Graph forms
for C4 [ 506, 11 ] = AT[506,3]
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On this page are computer-accessible forms for the graph C4[ 506, 11 ] =
AT[506,3].
(I) Following is a form readable by MAGMA:
g:=Graph<506|{ {200, 201}, {404, 405}, {398, 399}, {1, 3}, {385, 387}, {260,
262}, {293, 295}, {1, 2}, {356, 359}, {328, 331}, {317, 318}, {133, 134}, {45,
46}, {1, 5}, {417, 421}, {2, 6}, {1, 4}, {488, 493}, {2, 7}, {49, 55}, {473,
479}, {386, 388}, {251, 252}, {3, 11}, {448, 456}, {4, 12}, {452, 461}, {486,
495}, {2, 8}, {466, 472}, {437, 447}, {5, 15}, {4, 14}, {3, 9}, {179, 185},
{193, 203}, {273, 282}, {177, 189}, {480, 492}, {464, 476}, {257, 269}, {166,
171}, {353, 364}, {3, 13}, {471, 473}, {470, 472}, {468, 474}, {420, 426}, {4,
10}, {294, 296}, {407, 408}, {6, 22}, {485, 501}, {394, 410}, {10, 26}, {9, 25},
{8, 24}, {7, 23}, {6, 20}, {12, 30}, {7, 21}, {8, 27}, {335, 348}, {262, 277},
{5, 17}, {8, 28}, {7, 19}, {360, 381}, {6, 16}, {484, 498}, {330, 348}, {11,
29}, {9, 31}, {256, 278}, {258, 276}, {5, 18}, {393, 414}, {494, 503}, {194,
216}, {299, 305}, {258, 281}, {362, 369}, {333, 342}, {361, 373}, {416, 445},
{330, 341}, {363, 372}, {324, 356}, {459, 491}, {141, 172}, {475, 506}, {460,
493}, {452, 485}, {13, 47}, {474, 504}, {335, 365}, {92, 126}, {17, 50}, {453,
486}, {21, 54}, {156, 191}, {14, 42}, {468, 496}, {340, 368}, {195, 230}, {450,
487}, {14, 40}, {395, 429}, {323, 357}, {18, 52}, {15, 41}, {16, 55}, {451,
484}, {448, 487}, {20, 51}, {17, 57}, {21, 61}, {268, 292}, {18, 59}, {336,
377}, {9, 35}, {451, 489}, {384, 426}, {13, 39}, {12, 38}, {11, 33}, {10, 32},
{19, 56}, {19, 63}, {453, 489}, {406, 442}, {452, 489}, {10, 36}, {20, 58}, {16,
62}, {12, 34}, {11, 37}, {77, 125}, {401, 417}, {82, 98}, {266, 314}, {386,
435}, {69, 119}, {331, 377}, {322, 368}, {286, 300}, {15, 60}, {455, 500}, {76,
121}, {396, 441}, {207, 249}, {285, 299}, {396, 436}, {458, 498}, {449, 505},
{15, 53}, {198, 252}, {16, 43}, {156, 167}, {197, 254}, {199, 251}, {13, 48},
{19, 46}, {17, 44}, {463, 497}, {14, 49}, {338, 365}, {151, 168}, {18, 45}, {28,
92}, {439, 503}, {438, 502}, {138, 202}, {437, 500}, {27, 89}, {32, 100}, {51,
119}, {40, 108}, {35, 103}, {34, 102}, {33, 101}, {24, 93}, {430, 491}, {409,
476}, {31, 90}, {290, 359}, {30, 88}, {447, 505}, {317, 379}, {48, 118}, {41,
111}, {174, 232}, {37, 109}, {434, 506}, {44, 100}, {38, 110}, {263, 334}, {441,
496}, {29, 87}, {132, 206}, {24, 83}, {53, 126}, {174, 229}, {36, 104}, {304,
380}, {39, 107}, {38, 106}, {37, 105}, {53, 120}, {424, 485}, {150, 219}, {28,
