Graph forms
for C4 [ 312, 52 ] = SS[312,1]
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On this page are computer-accessible forms for the graph C4[ 312, 52 ] =
SS[312,1].
(I) Following is a form readable by MAGMA:
g:=Graph<312|{ {14, 15}, {264, 265}, {48, 49}, {24, 25}, {22, 23}, {1, 3}, {60,
62}, {44, 46}, {28, 30}, {13, 15}, {1, 2}, {36, 39}, {24, 27}, {20, 23}, {1, 5},
{59, 63}, {57, 61}, {43, 47}, {34, 38}, {33, 37}, {105, 109}, {1, 4}, {264,
269}, {186, 191}, {26, 31}, {106, 111}, {107, 110}, {27, 29}, {187, 189}, {40,
46}, {42, 45}, {185, 190}, {34, 42}, {36, 44}, {38, 47}, {262, 271}, {256, 265},
{33, 43}, {262, 268}, {39, 45}, {35, 41}, {19, 24}, {292, 303}, {261, 270},
{180, 191}, {35, 40}, {23, 28}, {32, 44}, {290, 302}, {289, 301}, {263, 267},
{21, 24}, {176, 189}, {23, 26}, {96, 111}, {261, 266}, {178, 189}, {177, 190},
{105, 121}, {175, 191}, {174, 190}, {106, 122}, {107, 123}, {108, 124}, {96,
114}, {106, 120}, {103, 116}, {299, 312}, {295, 308}, {291, 304}, {108, 120},
{294, 306}, {293, 305}, {37, 48}, {104, 125}, {101, 115}, {102, 113}, {288,
311}, {263, 272}, {33, 57}, {258, 282}, {34, 58}, {102, 126}, {41, 48}, {259,
282}, {108, 117}, {10, 16}, {259, 281}, {257, 283}, {46, 52}, {11, 17}, {101,
127}, {104, 114}, {296, 307}, {300, 311}, {14, 18}, {298, 310}, {297, 309}, {47,
51}, {106, 118}, {107, 119}, {108, 112}, {257, 284}, {260, 281}, {12, 18}, {258,
284}, {14, 16}, {105, 119}, {107, 117}, {14, 17}, {260, 283}, {256, 287}, {45,
50}, {36, 59}, {35, 60}, {105, 118}, {269, 301}, {274, 306}, {273, 305}, {270,
302}, {89, 120}, {88, 123}, {88, 126}, {275, 308}, {287, 312}, {279, 304}, {276,
307}, {85, 125}, {286, 310}, {285, 309}, {282, 306}, {281, 305}, {86, 127}, {92,
118}, {87, 124}, {95, 116}, {82, 126}, {93, 113}, {91, 119}, {86, 122}, {85,
121}, {15, 34}, {94, 115}, {81, 127}, {94, 112}, {83, 125}, {90, 117}, {284,
307}, {283, 308}, {93, 109}, {95, 110}, {11, 56}, {267, 312}, {18, 33}, {16,
35}, {17, 36}, {31, 42}, {29, 43}, {280, 302}, {30, 41}, {25, 32}, {277, 303},
{12, 55}, {278, 301}, {268, 311}, {13, 54}, {265, 309}, {266, 310}, {10, 53},
{272, 303}, {271, 304}, {18, 83}, {22, 87}, {20, 85}, {16, 82}, {144, 210},
{146, 208}, {164, 230}, {39, 100}, {175, 236}, {37, 97}, {173, 233}, {38, 98},
{17, 84}, {174, 235}, {19, 86}, {165, 224}, {158, 216}, {161, 231}, {163, 229},
{159, 215}, {162, 232}, {40, 99}, {43, 96}, {155, 208}, {157, 214}, {21, 88},
{151, 199}, {152, 201}, {181, 228}, {177, 224}, {154, 200}, {156, 206}, {8, 91},
{9, 90}, {132, 215}, {149, 198}, {153, 205}, {154, 207}, {183, 226}, {131, 213},
{129, 214}, {182, 225}, {169, 241}, {170, 242}, {141, 212}, {157, 196}, {130,
216}, {176, 234}, {148, 206}, {7, 92}, {184, 227}, {151, 204}, {156, 199}, {143,
