G:=PermutationGroup<660 | \[ 2, 1, 5, 7, 3, 10, 4, 13, 15, 6, 18, 19, 8, 22, 9, 24, 26, 11, 12, 30, 32, 14, 35, 16, 38, 17, 40, 42, 44, 20, 47, 21, 49, 51, 23, 54, 56, 25, 59, 27, 62, 28, 63, 29, 66, 68, 31, 71, 33, 74, 34, 75, 77, 36, 80, 37, 82, 58, 39, 86, 88, 41, 43, 91, 92, 45, 95, 46, 97, 70, 48, 101, 103, 50, 52, 106, 53, 108, 110, 55, 113, 57, 116, 117, 119, 60, 87, 61, 123, 125, 64, 65, 128, 130, 67, 133, 69, 136, 137, 139, 72, 102, 73, 143, 145, 76, 147, 78, 109, 79, 151, 153, 81, 156, 158, 83, 84, 161, 85, 163, 155, 165, 89, 168, 90, 171, 173, 93, 129, 94, 177, 179, 96, 182, 184, 98, 99, 187, 100, 189, 181, 191, 104, 194, 105, 197, 107, 200, 202, 204, 111, 152, 112, 208, 121, 114, 211, 115, 213, 215, 118, 217, 120, 216, 122, 221, 223, 124, 225, 226, 126, 172, 127, 230, 232, 234, 131, 178, 132, 238, 141, 134, 241, 135, 243, 245, 138, 247, 140, 246, 142, 251, 253, 144, 255, 256, 146, 198, 259, 148, 262, 149, 264, 150, 249, 268, 269, 154, 263, 272, 157, 242, 159, 277, 160, 164, 162, 282, 235, 284, 166, 286, 167, 288, 169, 170, 292, 293, 294, 174, 297, 175, 299, 176, 219, 303, 304, 180, 298, 307, 183, 212, 185, 311, 186, 190, 188, 316, 205, 318, 192, 276, 193, 321, 195, 196, 325, 326, 199, 328, 330, 201, 209, 203, 334, 335, 337, 206, 207, 289, 340, 210, 342, 344, 333, 252, 214, 349, 350, 352, 354, 218, 357, 220, 359, 222, 287, 224, 270, 323, 364, 227, 228, 229, 368, 370, 231, 239, 233, 374, 375, 377, 236, 237, 322, 380, 240, 382, 384, 373, 244, 388, 389, 391, 393, 248, 396, 250, 398, 320, 254, 305, 290, 402, 257, 258, 405, 260, 408, 261, 410, 372, 275, 265, 266, 415, 267, 338, 339, 271, 419, 273, 421, 274, 403, 424, 361, 426, 278, 279, 429, 280, 431, 281, 433, 435, 283, 438, 285, 399, 347, 442, 423, 291, 385, 446, 447, 295, 449, 296, 451, 332, 310, 300, 301, 407, 302, 378, 379, 306, 458, 308, 460, 309, 365, 463, 464, 312, 313, 467, 314, 469, 315, 471, 473, 317, 476, 319, 360, 479, 462, 324, 345, 418, 327, 406, 376, 329, 484, 331, 487, 489, 490, 491, 336, 494, 495, 404, 341, 459, 343, 422, 363, 346, 425, 348, 502, 503, 351, 468, 353, 506, 355, 508, 356, 509, 437, 358, 513, 515, 441, 362, 481, 480, 517, 366, 367, 448, 369, 512, 371, 522, 518, 524, 525, 527, 528, 381, 420, 383, 461, 401, 386, 387, 534, 535, 390, 430, 392, 538, 394, 540, 395, 541, 475, 397, 544, 546, 400, 444, 443, 548, 549, 409, 519, 552, 411, 555, 412, 413, 414, 500, 558, 416, 417, 562, 520, 564, 499, 492, 568, 427, 428, 571, 573, 432, 574, 434, 436, 577, 578, 450, 439, 581, 440, 584, 445, 453, 485, 497, 587, 452, 560, 454, 455, 532, 456, 457, 593, 583, 531, 526, 598, 465, 466, 601, 603, 470, 604, 472, 474, 607, 608, 477, 611, 478, 613, 482, 483, 615, 563, 486, 617, 616, 488, 620, 610, 