<n|LP>; 
signature:=[0,2,4,48];
genus:=12;
r:=#signature-1;
g0:=signature[1];
dim:=3*g0-3+r;
S:=Sym(gp_id[1]);

// Here we add an action to data.
gen_vectors:=[[49, 51, 50, 52, 54, 53, 58, 60, 59, 55, 57, 56, 70, 72, 71, 67, 69, 68, 64, 66, 65, 61, 63, 62, 85, 87, 86, 88, 90, 89, 94, 96, 95, 91, 93, 92, 73, 75, 74, 76, 78, 77, 82, 84, 83, 79, 81, 80, 1, 3, 2, 4, 6, 5, 10, 12, 11, 7, 9, 8, 22, 24, 23, 19, 21, 20, 16, 18, 17, 13, 15, 14, 37, 39, 38, 40, 42, 41, 46, 48, 47, 43, 45, 44, 25, 27, 26, 28, 30, 29, 34, 36, 35, 31, 33, 32], [77, 76, 78, 74, 73, 75, 80, 79, 81, 83, 82, 84, 92, 91, 93, 95, 94, 96, 86, 85, 87, 89, 88, 90, 50, 49, 51, 53, 52, 54, 59, 58, 60, 56, 55, 57, 71, 70, 72, 68, 67, 69, 65, 64, 66, 62, 61, 63, 29, 28, 30, 26, 25, 27, 32, 31, 33, 35, 34, 36, 44, 43, 45, 47, 46, 48, 38, 37, 39, 41, 40, 42, 2, 1, 3, 5, 4, 6, 11, 10, 12, 8, 7, 9, 23, 22, 24, 20, 19, 21, 17, 16, 18, 14, 13, 15], [39, 37, 38, 42, 40, 41, 45, 43, 44, 48, 46, 47, 33, 31, 32, 36, 34, 35, 30, 28, 29, 27, 25, 26, 6, 4, 5, 3, 1, 2, 12, 10, 11, 9, 7, 8, 18, 16, 17, 15, 13, 14, 24, 22, 23, 21, 19, 20, 87, 85, 86, 90, 88, 89, 93, 91, 92, 96, 94, 95, 81, 79, 80, 84, 82, 83, 78, 76, 77, 75, 73, 74, 54, 52, 53, 51, 49, 50, 60, 58, 59, 57, 55, 56, 66, 64, 65, 63, 61, 62, 72, 70, 71, 69, 67, 68]];
cc:=[3,6,20];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=1;
gen_vect_label:=1;
is_hyperelliptic:=true;
hyp_involution:=S![4, 5, 6, 1, 2, 3, 10, 11, 12, 7, 8, 9, 16, 17, 18, 13, 14, 15, 22, 23, 24, 19, 20, 21, 28, 29, 30, 25, 26, 27, 34, 35, 36, 31, 32, 33, 40, 41, 42, 37, 38, 39, 46, 47, 48, 43, 44, 45, 52, 53, 54, 49, 50, 51, 58, 59, 60, 55, 56, 57, 64, 65, 66, 61, 62, 63, 70, 71, 72, 67, 68, 69, 76, 77, 78, 73, 74, 75, 82, 83, 84, 79, 80, 81, 88, 89, 90, 85, 86, 87, 94, 95, 96, 91, 92, 93];
is_cyclic_trigonal:=false;
Append(~data, rec<RecFormat | group:=G, gp_id:=gp_id, signature:=signature, gen_vectors:=gen_vectors_as_perm, conj_classes:=cc, genus:=genus, dimension:=dim, r:=r, g0:=g0, passport_label:= passport_label,gen_vect_label:=gen_vect_label, braid_class:=braid_class, topological_class:=topological_class, is_hyperelliptic:=is_hyperelliptic, hyp_involution:=hyp_involution,is_cyclic_trigonal:=is_cyclic_trigonal >);

// Here we add an action to data.
