// Magma code for the lmfdb family of higher genus curves 7.72-25.0.3-3-6.1
// 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:=[72,25];
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:=[0,3,3,6];
genus:=7;
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:=[[25, 26, 31, 32, 27, 28, 29, 30, 33, 34, 39, 40, 35, 36, 37, 38, 41, 42, 47, 48, 43, 44, 45, 46, 49, 50, 55, 56, 51, 52, 53, 54, 57, 58, 63, 64, 59, 60, 61, 62, 65, 66, 71, 72, 67, 68, 69, 70, 1, 2, 7, 8, 3, 4, 5, 6, 9, 10, 15, 16, 11, 12, 13, 14, 17, 18, 23, 24, 19, 20, 21, 22], [37, 38, 35, 36, 40, 39, 34, 33, 45, 46, 43, 44, 48, 47, 42, 41, 29, 30, 27, 28, 32, 31, 26, 25, 61, 62, 59, 60, 64, 63, 58, 57, 69, 70, 67, 68, 72, 71, 66, 65, 53, 54, 51, 52, 56, 55, 50, 49, 13, 14, 11, 12, 16, 15, 10, 9, 21, 22, 19, 20, 24, 23, 18, 17, 5, 6, 3, 4, 8, 7, 2, 1], [44, 43, 45, 46, 41, 42, 48, 47, 28, 27, 29, 30, 25, 26, 32, 31, 36, 35, 37, 38, 33, 34, 40, 39, 68, 67, 69, 70, 65, 66, 72, 71, 52, 51, 53, 54, 49, 50, 56, 55, 60, 59, 61, 62, 57, 58, 64, 63, 20, 19, 21, 22, 17, 18, 24, 23, 4, 3, 5, 6, 1, 2, 8, 7, 12, 11, 13, 14, 9, 10, 16, 15]];
cc:=[5,7,18];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=1;
gen_vect_label:=1;
braid_class:=1;
topological_class:=[1, 1];
full_auto:=[144,127];
full_sign:=[0,2,3,12];
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>);
