// Magma code for the lmfdb family of higher genus curves 13.27-1.0.27-27-27
// 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:=[27,1];
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:=[0,27,27,27];
genus:=13;
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:=[[10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 4, 5, 6, 7, 8, 9, 2, 3, 1], [10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 4, 5, 6, 7, 8, 9, 2, 3, 1], [18, 16, 17, 10, 11, 12, 13, 14, 15, 27, 25, 26, 19, 20, 21, 22, 23, 24, 1, 2, 3, 4, 5, 6, 7, 8, 9]];
cc:=[10,10,26];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=1;
gen_vect_label:=1;
full_auto:=[54,2];
full_sign:=[0,2,27,54];
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, full_auto:=full_auto, full_sign:=full_sign>);

// Here we add an action to data.
gen_vectors:=[[10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 4, 5, 6, 7, 8, 9, 2, 3, 1], [13, 14, 15, 16, 17, 18, 11, 12, 10, 22, 23, 24, 25, 26, 27, 20, 21, 19, 7, 8, 9, 2, 3, 1, 5, 6, 4], [15, 13, 14, 18, 16, 17, 10, 11, 12, 24, 22, 23, 27, 25, 26, 19, 20, 21, 9, 7, 8, 1, 2, 3, 4, 5, 6]];
cc:=[10,12,24];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=2;
gen_vect_label:=1;
is_hyperelliptic:=false;
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,is_cyclic_trigonal:=is_cyclic_trigonal >);

// Here we add an action to data.
gen_vectors:=[[10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 4, 5, 6, 7, 8, 9, 2, 3, 1], [16, 17, 18, 11, 12, 10, 14, 15, 13, 25, 26, 27, 20, 21, 19, 23, 24, 22, 2, 3, 1, 5, 6, 4, 8, 9, 7], [12, 10, 11, 15, 13, 14, 18, 16, 17, 21, 19, 20, 24, 22, 23, 27, 25, 26, 6, 4, 5, 9, 7, 8, 1, 2, 3]];
cc:=[10,14,22];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=3;
gen_vect_label:=1;
is_hyperelliptic:=false;
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,is_cyclic_trigonal:=is_cyclic_trigonal >);

// Here we add an action to data.
gen_vectors:=[[10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 4, 5, 6, 7, 8, 9, 2, 3, 1], [11, 12, 10, 14, 15, 13, 17, 18, 16, 20, 21, 19, 23, 24, 22, 26, 27, 25, 5, 6, 4, 8, 9, 7, 3, 1, 2], [17, 18, 16, 12, 10, 11, 15, 13, 14, 26, 27, 25, 21, 19, 20, 24, 22, 23, 3, 1, 2, 6, 4, 5, 9, 7, 8]];
cc:=[10,16,20];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=4;
gen_vect_label:=1;
is_hyperelliptic:=false;
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,is_cyclic_trigonal:=is_cyclic_trigonal >);

// Here we add an action to data.
gen_vectors:=[[10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 4, 5, 6, 7, 8, 9, 2, 3, 1], [14, 15, 13, 17, 18, 16, 12, 10, 11, 23, 24, 22, 26, 27, 25, 21, 19, 20, 8, 9, 7, 3, 1, 2, 6, 4, 5], [14, 15, 13, 17, 18, 16, 12, 10, 11, 23, 24, 22, 26, 27, 25, 21, 19, 20, 8, 9, 7, 3, 1, 2, 6, 4, 5]];
cc:=[10,18,18];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=5;
gen_vect_label:=1;
full_auto:=[54,2];
full_sign:=[0,2,27,54];
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, full_auto:=full_auto, full_sign:=full_sign>);

// Here we add an action to data.
gen_vectors:=[[19, 20, 21, 22, 23, 24, 25, 26, 27, 4, 5, 6, 7, 8, 9, 2, 3, 1, 13, 14, 15, 16, 17, 18, 11, 12, 10], [19, 20, 21, 22, 23, 24, 25, 26, 27, 4, 5, 6, 7, 8, 9, 2, 3, 1, 13, 14, 15, 16, 17, 18, 11, 12, 10], [24, 22, 23, 27, 25, 26, 19, 20, 21, 9, 7, 8, 1, 2, 3, 4, 5, 6, 18, 16, 17, 10, 11, 12, 13, 14, 15]];
cc:=[11,11,25];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=6;
gen_vect_label:=1;
full_auto:=[54,2];
full_sign:=[0,2,27,54];
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, full_auto:=full_auto, full_sign:=full_sign>);

