// Magma code for the lmfdb family of higher genus curves 10.54-12.0.3-6-6
// 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:=[54,12];
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:=[0,3,6,6];
genus:=10;
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:=[[5, 6, 4, 8, 9, 7, 2, 3, 1, 14, 15, 13, 17, 18, 16, 11, 12, 10, 23, 24, 22, 26, 27, 25, 20, 21, 19, 32, 33, 31, 35, 36, 34, 29, 30, 28, 41, 42, 40, 44, 45, 43, 38, 39, 37, 50, 51, 49, 53, 54, 52, 47, 48, 46], [37, 39, 38, 40, 42, 41, 43, 45, 44, 46, 48, 47, 49, 51, 50, 52, 54, 53, 28, 30, 29, 31, 33, 32, 34, 36, 35, 10, 12, 11, 13, 15, 14, 16, 18, 17, 19, 21, 20, 22, 24, 23, 25, 27, 26, 1, 3, 2, 4, 6, 5, 7, 9, 8], [54, 53, 52, 48, 47, 46, 51, 50, 49, 36, 35, 34, 30, 29, 28, 33, 32, 31, 45, 44, 43, 39, 38, 37, 42, 41, 40, 27, 26, 25, 21, 20, 19, 24, 23, 22, 9, 8, 7, 3, 2, 1, 6, 5, 4, 18, 17, 16, 12, 11, 10, 15, 14, 13]];
cc:=[12,22,25];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=1;
gen_vect_label:=1;
full_auto:=[216,158];
full_sign:=[0,2,4,6];
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:=[[5, 6, 4, 8, 9, 7, 2, 3, 1, 14, 15, 13, 17, 18, 16, 11, 12, 10, 23, 24, 22, 26, 27, 25, 20, 21, 19, 32, 33, 31, 35, 36, 34, 29, 30, 28, 41, 42, 40, 44, 45, 43, 38, 39, 37, 50, 51, 49, 53, 54, 52, 47, 48, 46], [46, 48, 47, 49, 51, 50, 52, 54, 53, 28, 30, 29, 31, 33, 32, 34, 36, 35, 37, 39, 38, 40, 42, 41, 43, 45, 44, 19, 21, 20, 22, 24, 23, 25, 27, 26, 1, 3, 2, 4, 6, 5, 7, 9, 8, 10, 12, 11, 13, 15, 14, 16, 18, 17], [45, 44, 43, 39, 38, 37, 42, 41, 40, 54, 53, 52, 48, 47, 46, 51, 50, 49, 36, 35, 34, 30, 29, 28, 33, 32, 31, 18, 17, 16, 12, 11, 10, 15, 14, 13, 27, 26, 25, 21, 20, 19, 24, 23, 22, 9, 8, 7, 3, 2, 1, 6, 5, 4]];
cc:=[12,23,26];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=2;
gen_vect_label:=1;
full_auto:=[216,158];
full_sign:=[0,2,4,6];
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:=[[5, 6, 4, 8, 9, 7, 2, 3, 1, 14, 15, 13, 17, 18, 16, 11, 12, 10, 23, 24, 22, 26, 27, 25, 20, 21, 19, 32, 33, 31, 35, 36, 34, 29, 30, 28, 41, 42, 40, 44, 45, 43, 38, 39, 37, 50, 51, 49, 53, 54, 52, 47, 48, 46], [40, 42, 41, 43, 45, 44, 37, 39, 38, 49, 51, 50, 52, 54, 53, 46, 48, 47, 31, 33, 32, 34, 36, 35, 28, 30, 29, 13, 15, 14, 16, 18, 17, 10, 12, 11, 22, 24, 23, 25, 27, 26, 19, 21, 20, 4, 6, 5, 7, 9, 8, 1, 3, 2], [51, 50, 49, 54, 53, 52, 48, 47, 46, 33, 32, 31, 36, 35, 34, 30, 29, 28, 42, 41, 40, 45, 44, 43, 39, 38, 37, 24, 23, 22, 27, 26, 25, 21, 20, 19, 6, 5, 4, 9, 8, 7, 3, 2, 1, 15, 14, 13, 18, 17, 16, 12, 11, 10]];
