// Magma code for the lmfdb family of higher genus curves 3.8-5.0.2-2-2-2-2
// 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:=[8,5];
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:=[0,2,2,2,2,2];
genus:=3;
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:=[[2, 1, 4, 3, 6, 5, 8, 7], [2, 1, 4, 3, 6, 5, 8, 7], [3, 4, 1, 2, 7, 8, 5, 6], [5, 6, 7, 8, 1, 2, 3, 4], [7, 8, 5, 6, 3, 4, 1, 2]];
cc:=[2,2,3,5,7];
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![2, 1, 4, 3, 6, 5, 8, 7];
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:=[[2, 1, 4, 3, 6, 5, 8, 7], [2, 1, 4, 3, 6, 5, 8, 7], [3, 4, 1, 2, 7, 8, 5, 6], [6, 5, 8, 7, 2, 1, 4, 3], [8, 7, 6, 5, 4, 3, 2, 1]];
cc:=[2,2,3,6,8];
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![2, 1, 4, 3, 6, 5, 8, 7];
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:=[[2, 1, 4, 3, 6, 5, 8, 7], [2, 1, 4, 3, 6, 5, 8, 7], [4, 3, 2, 1, 8, 7, 6, 5], [5, 6, 7, 8, 1, 2, 3, 4], [8, 7, 6, 5, 4, 3, 2, 1]];
cc:=[2,2,4,5,8];
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![2, 1, 4, 3, 6, 5, 8, 7];
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:=[[2, 1, 4, 3, 6, 5, 8, 7], [2, 1, 4, 3, 6, 5, 8, 7], [4, 3, 2, 1, 8, 7, 6, 5], [6, 5, 8, 7, 2, 1, 4, 3], [7, 8, 5, 6, 3, 4, 1, 2]];
cc:=[2,2,4,6,7];
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![2, 1, 4, 3, 6, 5, 8, 7];
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:=[[2, 1, 4, 3, 6, 5, 8, 7], [3, 4, 1, 2, 7, 8, 5, 6], [3, 4, 1, 2, 7, 8, 5, 6], [5, 6, 7, 8, 1, 2, 3, 4], [6, 5, 8, 7, 2, 1, 4, 3]];
cc:=[2,3,3,5,6];
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![3, 4, 1, 2, 7, 8, 5, 6];
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:=[[2, 1, 4, 3, 6, 5, 8, 7], [3, 4, 1, 2, 7, 8, 5, 6], [3, 4, 1, 2, 7, 8, 5, 6], [7, 8, 5, 6, 3, 4, 1, 2], [8, 7, 6, 5, 4, 3, 2, 1]];
cc:=[2,3,3,7,8];
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![3, 4, 1, 2, 7, 8, 5, 6];
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:=[[2, 1, 4, 3, 6, 5, 8, 7], [3, 4, 1, 2, 7, 8, 5, 6], [4, 3, 2, 1, 8, 7, 6, 5], [5, 6, 7, 8, 1, 2, 3, 4], [5, 6, 7, 8, 1, 2, 3, 4]];
cc:=[2,3,4,5,5];
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];
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:=[[2, 1, 4, 3, 6, 5, 8, 7], [3, 4, 1, 2, 7, 8, 5, 6], [4, 3, 2, 1, 8, 7, 6, 5], [6, 5, 8, 7, 2, 1, 4, 3], [6, 5, 8, 7, 2, 1, 4, 3]];
cc:=[2,3,4,6,6];
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![6, 5, 8, 7, 2, 1, 4, 3];
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:=[[2, 1, 4, 3, 6, 5, 8, 7], [3, 4, 1, 2, 7, 8, 5, 6], [4, 3, 2, 1, 8, 7, 6, 5], [7, 8, 5, 6, 3, 4, 1, 2], [7, 8, 5, 6, 3, 4, 1, 2]];
cc:=[2,3,4,7,7];
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![7, 8, 5, 6, 3, 4, 1, 2];
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:=[[2, 1, 4, 3, 6, 5, 8, 7], [3, 4, 1, 2, 7, 8, 5, 6], [4, 3, 2, 1, 8, 7, 6, 5], [8, 7, 6, 5, 4, 3, 2, 1], [8, 7, 6, 5, 4, 3, 2, 1]];
cc:=[2,3,4,8,8];
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![8, 7, 6, 5, 4, 3, 2, 1];