// Here we add an action to data.
gen_vectors:=[[19, 20, 21, 22, 23, 24, 25, 26, 27, 4, 5, 6, 7, 8, 9, 2, 3, 1, 13, 14, 15, 16, 17, 18, 11, 12, 10], [22, 23, 24, 25, 26, 27, 20, 21, 19, 7, 8, 9, 2, 3, 1, 5, 6, 4, 16, 17, 18, 11, 12, 10, 14, 15, 13], [21, 19, 20, 24, 22, 23, 27, 25, 26, 6, 4, 5, 9, 7, 8, 1, 2, 3, 15, 13, 14, 18, 16, 17, 10, 11, 12]];
cc:=[11,13,23];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=7;
gen_vect_label:=1;
is_hyperelliptic:=false;
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,is_cyclic_trigonal:=is_cyclic_trigonal >);

// Here we add an action to data.
gen_vectors:=[[19, 20, 21, 22, 23, 24, 25, 26, 27, 4, 5, 6, 7, 8, 9, 2, 3, 1, 13, 14, 15, 16, 17, 18, 11, 12, 10], [25, 26, 27, 20, 21, 19, 23, 24, 22, 2, 3, 1, 5, 6, 4, 8, 9, 7, 11, 12, 10, 14, 15, 13, 17, 18, 16], [26, 27, 25, 21, 19, 20, 24, 22, 23, 3, 1, 2, 6, 4, 5, 9, 7, 8, 12, 10, 11, 15, 13, 14, 18, 16, 17]];
cc:=[11,15,21];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=8;
gen_vect_label:=1;
is_hyperelliptic:=false;
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,is_cyclic_trigonal:=is_cyclic_trigonal >);

// Here we add an action to data.
gen_vectors:=[[19, 20, 21, 22, 23, 24, 25, 26, 27, 4, 5, 6, 7, 8, 9, 2, 3, 1, 13, 14, 15, 16, 17, 18, 11, 12, 10], [20, 21, 19, 23, 24, 22, 26, 27, 25, 5, 6, 4, 8, 9, 7, 3, 1, 2, 14, 15, 13, 17, 18, 16, 12, 10, 11], [23, 24, 22, 26, 27, 25, 21, 19, 20, 8, 9, 7, 3, 1, 2, 6, 4, 5, 17, 18, 16, 12, 10, 11, 15, 13, 14]];
cc:=[11,17,19];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=9;
gen_vect_label:=1;
is_hyperelliptic:=false;
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,is_cyclic_trigonal:=is_cyclic_trigonal >);

// Here we add an action to data.
gen_vectors:=[[19, 20, 21, 22, 23, 24, 25, 26, 27, 4, 5, 6, 7, 8, 9, 2, 3, 1, 13, 14, 15, 16, 17, 18, 11, 12, 10], [27, 25, 26, 19, 20, 21, 22, 23, 24, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18], [27, 25, 26, 19, 20, 21, 22, 23, 24, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18]];
cc:=[11,27,27];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=10;
gen_vect_label:=1;
full_auto:=[54,2];
full_sign:=[0,2,27,54];
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, full_auto:=full_auto, full_sign:=full_sign>);

// Here we add an action to data.
gen_vectors:=[[13, 14, 15, 16, 17, 18, 11, 12, 10, 22, 23, 24, 25, 26, 27, 20, 21, 19, 7, 8, 9, 2, 3, 1, 5, 6, 4], [13, 14, 15, 16, 17, 18, 11, 12, 10, 22, 23, 24, 25, 26, 27, 20, 21, 19, 7, 8, 9, 2, 3, 1, 5, 6, 4], [12, 10, 11, 15, 13, 14, 18, 16, 17, 21, 19, 20, 24, 22, 23, 27, 25, 26, 6, 4, 5, 9, 7, 8, 1, 2, 3]];
cc:=[12,12,22];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=11;
gen_vect_label:=1;
full_auto:=[54,2];
full_sign:=[0,2,27,54];
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, full_auto:=full_auto, full_sign:=full_sign>);

