Graph forms
for C4 [ 264, 9 ] = PS(22,24;5)
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On this page are computer-accessible forms for the graph C4[ 264, 9 ] =
PS(22,24;5).
(I) Following is a form readable by MAGMA:
g:=Graph<264|{ {24, 27}, {240, 243}, {120, 123}, {96, 99}, {48, 51}, {72, 75},
{144, 147}, {168, 171}, {192, 195}, {216, 219}, {16, 26}, {240, 250}, {117,
127}, {116, 126}, {113, 123}, {112, 122}, {96, 106}, {17, 27}, {20, 30}, {21,
31}, {48, 58}, {64, 74}, {65, 75}, {68, 78}, {69, 79}, {144, 154}, {160, 170},
{161, 171}, {164, 174}, {165, 175}, {192, 202}, {208, 218}, {209, 219}, {212,
222}, {213, 223}, {4, 15}, {244, 255}, {132, 143}, {128, 139}, {100, 111}, {84,
95}, {32, 43}, {36, 47}, {52, 63}, {80, 91}, {148, 159}, {176, 187}, {180, 191},
{196, 207}, {224, 235}, {228, 239}, {1, 13}, {243, 255}, {242, 254}, {241, 253},
{131, 143}, {130, 142}, {129, 141}, {128, 140}, {99, 111}, {98, 110}, {97, 109},
{2, 14}, {3, 15}, {32, 44}, {33, 45}, {34, 46}, {35, 47}, {49, 61}, {50, 62},
{51, 63}, {80, 92}, {81, 93}, {82, 94}, {83, 95}, {145, 157}, {146, 158}, {147,
159}, {176, 188}, {177, 189}, {178, 190}, {179, 191}, {193, 205}, {194, 206},
{195, 207}, {224, 236}, {225, 237}, {226, 238}, {227, 239}, {3, 14}, {243, 254},
{131, 142}, {129, 140}, {119, 122}, {99, 110}, {23, 26}, {33, 44}, {35, 46},
{51, 62}, {71, 74}, {81, 92}, {83, 94}, {147, 158}, {167, 170}, {177, 188},
{179, 190}, {195, 206}, {215, 218}, {225, 236}, {227, 238}, {18, 28}, {115,
125}, {114, 124}, {19, 29}, {66, 76}, {67, 77}, {162, 172}, {163, 173}, {210,
220}, {211, 221}, {2, 13}, {242, 253}, {130, 141}, {118, 121}, {112, 127}, {98,
109}, {16, 31}, {22, 25}, {34, 45}, {50, 61}, {64, 79}, {70, 73}, {82, 93},
{146, 157}, {160, 175}, {166, 169}, {178, 189}, {194, 205}, {208, 223}, {214,
217}, {226, 237}, {13, 28}, {237, 252}, {235, 250}, {233, 248}, {231, 246},
{139, 154}, {137, 152}, {135, 150}, {133, 148}, {111, 126}, {109, 124}, {15,
30}, {37, 52}, {39, 54}, {41, 56}, {43, 58}, {45, 60}, {65, 80}, {67, 82}, {69,
84}, {141, 156}, {161, 176}, {163, 178}, {165, 180}, {205, 220}, {207, 222},
{229, 244}, {14, 29}, {234, 249}, {138, 153}, {134, 149}, {110, 125}, {38, 53},
{42, 57}, {66, 81}, {162, 177}, {206, 221}, {230, 245}, {4, 16}, {132, 144},
{108, 120}, {103, 115}, {102, 114}, {101, 113}, {100, 112}, {5, 17}, {6, 18},
{7, 19}, {12, 24}, {36, 48}, {76, 88}, {77, 89}, {78, 90}, {79, 91}, {172, 184},
{173, 185}, {174, 186}, {175, 187}, {196, 208}, {197, 209}, {198, 210}, {199,
211}, {204, 216}, {228, 240}, {5, 16}, {103, 114}, {101, 112}, {7, 18}, {77,
88}, {79, 90}, {173, 184}, {175, 186}, {197, 208}, {199, 210}, {15, 25}, {239,
249}, {238, 248}, {231, 241}, {135, 145}, {111, 121}, {39, 49}, {46, 56}, {47,