493, 621, 523, 592, 496, 551, 498, 624, 596, 626, 501, 628, 575, 504, 630, 505, 507, 570, 622, 510, 511, 631, 591, 514, 612, 530, 516, 633, 594, 521, 635, 634, 637, 580, 561, 529, 586, 638, 566, 640, 533, 642, 605, 536, 623, 537, 539, 600, 619, 542, 543, 644, 557, 545, 582, 547, 646, 550, 554, 553, 618, 606, 556, 559, 576, 602, 565, 649, 567, 632, 569, 652, 572, 579, 627, 585, 589, 588, 636, 590, 595, 651, 597, 645, 599, 653, 609, 641, 614, 650, 655, 625, 647, 639, 629, 643, 658, 648, 659, 660, 654, 656, 657 ], \[ 3, 4, 6, 8, 9, 11, 12, 14, 16, 17, 1, 20, 21, 2, 23, 25, 27, 28, 29, 31, 33, 34, 36, 37, 5, 39, 41, 43, 45, 46, 7, 48, 50, 52, 53, 55, 57, 58, 60, 61, 10, 51, 64, 65, 67, 69, 70, 72, 73, 13, 42, 76, 78, 79, 15, 81, 83, 84, 85, 87, 49, 89, 90, 18, 93, 94, 19, 96, 98, 99, 100, 102, 40, 104, 105, 22, 107, 109, 111, 112, 114, 115, 24, 118, 120, 121, 26, 122, 124, 82, 126, 127, 129, 131, 132, 134, 135, 30, 138, 140, 141, 32, 142, 144, 97, 146, 148, 149, 35, 150, 152, 154, 155, 157, 63, 159, 160, 38, 162, 164, 153, 166, 167, 169, 170, 172, 174, 175, 44, 176, 178, 180, 181, 183, 75, 185, 186, 47, 188, 190, 179, 192, 193, 195, 196, 198, 199, 201, 203, 205, 206, 54, 207, 168, 209, 210, 56, 212, 214, 151, 216, 218, 219, 59, 220, 222, 224, 80, 62, 223, 227, 228, 229, 231, 233, 235, 236, 66, 237, 194, 239, 240, 68, 242, 244, 177, 246, 248, 249, 71, 250, 252, 254, 95, 74, 253, 257, 258, 260, 261, 77, 263, 265, 266, 267, 117, 86, 270, 271, 273, 274, 275, 276, 278, 279, 280, 281, 283, 163, 165, 285, 88, 287, 289, 290, 291, 268, 91, 295, 296, 92, 298, 300, 301, 302, 137, 101, 305, 306, 308, 309, 310, 286, 312, 313, 314, 315, 317, 189, 191, 319, 103, 320, 322, 323, 324, 303, 106, 327, 329, 200, 331, 332, 333, 108, 336, 110, 338, 339, 264, 113, 341, 343, 345, 346, 347, 348, 116, 351, 353, 355, 356, 119, 358, 360, 361, 125, 362, 123, 363, 318, 365, 366, 367, 369, 230, 371, 372, 373, 128, 376, 130, 378, 379, 299, 133, 381, 383, 385, 386, 387, 136, 390, 392, 394, 395, 139, 397, 399, 145, 400, 143, 401, 284, 403, 404, 406, 407, 147, 409, 411, 412, 208, 413, 414, 416, 417, 171, 418, 259, 307, 420, 156, 422, 423, 158, 425, 342, 427, 428, 430, 352, 161, 432, 434, 436, 437, 256, 439, 440, 441, 344, 443, 444, 445, 429, 448, 415, 173, 450, 452, 453, 238, 454, 455, 456, 457, 197, 446, 294, 272, 459, 182, 461, 462, 184, 382, 465, 466, 468, 391, 187, 470, 472, 474, 475, 226, 477, 478, 384, 480, 481, 482, 467, 326, 340, 483, 408, 485, 486, 488, 202, 374, 492, 493, 204, 496, 497, 498, 277, 499, 288, 211, 500, 213, 501, 388, 504, 447, 215, 505, 476, 507, 217, 487, 510, 511, 512, 514, 221, 243, 375, 225, 516, 518, 519, 293, 380, 449, 520, 521, 523, 232, 334, 526, 234, 529, 530, 311, 531, 