// Magma code for the lmfdb family of higher genus curves 13.72-44.0.3-6-6.1
// 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:=[72,44];
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:=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:=[[14, 15, 13, 20, 21, 19, 23, 24, 22, 17, 18, 16, 26, 27, 25, 32, 33, 31, 35, 36, 34, 29, 30, 28, 2, 3, 1, 8, 9, 7, 11, 12, 10, 5, 6, 4, 50, 51, 49, 56, 57, 55, 59, 60, 58, 53, 54, 52, 62, 63, 61, 68, 69, 67, 71, 72, 70, 65, 66, 64, 38, 39, 37, 44, 45, 43, 47, 48, 46, 41, 42, 40], [58, 60, 59, 52, 54, 53, 49, 51, 50, 55, 57, 56, 70, 72, 71, 64, 66, 65, 61, 63, 62, 67, 69, 68, 46, 48, 47, 40, 42, 41, 37, 39, 38, 43, 45, 44, 22, 24, 23, 16, 18, 17, 13, 15, 14, 19, 21, 20, 34, 36, 35, 28, 30, 29, 25, 27, 26, 31, 33, 32, 10, 12, 11, 4, 6, 5, 1, 3, 2, 7, 9, 8], [54, 53, 52, 60, 59, 58, 57, 56, 55, 51, 50, 49, 66, 65, 64, 72, 71, 70, 69, 68, 67, 63, 62, 61, 42, 41, 40, 48, 47, 46, 45, 44, 43, 39, 38, 37, 18, 17, 16, 24, 23, 22, 21, 20, 19, 15, 14, 13, 30, 29, 28, 36, 35, 34, 33, 32, 31, 27, 26, 25, 6, 5, 4, 12, 11, 10, 9, 8, 7, 3, 2, 1]];
cc:=[8,11,11];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=1;
gen_vect_label:=1;
full_auto:=[144,190];
full_sign:=[0,2,6,6];
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>);
