Graph forms
for C4 [ 320, 51 ] = MSZ(20,16,3,7)
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On this page are computer-accessible forms for the graph C4[ 320, 51 ] =
MSZ(20,16,3,7).
(I) Following is a form readable by MAGMA:
g:=Graph<320|{ {2, 3}, {318, 319}, {316, 317}, {314, 315}, {312, 313}, {310,
311}, {308, 309}, {306, 307}, {304, 305}, {302, 303}, {298, 299}, {296, 297},
{294, 295}, {292, 293}, {290, 291}, {288, 289}, {286, 287}, {284, 285}, {282,
283}, {278, 279}, {276, 277}, {274, 275}, {272, 273}, {270, 271}, {268, 269},
{266, 267}, {264, 265}, {262, 263}, {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}, {218, 219}, {216, 217}, {214, 215}, {212, 213}, {210, 211},
{208, 209}, {206, 207}, {204, 205}, {202, 203}, {198, 199}, {104, 105}, {102,
103}, {98, 99}, {96, 97}, {94, 95}, {92, 93}, {90, 91}, {88, 89}, {86, 87}, {84,
85}, {82, 83}, {78, 79}, {76, 77}, {74, 75}, {72, 73}, {70, 71}, {68, 69}, {66,
67}, {64, 65}, {4, 5}, {6, 7}, {8, 9}, {10, 11}, {12, 13}, {14, 15}, {16, 17},
{18, 19}, {22, 23}, {24, 25}, {26, 27}, {28, 29}, {30, 31}, {32, 33}, {34, 35},
{36, 37}, {38, 39}, {42, 43}, {44, 45}, {46, 47}, {48, 49}, {50, 51}, {52, 53},
{54, 55}, {56, 57}, {58, 59}, {62, 63}, {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},
{142, 143}, {144, 145}, {146, 147}, {148, 149}, {150, 151}, {152, 153}, {154,
155}, {156, 157}, {158, 159}, {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},
{1, 2}, {317, 318}, {313, 314}, {309, 310}, {305, 306}, {301, 302}, {300, 303},
{297, 298}, {293, 294}, {289, 290}, {285, 286}, {281, 282}, {280, 283}, {277,
278}, {273, 274}, {269, 270}, {265, 266}, {261, 262}, {260, 263}, {257, 258},
{253, 254}, {249, 250}, {245, 246}, {241, 242}, {240, 243}, {237, 238}, {233,
234}, {229, 230}, {225, 226}, {221, 222}, {220, 223}, {217, 218}, {213, 214},
{209, 210}, {205, 206}, {201, 202}, {200, 203}, {197, 198}, {105, 106}, {101,
102}, {100, 103}, {97, 98}, {93, 94}, {89, 90}, {85, 86}, {81, 82}, {80, 83},
{77, 78}, {73, 74}, {69, 70}, {65, 66}, {5, 6}, {9, 10}, {13, 14}, {17, 18},
{20, 23}, {21, 22}, {25, 26}, {29, 30}, {33, 34}, {37, 38}, {40, 43}, {41, 42},
{45, 46}, {49, 50}, {53, 54}, {57, 58}, {60, 63}, {61, 62}, {109, 110}, {113,
114}, {117, 118}, {120, 123}, {121, 122}, {125, 126}, {129, 130}, {133, 134},
{137, 138}, {140, 143}, {141, 142}, {145, 146}, {149, 150}, {153, 154}, {157,
158}, {160, 163}, {161, 162}, {165, 166}, {169, 170}, {173, 174}, {177, 178},
{180, 183}, {181, 182}, {185, 186}, {189, 190}, {193, 194}, {3, 4}, {315, 316},
{307, 308}, {299, 300}, {298, 301}, {291, 292}, {283, 284}, {275, 276}, {267,
268}, {259, 260}, {258, 261}, {251, 252}, {243, 244}, {235, 236}, {227, 228},
