// Magma code for the lmfdb family of higher genus curves 7.64-38.0.2-4-16
// 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:=[64,38];
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:=[0,2,4,16];
genus:=7;
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:=[[17, 18, 20, 19, 21, 22, 24, 23, 27, 28, 25, 26, 31, 32, 29, 30, 1, 2, 4, 3, 5, 6, 8, 7, 11, 12, 9, 10, 15, 16, 13, 14, 49, 50, 52, 51, 53, 54, 56, 55, 59, 60, 57, 58, 63, 64, 61, 62, 33, 34, 36, 35, 37, 38, 40, 39, 43, 44, 41, 42, 47, 48, 45, 46], [35, 36, 33, 34, 39, 40, 37, 38, 42, 41, 43, 44, 46, 45, 47, 48, 59, 60, 57, 58, 63, 64, 61, 62, 51, 52, 49, 50, 55, 56, 53, 54, 7, 8, 5, 6, 3, 4, 1, 2, 14, 13, 15, 16, 10, 9, 11, 12, 31, 32, 29, 30, 27, 28, 25, 26, 23, 24, 21, 22, 19, 20, 17, 18], [56, 55, 53, 54, 52, 51, 49, 50, 64, 63, 61, 62, 60, 59, 57, 58, 45, 46, 47, 48, 41, 42, 43, 44, 40, 39, 37, 38, 36, 35, 33, 34, 20, 19, 17, 18, 24, 23, 21, 22, 28, 27, 25, 26, 32, 31, 29, 30, 9, 10, 11, 12, 13, 14, 15, 16, 4, 3, 1, 2, 8, 7, 5, 6]];
cc:=[5,9,16];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=1;
gen_vect_label:=1;
braid_class:=1;
topological_class:=[1, 1];
is_hyperelliptic:=true;
hyp_involution:=S![5, 6, 7, 8, 1, 2, 3, 4, 13, 14, 15, 16, 9, 10, 11, 12, 21, 22, 23, 24, 17, 18, 19, 20, 29, 30, 31, 32, 25, 26, 27, 28, 37, 38, 39, 40, 33, 34, 35, 36, 45, 46, 47, 48, 41, 42, 43, 44, 53, 54, 55, 56, 49, 50, 51, 52, 61, 62, 63, 64, 57, 58, 59, 60];
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:=[[17, 18, 20, 19, 21, 22, 24, 23, 27, 28, 25, 26, 31, 32, 29, 30, 1, 2, 4, 3, 5, 6, 8, 7, 11, 12, 9, 10, 15, 16, 13, 14, 49, 50, 52, 51, 53, 54, 56, 55, 59, 60, 57, 58, 63, 64, 61, 62, 33, 34, 36, 35, 37, 38, 40, 39, 43, 44, 41, 42, 47, 48, 45, 46], [34, 33, 35, 36, 38, 37, 39, 40, 44, 43, 42, 41, 48, 47, 46, 45, 58, 57, 59, 60, 62, 61, 63, 64, 50, 49, 51, 52, 54, 53, 55, 56, 6, 5, 7, 8, 2, 1, 3, 4, 16, 15, 14, 13, 12, 11, 10, 9, 30, 29, 31, 32, 26, 25, 27, 28, 22, 21, 23, 24, 18, 17, 19, 20], [54, 53, 56, 55, 50, 49, 52, 51, 62, 61, 64, 63, 58, 57, 60, 59, 48, 47, 45, 46, 44, 43, 41, 42, 38, 37, 40, 39, 34, 33, 36, 35, 18, 17, 20, 19, 22, 21, 24, 23, 26, 25, 28, 27, 30, 29, 32, 31, 12, 11, 9, 10, 16, 15, 13, 14, 2, 1, 4, 3, 6, 5, 8, 7]];
cc:=[5,9,18];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=2;
gen_vect_label:=1;
braid_class:=1;
topological_class:=[1, 1];
is_hyperelliptic:=true;
