// Magma code for the lmfdb family of higher genus curves 10.168-42.0.2-4-7.1
// 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:=[168,42];
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:=[0,2,4,7];
genus:=10;
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:=[[5, 9, 45, 88, 1, 77, 104, 12, 2, 17, 32, 8, 154, 125, 19, 23, 10, 39, 15, 91, 160, 26, 16, 66, 151, 22, 84, 139, 33, 114, 38, 11, 29, 147, 48, 40, 163, 31, 18, 36, 98, 69, 47, 51, 3, 130, 43, 35, 146, 54, 44, 59, 74, 50, 112, 167, 61, 65, 52, 81, 57, 133, 118, 68, 58, 24, 109, 64, 42, 97, 75, 156, 80, 53, 71, 105, 6, 82, 121, 73, 60, 78, 140, 27, 89, 93, 129, 4, 85, 161, 20, 96, 86, 101, 116, 92, 70, 41, 103, 107, 94, 123, 99, 7, 76, 110, 100, 150, 67, 106, 168, 55, 117, 30, 122, 95, 113, 63, 132, 124, 79, 115, 102, 120, 14, 153, 131, 135, 87, 46, 127, 119, 62, 138, 128, 143, 158, 134, 28, 83, 145, 149, 136, 165, 141, 49, 34, 152, 142, 108, 25, 148, 126, 13, 159, 72, 164, 137, 155, 21, 90, 166, 37, 157, 144, 162, 56, 111], [24, 131, 102, 13, 72, 127, 21, 52, 40, 123, 6, 149, 36, 49, 59, 33, 158, 27, 86, 29, 70, 3, 110, 137, 20, 79, 106, 14, 80, 19, 46, 118, 142, 15, 126, 73, 12, 67, 167, 93, 8, 161, 66, 89, 144, 55, 30, 85, 63, 10, 82, 165, 48, 107, 78, 7, 17, 75, 116, 69, 128, 71, 28, 45, 152, 95, 62, 37, 148, 56, 38, 61, 4, 160, 100, 57, 168, 31, 54, 25, 125, 135, 50, 119, 108, 47, 18, 97, 156, 43, 105, 136, 124, 39, 90, 65, 120, 133, 143, 117, 74, 111, 2, 113, 154, 87, 26, 53, 104, 163, 22, 98, 164, 103, 130, 34, 58, 99, 42, 157, 96, 151, 83, 9, 92, 77, 150, 5, 60, 139, 114, 1, 147, 94, 166, 81, 132, 23, 162, 91, 101, 159, 32, 153, 44, 155, 112, 129, 68, 11, 146, 121, 64, 140, 122, 145, 88, 76, 16, 141, 84, 115, 138, 109, 41, 51, 134, 35], [119, 99, 26, 80, 135, 32, 167, 98, 120, 54, 108, 163, 88, 139, 147, 155, 61, 129, 114, 151, 104, 168, 134, 5, 73, 100, 39, 118, 91, 43, 82, 136, 23, 95, 111, 154, 64, 75, 101, 2, 144, 132, 161, 141, 68, 38, 93, 74, 125, 140, 162, 12, 150, 121, 130, 97, 105, 113, 19, 87, 156, 109, 146, 126, 92, 47, 31, 142, 81, 160, 133, 1, 40, 94, 65, 137, 153, 112, 22, 33, 143, 44, 102, 90, 35, 15, 110, 164, 51, 116, 83, 14, 36, 138, 24, 79, 4, 55, 63, 71, 145, 45, 30, 67, 20, 84, 50, 89, 157, 16, 123, 34, 7, 127, 166, 52, 107, 11, 27, 70, 148, 159, 17, 86, 60, 48, 77, 57, 152, 122, 9, 158, 41, 56, 78, 96, 66, 37, 46, 13, 21, 29, 103, 3, 72, 25, 62, 42, 8, 131, 115, 58, 165, 76, 49, 85, 124, 10, 149, 53, 69, 28, 106, 117, 59, 128, 18, 6]];
cc:=[2,4,5];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=1;
gen_vect_label:=1;
is_hyperelliptic:=false;
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,is_cyclic_trigonal:=is_cyclic_trigonal >);