{219, 220}, {218, 221}, {211, 212}, {203, 204}, {99, 100}, {98, 101}, {91, 92},
{83, 84}, {75, 76}, {67, 68}, {11, 12}, {18, 21}, {19, 20}, {27, 28}, {35, 36},
{43, 44}, {51, 52}, {58, 61}, {59, 60}, {107, 108}, {115, 116}, {123, 124},
{131, 132}, {138, 141}, {139, 140}, {147, 148}, {155, 156}, {163, 164}, {171,
172}, {178, 181}, {179, 180}, {187, 188}, {195, 196}, {7, 8}, {311, 312}, {295,
296}, {279, 280}, {278, 281}, {263, 264}, {247, 248}, {231, 232}, {215, 216},
{199, 200}, {198, 201}, {103, 104}, {87, 88}, {71, 72}, {23, 24}, {38, 41}, {39,
40}, {55, 56}, {118, 121}, {119, 120}, {135, 136}, {151, 152}, {167, 168}, {183,
184}, {1, 20}, {201, 220}, {41, 60}, {161, 180}, {8, 31}, {296, 319}, {288,
311}, {264, 287}, {256, 279}, {232, 255}, {224, 247}, {104, 127}, {96, 119},
{72, 95}, {64, 87}, {32, 55}, {128, 151}, {136, 159}, {168, 191}, {192, 215},
{2, 25}, {294, 317}, {290, 313}, {262, 285}, {230, 253}, {226, 249}, {102, 125},
{70, 93}, {66, 89}, {6, 29}, {34, 57}, {130, 153}, {134, 157}, {162, 185}, {166,
189}, {194, 217}, {101, 120}, {261, 280}, {4, 27}, {303, 304}, {292, 315}, {271,
272}, {239, 240}, {238, 241}, {228, 251}, {207, 208}, {196, 219}, {79, 80}, {78,
81}, {68, 91}, {15, 16}, {36, 59}, {47, 48}, {111, 112}, {132, 155}, {143, 144},
{164, 187}, {175, 176}, {10, 33}, {286, 309}, {282, 305}, {270, 293}, {266,
289}, {222, 245}, {206, 229}, {202, 225}, {94, 117}, {90, 113}, {74, 97}, {14,
37}, {26, 49}, {30, 53}, {142, 165}, {154, 177}, {141, 160}, {221, 240}, {12,
35}, {284, 307}, {268, 291}, {204, 227}, {92, 115}, {76, 99}, {28, 51}, {156,
179}, {81, 100}, {281, 300}, {16, 39}, {272, 295}, {216, 239}, {208, 231}, {88,
111}, {24, 47}, {144, 167}, {152, 175}, {22, 45}, {274, 297}, {214, 237}, {210,
233}, {86, 109}, {82, 105}, {146, 169}, {150, 173}, {21, 40}, {31, 32}, {287,
288}, {276, 299}, {223, 224}, {212, 235}, {95, 96}, {84, 107}, {148, 171}, {158,
161}, {159, 160}, {42, 65}, {46, 69}, {62, 85}, {170, 193}, {174, 197}, {186,
209}, {190, 213}, {61, 80}, {301, 320}, {44, 67}, {172, 195}, {188, 211}, {48,
71}, {56, 79}, {176, 199}, {184, 207}, {50, 73}, {54, 77}, {182, 205}, {181,
200}, {52, 75}, {319, 320}, {63, 64}, {191, 192}, {39, 162}, {79, 202}, {119,
242}, {59, 182}, {1, 144}, {105, 248}, {103, 246}, {101, 244}, {97, 240}, {77,
220}, {75, 218}, {73, 216}, {71, 214}, {69, 212}, {67, 210}, {65, 208}, {3,
146}, {5, 148}, {7, 150}, {9, 152}, {11, 154}, {13, 156}, {15, 158}, {33, 176},
{35, 178}, {37, 180}, {41, 184}, {43, 186}, {45, 188}, {47, 190}, {107, 250},
{109, 252}, {111, 254}, {19, 142}, {4, 181}, {95, 238}, {93, 236}, {91, 234},
{89, 232}, {87, 230}, {85, 228}, {83, 226}, {81, 224}, {78, 255}, {76, 253},
{74, 251}, {72, 249}, {70, 247}, {68, 245}, {66, 243}, {64, 241}, {6, 183}, {8,
