C4graphGraph forms for C4 [ 512, 176 ] = UG(ATD[512,368])

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On this page are computer-accessible forms for the graph C4[ 512, 176 ] = UG(ATD[512,368]).

(I) Following is a form readable by MAGMA:

g:=Graph<512|{ {264, 265}, {484, 485}, {296, 297}, {328, 329}, {360, 361}, {392, 393}, {424, 425}, {105, 107}, {480, 482}, {457, 459}, {277, 279}, {260, 262}, {245, 247}, {228, 230}, {213, 215}, {212, 214}, {177, 179}, {145, 147}, {292, 294}, {309, 311}, {324, 326}, {341, 343}, {356, 358}, {373, 375}, {388, 390}, {405, 407}, {420, 422}, {1, 2}, {505, 506}, {232, 235}, {200, 203}, {24, 27}, {61, 62}, {76, 79}, {116, 119}, {160, 163}, {1, 4}, {233, 236}, {195, 198}, {3, 6}, {40, 45}, {89, 92}, {106, 111}, {144, 149}, {72, 78}, {451, 453}, {266, 268}, {298, 300}, {330, 332}, {362, 364}, {394, 396}, {426, 428}, {2, 5}, {505, 510}, {179, 180}, {8, 15}, {25, 30}, {65, 70}, {129, 134}, {3, 10}, {5, 12}, {7, 14}, {98, 107}, {53, 63}, {503, 509}, {487, 493}, {480, 490}, {260, 270}, {228, 238}, {177, 187}, {87, 93}, {160, 170}, {292, 302}, {324, 334}, {356, 366}, {388, 398}, {420, 430}, {2, 9}, {484, 495}, {6, 13}, {130, 142}, {164, 168}, {52, 57}, {483, 494}, {449, 460}, {193, 204}, {182, 184}, {486, 488}, {451, 461}, {227, 237}, {195, 205}, {278, 280}, {291, 301}, {342, 344}, {355, 365}, {406, 408}, {419, 429}, {438, 440}, {4, 11}, {503, 504}, {455, 456}, {258, 269}, {246, 249}, {96, 111}, {310, 313}, {322, 333}, {374, 377}, {386, 397}, {4, 20}, {492, 508}, {267, 283}, {5, 21}, {6, 22}, {7, 23}, {8, 24}, {9, 25}, {10, 26}, {11, 27}, {12, 28}, {13, 29}, {14, 30}, {15, 31}, {299, 315}, {331, 347}, {363, 379}, {395, 411}, {68, 85}, {234, 251}, {110, 127}, {132, 149}, {175, 190}, {427, 442}, {231, 245}, {458, 472}, {455, 469}, {454, 468}, {263, 277}, {236, 254}, {295, 309}, {327, 341}, {359, 373}, {391, 405}, {423, 437}, {428, 446}, {199, 212}, {461, 478}, {268, 287}, {201, 218}, {300, 319}, {332, 351}, {364, 383}, {396, 415}, {64, 84}, {67, 87}, {97, 117}, {141, 153}, {166, 178}, {130, 151}, {203, 222}, {168, 189}, {70, 80}, {487, 497}, {133, 147}, {136, 158}, {161, 183}, {47, 56}, {483, 500}, {459, 476}, {202, 221}, {76, 91}, {100, 124}, {481, 505}, {103, 127}, {96, 121}, {458, 467}, {263, 286}, {99, 122}, {295, 318}, {327, 350}, {359, 382}, {391, 414}, {98, 120}, {231, 253}, {201, 211}, {134, 156}, {135, 157}, {423, 445}, {167, 188}, {199, 220}, {419, 447}, {449, 477}, {71, 90}, {488, 501}, {482, 511}, {454, 475}, {235, 246}, {196, 217}, {132, 154}, {485, 507}, {482, 508}, {264, 278}, {234, 244}, {133, 155}, {296, 310}, {328, 342}, {360, 374}, {392, 406}, {424, 438}, {32, 63}, {267, 276}, {202, 213}, {166, 185}, {167, 184}, {299, 308}, {331, 340}, {363, 372}, {395, 404}, {427, 436}, {21, 53}, {477, 509}, {471, 503}, {457, 489}, {452, 484}, {273, 305}, {272, 304}, {271, 303}, {261, 293}, {197, 229}, {22, 54}, {86, 118}, {159, 191}, {279, 311}, {280, 312}, {281, 313}, {282, 314}, {325, 357}, {335, 367}, {336, 368}, {337, 369}, {343, 375}, {344, 376}, {345, 377}, {346, 378}, {389, 421}, {399, 431}, {400, 432}, {401, 433}, {18, 51}, {478, 511}, {466, 499}, {276, 309}, {216, 249}, {214, 247}, {208, 241}, {206, 239}, {193, 224}, {25, 56}, {27, 58}, {29, 60}, {31, 62}, {340, 373}, {404, 437}, {409, 440}, {9, 43}, {269, 303}, {265, 299}, {258, 288}, {221, 255}, {12, 46}, {13, 47}, {16, 50}, {137, 171}, {147, 177}, {322, 352}, {329, 363}, {333, 367}, {386, 416}, {393, 427}, {397, 431}, {26, 57}, {475, 504}, {474, 505}, {463, 492}, {272, 307}, {217, 250}, {204, 239}, {30, 61}, {336, 371}, {400, 435}, {410, 441}, {136, 172}, {465, 501}, {463, 491}, {413, 441}, {144, 181}, {478, 507}, {475, 510}, {467, 502}, {452, 481}, {450, 487}, {223, 250}, {209, 244}, {200, 237}, {146, 183}, {149, 176}, {155, 190}, {278, 307}, {342, 371}, {406, 