gen_vectors:=[[49, 51, 50, 52, 54, 53, 58, 60, 59, 55, 57, 56, 70, 72, 71, 67, 69, 68, 64, 66, 65, 61, 63, 62, 85, 87, 86, 88, 90, 89, 94, 96, 95, 91, 93, 92, 73, 75, 74, 76, 78, 77, 82, 84, 83, 79, 81, 80, 1, 3, 2, 4, 6, 5, 10, 12, 11, 7, 9, 8, 22, 24, 23, 19, 21, 20, 16, 18, 17, 13, 15, 14, 37, 39, 38, 40, 42, 41, 46, 48, 47, 43, 45, 44, 25, 27, 26, 28, 30, 29, 34, 36, 35, 31, 33, 32], [81, 80, 79, 84, 83, 82, 75, 74, 73, 78, 77, 76, 87, 86, 85, 90, 89, 88, 96, 95, 94, 93, 92, 91, 60, 59, 58, 57, 56, 55, 54, 53, 52, 51, 50, 49, 66, 65, 64, 63, 62, 61, 69, 68, 67, 72, 71, 70, 33, 32, 31, 36, 35, 34, 27, 26, 25, 30, 29, 28, 39, 38, 37, 42, 41, 40, 48, 47, 46, 45, 44, 43, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 18, 17, 16, 15, 14, 13, 21, 20, 19, 24, 23, 22], [44, 45, 43, 47, 48, 46, 41, 42, 40, 38, 39, 37, 29, 30, 28, 26, 27, 25, 35, 36, 34, 32, 33, 31, 11, 12, 10, 8, 9, 7, 2, 3, 1, 5, 6, 4, 23, 24, 22, 20, 21, 19, 14, 15, 13, 17, 18, 16, 92, 93, 91, 95, 96, 94, 89, 90, 88, 86, 87, 85, 77, 78, 76, 74, 75, 73, 83, 84, 82, 80, 81, 79, 59, 60, 58, 56, 57, 55, 50, 51, 49, 53, 54, 52, 71, 72, 70, 68, 69, 67, 62, 63, 61, 65, 66, 64]];
cc:=[3,6,21];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=2;
gen_vect_label:=1;
is_hyperelliptic:=true;
hyp_involution:=S![4, 5, 6, 1, 2, 3, 10, 11, 12, 7, 8, 9, 16, 17, 18, 13, 14, 15, 22, 23, 24, 19, 20, 21, 28, 29, 30, 25, 26, 27, 34, 35, 36, 31, 32, 33, 40, 41, 42, 37, 38, 39, 46, 47, 48, 43, 44, 45, 52, 53, 54, 49, 50, 51, 58, 59, 60, 55, 56, 57, 64, 65, 66, 61, 62, 63, 70, 71, 72, 67, 68, 69, 76, 77, 78, 73, 74, 75, 82, 83, 84, 79, 80, 81, 88, 89, 90, 85, 86, 87, 94, 95, 96, 91, 92, 93];
is_cyclic_trigonal:=false;
Append(~data, rec<RecFormat | group:=G, gp_id:=gp_id, signature:=signature, gen_vectors:=gen_vectors_as_perm, conj_classes:=cc, genus:=genus, dimension:=dim, r:=r, g0:=g0, passport_label:= passport_label,gen_vect_label:=gen_vect_label, braid_class:=braid_class, topological_class:=topological_class, is_hyperelliptic:=is_hyperelliptic, hyp_involution:=hyp_involution,is_cyclic_trigonal:=is_cyclic_trigonal >);

// Here we add an action to data.