211}, {158, 194}, {159, 195}, {150, 203}, {152, 197}, {15, 81}, {145, 207},
{147, 205}, {150, 200}, {155, 197}, {6, 89}, {172, 243}, {142, 209}, {149, 202},
{153, 198}, {171, 244}, {137, 232}, {187, 218}, {181, 212}, {160, 193}, {165,
196}, {128, 226}, {185, 219}, {134, 228}, {6, 101}, {179, 208}, {166, 194},
{167, 195}, {183, 210}, {188, 217}, {133, 227}, {186, 220}, {135, 225}, {176,
215}, {182, 209}, {145, 249}, {146, 250}, {140, 229}, {168, 193}, {170, 195},
{136, 226}, {169, 194}, {184, 211}, {180, 223}, {60, 80}, {178, 222}, {138,
230}, {139, 231}, {172, 193}, {173, 192}, {8, 102}, {179, 221}, {9, 103}, {7,
104}, {147, 252}, {148, 251}, {171, 196}, {55, 71}, {52, 70}, {184, 202}, {53,
71}, {140, 254}, {44, 95}, {187, 200}, {179, 192}, {54, 69}, {53, 70}, {40, 92},
{42, 94}, {41, 93}, {137, 253}, {139, 255}, {59, 78}, {160, 213}, {49, 71},
{174, 216}, {57, 79}, {168, 222}, {50, 69}, {58, 77}, {25, 97}, {59, 67}, {57,
65}, {162, 218}, {163, 219}, {167, 223}, {26, 99}, {181, 204}, {58, 64}, {175,
213}, {51, 72}, {188, 199}, {180, 207}, {173, 214}, {166, 221}, {169, 210},
{170, 209}, {37, 89}, {188, 192}, {186, 198}, {185, 197}, {39, 91}, {38, 90},
{56, 69}, {182, 203}, {161, 220}, {164, 217}, {28, 98}, {183, 201}, {60, 66},
{58, 68}, {56, 70}, {54, 72}, {27, 100}, {178, 205}, {177, 206}, {55, 72}, {171,
212}, {172, 211}, {32, 161}, {48, 177}, {32, 165}, {63, 184}, {112, 247}, {62,
183}, {61, 182}, {10, 152}, {62, 172}, {114, 224}, {123, 232}, {61, 169}, {63,
171}, {111, 248}, {109, 245}, {110, 246}, {124, 229}, {125, 228}, {12, 150},
{46, 180}, {13, 151}, {127, 227}, {47, 178}, {122, 231}, {11, 149}, {45, 179},
{121, 230}, {126, 225}, {109, 204}, {120, 217}, {110, 203}, {111, 202}, {10,
162}, {12, 164}, {11, 163}, {116, 221}, {117, 220}, {13, 161}, {118, 218}, {119,
219}, {115, 222}, {113, 223}, {63, 144}, {61, 141}, {62, 142}, {30, 168}, {31,
167}, {112, 201}, {29, 166}, {31, 164}, {30, 163}, {29, 162}, {85, 149}, {87,
150}, {75, 136}, {95, 156}, {93, 153}, {94, 154}, {78, 136}, {77, 133}, {82,
154}, {81, 153}, {77, 132}, {89, 144}, {79, 134}, {52, 254}, {65, 138}, {76,
135}, {66, 137}, {49, 253}, {74, 134}, {73, 133}, {50, 255}, {79, 130}, {86,
152}, {64, 143}, {88, 151}, {84, 155}, {83, 156}, {78, 129}, {68, 139}, {67,
140}, {81, 129}, {82, 130}, {76, 158}, {76, 159}, {92, 143}, {80, 131}, {56,
236}, {90, 142}, {84, 128}, {73, 157}, {70, 146}, {74, 159}, {75, 158}, {69,
147}, {91, 141}, {71, 145}, {74, 157}, {87, 128}, {84, 131}, {83, 132}, {80,
135}, {76, 148}, {74, 147}, {75, 145}, {73, 146}, {72, 148}, {55, 234}, {53,
235}, {54, 233}, {19, 243}, {26, 250}, {25, 249}, {20, 244}, {97, 129}, {98,
131}, {104, 137}, {20, 240}, {8, 238}, {100, 130}, {21, 242}, {79, 168}, {28,
