// Magma code for the lmfdb family of higher genus curves 10.432-734.0.2-3-8.1
// 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:=[432,734];
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:=[0,2,3,8];
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:=[[217, 219, 218, 222, 221, 220, 224, 223, 225, 226, 228, 227, 231, 230, 229, 233, 232, 234, 280, 282, 281, 285, 284, 283, 287, 286, 288, 271, 273, 272, 276, 275, 274, 278, 277, 279, 262, 264, 263, 267, 266, 265, 269, 268, 270, 253, 255, 254, 258, 257, 256, 260, 259, 261, 244, 246, 245, 249, 248, 247, 251, 250, 252, 235, 237, 236, 240, 239, 238, 242, 241, 243, 361, 363, 362, 366, 365, 364, 368, 367, 369, 370, 372, 371, 375, 374, 373, 377, 376, 378, 424, 426, 425, 429, 428, 427, 431, 430, 432, 415, 417, 416, 420, 419, 418, 422, 421, 423, 406, 408, 407, 411, 410, 409, 413, 412, 414, 397, 399, 398, 402, 401, 400, 404, 403, 405, 388, 390, 389, 393, 392, 391, 395, 394, 396, 379, 381, 380, 384, 383, 382, 386, 385, 387, 289, 291, 290, 294, 293, 292, 296, 295, 297, 298, 300, 299, 303, 302, 301, 305, 304, 306, 352, 354, 353, 357, 356, 355, 359, 358, 360, 343, 345, 344, 348, 347, 346, 350, 349, 351, 334, 336, 335, 339, 338, 337, 341, 340, 342, 325, 327, 326, 330, 329, 328, 332, 331, 333, 316, 318, 317, 321, 320, 319, 323, 322, 324, 307, 309, 308, 312, 311, 310, 314, 313, 315, 1, 3, 2, 6, 5, 4, 8, 7, 9, 10, 12, 11, 15, 14, 13, 17, 16, 18, 64, 66, 65, 69, 68, 67, 71, 70, 72, 55, 57, 56, 60, 59, 58, 62, 61, 63, 46, 48, 47, 51, 50, 49, 53, 52, 54, 37, 39, 38, 42, 41, 40, 44, 43, 45, 28, 30, 29, 33, 32, 31, 35, 34, 36, 19, 21, 20, 24, 23, 22, 26, 25, 27, 145, 147, 146, 150, 149, 148, 152, 151, 153, 154, 156, 155, 159, 158, 157, 161, 160, 162, 208, 210, 209, 213, 212, 211, 215, 214, 216, 199, 201, 200, 204, 203, 202, 206, 205, 207, 190, 192, 191, 195, 194, 193, 197, 196, 198, 181, 183, 182, 186, 185, 184, 188, 187, 189, 172, 174, 173, 177, 176, 175, 179, 178, 180, 163, 165, 164, 168, 167, 166, 170, 169, 171, 73, 75, 74, 78, 77, 76, 80, 79, 81, 82, 84, 83, 87, 86, 85, 89, 88, 90, 136, 138, 137, 141, 140, 139, 143, 142, 144, 127, 129, 128, 132, 131, 130, 134, 133, 135, 118, 120, 119, 123, 122, 121, 125, 124, 126, 109, 111, 110, 114, 113, 112, 116, 115, 117, 100, 102, 101, 105, 104, 103, 107, 106, 108, 91, 93, 92, 96, 95, 94, 98, 97, 99], [115, 109, 112, 114, 117, 111, 110, 113, 116, 124, 118, 121, 123, 126, 120, 119, 122, 125, 97, 91, 94, 96, 99, 93, 92, 95, 98, 106, 100, 103, 105, 108, 102, 101, 104, 107, 133, 127, 130, 132, 135, 129, 128, 131, 134, 142, 136, 139, 141, 144, 138, 137, 140, 143, 79, 73, 76, 78, 81, 75, 74, 77, 80, 88, 82, 85, 87, 90, 84, 83, 86, 89, 187, 181, 184, 186, 189, 183, 182, 185, 188, 196, 190, 193, 195, 198, 192, 191, 194, 197, 169, 163, 166, 168, 171, 165, 164, 167, 170, 178, 172, 175, 177, 180, 174, 173, 176, 179, 205, 199, 202, 204, 207, 201, 200, 203, 206, 214, 208, 211, 213, 216, 210, 209, 212, 215, 151, 145, 148, 150, 153, 147, 146, 149, 152, 160, 154, 157, 159, 162, 156, 155, 158, 161, 43, 37, 40, 42, 45, 39, 38, 41, 44, 52, 46, 49, 51, 54, 48, 47, 50, 53, 25, 19, 22, 24, 27, 21, 20, 23, 26, 34, 28, 31, 33, 36, 30, 29, 32, 35, 61, 55, 58, 60, 63, 57, 56, 59, 62, 70, 64, 67, 69, 72, 66, 65, 68, 71, 7, 1, 4, 6, 9, 3, 