57}, {70, 80}, {71, 81}, {142, 152}, {143, 153}, {166, 176}, {167, 177}, {207,
217}, {6, 17}, {236, 251}, {102, 113}, {44, 59}, {68, 83}, {78, 89}, {140, 155},
{164, 179}, {174, 185}, {198, 209}, {1, 24}, {97, 120}, {193, 216}, {38, 60},
{237, 247}, {236, 246}, {233, 243}, {232, 242}, {140, 150}, {137, 147}, {136,
146}, {134, 156}, {40, 50}, {41, 51}, {44, 54}, {45, 55}, {72, 82}, {141, 151},
{168, 178}, {230, 252}, {8, 19}, {108, 119}, {104, 115}, {12, 23}, {76, 87},
{172, 183}, {200, 211}, {204, 215}, {8, 20}, {107, 119}, {106, 118}, {105, 117},
{104, 116}, {9, 21}, {10, 22}, {11, 23}, {73, 85}, {74, 86}, {75, 87}, {169,
181}, {170, 182}, {171, 183}, {200, 212}, {201, 213}, {202, 214}, {203, 215},
{9, 20}, {239, 242}, {107, 118}, {105, 116}, {11, 22}, {47, 50}, {75, 86}, {143,
146}, {171, 182}, {201, 212}, {203, 214}, {37, 59}, {235, 245}, {234, 244},
{139, 149}, {138, 148}, {133, 155}, {42, 52}, {43, 53}, {229, 251}, {10, 21},
{238, 241}, {232, 247}, {136, 151}, {106, 117}, {40, 55}, {46, 49}, {74, 85},
{142, 145}, {170, 181}, {202, 213}, {25, 48}, {73, 96}, {217, 240}, {14, 36},
{158, 180}, {206, 228}, {13, 35}, {157, 179}, {205, 227}, {17, 32}, {93, 108},
{91, 106}, {89, 104}, {87, 102}, {85, 100}, {19, 34}, {21, 36}, {157, 172},
{159, 174}, {209, 224}, {211, 226}, {213, 228}, {18, 33}, {90, 105}, {86, 101},
{158, 173}, {210, 225}, {28, 40}, {84, 96}, {29, 41}, {30, 42}, {31, 43}, {148,
160}, {149, 161}, {150, 162}, {151, 163}, {156, 168}, {220, 232}, {221, 233},
{222, 234}, {223, 235}, {29, 40}, {31, 42}, {149, 160}, {151, 162}, {221, 232},
{223, 234}, {22, 32}, {95, 105}, {94, 104}, {87, 97}, {23, 33}, {159, 169},
{214, 224}, {215, 225}, {20, 35}, {92, 107}, {30, 41}, {150, 161}, {212, 227},
{222, 233}, {145, 168}, {24, 34}, {93, 103}, {92, 102}, {89, 99}, {88, 98}, {86,
108}, {216, 226}, {28, 39}, {152, 163}, {156, 167}, {220, 231}, {25, 37}, {26,
38}, {27, 39}, {152, 164}, {153, 165}, {154, 166}, {155, 167}, {217, 229}, {218,
230}, {219, 231}, {27, 38}, {95, 98}, {153, 164}, {155, 166}, {219, 230}, {85,
107}, {91, 101}, {90, 100}, {26, 37}, {94, 97}, {88, 103}, {154, 165}, {218,
229}, {169, 192}, {62, 84}, {61, 83}, {61, 76}, {63, 78}, {181, 196}, {183,
198}, {185, 200}, {187, 202}, {189, 204}, {62, 77}, {182, 197}, {186, 201}, {52,
64}, {53, 65}, {54, 66}, {55, 67}, {60, 72}, {180, 192}, {53, 64}, {55, 66},
{63, 73}, {183, 193}, {190, 200}, {191, 201}, {54, 65}, {188, 203}, {49, 72},
{182, 204}, {184, 194}, {185, 195}, {188, 198}, {189, 199}, {56, 67}, {60, 71},
{56, 68}, {57, 69}, {58, 70}, {59, 71}, {57, 68}, {59, 70}, {191, 194}, {181,
203}, {186, 196}, {187, 197}, {58, 69}, {184, 199}, {190, 193}, {121, 144},
