// Magma code for the lmfdb family of higher genus curves 8.168-42.0.3-3-4.1
// 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:=[0,3,3,4];
genus:=8;
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:=[[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], [121, 69, 136, 63, 151, 162, 33, 100, 62, 164, 70, 74, 134, 89, 135, 55, 115, 49, 81, 99, 152, 156, 48, 101, 56, 88, 113, 40, 128, 76, 24, 161, 60, 106, 96, 107, 83, 3, 126, 53, 127, 145, 163, 27, 94, 21, 109, 120, 75, 142, 20, 122, 28, 32, 92, 131, 93, 13, 157, 7, 39, 141, 110, 114, 6, 143, 14, 130, 155, 82, 86, 34, 66, 119, 18, 148, 138, 149, 41, 45, 168, 11, 85, 103, 37, 153, 52, 147, 67, 78, 117, 16, 146, 80, 154, 158, 50, 5, 51, 139, 31, 133, 165, 15, 68, 72, 132, 17, 140, 4, 29, 124, 44, 160, 108, 77, 144, 22, 12, 23, 167, 87, 42, 137, 43, 61, 79, 111, 10, 105, 25, 36, 159, 58, 104, 38, 112, 116, 8, 47, 9, 97, 73, 91, 123, 57, 26, 30, 90, 59, 98, 46, 71, 166, 2, 118, 150, 35, 102, 64, 54, 65, 125, 129, 84, 95, 1, 19], [166, 157, 37, 109, 42, 64, 62, 138, 143, 128, 81, 133, 57, 69, 103, 94, 107, 74, 112, 50, 48, 117, 122, 30, 130, 35, 43, 55, 110, 150, 100, 53, 105, 71, 160, 131, 87, 135, 60, 140, 78, 125, 124, 115, 79, 151, 84, 22, 20, 96, 101, 86, 39, 91, 15, 27, 145, 136, 149, 32, 154, 8, 6, 159, 164, 72, 88, 77, 1, 13, 152, 108, 142, 11, 147, 29, 118, 89, 129, 93, 18, 98, 36, 167, 82, 73, 121, 25, 126, 148, 146, 54, 59, 44, 165, 49, 141, 153, 19, 10, 23, 158, 28, 134, 132, 33, 38, 114, 46, 119, 127, 139, 26, 66, 16, 137, 21, 155, 76, 47, 3, 51, 144, 56, 162, 41, 40, 31, 163, 67, 168, 106, 104, 12, 17, 2, 123, 7, 99, 111, 61, 52, 65, 116, 70, 92, 90, 75, 80, 156, 4, 161, 85, 97, 68, 24, 58, 95, 63, 113, 34, 5, 45, 9, 102, 14, 120, 83]];
cc:=[3,3,4];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=1;
gen_vect_label:=1;
full_auto:=[336,208];
full_sign:=[0,2,3,8];
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>);

// Here we add an action to data.
gen_vectors:=[[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], [36, 165, 156, 66, 111, 70, 131, 127, 137, 142, 59, 83, 63, 40, 106, 102, 93, 52, 76, 56, 33, 29, 116, 121, 45, 132, 49, 110, 99, 109, 149, 73, 55, 77, 19, 134, 130, 86, 80, 62, 84, 12, 78, 123, 114, 24, 153, 28, 89, 85, 95, 100, 17, 41, 21, 82, 148, 144, 135, 10, 34, 14, 75, 71, 158, 163, 3, 90, 7, 152, 141, 151, 107, 31, 13, 35, 61, 92, 88, 128, 38, 20, 42, 54, 120, 81, 72, 150, 27, 154, 47, 43, 53, 58, 143, 167, 147, 124, 22, 18, 9, 136, 160, 140, 117, 113, 32, 37, 129, 48, 133, 26, 15, 25, 65, 157, 139, 161, 103, 50, 46, 2, 164, 146, 168, 96, 162, 39, 30, 108, 69, 112, 5, 1, 11, 16, 101, 125, 105, 166, 64, 60, 51, 94, 118, 98, 159, 155, 74, 79, 87, 6, 91, 68, 57, 67, 23, 115, 97, 119, 145, 8, 4, 44, 122, 104, 126, 138], [136, 121, 69, 162, 63, 151, 68, 164, 100, 62, 134, 70, 74, 61, 115, 135, 55, 99, 49, 81, 54, 101, 156, 48, 113, 56, 88, 47, 24, 128, 76, 106, 161, 60, 75, 3, 107, 83, 127, 126, 53, 82, 94, 163, 27, 120, 21, 109, 26, 122, 142, 20, 92, 28, 32, 19, 157, 93, 13, 141, 7, 39, 12, 143, 114, 6, 155, 14, 130, 5, 66, 86, 34, 148, 119, 18, 33, 45, 149, 41, 85, 168, 11, 40, 52, 37, 153, 78, 147, 67, 152, 80, 16, 146, 50, 154, 158, 145, 31, 51, 139, 15, 133, 165, 138, 17, 72, 132, 29, 140, 4, 131, 108, 44, 160, 22, 77, 144, 159, 87, 23, 167, 43, 42, 137, 166, 10, 79, 111, 36, 105, 25, 110, 38, 58, 104, 8, 112, 116, 103, 73, 9, 97, 57, 91, 123, 96, 59, 30, 90, 71, 98, 46, 89, 150, 2, 118, 64, 35, 102, 117, 129, 65, 125, 1, 84, 95, 124]];
cc:=[3,3,4];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=1;
gen_vect_label:=2;
full_auto:=[336,208];
full_sign:=[0,2,3,8];
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>);