// Here we add an action to data.
gen_vectors:=[[13, 14, 15, 16, 17, 18, 11, 12, 10, 22, 23, 24, 25, 26, 27, 20, 21, 19, 7, 8, 9, 2, 3, 1, 5, 6, 4], [16, 17, 18, 11, 12, 10, 14, 15, 13, 25, 26, 27, 20, 21, 19, 23, 24, 22, 2, 3, 1, 5, 6, 4, 8, 9, 7], [17, 18, 16, 12, 10, 11, 15, 13, 14, 26, 27, 25, 21, 19, 20, 24, 22, 23, 3, 1, 2, 6, 4, 5, 9, 7, 8]];
cc:=[12,14,20];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=12;
gen_vect_label:=1;
is_hyperelliptic:=false;
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,is_cyclic_trigonal:=is_cyclic_trigonal >);

// Here we add an action to data.
gen_vectors:=[[13, 14, 15, 16, 17, 18, 11, 12, 10, 22, 23, 24, 25, 26, 27, 20, 21, 19, 7, 8, 9, 2, 3, 1, 5, 6, 4], [11, 12, 10, 14, 15, 13, 17, 18, 16, 20, 21, 19, 23, 24, 22, 26, 27, 25, 5, 6, 4, 8, 9, 7, 3, 1, 2], [14, 15, 13, 17, 18, 16, 12, 10, 11, 23, 24, 22, 26, 27, 25, 21, 19, 20, 8, 9, 7, 3, 1, 2, 6, 4, 5]];
cc:=[12,16,18];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=13;
gen_vect_label:=1;
is_hyperelliptic:=false;
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,is_cyclic_trigonal:=is_cyclic_trigonal >);

// Here we add an action to data.
gen_vectors:=[[13, 14, 15, 16, 17, 18, 11, 12, 10, 22, 23, 24, 25, 26, 27, 20, 21, 19, 7, 8, 9, 2, 3, 1, 5, 6, 4], [18, 16, 17, 10, 11, 12, 13, 14, 15, 27, 25, 26, 19, 20, 21, 22, 23, 24, 1, 2, 3, 4, 5, 6, 7, 8, 9], [18, 16, 17, 10, 11, 12, 13, 14, 15, 27, 25, 26, 19, 20, 21, 22, 23, 24, 1, 2, 3, 4, 5, 6, 7, 8, 9]];
cc:=[12,26,26];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=14;
gen_vect_label:=1;
full_auto:=[54,2];
full_sign:=[0,2,27,54];
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, full_auto:=full_auto, full_sign:=full_sign>);

// Here we add an action to data.
gen_vectors:=[[22, 23, 24, 25, 26, 27, 20, 21, 19, 7, 8, 9, 2, 3, 1, 5, 6, 4, 16, 17, 18, 11, 12, 10, 14, 15, 13], [22, 23, 24, 25, 26, 27, 20, 21, 19, 7, 8, 9, 2, 3, 1, 5, 6, 4, 16, 17, 18, 11, 12, 10, 14, 15, 13], [26, 27, 25, 21, 19, 20, 24, 22, 23, 3, 1, 2, 6, 4, 5, 9, 7, 8, 12, 10, 11, 15, 13, 14, 18, 16, 17]];
cc:=[13,13,21];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=15;
gen_vect_label:=1;
full_auto:=[54,2];
full_sign:=[0,2,27,54];
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, full_auto:=full_auto, full_sign:=full_sign>);

// Here we add an action to data.
gen_vectors:=[[22, 23, 24, 25, 26, 27, 20, 21, 19, 7, 8, 9, 2, 3, 1, 5, 6, 4, 16, 17, 18, 11, 12, 10, 14, 15, 13], [25, 26, 27, 20, 21, 19, 23, 24, 22, 2, 3, 1, 5, 6, 4, 8, 9, 7, 11, 12, 10, 14, 15, 13, 17, 18, 16], [23, 24, 22, 26, 27, 25, 21, 19, 20, 8, 9, 7, 3, 1, 2, 6, 4, 5, 17, 18, 16, 12, 10, 11, 15, 13, 14]];
cc:=[13,15,19];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=16;
gen_vect_label:=1;
is_hyperelliptic:=false;
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,is_cyclic_trigonal:=is_cyclic_trigonal >);