hyp_involution:=S![5, 6, 7, 8, 1, 2, 3, 4, 13, 14, 15, 16, 9, 10, 11, 12, 21, 22, 23, 24, 17, 18, 19, 20, 29, 30, 31, 32, 25, 26, 27, 28, 37, 38, 39, 40, 33, 34, 35, 36, 45, 46, 47, 48, 41, 42, 43, 44, 53, 54, 55, 56, 49, 50, 51, 52, 61, 62, 63, 64, 57, 58, 59, 60];
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:=[[17, 18, 20, 19, 21, 22, 24, 23, 27, 28, 25, 26, 31, 32, 29, 30, 1, 2, 4, 3, 5, 6, 8, 7, 11, 12, 9, 10, 15, 16, 13, 14, 49, 50, 52, 51, 53, 54, 56, 55, 59, 60, 57, 58, 63, 64, 61, 62, 33, 34, 36, 35, 37, 38, 40, 39, 43, 44, 41, 42, 47, 48, 45, 46], [36, 35, 34, 33, 40, 39, 38, 37, 41, 42, 44, 43, 45, 46, 48, 47, 60, 59, 58, 57, 64, 63, 62, 61, 52, 51, 50, 49, 56, 55, 54, 53, 8, 7, 6, 5, 4, 3, 2, 1, 13, 14, 16, 15, 9, 10, 12, 11, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17], [55, 56, 54, 53, 51, 52, 50, 49, 63, 64, 62, 61, 59, 60, 58, 57, 46, 45, 48, 47, 42, 41, 44, 43, 39, 40, 38, 37, 35, 36, 34, 33, 19, 20, 18, 17, 23, 24, 22, 21, 27, 28, 26, 25, 31, 32, 30, 29, 10, 9, 12, 11, 14, 13, 16, 15, 3, 4, 2, 1, 7, 8, 6, 5]];
cc:=[5,9,20];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=3;
gen_vect_label:=1;
braid_class:=1;
topological_class:=[1, 1];
is_hyperelliptic:=true;
hyp_involution:=S![5, 6, 7, 8, 1, 2, 3, 4, 13, 14, 15, 16, 9, 10, 11, 12, 21, 22, 23, 24, 17, 18, 19, 20, 29, 30, 31, 32, 25, 26, 27, 28, 37, 38, 39, 40, 33, 34, 35, 36, 45, 46, 47, 48, 41, 42, 43, 44, 53, 54, 55, 56, 49, 50, 51, 52, 61, 62, 63, 64, 57, 58, 59, 60];
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:=[[17, 18, 20, 19, 21, 22, 24, 23, 27, 28, 25, 26, 31, 32, 29, 30, 1, 2, 4, 3, 5, 6, 8, 7, 11, 12, 9, 10, 15, 16, 13, 14, 49, 50, 52, 51, 53, 54, 56, 55, 59, 60, 57, 58, 63, 64, 61, 62, 33, 34, 36, 35, 37, 38, 40, 39, 43, 44, 41, 42, 47, 48, 45, 46], [33, 34, 36, 35, 37, 38, 40, 39, 43, 44, 41, 42, 47, 48, 45, 46, 57, 58, 60, 59, 61, 62, 64, 63, 49, 50, 52, 51, 53, 54, 56, 55, 5, 6, 8, 7, 1, 2, 4, 3, 15, 16, 13, 14, 11, 12, 9, 10, 29, 30, 32, 31, 25, 26, 28, 27, 21, 22, 24, 23, 17, 18, 20, 19], [53, 54, 55, 56, 49, 50, 51, 52, 61, 62, 63, 64, 57, 58, 59, 60, 47, 48, 46, 45, 43, 44, 42, 41, 37, 38, 39, 40, 33, 34, 35, 36, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 11, 12, 10, 9, 15, 16, 14, 13, 1, 2, 3, 4, 5, 6, 7, 8]];
cc:=[5,9,22];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=4;
gen_vect_label:=1;
braid_class:=1;
topological_class:=[1, 1];
is_hyperelliptic:=true;