82}, {49, 127}, {176, 254}, {25, 86}, {440, 503}, {54, 121}, {31, 80}, {301,
381}, {438, 486}, {31, 78}, {446, 495}, {425, 504}, {23, 69}, {395, 473}, {313,
363}, {165, 247}, {26, 73}, {415, 460}, {27, 72}, {191, 236}, {20, 64}, {27,
79}, {23, 67}, {22, 66}, {21, 65}, {191, 235}, {28, 73}, {403, 454}, {145, 196},
{128, 213}, {30, 75}, {303, 378}, {187, 237}, {301, 379}, {29, 74}, {412, 459},
{140, 212}, {429, 501}, {394, 466}, {388, 476}, {23, 78}, {431, 502}, {424,
497}, {388, 477}, {36, 125}, {35, 122}, {22, 76}, {413, 455}, {131, 217}, {47,
117}, {46, 116}, {43, 113}, {42, 112}, {160, 250}, {22, 77}, {389, 478}, {292,
383}, {24, 68}, {435, 495}, {26, 71}, {38, 120}, {397, 467}, {396, 466}, {45,
115}, {44, 114}, {25, 70}, {41, 118}, {36, 123}, {35, 124}, {42, 74}, {141,
237}, {182, 215}, {409, 504}, {305, 336}, {183, 214}, {52, 86}, {394, 488}, {58,
88}, {54, 84}, {56, 91}, {173, 206}, {47, 75}, {315, 351}, {161, 197}, {284,
376}, {299, 335}, {37, 64}, {423, 450}, {405, 496}, {389, 480}, {182, 211},
{412, 506}, {414, 504}, {157, 250}, {404, 499}, {158, 249}, {159, 248}, {184,
208}, {445, 469}, {386, 490}, {318, 342}, {170, 195}, {424, 449}, {268, 358},
{425, 450}, {283, 375}, {434, 478}, {413, 497}, {261, 362}, {433, 478}, {432,
479}, {259, 371}, {291, 339}, {292, 340}, {32, 81}, {163, 210}, {139, 249},
{401, 483}, {400, 482}, {385, 499}, {266, 376}, {260, 375}, {430, 477}, {402,
481}, {289, 341}, {446, 458}, {415, 491}, {33, 84}, {281, 367}, {447, 457},
{438, 448}, {34, 85}, {418, 469}, {387, 500}, {411, 483}, {431, 471}, {25, 96},
{155, 226}, {286, 359}, {287, 357}, {26, 97}, {428, 471}, {32, 91}, {30, 99},
{392, 501}, {50, 79}, {34, 95}, {29, 98}, {393, 502}, {33, 94}, {80, 208}, {86,
214}, {81, 209}, {62, 191}, {340, 470}, {351, 477}, {92, 223}, {355, 480}, {325,
454}, {372, 496}, {373, 497}, {89, 220}, {102, 227}, {91, 222}, {121, 255},
{350, 472}, {345, 479}, {83, 212}, {90, 221}, {70, 206}, {367, 487}, {303, 423},
{71, 207}, {298, 418}, {312, 433}, {66, 200}, {325, 463}, {67, 201}, {285, 407},
{79, 196}, {370, 505}, {78, 194}, {382, 498}, {123, 247}, {46, 160}, {364, 482},
{308, 443}, {365, 482}, {104, 248}, {105, 249}, {268, 412}, {87, 198}, {355,
498}, {349, 460}, {94, 204}, {318, 428}, {311, 421}, {109, 255}, {108, 254},
{101, 247}, {100, 246}, {95, 205}, {89, 202}, {97, 242}, {96, 243}, {77, 217},
{346, 462}, {285, 393}, {297, 445}, {86, 195}, {354, 503}, {344, 461}, {62,
168}, {327, 465}, {304, 422}, {107, 253}, {99, 245}, {98, 244}, {93, 203}, {69,
211}, {63, 169}, {54, 161}, {366, 505}, {82, 197}, {79, 216}, {263, 400}, {66,
218}, {328, 464}, {323, 475}, {67, 219}, {122, 227}, {265, 400}, {56, 162},
