
print "The Lie group G( 2, 4 ) represented as a permutation";
print "group of degree 416. ";
print "Order: 251 596 800 = 2^12 * 3^3 * 5^2 * 7 * 13.  ";
print "Base: 1,2,3,4,5,6,7. ";
print "Group: G";

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