{110, 132}, {109, 131}, {113, 128}, {117, 132}, {115, 130}, {12, 254}, {114,
129}, {124, 136}, {127, 139}, {126, 138}, {125, 137}, {125, 136}, {127, 138},
{11, 253}, {119, 129}, {118, 128}, {116, 131}, {126, 137}, {4, 253}, {6, 255},
{120, 130}, {5, 254}, {124, 135}, {121, 133}, {123, 135}, {122, 134}, {123,
134}, {1, 255}, {122, 133}, {2, 256}, {3, 257}, {6, 260}, {7, 261}, {10, 264},
{2, 263}, {4, 258}, {5, 259}, {1, 262}, {7, 256}, {8, 257}, {10, 259}, {12,
261}, {3, 264}, {9, 258}, {8, 262}, {9, 263}, {11, 260}, {244, 256}, {252, 264},
{247, 259}, {246, 258}, {245, 257}, {245, 256}, {247, 258}, {246, 257}, {241,
264}, {248, 259}, {252, 263}, {248, 260}, {251, 263}, {250, 262}, {249, 261},
{249, 260}, {251, 262}, {250, 261} }>;
(II) A more general form is to represent the graph as the orbit of {24, 27}
under the group generated by the following permutations:
a: (2, 12)(3, 11)(4, 10)(5, 9)(6, 8)(13, 24)(14, 23)(15, 22)(16, 21)(17, 20)(18,
19)(26, 36)(27, 35)(28, 34)(29, 33)(30, 32)(37, 48)(38, 47)(39, 46)(40, 45)(41,
44)(42, 43)(50, 60)(51, 59)(52, 58)(53, 57)(54, 56)(61, 72)(62, 71)(63, 70)(64,
69)(65, 68)(66, 67)(74, 84)(75, 83)(76, 82)(77, 81)(78, 80)(85, 96)(86, 95)(87,
94)(88, 93)(89, 92)(90, 91)(98, 108)(99, 107)(100, 106)(101, 105)(102, 104)(109,
120)(110, 119)(111, 118)(112, 117)(113, 116)(114, 115)(122, 132)(123, 131)(124,
130)(125, 129)(126, 128)(133, 144)(134, 143)(135, 142)(136, 141)(137, 140)(138,
139)(146, 156)(147, 155)(148, 154)(149, 153)(150, 152)(157, 168)(158, 167)(159,
166)(160, 165)(161, 164)(162, 163)(170, 180)(171, 179)(172, 178)(173, 177)(174,
176)(181, 192)(182, 191)(183, 190)(184, 189)(185, 188)(186, 187)(194, 204)(195,
203)(196, 202)(197, 201)(198, 200)(205, 216)(206, 215)(207, 214)(208, 213)(209,
212)(210, 211)(218, 228)(219, 227)(220, 226)(221, 225)(222, 224)(229, 240)(230,
239)(231, 238)(232, 237)(233, 236)(234, 235)(242, 252)(243, 251)(244, 250)(245,
249)(246, 248)(253, 264)(254, 263)(255, 262)(256, 261)(257, 260)(258, 259) (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: (1, 13, 2, 14, 3, 15, 4, 16, 5, 17, 6, 18, 7, 19, 8, 20, 9, 21, 10, 22, 11,
23, 12, 24)(25, 253, 26, 254, 27, 255, 28, 256, 29, 257, 30, 258, 31, 259, 32,
260, 33, 261, 34, 262, 35, 263, 36, 264)(37, 242, 38, 243, 39, 244, 40, 245, 41,
246, 42, 247, 43, 248, 44, 249, 45, 250, 46, 251, 47, 252, 48, 241)(49, 229, 50,
230, 51, 231, 52, 232, 53, 233, 54, 234, 55, 235, 56, 236, 57, 237, 58, 238, 59,
239, 60, 240)(61, 218, 62, 219, 63, 220, 64, 221, 65, 222, 66, 223, 67, 224, 68,
225, 69, 226, 70, 227, 71, 228, 72, 217)(73, 205, 74, 206, 75, 207, 76, 208, 77,
209, 78, 210, 79, 211, 80, 212, 81, 213, 82, 214, 83, 215, 84, 216)(85, 194, 86,
