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