// Magma code for the lmfdb family of higher genus curves 12.50-2.0.2-25-50
// 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:=[50,2];
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:=[0,2,25,50];
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:=[[26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], [6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 2, 3, 4, 5, 1, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 27, 28, 29, 30, 26], [50, 46, 47, 48, 49, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 25, 21, 22, 23, 24, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]];
cc:=[2,11,50];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=1;
gen_vect_label:=1;
is_hyperelliptic:=true;
hyp_involution:=S![26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25];
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:=[[26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], [11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 2, 3, 4, 5, 1, 7, 8, 9, 10, 6, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 27, 28, 29, 30, 26, 32, 33, 34, 35, 31], [45, 41, 42, 43, 44, 50, 46, 47, 48, 49, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 20, 16, 17, 18, 19, 25, 21, 22, 23, 24, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]];
cc:=[2,12,40];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=2;
gen_vect_label:=1;
is_hyperelliptic:=true;
hyp_involution:=S![26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25];
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:=[[26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], [16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 2, 3, 4, 5, 1, 7, 8, 9, 10, 6, 12, 13, 14, 15, 11, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 27, 28, 29, 30, 26, 32, 33, 34, 35, 31, 37, 38, 39, 40, 36], [40, 36, 37, 38, 39, 45, 41, 42, 43, 44, 50, 46, 47, 48, 49, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 15, 11, 12, 13, 14, 20, 16, 17, 18, 19, 25, 21, 22, 23, 24, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]];
cc:=[2,13,49];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=3;
gen_vect_label:=1;
is_hyperelliptic:=true;
hyp_involution:=S![26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25];
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:=[[26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], [21, 22, 23, 24, 25, 2, 3, 4, 5, 1, 7, 8, 9, 10, 6, 12, 13, 14, 15, 11, 17, 18, 19, 20, 16, 46, 47, 48, 49, 50, 27, 28, 29, 30, 26, 32, 33, 34, 35, 31, 37, 38, 39, 40, 36, 42, 43, 44, 45, 41], [35, 31, 32, 33, 34, 40, 36, 37, 38, 39, 45, 41, 42, 43, 44, 50, 46, 47, 48, 49, 26, 27, 28, 29, 30, 10, 6, 7, 8, 9, 15, 11, 12, 13, 14, 20, 16, 17, 18, 19, 25, 21, 22, 23, 24, 1, 2, 3, 4, 5]];
cc:=[2,14,39];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=4;
gen_vect_label:=1;
is_hyperelliptic:=true;
hyp_involution:=S![26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25];
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:=[[26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], [7, 8, 9, 10, 6, 12, 13, 14, 15, 11, 17, 18, 19, 20, 16, 22, 23, 24, 25, 21, 3, 4, 5, 1, 2, 32, 33, 34, 35, 31, 37, 38, 39, 40, 36, 42, 43, 44, 45, 41, 47, 48, 49, 50, 46, 28, 29, 30, 26, 27], [49, 50, 46, 47, 48, 30, 26, 27, 28, 29, 35, 31, 32, 33, 34, 40, 36, 37, 38, 39, 45, 41, 42, 43, 44, 24, 25, 21, 22, 23, 5, 1, 2, 3, 4, 10, 6, 7, 8, 9, 15, 11, 12, 13, 14, 20, 16, 17, 18, 19]];
cc:=[2,15,38];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=5;