195, 87, 196, 88, 197, 89, 198, 90, 199, 91, 200, 92, 201, 93, 202, 94, 203, 95,
204, 96, 193)(97, 181, 98, 182, 99, 183, 100, 184, 101, 185, 102, 186, 103, 187,
104, 188, 105, 189, 106, 190, 107, 191, 108, 192)(109, 170, 110, 171, 111, 172,
112, 173, 113, 174, 114, 175, 115, 176, 116, 177, 117, 178, 118, 179, 119, 180,
120, 169)(121, 157, 122, 158, 123, 159, 124, 160, 125, 161, 126, 162, 127, 163,
128, 164, 129, 165, 130, 166, 131, 167, 132, 168)(133, 146, 134, 147, 135, 148,
136, 149, 137, 150, 138, 151, 139, 152, 140, 153, 141, 154, 142, 155, 143, 156,
144, 145)
c: (2, 6)(3, 11)(5, 9)(8, 12)(13, 255)(14, 260)(15, 253)(16, 258)(17, 263)(18,
256)(19, 261)(20, 254)(21, 259)(22, 264)(23, 257)(24, 262)(25, 241)(26, 246)(27,
251)(28, 244)(29, 249)(30, 242)(31, 247)(32, 252)(33, 245)(34, 250)(35, 243)(36,
248)(37, 231)(38, 236)(39, 229)(40, 234)(41, 239)(42, 232)(43, 237)(44, 230)(45,
235)(46, 240)(47, 233)(48, 238)(49, 217)(50, 222)(51, 227)(52, 220)(53, 225)(54,
218)(55, 223)(56, 228)(57, 221)(58, 226)(59, 219)(60, 224)(61, 207)(62, 212)(63,
205)(64, 210)(65, 215)(66, 208)(67, 213)(68, 206)(69, 211)(70, 216)(71, 209)(72,
214)(73, 193)(74, 198)(75, 203)(76, 196)(77, 201)(78, 194)(79, 199)(80, 204)(81,
197)(82, 202)(83, 195)(84, 200)(85, 183)(86, 188)(87, 181)(88, 186)(89, 191)(90,
184)(91, 189)(92, 182)(93, 187)(94, 192)(95, 185)(96, 190)(97, 169)(98, 174)(99,
179)(100, 172)(101, 177)(102, 170)(103, 175)(104, 180)(105, 173)(106, 178)(107,
171)(108, 176)(109, 159)(110, 164)(111, 157)(112, 162)(113, 167)(114, 160)(115,
165)(116, 158)(117, 163)(118, 168)(119, 161)(120, 166)(121, 145)(122, 150)(123,
155)(124, 148)(125, 153)(126, 146)(127, 151)(128, 156)(129, 149)(130, 154)(131,
147)(132, 152)(133, 135)(134, 140)(136, 138)(137, 143)(139, 141)(142, 144)
d: (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12)(13, 14, 15, 16, 17, 18, 19, 20, 21,
22, 23, 24)(25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36)(37, 38, 39, 40, 41,
42, 43, 44, 45, 46, 47, 48)(49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60)(61,
62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72)(73, 74, 75, 76, 77, 78, 79, 80, 81,
82, 83, 84)(85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96)(97, 98, 99, 100,
101, 102, 103, 104, 105, 106, 107, 108)(109, 110, 111, 112, 113, 114, 115, 116,
117, 118, 119, 120)(121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131,
132)(133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144)(145, 146, 147,
148, 149, 150, 151, 152, 153, 154, 155, 156)(157, 158, 159, 160, 161, 162, 163,
164, 165, 166, 167, 168)(169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179,
180)(181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192)(193, 194, 195,