hyp_involution:=S![5, 6, 7, 8, 1, 2, 3, 4, 13, 14, 15, 16, 9, 10, 11, 12, 21, 22, 23, 24, 17, 18, 19, 20, 29, 30, 31, 32, 25, 26, 27, 28, 37, 38, 39, 40, 33, 34, 35, 36, 45, 46, 47, 48, 41, 42, 43, 44, 53, 54, 55, 56, 49, 50, 51, 52, 61, 62, 63, 64, 57, 58, 59, 60];
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:=[[17, 18, 20, 19, 21, 22, 24, 23, 27, 28, 25, 26, 31, 32, 29, 30, 1, 2, 4, 3, 5, 6, 8, 7, 11, 12, 9, 10, 15, 16, 13, 14, 49, 50, 52, 51, 53, 54, 56, 55, 59, 60, 57, 58, 63, 64, 61, 62, 33, 34, 36, 35, 37, 38, 40, 39, 43, 44, 41, 42, 47, 48, 45, 46], [37, 38, 40, 39, 33, 34, 36, 35, 47, 48, 45, 46, 43, 44, 41, 42, 61, 62, 64, 63, 57, 58, 60, 59, 53, 54, 56, 55, 49, 50, 52, 51, 1, 2, 4, 3, 5, 6, 8, 7, 11, 12, 9, 10, 15, 16, 13, 14, 25, 26, 28, 27, 29, 30, 32, 31, 17, 18, 20, 19, 21, 22, 24, 23], [49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 43, 44, 42, 41, 47, 48, 46, 45, 33, 34, 35, 36, 37, 38, 39, 40, 21, 22, 23, 24, 17, 18, 19, 20, 29, 30, 31, 32, 25, 26, 27, 28, 15, 16, 14, 13, 11, 12, 10, 9, 5, 6, 7, 8, 1, 2, 3, 4]];
cc:=[5,10,15];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=5;
gen_vect_label:=1;
braid_class:=1;
topological_class:=[1, 1];
is_hyperelliptic:=true;
hyp_involution:=S![5, 6, 7, 8, 1, 2, 3, 4, 13, 14, 15, 16, 9, 10, 11, 12, 21, 22, 23, 24, 17, 18, 19, 20, 29, 30, 31, 32, 25, 26, 27, 28, 37, 38, 39, 40, 33, 34, 35, 36, 45, 46, 47, 48, 41, 42, 43, 44, 53, 54, 55, 56, 49, 50, 51, 52, 61, 62, 63, 64, 57, 58, 59, 60];
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:=[[17, 18, 20, 19, 21, 22, 24, 23, 27, 28, 25, 26, 31, 32, 29, 30, 1, 2, 4, 3, 5, 6, 8, 7, 11, 12, 9, 10, 15, 16, 13, 14, 49, 50, 52, 51, 53, 54, 56, 55, 59, 60, 57, 58, 63, 64, 61, 62, 33, 34, 36, 35, 37, 38, 40, 39, 43, 44, 41, 42, 47, 48, 45, 46], [40, 39, 38, 37, 36, 35, 34, 33, 45, 46, 48, 47, 41, 42, 44, 43, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 53, 52, 51, 50, 49, 4, 3, 2, 1, 8, 7, 6, 5, 9, 10, 12, 11, 13, 14, 16, 15, 28, 27, 26, 25, 32, 31, 30, 29, 20, 19, 18, 17, 24, 23, 22, 21], [51, 52, 50, 49, 55, 56, 54, 53, 59, 60, 58, 57, 63, 64, 62, 61, 42, 41, 44, 43, 46, 45, 48, 47, 35, 36, 34, 33, 39, 40, 38, 37, 23, 24, 22, 21, 19, 20, 18, 17, 31, 32, 30, 29, 27, 28, 26, 25, 14, 13, 16, 15, 10, 9, 12, 11, 7, 8, 6, 5, 3, 4, 2, 1]];
cc:=[5,10,17];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=6;
gen_vect_label:=1;
braid_class:=1;
topological_class:=[1, 1];
is_hyperelliptic:=true;
hyp_involution:=S![5, 6, 7, 8, 1, 2, 3, 4, 13, 14, 15, 16, 9, 10, 11, 12, 21, 22, 23, 24, 17, 18, 19, 20, 29, 30, 31, 32, 25, 26, 27, 28, 37, 38, 39, 40, 33, 34, 35, 36, 45, 46, 47, 48, 41, 42, 43, 44, 53, 54, 55, 56, 49, 50, 51, 52, 61, 62, 63, 64, 57, 58, 59, 60];