{361, 499}, {325, 479}, {324, 478}, {102, 252}, {61, 167}, {60, 166}, {57, 163},
{78, 213}, {353, 506}, {328, 467}, {320, 475}, {106, 241}, {112, 236}, {295,
443}, {321, 476}, {363, 502}, {58, 164}, {369, 495}, {117, 235}, {101, 251},
{100, 250}, {76, 210}, {73, 215}, {59, 165}, {88, 199}, {362, 501}, {322, 477},
{316, 419}, {315, 420}, {43, 139}, {366, 462}, {303, 399}, {51, 147}, {50, 146},
{49, 144}, {378, 475}, {333, 492}, {307, 402}, {39, 133}, {71, 229}, {70, 228},
{59, 153}, {58, 152}, {47, 141}, {298, 392}, {75, 232}, {291, 384}, {42, 142},
{48, 148}, {284, 440}, {329, 492}, {55, 145}, {332, 490}, {327, 481}, {326,
480}, {61, 155}, {60, 154}, {52, 147}, {381, 474}, {308, 403}, {68, 227}, {300,
390}, {350, 500}, {345, 499}, {322, 488}, {302, 389}, {92, 240}, {95, 243}, {94,
242}, {93, 241}, {283, 439}, {74, 231}, {40, 134}, {323, 493}, {72, 230}, {57,
151}, {127, 207}, {337, 481}, {289, 401}, {39, 149}, {45, 159}, {44, 158}, {269,
447}, {50, 129}, {59, 136}, {48, 132}, {375, 451}, {346, 494}, {91, 239}, {90,
238}, {89, 237}, {88, 236}, {290, 406}, {41, 156}, {347, 494}, {60, 137}, {267,
446}, {43, 157}, {371, 453}, {52, 130}, {55, 128}, {374, 449}, {305, 390}, {61,
138}, {310, 398}, {107, 210}, {343, 494}, {284, 421}, {53, 143}, {309, 399},
{56, 131}, {337, 490}, {103, 220}, {63, 132}, {87, 235}, {261, 441}, {84, 233},
{304, 397}, {95, 226}, {93, 224}, {40, 150}, {57, 135}, {51, 140}, {338, 493},
{94, 225}, {85, 234}, {80, 144}, {346, 411}, {113, 178}, {383, 444}, {334, 397},
{81, 148}, {123, 190}, {378, 444}, {106, 173}, {122, 189}, {108, 171}, {275,
468}, {294, 481}, {256, 456}, {262, 462}, {339, 410}, {287, 469}, {364, 422},
{296, 483}, {368, 443}, {360, 419}, {257, 461}, {270, 448}, {349, 403}, {329,
390}, {343, 408}, {316, 492}, {314, 491}, {85, 135}, {279, 452}, {353, 437},
{110, 187}, {306, 487}, {276, 449}, {278, 451}, {109, 186}, {277, 450}, {87,
143}, {82, 139}, {331, 402}, {286, 455}, {83, 136}, {90, 129}, {319, 483}, {352,
444}, {280, 453}, {380, 417}, {326, 411}, {311, 490}, {283, 454}, {314, 484},
{344, 440}, {99, 130}, {341, 436}, {321, 416}, {300, 461}, {302, 463}, {334,
428}, {296, 459}, {301, 462}, {309, 465}, {297, 460}, {358, 387}, {319, 474},
{307, 470}, {310, 464}, {332, 427}, {266, 482}, {383, 407}, {360, 384}, {330,
418}, {84, 189}, {339, 442}, {64, 170}, {324, 430}, {320, 426}, {81, 187}, {80,
186}, {72, 162}, {65, 171}, {271, 485}, {85, 190}, {348, 439}, {326, 429}, {317,
470}, {127, 146}, {293, 456}, {295, 458}, {64, 174}, {321, 431}, {67, 173}, {66,
172}, {65, 175}, {83, 188}, {294, 457}, {343, 422}, {377, 395}, {68, 176}, {77,
