// Magma code for the lmfdb family of higher genus curves 15.294-7.0.2-3-14.1
// 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:=[294,7];
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:=[0,2,3,14];
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:=[[148, 155, 162, 169, 176, 183, 190, 149, 156, 163, 170, 177, 184, 191, 150, 157, 164, 171, 178, 185, 192, 151, 158, 165, 172, 179, 186, 193, 152, 159, 166, 173, 180, 187, 194, 153, 160, 167, 174, 181, 188, 195, 154, 161, 168, 175, 182, 189, 196, 246, 253, 260, 267, 274, 281, 288, 247, 254, 261, 268, 275, 282, 289, 248, 255, 262, 269, 276, 283, 290, 249, 256, 263, 270, 277, 284, 291, 250, 257, 264, 271, 278, 285, 292, 251, 258, 265, 272, 279, 286, 293, 252, 259, 266, 273, 280, 287, 294, 197, 204, 211, 218, 225, 232, 239, 198, 205, 212, 219, 226, 233, 240, 199, 206, 213, 220, 227, 234, 241, 200, 207, 214, 221, 228, 235, 242, 201, 208, 215, 222, 229, 236, 243, 202, 209, 216, 223, 230, 237, 244, 203, 210, 217, 224, 231, 238, 245, 1, 8, 15, 22, 29, 36, 43, 2, 9, 16, 23, 30, 37, 44, 3, 10, 17, 24, 31, 38, 45, 4, 11, 18, 25, 32, 39, 46, 5, 12, 19, 26, 33, 40, 47, 6, 13, 20, 27, 34, 41, 48, 7, 14, 21, 28, 35, 42, 49, 99, 106, 113, 120, 127, 134, 141, 100, 107, 114, 121, 128, 135, 142, 101, 108, 115, 122, 129, 136, 143, 102, 109, 116, 123, 130, 137, 144, 103, 110, 117, 124, 131, 138, 145, 104, 111, 118, 125, 132, 139, 146, 105, 112, 119, 126, 133, 140, 147, 50, 57, 64, 71, 78, 85, 92, 51, 58, 65, 72, 79, 86, 93, 52, 59, 66, 73, 80, 87, 94, 53, 60, 67, 74, 81, 88, 95, 54, 61, 68, 75, 82, 89, 96, 55, 62, 69, 76, 83, 90, 97, 56, 63, 70, 77, 84, 91, 98], [58, 62, 59, 63, 60, 57, 61, 72, 76, 73, 77, 74, 71, 75, 86, 90, 87, 91, 88, 85, 89, 51, 55, 52, 56, 53, 50, 54, 65, 69, 66, 70, 67, 64, 68, 79, 83, 80, 84, 81, 78, 82, 93, 97, 94, 98, 95, 92, 96, 107, 111, 108, 112, 109, 106, 110, 121, 125, 122, 126, 123, 120, 124, 135, 139, 136, 140, 137, 134, 138, 100, 104, 101, 105, 102, 99, 103, 114, 118, 115, 119, 116, 113, 117, 128, 132, 129, 133, 130, 127, 131, 142, 146, 143, 147, 144, 141, 145, 9, 13, 10, 14, 11, 8, 12, 23, 27, 24, 28, 25, 22, 26, 37, 41, 38, 42, 39, 36, 40, 2, 6, 3, 7, 4, 1, 5, 16, 20, 17, 21, 18, 15, 19, 30, 34, 31, 35, 32, 29, 33, 44, 48, 45, 49, 46, 43, 47, 205, 209, 206, 210, 207, 204, 208, 219, 223, 220, 224, 221, 218, 222, 233, 237, 234, 238, 235, 232, 236, 198, 202, 199, 203, 200, 197, 201, 212, 216, 213, 217, 214, 211, 215, 226, 230, 227, 231, 228, 225, 229, 240, 244, 241, 245, 242, 239, 243, 254, 258, 255, 259, 256, 253, 257, 268, 272, 269, 273, 270, 267, 271, 282, 286, 283, 287, 284, 281, 285, 247, 251, 248, 252, 249, 246, 250, 261, 265, 262, 266, 263, 260, 264, 275, 279, 276, 280, 277, 274, 278, 289, 293, 290, 294, 291, 288, 292, 156, 160, 157, 161, 158, 155, 159, 170, 174, 171, 175, 172, 169, 173, 184, 188, 185, 189, 186, 183, 187, 149, 153, 150, 154, 151, 148, 152, 163, 167, 164, 168, 165, 162, 166, 177, 181, 178, 182, 179, 176, 180, 191, 195, 192, 196, 193, 190, 194], [235, 200, 214, 228, 242, 207, 221, 232, 197, 211, 225, 239, 204, 218, 236, 201, 215, 229, 243, 208, 222, 233, 198, 212, 226, 240, 205, 219, 237, 202, 216, 230, 244, 209, 223, 234, 199, 213, 227, 241, 206, 220, 238, 203, 217, 231, 245, 210, 224, 186, 151, 165, 179, 193, 158, 172, 183, 148, 162, 176, 190, 155, 169, 187, 152, 166, 180, 194, 159, 173, 184, 149, 163, 177, 191, 156, 170, 188, 153, 167, 181, 195, 160, 174, 185, 150, 164, 178, 192, 157, 171, 189, 154, 168, 182, 196, 161, 175, 284, 249, 263, 277, 291, 256, 270, 281, 246, 260, 274, 288, 253, 267, 285, 250, 264, 278, 292, 257, 271, 282, 247, 261, 275, 289, 254, 268, 286, 251, 265, 279, 293, 258, 272, 283, 248, 262, 276, 290, 255, 269, 287, 252, 266, 280, 294, 259, 273, 88, 53, 67, 81, 95, 60, 74, 85, 50, 64, 78, 92, 57, 71, 89, 54, 68, 82, 96, 61, 75, 86, 51, 65, 79, 93, 58, 72, 90, 55, 69, 83, 97, 62, 76, 87, 52, 66, 80, 94, 59, 73, 91, 56, 70, 84, 98, 63, 77, 39, 4, 18, 32, 46, 11, 25, 36, 1, 15, 29, 43, 8, 22, 40, 5, 19, 33, 47, 12, 26, 37, 2, 16, 30, 44, 9, 23, 41, 6, 20, 34, 48, 13, 27, 38, 3, 17, 31, 45, 10, 24, 42, 7, 21, 35, 49, 14, 28, 137, 102, 116, 130, 144, 109, 123, 134, 99, 113, 127, 141, 106, 120, 138, 103, 117, 131, 145, 110, 124, 135, 100, 114, 128, 142, 107, 121, 139, 104, 118, 132, 146, 111, 125, 136, 101, 115, 129, 143, 108, 122, 140, 105, 119, 133, 147, 112, 126]];
cc:=[2,3,15];
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 >);