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:=[[17, 18, 20, 19, 21, 22, 24, 23, 27, 28, 25, 26, 31, 32, 29, 30, 1, 2, 4, 3, 5, 6, 8, 7, 11, 12, 9, 10, 15, 16, 13, 14, 49, 50, 52, 51, 53, 54, 56, 55, 59, 60, 57, 58, 63, 64, 61, 62, 33, 34, 36, 35, 37, 38, 40, 39, 43, 44, 41, 42, 47, 48, 45, 46], [38, 37, 39, 40, 34, 33, 35, 36, 48, 47, 46, 45, 44, 43, 42, 41, 62, 61, 63, 64, 58, 57, 59, 60, 54, 53, 55, 56, 50, 49, 51, 52, 2, 1, 3, 4, 6, 5, 7, 8, 12, 11, 10, 9, 16, 15, 14, 13, 26, 25, 27, 28, 30, 29, 31, 32, 18, 17, 19, 20, 22, 21, 23, 24], [50, 49, 52, 51, 54, 53, 56, 55, 58, 57, 60, 59, 62, 61, 64, 63, 44, 43, 41, 42, 48, 47, 45, 46, 34, 33, 36, 35, 38, 37, 40, 39, 22, 21, 24, 23, 18, 17, 20, 19, 30, 29, 32, 31, 26, 25, 28, 27, 16, 15, 13, 14, 12, 11, 9, 10, 6, 5, 8, 7, 2, 1, 4, 3]];
cc:=[5,10,19];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=7;
gen_vect_label:=1;
braid_class:=1;
topological_class:=[1, 1];
is_hyperelliptic:=true;
hyp_involution:=S![5, 6, 7, 8, 1, 2, 3, 4, 13, 14, 15, 16, 9, 10, 11, 12, 21, 22, 23, 24, 17, 18, 19, 20, 29, 30, 31, 32, 25, 26, 27, 28, 37, 38, 39, 40, 33, 34, 35, 36, 45, 46, 47, 48, 41, 42, 43, 44, 53, 54, 55, 56, 49, 50, 51, 52, 61, 62, 63, 64, 57, 58, 59, 60];
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:=[[17, 18, 20, 19, 21, 22, 24, 23, 27, 28, 25, 26, 31, 32, 29, 30, 1, 2, 4, 3, 5, 6, 8, 7, 11, 12, 9, 10, 15, 16, 13, 14, 49, 50, 52, 51, 53, 54, 56, 55, 59, 60, 57, 58, 63, 64, 61, 62, 33, 34, 36, 35, 37, 38, 40, 39, 43, 44, 41, 42, 47, 48, 45, 46], [39, 40, 37, 38, 35, 36, 33, 34, 46, 45, 47, 48, 42, 41, 43, 44, 63, 64, 61, 62, 59, 60, 57, 58, 55, 56, 53, 54, 51, 52, 49, 50, 3, 4, 1, 2, 7, 8, 5, 6, 10, 9, 11, 12, 14, 13, 15, 16, 27, 28, 25, 26, 31, 32, 29, 30, 19, 20, 17, 18, 23, 24, 21, 22], [52, 51, 49, 50, 56, 55, 53, 54, 60, 59, 57, 58, 64, 63, 61, 62, 41, 42, 43, 44, 45, 46, 47, 48, 36, 35, 33, 34, 40, 39, 37, 38, 24, 23, 21, 22, 20, 19, 17, 18, 32, 31, 29, 30, 28, 27, 25, 26, 13, 14, 15, 16, 9, 10, 11, 12, 8, 7, 5, 6, 4, 3, 1, 2]];
cc:=[5,10,21];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=8;
gen_vect_label:=1;
braid_class:=1;
topological_class:=[1, 1];
is_hyperelliptic:=true;
hyp_involution:=S![5, 6, 7, 8, 1, 2, 3, 4, 13, 14, 15, 16, 9, 10, 11, 12, 21, 22, 23, 24, 17, 18, 19, 20, 29, 30, 31, 32, 25, 26, 27, 28, 37, 38, 39, 40, 33, 34, 35, 36, 45, 46, 47, 48, 41, 42, 43, 44, 53, 54, 55, 56, 49, 50, 51, 52, 61, 62, 63, 64, 57, 58, 59, 60];