435}, {10, 44}, {461, 491}, {448, 486}, {274, 308}, {222, 248}, {213, 243}, {212, 242}, {211, 245}, {11, 45}, {137, 175}, {138, 172}, {139, 173}, {338, 372}, {402, 436}, {19, 52}, {477, 506}, {471, 496}, {266, 301}, {28, 59}, {145, 182}, {277, 306}, {285, 314}, {287, 312}, {330, 365}, {341, 370}, {349, 378}, {351, 376}, {394, 429}, {405, 434}, {89, 113}, {259, 299}, {194, 234}, {128, 168}, {129, 169}, {323, 363}, {387, 427}, {415, 439}, {68, 109}, {479, 502}, {256, 297}, {192, 233}, {75, 98}, {131, 170}, {156, 181}, {320, 361}, {384, 425}, {74, 96}, {474, 496}, {262, 300}, {198, 236}, {326, 364}, {390, 428}, {69, 110}, {257, 298}, {321, 362}, {385, 426}, {404, 447}, {135, 171}, {270, 290}, {269, 289}, {333, 353}, {334, 354}, {397, 417}, {398, 418}, {402, 446}, {89, 116}, {453, 488}, {274, 319}, {261, 296}, {210, 255}, {204, 225}, {325, 360}, {338, 383}, {389, 424}, {66, 108}, {473, 503}, {275, 317}, {256, 302}, {197, 235}, {80, 126}, {140, 162}, {320, 366}, {339, 381}, {384, 430}, {24, 55}, {456, 487}, {215, 248}, {209, 254}, {205, 226}, {196, 235}, {73, 102}, {403, 444}, {408, 439}, {16, 32}, {450, 498}, {17, 33}, {18, 34}, {19, 35}, {67, 115}, {83, 99}, {65, 112}, {448, 497}, {80, 97}, {95, 110}, {140, 189}, {142, 191}, {143, 190}, {23, 37}, {76, 127}, {464, 483}, {78, 125}, {87, 100}, {94, 109}, {141, 190}, {148, 167}, {265, 317}, {266, 318}, {329, 381}, {330, 382}, {27, 46}, {200, 253}, {393, 444}, {17, 39}, {479, 489}, {273, 295}, {77, 123}, {88, 110}, {159, 169}, {337, 359}, {401, 423}, {208, 231}, {453, 498}, {221, 234}, {394, 445}, {84, 108}, {387, 443}, {21, 44}, {469, 492}, {73, 112}, {74, 115}, {75, 114}, {68, 126}, {466, 488}, {262, 316}, {257, 315}, {198, 252}, {128, 186}, {129, 187}, {138, 176}, {139, 177}, {148, 174}, {321, 379}, {326, 380}, {20, 47}, {456, 499}, {192, 251}, {86, 109}, {143, 180}, {385, 442}, {154, 166}, {465, 493}, {207, 243}, {206, 242}, {142, 179}, {467, 494}, {457, 500}, {271, 306}, {205, 240}, {335, 370}, {390, 443}, {399, 434}, {14, 48}, {270, 304}, {210, 236}, {194, 252}, {15, 49}, {140, 178}, {150, 168}, {155, 165}, {334, 368}, {398, 432}, {12, 51}, {275, 300}, {259, 316}, {207, 240}, {23, 40}, {66, 125}, {131, 188}, {323, 380}, {339, 364}, {403, 428}, {59, 122}, {45, 111}, {53, 119}, {62, 124}, {59, 127}, {158, 219}, {28, 90}, {29, 91}, {49, 118}, {60, 123}, {157, 218}, {58, 114}, {185, 241}, {286, 342}, {318, 374}, {61, 116}, {26, 80}, {31, 85}, {315, 369}, {283, 336}, {414, 469}, {31, 83}, {153, 213}, {28, 81}, {187, 246}, {54, 120}, {55, 121}, {29, 82}, {143, 192}, {48, 96}, {49, 97}, {51, 98}, {191, 238}, {144, 193}, {146, 195}, {150, 196}, {445, 495}, {178, 224}, {55, 100}, {183, 228}, {59, 104}, {145, 194}, {62, 106}, {276, 320}, {63, 107}, {308, 352}, {411, 463}, {60, 105}, {447, 490}, {182, 227}, {180, 225}, {157, 200}, {285, 328}, {317, 360}, {25, 79}, {53, 99}, {151, 193}, {279, 321}, {311, 353}, {158, 201}, {191, 232}, {181, 226}, {407, 448}, {21, 77}, {22, 78}, {151, 207}, {284, 324}, {286, 326}, {287, 327}, {315, 355}, {316, 356}, {318, 358}, {319, 359}, {412, 452}, {444, 484}, {283, 322}, {284, 325}, {316, 357}, {408, 449}, {410, 451}, {415, 454}, {441, 480}, {43, 113}, {447, 485}, {189, 231}, {185, 227}, {280, 322}, {281, 323}, {312, 354}, {313, 355}, {411, 449}, {413, 455}, {443, 481}, {46, 117}, {152, 195}, {156, 199}, {409, 450}, {414, 453}, {443, 480}, {20, 73}, {446, 483}, {187, 230}, {56, 101}, {58, 103}, {152, 197}, {44, 114}, {186, 228}, {154, 196}, {282, 324}, {314, 356}, {57, 102}, {186, 229}, {58, 101}, {153, 198}, {412, 451}, {445, 482}, {293, 325}, {303, 335}, {304, 336}, {305, 337}, {311, 343}, {312, 344}, {313, 345}, {314, 346}, {436, 468}, {33, 64}, {35, 66}, {37, 68}, {39, 70}, {308, 341}, {421, 452}, {431, 462}, {433, 464}, {434, 467}, {42, 72}, {181, 215}, {180, 214}, {179, 