185}, {10, 187}, {12, 189}, {14, 191}, {17, 160}, {21, 164}, {23, 166}, {25,
168}, {27, 170}, {29, 172}, {31, 174}, {99, 222}, {2, 199}, {42, 239}, {22,
219}, {16, 193}, {18, 195}, {20, 197}, {24, 201}, {26, 203}, {28, 205}, {30,
207}, {48, 225}, {50, 227}, {52, 229}, {54, 231}, {56, 233}, {58, 235}, {60,
237}, {106, 129}, {110, 133}, {122, 145}, {126, 149}, {108, 131}, {124, 147},
{32, 209}, {63, 206}, {34, 211}, {36, 213}, {38, 215}, {40, 217}, {44, 221},
{46, 223}, {49, 192}, {51, 194}, {53, 196}, {55, 198}, {57, 200}, {61, 204},
{121, 140}, {112, 135}, {114, 137}, {116, 139}, {127, 128}, {5, 302}, {17, 314},
{19, 316}, {7, 304}, {15, 312}, {9, 306}, {13, 310}, {62, 259}, {1, 318}, {11,
308}, {3, 320}, {82, 279}, {122, 319}, {102, 299}, {80, 257}, {94, 271}, {92,
269}, {90, 267}, {88, 265}, {86, 263}, {84, 261}, {112, 289}, {114, 291}, {116,
293}, {118, 295}, {120, 297}, {124, 301}, {126, 303}, {96, 273}, {104, 281},
{100, 277}, {98, 275}, {106, 283}, {108, 285}, {110, 287}, {113, 256}, {115,
258}, {117, 260}, {121, 264}, {123, 266}, {125, 268}, {127, 270}, {159, 282},
{139, 262}, {129, 272}, {131, 274}, {133, 276}, {135, 278}, {137, 280}, {141,
284}, {143, 286}, {161, 304}, {163, 306}, {165, 308}, {167, 310}, {169, 312},
{171, 314}, {173, 316}, {175, 318}, {179, 302}, {128, 305}, {130, 307}, {132,
309}, {134, 311}, {136, 313}, {138, 315}, {140, 317}, {145, 288}, {147, 290},
{149, 292}, {151, 294}, {153, 296}, {155, 298}, {157, 300}, {234, 257}, {254,
277}, {250, 273}, {236, 259}, {252, 275}, {177, 320}, {241, 260}, {248, 271},
{242, 265}, {246, 269}, {244, 267}, {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: (2, 318, 20, 144)(3, 175, 19, 167)(4, 152, 18, 310)(5, 9, 17, 13)(6, 306, 16,
156)(7, 163, 15, 179)(8, 160, 14, 302)(10, 314, 12, 148)(11, 171)(21, 311, 181,
151)(22, 288, 200, 294)(23, 145, 199, 317)(24, 122, 198, 140)(25, 319, 197,
143)(26, 296, 196, 286)(27, 153, 195, 309)(28, 130, 194, 132)(29, 307, 193,
155)(30, 284, 192, 298)(31, 141, 191, 301)(32, 138, 190, 124)(33, 315, 189,
147)(34, 292, 188, 290)(35, 149, 187, 313)(36, 126, 186, 136)(37, 303, 185,
159)(38, 300, 184, 282)(39, 157, 183, 305)(40, 134, 182, 128)(41, 281)(42, 278,
60, 104)(43, 135, 59, 127)(44, 112, 58, 270)(45, 289, 57, 293)(46, 266, 56,
116)(47, 123, 55, 139)(48, 120, 54, 262)(49, 297, 53, 285)(50, 274, 52, 108)(51,
131)(61, 271, 221, 111)(62, 248, 240, 254)(63, 105, 239, 277)(64, 82, 238,
100)(65, 279, 237, 103)(66, 256, 236, 246)(67, 113, 235, 269)(68, 90, 234,
92)(69, 267, 233, 115)(70, 244, 232, 258)(71, 101, 231, 261)(72, 98, 230,
84)(73, 275, 229, 107)(74, 252, 228, 250)(75, 109, 227, 273)(76, 86, 226,
96)(77, 263, 225, 119)(78, 260, 224, 242)(79, 117, 223, 265)(80, 94, 222,
