Graph forms
for C4 [ 240, 139 ] =
PL(CS(Pr_10(1,1,2,2)[5^12],1))
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On this page are computer-accessible forms for the graph C4[ 240, 139 ] =
PL(CS(Pr_10(1,1,2,2)[5^12],1)).
(I) Following is a form readable by MAGMA:
g:=Graph<240|{ {85, 125}, {80, 121}, {85, 124}, {86, 124}, {86, 125}, {77, 125},
{78, 126}, {77, 126}, {78, 125}, {79, 121}, {45, 124}, {46, 124}, {46, 123},
{45, 123}, {8, 127}, {1, 121}, {2, 122}, {7, 127}, {4, 126}, {1, 122}, {2, 121},
{4, 127}, {3, 127}, {6, 122}, {3, 126}, {6, 123}, {5, 123}, {5, 122}, {3, 131},
{112, 240}, {71, 199}, {58, 186}, {75, 203}, {100, 228}, {2, 131}, {71, 198},
{59, 186}, {53, 180}, {74, 203}, {100, 229}, {59, 185}, {61, 191}, {60, 190},
{98, 224}, {109, 239}, {58, 185}, {99, 224}, {10, 142}, {70, 194}, {69, 193},
{90, 222}, {91, 223}, {97, 229}, {110, 234}, {111, 235}, {10, 143}, {117, 240},
{90, 223}, {91, 222}, {97, 228}, {110, 235}, {111, 234}, {2, 132}, {54, 176},
{9, 143}, {74, 204}, {104, 238}, {3, 132}, {70, 193}, {69, 194}, {57, 190}, {55,
176}, {7, 128}, {9, 142}, {75, 204}, {104, 239}, {1, 137}, {120, 240}, {65,
201}, {64, 200}, {6, 142}, {8, 128}, {1, 136}, {60, 181}, {7, 142}, {108, 229},
{7, 141}, {80, 218}, {101, 239}, {106, 224}, {107, 225}, {108, 230}, {6, 141},
{80, 219}, {101, 238}, {106, 225}, {107, 224}, {4, 136}, {66, 206}, {63, 179},
{57, 181}, {56, 180}, {82, 222}, {102, 234}, {105, 229}, {4, 137}, {68, 201},
{67, 206}, {63, 178}, {16, 157}, {45, 160}, {83, 222}, {96, 237}, {103, 234},
{16, 158}, {72, 198}, {67, 205}, {83, 221}, {96, 238}, {103, 233}, {66, 205},
{72, 199}, {82, 221}, {102, 233}, {105, 230}, {12, 156}, {114, 226}, {71, 215},
{62, 174}, {61, 173}, {48, 160}, {49, 161}, {12, 157}, {115, 226}, {70, 215},
{15, 158}, {10, 152}, {117, 231}, {116, 230}, {115, 225}, {59, 169}, {15, 157},
{11, 152}, {114, 225}, {65, 210}, {62, 173}, {61, 174}, {59, 168}, {56, 171},
{9, 157}, {72, 220}, {60, 168}, {13, 153}, {50, 166}, {9, 156}, {60, 169}, {52,
161}, {13, 152}, {51, 166}, {5, 147}, {69, 211}, {68, 210}, {14, 152}, {51,
165}, {77, 219}, {5, 146}, {113, 230}, {14, 153}, {50, 165}, {77, 218}, {11,
147}, {73, 209}, {55, 175}, {12, 148}, {78, 214}, {54, 175}, {73, 208}, {69,
220}, {58, 163}, {79, 214}, {8, 146}, {118, 236}, {57, 163}, {79, 213}, {8,
147}, {119, 236}, {72, 211}, {49, 170}, {78, 213}, {11, 151}, {119, 235}, {76,
208}, {10, 151}, {118, 235}, {57, 164}, {76, 209}, {109, 240}, {52, 170}, {70,
216}, {58, 164}, {53, 171}, {11, 148}, {120, 231}, {112, 239}, {71, 216}, {12,
147}, {17, 177}, {118, 214}, {52, 148}, {22, 182}, {27, 187}, {28, 188}, {37,
133}, {44, 140}, {17, 176}, {118, 215}, {115, 210}, {52, 149}, {23, 182}, {37,
132}, {40, 137}, {41, 136}, {44, 141}, {49, 144}, {23, 181}, {117, 215}, {115,
209}, {24, 186}, {38, 132}, {40, 138}, {42, 136}, {50, 144}, {22, 181}, {120,
219}, {117, 214}, {24, 187}, {38, 133}, {20, 176}, {120, 220}, {27, 191}, {41,
141}, {20, 177}, {116, 209}, {23, 178}, {26, 191}, {23, 177}, {116, 210}, {56,
158}, {51, 149}, {27, 188}, {56, 159}, {28, 187}, {43, 140}, {48, 151}, {51,
148}, {111, 200}, {43, 131}, {55, 159}, {111, 199}, {24, 177}, {116, 221}, {55,
158}, {13, 167}, {24, 178}, {13, 166}, {119, 220}, {14, 162}, {119, 219}, {113,
221}, {54, 154}, {53, 153}, {26, 182}, {110, 194}, {15, 162}, {26, 183}, {39,
138}, {42, 135}, {110, 195}, {15, 161}, {21, 187}, {25, 183}, {39, 137}, {41,