cc:=[12,24,27];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=3;
gen_vect_label:=1;
full_auto:=[216,158];
full_sign:=[0,2,4,6];
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:=[[9, 7, 8, 3, 1, 2, 6, 4, 5, 18, 16, 17, 12, 10, 11, 15, 13, 14, 27, 25, 26, 21, 19, 20, 24, 22, 23, 36, 34, 35, 30, 28, 29, 33, 31, 32, 45, 43, 44, 39, 37, 38, 42, 40, 41, 54, 52, 53, 48, 46, 47, 51, 49, 50], [37, 39, 38, 40, 42, 41, 43, 45, 44, 46, 48, 47, 49, 51, 50, 52, 54, 53, 28, 30, 29, 31, 33, 32, 34, 36, 35, 10, 12, 11, 13, 15, 14, 16, 18, 17, 19, 21, 20, 22, 24, 23, 25, 27, 26, 1, 3, 2, 4, 6, 5, 7, 9, 8], [50, 49, 51, 53, 52, 54, 47, 46, 48, 32, 31, 33, 35, 34, 36, 29, 28, 30, 41, 40, 42, 44, 43, 45, 38, 37, 39, 23, 22, 24, 26, 25, 27, 20, 19, 21, 5, 4, 6, 8, 7, 9, 2, 1, 3, 14, 13, 15, 17, 16, 18, 11, 10, 12]];
cc:=[13,22,27];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=4;
gen_vect_label:=1;
full_auto:=[216,158];
full_sign:=[0,2,4,6];
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:=[[9, 7, 8, 3, 1, 2, 6, 4, 5, 18, 16, 17, 12, 10, 11, 15, 13, 14, 27, 25, 26, 21, 19, 20, 24, 22, 23, 36, 34, 35, 30, 28, 29, 33, 31, 32, 45, 43, 44, 39, 37, 38, 42, 40, 41, 54, 52, 53, 48, 46, 47, 51, 49, 50], [46, 48, 47, 49, 51, 50, 52, 54, 53, 28, 30, 29, 31, 33, 32, 34, 36, 35, 37, 39, 38, 40, 42, 41, 43, 45, 44, 19, 21, 20, 22, 24, 23, 25, 27, 26, 1, 3, 2, 4, 6, 5, 7, 9, 8, 10, 12, 11, 13, 15, 14, 16, 18, 17], [41, 40, 42, 44, 43, 45, 38, 37, 39, 50, 49, 51, 53, 52, 54, 47, 46, 48, 32, 31, 33, 35, 34, 36, 29, 28, 30, 14, 13, 15, 17, 16, 18, 11, 10, 12, 23, 22, 24, 26, 25, 27, 20, 19, 21, 5, 4, 6, 8, 7, 9, 2, 1, 3]];
cc:=[13,23,24];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=5;
gen_vect_label:=1;
full_auto:=[216,158];
full_sign:=[0,2,4,6];
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:=[[9, 7, 8, 3, 1, 2, 6, 4, 5, 18, 16, 17, 12, 10, 11, 15, 13, 14, 27, 25, 26, 21, 19, 20, 24, 22, 23, 36, 34, 35, 30, 28, 29, 33, 31, 32, 45, 43, 44, 39, 37, 38, 42, 40, 41, 54, 52, 53, 48, 46, 47, 51, 49, 50], [52, 54, 53, 46, 48, 47, 49, 51, 50, 34, 36, 35, 28, 30, 29, 31, 33, 32, 43, 45, 44, 37, 39, 38, 40, 42, 41, 25, 27, 26, 19, 21, 20, 22, 24, 23, 7, 9, 8, 1, 3, 2, 4, 6, 5, 16, 18, 17, 10, 12, 11, 13, 15, 14], [44, 43, 45, 38, 37, 39, 41, 40, 42, 53, 52, 54, 47, 46, 48, 50, 49, 51, 35, 34, 36, 29, 28, 30, 32, 31, 33, 17, 16, 18, 11, 10, 12, 14, 13, 15, 26, 25, 27, 20, 19, 21, 23, 22, 24, 8, 7, 9, 2, 1, 3, 5, 4, 6]];