251}, {27, 252}, {22, 241}, {99, 132}, {103, 128}, {7, 239}, {73, 160}, {78,
167}, {64, 170}, {102, 140}, {6, 237}, {77, 166}, {75, 160}, {68, 175}, {100,
143}, {65, 173}, {103, 139}, {67, 174}, {97, 142}, {98, 141}, {101, 138}, {7,
246}, {9, 248}, {66, 176}, {6, 245}, {99, 144}, {64, 181}, {80, 165}, {21, 237},
{66, 186}, {65, 185}, {9, 240}, {22, 239}, {96, 155}, {19, 238}, {8, 247}, {68,
187}, {67, 188}, {4, 301}, {5, 302}, {3, 303}, {3, 306}, {5, 308}, {2, 304},
{49, 259}, {2, 305}, {51, 256}, {50, 257}, {4, 311}, {3, 310}, {52, 258}, {2,
309}, {51, 260}, {4, 307}, {5, 312}, {116, 262}, {113, 261}, {115, 263}, {121,
257}, {122, 258}, {114, 264}, {123, 260}, {124, 259}, {135, 262}, {134, 261},
{138, 256}, {133, 264}, {136, 263}, {191, 300}, {189, 297}, {190, 298}, {218,
280}, {224, 291}, {237, 296}, {239, 295}, {220, 277}, {238, 293}, {219, 279},
{217, 278}, {200, 283}, {248, 299}, {244, 288}, {240, 294}, {249, 289}, {250,
290}, {196, 286}, {199, 284}, {247, 300}, {193, 285}, {246, 298}, {245, 297},
{198, 282}, {197, 281}, {194, 287}, {251, 292}, {255, 288}, {252, 291}, {245,
277}, {254, 286}, {253, 285}, {246, 278}, {244, 277}, {195, 288}, {239, 268},
{236, 271}, {242, 278}, {243, 279}, {235, 270}, {238, 267}, {207, 296}, {237,
266}, {234, 269}, {232, 271}, {201, 289}, {252, 276}, {251, 275}, {250, 274},
{249, 273}, {230, 270}, {206, 294}, {205, 293}, {202, 290}, {241, 280}, {231,
269}, {192, 299}, {241, 285}, {242, 287}, {243, 286}, {203, 292}, {248, 279},
{247, 280}, {204, 291}, {213, 293}, {226, 274}, {225, 273}, {214, 294}, {254,
268}, {255, 267}, {229, 272}, {208, 295}, {253, 266}, {228, 275}, {227, 276},
{209, 297}, {234, 274}, {233, 273}, {210, 298}, {233, 272}, {240, 265}, {223,
292}, {221, 289}, {222, 290}, {211, 300}, {236, 275}, {235, 276}, {216, 295},
{215, 296}, {212, 299} }>;
(II) A more general form is to represent the graph as the orbit of {14, 15}
under the group generated by the following permutations:
a: (1, 10, 63, 256, 207, 243, 33, 195, 305, 35, 212, 72, 191, 219, 83, 255, 259,
92, 192, 234, 247, 190, 77, 263, 253, 100, 214, 189, 102, 224, 34, 303, 232, 36,
240, 200, 254, 96, 31)(2, 16, 171, 51, 180, 279, 18, 288, 281, 40, 299, 55, 300,
185, 132, 267, 49, 143, 173, 176, 8, 177, 58, 272, 137, 39, 294, 187, 140, 114,
42, 3, 162, 59, 265, 154, 286, 43, 167)(4, 152, 144, 287, 145, 172, 57, 159,
293, 41, 181, 54, 186, 119, 156, 139, 124, 7, 179, 274, 280, 174, 133, 115, 266,
27, 129, 297, 126, 165, 38, 292, 271, 17, 20, 283, 52, 111, 164)(5, 53, 184,
138, 296, 19, 37, 170, 273, 60, 141, 148, 175, 163, 125, 50, 282, 118, 188, 269,
112, 298, 166, 136, 285, 130, 157, 178, 113, 291, 15, 277, 123, 44, 9, 150, 268,
155, 26)(6, 21, 25, 142, 182, 135, 131, 28, 275, 56, 149, 121, 284, 122, 120,