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:=[[2, 1, 4, 3, 6, 5, 8, 7], [4, 3, 2, 1, 8, 7, 6, 5], [4, 3, 2, 1, 8, 7, 6, 5], [5, 6, 7, 8, 1, 2, 3, 4], [6, 5, 8, 7, 2, 1, 4, 3]];
cc:=[2,4,4,5,6];
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![4, 3, 2, 1, 8, 7, 6, 5];
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:=[[2, 1, 4, 3, 6, 5, 8, 7], [4, 3, 2, 1, 8, 7, 6, 5], [4, 3, 2, 1, 8, 7, 6, 5], [7, 8, 5, 6, 3, 4, 1, 2], [8, 7, 6, 5, 4, 3, 2, 1]];
cc:=[2,4,4,7,8];
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![4, 3, 2, 1, 8, 7, 6, 5];
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:=[[2, 1, 4, 3, 6, 5, 8, 7], [5, 6, 7, 8, 1, 2, 3, 4], [5, 6, 7, 8, 1, 2, 3, 4], [7, 8, 5, 6, 3, 4, 1, 2], [8, 7, 6, 5, 4, 3, 2, 1]];
cc:=[2,5,5,7,8];
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];
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:=[[2, 1, 4, 3, 6, 5, 8, 7], [5, 6, 7, 8, 1, 2, 3, 4], [6, 5, 8, 7, 2, 1, 4, 3], [7, 8, 5, 6, 3, 4, 1, 2], [7, 8, 5, 6, 3, 4, 1, 2]];
cc:=[2,5,6,7,7];
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![7, 8, 5, 6, 3, 4, 1, 2];
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:=[[2, 1, 4, 3, 6, 5, 8, 7], [5, 6, 7, 8, 1, 2, 3, 4], [6, 5, 8, 7, 2, 1, 4, 3], [8, 7, 6, 5, 4, 3, 2, 1], [8, 7, 6, 5, 4, 3, 2, 1]];
cc:=[2,5,6,8,8];
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![8, 7, 6, 5, 4, 3, 2, 1];
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:=[[2, 1, 4, 3, 6, 5, 8, 7], [6, 5, 8, 7, 2, 1, 4, 3], [6, 5, 8, 7, 2, 1, 4, 3], [7, 8, 5, 6, 3, 4, 1, 2], [8, 7, 6, 5, 4, 3, 2, 1]];
cc:=[2,6,6,7,8];
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![6, 5, 8, 7, 2, 1, 4, 3];
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:=[[3, 4, 1, 2, 7, 8, 5, 6], [3, 4, 1, 2, 7, 8, 5, 6], [4, 3, 2, 1, 8, 7, 6, 5], [5, 6, 7, 8, 1, 2, 3, 4], [8, 7, 6, 5, 4, 3, 2, 1]];
cc:=[3,3,4,5,8];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=17;
gen_vect_label:=1;
braid_class:=1;
topological_class:=[1, 1];
is_hyperelliptic:=true;
hyp_involution:=S![3, 4, 1, 2, 7, 8, 5, 6];
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:=[[3, 4, 1, 2, 7, 8, 5, 6], [3, 4, 1, 2, 7, 8, 5, 6], [4, 3, 2, 1, 8, 7, 6, 5], [6, 5, 8, 7, 2, 1, 4, 3], [7, 8, 5, 6, 3, 4, 1, 2]];
cc:=[3,3,4,6,7];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=18;
gen_vect_label:=1;
braid_class:=1;
topological_class:=[1, 1];
is_hyperelliptic:=true;
hyp_involution:=S![3, 4, 1, 2, 7, 8, 5, 6];
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:=[[3, 4, 1, 2, 7, 8, 5, 6], [4, 3, 2, 1, 8, 7, 6, 5], [4, 3, 2, 1, 8, 7, 6, 5], [5, 6, 7, 8, 1, 2, 3, 4], [7, 8, 5, 6, 3, 4, 1, 2]];
cc:=[3,4,4,5,7];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=19;
gen_vect_label:=1;
braid_class:=1;
topological_class:=[1, 1];
is_hyperelliptic:=true;
hyp_involution:=S![4, 3, 2, 1, 8, 7, 6, 5];
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:=[[3, 4, 1, 2, 7, 8, 5, 6], [4, 3, 2, 1, 8, 7, 6, 5], [4, 3, 2, 1, 8, 7, 6, 5], [6, 5, 8, 7, 2, 1, 4, 3], [8, 7, 6, 5, 4, 3, 2, 1]];
cc:=[3,4,4,6,8];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=20;
gen_vect_label:=1;
braid_class:=1;
topological_class:=[1, 1];