gen_vect_label:=1;
is_hyperelliptic:=true;
hyp_involution:=S![26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25];
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:=[[26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], [12, 13, 14, 15, 11, 17, 18, 19, 20, 16, 22, 23, 24, 25, 21, 3, 4, 5, 1, 2, 8, 9, 10, 6, 7, 37, 38, 39, 40, 36, 42, 43, 44, 45, 41, 47, 48, 49, 50, 46, 28, 29, 30, 26, 27, 33, 34, 35, 31, 32], [44, 45, 41, 42, 43, 49, 50, 46, 47, 48, 30, 26, 27, 28, 29, 35, 31, 32, 33, 34, 40, 36, 37, 38, 39, 19, 20, 16, 17, 18, 24, 25, 21, 22, 23, 5, 1, 2, 3, 4, 10, 6, 7, 8, 9, 15, 11, 12, 13, 14]];
cc:=[2,16,48];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=6;
gen_vect_label:=1;
is_hyperelliptic:=true;
hyp_involution:=S![26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25];
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:=[[26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], [17, 18, 19, 20, 16, 22, 23, 24, 25, 21, 3, 4, 5, 1, 2, 8, 9, 10, 6, 7, 13, 14, 15, 11, 12, 42, 43, 44, 45, 41, 47, 48, 49, 50, 46, 28, 29, 30, 26, 27, 33, 34, 35, 31, 32, 38, 39, 40, 36, 37], [39, 40, 36, 37, 38, 44, 45, 41, 42, 43, 49, 50, 46, 47, 48, 30, 26, 27, 28, 29, 35, 31, 32, 33, 34, 14, 15, 11, 12, 13, 19, 20, 16, 17, 18, 24, 25, 21, 22, 23, 5, 1, 2, 3, 4, 10, 6, 7, 8, 9]];
cc:=[2,17,37];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=7;
gen_vect_label:=1;
is_hyperelliptic:=true;
hyp_involution:=S![26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25];
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:=[[26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], [22, 23, 24, 25, 21, 3, 4, 5, 1, 2, 8, 9, 10, 6, 7, 13, 14, 15, 11, 12, 18, 19, 20, 16, 17, 47, 48, 49, 50, 46, 28, 29, 30, 26, 27, 33, 34, 35, 31, 32, 38, 39, 40, 36, 37, 43, 44, 45, 41, 42], [34, 35, 31, 32, 33, 39, 40, 36, 37, 38, 44, 45, 41, 42, 43, 49, 50, 46, 47, 48, 30, 26, 27, 28, 29, 9, 10, 6, 7, 8, 14, 15, 11, 12, 13, 19, 20, 16, 17, 18, 24, 25, 21, 22, 23, 5, 1, 2, 3, 4]];
cc:=[2,18,47];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=8;
gen_vect_label:=1;
is_hyperelliptic:=true;
hyp_involution:=S![26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25];
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:=[[26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], [8, 9, 10, 6, 7, 13, 14, 15, 11, 12, 18, 19, 20, 16, 17, 23, 24, 25, 21, 22, 4, 5, 1, 2, 3, 33, 34, 35, 31, 32, 38, 39, 40, 36, 37, 43, 44, 45, 41, 42, 48, 49, 50, 46, 47, 29, 30, 26, 27, 28], [48, 49, 50, 46, 47, 29, 30, 26, 27, 28, 34, 35, 31, 32, 33, 39, 40, 36, 37, 38, 44, 45, 41, 42, 43, 23, 24, 25, 21, 22, 4, 5, 1, 2, 3, 9, 10, 6, 7, 8, 14, 15, 11, 12, 13, 19, 20, 16, 17, 18]];
cc:=[2,19,46];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=9;
gen_vect_label:=1;
is_hyperelliptic:=true;
hyp_involution:=S![26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25];
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:=[[26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], [13, 14, 15, 11, 12, 18, 19, 20, 16, 17, 23, 24, 25, 21, 22, 4, 5, 1, 2, 3, 9, 10, 6, 7, 8, 38, 39, 40, 36, 37, 43, 44, 45, 41, 42, 48, 49, 50, 46, 47, 29, 30, 26, 27, 28, 34, 35, 31, 32, 33], [43, 44, 45, 41, 42, 48, 49, 50, 46, 47, 29, 30, 26, 27, 28, 34, 35, 31, 32, 33, 39, 40, 36, 37, 38, 18, 19, 20, 16, 17, 23, 24, 25, 21, 22, 4, 5, 1, 2, 3, 9, 10, 6, 7, 8, 14, 15, 11, 12, 13]];
cc:=[2,20,36];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=10;
gen_vect_label:=1;
is_hyperelliptic:=true;