gen_vectors:=[[49, 51, 50, 52, 54, 53, 58, 60, 59, 55, 57, 56, 70, 72, 71, 67, 69, 68, 64, 66, 65, 61, 63, 62, 85, 87, 86, 88, 90, 89, 94, 96, 95, 91, 93, 92, 73, 75, 74, 76, 78, 77, 82, 84, 83, 79, 81, 80, 1, 3, 2, 4, 6, 5, 10, 12, 11, 7, 9, 8, 22, 24, 23, 19, 21, 20, 16, 18, 17, 13, 15, 14, 37, 39, 38, 40, 42, 41, 46, 48, 47, 43, 45, 44, 25, 27, 26, 28, 30, 29, 34, 36, 35, 31, 33, 32], [78, 77, 76, 75, 74, 73, 81, 80, 79, 84, 83, 82, 93, 92, 91, 96, 95, 94, 87, 86, 85, 90, 89, 88, 51, 50, 49, 54, 53, 52, 60, 59, 58, 57, 56, 55, 72, 71, 70, 69, 68, 67, 66, 65, 64, 63, 62, 61, 30, 29, 28, 27, 26, 25, 33, 32, 31, 36, 35, 34, 45, 44, 43, 48, 47, 46, 39, 38, 37, 42, 41, 40, 3, 2, 1, 6, 5, 4, 12, 11, 10, 9, 8, 7, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13], [38, 39, 37, 41, 42, 40, 44, 45, 43, 47, 48, 46, 32, 33, 31, 35, 36, 34, 29, 30, 28, 26, 27, 25, 5, 6, 4, 2, 3, 1, 11, 12, 10, 8, 9, 7, 17, 18, 16, 14, 15, 13, 23, 24, 22, 20, 21, 19, 86, 87, 85, 89, 90, 88, 92, 93, 91, 95, 96, 94, 80, 81, 79, 83, 84, 82, 77, 78, 76, 74, 75, 73, 53, 54, 52, 50, 51, 49, 59, 60, 58, 56, 57, 55, 65, 66, 64, 62, 63, 61, 71, 72, 70, 68, 69, 67]];
cc:=[3,6,22];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=3;
gen_vect_label:=1;
is_hyperelliptic:=true;
hyp_involution:=S![4, 5, 6, 1, 2, 3, 10, 11, 12, 7, 8, 9, 16, 17, 18, 13, 14, 15, 22, 23, 24, 19, 20, 21, 28, 29, 30, 25, 26, 27, 34, 35, 36, 31, 32, 33, 40, 41, 42, 37, 38, 39, 46, 47, 48, 43, 44, 45, 52, 53, 54, 49, 50, 51, 58, 59, 60, 55, 56, 57, 64, 65, 66, 61, 62, 63, 70, 71, 72, 67, 68, 69, 76, 77, 78, 73, 74, 75, 82, 83, 84, 79, 80, 81, 88, 89, 90, 85, 86, 87, 94, 95, 96, 91, 92, 93];
is_cyclic_trigonal:=false;
Append(~data, rec<RecFormat | group:=G, gp_id:=gp_id, signature:=signature, gen_vectors:=gen_vectors_as_perm, conj_classes:=cc, genus:=genus, dimension:=dim, r:=r, g0:=g0, passport_label:= passport_label,gen_vect_label:=gen_vect_label, braid_class:=braid_class, topological_class:=topological_class, is_hyperelliptic:=is_hyperelliptic, hyp_involution:=hyp_involution,is_cyclic_trigonal:=is_cyclic_trigonal >);

// Here we add an action to data.
gen_vectors:=[[49, 51, 50, 52, 54, 53, 58, 60, 59, 55, 57, 56, 70, 72, 71, 67, 69, 68, 64, 66, 65, 61, 63, 62, 85, 87, 86, 88, 90, 89, 94, 96, 95, 91, 93, 92, 73, 75, 74, 76, 78, 77, 82, 84, 83, 79, 81, 80, 1, 3, 2, 4, 6, 5, 10, 12, 11, 7, 9, 8, 22, 24, 23, 19, 21, 20, 16, 18, 17, 13, 15, 14, 37, 39, 38, 40, 42, 41, 46, 48, 47, 43, 45, 44, 25, 27, 26, 28, 30, 29, 34, 36, 35, 31, 33, 32], [83, 82, 84, 80, 79, 81, 77, 76, 78, 74, 73, 75, 89, 88, 90, 86, 85, 87, 92, 91, 93, 95, 94, 96, 56, 55, 57, 59, 58, 60, 50, 49, 51, 53, 52, 54, 62, 61, 63, 65, 64, 66, 71, 70, 72, 68, 67, 69, 35, 34, 36, 32, 31, 33, 29, 28, 30, 26, 25, 27, 41, 40, 42, 38, 37, 39, 44, 43, 45, 47, 46, 48, 8, 7, 9, 11, 10, 12, 2, 