// Magma code for the lmfdb family of higher genus curves 11.80-28.0.2-8-8.2
// 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:=[80,28];
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:=[0,2,8,8];
genus:=11;
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:=[[31, 35, 34, 33, 32, 36, 40, 39, 38, 37, 26, 30, 29, 28, 27, 21, 25, 24, 23, 22, 16, 20, 19, 18, 17, 11, 15, 14, 13, 12, 1, 5, 4, 3, 2, 6, 10, 9, 8, 7, 71, 75, 74, 73, 72, 76, 80, 79, 78, 77, 66, 70, 69, 68, 67, 61, 65, 64, 63, 62, 56, 60, 59, 58, 57, 51, 55, 54, 53, 52, 41, 45, 44, 43, 42, 46, 50, 49, 48, 47], [54, 52, 55, 53, 51, 59, 57, 60, 58, 56, 49, 47, 50, 48, 46, 44, 42, 45, 43, 41, 74, 72, 75, 73, 71, 79, 77, 80, 78, 76, 69, 67, 70, 68, 66, 64, 62, 65, 63, 61, 9, 7, 10, 8, 6, 4, 2, 5, 3, 1, 19, 17, 20, 18, 16, 14, 12, 15, 13, 11, 29, 27, 30, 28, 26, 24, 22, 25, 23, 21, 39, 37, 40, 38, 36, 34, 32, 35, 33, 31], [77, 80, 78, 76, 79, 72, 75, 73, 71, 74, 62, 65, 63, 61, 64, 67, 70, 68, 66, 69, 52, 55, 53, 51, 54, 57, 60, 58, 56, 59, 47, 50, 48, 46, 49, 42, 45, 43, 41, 44, 22, 25, 23, 21, 24, 27, 30, 28, 26, 29, 32, 35, 33, 31, 34, 37, 40, 38, 36, 39, 7, 10, 8, 6, 9, 2, 5, 3, 1, 4, 17, 20, 18, 16, 19, 12, 15, 13, 11, 14]];
cc:=[3,11,15];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=2;
gen_vect_label:=1;
full_auto:=[160,82];
full_sign:=[0,2,4,8];
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>);
