// Magma code for the lmfdb family of higher genus curves 15.168-43.0.3-3-6.1
// 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:=[168,43];
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:=15;
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:=[[57, 61, 63, 59, 62, 58, 60, 64, 73, 77, 79, 75, 78, 74, 76, 80, 89, 93, 95, 91, 94, 90, 92, 96, 105, 109, 111, 107, 110, 106, 108, 112, 65, 69, 71, 67, 70, 66, 68, 72, 81, 85, 87, 83, 86, 82, 84, 88, 97, 101, 103, 99, 102, 98, 100, 104, 113, 117, 119, 115, 118, 114, 116, 120, 129, 133, 135, 131, 134, 130, 132, 136, 145, 149, 151, 147, 150, 146, 148, 152, 161, 165, 167, 163, 166, 162, 164, 168, 121, 125, 127, 123, 126, 122, 124, 128, 137, 141, 143, 139, 142, 138, 140, 144, 153, 157, 159, 155, 158, 154, 156, 160, 1, 5, 7, 3, 6, 2, 4, 8, 17, 21, 23, 19, 22, 18, 20, 24, 33, 37, 39, 35, 38, 34, 36, 40, 49, 53, 55, 51, 54, 50, 52, 56, 9, 13, 15, 11, 14, 10, 12, 16, 25, 29, 31, 27, 30, 26, 28, 32, 41, 45, 47, 43, 46, 42, 44, 48], [110, 111, 107, 106, 109, 112, 108, 105, 70, 71, 67, 66, 69, 72, 68, 65, 86, 87, 83, 82, 85, 88, 84, 81, 102, 103, 99, 98, 101, 104, 100, 97, 62, 63, 59, 58, 61, 64, 60, 57, 78, 79, 75, 74, 77, 80, 76, 73, 94, 95, 91, 90, 93, 96, 92, 89, 166, 167, 163, 162, 165, 168, 164, 161, 126, 127, 123, 122, 125, 128, 124, 121, 142, 143, 139, 138, 141, 144, 140, 137, 158, 159, 155, 154, 157, 160, 156, 153, 118, 119, 115, 114, 117, 120, 116, 113, 134, 135, 131, 130, 133, 136, 132, 129, 150, 151, 147, 146, 149, 152, 148, 145, 54, 55, 51, 50, 53, 56, 52, 49, 14, 15, 11, 10, 13, 16, 12, 9, 30, 31, 27, 26, 29, 32, 28, 25, 46, 47, 43, 42, 45, 48, 44, 41, 6, 7, 3, 2, 5, 8, 4, 1, 22, 23, 19, 18, 21, 24, 20, 17, 38, 39, 35, 34, 37, 40, 36, 33], [80, 79, 76, 75, 74, 73, 78, 77, 96, 95, 92, 91, 90, 89, 94, 93, 112, 111, 108, 107, 106, 105, 110, 109, 72, 71, 68, 67, 66, 65, 70, 69, 88, 87, 84, 83, 82, 81, 86, 85, 104, 103, 100, 99, 98, 97, 102, 101, 64, 63, 60, 59, 58, 57, 62, 61, 136, 135, 132, 131, 130, 129, 134, 133, 152, 151, 148, 147, 146, 145, 150, 149, 168, 167, 164, 163, 162, 161, 166, 165, 128, 127, 124, 123, 122, 121, 126, 125, 144, 143, 140, 139, 138, 137, 142, 141, 160, 159, 156, 155, 154, 153, 158, 157, 120, 119, 116, 115, 114, 113, 118, 117, 24, 23, 20, 19, 18, 17, 22, 21, 40, 39, 36, 35, 34, 33, 38, 37, 56, 55, 52, 51, 50, 49, 54, 53, 16, 15, 12, 11, 10, 9, 14, 13, 32, 31, 28, 27, 26, 25, 30, 29, 48, 47, 44, 43, 42, 41, 46, 45, 8, 7, 4, 3, 2, 1, 6, 5]];
cc:=[3,3,5];
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 >);

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