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