// Here we add an action to data.
gen_vectors:=[[22, 23, 24, 25, 26, 27, 20, 21, 19, 7, 8, 9, 2, 3, 1, 5, 6, 4, 16, 17, 18, 11, 12, 10, 14, 15, 13], [20, 21, 19, 23, 24, 22, 26, 27, 25, 5, 6, 4, 8, 9, 7, 3, 1, 2, 14, 15, 13, 17, 18, 16, 12, 10, 11], [20, 21, 19, 23, 24, 22, 26, 27, 25, 5, 6, 4, 8, 9, 7, 3, 1, 2, 14, 15, 13, 17, 18, 16, 12, 10, 11]];
cc:=[13,17,17];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=17;
gen_vect_label:=1;
full_auto:=[54,2];
full_sign:=[0,2,27,54];
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, full_auto:=full_auto, full_sign:=full_sign>);

// Here we add an action to data.
gen_vectors:=[[22, 23, 24, 25, 26, 27, 20, 21, 19, 7, 8, 9, 2, 3, 1, 5, 6, 4, 16, 17, 18, 11, 12, 10, 14, 15, 13], [24, 22, 23, 27, 25, 26, 19, 20, 21, 9, 7, 8, 1, 2, 3, 4, 5, 6, 18, 16, 17, 10, 11, 12, 13, 14, 15], [27, 25, 26, 19, 20, 21, 22, 23, 24, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18]];
cc:=[13,25,27];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=18;
gen_vect_label:=1;
is_hyperelliptic:=false;
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,is_cyclic_trigonal:=is_cyclic_trigonal >);

// Here we add an action to data.
gen_vectors:=[[16, 17, 18, 11, 12, 10, 14, 15, 13, 25, 26, 27, 20, 21, 19, 23, 24, 22, 2, 3, 1, 5, 6, 4, 8, 9, 7], [16, 17, 18, 11, 12, 10, 14, 15, 13, 25, 26, 27, 20, 21, 19, 23, 24, 22, 2, 3, 1, 5, 6, 4, 8, 9, 7], [14, 15, 13, 17, 18, 16, 12, 10, 11, 23, 24, 22, 26, 27, 25, 21, 19, 20, 8, 9, 7, 3, 1, 2, 6, 4, 5]];
cc:=[14,14,18];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=19;
gen_vect_label:=1;
full_auto:=[54,2];
full_sign:=[0,2,27,54];
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, full_auto:=full_auto, full_sign:=full_sign>);

// Here we add an action to data.
gen_vectors:=[[16, 17, 18, 11, 12, 10, 14, 15, 13, 25, 26, 27, 20, 21, 19, 23, 24, 22, 2, 3, 1, 5, 6, 4, 8, 9, 7], [11, 12, 10, 14, 15, 13, 17, 18, 16, 20, 21, 19, 23, 24, 22, 26, 27, 25, 5, 6, 4, 8, 9, 7, 3, 1, 2], [11, 12, 10, 14, 15, 13, 17, 18, 16, 20, 21, 19, 23, 24, 22, 26, 27, 25, 5, 6, 4, 8, 9, 7, 3, 1, 2]];
cc:=[14,16,16];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=20;
gen_vect_label:=1;
full_auto:=[54,2];
full_sign:=[0,2,27,54];
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, full_auto:=full_auto, full_sign:=full_sign>);

// Here we add an action to data.
gen_vectors:=[[16, 17, 18, 11, 12, 10, 14, 15, 13, 25, 26, 27, 20, 21, 19, 23, 24, 22, 2, 3, 1, 5, 6, 4, 8, 9, 7], [15, 13, 14, 18, 16, 17, 10, 11, 12, 24, 22, 23, 27, 25, 26, 19, 20, 21, 9, 7, 8, 1, 2, 3, 4, 5, 6], [18, 16, 17, 10, 11, 12, 13, 14, 15, 27, 25, 26, 19, 20, 21, 22, 23, 24, 1, 2, 3, 4, 5, 6, 7, 8, 9]];
cc:=[14,24,26];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=21;
gen_vect_label:=1;
is_hyperelliptic:=false;
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,is_cyclic_trigonal:=is_cyclic_trigonal >);