hyp_involution:=S![26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25];
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:=[[26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], [18, 19, 20, 16, 17, 23, 24, 25, 21, 22, 4, 5, 1, 2, 3, 9, 10, 6, 7, 8, 14, 15, 11, 12, 13, 43, 44, 45, 41, 42, 48, 49, 50, 46, 47, 29, 30, 26, 27, 28, 34, 35, 31, 32, 33, 39, 40, 36, 37, 38], [38, 39, 40, 36, 37, 43, 44, 45, 41, 42, 48, 49, 50, 46, 47, 29, 30, 26, 27, 28, 34, 35, 31, 32, 33, 13, 14, 15, 11, 12, 18, 19, 20, 16, 17, 23, 24, 25, 21, 22, 4, 5, 1, 2, 3, 9, 10, 6, 7, 8]];
cc:=[2,21,45];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=11;
gen_vect_label:=1;
is_hyperelliptic:=true;
hyp_involution:=S![26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25];
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:=[[26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], [23, 24, 25, 21, 22, 4, 5, 1, 2, 3, 9, 10, 6, 7, 8, 14, 15, 11, 12, 13, 19, 20, 16, 17, 18, 48, 49, 50, 46, 47, 29, 30, 26, 27, 28, 34, 35, 31, 32, 33, 39, 40, 36, 37, 38, 44, 45, 41, 42, 43], [33, 34, 35, 31, 32, 38, 39, 40, 36, 37, 43, 44, 45, 41, 42, 48, 49, 50, 46, 47, 29, 30, 26, 27, 28, 8, 9, 10, 6, 7, 13, 14, 15, 11, 12, 18, 19, 20, 16, 17, 23, 24, 25, 21, 22, 4, 5, 1, 2, 3]];
cc:=[2,22,35];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=12;
gen_vect_label:=1;
is_hyperelliptic:=true;
hyp_involution:=S![26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25];
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:=[[26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], [9, 10, 6, 7, 8, 14, 15, 11, 12, 13, 19, 20, 16, 17, 18, 24, 25, 21, 22, 23, 5, 1, 2, 3, 4, 34, 35, 31, 32, 33, 39, 40, 36, 37, 38, 44, 45, 41, 42, 43, 49, 50, 46, 47, 48, 30, 26, 27, 28, 29], [47, 48, 49, 50, 46, 28, 29, 30, 26, 27, 33, 34, 35, 31, 32, 38, 39, 40, 36, 37, 43, 44, 45, 41, 42, 22, 23, 24, 25, 21, 3, 4, 5, 1, 2, 8, 9, 10, 6, 7, 13, 14, 15, 11, 12, 18, 19, 20, 16, 17]];
cc:=[2,23,34];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=13;
gen_vect_label:=1;
is_hyperelliptic:=true;
hyp_involution:=S![26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25];
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:=[[26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], [14, 15, 11, 12, 13, 19, 20, 16, 17, 18, 24, 25, 21, 22, 23, 5, 1, 2, 3, 4, 10, 6, 7, 8, 9, 39, 40, 36, 37, 38, 44, 45, 41, 42, 43, 49, 50, 46, 47, 48, 30, 26, 27, 28, 29, 35, 31, 32, 33, 34], [42, 43, 44, 45, 41, 47, 48, 49, 50, 46, 28, 29, 30, 26, 27, 33, 34, 35, 31, 32, 38, 39, 40, 36, 37, 17, 18, 19, 20, 16, 22, 23, 24, 25, 21, 3, 4, 5, 1, 2, 8, 9, 10, 6, 7, 13, 14, 15, 11, 12]];
cc:=[2,24,44];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=14;
gen_vect_label:=1;
is_hyperelliptic:=true;
hyp_involution:=S![26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25];
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:=[[26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], [19, 20, 16, 17, 18, 24, 25, 21, 22, 23, 5, 1, 2, 3, 4, 10, 6, 7, 8, 9, 15, 11, 12, 13, 14, 44, 45, 41, 42, 43, 49, 50, 46, 47, 48, 30, 26, 27, 28, 29, 35, 31, 32, 33, 34, 40, 36, 37, 38, 39], [37, 38, 39, 40, 36, 42, 43, 44, 45, 41, 47, 48, 49, 50, 46, 28, 29, 30, 26, 27, 33, 34, 35, 31, 32, 12, 13, 14, 15, 11, 17, 18, 19, 20, 16, 22, 23, 24, 25, 21, 3, 4, 5, 1, 2, 8, 9, 10, 6, 7]];
cc:=[2,25,33];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=15;
gen_vect_label:=1;
is_hyperelliptic:=true;
hyp_involution:=S![26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25];