185}, {76, 184}, {71, 179}, {70, 178}, {69, 177}, {124, 137}, {288, 469}, {274,
484}, {382, 392}, {313, 463}, {293, 467}, {273, 486}, {344, 416}, {272, 489},
{366, 404}, {367, 405}, {338, 425}, {72, 180}, {379, 391}, {347, 423}, {75,
183}, {74, 182}, {73, 181}, {65, 188}, {380, 385}, {342, 427}, {68, 185}, {312,
454}, {62, 193}, {347, 420}, {63, 192}, {302, 465}, {186, 424}, {187, 425},
{179, 423}, {177, 422}, {246, 488}, {111, 333}, {115, 337}, {114, 336}, {244,
471}, {119, 338}, {238, 456}, {239, 457}, {183, 400}, {168, 385}, {170, 387},
{169, 386}, {245, 472}, {247, 473}, {171, 388}, {169, 408}, {227, 466}, {170,
409}, {231, 468}, {230, 467}, {255, 457}, {242, 458}, {243, 459}, {233, 464},
{234, 465}, {112, 334}, {113, 335}, {168, 407}, {248, 455}, {116, 309}, {125,
316}, {120, 313}, {103, 293}, {106, 296}, {197, 384}, {203, 398}, {248, 445},
{116, 306}, {117, 307}, {223, 409}, {124, 315}, {216, 415}, {246, 446}, {211,
410}, {213, 412}, {215, 414}, {205, 391}, {241, 443}, {214, 413}, {244, 441},
{104, 294}, {105, 295}, {229, 427}, {242, 444}, {244, 442}, {212, 411}, {225,
432}, {229, 436}, {219, 392}, {223, 396}, {240, 419}, {228, 432}, {211, 390},
{220, 393}, {222, 395}, {231, 434}, {239, 442}, {104, 318}, {105, 319}, {199,
401}, {226, 436}, {193, 406}, {210, 389}, {221, 394}, {230, 433}, {239, 440},
{109, 309}, {110, 310}, {238, 439}, {103, 317}, {126, 292}, {200, 402}, {201,
403}, {206, 404}, {207, 405}, {236, 438}, {232, 435}, {218, 391}, {235, 437},
{127, 288}, {202, 426}, {108, 270}, {115, 273}, {228, 391}, {253, 414}, {254,
413}, {251, 415}, {243, 406}, {107, 269}, {204, 427}, {217, 432}, {218, 433},
{222, 435}, {224, 397}, {226, 399}, {110, 256}, {111, 257}, {221, 434}, {225,
398}, {101, 276}, {126, 271}, {124, 269}, {122, 267}, {120, 265}, {118, 263},
{116, 261}, {114, 259}, {112, 258}, {234, 408}, {102, 277}, {125, 270}, {121,
266}, {118, 261}, {117, 262}, {115, 260}, {123, 268}, {216, 431}, {212, 428},
{213, 429}, {214, 430}, {98, 283}, {217, 416}, {96, 282}, {219, 417}, {222,
420}, {223, 421}, {224, 410}, {97, 282}, {96, 285}, {114, 271}, {111, 274},
{220, 418}, {221, 419}, {97, 286}, {119, 264}, {113, 270}, {99, 284}, {232,
361}, {252, 382}, {241, 373}, {142, 264}, {240, 374}, {140, 267}, {250, 370},
{181, 313}, {233, 356}, {175, 289}, {238, 352}, {194, 333}, {128, 272}, {131,
275}, {130, 274}, {129, 273}, {176, 288}, {133, 276}, {137, 280}, {135, 278},
{240, 354}, {134, 277}, {138, 281}, {245, 352}, {218, 332}, {159, 264}, {253,
357}, {132, 287}, {136, 279}, {129, 289}, {130, 291}, {192, 354}, {180, 279},