// Here we add an action to data.
gen_vectors:=[[25, 26, 27, 20, 21, 19, 23, 24, 22, 2, 3, 1, 5, 6, 4, 8, 9, 7, 11, 12, 10, 14, 15, 13, 17, 18, 16], [25, 26, 27, 20, 21, 19, 23, 24, 22, 2, 3, 1, 5, 6, 4, 8, 9, 7, 11, 12, 10, 14, 15, 13, 17, 18, 16], [20, 21, 19, 23, 24, 22, 26, 27, 25, 5, 6, 4, 8, 9, 7, 3, 1, 2, 14, 15, 13, 17, 18, 16, 12, 10, 11]];
cc:=[15,15,17];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=22;
gen_vect_label:=1;
full_auto:=[54,2];
full_sign:=[0,2,27,54];
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, full_auto:=full_auto, full_sign:=full_sign>);

// Here we add an action to data.
gen_vectors:=[[25, 26, 27, 20, 21, 19, 23, 24, 22, 2, 3, 1, 5, 6, 4, 8, 9, 7, 11, 12, 10, 14, 15, 13, 17, 18, 16], [21, 19, 20, 24, 22, 23, 27, 25, 26, 6, 4, 5, 9, 7, 8, 1, 2, 3, 15, 13, 14, 18, 16, 17, 10, 11, 12], [27, 25, 26, 19, 20, 21, 22, 23, 24, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18]];
cc:=[15,23,27];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=23;
gen_vect_label:=1;
is_hyperelliptic:=false;
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,is_cyclic_trigonal:=is_cyclic_trigonal >);

// Here we add an action to data.
gen_vectors:=[[25, 26, 27, 20, 21, 19, 23, 24, 22, 2, 3, 1, 5, 6, 4, 8, 9, 7, 11, 12, 10, 14, 15, 13, 17, 18, 16], [24, 22, 23, 27, 25, 26, 19, 20, 21, 9, 7, 8, 1, 2, 3, 4, 5, 6, 18, 16, 17, 10, 11, 12, 13, 14, 15], [24, 22, 23, 27, 25, 26, 19, 20, 21, 9, 7, 8, 1, 2, 3, 4, 5, 6, 18, 16, 17, 10, 11, 12, 13, 14, 15]];
cc:=[15,25,25];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=24;
gen_vect_label:=1;
full_auto:=[54,2];
full_sign:=[0,2,27,54];
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, full_auto:=full_auto, full_sign:=full_sign>);

// Here we add an action to data.
gen_vectors:=[[11, 12, 10, 14, 15, 13, 17, 18, 16, 20, 21, 19, 23, 24, 22, 26, 27, 25, 5, 6, 4, 8, 9, 7, 3, 1, 2], [12, 10, 11, 15, 13, 14, 18, 16, 17, 21, 19, 20, 24, 22, 23, 27, 25, 26, 6, 4, 5, 9, 7, 8, 1, 2, 3], [18, 16, 17, 10, 11, 12, 13, 14, 15, 27, 25, 26, 19, 20, 21, 22, 23, 24, 1, 2, 3, 4, 5, 6, 7, 8, 9]];
cc:=[16,22,26];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=25;
gen_vect_label:=1;
is_hyperelliptic:=false;
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,is_cyclic_trigonal:=is_cyclic_trigonal >);

// Here we add an action to data.
gen_vectors:=[[11, 12, 10, 14, 15, 13, 17, 18, 16, 20, 21, 19, 23, 24, 22, 26, 27, 25, 5, 6, 4, 8, 9, 7, 3, 1, 2], [15, 13, 14, 18, 16, 17, 10, 11, 12, 24, 22, 23, 27, 25, 26, 19, 20, 21, 9, 7, 8, 1, 2, 3, 4, 5, 6], [15, 13, 14, 18, 16, 17, 10, 11, 12, 24, 22, 23, 27, 25, 26, 19, 20, 21, 9, 7, 8, 1, 2, 3, 4, 5, 6]];
cc:=[16,24,24];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=26;
gen_vect_label:=1;
full_auto:=[54,2];
full_sign:=[0,2,27,54];
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, full_auto:=full_auto, full_sign:=full_sign>);