cc:=[13,25,26];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=6;
gen_vect_label:=1;
full_auto:=[216,158];
full_sign:=[0,2,4,6];
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, 2, 3, 1, 5, 6, 4, 8, 9, 7, 38, 39, 37, 41, 42, 40, 44, 45, 43, 47, 48, 46, 50, 51, 49, 53, 54, 52, 29, 30, 28, 32, 33, 31, 35, 36, 34], [31, 33, 32, 34, 36, 35, 28, 30, 29, 40, 42, 41, 43, 45, 44, 37, 39, 38, 49, 51, 50, 52, 54, 53, 46, 48, 47, 4, 6, 5, 7, 9, 8, 1, 3, 2, 13, 15, 14, 16, 18, 17, 10, 12, 11, 22, 24, 23, 25, 27, 26, 19, 21, 20], [54, 53, 52, 48, 47, 46, 51, 50, 49, 36, 35, 34, 30, 29, 28, 33, 32, 31, 45, 44, 43, 39, 38, 37, 42, 41, 40, 27, 26, 25, 21, 20, 19, 24, 23, 22, 9, 8, 7, 3, 2, 1, 6, 5, 4, 18, 17, 16, 12, 11, 10, 15, 14, 13]];
cc:=[14,20,25];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=7;
gen_vect_label:=1;
full_auto:=[216,158];
full_sign:=[0,2,4,6];
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, 2, 3, 1, 5, 6, 4, 8, 9, 7, 38, 39, 37, 41, 42, 40, 44, 45, 43, 47, 48, 46, 50, 51, 49, 53, 54, 52, 29, 30, 28, 32, 33, 31, 35, 36, 34], [34, 36, 35, 28, 30, 29, 31, 33, 32, 43, 45, 44, 37, 39, 38, 40, 42, 41, 52, 54, 53, 46, 48, 47, 49, 51, 50, 7, 9, 8, 1, 3, 2, 4, 6, 5, 16, 18, 17, 10, 12, 11, 13, 15, 14, 25, 27, 26, 19, 21, 20, 22, 24, 23], [51, 50, 49, 54, 53, 52, 48, 47, 46, 33, 32, 31, 36, 35, 34, 30, 29, 28, 42, 41, 40, 45, 44, 43, 39, 38, 37, 24, 23, 22, 27, 26, 25, 21, 20, 19, 6, 5, 4, 9, 8, 7, 3, 2, 1, 15, 14, 13, 18, 17, 16, 12, 11, 10]];
cc:=[14,21,27];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=8;
gen_vect_label:=1;
full_auto:=[216,158];
full_sign:=[0,2,4,6];
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, 2, 3, 1, 5, 6, 4, 8, 9, 7, 38, 39, 37, 41, 42, 40, 44, 45, 43, 47, 48, 46, 50, 51, 49, 53, 54, 52, 29, 30, 28, 32, 33, 31, 35, 36, 34], [40, 42, 41, 43, 45, 44, 37, 39, 38, 49, 51, 50, 52, 54, 53, 46, 48, 47, 31, 33, 32, 34, 36, 35, 28, 30, 29, 13, 15, 14, 16, 18, 17, 10, 12, 11, 22, 24, 23, 25, 27, 26, 19, 21, 20, 4, 6, 5, 7, 9, 8, 1, 3, 2], [45, 44, 43, 39, 38, 37, 42, 41, 40, 54, 53, 52, 48, 47, 46, 51, 50, 49, 36, 35, 34, 30, 29, 28, 33, 32, 31, 18, 17, 16, 12, 11, 10, 15, 14, 13, 27, 26, 25, 21, 20, 19, 24, 23, 22, 9, 8, 7, 3, 2, 1, 6, 5, 4]];
cc:=[14,24,26];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=9;
gen_vect_label:=1;
full_auto:=[216,158];
full_sign:=[0,2,4,6];