209}, {52, 86}, {297, 331}, {301, 335}, {305, 339}, {421, 455}, {34, 65}, {188, 223}, {38, 69}, {172, 207}, {291, 320}, {425, 458}, {429, 462}, {433, 466}, {174, 202}, {437, 465}, {438, 466}, {171, 206}, {189, 216}, {310, 339}, {442, 479}, {178, 212}, {306, 340}, {319, 345}, {426, 460}, {36, 67}, {169, 206}, {298, 333}, {309, 338}, {317, 346}, {440, 479}, {163, 203}, {446, 470}, {164, 204}, {165, 205}, {170, 194}, {416, 456}, {417, 457}, {418, 458}, {56, 81}, {169, 192}, {288, 329}, {290, 331}, {435, 474}, {436, 477}, {439, 478}, {184, 210}, {294, 332}, {57, 82}, {161, 202}, {172, 199}, {174, 197}, {289, 330}, {444, 471}, {301, 321}, {430, 450}, {38, 75}, {39, 74}, {49, 92}, {293, 328}, {302, 323}, {306, 351}, {416, 461}, {422, 459}, {429, 448}, {41, 71}, {183, 217}, {182, 216}, {288, 334}, {307, 349}, {434, 476}, {440, 470}, {441, 471}, {176, 223}, {45, 93}, {46, 94}, {47, 95}, {55, 71}, {175, 222}, {426, 475}, {40, 90}, {41, 91}, {48, 66}, {43, 88}, {425, 474}, {32, 84}, {33, 85}, {34, 86}, {35, 87}, {297, 349}, {298, 350}, {188, 201}, {42, 92}, {54, 64}, {432, 454}, {63, 72}, {304, 327}, {43, 83}, {61, 69}, {163, 219}, {164, 220}, {165, 221}, {435, 459}, {417, 472}, {170, 208}, {171, 209}, {289, 347}, {294, 348}, {50, 73}, {54, 77}, {176, 203}, {418, 473}, {36, 88}, {37, 89}, {175, 211}, {60, 65}, {173, 208}, {303, 338}, {50, 76}, {290, 348}, {430, 464}, {431, 465}, {173, 210}, {302, 337}, {307, 332}, {422, 473}, {432, 463}, {122, 185}, {93, 152}, {95, 154}, {81, 151}, {124, 186}, {77, 138}, {94, 153}, {350, 406}, {382, 438}, {82, 152}, {104, 162}, {379, 433}, {347, 400}, {108, 160}, {79, 128}, {119, 184}, {81, 129}, {82, 130}, {83, 131}, {84, 132}, {112, 161}, {119, 163}, {340, 384}, {372, 416}, {349, 392}, {381, 424}, {116, 162}, {118, 160}, {343, 385}, {375, 417}, {95, 136}, {117, 173}, {118, 174}, {121, 161}, {348, 388}, {350, 390}, {351, 391}, {379, 419}, {380, 420}, {382, 422}, {383, 423}, {94, 135}, {126, 167}, {347, 386}, {348, 389}, {380, 421}, {78, 148}, {79, 149}, {120, 162}, {124, 166}, {344, 386}, {345, 387}, {376, 418}, {377, 419}, {93, 134}, {122, 164}, {123, 165}, {346, 388}, {378, 420}, {90, 133}, {357, 389}, {367, 399}, {368, 400}, {369, 401}, {375, 407}, {376, 408}, {377, 409}, {378, 410}, {372, 405}, {361, 395}, {365, 399}, {369, 403}, {355, 384}, {374, 403}, {107, 141}, {370, 404}, {383, 409}, {104, 143}, {113, 150}, {115, 148}, {362, 397}, {373, 402}, {381, 410}, {101, 140}, {103, 142}, {352, 393}, {354, 395}, {99, 137}, {117, 159}, {358, 396}, {102, 141}, {353, 394}, {101, 137}, {102, 138}, {126, 146}, {365, 385}, {357, 392}, {366, 387}, {370, 415}, {352, 398}, {371, 413}, {100, 139}, {361, 413}, {362, 414}, {104, 157}, {106, 159}, {125, 136}, {112, 134}, {105, 158}, {114, 133}, {115, 132}, {368, 391}, {105, 144}, {111, 150}, {97, 155}, {113, 139}, {353, 411}, {358, 412}, {103, 156}, {106, 145}, {120, 131}, {121, 130}, {123, 135}, {125, 128}, {367, 402}, {108, 146}, {109, 147}, {354, 412}, {366, 401}, {371, 396}, {1, 407}, {85, 500}, {75, 489}, {88, 506}, {91, 508}, {92, 502}, {69, 494}, {1, 437}, {3, 439}, {74, 511}, {64, 502}, {67, 504}, {71, 507}, {72, 500}, {7, 442}, {34, 486}, {4, 460}, {16, 472}, {17, 473}, {44, 486}, {251, 305}, {220, 278}, {218, 272}, {48, 506}, {52, 511}, {253, 310}, {18, 476}, {36, 490}, {50, 509}, {10, 472}, {33, 499}, {211, 256}, {37, 497}, {244, 288}, {39, 498}, {215, 258}, {2, 468}, {247, 289}, {3, 469}, {7, 464}, {255, 296}, {223, 264}, {214, 257}, {42, 498}, {252, 292}, {251, 291}, {218, 258}, {222, 263}, {254, 295}, {252, 293}, {6, 476}, {249, 291}, {248, 290}, {220, 262}, {42, 496}, {216, 259}, {253, 294}, {40, 501}, {217, 260}, {8, 470}, {250, 292}, {219, 261}, {32, 510}, {51, 493}, {219, 260}, {9, 489}, {250, 282}, {249, 281}, {248, 280}, {247, 279}, {241, 273}, {240, 272}, {239, 271}, {229, 