2, 5, 8, 16, 10, 13, 15, 18, 12, 11, 14, 17, 331, 325, 328, 330, 333, 327, 326, 329, 332, 340, 334, 337, 339, 342, 336, 335, 338, 341, 313, 307, 310, 312, 315, 309, 308, 311, 314, 322, 316, 319, 321, 324, 318, 317, 320, 323, 349, 343, 346, 348, 351, 345, 344, 347, 350, 358, 352, 355, 357, 360, 354, 353, 356, 359, 295, 289, 292, 294, 297, 291, 290, 293, 296, 304, 298, 301, 303, 306, 300, 299, 302, 305, 403, 397, 400, 402, 405, 399, 398, 401, 404, 412, 406, 409, 411, 414, 408, 407, 410, 413, 385, 379, 382, 384, 387, 381, 380, 383, 386, 394, 388, 391, 393, 396, 390, 389, 392, 395, 421, 415, 418, 420, 423, 417, 416, 419, 422, 430, 424, 427, 429, 432, 426, 425, 428, 431, 367, 361, 364, 366, 369, 363, 362, 365, 368, 376, 370, 373, 375, 378, 372, 371, 374, 377, 259, 253, 256, 258, 261, 255, 254, 257, 260, 268, 262, 265, 267, 270, 264, 263, 266, 269, 241, 235, 238, 240, 243, 237, 236, 239, 242, 250, 244, 247, 249, 252, 246, 245, 248, 251, 277, 271, 274, 276, 279, 273, 272, 275, 278, 286, 280, 283, 285, 288, 282, 281, 284, 287, 223, 217, 220, 222, 225, 219, 218, 221, 224, 232, 226, 229, 231, 234, 228, 227, 230, 233], [318, 323, 319, 317, 322, 321, 316, 324, 320, 309, 314, 310, 308, 313, 312, 307, 315, 311, 354, 359, 355, 353, 358, 357, 352, 360, 356, 345, 350, 346, 344, 349, 348, 343, 351, 347, 291, 296, 292, 290, 295, 294, 289, 297, 293, 300, 305, 301, 299, 304, 303, 298, 306, 302, 336, 341, 337, 335, 340, 339, 334, 342, 338, 327, 332, 328, 326, 331, 330, 325, 333, 329, 246, 251, 247, 245, 250, 249, 244, 252, 248, 237, 242, 238, 236, 241, 240, 235, 243, 239, 282, 287, 283, 281, 286, 285, 280, 288, 284, 273, 278, 274, 272, 277, 276, 271, 279, 275, 219, 224, 220, 218, 223, 222, 217, 225, 221, 228, 233, 229, 227, 232, 231, 226, 234, 230, 264, 269, 265, 263, 268, 267, 262, 270, 266, 255, 260, 256, 254, 259, 258, 253, 261, 257, 390, 395, 391, 389, 394, 393, 388, 396, 392, 381, 386, 382, 380, 385, 384, 379, 387, 383, 426, 431, 427, 425, 430, 429, 424, 432, 428, 417, 422, 418, 416, 421, 420, 415, 423, 419, 363, 368, 364, 362, 367, 366, 361, 369, 365, 372, 377, 373, 371, 376, 375, 370, 378, 374, 408, 413, 409, 407, 412, 411, 406, 414, 410, 399, 404, 400, 398, 403, 402, 397, 405, 401, 102, 107, 103, 101, 106, 105, 100, 108, 104, 93, 98, 94, 92, 97, 96, 91, 99, 95, 138, 143, 139, 137, 142, 141, 136, 144, 140, 129, 134, 130, 128, 133, 132, 127, 135, 131, 75, 80, 76, 74, 79, 78, 73, 81, 77, 84, 89, 85, 83, 88, 87, 82, 90, 86, 120, 125, 121, 119, 124, 123, 118, 126, 122, 111, 116, 112, 110, 115, 114, 109, 117, 113, 30, 35, 31, 29, 34, 33, 28, 36, 32, 21, 26, 22, 20, 25, 24, 19, 27, 23, 66, 71, 67, 65, 70, 69, 64, 72, 68, 57, 62, 58, 56, 61, 60, 55, 63, 59, 3, 8, 4, 2, 7, 6, 1, 9, 5, 12, 17, 13, 11, 16, 15, 10, 18, 14, 48, 53, 49, 47, 52, 51, 46, 54, 50, 39, 44, 40, 38, 43, 42, 37, 45, 41, 174, 179, 175, 173, 178, 177, 172, 180, 176, 165, 170, 166, 164, 169, 168, 163, 171, 167, 210, 215, 211, 209, 214, 213, 208, 216, 212, 201, 206, 202, 200, 205, 204, 199, 207, 203, 147, 152, 148, 146, 151, 150, 145, 153, 149, 156, 161, 157, 155, 160, 159, 154, 162, 158, 192, 197, 193, 191, 196, 195, 190, 198, 194, 183, 188, 184, 182, 187, 186, 181, 189, 185]];
cc:=[3,6,10];
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 >);