{141, 297}, {142, 298}, {153, 319}, {182, 272}, {224, 327}, {225, 329}, {154,
304}, {155, 305}, {178, 280}, {245, 345}, {140, 290}, {208, 383}, {163, 275},
{166, 278}, {192, 368}, {193, 369}, {139, 314}, {133, 311}, {177, 259}, {179,
257}, {186, 264}, {128, 307}, {184, 267}, {163, 279}, {215, 355}, {205, 376},
{152, 302}, {153, 303}, {180, 258}, {196, 370}, {131, 308}, {209, 358}, {162,
282}, {188, 260}, {150, 300}, {151, 301}, {200, 371}, {204, 375}, {175, 275},
{165, 280}, {190, 259}, {201, 372}, {203, 374}, {134, 312}, {149, 299}, {174,
272}, {173, 274}, {202, 373}, {164, 356}, {165, 357}, {166, 358}, {167, 359},
{161, 352}, {157, 351}, {158, 349}, {162, 353}, {155, 351}, {172, 360}, {178,
374}, {152, 350}, {164, 354}, {175, 361}, {181, 370}, {144, 344}, {149, 349},
{148, 348}, {147, 347}, {146, 346}, {145, 345}, {169, 355}, {234, 288}, {180,
376}, {142, 320}, {143, 321}, {188, 365}, {190, 367}, {144, 322}, {153, 331},
{152, 330}, {149, 327}, {148, 326}, {145, 323}, {167, 372}, {184, 363}, {189,
366}, {135, 339}, {185, 364}, {146, 324}, {147, 325}, {154, 332}, {164, 371},
{143, 343}, {161, 377}, {192, 281}, {154, 320}, {176, 362}, {136, 340}, {138,
342}, {137, 341}, {172, 369}, {150, 328}, {151, 329}, {160, 382}, {253, 291},
{158, 380}, {159, 381}, {237, 271}, {181, 337}, {204, 297}, {156, 378}, {157,
379}, {183, 336}, {205, 298}, {208, 311}, {209, 312}, {228, 265}, {231, 265},
{194, 306}, {195, 306}, {246, 263}, {196, 310}, {198, 308}, {209, 290}, {233,
287}, {199, 316}, {198, 315}, {160, 350}, {255, 256} }>;
(II) A more general form is to represent the graph as the orbit of {200, 201}
under the group generated by the following permutations:
a: (1, 2)(3, 6)(4, 7)(5, 8)(9, 16)(10, 19)(11, 20)(12, 21)(13, 22)(14, 23)(15,
24)(17, 27)(18, 28)(25, 43)(26, 46)(29, 51)(30, 54)(31, 55)(32, 56)(33, 58)(34,
61)(35, 62)(36, 63)(37, 64)(38, 65)(39, 66)(40, 67)(41, 68)(42, 69)(44, 72)(45,
73)(47, 76)(48, 77)(49, 78)(50, 79)(52, 82)(53, 83)(57, 89)(59, 92)(60, 93)(70,
113)(71, 116)(74, 119)(75, 121)(80, 128)(81, 131)(84, 88)(85, 138)(86, 139)(87,
140)(90, 145)(94, 152)(95, 155)(96, 157)(97, 160)(98, 147)(99, 161)(100,
162)(101, 164)(102, 167)(103, 168)(104, 169)(105, 170)(106, 171)(107, 172)(108,
173)(109, 174)(110, 175)(111, 176)(112, 177)(114, 180)(115, 181)(117, 184)(118,
185)(120, 188)(122, 191)(123, 192)(124, 193)(125, 132)(126, 136)(127, 194)(129,
196)(130, 197)(133, 200)(134, 201)(135, 202)(137, 203)(141, 210)(142, 211)(143,
212)(144, 213)(146, 216)(148, 217)(149, 218)(150, 219)(151, 220)(153, 223)(154,
224)(156, 227)(158, 230)(159, 215)(163, 237)(165, 240)(166, 241)(179, 261)(182,