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:=[[21, 22, 24, 23, 17, 18, 20, 19, 31, 32, 29, 30, 27, 28, 25, 26, 5, 6, 8, 7, 1, 2, 4, 3, 15, 16, 13, 14, 11, 12, 9, 10, 53, 54, 56, 55, 49, 50, 52, 51, 63, 64, 61, 62, 59, 60, 57, 58, 37, 38, 40, 39, 33, 34, 36, 35, 47, 48, 45, 46, 43, 44, 41, 42], [33, 34, 36, 35, 37, 38, 40, 39, 43, 44, 41, 42, 47, 48, 45, 46, 57, 58, 60, 59, 61, 62, 64, 63, 49, 50, 52, 51, 53, 54, 56, 55, 5, 6, 8, 7, 1, 2, 4, 3, 15, 16, 13, 14, 11, 12, 9, 10, 29, 30, 32, 31, 25, 26, 28, 27, 21, 22, 24, 23, 17, 18, 20, 19], [49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 43, 44, 42, 41, 47, 48, 46, 45, 33, 34, 35, 36, 37, 38, 39, 40, 21, 22, 23, 24, 17, 18, 19, 20, 29, 30, 31, 32, 25, 26, 27, 28, 15, 16, 14, 13, 11, 12, 10, 9, 5, 6, 7, 8, 1, 2, 3, 4]];
cc:=[6,9,15];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=9;
gen_vect_label:=1;
braid_class:=1;
topological_class:=[1, 1];
is_hyperelliptic:=true;
hyp_involution:=S![5, 6, 7, 8, 1, 2, 3, 4, 13, 14, 15, 16, 9, 10, 11, 12, 21, 22, 23, 24, 17, 18, 19, 20, 29, 30, 31, 32, 25, 26, 27, 28, 37, 38, 39, 40, 33, 34, 35, 36, 45, 46, 47, 48, 41, 42, 43, 44, 53, 54, 55, 56, 49, 50, 51, 52, 61, 62, 63, 64, 57, 58, 59, 60];
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:=[[21, 22, 24, 23, 17, 18, 20, 19, 31, 32, 29, 30, 27, 28, 25, 26, 5, 6, 8, 7, 1, 2, 4, 3, 15, 16, 13, 14, 11, 12, 9, 10, 53, 54, 56, 55, 49, 50, 52, 51, 63, 64, 61, 62, 59, 60, 57, 58, 37, 38, 40, 39, 33, 34, 36, 35, 47, 48, 45, 46, 43, 44, 41, 42], [36, 35, 34, 33, 40, 39, 38, 37, 41, 42, 44, 43, 45, 46, 48, 47, 60, 59, 58, 57, 64, 63, 62, 61, 52, 51, 50, 49, 56, 55, 54, 53, 8, 7, 6, 5, 4, 3, 2, 1, 13, 14, 16, 15, 9, 10, 12, 11, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17], [51, 52, 50, 49, 55, 56, 54, 53, 59, 60, 58, 57, 63, 64, 62, 61, 42, 41, 44, 43, 46, 45, 48, 47, 35, 36, 34, 33, 39, 40, 38, 37, 23, 24, 22, 21, 19, 20, 18, 17, 31, 32, 30, 29, 27, 28, 26, 25, 14, 13, 16, 15, 10, 9, 12, 11, 7, 8, 6, 5, 3, 4, 2, 1]];
cc:=[6,9,17];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=10;
gen_vect_label:=1;
braid_class:=1;
topological_class:=[1, 1];
is_hyperelliptic:=true;
hyp_involution:=S![5, 6, 7, 8, 1, 2, 3, 4, 13, 14, 15, 16, 9, 10, 11, 12, 21, 22, 23, 24, 17, 18, 19, 20, 29, 30, 31, 32, 25, 26, 27, 28, 37, 38, 39, 40, 33, 34, 35, 36, 45, 46, 47, 48, 41, 42, 43, 44, 53, 54, 55, 56, 49, 50, 51, 52, 61, 62, 63, 64, 57, 58, 59, 60];