261}, {19, 499}, {14, 495}, {244, 277}, {237, 271}, {241, 275}, {19, 496}, {232, 267}, {227, 256}, {233, 269}, {246, 275}, {255, 282}, {30, 504}, {242, 276}, {8, 495}, {254, 281}, {245, 274}, {41, 462}, {38, 462}, {24, 497}, {226, 267}, {224, 265}, {38, 460}, {230, 268}, {5, 494}, {225, 266}, {22, 509}, {237, 257}, {229, 264}, {242, 287}, {238, 259}, {224, 270}, {243, 285}, {20, 507}, {17, 481}, {36, 470}, {13, 510}, {232, 285}, {11, 508}, {240, 263}, {233, 286}, {26, 493}, {18, 491}, {15, 501}, {230, 284}, {225, 283}, {16, 491}, {23, 490}, {239, 274}, {41, 468}, {226, 284}, {238, 273}, {243, 268}, {35, 512}, {70, 512}, {485, 512}, {492, 512} }>;

(II) A more general form is to represent the graph as the orbit of {264, 265} under the group generated by the following permutations:

a: (2, 437)(3, 491)(4, 407)(5, 404)(6, 461)(7, 470)(8, 442)(9, 423)(10, 463)(11, 375)(12, 370)(13, 416)(14, 440)(15, 427)(16, 469)(18, 439)(19, 474)(20, 405)(21, 395)(22, 451)(23, 446)(24, 385)(25, 383)(26, 432)(27, 343)(28, 335)(29, 386)(30, 409)(31, 387)(32, 455)(33, 481)(34, 408)(35, 425)(36, 464)(37, 428)(38, 429)(39, 473)(40, 402)(41, 431)(42, 471)(43, 401)(44, 411)(45, 373)(46, 341)(47, 372)(48, 438)(49, 393)(50, 414)(51, 415)(52, 435)(53, 361)(54, 412)(55, 365)(56, 338)(57, 400)(58, 311)(59, 301)(60, 344)(61, 377)(62, 345)(63, 413)(64, 452)(65, 376)(66, 424)(67, 430)(68, 390)(69, 419)(70, 418)(71, 399)(72, 441)(73, 391)(74, 422)(75, 394)(76, 362)(77, 354)(78, 410)(79, 364)(80, 398)(81, 303)(82, 347)(83, 366)(84, 421)(85, 443)(86, 406)(87, 384)(88, 433)(89, 403)(90, 367)(91, 397)(92, 444)(93, 340)(94, 327)(95, 363)(96, 382)(97, 352)(98, 396)(99, 320)(100, 355)(101, 309)(102, 368)(103, 279)(104, 266)(105, 342)(106, 319)(107, 371)(108, 389)(109, 350)(110, 379)(111, 359)(112, 351)(113, 369)(114, 353)(115, 420)(116, 374)(117, 308)(118, 392)(119, 360)(120, 358)(121, 330)(122, 291)(123, 312)(124, 313)(125, 381)(126, 388)(127, 321)(128, 339)(129, 271)(130, 289)(131, 356)(132, 380)(133, 333)(134, 306)(135, 287)(136, 329)(137, 276)(138, 334)(139, 315)(140, 295)(141, 336)(142, 247)(143, 225)(144, 286)(145, 300)(146, 348)(147, 298)(148, 378)(149, 326)(150, 337)(151, 269)(152, 331)(153, 304)(154, 323)(155, 322)(156, 277)(157, 268)(158, 328)(159, 274)(160, 357)(161, 332)(162, 318)(163, 325)(164, 251)(165, 280)(166, 281)(167, 346)(168, 305)(169, 239)(170, 316)(171, 242)(172, 288)(173, 299)(174, 349)(175, 267)(176, 324)(177, 257)(178, 254)(179, 214)(181, 263)(182, 275)(183, 294)(184, 317)(185, 249)(186, 310)(187, 237)(188, 314)(189, 273)(190, 283)(191, 245)(192, 204)(193, 233)(194, 262)(195, 290)(196, 302)(197, 297)(198, 270)(199, 244)(200, 230)(201, 285)(202, 307)(203, 284)(205, 248)(207, 258)(208, 259)(209, 212)(210, 265)(211, 232)(213, 272)(215, 240)(216, 241)(217, 292)(218, 243)(219, 293)(220, 234)(221, 278)(222, 226)(223, 282)(224, 236)(227, 246)(228, 253)(229, 296)(231, 238)(235, 256)(252, 260)(255, 264)(417, 508)(426, 497)(434, 507)(436, 501)(445, 489)(447, 494)(448, 460)(449, 486)(450, 504)(453, 509)(454, 493)(456, 510)(457, 482)(458, 512)(459, 511)(465, 468)(466, 506)(467, 485)(472, 492)(475, 487)(476, 478)(477, 488)(479, 495)(480, 500)(483, 490)(484, 502)(498, 503)(499, 505)
b: (2, 4)(3, 7)(5, 11)(6, 14)(8, 18)(9, 20)(10, 23)(12, 27)(13, 30)(15, 34)(16, 36)(19, 42)(21, 45)(22, 48)(24, 51)(25, 47)(26, 37)(28, 58)(29, 61)(31, 65)(32, 67)(33, 39)(35, 72)(38, 41)(40, 44)(43, 73)(49, 86)(50, 88)(52, 92)(53, 93)(54, 96)(55, 98)(57, 89)(59, 103)(60, 62)(63, 87)(64, 74)(66, 78)(68, 80)(69, 91)(70, 85)(71, 75)(76, 110)(77, 111)(79, 95)(81, 101)(82, 116)(83, 112)(84, 115)(90, 114)(94, 117)(97, 109)(99, 134)(100, 107)(102, 113)(104, 142)(105, 124)(106, 123)(108, 148)(119, 152)(120, 121)(122, 156)(128, 136)(129, 137)(130, 162)(131, 161)(135, 159)(138, 150)(139, 141)(140, 151)(143, 179)(144, 