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:=[[21, 19, 20, 24, 22, 23, 27, 25, 26, 3, 1, 2, 6, 4, 5, 9, 7, 8, 12, 10, 11, 15, 13, 14, 18, 16, 17, 48, 46, 47, 51, 49, 50, 54, 52, 53, 30, 28, 29, 33, 31, 32, 36, 34, 35, 39, 37, 38, 42, 40, 41, 45, 43, 44], [31, 33, 32, 34, 36, 35, 28, 30, 29, 40, 42, 41, 43, 45, 44, 37, 39, 38, 49, 51, 50, 52, 54, 53, 46, 48, 47, 4, 6, 5, 7, 9, 8, 1, 3, 2, 13, 15, 14, 16, 18, 17, 10, 12, 11, 22, 24, 23, 25, 27, 26, 19, 21, 20], [44, 43, 45, 38, 37, 39, 41, 40, 42, 53, 52, 54, 47, 46, 48, 50, 49, 51, 35, 34, 36, 29, 28, 30, 32, 31, 33, 17, 16, 18, 11, 10, 12, 14, 13, 15, 26, 25, 27, 20, 19, 21, 23, 22, 24, 8, 7, 9, 2, 1, 3, 5, 4, 6]];
cc:=[15,20,26];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=10;
gen_vect_label:=1;
full_auto:=[216,158];
full_sign:=[0,2,4,6];
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:=[[21, 19, 20, 24, 22, 23, 27, 25, 26, 3, 1, 2, 6, 4, 5, 9, 7, 8, 12, 10, 11, 15, 13, 14, 18, 16, 17, 48, 46, 47, 51, 49, 50, 54, 52, 53, 30, 28, 29, 33, 31, 32, 36, 34, 35, 39, 37, 38, 42, 40, 41, 45, 43, 44], [34, 36, 35, 28, 30, 29, 31, 33, 32, 43, 45, 44, 37, 39, 38, 40, 42, 41, 52, 54, 53, 46, 48, 47, 49, 51, 50, 7, 9, 8, 1, 3, 2, 4, 6, 5, 16, 18, 17, 10, 12, 11, 13, 15, 14, 25, 27, 26, 19, 21, 20, 22, 24, 23], [41, 40, 42, 44, 43, 45, 38, 37, 39, 50, 49, 51, 53, 52, 54, 47, 46, 48, 32, 31, 33, 35, 34, 36, 29, 28, 30, 14, 13, 15, 17, 16, 18, 11, 10, 12, 23, 22, 24, 26, 25, 27, 20, 19, 21, 5, 4, 6, 8, 7, 9, 2, 1, 3]];
cc:=[15,21,24];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=11;
gen_vect_label:=1;
full_auto:=[216,158];
full_sign:=[0,2,4,6];
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:=[[21, 19, 20, 24, 22, 23, 27, 25, 26, 3, 1, 2, 6, 4, 5, 9, 7, 8, 12, 10, 11, 15, 13, 14, 18, 16, 17, 48, 46, 47, 51, 49, 50, 54, 52, 53, 30, 28, 29, 33, 31, 32, 36, 34, 35, 39, 37, 38, 42, 40, 41, 45, 43, 44], [52, 54, 53, 46, 48, 47, 49, 51, 50, 34, 36, 35, 28, 30, 29, 31, 33, 32, 43, 45, 44, 37, 39, 38, 40, 42, 41, 25, 27, 26, 19, 21, 20, 22, 24, 23, 7, 9, 8, 1, 3, 2, 4, 6, 5, 16, 18, 17, 10, 12, 11, 13, 15, 14], [50, 49, 51, 53, 52, 54, 47, 46, 48, 32, 31, 33, 35, 34, 36, 29, 28, 30, 41, 40, 42, 44, 43, 45, 38, 37, 39, 23, 22, 24, 26, 25, 27, 20, 19, 21, 5, 4, 6, 8, 7, 9, 2, 1, 3, 14, 13, 15, 17, 16, 18, 11, 10, 12]];
cc:=[15,25,27];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=12;
gen_vect_label:=1;
full_auto:=[216,158];
full_sign:=[0,2,4,6];