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:=[[21, 22, 24, 23, 17, 18, 20, 19, 31, 32, 29, 30, 27, 28, 25, 26, 5, 6, 8, 7, 1, 2, 4, 3, 15, 16, 13, 14, 11, 12, 9, 10, 53, 54, 56, 55, 49, 50, 52, 51, 63, 64, 61, 62, 59, 60, 57, 58, 37, 38, 40, 39, 33, 34, 36, 35, 47, 48, 45, 46, 43, 44, 41, 42], [34, 33, 35, 36, 38, 37, 39, 40, 44, 43, 42, 41, 48, 47, 46, 45, 58, 57, 59, 60, 62, 61, 63, 64, 50, 49, 51, 52, 54, 53, 55, 56, 6, 5, 7, 8, 2, 1, 3, 4, 16, 15, 14, 13, 12, 11, 10, 9, 30, 29, 31, 32, 26, 25, 27, 28, 22, 21, 23, 24, 18, 17, 19, 20], [50, 49, 52, 51, 54, 53, 56, 55, 58, 57, 60, 59, 62, 61, 64, 63, 44, 43, 41, 42, 48, 47, 45, 46, 34, 33, 36, 35, 38, 37, 40, 39, 22, 21, 24, 23, 18, 17, 20, 19, 30, 29, 32, 31, 26, 25, 28, 27, 16, 15, 13, 14, 12, 11, 9, 10, 6, 5, 8, 7, 2, 1, 4, 3]];
cc:=[6,9,19];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=11;
gen_vect_label:=1;
braid_class:=1;
topological_class:=[1, 1];
is_hyperelliptic:=true;
hyp_involution:=S![5, 6, 7, 8, 1, 2, 3, 4, 13, 14, 15, 16, 9, 10, 11, 12, 21, 22, 23, 24, 17, 18, 19, 20, 29, 30, 31, 32, 25, 26, 27, 28, 37, 38, 39, 40, 33, 34, 35, 36, 45, 46, 47, 48, 41, 42, 43, 44, 53, 54, 55, 56, 49, 50, 51, 52, 61, 62, 63, 64, 57, 58, 59, 60];
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:=[[21, 22, 24, 23, 17, 18, 20, 19, 31, 32, 29, 30, 27, 28, 25, 26, 5, 6, 8, 7, 1, 2, 4, 3, 15, 16, 13, 14, 11, 12, 9, 10, 53, 54, 56, 55, 49, 50, 52, 51, 63, 64, 61, 62, 59, 60, 57, 58, 37, 38, 40, 39, 33, 34, 36, 35, 47, 48, 45, 46, 43, 44, 41, 42], [35, 36, 33, 34, 39, 40, 37, 38, 42, 41, 43, 44, 46, 45, 47, 48, 59, 60, 57, 58, 63, 64, 61, 62, 51, 52, 49, 50, 55, 56, 53, 54, 7, 8, 5, 6, 3, 4, 1, 2, 14, 13, 15, 16, 10, 9, 11, 12, 31, 32, 29, 30, 27, 28, 25, 26, 23, 24, 21, 22, 19, 20, 17, 18], [52, 51, 49, 50, 56, 55, 53, 54, 60, 59, 57, 58, 64, 63, 61, 62, 41, 42, 43, 44, 45, 46, 47, 48, 36, 35, 33, 34, 40, 39, 37, 38, 24, 23, 21, 22, 20, 19, 17, 18, 32, 31, 29, 30, 28, 27, 25, 26, 13, 14, 15, 16, 9, 10, 11, 12, 8, 7, 5, 6, 4, 3, 1, 2]];
cc:=[6,9,21];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=12;
gen_vect_label:=1;
braid_class:=1;
topological_class:=[1, 1];
is_hyperelliptic:=true;
hyp_involution:=S![5, 6, 7, 8, 1, 2, 3, 4, 13, 14, 15, 16, 9, 10, 11, 12, 21, 22, 23, 24, 17, 18, 19, 20, 29, 30, 31, 32, 25, 26, 27, 28, 37, 38, 39, 40, 33, 34, 35, 36, 45, 46, 47, 48, 41, 42, 43, 44, 53, 54, 55, 56, 49, 50, 51, 52, 61, 62, 63, 64, 57, 58, 59, 60];