166)(145, 165)(146, 167)(147, 155)(149, 154)(153, 173)(157, 191)(158, 186)(160, 174)(163, 197)(164, 199)(168, 172)(169, 171)(170, 202)(175, 187)(176, 196)(177, 190)(178, 193)(181, 185)(182, 205)(183, 188)(184, 195)(189, 207)(192, 209)(194, 221)(198, 210)(200, 232)(201, 228)(203, 235)(204, 212)(208, 213)(211, 230)(214, 225)(215, 241)(216, 240)(217, 223)(218, 238)(219, 229)(222, 246)(226, 227)(231, 243)(233, 254)(237, 267)(239, 242)(244, 251)(245, 268)(247, 266)(248, 275)(249, 263)(252, 255)(253, 285)(256, 284)(257, 283)(258, 273)(259, 272)(260, 264)(262, 278)(265, 270)(269, 295)(271, 276)(274, 287)(277, 291)(279, 301)(280, 300)(281, 286)(282, 292)(288, 305)(289, 318)(290, 317)(293, 296)(294, 314)(297, 325)(298, 322)(299, 304)(302, 324)(303, 309)(306, 320)(307, 316)(308, 327)(310, 328)(311, 335)(312, 319)(313, 342)(315, 336)(323, 326)(329, 339)(330, 358)(331, 360)(332, 356)(334, 337)(340, 361)(343, 370)(344, 345)(346, 348)(347, 374)(349, 357)(350, 352)(351, 366)(353, 367)(354, 359)(355, 371)(362, 379)(363, 364)(365, 396)(368, 369)(372, 383)(373, 395)(375, 404)(376, 387)(377, 386)(378, 389)(382, 412)(384, 413)(385, 415)(390, 398)(391, 401)(393, 406)(394, 399)(397, 419)(400, 403)(402, 411)(405, 423)(407, 437)(408, 427)(409, 416)(410, 424)(414, 433)(417, 447)(418, 443)(420, 421)(422, 452)(425, 441)(426, 454)(428, 432)(429, 431)(430, 455)(434, 445)(435, 444)(436, 449)(438, 451)(439, 442)(440, 461)(446, 463)(448, 465)(450, 456)(453, 466)(457, 485)(458, 480)(459, 484)(460, 468)(464, 469)(467, 482)(470, 491)(471, 474)(472, 490)(473, 481)(476, 495)(478, 479)(483, 492)(486, 501)(489, 507)(493, 497)(494, 508)(498, 499)(500, 512)(502, 511)(503, 505)(504, 510)(506, 509)
c: (1, 2, 5, 12, 28, 59, 104, 143, 180, 214, 247, 279, 311, 343, 375, 407)(3, 8, 13, 31, 60, 106, 144, 182, 215, 249, 280, 313, 344, 377, 408, 440)(4, 9, 21, 46, 81, 122, 157, 192, 225, 257, 289, 321, 353, 385, 417, 448)(6, 15, 29, 62, 105, 145, 181, 216, 248, 281, 312, 345, 376, 409, 439, 470)(7, 16, 37, 73, 113, 138, 173, 207, 241, 272, 305, 336, 369, 400, 433, 463)(10, 24, 47, 83, 123, 159, 193, 227, 258, 291, 322, 355, 386, 419, 449, 479)(11, 25, 53, 94, 129, 164, 200, 233, 266, 298, 330, 362, 394, 426, 457, 486)(14, 32, 68, 112, 150, 176, 210, 243, 275, 307, 339, 371, 403, 435, 466, 492)(17, 39, 74, 115, 148, 174, 197, 229, 261, 293, 325, 357, 389, 421, 452, 481)(18, 40, 76, 116, 141, 177, 199, 231, 263, 295, 327, 359, 391, 423, 454, 483)(19, 35, 66, 108, 146, 183, 217, 250, 282, 314, 346, 378, 410, 441, 471, 496)(20, 43, 77, 117, 151, 185, 218, 251, 283, 315, 347, 379, 411, 442, 472, 497)(22, 49, 82, 124, 158, 194, 226, 259, 290, 323, 354, 387, 418, 450, 478, 36)(23, 50, 89, 102, 139, 172, 208, 240, 273, 304, 337, 368, 401, 432, 464, 491)(26, 55, 95, 131, 165, 191, 224, 256, 288, 320, 352, 384, 416, 447, 477, 502)(27, 56, 99, 135, 169, 204, 237, 269, 301, 333, 365, 397, 429, 460, 489, 44)(30, 63, 109, 134, 168, 203, 236, 268, 300, 332, 364, 396, 428, 459, 488, 508)(33, 70, 96, 132, 167, 202, 235, 264, 296, 328, 360, 392, 424, 455, 484, 505)(34, 45, 79, 119, 153, 187, 220, 253, 286, 318, 350, 382, 414, 445, 475, 500)(38, 75, 114, 58, 101, 137, 171, 206, 239, 271, 303, 335, 367, 399, 431, 462)(41, 69, 98, 133, 103, 140, 175, 209, 242, 274, 306, 338, 370, 402, 434, 465)(42, 52, 87, 125, 160, 195, 228, 260, 292, 324, 356, 388, 420, 451, 480, 503)(48, 84, 126, 161, 196, 223, 255, 285, 317, 349, 381, 413, 444, 474, 499, 512)(51, 90, 127, 162, 190, 179, 212, 245, 277, 309, 341, 373, 405, 437, 468, 494)(54, 97, 130, 166, 201, 234, 267, 299, 331, 363, 395, 427, 458, 487, 507, 88)(57, 100, 136, 170, 205, 238, 270, 302, 334, 366, 398, 430, 461, 490, 509, 92)(61, 107, 147, 156, 189, 222, 254, 287, 319, 351, 383, 415, 446, 476, 501, 91)(64, 80, 121, 154, 188, 221, 232, 265, 297, 329, 361, 393, 425, 456, 485, 506)(65, 111, 149, 184, 213, 246, 278, 310, 342, 374, 406, 438, 469, 495, 510, 85)(67, 78, 118, 152, 186, 219, 252, 284, 316, 348, 380, 412, 443, 473, 498, 511)(71, 110, 120, 155, 142, 178, 211, 244, 276, 308, 340, 372, 404, 436, 467, 493)(72, 86, 93, 128, 163, 198, 230, 262, 294, 326, 358, 390, 422, 453, 482, 504)