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:=[[14, 15, 13, 17, 18, 16, 11, 12, 10, 23, 24, 22, 26, 27, 25, 20, 21, 19, 5, 6, 4, 8, 9, 7, 2, 3, 1, 41, 42, 40, 44, 45, 43, 38, 39, 37, 50, 51, 49, 53, 54, 52, 47, 48, 46, 32, 33, 31, 35, 36, 34, 29, 30, 28], [31, 33, 32, 34, 36, 35, 28, 30, 29, 40, 42, 41, 43, 45, 44, 37, 39, 38, 49, 51, 50, 52, 54, 53, 46, 48, 47, 4, 6, 5, 7, 9, 8, 1, 3, 2, 13, 15, 14, 16, 18, 17, 10, 12, 11, 22, 24, 23, 25, 27, 26, 19, 21, 20], [51, 50, 49, 54, 53, 52, 48, 47, 46, 33, 32, 31, 36, 35, 34, 30, 29, 28, 42, 41, 40, 45, 44, 43, 39, 38, 37, 24, 23, 22, 27, 26, 25, 21, 20, 19, 6, 5, 4, 9, 8, 7, 3, 2, 1, 15, 14, 13, 18, 17, 16, 12, 11, 10]];
cc:=[16,20,27];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=13;
gen_vect_label:=1;
full_auto:=[216,158];
full_sign:=[0,2,4,6];
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:=[[14, 15, 13, 17, 18, 16, 11, 12, 10, 23, 24, 22, 26, 27, 25, 20, 21, 19, 5, 6, 4, 8, 9, 7, 2, 3, 1, 41, 42, 40, 44, 45, 43, 38, 39, 37, 50, 51, 49, 53, 54, 52, 47, 48, 46, 32, 33, 31, 35, 36, 34, 29, 30, 28], [34, 36, 35, 28, 30, 29, 31, 33, 32, 43, 45, 44, 37, 39, 38, 40, 42, 41, 52, 54, 53, 46, 48, 47, 49, 51, 50, 7, 9, 8, 1, 3, 2, 4, 6, 5, 16, 18, 17, 10, 12, 11, 13, 15, 14, 25, 27, 26, 19, 21, 20, 22, 24, 23], [48, 47, 46, 51, 50, 49, 54, 53, 52, 30, 29, 28, 33, 32, 31, 36, 35, 34, 39, 38, 37, 42, 41, 40, 45, 44, 43, 21, 20, 19, 24, 23, 22, 27, 26, 25, 3, 2, 1, 6, 5, 4, 9, 8, 7, 12, 11, 10, 15, 14, 13, 18, 17, 16]];
cc:=[16,21,23];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=14;
gen_vect_label:=1;
full_auto:=[216,158];
full_sign:=[0,2,4,6];
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:=[[14, 15, 13, 17, 18, 16, 11, 12, 10, 23, 24, 22, 26, 27, 25, 20, 21, 19, 5, 6, 4, 8, 9, 7, 2, 3, 1, 41, 42, 40, 44, 45, 43, 38, 39, 37, 50, 51, 49, 53, 54, 52, 47, 48, 46, 32, 33, 31, 35, 36, 34, 29, 30, 28], [37, 39, 38, 40, 42, 41, 43, 45, 44, 46, 48, 47, 49, 51, 50, 52, 54, 53, 28, 30, 29, 31, 33, 32, 34, 36, 35, 10, 12, 11, 13, 15, 14, 16, 18, 17, 19, 21, 20, 22, 24, 23, 25, 27, 26, 1, 3, 2, 4, 6, 5, 7, 9, 8], [45, 44, 43, 39, 38, 37, 42, 41, 40, 54, 53, 52, 48, 47, 46, 51, 50, 49, 36, 35, 34, 30, 29, 28, 33, 32, 31, 18, 17, 16, 12, 11, 10, 15, 14, 13, 27, 26, 25, 21, 20, 19, 24, 23, 22, 9, 8, 7, 3, 2, 1, 6, 5, 4]];
cc:=[16,22,26];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=15;
gen_vect_label:=1;
full_auto:=[216,158];
full_sign:=[0,2,4,6];