321, 241, 532, 533, 349, 536, 405, 245, 537, 438, 539, 247, 522, 542, 543, 484, 545, 251, 335, 255, 547, 489, 550, 354, 551, 553, 554, 262, 325, 556, 557, 479, 559, 560, 561, 563, 269, 565, 566, 567, 569, 471, 570, 572, 509, 431, 575, 576, 506, 282, 579, 393, 580, 582, 583, 585, 548, 292, 304, 586, 588, 589, 297, 590, 591, 442, 555, 592, 594, 595, 596, 597, 599, 433, 600, 602, 541, 469, 605, 606, 538, 316, 609, 610, 612, 564, 614, 517, 435, 328, 330, 616, 618, 549, 619, 513, 491, 473, 368, 622, 573, 604, 337, 623, 625, 620, 627, 587, 629, 581, 628, 350, 624, 615, 534, 584, 631, 503, 357, 490, 578, 359, 630, 632, 364, 370, 634, 636, 558, 544, 525, 603, 574, 377, 639, 637, 641, 552, 643, 611, 642, 389, 638, 621, 502, 613, 644, 535, 396, 524, 608, 398, 645, 402, 647, 648, 546, 410, 649, 421, 650, 651, 617, 495, 419, 633, 424, 601, 426, 635, 653, 508, 640, 654, 515, 451, 460, 528, 458, 646, 463, 571, 464, 652, 540, 626, 593, 598, 527, 562, 494, 656, 657, 568, 658, 607, 577, 655, 660, 659 ] /* order = 887040 = 2^8 * 3^2 * 5 * 7 * 11 */ >; /////////////////////////////////////////////////////////////////////////// gens:=[ Matrix(GF(3),56,56,[ 0, 0, 0, 1, 1, 1, 1, 0, 0, 2, 0, 2, 1, 0, 1, 2, 2, 2, 0, 1, 1, 2, 2, 0, 1, 0, 1, 0, 0, 1, 2, 2, 1, 1, 2, 0, 2, 1, 0, 1, 1, 2, 1, 1, 0, 1, 1, 2, 0, 1, 1, 2, 0, 2, 2, 0, 2, 0, 2, 1, 1, 1, 2, 2, 0, 0, 2, 2, 0, 2, 0, 0, 2, 2, 2, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 2, 1, 2, 0, 1, 2, 1, 2, 1, 2, 0, 1, 0, 2, 2, 2, 1, 1, 2, 0, 2, 1, 2, 2, 1, 0, 0, 2, 1, 2, 0, 1, 2, 1, 2, 1, 0, 1, 0, 2, 1, 2, 1, 0, 0, 1, 0, 2, 0, 1, 0, 2, 0, 1, 2, 1, 0, 0, 1, 2, 2, 2, 2, 0, 2, 1, 2, 2, 1, 1, 1, 0, 0, 2, 0, 1, 0, 2, 2, 0, 2, 2, 2, 2, 2, 0, 1, 2, 0, 1, 1, 1, 1, 1, 0, 2, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 1, 2, 0, 1, 1, 2, 2, 0, 2, 2, 2, 1, 1, 1, 1, 1, 0, 0, 2, 0, 0, 0, 0, 2, 2, 1, 0, 2, 0, 2, 0, 1, 2, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 2, 0, 2, 1, 2, 1, 1, 0, 0, 1, 2, 0, 0, 2, 2, 1, 0, 2, 1, 1, 1, 0, 1, 1, 0, 2, 0, 2, 1, 0, 1, 2, 0, 2, 1, 1, 1, 1, 2, 1, 1, 2, 2, 2, 1, 1, 2, 0, 1, 2, 2, 2, 0, 1, 0, 1, 1, 2, 1, 2, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 2, 0, 2, 0, 1, 0, 2, 0, 0, 1, 2, 0, 2, 2, 1, 2, 0, 1, 0, 2, 0, 2, 2, 0, 0, 2, 0, 2, 2, 1, 0, 0, 2, 1, 1, 1, 0, 0, 1, 0, 1, 1, 2, 0, 1, 0, 2, 2, 2, 1, 1, 2, 2, 0, 0, 1, 1, 0, 2, 2, 2, 2, 0, 1, 1, 0, 1, 1, 2, 0, 1, 1, 0, 1, 0, 1, 2, 0, 1, 2, 1, 2, 0, 2, 1, 0, 0, 1, 1, 2, 1, 2, 2, 2, 0, 0, 0, 2, 2, 1, 0, 0, 1, 0, 0, 1, 2, 2, 1, 2, 2, 2, 2, 1, 0, 1, 0, 2, 1, 0, 0, 2, 0, 1, 1, 2, 0, 1, 0, 0, 1, 2, 2, 1, 2, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 2, 0, 2, 0, 2, 1, 1, 2, 1, 0, 0, 0, 1, 1, 2, 0, 0, 0, 2, 1, 0, 2, 0, 2, 0, 2, 0, 2, 1, 2, 