278, 289, 183, 169, 158, 160, 168, 134, 147, 153, 109, 151, 161, 117, 110, 116,
128, 22, 295, 146, 290, 270, 276, 127)(11, 85, 257, 258, 106, 217, 301, 201,
210, 194, 75, 193, 79, 74, 205, 93, 204, 13, 220, 107, 95, 103, 87, 239, 208,
250, 302, 235, 227, 101, 237, 24, 97, 209, 225, 80, 98, 251, 236)(12, 311, 197,
99, 312, 71, 211, 65, 215, 238, 48, 64, 233, 66, 91, 206, 68, 229, 104, 45, 306,
218, 67, 264, 94, 310, 29, 78, 309, 82, 196, 47, 223, 304, 14, 244, 260, 46,
248)(23, 308, 70, 202, 230, 307, 86, 89, 242, 249, 62, 61, 76, 213, 30, 228, 69,
198, 105, 199, 231, 108, 246, 221, 226, 241, 216, 73, 222, 261, 252, 81, 245,
88, 32, 90, 203, 262, 84) (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, 3, 4, 5)(6, 7, 8, 9)(10, 11, 13, 12)(15, 18, 16, 17)(19, 20, 21, 22)(23,
24)(25, 26, 27, 28)(29, 30, 32, 31)(33, 35, 36, 34)(37, 40, 39, 38)(41, 44, 42,
43)(45, 47, 48, 46)(49, 52, 50, 51)(53, 56, 54, 55)(57, 60, 59, 58)(61, 62, 63,
64)(65, 66, 67, 68)(69, 72, 71, 70)(73, 74, 76, 75)(77, 79, 80, 78)(81, 83, 82,
84)(85, 88, 87, 86)(89, 92, 91, 90)(93, 95, 94, 96)(97, 99, 100, 98)(101, 104,
102, 103)(105, 107, 108, 106)(109, 110, 112, 111)(113, 116, 115, 114)(117, 120,
118, 119)(121, 123, 124, 122)(125, 126, 128, 127)(129, 132, 130, 131)(133, 134,
135, 136)(137, 140, 139, 138)(141, 142, 144, 143)(145, 146, 147, 148)(149, 151,
150, 152)(153, 156, 154, 155)(157, 159, 158, 160)(161, 164, 162, 163)(165, 167,
166, 168)(169, 172, 171, 170)(173, 176, 174, 175)(177, 180, 179, 178)(181, 182,
183, 184)(185, 186, 188, 187)(189, 190, 191, 192)(193, 196, 195, 194)(197, 198,
199, 200)(201, 202, 204, 203)(205, 206, 207, 208)(209, 210, 211, 212)(213, 214,
215, 216)(217, 218, 219, 220)(221, 222, 224, 223)(225, 226, 227, 228)(229, 231,
230, 232)(233, 234, 235, 236)(237, 239, 238, 240)(241, 243, 244, 242)(245, 246,
247, 248)(249, 250, 252, 251)(253, 254, 255, 256)(257, 260, 259, 258)(261, 262,
263, 264)(265, 266, 268, 267)(269, 270, 271, 272)(273, 274, 276, 275)(277, 278,
280, 279)(281, 282, 284, 283)(285, 286, 288, 287)(289, 290, 291, 292)(293, 294,
296, 295)(297, 298, 300, 299)(301, 302, 304, 303)(305, 306, 307, 308)(309, 310,
311, 312)
C4[ 312, 52 ]
312
-1 2 3 4 5
-2 1 309 304 305
-3 1 310 303 306
-4 1 311 301 307
-5 308 1 312 302
-6 89 101 245 237
-7 92 246 104 239
-8 91 102 247 238
-9 90 103 248 240
-10 16 162 53 152
-11 56 17 149 163
-12 55 18 150 164
-13 15 161 151 54
-14 15 16 17 18
-15 34 13 14 81
-16 35 14 82 10
-17 11 14 36 84
-18 33 12 14 83
-19 243 24 238 86
-20 23 244 85 240
-21 88 242 24 237
-22 23 239 87 241
-23 22 26 28 20
-24 25 27 19 21
-25 24 249 97 32
-26 99 23 250 31
-27 100 24 29 252
-28 23 30 251 98
-29 166 27 162 43
-30 168 28 41 163
-31 167 26 42 164
-32 44 165 25 161