1, 3, 5, 4, 6, 14, 13, 15, 17, 16, 18, 23, 22, 24, 20, 19, 21], [48, 46, 47, 45, 43, 44, 39, 37, 38, 42, 40, 41, 27, 25, 26, 30, 28, 29, 33, 31, 32, 36, 34, 35, 9, 7, 8, 12, 10, 11, 6, 4, 5, 3, 1, 2, 21, 19, 20, 24, 22, 23, 18, 16, 17, 15, 13, 14, 96, 94, 95, 93, 91, 92, 87, 85, 86, 90, 88, 89, 75, 73, 74, 78, 76, 77, 81, 79, 80, 84, 82, 83, 57, 55, 56, 60, 58, 59, 54, 52, 53, 51, 49, 50, 69, 67, 68, 72, 70, 71, 66, 64, 65, 63, 61, 62]];
cc:=[3,6,23];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=4;
gen_vect_label:=1;
is_hyperelliptic:=true;
hyp_involution:=S![4, 5, 6, 1, 2, 3, 10, 11, 12, 7, 8, 9, 16, 17, 18, 13, 14, 15, 22, 23, 24, 19, 20, 21, 28, 29, 30, 25, 26, 27, 34, 35, 36, 31, 32, 33, 40, 41, 42, 37, 38, 39, 46, 47, 48, 43, 44, 45, 52, 53, 54, 49, 50, 51, 58, 59, 60, 55, 56, 57, 64, 65, 66, 61, 62, 63, 70, 71, 72, 67, 68, 69, 76, 77, 78, 73, 74, 75, 82, 83, 84, 79, 80, 81, 88, 89, 90, 85, 86, 87, 94, 95, 96, 91, 92, 93];
is_cyclic_trigonal:=false;
Append(~data, rec<RecFormat | group:=G, gp_id:=gp_id, signature:=signature, gen_vectors:=gen_vectors_as_perm, conj_classes:=cc, genus:=genus, dimension:=dim, r:=r, g0:=g0, passport_label:= passport_label,gen_vect_label:=gen_vect_label, braid_class:=braid_class, topological_class:=topological_class, is_hyperelliptic:=is_hyperelliptic, hyp_involution:=hyp_involution,is_cyclic_trigonal:=is_cyclic_trigonal >);

// Here we add an action to data.
gen_vectors:=[[49, 51, 50, 52, 54, 53, 58, 60, 59, 55, 57, 56, 70, 72, 71, 67, 69, 68, 64, 66, 65, 61, 63, 62, 85, 87, 86, 88, 90, 89, 94, 96, 95, 91, 93, 92, 73, 75, 74, 76, 78, 77, 82, 84, 83, 79, 81, 80, 1, 3, 2, 4, 6, 5, 10, 12, 11, 7, 9, 8, 22, 24, 23, 19, 21, 20, 16, 18, 17, 13, 15, 14, 37, 39, 38, 40, 42, 41, 46, 48, 47, 43, 45, 44, 25, 27, 26, 28, 30, 29, 34, 36, 35, 31, 33, 32], [74, 73, 75, 77, 76, 78, 83, 82, 84, 80, 79, 81, 95, 94, 96, 92, 91, 93, 89, 88, 90, 86, 85, 87, 53, 52, 54, 50, 49, 51, 56, 55, 57, 59, 58, 60, 68, 67, 69, 71, 70, 72, 62, 61, 63, 65, 64, 66, 26, 25, 27, 29, 28, 30, 35, 34, 36, 32, 31, 33, 47, 46, 48, 44, 43, 45, 41, 40, 42, 38, 37, 39, 5, 4, 6, 2, 1, 3, 8, 7, 9, 11, 10, 12, 20, 19, 21, 23, 22, 24, 14, 13, 15, 17, 16, 18], [42, 40, 41, 39, 37, 38, 48, 46, 47, 45, 43, 44, 36, 34, 35, 33, 31, 32, 27, 25, 26, 30, 28, 29, 3, 1, 2, 6, 4, 5, 9, 7, 8, 12, 10, 11, 15, 13, 14, 18, 16, 17, 21, 19, 20, 24, 22, 23, 90, 88, 89, 87, 85, 86, 96, 94, 95, 93, 91, 92, 84, 82, 83, 81, 79, 80, 75, 73, 74, 78, 76, 77, 51, 49, 50, 54, 52, 53, 57, 55, 56, 60, 58, 59, 63, 61, 62, 66, 64, 65, 69, 67, 68, 72, 70, 71]];
cc:=[3,6,24];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=5;
gen_vect_label:=1;
is_hyperelliptic:=true;