is_hyperelliptic:=true;
hyp_involution:=S![4, 3, 2, 1, 8, 7, 6, 5];
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:=[[3, 4, 1, 2, 7, 8, 5, 6], [5, 6, 7, 8, 1, 2, 3, 4], [5, 6, 7, 8, 1, 2, 3, 4], [6, 5, 8, 7, 2, 1, 4, 3], [8, 7, 6, 5, 4, 3, 2, 1]];
cc:=[3,5,5,6,8];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=21;
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];
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:=[[3, 4, 1, 2, 7, 8, 5, 6], [5, 6, 7, 8, 1, 2, 3, 4], [6, 5, 8, 7, 2, 1, 4, 3], [6, 5, 8, 7, 2, 1, 4, 3], [7, 8, 5, 6, 3, 4, 1, 2]];
cc:=[3,5,6,6,7];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=22;
gen_vect_label:=1;
braid_class:=1;
topological_class:=[1, 1];
is_hyperelliptic:=true;
hyp_involution:=S![6, 5, 8, 7, 2, 1, 4, 3];
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:=[[3, 4, 1, 2, 7, 8, 5, 6], [5, 6, 7, 8, 1, 2, 3, 4], [7, 8, 5, 6, 3, 4, 1, 2], [8, 7, 6, 5, 4, 3, 2, 1], [8, 7, 6, 5, 4, 3, 2, 1]];
cc:=[3,5,7,8,8];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=23;
gen_vect_label:=1;
braid_class:=1;
topological_class:=[1, 1];
is_hyperelliptic:=true;
hyp_involution:=S![8, 7, 6, 5, 4, 3, 2, 1];
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:=[[3, 4, 1, 2, 7, 8, 5, 6], [6, 5, 8, 7, 2, 1, 4, 3], [7, 8, 5, 6, 3, 4, 1, 2], [7, 8, 5, 6, 3, 4, 1, 2], [8, 7, 6, 5, 4, 3, 2, 1]];
cc:=[3,6,7,7,8];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=24;
gen_vect_label:=1;
braid_class:=1;
topological_class:=[1, 1];
is_hyperelliptic:=true;
hyp_involution:=S![7, 8, 5, 6, 3, 4, 1, 2];
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:=[[4, 3, 2, 1, 8, 7, 6, 5], [5, 6, 7, 8, 1, 2, 3, 4], [5, 6, 7, 8, 1, 2, 3, 4], [6, 5, 8, 7, 2, 1, 4, 3], [7, 8, 5, 6, 3, 4, 1, 2]];
cc:=[4,5,5,6,7];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=25;
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];
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:=[[4, 3, 2, 1, 8, 7, 6, 5], [5, 6, 7, 8, 1, 2, 3, 4], [6, 5, 8, 7, 2, 1, 4, 3], [6, 5, 8, 7, 2, 1, 4, 3], [8, 7, 6, 5, 4, 3, 2, 1]];
cc:=[4,5,6,6,8];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=26;
gen_vect_label:=1;
braid_class:=1;
topological_class:=[1, 1];
is_hyperelliptic:=true;
hyp_involution:=S![6, 5, 8, 7, 2, 1, 4, 3];
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:=[[4, 3, 2, 1, 8, 7, 6, 5], [5, 6, 7, 8, 1, 2, 3, 4], [7, 8, 5, 6, 3, 4, 1, 2], [7, 8, 5, 6, 3, 4, 1, 2], [8, 7, 6, 5, 4, 3, 2, 1]];
cc:=[4,5,7,7,8];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=27;
gen_vect_label:=1;
braid_class:=1;
topological_class:=[1, 1];
is_hyperelliptic:=true;
hyp_involution:=S![7, 8, 5, 6, 3, 4, 1, 2];
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:=[[4, 3, 2, 1, 8, 7, 6, 5], [6, 5, 8, 7, 2, 1, 4, 3], [7, 8, 5, 6, 3, 4, 1, 2], [8, 7, 6, 5, 4, 3, 2, 1], [8, 7, 6, 5, 4, 3, 2, 1]];
cc:=[4,6,7,8,8];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=28;
gen_vect_label:=1;
braid_class:=1;
topological_class:=[1, 1];
is_hyperelliptic:=true;
hyp_involution:=S![8, 7, 6, 5, 4, 3, 2, 1];
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 >);