196, 197, 198, 199, 200, 201, 202, 203, 204)(205, 206, 207, 208, 209, 210, 211,
212, 213, 214, 215, 216)(217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227,
228)(229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240)(241, 242, 243,
244, 245, 246, 247, 248, 249, 250, 251, 252)(253, 254, 255, 256, 257, 258, 259,
260, 261, 262, 263, 264)
C4[ 264, 9 ]
264
-1 13 24 255 262
-2 13 14 256 263
-3 264 14 15 257
-4 253 15 16 258
-5 254 16 17 259
-6 255 17 18 260
-7 256 18 19 261
-8 257 19 20 262
-9 258 20 21 263
-10 22 264 259 21
-11 22 253 23 260
-12 23 254 24 261
-13 1 2 35 28
-14 2 3 36 29
-15 3 25 4 30
-16 4 26 5 31
-17 5 27 6 32
-18 33 6 28 7
-19 34 7 29 8
-20 35 8 30 9
-21 36 9 31 10
-22 11 25 10 32
-23 11 33 12 26
-24 1 12 34 27
-25 22 15 37 48
-26 23 37 16 38
-27 24 38 17 39
-28 13 39 18 40
-29 14 40 19 41
-30 15 41 20 42
-31 16 42 21 43
-32 22 44 17 43
-33 44 23 45 18
-34 45 24 46 19
-35 13 46 47 20
-36 14 47 48 21
-37 25 26 59 52
-38 26 27 60 53
-39 27 49 28 54
-40 55 28 50 29
-41 56 29 51 30
-42 57 30 52 31
-43 58 31 53 32
-44 33 59 32 54
-45 33 55 34 60
-46 34 56 35 49
-47 35 57 36 50
-48 25 36 58 51
-49 46 39 61 72
-50 47 61 40 62
-51 48 62 41 63
-52 37 63 42 64
-53 38 64 43 65
-54 44 66 39 65
-55 66 45 67 40
-56 67 46 68 41
-57 68 47 69 42
-58 69 48 70 43
-59 44 37 70 71
-60 45 38 71 72
-61 49 50 83 76
-62 77 50 51 84
-63 78 51 73 52
-64 79 52 74 53
-65 80 53 75 54
-66 55 81 54 76
-67 55 77 56 82
-68 56 78 57 83
-69 57 79 58 84
-70 58 80 59 73
-71 59 81 60 74
-72 49 60 82 75
-73 70 63 85 96
-74 71 85 64 86
-75 72 86 65 87
-76 66 88 61 87
-77 88 67 89 62
-78 89 68 90 63
-79 90 69 91 64
-80 91 70 92 65
-81 66 92 71 93
-82 67 93 72 94
-83 68 61 94 95
-84 69 62 95 96
-85 100 73 74 107
-86 101 74 75 108
-87 102 75 97 76
-88 77 103 76 98
-89 77 99 78 104
-90 78 100 79 105
-91 79 101 80 106
-92 80 102 81 107
-93 81 103 82 108
-94 82 104 83 97
-95 83 105 84 98
-96 99 73 84 106
-97 94 87 109 120
-98 88 110 95 109
-99 110 89 111 96
-100 111 90 112 85
-101 112 91 113 86
-102 113 92 114 87
-103 88 114 93 115
-104 89 115 94 116
-105 90 116 95 117
-106 91 117 96 118
-107 92 85 118 119
-108 93 86 119 120
-109 124 97 98 131
-110 99 132 125 98
-111 99 121 100 126
-112 100 122 101 127
-113 101 123 102 128
-114 102 124 103 129
-115 103 125 104 130
-116 104 126 105 131
-117 132 105 127 106
-118 121 106 128 107
-119 122 107 129 108
-120 123 97 108 130
-121 111 133 144 118
-122 133 112 134 119
-123 134 113 135 120
-124 135 114 136 109
-125 110 136 115 137
-126 111 137 116 138
-127 112 138 117 139
-128 113 139 118 140
-129 114 140 119 141
-130 115 141 120 142
-131 143 116 109 142
-132 110 143 144 117
-133 121 122 155 148
-134 122 123 156 149