-33 57 37 18 43
-34 58 15 38 42
-35 16 60 40 41
-36 44 59 17 39
-37 33 89 48 97
-38 34 90 47 98
-39 45 100 36 91
-40 99 35 46 92
-41 35 48 93 30
-42 34 45 94 31
-43 33 47 29 96
-44 46 36 95 32
-45 179 39 50 42
-46 44 180 40 52
-47 178 38 51 43
-48 177 37 49 41
-49 253 48 71 259
-50 45 255 69 257
-51 47 256 72 260
-52 254 46 70 258
-53 70 235 71 10
-54 13 233 69 72
-55 12 234 71 72
-56 11 69 70 236
-57 33 79 61 65
-58 77 34 68 64
-59 67 78 36 63
-60 66 35 80 62
-61 57 169 182 141
-62 60 172 183 142
-63 144 59 171 184
-64 143 58 170 181
-65 57 138 173 185
-66 176 60 137 186
-67 188 59 140 174
-68 187 58 139 175
-69 56 147 50 54
-70 56 146 52 53
-71 55 145 49 53
-72 55 148 51 54
-73 133 146 157 160
-74 134 157 147 159
-75 145 136 158 160
-76 135 158 148 159
-77 132 133 166 58
-78 167 59 136 129
-79 57 134 168 130
-80 165 135 60 131
-81 15 127 129 153
-82 154 16 126 130
-83 132 156 125 18
-84 155 17 128 131
-85 121 125 149 20
-86 122 127 19 152
-87 22 124 128 150
-88 123 126 151 21
-89 144 37 6 120
-90 38 117 9 142
-91 39 8 119 141
-92 143 7 40 118
-93 113 41 109 153
-94 154 112 115 42
-95 44 110 156 116
-96 111 155 114 43
-97 25 37 129 142
-98 38 28 141 131
-99 132 144 26 40
-100 143 27 39 130
-101 115 6 127 138
-102 113 126 8 140
-103 116 128 139 9
-104 114 125 137 7
-105 121 118 119 109
-106 111 122 118 120
-107 110 123 117 119
-108 112 124 117 120
-109 245 93 105 204
-110 246 203 95 107
-111 202 248 106 96
-112 201 247 94 108
-113 102 223 93 261
-114 264 224 104 96
-115 101 222 94 263
-116 221 103 95 262
-117 220 90 107 108
-118 92 105 106 218
-119 91 105 107 219
-120 89 106 217 108
-121 257 105 85 230
-122 231 258 106 86
-123 88 232 260 107
-124 259 108 229 87
-125 104 83 85 228
-126 88 102 82 225
-127 101 81 227 86
-128 103 226 84 87
-129 78 81 214 97
-130 100 79 82 216
-131 80 213 84 98
-132 77 99 83 215
-133 77 264 73 227
-134 79 74 228 261
-135 80 225 262 76
-136 78 226 75 263
-137 66 253 232 104
-138 101 256 65 230
-139 231 68 255 103
-140 67 254 102 229
-141 91 212 61 98
-142 209 90 62 97
-143 100 211 92 64
-144 99 89 210 63
-145 71 249 75 207
-146 70 73 250 208
-147 69 205 74 252
-148 72 206 251 76
-149 11 198 202 85
-150 12 200 203 87
-151 88 199 13 204
-152 201 86 10 197
-153 198 81 93 205
-154 200 82 94 207
-155 84 96 197 208
-156 199 83 95 206
-157 214 73 74 196
-158 194 216 75 76
-159 215 74 195 76
-160 213 193 73 75
-161 220 231 13 32
-162 232 29 218 10
-163 11 30 229 219
-164 12 217 31 230
-165 80 224 196 32
-166 77 221 29 194
-167 78 223 195 31
-168 79 222 193 30
-169 210 61 194 241
-170 209 242 195 64
-171 244 212 63 196
-172 243 211 193 62
-173 233 192 214 65
-174 67 190 235 216
-175 68 191 213 236
-176 66 189 234 215
-177 190 48 224 206
-178 189 222 47 205