// Here we add an action to data.
gen_vectors:=[[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], [11, 50, 90, 44, 103, 91, 3, 4, 22, 34, 16, 124, 35, 10, 25, 1, 41, 9, 159, 42, 17, 18, 57, 153, 65, 138, 154, 24, 116, 162, 13, 37, 47, 14, 31, 165, 113, 20, 30, 68, 21, 38, 53, 8, 132, 2, 145, 133, 45, 46, 64, 76, 58, 166, 77, 52, 67, 43, 83, 51, 117, 84, 59, 60, 15, 111, 23, 96, 112, 66, 158, 120, 55, 79, 5, 56, 73, 123, 155, 62, 72, 26, 63, 80, 95, 134, 6, 128, 19, 7, 87, 88, 106, 118, 100, 40, 119, 94, 109, 85, 125, 93, 75, 126, 101, 102, 141, 69, 149, 54, 70, 108, 32, 78, 97, 121, 131, 98, 115, 81, 29, 104, 114, 152, 105, 122, 137, 92, 48, 86, 61, 49, 129, 130, 148, 160, 142, 82, 161, 136, 151, 127, 167, 135, 33, 168, 143, 144, 99, 27, 107, 12, 28, 150, 74, 36, 139, 163, 89, 140, 157, 39, 71, 146, 156, 110, 147, 164], [15, 48, 105, 10, 74, 86, 89, 43, 20, 126, 3, 151, 30, 33, 64, 13, 161, 24, 88, 37, 40, 8, 69, 140, 17, 81, 149, 152, 120, 41, 49, 115, 144, 9, 12, 155, 34, 70, 164, 95, 16, 19, 57, 6, 147, 52, 32, 128, 131, 1, 62, 168, 45, 109, 72, 75, 22, 55, 119, 66, 130, 79, 82, 50, 27, 98, 59, 39, 107, 110, 162, 83, 7, 157, 102, 51, 54, 113, 76, 28, 122, 137, 58, 61, 99, 132, 21, 94, 158, 2, 5, 127, 104, 42, 87, 67, 114, 117, 148, 97, 77, 108, 4, 121, 124, 92, 153, 56, 101, 165, 65, 68, 36, 125, 133, 31, 60, 93, 96, 71, 118, 154, 80, 11, 100, 103, 141, 90, 63, 136, 116, 44, 47, 85, 146, 84, 129, 25, 156, 159, 106, 139, 35, 150, 46, 163, 166, 134, 111, 14, 143, 123, 23, 26, 78, 167, 91, 73, 18, 135, 138, 29, 160, 112, 38, 53, 142, 145]];
cc:=[3,3,4];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=1;
gen_vect_label:=3;
full_auto:=[336,208];
full_sign:=[0,2,3,8];
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>);

// Here we add an action to data.
gen_vectors:=[[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], [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], [83, 95, 150, 114, 140, 145, 36, 111, 116, 73, 93, 168, 159, 127, 132, 165, 80, 142, 119, 124, 106, 76, 144, 87, 163, 105, 96, 29, 139, 4, 59, 86, 28, 68, 99, 104, 25, 52, 149, 7, 47, 134, 41, 137, 108, 156, 98, 103, 78, 153, 158, 31, 135, 126, 117, 85, 90, 123, 38, 100, 161, 166, 148, 34, 102, 129, 121, 147, 138, 71, 97, 46, 17, 128, 70, 26, 141, 146, 67, 10, 107, 49, 5, 92, 167, 11, 66, 30, 56, 61, 120, 27, 32, 157, 9, 84, 75, 43, 48, 81, 164, 58, 35, 40, 22, 160, 60, 3, 79, 21, 12, 113, 55, 88, 143, 2, 112, 152, 15, 20, 109, 136, 65, 91, 131, 50, 125, 53, 24, 72, 14, 19, 162, 69, 74, 115, 51, 42, 33, 1, 6, 39, 122, 16, 77, 82, 64, 118, 18, 45, 37, 63, 54, 155, 13, 130, 101, 44, 154, 110, 57, 62, 151, 94, 23, 133, 89, 8]];
cc:=[3,3,4];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=1;
gen_vect_label:=4;
full_auto:=[336,208];
full_sign:=[0,2,3,8];
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>);