-135 123 145 124 150
-136 124 146 125 151
-137 125 147 126 152
-138 126 148 127 153
-139 154 127 149 128
-140 155 128 150 129
-141 156 129 151 130
-142 145 130 152 131
-143 132 146 131 153
-144 121 132 154 147
-145 135 157 168 142
-146 143 157 136 158
-147 144 158 137 159
-148 133 159 138 160
-149 134 160 139 161
-150 135 161 140 162
-151 136 162 141 163
-152 137 163 142 164
-153 143 165 138 164
-154 165 144 166 139
-155 133 166 167 140
-156 134 167 168 141
-157 145 146 179 172
-158 146 147 180 173
-159 147 169 148 174
-160 148 170 149 175
-161 176 149 171 150
-162 177 150 172 151
-163 178 151 173 152
-164 179 152 174 153
-165 154 180 153 175
-166 154 176 155 169
-167 155 177 156 170
-168 145 156 178 171
-169 166 159 181 192
-170 167 181 160 182
-171 168 182 161 183
-172 157 183 162 184
-173 158 184 163 185
-174 159 185 164 186
-175 165 187 160 186
-176 187 166 188 161
-177 188 167 189 162
-178 189 168 190 163
-179 157 190 191 164
-180 165 158 191 192
-181 169 170 203 196
-182 170 171 204 197
-183 198 171 193 172
-184 199 172 194 173
-185 200 173 195 174
-186 201 174 196 175
-187 176 202 175 197
-188 176 198 177 203
-189 177 199 178 204
-190 178 200 179 193
-191 179 201 180 194
-192 169 180 202 195
-193 190 183 205 216
-194 191 205 184 206
-195 192 206 185 207
-196 181 207 186 208
-197 187 209 182 208
-198 209 188 210 183
-199 210 189 211 184
-200 211 190 212 185
-201 212 191 213 186
-202 187 213 192 214
-203 188 181 214 215
-204 189 182 215 216
-205 220 193 194 227
-206 221 194 195 228
-207 222 195 217 196
-208 223 196 218 197
-209 198 224 197 219
-210 198 220 199 225
-211 199 221 200 226
-212 200 222 201 227
-213 201 223 202 228
-214 202 224 203 217
-215 203 225 204 218
-216 193 204 226 219
-217 214 207 229 240
-218 215 229 208 230
-219 209 231 216 230
-220 231 210 232 205
-221 232 211 233 206
-222 233 212 234 207
-223 234 213 235 208
-224 209 235 214 236
-225 210 236 215 237
-226 211 237 216 238
-227 212 205 238 239
-228 213 206 239 240
-229 244 217 218 251
-230 245 218 219 252
-231 220 246 219 241
-232 220 242 221 247
-233 221 243 222 248
-234 222 244 223 249
-235 223 245 224 250
-236 224 246 225 251
-237 225 247 226 252
-238 226 248 227 241
-239 242 227 249 228
-240 243 217 228 250
-241 231 253 264 238
-242 253 232 254 239
-243 254 233 255 240
-244 255 234 256 229
-245 256 235 257 230
-246 231 257 236 258
-247 232 258 237 259
-248 233 259 238 260
-249 234 260 239 261
-250 235 261 240 262
-251 236 229 262 263
-252 264 237 230 263
-253 11 242 4 241
-254 242 12 243 5
-255 1 243 244 6
-256 2 244 245 7
-257 3 245 246 8
-258 4 246 247 9
-259 5 247 248 10
-260 11 6 248 249
-261 12 7 249 250
-262 1 8 250 251
-263 2 9 251 252
-264 3 10 241 252
0