hyp_involution:=S![4, 5, 6, 1, 2, 3, 10, 11, 12, 7, 8, 9, 16, 17, 18, 13, 14, 15, 22, 23, 24, 19, 20, 21, 28, 29, 30, 25, 26, 27, 34, 35, 36, 31, 32, 33, 40, 41, 42, 37, 38, 39, 46, 47, 48, 43, 44, 45, 52, 53, 54, 49, 50, 51, 58, 59, 60, 55, 56, 57, 64, 65, 66, 61, 62, 63, 70, 71, 72, 67, 68, 69, 76, 77, 78, 73, 74, 75, 82, 83, 84, 79, 80, 81, 88, 89, 90, 85, 86, 87, 94, 95, 96, 91, 92, 93];
is_cyclic_trigonal:=false;
Append(~data, rec<RecFormat | group:=G, gp_id:=gp_id, signature:=signature, gen_vectors:=gen_vectors_as_perm, conj_classes:=cc, genus:=genus, dimension:=dim, r:=r, g0:=g0, passport_label:= passport_label,gen_vect_label:=gen_vect_label, braid_class:=braid_class, topological_class:=topological_class, is_hyperelliptic:=is_hyperelliptic, hyp_involution:=hyp_involution,is_cyclic_trigonal:=is_cyclic_trigonal >);

// Here we add an action to data.
gen_vectors:=[[49, 51, 50, 52, 54, 53, 58, 60, 59, 55, 57, 56, 70, 72, 71, 67, 69, 68, 64, 66, 65, 61, 63, 62, 85, 87, 86, 88, 90, 89, 94, 96, 95, 91, 93, 92, 73, 75, 74, 76, 78, 77, 82, 84, 83, 79, 81, 80, 1, 3, 2, 4, 6, 5, 10, 12, 11, 7, 9, 8, 22, 24, 23, 19, 21, 20, 16, 18, 17, 13, 15, 14, 37, 39, 38, 40, 42, 41, 46, 48, 47, 43, 45, 44, 25, 27, 26, 28, 30, 29, 34, 36, 35, 31, 33, 32], [84, 83, 82, 81, 80, 79, 78, 77, 76, 75, 74, 73, 90, 89, 88, 87, 86, 85, 93, 92, 91, 96, 95, 94, 57, 56, 55, 60, 59, 58, 51, 50, 49, 54, 53, 52, 63, 62, 61, 66, 65, 64, 72, 71, 70, 69, 68, 67, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 42, 41, 40, 39, 38, 37, 45, 44, 43, 48, 47, 46, 9, 8, 7, 12, 11, 10, 3, 2, 1, 6, 5, 4, 15, 14, 13, 18, 17, 16, 24, 23, 22, 21, 20, 19], [47, 48, 46, 44, 45, 43, 38, 39, 37, 41, 42, 40, 26, 27, 25, 29, 30, 28, 32, 33, 31, 35, 36, 34, 8, 9, 7, 11, 12, 10, 5, 6, 4, 2, 3, 1, 20, 21, 19, 23, 24, 22, 17, 18, 16, 14, 15, 13, 95, 96, 94, 92, 93, 91, 86, 87, 85, 89, 90, 88, 74, 75, 73, 77, 78, 76, 80, 81, 79, 83, 84, 82, 56, 57, 55, 59, 60, 58, 53, 54, 52, 50, 51, 49, 68, 69, 67, 71, 72, 70, 65, 66, 64, 62, 63, 61]];
cc:=[3,6,25];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=6;
gen_vect_label:=1;
is_hyperelliptic:=true;
hyp_involution:=S![4, 5, 6, 1, 2, 3, 10, 11, 12, 7, 8, 9, 16, 17, 18, 13, 14, 15, 22, 23, 24, 19, 20, 21, 28, 29, 30, 25, 26, 27, 34, 35, 36, 31, 32, 33, 40, 41, 42, 37, 38, 39, 46, 47, 48, 43, 44, 45, 52, 53, 54, 49, 50, 51, 58, 59, 60, 55, 56, 57, 64, 65, 66, 61, 62, 63, 70, 71, 72, 67, 68, 69, 76, 77, 78, 73, 74, 75, 82, 83, 84, 79, 80, 81, 88, 89, 90, 85, 86, 87, 94, 95, 96, 91, 92, 93];
is_cyclic_trigonal:=false;
Append(~data, rec<RecFormat | group:=G, gp_id:=gp_id, signature:=signature, gen_vectors:=gen_vectors_as_perm, conj_classes:=cc, genus:=genus, dimension:=dim, r:=r, g0:=g0, passport_label:= passport_label,gen_vect_label:=gen_vect_label, braid_class:=braid_class, topological_class:=topological_class, is_hyperelliptic:=is_hyperelliptic, hyp_involution:=hyp_involution,is_cyclic_trigonal:=is_cyclic_trigonal >);

// Here we add an action to data.