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:=[[27, 25, 26, 21, 19, 20, 24, 22, 23, 9, 7, 8, 3, 1, 2, 6, 4, 5, 18, 16, 17, 12, 10, 11, 15, 13, 14, 54, 52, 53, 48, 46, 47, 51, 49, 50, 36, 34, 35, 30, 28, 29, 33, 31, 32, 45, 43, 44, 39, 37, 38, 42, 40, 41], [31, 33, 32, 34, 36, 35, 28, 30, 29, 40, 42, 41, 43, 45, 44, 37, 39, 38, 49, 51, 50, 52, 54, 53, 46, 48, 47, 4, 6, 5, 7, 9, 8, 1, 3, 2, 13, 15, 14, 16, 18, 17, 10, 12, 11, 22, 24, 23, 25, 27, 26, 19, 21, 20], [38, 37, 39, 41, 40, 42, 44, 43, 45, 47, 46, 48, 50, 49, 51, 53, 52, 54, 29, 28, 30, 32, 31, 33, 35, 34, 36, 11, 10, 12, 14, 13, 15, 17, 16, 18, 20, 19, 21, 23, 22, 24, 26, 25, 27, 2, 1, 3, 5, 4, 6, 8, 7, 9]];
cc:=[17,20,22];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=16;
gen_vect_label:=1;
full_auto:=[216,158];
full_sign:=[0,2,4,6];
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:=[[27, 25, 26, 21, 19, 20, 24, 22, 23, 9, 7, 8, 3, 1, 2, 6, 4, 5, 18, 16, 17, 12, 10, 11, 15, 13, 14, 54, 52, 53, 48, 46, 47, 51, 49, 50, 36, 34, 35, 30, 28, 29, 33, 31, 32, 45, 43, 44, 39, 37, 38, 42, 40, 41], [34, 36, 35, 28, 30, 29, 31, 33, 32, 43, 45, 44, 37, 39, 38, 40, 42, 41, 52, 54, 53, 46, 48, 47, 49, 51, 50, 7, 9, 8, 1, 3, 2, 4, 6, 5, 16, 18, 17, 10, 12, 11, 13, 15, 14, 25, 27, 26, 19, 21, 20, 22, 24, 23], [44, 43, 45, 38, 37, 39, 41, 40, 42, 53, 52, 54, 47, 46, 48, 50, 49, 51, 35, 34, 36, 29, 28, 30, 32, 31, 33, 17, 16, 18, 11, 10, 12, 14, 13, 15, 26, 25, 27, 20, 19, 21, 23, 22, 24, 8, 7, 9, 2, 1, 3, 5, 4, 6]];
cc:=[17,21,26];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=17;
gen_vect_label:=1;
full_auto:=[216,158];
full_sign:=[0,2,4,6];
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:=[[27, 25, 26, 21, 19, 20, 24, 22, 23, 9, 7, 8, 3, 1, 2, 6, 4, 5, 18, 16, 17, 12, 10, 11, 15, 13, 14, 54, 52, 53, 48, 46, 47, 51, 49, 50, 36, 34, 35, 30, 28, 29, 33, 31, 32, 45, 43, 44, 39, 37, 38, 42, 40, 41], [46, 48, 47, 49, 51, 50, 52, 54, 53, 28, 30, 29, 31, 33, 32, 34, 36, 35, 37, 39, 38, 40, 42, 41, 43, 45, 44, 19, 21, 20, 22, 24, 23, 25, 27, 26, 1, 3, 2, 4, 6, 5, 7, 9, 8, 10, 12, 11, 13, 15, 14, 16, 18, 17], [50, 49, 51, 53, 52, 54, 47, 46, 48, 32, 31, 33, 35, 34, 36, 29, 28, 30, 41, 40, 42, 44, 43, 45, 38, 37, 39, 23, 22, 24, 26, 25, 27, 20, 19, 21, 5, 4, 6, 8, 7, 9, 2, 1, 3, 14, 13, 15, 17, 16, 18, 11, 10, 12]];
cc:=[17,23,27];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=18;
gen_vect_label:=1;
full_auto:=[216,158];
full_sign:=[0,2,4,6];
