// Magma code for the lmfdb family of higher genus curves 3.168-42.0.2-3-7.1.1
// 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:=[0,2,3,7];
genus:=3;
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], [2, 3, 1, 5, 6, 4, 77, 9, 10, 8, 12, 13, 11, 154, 16, 17, 15, 19, 20, 18, 91, 23, 24, 22, 26, 27, 25, 84, 30, 31, 29, 33, 34, 32, 147, 37, 38, 36, 40, 41, 39, 98, 44, 45, 43, 47, 48, 46, 35, 51, 52, 50, 54, 55, 53, 112, 58, 59, 57, 61, 62, 60, 133, 65, 66, 64, 68, 69, 67, 42, 72, 73, 71, 75, 76, 74, 105, 79, 80, 78, 82, 83, 81, 140, 86, 87, 85, 89, 90, 88, 161, 93, 94, 92, 96, 97, 95, 70, 100, 101, 99, 103, 104, 102, 7, 107, 108, 106, 110, 111, 109, 168, 114, 115, 113, 117, 118, 116, 63, 121, 122, 120, 124, 125, 123, 14, 128, 129, 127, 131, 132, 130, 119, 135, 136, 134, 138, 139, 137, 28, 142, 143, 141, 145, 146, 144, 49, 149, 150, 148, 152, 153, 151, 126, 156, 157, 155, 159, 160, 158, 21, 163, 164, 162, 166, 167, 165, 56], [45, 5, 9, 77, 88, 1, 76, 17, 12, 2, 154, 32, 8, 153, 10, 19, 23, 91, 39, 15, 90, 66, 26, 16, 84, 151, 22, 83, 38, 33, 114, 147, 11, 29, 146, 31, 40, 163, 98, 18, 36, 97, 3, 47, 51, 35, 130, 43, 34, 59, 54, 44, 112, 74, 50, 111, 52, 61, 65, 133, 81, 57, 132, 24, 68, 58, 42, 109, 64, 41, 80, 75, 156, 105, 53, 71, 104, 73, 82, 121, 140, 60, 78, 139, 129, 89, 93, 161, 4, 85, 160, 101, 96, 86, 70, 116, 92, 69, 94, 103, 107, 7, 123, 99, 6, 150, 110, 100, 168, 67, 106, 167, 122, 117, 30, 63, 95, 113, 62, 115, 124, 79, 14, 102, 120, 13, 87, 131, 135, 119, 46, 127, 118, 143, 138, 128, 28, 158, 134, 27, 136, 145, 149, 49, 165, 141, 48, 108, 152, 142, 126, 25, 148, 125, 164, 159, 72, 21, 137, 155, 20, 157, 166, 37, 56, 144, 162, 55]];
cc:=[2,3,5];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=1;
gen_vect_label:=1;
braid_class:=[1, 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:=[[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], [108, 140, 116, 141, 30, 83, 26, 80, 168, 95, 155, 86, 111, 54, 73, 119, 144, 120, 149, 132, 61, 129, 105, 165, 92, 37, 76, 5, 52, 28, 88, 64, 93, 139, 82, 59, 7, 151, 43, 142, 104, 75, 150, 98, 158, 99, 72, 41, 68, 38, 126, 137, 113, 128, 153, 12, 31, 161, 102, 162, 107, 90, 19, 87, 147, 123, 134, 79, 34, 47, 10, 70, 130, 22, 135, 97, 40, 17, 49, 109, 1, 100, 146, 33, 24, 56, 32, 57, 114, 167, 110, 164, 84, 11, 71, 2, 27, 138, 157, 35, 60, 36, 65, 48, 145, 45, 21, 81, 8, 121, 160, 89, 136, 112, 4, 148, 9, 55, 166, 143, 91, 67, 127, 58, 20, 159, 66, 14, 74, 15, 156, 125, 152, 122, 42, 53, 29, 44, 69, 96, 115, 77, 18, 78, 23, 6, 103, 3, 63, 39, 50, 163, 118, 131, 94, 154, 46, 106, 51, 13, 124, 101, 133, 25, 85, 16, 62, 117], [60, 92, 152, 122, 139, 49, 163, 67, 113, 75, 101, 167, 21, 135, 46, 162, 82, 136, 118, 14, 100, 53, 141, 89, 157, 104, 70, 114, 158, 1, 61, 129, 27, 42, 107, 123, 22, 54, 108, 6, 35, 128, 18, 134, 110, 164, 97, 7, 121, 25, 155, 33, 143, 125, 63, 93, 4, 120, 40, 94, 160, 56, 142, 11, 99, 131, 115, 146, 28, 156, 116, 43, 19, 87, 69, 84, 149, 165, 64, 12, 150, 48, 77, 86, 144, 8, 68, 38, 55, 133, 79, 151, 29, 159, 17, 83, 105, 51, 130, 78, 166, 52, 34, 98, 16, 137, 57, 5, 73, 20, 154, 30, 74, 85, 145, 45, 111, 126, 23, 39, 106, 138, 24, 90, 119, 44, 102, 50, 26, 80, 13, 91, 37, 109, 71, 117, 59, 41, 147, 9, 88, 36, 124, 10, 76, 140, 58, 95, 15, 47, 31, 62, 112, 72, 32, 127, 103, 3, 153, 168, 65, 81, 148, 96, 66, 132, 161, 2]];
cc:=[2,3,6];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=2;
gen_vect_label:=1;
braid_class:=[2, 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 >);