264)(183, 266)(186, 272)(187, 275)(189, 236)(190, 281)(195, 249)(198, 290)(199,
233)(204, 302)(205, 305)(206, 270)(207, 306)(208, 307)(209, 308)(214, 314)(221,
323)(222, 239)(225, 330)(228, 335)(229, 309)(231, 338)(232, 255)(234, 342)(235,
267)(238, 345)(242, 350)(243, 351)(244, 347)(245, 352)(246, 353)(247, 354)(248,
355)(250, 282)(251, 356)(252, 359)(253, 360)(254, 274)(256, 361)(257, 362)(258,
259)(260, 313)(262, 363)(263, 364)(265, 365)(268, 368)(269, 369)(271, 279)(273,
370)(276, 371)(277, 372)(278, 373)(280, 374)(283, 325)(284, 377)(285, 379)(286,
382)(287, 316)(288, 333)(289, 310)(291, 384)(292, 340)(293, 385)(294, 386)(295,
387)(296, 388)(297, 389)(298, 390)(299, 391)(300, 392)(301, 393)(303, 396)(304,
397)(311, 402)(312, 403)(315, 406)(317, 407)(318, 408)(319, 409)(320, 410)(321,
411)(322, 412)(324, 415)(326, 416)(327, 332)(328, 417)(329, 418)(331, 421)(334,
422)(336, 376)(339, 426)(341, 398)(343, 428)(344, 429)(346, 431)(348, 432)(349,
433)(357, 419)(358, 443)(366, 438)(375, 463)(378, 466)(380, 467)(381, 414)(383,
470)(394, 475)(395, 440)(399, 436)(400, 482)(401, 464)(404, 448)(405, 487)(413,
484)(420, 442)(423, 441)(424, 489)(425, 468)(427, 465)(430, 491)(434, 493)(435,
457)(437, 446)(439, 479)(444, 472)(445, 480)(447, 495)(449, 453)(450, 496)(451,
497)(452, 485)(455, 498)(456, 499)(458, 500)(459, 477)(460, 478)(461, 501)(462,
502)(469, 492)(471, 494)(473, 503)(474, 504)(476, 483)(481, 490)(486, 505)(488,
506) (III) Last is Groups&Graphs. Copy everything between (not including)
the lines of asterisks into a plain text file and save it as "graph.txt". Then
launch G&G (Groups&Graphs) and select Read Text from the File menu.
**************
&Graph **************
b: (2, 5, 4)(6, 18, 12)(7, 15, 14)(8, 17, 10)(9, 13, 11)(16, 45, 38)(19, 53,
49)(20, 52, 30)(21, 60, 40)(22, 59, 34)(23, 41, 42)(24, 57, 36)(25, 47, 37)(26,
27, 44)(28, 50, 32)(29, 31, 48)(33, 35, 39)(43, 115, 110)(46, 120, 55)(51, 130,
88)(54, 137, 134)(56, 126, 127)(58, 147, 99)(61, 154, 150)(62, 159, 106)(63,
143, 144)(64, 86, 75)(65, 166, 108)(66, 153, 95)(67, 156, 142)(68, 163, 123)(69,
111, 112)(70, 117, 109)(71, 72, 114)(73, 79, 100)(74, 78, 118)(76, 165, 102)(77,
136, 85)(80, 132, 87)(81, 82, 129)(83, 135, 125)(84, 124, 133)(89, 158, 97)(90,
148, 98)(91, 92, 146)(93, 151, 104)(94, 103, 149)(96, 141, 105)(101, 122,
107)(113, 260, 256)(116, 265, 128)(119, 274, 236)(121, 280, 277)(131, 292,
288)(138, 304, 300)(139, 273, 187)(140, 291, 199)(145, 160, 313)(152, 325,
245)(155, 332, 328)(157, 337, 310)(161, 341, 312)(162, 271, 207)(164, 347,
284)(167, 320, 219)(168, 248, 241)(169, 321, 322)(170, 214, 232)(172, 319,