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:=[[21, 22, 24, 23, 17, 18, 20, 19, 31, 32, 29, 30, 27, 28, 25, 26, 5, 6, 8, 7, 1, 2, 4, 3, 15, 16, 13, 14, 11, 12, 9, 10, 53, 54, 56, 55, 49, 50, 52, 51, 63, 64, 61, 62, 59, 60, 57, 58, 37, 38, 40, 39, 33, 34, 36, 35, 47, 48, 45, 46, 43, 44, 41, 42], [39, 40, 37, 38, 35, 36, 33, 34, 46, 45, 47, 48, 42, 41, 43, 44, 63, 64, 61, 62, 59, 60, 57, 58, 55, 56, 53, 54, 51, 52, 49, 50, 3, 4, 1, 2, 7, 8, 5, 6, 10, 9, 11, 12, 14, 13, 15, 16, 27, 28, 25, 26, 31, 32, 29, 30, 19, 20, 17, 18, 23, 24, 21, 22], [56, 55, 53, 54, 52, 51, 49, 50, 64, 63, 61, 62, 60, 59, 57, 58, 45, 46, 47, 48, 41, 42, 43, 44, 40, 39, 37, 38, 36, 35, 33, 34, 20, 19, 17, 18, 24, 23, 21, 22, 28, 27, 25, 26, 32, 31, 29, 30, 9, 10, 11, 12, 13, 14, 15, 16, 4, 3, 1, 2, 8, 7, 5, 6]];
cc:=[6,10,16];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=13;
gen_vect_label:=1;
braid_class:=1;
topological_class:=[1, 1];
is_hyperelliptic:=true;
hyp_involution:=S![5, 6, 7, 8, 1, 2, 3, 4, 13, 14, 15, 16, 9, 10, 11, 12, 21, 22, 23, 24, 17, 18, 19, 20, 29, 30, 31, 32, 25, 26, 27, 28, 37, 38, 39, 40, 33, 34, 35, 36, 45, 46, 47, 48, 41, 42, 43, 44, 53, 54, 55, 56, 49, 50, 51, 52, 61, 62, 63, 64, 57, 58, 59, 60];
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:=[[21, 22, 24, 23, 17, 18, 20, 19, 31, 32, 29, 30, 27, 28, 25, 26, 5, 6, 8, 7, 1, 2, 4, 3, 15, 16, 13, 14, 11, 12, 9, 10, 53, 54, 56, 55, 49, 50, 52, 51, 63, 64, 61, 62, 59, 60, 57, 58, 37, 38, 40, 39, 33, 34, 36, 35, 47, 48, 45, 46, 43, 44, 41, 42], [38, 37, 39, 40, 34, 33, 35, 36, 48, 47, 46, 45, 44, 43, 42, 41, 62, 61, 63, 64, 58, 57, 59, 60, 54, 53, 55, 56, 50, 49, 51, 52, 2, 1, 3, 4, 6, 5, 7, 8, 12, 11, 10, 9, 16, 15, 14, 13, 26, 25, 27, 28, 30, 29, 31, 32, 18, 17, 19, 20, 22, 21, 23, 24], [54, 53, 56, 55, 50, 49, 52, 51, 62, 61, 64, 63, 58, 57, 60, 59, 48, 47, 45, 46, 44, 43, 41, 42, 38, 37, 40, 39, 34, 33, 36, 35, 18, 17, 20, 19, 22, 21, 24, 23, 26, 25, 28, 27, 30, 29, 32, 31, 12, 11, 9, 10, 16, 15, 13, 14, 2, 1, 4, 3, 6, 5, 8, 7]];
cc:=[6,10,18];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=14;
gen_vect_label:=1;
braid_class:=1;
topological_class:=[1, 1];
is_hyperelliptic:=true;
hyp_involution:=S![5, 6, 7, 8, 1, 2, 3, 4, 13, 14, 15, 16, 9, 10, 11, 12, 21, 22, 23, 24, 17, 18, 19, 20, 29, 30, 31, 32, 25, 26, 27, 28, 37, 38, 39, 40, 33, 34, 35, 36, 45, 46, 47, 48, 41, 42, 43, 44, 53, 54, 55, 56, 49, 50, 51, 52, 61, 62, 63, 64, 57, 58, 59, 60];