// Here we add an action to data.
gen_vectors:=[[20, 21, 19, 23, 24, 22, 26, 27, 25, 5, 6, 4, 8, 9, 7, 3, 1, 2, 14, 15, 13, 17, 18, 16, 12, 10, 11], [26, 27, 25, 21, 19, 20, 24, 22, 23, 3, 1, 2, 6, 4, 5, 9, 7, 8, 12, 10, 11, 15, 13, 14, 18, 16, 17], [27, 25, 26, 19, 20, 21, 22, 23, 24, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18]];
cc:=[17,21,27];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=27;
gen_vect_label:=1;
is_hyperelliptic:=false;
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,is_cyclic_trigonal:=is_cyclic_trigonal >);

// Here we add an action to data.
gen_vectors:=[[20, 21, 19, 23, 24, 22, 26, 27, 25, 5, 6, 4, 8, 9, 7, 3, 1, 2, 14, 15, 13, 17, 18, 16, 12, 10, 11], [21, 19, 20, 24, 22, 23, 27, 25, 26, 6, 4, 5, 9, 7, 8, 1, 2, 3, 15, 13, 14, 18, 16, 17, 10, 11, 12], [24, 22, 23, 27, 25, 26, 19, 20, 21, 9, 7, 8, 1, 2, 3, 4, 5, 6, 18, 16, 17, 10, 11, 12, 13, 14, 15]];
cc:=[17,23,25];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=28;
gen_vect_label:=1;
is_hyperelliptic:=false;
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,is_cyclic_trigonal:=is_cyclic_trigonal >);

// Here we add an action to data.
gen_vectors:=[[14, 15, 13, 17, 18, 16, 12, 10, 11, 23, 24, 22, 26, 27, 25, 21, 19, 20, 8, 9, 7, 3, 1, 2, 6, 4, 5], [17, 18, 16, 12, 10, 11, 15, 13, 14, 26, 27, 25, 21, 19, 20, 24, 22, 23, 3, 1, 2, 6, 4, 5, 9, 7, 8], [18, 16, 17, 10, 11, 12, 13, 14, 15, 27, 25, 26, 19, 20, 21, 22, 23, 24, 1, 2, 3, 4, 5, 6, 7, 8, 9]];
cc:=[18,20,26];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=29;
gen_vect_label:=1;
is_hyperelliptic:=false;
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,is_cyclic_trigonal:=is_cyclic_trigonal >);

// Here we add an action to data.
gen_vectors:=[[14, 15, 13, 17, 18, 16, 12, 10, 11, 23, 24, 22, 26, 27, 25, 21, 19, 20, 8, 9, 7, 3, 1, 2, 6, 4, 5], [12, 10, 11, 15, 13, 14, 18, 16, 17, 21, 19, 20, 24, 22, 23, 27, 25, 26, 6, 4, 5, 9, 7, 8, 1, 2, 3], [15, 13, 14, 18, 16, 17, 10, 11, 12, 24, 22, 23, 27, 25, 26, 19, 20, 21, 9, 7, 8, 1, 2, 3, 4, 5, 6]];
cc:=[18,22,24];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=30;
gen_vect_label:=1;
is_hyperelliptic:=false;
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,is_cyclic_trigonal:=is_cyclic_trigonal >);

// Here we add an action to data.
gen_vectors:=[[23, 24, 22, 26, 27, 25, 21, 19, 20, 8, 9, 7, 3, 1, 2, 6, 4, 5, 17, 18, 16, 12, 10, 11, 15, 13, 14], [23, 24, 22, 26, 27, 25, 21, 19, 20, 8, 9, 7, 3, 1, 2, 6, 4, 5, 17, 18, 16, 12, 10, 11, 15, 13, 14], [27, 25, 26, 19, 20, 21, 22, 23, 24, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18]];
cc:=[19,19,27];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=31;
gen_vect_label:=1;
full_auto:=[54,2];
full_sign:=[0,2,27,54];
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, full_auto:=full_auto, full_sign:=full_sign>);