2, 2, 2, 0, 1, 1, 1, 2, 0, 0, 0, 1, 0, 2, 2, 1, 1, 1, 2, 0, 2, 0, 2, 2, 1, 0, 0, 0, 0, 2, 1, 2, 2, 0, 1, 0, 2, 2, 2, 1, 0, 1, 1, 2, 0, 0, 0, 0, 1, 0, 2, 0, 1, 1, 1, 2, 2, 2, 2, 2, 2, 1, 1, 0, 2, 0, 0, 2, 1, 2, 0, 2, 2, 1, 2, 2, 1, 2, 2, 2, 0, 1, 0, 1, 2, 2, 1, 0, 1, 2, 2, 2, 1, 1, 1, 1, 0, 1, 2, 0, 2, 0, 0, 2, 2, 1, 2, 0, 1, 1, 1, 0, 2, 0, 1, 1, 0, 0, 1, 1, 0, 2, 1, 0, 1, 2, 2, 1, 0, 0, 0, 2, 0, 0, 0, 1, 2, 2, 1, 0, 0, 0, 2, 2, 2, 2, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 1, 1, 1, 2, 0, 1, 1, 2, 1, 2, 1, 0, 0, 0, 1, 1, 2, 1, 1, 2, 0, 1, 1, 0, 1, 1, 1, 2, 1, 1, 0, 0, 2, 2, 2, 2, 0, 0, 2, 2, 0, 1, 0, 2, 0, 0, 0, 2, 0, 1, 1, 2, 2, 1, 2, 2, 2, 0, 1, 2, 1, 0, 1, 1, 2, 2, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 2, 0, 1, 2, 1, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 0, 1, 0, 2, 2, 2, 0, 0, 1, 1, 2, 1, 2, 1, 1, 1, 0, 1, 2, 0, 1, 1, 2, 1, 0, 1, 0, 0, 2, 1, 2, 0, 1, 2, 0, 2, 2, 2, 1, 1, 1, 0, 1, 1, 2, 0, 1, 0, 1, 2, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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2, 1, 0, 1, 2, 1, 1, 1, 0, 1, 1, 0, 2, 0, 0, 0, 1, 2, 0, 2, 0, 2, 1, 0, 0, 2, 2, 1, 1, 1, 2, 2, 1, 2, 0, 2, 1, 2, 2, 2, 1, 2, 2, 1, 2, 0, 1, 2, 1, 1, 0, 2, 2, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 1, 1, 1, 1, 0, 1, 2, 1, 0, 0, 2, 1, 0, 2, 2, 1, 1, 0, 2, 0, 2, 0, 0, 2, 0, 2, 2, 2, 0, 2, 1, 0, 1, 0, 2, 2, 0, 2, 1, 2, 0, 2, 1, 1, 1, 0, 2, 2, 1, 2, 1, 0, 1, 1, 2, 0, 0, 2, 2, 0, 0, 2, 1, 0, 1, 2, 2, 2, 1, 2, 2, 2, 0, 2, 0, 1, 1, 2, 0, 1, 0, 0, 2, 1, 2, 1, 2, 0, 2, 1, 2, 1, 0, 0, 0, 2, 1, 2, 2, 1, 1, 1, 2, 2, 2, 0, 1, 1, 0, 1, 2, 2, 2, 0, 2, 2, 2, 2, 0, 2, 2, 1, 2, 2, 1, 1, 0, 0, 2, 2, 1, 1, 0, 0, 1, 2, 1, 2, 2, 0, 1, 2, 0, 2, 2, 2, 1, 2, 2, 2, 2, 1, 1, 1, 0, 2, 0, 0, 0, 0, 2, 2, 2, 1, 0, 2, 0, 1, 0, 1, 1, 1, 1, 0, 2, 1, 1, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 1, 2, 0, 0, 2, 2, 1, 2, 0, 2, 0, 0, 2, 0, 0, 1, 2, 2, 2, 2, 2, 1, 0, 2, 2, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 2, 2, 0, 1, 2, 2, 2, 1, 1, 2, 0, 2, 1, 0, 0, 1, 2, 1, 1, 2, 2, 2, 2, 0, 2, 1, 0, 2, 2, 0, 1, 0, 0, 0, 1, 1, 0, 2, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 2, 2, 2, 1, 1, 2, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 0, 1, 2, 1, 0, 0, 0, 0, 1, 0, 1, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 1, 1, 0, 0, 0, 2, 1, 2, 0, 2, 2, 0, 2, 1, 0, 1, 1, 2, 1, 0, 0, 0, 1, 1, 2, 1, 0, 2, 0, 0, 1, 0, 2, 1, 0, 2, 1, 0, 1, 2, 2, 2, 2, 0, 2, 2, 2, 2, 0, 0, 0, 2, 2, 0, 2, 2, 2, 2, 0, 2, 2, 2, 1, 2, 0, 0, 1, 0, 1, 0, 2, 1, 1, 1, 0, 2, 0, 0, 1, 0, 1, 0, 1, 2, 0, 1, 1, 1, 2 ]) ]; D56:=GModule(G,gens); print("the simple 2.M22-module D56 over GF(3); a permutation representation of 2.M22 on 660 points");