88)(81, 241)(83, 95, 99, 87)(85, 249, 97, 253)(89, 257, 93, 245)(102, 208, 280,
214)(106, 216, 276, 206)(110, 204, 272, 218)(114, 212, 268, 210)(118, 220, 264,
202)(121, 201)(125, 209, 137, 213)(129, 217, 133, 205)(142, 168, 320, 174)(146,
176, 316, 166)(150, 164, 312, 178)(154, 172, 308, 170)(158, 180, 304, 162)(165,
169, 177, 173)(203, 295, 219, 287)(207, 283, 215, 299)(211, 291)(243, 255, 259,
247) (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, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20)(21,
142, 23, 144, 25, 146, 27, 148, 29, 150, 31, 152, 33, 154, 35, 156, 37, 158, 39,
160)(22, 143, 24, 145, 26, 147, 28, 149, 30, 151, 32, 153, 34, 155, 36, 157, 38,
159, 40, 141)(41, 282, 43, 284, 45, 286, 47, 288, 49, 290, 51, 292, 53, 294, 55,
296, 57, 298, 59, 300)(42, 283, 44, 285, 46, 287, 48, 289, 50, 291, 52, 293, 54,
295, 56, 297, 58, 299, 60, 281)(61, 102, 63, 104, 65, 106, 67, 108, 69, 110, 71,
112, 73, 114, 75, 116, 77, 118, 79, 120)(62, 103, 64, 105, 66, 107, 68, 109, 70,
111, 72, 113, 74, 115, 76, 117, 78, 119, 80, 101)(81, 242, 83, 244, 85, 246, 87,
248, 89, 250, 91, 252, 93, 254, 95, 256, 97, 258, 99, 260)(82, 243, 84, 245, 86,
247, 88, 249, 90, 251, 92, 253, 94, 255, 96, 257, 98, 259, 100, 241)(121, 202,
123, 204, 125, 206, 127, 208, 129, 210, 131, 212, 133, 214, 135, 216, 137, 218,
139, 220)(122, 203, 124, 205, 126, 207, 128, 209, 130, 211, 132, 213, 134, 215,
136, 217, 138, 219, 140, 201)(161, 162, 163, 164, 165, 166, 167, 168, 169, 170,
171, 172, 173, 174, 175, 176, 177, 178, 179, 180)(181, 302, 183, 304, 185, 306,
187, 308, 189, 310, 191, 312, 193, 314, 195, 316, 197, 318, 199, 320)(182, 303,
184, 305, 186, 307, 188, 309, 190, 311, 192, 313, 194, 315, 196, 317, 198, 319,
200, 301)(221, 262, 223, 264, 225, 266, 227, 268, 229, 270, 231, 272, 233, 274,
235, 276, 237, 278, 239, 280)(222, 263, 224, 265, 226, 267, 228, 269, 230, 271,
232, 273, 234, 275, 236, 277, 238, 279, 240, 261)
C4[ 320, 51 ]
320
-1 144 2 20 318
-2 1 199 3 25
-3 320 2 146 4
-4 3 5 27 181
-5 4 148 302 6
-6 5 7 29 183
-7 6 150 304 8
-8 7 9 31 185
-9 8 152 306 10
-10 11 33 187 9
-11 154 308 12 10
-12 11 13 35 189
-13 12 156 310 14
-14 13 15 37 191
-15 14 158 312 16
-16 15 17 39 193
-17 16 160 314 18
-18 17 19 195 21
-19 18 316 20 142
-20 1 23 19 197
-21 22 18 40 164
-22 23 45 21 219
-23 22 166 24 20
-24 23 25 47 201
-25 2 24 168 26
-26 25 27 49 203
-27 4 26 170 28
-28 27 29 51 205
-29 6 28 172 30
-30 29 31 53 207
-31 8 30 174 32
-32 33 55 209 31
-33 176 34 10 32
-34 33 35 57 211
-35 12 34 178 36
-36 35 37 59 213
-37 14 36 180 38
-38 37 39 215 41
-39 16 38 40 162
-40 39 217 21 43
-41 38 60 184 42
-42 41 239 43 65
-43 44 40 42 186
-44 45 67 221 43
-45 22 44 188 46