gen_vectors:=[[49, 51, 50, 52, 54, 53, 58, 60, 59, 55, 57, 56, 70, 72, 71, 67, 69, 68, 64, 66, 65, 61, 63, 62, 85, 87, 86, 88, 90, 89, 94, 96, 95, 91, 93, 92, 73, 75, 74, 76, 78, 77, 82, 84, 83, 79, 81, 80, 1, 3, 2, 4, 6, 5, 10, 12, 11, 7, 9, 8, 22, 24, 23, 19, 21, 20, 16, 18, 17, 13, 15, 14, 37, 39, 38, 40, 42, 41, 46, 48, 47, 43, 45, 44, 25, 27, 26, 28, 30, 29, 34, 36, 35, 31, 33, 32], [75, 74, 73, 78, 77, 76, 84, 83, 82, 81, 80, 79, 96, 95, 94, 93, 92, 91, 90, 89, 88, 87, 86, 85, 54, 53, 52, 51, 50, 49, 57, 56, 55, 60, 59, 58, 69, 68, 67, 72, 71, 70, 63, 62, 61, 66, 65, 64, 27, 26, 25, 30, 29, 28, 36, 35, 34, 33, 32, 31, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 6, 5, 4, 3, 2, 1, 9, 8, 7, 12, 11, 10, 21, 20, 19, 24, 23, 22, 15, 14, 13, 18, 17, 16], [41, 42, 40, 38, 39, 37, 47, 48, 46, 44, 45, 43, 35, 36, 34, 32, 33, 31, 26, 27, 25, 29, 30, 28, 2, 3, 1, 5, 6, 4, 8, 9, 7, 11, 12, 10, 14, 15, 13, 17, 18, 16, 20, 21, 19, 23, 24, 22, 89, 90, 88, 86, 87, 85, 95, 96, 94, 92, 93, 91, 83, 84, 82, 80, 81, 79, 74, 75, 73, 77, 78, 76, 50, 51, 49, 53, 54, 52, 56, 57, 55, 59, 60, 58, 62, 63, 61, 65, 66, 64, 68, 69, 67, 71, 72, 70]];
cc:=[3,6,26];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=7;
gen_vect_label:=1;
is_hyperelliptic:=true;
hyp_involution:=S![4, 5, 6, 1, 2, 3, 10, 11, 12, 7, 8, 9, 16, 17, 18, 13, 14, 15, 22, 23, 24, 19, 20, 21, 28, 29, 30, 25, 26, 27, 34, 35, 36, 31, 32, 33, 40, 41, 42, 37, 38, 39, 46, 47, 48, 43, 44, 45, 52, 53, 54, 49, 50, 51, 58, 59, 60, 55, 56, 57, 64, 65, 66, 61, 62, 63, 70, 71, 72, 67, 68, 69, 76, 77, 78, 73, 74, 75, 82, 83, 84, 79, 80, 81, 88, 89, 90, 85, 86, 87, 94, 95, 96, 91, 92, 93];
is_cyclic_trigonal:=false;
Append(~data, rec<RecFormat | group:=G, gp_id:=gp_id, signature:=signature, gen_vectors:=gen_vectors_as_perm, conj_classes:=cc, genus:=genus, dimension:=dim, r:=r, g0:=g0, passport_label:= passport_label,gen_vect_label:=gen_vect_label, braid_class:=braid_class, topological_class:=topological_class, is_hyperelliptic:=is_hyperelliptic, hyp_involution:=hyp_involution,is_cyclic_trigonal:=is_cyclic_trigonal >);

// Here we add an action to data.