(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
C4[ 512, 176 ]
512
-1 407 2 4 437
-2 1 5 468 9
-3 6 469 10 439
-4 11 1 20 460
-5 12 2 21 494
-6 22 13 3 476
-7 23 442 464 14
-8 495 24 15 470
-9 2 25 489 43
-10 44 3 26 472
-11 45 508 4 27
-12 46 5 28 51
-13 47 510 6 29
-14 495 48 7 30
-15 49 501 8 31
-16 50 491 32 472
-17 33 473 39 481
-18 34 476 51 491
-19 496 35 499 52
-20 507 47 4 73
-21 44 77 5 53
-22 78 509 6 54
-23 37 490 7 40
-24 55 497 27 8
-25 56 79 30 9
-26 57 80 493 10
-27 11 24 46 58
-28 12 90 59 81
-29 13 91 60 82
-30 14 25 61 504
-31 15 83 62 85
-32 510 16 84 63
-33 499 17 85 64
-34 486 18 86 65
-35 66 512 19 87
-36 88 67 490 470
-37 23 89 68 497
-38 462 69 75 460
-39 498 70 17 74
-40 23 45 90 501
-41 462 91 71 468
-42 496 498 92 72
-43 88 113 83 9
-44 486 114 10 21
-45 11 111 93 40
-46 12 27 94 117
-47 56 13 95 20
-48 66 506 14 96
-49 15 92 118 97
-50 509 16 73 76
-51 12 18 493 98
-52 57 511 19 86
-53 99 63 119 21
-54 22 77 64 120
-55 121 100 24 71
-56 101 25 47 81
-57 102 26 82 52
-58 101 103 114 27
-59 122 104 28 127
-60 123 105 29 65
-61 69 116 62 30
-62 124 61 106 31
-63 72 107 53 32
-64 33 84 502 54
-65 34 112 70 60
-66 35 48 125 108
-67 36 115 504 87
-68 37 126 85 109
-69 110 38 61 494
-70 80 39 512 65
-71 55 507 90 41
-72 78 500 63 42
-73 112 102 50 20
-74 115 511 39 96
-75 114 38 489 98
-76 79 91 50 127
-77 123 138 21 54
-78 22 125 148 72
-79 25 149 128 76
-80 26 70 126 97
-81 56 28 129 151
-82 57 29 130 152
-83 99 31 43 131
-84 132 64 108 32
-85 33 68 500 31
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-87 67 100 35 93
-88 110 506 36 43
-89 113 37 92 116
-90 133 71 28 40
-91 508 29 41 76
-92 89 49 502 42
-93 45 134 152 87
-94 46 135 109 153
-95 110 154 47 136
-96 121 111 48 74
-97 155 80 49 117
-98 51 107 75 120
-99 122 137 83 53
-100 55 124 139 87
-101 56 58 137 140
-102 57 138 73 141
-103 156 58 127 142
-104 143 157 59 162
-105 144 158 60 107
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-107 105 63 141 98
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-109 68 147 94 86
-110 88 69 127 95
-111 45 106 150 96
-112 134 73 161 65
-113 89 139 150 43
-114 44 133 58 75
-115 132 67 148 74
-116 89 61 162 119
-117 46 159 173 97
-118 49 160 86 174
-119 116 184 53 163
-120 162 54 98 131
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-122 99 59 185 164
-123 77 165 135 60
-124 100 166 62 186
-125 66 78 136 128
-126 68 167 80 146
-127 110 59 103 76
-128 79 168 125 186
-129 187 134 81 169
-130 121 82 151 142
-131 188 170 83 120
-132 154 115 149 84
-133 155 90 114 147
-134 112 156 93 129
-135 123 157 94 171
-136 125 158 95 172
-137 99 101 171 175
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-139 100 177 113 173
-140 101 178 189 162
-141 102 190 107 153
-142 179 103 191 130
-143 190 180 104 192
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-145 147 182 106 194
-146 126 183 195 108
-147 133 177 145 109
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-150 111 113 168 196
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-155 165 133 190 97
-156 199 134 103 181
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-160 170 118 108 163
-161 121 112 202 183
-162 104 116 140 120
-163 203 160 119 219
-164 220 122 168 204
-165 155 221 123 205
-166 154 178 124 185
-167 188 126 148 184
-168 189 128 150 164
-169 159 192 129 206
-170 160 194 131 208
-171 209 135 137 206
-172 199 136 138 207
-173 210 117 139 208
-174 202 148 118 197
-175 211 222 190 137
-176 223 203 138 149
-177 187 179 147 139