-46 45 47 69 223
-47 24 46 190 48
-48 47 49 71 225
-49 26 48 192 50
-50 49 51 73 227
-51 28 50 194 52
-52 51 53 75 229
-53 30 52 196 54
-54 55 77 231 53
-55 198 56 32 54
-56 55 57 79 233
-57 34 56 200 58
-58 57 59 235 61
-59 36 58 60 182
-60 59 237 41 63
-61 58 80 204 62
-62 61 259 63 85
-63 60 62 206 64
-64 63 65 87 241
-65 66 42 64 208
-66 67 89 243 65
-67 44 66 210 68
-68 67 69 91 245
-69 46 68 212 70
-70 69 71 93 247
-71 48 70 214 72
-72 71 73 95 249
-73 50 72 216 74
-74 73 75 97 251
-75 52 74 218 76
-76 77 99 253 75
-77 220 78 54 76
-78 77 79 255 81
-79 56 78 80 202
-80 79 257 61 83
-81 78 100 224 82
-82 81 279 83 105
-83 80 82 226 84
-84 83 85 107 261
-85 62 84 228 86
-86 85 87 109 263
-87 88 64 86 230
-88 89 111 265 87
-89 66 88 232 90
-90 89 91 113 267
-91 68 90 234 92
-92 91 93 115 269
-93 70 92 236 94
-94 93 95 117 271
-95 72 94 238 96
-96 95 97 119 273
-97 74 96 240 98
-98 99 275 101 97
-99 100 222 76 98
-100 99 277 81 103
-101 244 102 98 120
-102 101 299 103 125
-103 100 102 246 104
-104 103 105 127 281
-105 82 104 248 106
-106 105 107 129 283
-107 84 106 250 108
-108 107 109 131 285
-109 110 86 108 252
-110 111 133 287 109
-111 88 110 254 112
-112 111 113 135 289
-113 90 112 256 114
-114 113 115 137 291
-115 92 114 258 116
-116 115 117 139 293
-117 94 116 260 118
-118 121 117 119 295
-119 242 96 118 120
-120 297 101 123 119
-121 264 122 118 140
-122 121 319 123 145
-123 122 266 124 120
-124 123 125 147 301
-125 102 124 268 126
-126 125 127 149 303
-127 104 126 270 128
-128 127 129 151 305
-129 106 128 272 130
-130 129 131 153 307
-131 132 108 130 274
-132 133 155 309 131
-133 110 132 276 134
-134 133 135 157 311
-135 112 134 278 136
-136 135 137 159 313
-137 114 136 280 138
-138 137 139 315 141
-139 116 138 140 262
-140 121 143 139 317
-141 138 160 284 142
-142 143 165 19 141
-143 286 144 140 142
-144 143 1 145 167
-145 122 144 288 146
-146 145 3 147 169
-147 124 146 290 148
-148 147 5 149 171
-149 126 148 292 150
-150 149 7 151 173
-151 128 150 294 152
-152 151 9 153 175
-153 154 130 152 296
-154 11 155 177 153
-155 132 154 298 156
-156 155 13 157 179
-157 134 156 300 158
-158 157 15 159 161
-159 136 158 160 282
-160 159 17 141 163
-161 158 180 304 162
-162 39 161 163 185
-163 160 162 306 164
-164 165 187 163 21
-165 308 166 142 164
-166 165 23 167 189
-167 144 166 310 168
-168 167 25 169 191
-169 146 168 312 170
-170 169 27 171 193
-171 148 170 314 172
-172 171 29 173 195
-173 150 172 316 174
-174 173 31 175 197
-175 176 152 174 318
-176 33 177 199 175
-177 154 176 320 178
-178 177 35 179 181
-179 156 178 180 302
-180 179 37 161 183
-181 178 200 4 182
-182 59 181 183 205
-183 180 6 182 184
-184 183 41 185 207
-185 8 162 184 186
-186 187 209 185 43