gen_vectors:=[[49, 51, 50, 52, 54, 53, 58, 60, 59, 55, 57, 56, 70, 72, 71, 67, 69, 68, 64, 66, 65, 61, 63, 62, 85, 87, 86, 88, 90, 89, 94, 96, 95, 91, 93, 92, 73, 75, 74, 76, 78, 77, 82, 84, 83, 79, 81, 80, 1, 3, 2, 4, 6, 5, 10, 12, 11, 7, 9, 8, 22, 24, 23, 19, 21, 20, 16, 18, 17, 13, 15, 14, 37, 39, 38, 40, 42, 41, 46, 48, 47, 43, 45, 44, 25, 27, 26, 28, 30, 29, 34, 36, 35, 31, 33, 32], [80, 79, 81, 83, 82, 84, 74, 73, 75, 77, 76, 78, 86, 85, 87, 89, 88, 90, 95, 94, 96, 92, 91, 93, 59, 58, 60, 56, 55, 57, 53, 52, 54, 50, 49, 51, 65, 64, 66, 62, 61, 63, 68, 67, 69, 71, 70, 72, 32, 31, 33, 35, 34, 36, 26, 25, 27, 29, 28, 30, 38, 37, 39, 41, 40, 42, 47, 46, 48, 44, 43, 45, 11, 10, 12, 8, 7, 9, 5, 4, 6, 2, 1, 3, 17, 16, 18, 14, 13, 15, 20, 19, 21, 23, 22, 24], [45, 43, 44, 48, 46, 47, 42, 40, 41, 39, 37, 38, 30, 28, 29, 27, 25, 26, 36, 34, 35, 33, 31, 32, 12, 10, 11, 9, 7, 8, 3, 1, 2, 6, 4, 5, 24, 22, 23, 21, 19, 20, 15, 13, 14, 18, 16, 17, 93, 91, 92, 96, 94, 95, 90, 88, 89, 87, 85, 86, 78, 76, 77, 75, 73, 74, 84, 82, 83, 81, 79, 80, 60, 58, 59, 57, 55, 56, 51, 49, 50, 54, 52, 53, 72, 70, 71, 69, 67, 68, 63, 61, 62, 66, 64, 65]];
cc:=[3,6,27];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=8;
gen_vect_label:=1;
is_hyperelliptic:=true;
hyp_involution:=S![4, 5, 6, 1, 2, 3, 10, 11, 12, 7, 8, 9, 16, 17, 18, 13, 14, 15, 22, 23, 24, 19, 20, 21, 28, 29, 30, 25, 26, 27, 34, 35, 36, 31, 32, 33, 40, 41, 42, 37, 38, 39, 46, 47, 48, 43, 44, 45, 52, 53, 54, 49, 50, 51, 58, 59, 60, 55, 56, 57, 64, 65, 66, 61, 62, 63, 70, 71, 72, 67, 68, 69, 76, 77, 78, 73, 74, 75, 82, 83, 84, 79, 80, 81, 88, 89, 90, 85, 86, 87, 94, 95, 96, 91, 92, 93];
is_cyclic_trigonal:=false;
Append(~data, rec<RecFormat | group:=G, gp_id:=gp_id, signature:=signature, gen_vectors:=gen_vectors_as_perm, conj_classes:=cc, genus:=genus, dimension:=dim, r:=r, g0:=g0, passport_label:= passport_label,gen_vect_label:=gen_vect_label, braid_class:=braid_class, topological_class:=topological_class, is_hyperelliptic:=is_hyperelliptic, hyp_involution:=hyp_involution,is_cyclic_trigonal:=is_cyclic_trigonal >);