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:=[[26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], [24, 25, 21, 22, 23, 5, 1, 2, 3, 4, 10, 6, 7, 8, 9, 15, 11, 12, 13, 14, 20, 16, 17, 18, 19, 49, 50, 46, 47, 48, 30, 26, 27, 28, 29, 35, 31, 32, 33, 34, 40, 36, 37, 38, 39, 45, 41, 42, 43, 44], [32, 33, 34, 35, 31, 37, 38, 39, 40, 36, 42, 43, 44, 45, 41, 47, 48, 49, 50, 46, 28, 29, 30, 26, 27, 7, 8, 9, 10, 6, 12, 13, 14, 15, 11, 17, 18, 19, 20, 16, 22, 23, 24, 25, 21, 3, 4, 5, 1, 2]];
cc:=[2,26,43];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=16;
gen_vect_label:=1;
is_hyperelliptic:=true;
hyp_involution:=S![26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25];
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:=[[26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], [10, 6, 7, 8, 9, 15, 11, 12, 13, 14, 20, 16, 17, 18, 19, 25, 21, 22, 23, 24, 1, 2, 3, 4, 5, 35, 31, 32, 33, 34, 40, 36, 37, 38, 39, 45, 41, 42, 43, 44, 50, 46, 47, 48, 49, 26, 27, 28, 29, 30], [46, 47, 48, 49, 50, 27, 28, 29, 30, 26, 32, 33, 34, 35, 31, 37, 38, 39, 40, 36, 42, 43, 44, 45, 41, 21, 22, 23, 24, 25, 2, 3, 4, 5, 1, 7, 8, 9, 10, 6, 12, 13, 14, 15, 11, 17, 18, 19, 20, 16]];
cc:=[2,27,42];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=17;
gen_vect_label:=1;
is_hyperelliptic:=true;
hyp_involution:=S![26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25];
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:=[[26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], [15, 11, 12, 13, 14, 20, 16, 17, 18, 19, 25, 21, 22, 23, 24, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 40, 36, 37, 38, 39, 45, 41, 42, 43, 44, 50, 46, 47, 48, 49, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35], [41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 27, 28, 29, 30, 26, 32, 33, 34, 35, 31, 37, 38, 39, 40, 36, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 2, 3, 4, 5, 1, 7, 8, 9, 10, 6, 12, 13, 14, 15, 11]];
cc:=[2,28,32];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=18;
gen_vect_label:=1;
is_hyperelliptic:=true;
hyp_involution:=S![26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25];
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:=[[26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], [20, 16, 17, 18, 19, 25, 21, 22, 23, 24, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 45, 41, 42, 43, 44, 50, 46, 47, 48, 49, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40], [36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 27, 28, 29, 30, 26, 32, 33, 34, 35, 31, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 2, 3, 4, 5, 1, 7, 8, 9, 10, 6]];
cc:=[2,29,41];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=19;
gen_vect_label:=1;
is_hyperelliptic:=true;
hyp_involution:=S![26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25];
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:=[[26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], [25, 21, 22, 23, 24, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 50, 46, 47, 48, 49, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45], [31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 27, 28, 29, 30, 26, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 2, 3, 4, 5, 1]];
cc:=[2,30,31];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=20;
gen_vect_label:=1;
is_hyperelliptic:=true;
hyp_involution:=S![26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25];
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 >);