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, 11, 12, 10, 14, 15, 13, 26, 27, 25, 20, 21, 19, 23, 24, 22, 8, 9, 7, 2, 3, 1, 5, 6, 4, 44, 45, 43, 38, 39, 37, 41, 42, 40, 53, 54, 52, 47, 48, 46, 50, 51, 49, 35, 36, 34, 29, 30, 28, 32, 33, 31], [31, 33, 32, 34, 36, 35, 28, 30, 29, 40, 42, 41, 43, 45, 44, 37, 39, 38, 49, 51, 50, 52, 54, 53, 46, 48, 47, 4, 6, 5, 7, 9, 8, 1, 3, 2, 13, 15, 14, 16, 18, 17, 10, 12, 11, 22, 24, 23, 25, 27, 26, 19, 21, 20], [48, 47, 46, 51, 50, 49, 54, 53, 52, 30, 29, 28, 33, 32, 31, 36, 35, 34, 39, 38, 37, 42, 41, 40, 45, 44, 43, 21, 20, 19, 24, 23, 22, 27, 26, 25, 3, 2, 1, 6, 5, 4, 9, 8, 7, 12, 11, 10, 15, 14, 13, 18, 17, 16]];
cc:=[18,20,23];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=19;
gen_vect_label:=1;
full_auto:=[216,158];
full_sign:=[0,2,4,6];
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, 11, 12, 10, 14, 15, 13, 26, 27, 25, 20, 21, 19, 23, 24, 22, 8, 9, 7, 2, 3, 1, 5, 6, 4, 44, 45, 43, 38, 39, 37, 41, 42, 40, 53, 54, 52, 47, 48, 46, 50, 51, 49, 35, 36, 34, 29, 30, 28, 32, 33, 31], [34, 36, 35, 28, 30, 29, 31, 33, 32, 43, 45, 44, 37, 39, 38, 40, 42, 41, 52, 54, 53, 46, 48, 47, 49, 51, 50, 7, 9, 8, 1, 3, 2, 4, 6, 5, 16, 18, 17, 10, 12, 11, 13, 15, 14, 25, 27, 26, 19, 21, 20, 22, 24, 23], [54, 53, 52, 48, 47, 46, 51, 50, 49, 36, 35, 34, 30, 29, 28, 33, 32, 31, 45, 44, 43, 39, 38, 37, 42, 41, 40, 27, 26, 25, 21, 20, 19, 24, 23, 22, 9, 8, 7, 3, 2, 1, 6, 5, 4, 18, 17, 16, 12, 11, 10, 15, 14, 13]];
cc:=[18,21,25];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=20;
gen_vect_label:=1;
full_auto:=[216,158];
full_sign:=[0,2,4,6];
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, 11, 12, 10, 14, 15, 13, 26, 27, 25, 20, 21, 19, 23, 24, 22, 8, 9, 7, 2, 3, 1, 5, 6, 4, 44, 45, 43, 38, 39, 37, 41, 42, 40, 53, 54, 52, 47, 48, 46, 50, 51, 49, 35, 36, 34, 29, 30, 28, 32, 33, 31], [37, 39, 38, 40, 42, 41, 43, 45, 44, 46, 48, 47, 49, 51, 50, 52, 54, 53, 28, 30, 29, 31, 33, 32, 34, 36, 35, 10, 12, 11, 13, 15, 14, 16, 18, 17, 19, 21, 20, 22, 24, 23, 25, 27, 26, 1, 3, 2, 4, 6, 5, 7, 9, 8], [42, 41, 40, 45, 44, 43, 39, 38, 37, 51, 50, 49, 54, 53, 52, 48, 47, 46, 33, 32, 31, 36, 35, 34, 30, 29, 28, 15, 14, 13, 18, 17, 16, 12, 11, 10, 24, 23, 22, 27, 26, 25, 21, 20, 19, 6, 5, 4, 9, 8, 7, 3, 2, 1]];
cc:=[18,22,24];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=21;
gen_vect_label:=1;
full_auto:=[216,158];
full_sign:=[0,2,4,6];