-179 45 221 192 208
-180 46 223 191 207
-181 212 204 228 64
-182 209 203 225 61
-183 210 201 226 62
-184 211 202 227 63
-185 190 65 197 219
-186 66 198 220 191
-187 68 189 200 218
-188 67 199 192 217
-189 176 187 297 178
-190 177 298 174 185
-191 300 180 175 186
-192 188 299 179 173
-193 168 160 172 285
-194 166 287 158 169
-195 167 288 159 170
-196 165 286 157 171
-197 155 281 152 185
-198 149 282 153 186
-199 188 156 151 284
-200 154 187 150 283
-201 112 289 183 152
-202 111 290 149 184
-203 110 182 292 150
-204 181 291 151 109
-205 178 147 293 153
-206 177 156 148 294
-207 154 145 180 296
-208 155 146 179 295
-209 297 170 182 142
-210 144 298 169 183
-211 143 300 172 184
-212 299 181 171 141
-213 160 293 131 175
-214 157 129 173 294
-215 132 176 159 296
-216 158 130 174 295
-217 188 278 120 164
-218 187 280 118 162
-219 279 119 163 185
-220 277 117 161 186
-221 166 179 289 116
-222 178 168 290 115
-223 167 113 180 292
-224 165 177 114 291
-225 135 126 182 273
-226 136 128 183 274
-227 133 276 127 184
-228 275 134 125 181
-229 124 140 272 163
-230 121 138 270 164
-231 122 269 139 161
-232 123 137 271 162
-233 173 272 273 54
-234 55 176 269 274
-235 276 270 53 174
-236 275 56 271 175
-237 266 6 21 296
-238 267 293 8 19
-239 22 268 7 295
-240 265 294 9 20
-241 22 169 280 285
-242 287 278 170 21
-243 286 279 172 19
-244 277 288 171 20
-245 297 277 6 109
-246 110 298 278 7
-247 112 300 280 8
-248 111 299 279 9
-249 145 25 289 273
-250 146 26 290 274
-251 275 148 28 292
-252 276 147 27 291
-253 266 49 137 285
-254 286 268 52 140
-255 288 267 50 139
-256 265 287 138 51
-257 121 50 283 284
-258 122 282 52 284
-259 124 49 281 282
-260 123 281 51 283
-261 134 266 113 270
-262 135 268 116 271
-263 267 136 115 272
-264 133 265 114 269
-265 264 309 256 240
-266 253 310 237 261
-267 255 312 238 263
-268 254 311 239 262
-269 231 264 234 301
-270 235 302 261 230
-271 232 236 304 262
-272 233 303 229 263
-273 233 225 249 305
-274 234 226 250 306
-275 308 236 228 251
-276 235 227 252 307
-277 220 244 245 303
-278 242 246 301 217
-279 243 248 304 219
-280 247 302 218 241
-281 259 260 305 197
-282 198 258 259 306
-283 308 200 257 260
-284 199 257 258 307
-285 253 309 193 241
-286 243 254 310 196
-287 242 256 312 194
-288 244 255 311 195
-289 221 201 301 249
-290 222 202 302 250
-291 224 204 304 252
-292 223 203 303 251
-293 213 205 238 305
-294 214 206 240 306
-295 308 216 239 208
-296 215 237 207 307
-297 209 309 189 245
-298 210 310 190 246
-299 212 312 192 248
-300 211 311 191 247
-301 278 289 4 269
-302 290 5 280 270
-303 277 3 292 272
-304 2 279 291 271
-305 2 281 293 273
-306 3 282 294 274
-307 276 4 284 296
-308 275 5 283 295
-309 297 265 2 285
-310 286 298 266 3
-311 288 300 4 268
-312 287 299 267 5
0