// Here we add an action to data.
gen_vectors:=[[23, 24, 22, 26, 27, 25, 21, 19, 20, 8, 9, 7, 3, 1, 2, 6, 4, 5, 17, 18, 16, 12, 10, 11, 15, 13, 14], [26, 27, 25, 21, 19, 20, 24, 22, 23, 3, 1, 2, 6, 4, 5, 9, 7, 8, 12, 10, 11, 15, 13, 14, 18, 16, 17], [24, 22, 23, 27, 25, 26, 19, 20, 21, 9, 7, 8, 1, 2, 3, 4, 5, 6, 18, 16, 17, 10, 11, 12, 13, 14, 15]];
cc:=[19,21,25];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=32;
gen_vect_label:=1;
is_hyperelliptic:=false;
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,is_cyclic_trigonal:=is_cyclic_trigonal >);

// Here we add an action to data.
gen_vectors:=[[23, 24, 22, 26, 27, 25, 21, 19, 20, 8, 9, 7, 3, 1, 2, 6, 4, 5, 17, 18, 16, 12, 10, 11, 15, 13, 14], [21, 19, 20, 24, 22, 23, 27, 25, 26, 6, 4, 5, 9, 7, 8, 1, 2, 3, 15, 13, 14, 18, 16, 17, 10, 11, 12], [21, 19, 20, 24, 22, 23, 27, 25, 26, 6, 4, 5, 9, 7, 8, 1, 2, 3, 15, 13, 14, 18, 16, 17, 10, 11, 12]];
cc:=[19,23,23];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=33;
gen_vect_label:=1;
full_auto:=[54,2];
full_sign:=[0,2,27,54];
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, full_auto:=full_auto, full_sign:=full_sign>);

// Here we add an action to data.
gen_vectors:=[[17, 18, 16, 12, 10, 11, 15, 13, 14, 26, 27, 25, 21, 19, 20, 24, 22, 23, 3, 1, 2, 6, 4, 5, 9, 7, 8], [17, 18, 16, 12, 10, 11, 15, 13, 14, 26, 27, 25, 21, 19, 20, 24, 22, 23, 3, 1, 2, 6, 4, 5, 9, 7, 8], [15, 13, 14, 18, 16, 17, 10, 11, 12, 24, 22, 23, 27, 25, 26, 19, 20, 21, 9, 7, 8, 1, 2, 3, 4, 5, 6]];
cc:=[20,20,24];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=34;
gen_vect_label:=1;
full_auto:=[54,2];
full_sign:=[0,2,27,54];
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, full_auto:=full_auto, full_sign:=full_sign>);

// Here we add an action to data.
gen_vectors:=[[17, 18, 16, 12, 10, 11, 15, 13, 14, 26, 27, 25, 21, 19, 20, 24, 22, 23, 3, 1, 2, 6, 4, 5, 9, 7, 8], [12, 10, 11, 15, 13, 14, 18, 16, 17, 21, 19, 20, 24, 22, 23, 27, 25, 26, 6, 4, 5, 9, 7, 8, 1, 2, 3], [12, 10, 11, 15, 13, 14, 18, 16, 17, 21, 19, 20, 24, 22, 23, 27, 25, 26, 6, 4, 5, 9, 7, 8, 1, 2, 3]];
cc:=[20,22,22];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=35;
gen_vect_label:=1;
full_auto:=[54,2];
full_sign:=[0,2,27,54];
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, full_auto:=full_auto, full_sign:=full_sign>);

// Here we add an action to data.
gen_vectors:=[[26, 27, 25, 21, 19, 20, 24, 22, 23, 3, 1, 2, 6, 4, 5, 9, 7, 8, 12, 10, 11, 15, 13, 14, 18, 16, 17], [26, 27, 25, 21, 19, 20, 24, 22, 23, 3, 1, 2, 6, 4, 5, 9, 7, 8, 12, 10, 11, 15, 13, 14, 18, 16, 17], [21, 19, 20, 24, 22, 23, 27, 25, 26, 6, 4, 5, 9, 7, 8, 1, 2, 3, 15, 13, 14, 18, 16, 17, 10, 11, 12]];
cc:=[21,21,23];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=36;
gen_vect_label:=1;
full_auto:=[54,2];
full_sign:=[0,2,27,54];
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, full_auto:=full_auto, full_sign:=full_sign>);