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:=[[21, 22, 24, 23, 17, 18, 20, 19, 31, 32, 29, 30, 27, 28, 25, 26, 5, 6, 8, 7, 1, 2, 4, 3, 15, 16, 13, 14, 11, 12, 9, 10, 53, 54, 56, 55, 49, 50, 52, 51, 63, 64, 61, 62, 59, 60, 57, 58, 37, 38, 40, 39, 33, 34, 36, 35, 47, 48, 45, 46, 43, 44, 41, 42], [40, 39, 38, 37, 36, 35, 34, 33, 45, 46, 48, 47, 41, 42, 44, 43, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 53, 52, 51, 50, 49, 4, 3, 2, 1, 8, 7, 6, 5, 9, 10, 12, 11, 13, 14, 16, 15, 28, 27, 26, 25, 32, 31, 30, 29, 20, 19, 18, 17, 24, 23, 22, 21], [55, 56, 54, 53, 51, 52, 50, 49, 63, 64, 62, 61, 59, 60, 58, 57, 46, 45, 48, 47, 42, 41, 44, 43, 39, 40, 38, 37, 35, 36, 34, 33, 19, 20, 18, 17, 23, 24, 22, 21, 27, 28, 26, 25, 31, 32, 30, 29, 10, 9, 12, 11, 14, 13, 16, 15, 3, 4, 2, 1, 7, 8, 6, 5]];
cc:=[6,10,20];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=15;
gen_vect_label:=1;
braid_class:=1;
topological_class:=[1, 1];
is_hyperelliptic:=true;
hyp_involution:=S![5, 6, 7, 8, 1, 2, 3, 4, 13, 14, 15, 16, 9, 10, 11, 12, 21, 22, 23, 24, 17, 18, 19, 20, 29, 30, 31, 32, 25, 26, 27, 28, 37, 38, 39, 40, 33, 34, 35, 36, 45, 46, 47, 48, 41, 42, 43, 44, 53, 54, 55, 56, 49, 50, 51, 52, 61, 62, 63, 64, 57, 58, 59, 60];
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:=[[21, 22, 24, 23, 17, 18, 20, 19, 31, 32, 29, 30, 27, 28, 25, 26, 5, 6, 8, 7, 1, 2, 4, 3, 15, 16, 13, 14, 11, 12, 9, 10, 53, 54, 56, 55, 49, 50, 52, 51, 63, 64, 61, 62, 59, 60, 57, 58, 37, 38, 40, 39, 33, 34, 36, 35, 47, 48, 45, 46, 43, 44, 41, 42], [37, 38, 40, 39, 33, 34, 36, 35, 47, 48, 45, 46, 43, 44, 41, 42, 61, 62, 64, 63, 57, 58, 60, 59, 53, 54, 56, 55, 49, 50, 52, 51, 1, 2, 4, 3, 5, 6, 8, 7, 11, 12, 9, 10, 15, 16, 13, 14, 25, 26, 28, 27, 29, 30, 32, 31, 17, 18, 20, 19, 21, 22, 24, 23], [53, 54, 55, 56, 49, 50, 51, 52, 61, 62, 63, 64, 57, 58, 59, 60, 47, 48, 46, 45, 43, 44, 42, 41, 37, 38, 39, 40, 33, 34, 35, 36, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 11, 12, 10, 9, 15, 16, 14, 13, 1, 2, 3, 4, 5, 6, 7, 8]];
cc:=[6,10,22];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=16;
gen_vect_label:=1;
braid_class:=1;
topological_class:=[1, 1];
is_hyperelliptic:=true;
hyp_involution:=S![5, 6, 7, 8, 1, 2, 3, 4, 13, 14, 15, 16, 9, 10, 11, 12, 21, 22, 23, 24, 17, 18, 19, 20, 29, 30, 31, 32, 25, 26, 27, 28, 37, 38, 39, 40, 33, 34, 35, 36, 45, 46, 47, 48, 41, 42, 43, 44, 53, 54, 55, 56, 49, 50, 51, 52, 61, 62, 63, 64, 57, 58, 59, 60];
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 >);