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:=[[24, 22, 23, 27, 25, 26, 21, 19, 20, 6, 4, 5, 9, 7, 8, 3, 1, 2, 15, 13, 14, 18, 16, 17, 12, 10, 11, 51, 49, 50, 54, 52, 53, 48, 46, 47, 33, 31, 32, 36, 34, 35, 30, 28, 29, 42, 40, 41, 45, 43, 44, 39, 37, 38], [31, 33, 32, 34, 36, 35, 28, 30, 29, 40, 42, 41, 43, 45, 44, 37, 39, 38, 49, 51, 50, 52, 54, 53, 46, 48, 47, 4, 6, 5, 7, 9, 8, 1, 3, 2, 13, 15, 14, 16, 18, 17, 10, 12, 11, 22, 24, 23, 25, 27, 26, 19, 21, 20], [41, 40, 42, 44, 43, 45, 38, 37, 39, 50, 49, 51, 53, 52, 54, 47, 46, 48, 32, 31, 33, 35, 34, 36, 29, 28, 30, 14, 13, 15, 17, 16, 18, 11, 10, 12, 23, 22, 24, 26, 25, 27, 20, 19, 21, 5, 4, 6, 8, 7, 9, 2, 1, 3]];
cc:=[19,20,24];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=22;
gen_vect_label:=1;
full_auto:=[216,158];
full_sign:=[0,2,4,6];
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:=[[24, 22, 23, 27, 25, 26, 21, 19, 20, 6, 4, 5, 9, 7, 8, 3, 1, 2, 15, 13, 14, 18, 16, 17, 12, 10, 11, 51, 49, 50, 54, 52, 53, 48, 46, 47, 33, 31, 32, 36, 34, 35, 30, 28, 29, 42, 40, 41, 45, 43, 44, 39, 37, 38], [34, 36, 35, 28, 30, 29, 31, 33, 32, 43, 45, 44, 37, 39, 38, 40, 42, 41, 52, 54, 53, 46, 48, 47, 49, 51, 50, 7, 9, 8, 1, 3, 2, 4, 6, 5, 16, 18, 17, 10, 12, 11, 13, 15, 14, 25, 27, 26, 19, 21, 20, 22, 24, 23], [38, 37, 39, 41, 40, 42, 44, 43, 45, 47, 46, 48, 50, 49, 51, 53, 52, 54, 29, 28, 30, 32, 31, 33, 35, 34, 36, 11, 10, 12, 14, 13, 15, 17, 16, 18, 20, 19, 21, 23, 22, 24, 26, 25, 27, 2, 1, 3, 5, 4, 6, 8, 7, 9]];
cc:=[19,21,22];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=23;
gen_vect_label:=1;
full_auto:=[216,158];
full_sign:=[0,2,4,6];
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:=[[24, 22, 23, 27, 25, 26, 21, 19, 20, 6, 4, 5, 9, 7, 8, 3, 1, 2, 15, 13, 14, 18, 16, 17, 12, 10, 11, 51, 49, 50, 54, 52, 53, 48, 46, 47, 33, 31, 32, 36, 34, 35, 30, 28, 29, 42, 40, 41, 45, 43, 44, 39, 37, 38], [46, 48, 47, 49, 51, 50, 52, 54, 53, 28, 30, 29, 31, 33, 32, 34, 36, 35, 37, 39, 38, 40, 42, 41, 43, 45, 44, 19, 21, 20, 22, 24, 23, 25, 27, 26, 1, 3, 2, 4, 6, 5, 7, 9, 8, 10, 12, 11, 13, 15, 14, 16, 18, 17], [53, 52, 54, 47, 46, 48, 50, 49, 51, 35, 34, 36, 29, 28, 30, 32, 31, 33, 44, 43, 45, 38, 37, 39, 41, 40, 42, 26, 25, 27, 20, 19, 21, 23, 22, 24, 8, 7, 9, 2, 1, 3, 5, 4, 6, 17, 16, 18, 11, 10, 12, 14, 13, 15]];
cc:=[19,23,25];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=24;
gen_vect_label:=1;
full_auto:=[216,158];
full_sign:=[0,2,4,6];
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>);