-187 188 10 164 186
-188 187 45 189 211
-189 12 166 188 190
-190 189 47 191 213
-191 14 168 190 192
-192 191 49 193 215
-193 16 170 192 194
-194 193 51 195 217
-195 18 172 194 196
-196 195 53 197 219
-197 198 20 174 196
-198 55 199 201 197
-199 176 198 2 200
-200 199 57 181 203
-201 198 220 24 202
-202 79 201 203 225
-203 200 26 202 204
-204 203 61 205 227
-205 28 182 204 206
-206 205 63 207 229
-207 30 184 206 208
-208 209 231 207 65
-209 210 32 186 208
-210 209 67 211 233
-211 34 188 210 212
-212 211 69 213 235
-213 36 190 212 214
-214 213 71 215 237
-215 38 192 214 216
-216 215 73 217 239
-217 40 194 216 218
-218 221 217 75 219
-219 22 220 196 218
-220 77 201 223 219
-221 44 222 218 240
-222 99 221 223 245
-223 220 46 222 224
-224 223 81 225 247
-225 48 202 224 226
-226 225 83 227 249
-227 50 204 226 228
-228 227 85 229 251
-229 52 206 228 230
-230 231 253 229 87
-231 232 54 208 230
-232 231 89 233 255
-233 56 210 232 234
-234 233 91 235 257
-235 58 212 234 236
-236 235 93 237 259
-237 60 214 236 238
-238 237 95 239 241
-239 216 238 42 240
-240 221 243 239 97
-241 242 238 260 64
-242 243 265 119 241
-243 66 242 244 240
-244 243 101 245 267
-245 68 222 244 246
-246 245 103 247 269
-247 70 224 246 248
-248 247 105 249 271
-249 72 226 248 250
-250 249 107 251 273
-251 74 228 250 252
-252 253 275 251 109
-253 254 76 230 252
-254 253 111 255 277
-255 78 232 254 256
-256 255 113 257 279
-257 80 234 256 258
-258 257 115 259 261
-259 236 258 62 260
-260 259 117 241 263
-261 258 280 84 262
-262 139 261 263 285
-263 264 260 86 262
-264 121 265 287 263
-265 88 242 264 266
-266 265 123 267 289
-267 90 244 266 268
-268 267 125 269 291
-269 92 246 268 270
-270 269 127 271 293
-271 94 248 270 272
-272 271 129 273 295
-273 96 250 272 274
-274 275 297 273 131
-275 276 98 252 274
-276 275 133 277 299
-277 100 254 276 278
-278 277 135 279 281
-279 256 278 82 280
-280 279 137 261 283
-281 278 300 104 282
-282 159 281 283 305
-283 280 106 282 284
-284 283 141 285 307
-285 286 108 262 284
-286 143 287 309 285
-287 110 264 286 288
-288 287 145 289 311
-289 112 266 288 290
-290 289 147 291 313
-291 114 268 290 292
-292 291 149 293 315
-293 116 270 292 294
-294 293 151 295 317
-295 118 272 294 296
-296 297 319 295 153
-297 298 120 274 296
-298 297 155 299 301
-299 276 298 102 300
-300 299 157 281 303
-301 298 320 124 302
-302 179 301 5 303
-303 300 126 302 304
-304 303 7 161 305
-305 128 282 304 306
-306 305 9 163 307
-307 308 130 284 306
-308 11 165 309 307
-309 132 286 308 310
-310 309 13 167 311
-311 134 288 310 312
-312 311 15 169 313
-313 136 290 312 314
-314 313 17 171 315
-315 138 292 314 316
-316 315 19 173 317
-317 140 294 316 318
-318 319 1 317 175
-319 122 320 296 318
-320 319 177 3 301
0