-178 166 212 224 140
-179 209 177 180 142
-180 143 179 214 225
-181 144 156 215 226
-182 145 216 227 184
-183 146 161 217 228
-184 210 167 182 119
-185 122 166 227 241
-186 124 128 228 229
-187 177 246 129 230
-188 167 201 223 131
-189 231 168 216 140
-190 143 155 141 175
-191 232 159 238 142
-192 143 233 169 251
-193 144 224 204 151
-194 145 234 170 252
-195 198 146 205 152
-196 154 235 150 217
-197 235 152 174 229
-198 236 195 153 252
-199 220 156 212 172
-200 253 157 203 237
-201 188 211 158 218
-202 221 213 161 174
-203 176 200 222 163
-204 225 193 239 164
-205 165 226 195 240
-206 242 169 171 239
-207 243 172 151 240
-208 231 170 173 241
-209 254 244 179 171
-210 255 236 173 184
-211 201 245 256 175
-212 242 199 178 214
-213 243 202 215 153
-214 212 180 257 247
-215 213 181 258 248
-216 189 182 259 249
-217 183 260 250 196
-218 157 201 258 272
-219 158 260 261 163
-220 199 278 262 164
-221 165 255 234 202
-222 203 248 175 263
-223 176 264 188 250
-224 265 178 193 270
-225 266 180 204 283
-226 267 181 205 284
-227 256 182 237 185
-228 183 238 186 230
-229 264 261 186 197
-230 187 268 228 284
-231 253 189 245 208
-232 267 191 235 285
-233 286 192 236 269
-234 221 244 194 251
-235 232 246 196 197
-236 198 210 254 233
-237 200 257 227 271
-238 191 259 228 273
-239 204 271 206 274
-240 205 272 207 263
-241 275 185 273 208
-242 276 287 212 206
-243 213 268 207 285
-244 209 277 288 234
-245 231 211 247 274
-246 187 275 235 249
-247 245 289 279 214
-248 222 290 280 215
-249 246 291 281 216
-250 223 292 282 217
-251 234 192 291 305
-252 198 292 194 293
-253 231 200 310 294
-254 209 236 281 295
-255 210 221 282 296
-256 297 211 302 227
-257 298 214 237 315
-258 288 269 215 218
-259 299 216 238 316
-260 270 217 262 219
-261 293 229 219 296
-262 220 300 260 316
-263 286 222 277 240
-264 265 223 278 229
-265 264 299 224 317
-266 268 301 225 318
-267 232 276 226 283
-268 243 287 266 230
-269 233 289 258 303
-270 224 290 260 304
-271 237 303 239 306
-272 304 218 240 307
-273 238 305 295 241
-274 308 319 245 239
-275 300 246 317 241
-276 242 309 320 267
-277 244 279 306 263
-278 220 264 280 307
-279 277 321 311 247
-280 278 322 312 248
-281 254 323 313 249
-282 255 324 314 250
-283 267 322 225 336
-284 324 226 325 230
-285 232 243 314 328
-286 342 233 326 263
-287 242 268 312 327
-288 244 334 258 329
-289 330 247 269 347
-290 331 248 270 348
-291 320 301 249 251
-292 302 250 294 252
-293 325 261 328 252
-294 253 332 292 348
-295 254 309 273 318
-296 297 255 310 261
-297 331 256 349 296
-298 300 333 257 350
-299 308 265 259 315
-300 275 319 298 262
-301 266 321 291 335
-302 256 323 292 337
-303 269 335 271 338
-304 270 336 272 327
-305 337 251 273 339
-306 277 271 340 351
-307 332 278 272 349
-308 341 352 299 274
-309 276 311 338 295
-310 253 313 339 296
-311 309 353 343 279
-312 287 354 344 280
-313 310 355 345 281
-314 356 346 282 285
-315 299 355 257 369
-316 356 357 259 262
-317 275 265 346 360
-318 374 266 358 295
-319 300 345 359 274
-320 276 366 291 361
-321 279 301 379 362
-322 352 333 280 283
-323 363 302 281 380
-324 334 282 326 284
-325 357 293 360 284
-326 286 364 324 380
-327 341 287 304 350
-328 342 293 285 329
-329 363 288 381 328
-330 332 365 289 382
-331 297 290 347 340
-332 330 294 307 351
-333 298 353 322 367
-334 288 354 324 368
-335 301 367 303 370
-336 368 304 283 371
-337 302 369 359 305
-338 309 303 372 383
-339 364 310 381 305
-340 331 306 373 384
-341 308 343 370 327
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-343 341 385 375 311
-344 342 386 376 312
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-346 388 378 314 317
-347 331 386 289 400
-348 388 290 389 294
-349 297 378 392 307
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-351 332 376 391 306
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-354 312 334 412 395