243)(173, 191, 264)(174, 195, 183)(175, 358, 254)(176, 275, 268)(177, 257,
258)(178, 262, 255)(179, 180, 259)(181, 196, 250)(182, 194, 263)(184, 357,
252)(185, 279, 190)(186, 206, 235)(188, 278, 270)(189, 269, 276)(192, 343,
344)(193, 381, 296)(197, 289, 209)(198, 208, 287)(200, 303, 205)(201, 378,
298)(202, 380, 286)(203, 301, 294)(204, 293, 299)(210, 247, 227)(211, 333,
334)(212, 339, 316)(213, 261, 231)(215, 216, 246)(217, 340, 234)(218, 331,
226)(220, 349, 242)(221, 326, 244)(222, 223, 324)(224, 329, 318)(225, 317,
327)(228, 307, 309)(229, 230, 336)(233, 315, 311)(237, 249, 282)(238, 348,
283)(239, 240, 346)(251, 267, 253)(266, 453, 450)(272, 306, 400)(281, 422,
461)(285, 297, 295)(290, 384, 401)(302, 479, 472)(305, 427, 467)(308, 383,
469)(314, 486, 425)(323, 382, 363)(330, 454, 352)(335, 375, 456)(338, 484,
438)(342, 397, 390)(345, 350, 463)(351, 490, 464)(353, 485, 405)(354, 494,
440)(355, 431, 488)(356, 420, 421)(359, 426, 417)(360, 483, 406)(361, 387,
413)(362, 468, 412)(364, 452, 367)(365, 451, 448)(366, 447, 449)(368, 408,
416)(369, 474, 459)(371, 423, 376)(372, 475, 392)(373, 385, 455)(374, 462,
457)(377, 436, 433)(379, 481, 398)(386, 476, 477)(389, 473, 466)(391, 402,
399)(393, 460, 458)(394, 480, 471)(395, 396, 478)(403, 444, 418)(404, 437,
424)(407, 445, 443)(409, 430, 435)(410, 492, 428)(411, 442, 419)(414, 415,
446)(429, 441, 434)(432, 470, 465)(482, 489, 487)(491, 495, 504)(493, 498,
502)(496, 506, 501)(497, 499, 500)
c: (2, 3, 4)(6, 11, 14)(7, 13, 10)(8, 9, 12)(15, 17, 18)(16, 37, 42)(19, 48,
32)(20, 29, 49)(21, 39, 36)(22, 33, 40)(23, 47, 26)(24, 35, 34)(25, 38, 27)(28,
31, 30)(41, 44, 45)(43, 109, 112)(46, 118, 100)(50, 52, 53)(51, 87, 127)(54,
133, 125)(55, 64, 74)(56, 132, 81)(57, 59, 60)(58, 98, 144)(61, 149, 104)(62,
105, 142)(63, 148, 91)(65, 107, 123)(66, 94, 150)(67, 141, 97)(68, 122, 102)(69,
117, 71)(70, 110, 72)(73, 78, 75)(76, 101, 108)(77, 84, 134)(79, 86, 120)(80,
88, 82)(83, 124, 85)(89, 96, 106)(90, 99, 92)(93, 103, 95)(111, 114, 115)(113,
255, 258)(116, 263, 250)(119, 235, 207)(121, 276, 270)(126, 129, 130)(128, 174,
182)(131, 287, 209)(135, 136, 137)(138, 299, 294)(139, 186, 236)(140, 198,
288)(143, 146, 147)(145, 170, 231)(151, 153, 154)(152, 244, 322)(155, 327,
318)(156, 158, 159)(157, 309, 334)(160, 261, 246)(161, 311, 316)(162, 206,
187)(163, 165, 166)(164, 283, 344)(167, 349, 248)(168, 319, 320)(169, 326,
222)(171, 210, 247)(172, 242, 219)(173, 237, 282)(175, 253, 268)(176, 267,
252)(177, 262, 179)(178, 256, 180)(181, 194, 183)(184, 251, 254)(185, 189,
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