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-356 366 314 358 316
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-358 396 356 412 318
-359 319 337 382 373
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-361 320 413 360 395
-362 364 397 321 414
-363 323 379 372 329
-364 326 339 383 362
-365 330 385 355 399
-366 320 387 356 401
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-368 334 400 336 391
-369 401 315 337 403
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-371 396 342 336 413
-372 363 338 405 416
-373 375 402 359 340
-374 377 403 360 318
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-376 418 408 344 351
-377 374 419 409 345
-378 420 410 346 349
-379 363 419 321 433
-380 420 421 323 326
-381 410 424 339 329
-382 330 422 359 438
-383 364 409 423 338
-384 430 355 425 340
-385 343 365 442 426
-386 397 344 347 416
-387 366 443 345 427
-388 398 346 390 348
-389 421 357 424 348
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-391 368 414 405 351
-392 357 349 393 406
-393 352 444 392 427
-394 396 429 353 445
-395 354 411 404 361
-396 358 371 415 394
-397 386 431 362 417
-398 352 418 388 432
-399 365 431 367 434
-400 432 368 347 435
-401 366 433 423 369
-402 367 446 436 373
-403 374 444 369 428
-404 370 447 437 395
-405 407 434 391 372
-406 408 435 392 350
-407 1 375 448 405
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-409 440 377 383 450
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-411 353 463 449 395
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-413 441 455 371 361
-414 453 391 469 362
-415 396 454 370 439
-416 386 456 372 461
-417 375 397 457 472
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-419 429 377 379 447
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-421 452 389 455 380
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-424 389 381 425 438
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-426 385 475 460 428
-427 387 442 436 393
-428 390 446 403 426
-429 462 419 448 394
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-431 462 397 399 465
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-434 399 476 467 405
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-436 477 402 468 427
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-439 408 3 478 415
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-442 385 479 7 427
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-444 484 403 393 471
-445 495 423 394 482
-446 402 470 428 483
-447 419 485 490 404
-448 407 429 486 497
-449 408 411 477 460
-450 430 409 487 498
-451 453 410 412 461
-452 484 421 412 481
-453 451 498 488 414
-454 475 432 468 415
-455 421 456 413 469
-456 487 455 499 416
-457 489 500 459 417
-458 418 467 425 472
-459 476 422 435 457
-460 4 38 426 449
-461 451 478 491 416
-462 429 431 38 41
-463 432 411 491 492
-464 430 433 7 483
-465 431 501 437 493
-466 433 488 499 438
-467 434 458 502 494
-468 2 454 436 41
-469 3 455 414 492
-470 440 36 446 8
-471 441 496 444 503
-472 16 458 10 417
-473 418 422 17 503
-474 496 435 425 505
-475 454 510 426 504
-476 434 6 18 459
-477 506 509 436 449
-478 507 511 439 461
-479 440 442 489 502
-480 441 443 490 482
-481 452 443 17 505
-482 508 445 511 480
-483 464 500 446 494
-484 495 452 485 444
-485 484 507 512 447
-486 44 34 488 448
-487 497 456 493 450
-488 453 486 466 501
-489 457 479 9 75
-490 23 36 447 480
-491 463 16 18 461
-492 463 508 512 469
-493 465 487 26 51
-494 69 5 467 483
-495 484 14 445 8
-496 474 19 42 471
-497 24 487 37 448
-498 453 39 42 450
-499 33 466 456 19
-500 72 457 85 483
-501 465 15 488 40
-502 92 467 479 64
-503 473 509 471 504
-504 67 475 30 503
-505 506 474 510 481
-506 88 48 477 505
-507 485 71 478 20
-508 11 91 492 482
-509 22 477 50 503
-510 13 475 32 505
-511 478 52 74 482
-512 485 35 70 492
0

**************