135}, {47, 129}, {109, 195}, {14, 161}, {54, 153}, {53, 154}, {21, 186}, {25,
182}, {44, 131}, {47, 128}, {109, 194}, {18, 162}, {48, 128}, {87, 231}, {93,
237}, {18, 163}, {48, 129}, {86, 231}, {17, 163}, {46, 156}, {81, 227}, {17,
162}, {20, 167}, {47, 156}, {81, 226}, {93, 238}, {19, 167}, {47, 155}, {88,
236}, {46, 155}, {88, 237}, {16, 166}, {84, 226}, {94, 232}, {95, 233}, {16,
167}, {84, 227}, {94, 233}, {95, 232}, {112, 199}, {19, 171}, {21, 173}, {42,
146}, {85, 237}, {92, 228}, {112, 200}, {18, 171}, {21, 172}, {43, 146}, {85,
236}, {22, 172}, {43, 145}, {44, 150}, {45, 151}, {89, 227}, {19, 168}, {22,
173}, {42, 145}, {20, 168}, {113, 205}, {99, 223}, {50, 143}, {113, 204}, {89,
228}, {98, 223}, {18, 172}, {114, 204}, {49, 143}, {86, 232}, {19, 172}, {114,
205}, {41, 150}, {87, 232}, {92, 227}, {75, 139}, {95, 159}, {96, 160}, {75,
138}, {94, 154}, {97, 165}, {94, 155}, {97, 164}, {76, 138}, {93, 155}, {98,
164}, {76, 139}, {93, 154}, {98, 165}, {89, 145}, {102, 174}, {89, 144}, {92,
149}, {99, 170}, {102, 175}, {90, 144}, {92, 150}, {99, 169}, {101, 175}, {90,
145}, {101, 174}, {73, 133}, {74, 134}, {79, 130}, {91, 150}, {100, 169}, {91,
149}, {100, 170}, {73, 134}, {74, 133}, {105, 185}, {105, 184}, {108, 189}, {29,
207}, {80, 130}, {106, 184}, {108, 190}, {29, 206}, {103, 180}, {106, 185}, {30,
202}, {82, 134}, {103, 179}, {31, 202}, {82, 135}, {87, 130}, {107, 190}, {31,
201}, {81, 135}, {87, 129}, {107, 189}, {30, 201}, {81, 134}, {28, 196}, {83,
139}, {84, 140}, {28, 197}, {31, 198}, {88, 129}, {26, 192}, {31, 197}, {88,
130}, {27, 192}, {104, 179}, {25, 197}, {29, 193}, {104, 180}, {25, 196}, {29,
192}, {30, 192}, {30, 193}, {83, 140}, {84, 139}, {32, 197}, {32, 198}, {34,
202}, {34, 203}, {33, 203}, {33, 202}, {36, 207}, {35, 207}, {32, 206}, {32,
207}, {35, 211}, {34, 211}, {40, 217}, {38, 212}, {64, 178}, {39, 213}, {40,
218}, {35, 208}, {64, 179}, {38, 213}, {39, 212}, {36, 208}, {61, 200}, {66,
183}, {34, 212}, {65, 183}, {35, 212}, {33, 217}, {68, 188}, {33, 216}, {68,
189}, {65, 184}, {62, 196}, {66, 184}, {63, 196}, {36, 216}, {63, 195}, {37,
217}, {36, 217}, {62, 195}, {67, 189}, {37, 218}, {67, 188}, {64, 191}, {95,
160}, {96, 159} }>;
(II) A more general form is to represent the graph as the orbit of {85, 125}
under the group generated by the following permutations:
a: (2, 4)(5, 39, 6, 40)(7, 37, 8, 38)(9, 33, 12, 34)(10, 36, 11, 35)(13, 29, 14,
32)(15, 31, 16, 30)(17, 25, 19, 27)(18, 28, 20, 26)(21, 24, 23, 22)(41, 80, 42,
79)(43, 78, 44, 77)(45, 76)(46, 75)(47, 74)(48, 73)(49, 71, 51, 69)(50, 70, 52,
72)(53, 67, 54, 66)(55, 65, 56, 68)(57, 62, 59, 64)(58, 63, 60, 61)(81, 87)(82,
88)(83, 85)(84, 86)(89, 117, 92, 120)(90, 118, 91, 119)(93, 113)(94, 114)(95,
115)(96, 116)(97, 109, 100, 112)(98, 110, 99, 111)(101, 105, 104, 108)(102, 106,
103, 107)(121, 136)(122, 137)(123, 138)(124, 139)(125, 140)(126, 131)(127,
132)(128, 133)(129, 134)(130, 135)(141, 218, 146, 213)(142, 217, 147, 212)(143,
216, 148, 211)(144, 215, 149, 220)(145, 214, 150, 219)(151, 208)(152, 207)(153,
206)(154, 205)(155, 204)(156, 203)(157, 202)(158, 201)(159, 210)(160, 209)(161,
198, 166, 193)(162, 197, 167, 192)(163, 196, 168, 191)(164, 195, 169, 200)(165,
194, 170, 199)(171, 188, 176, 183)(172, 187, 177, 182)(173, 186, 178, 181)(174,
185, 179, 190)(175, 184, 180, 189)(221, 237)(222, 236)(223, 235)(224, 234)(225,
233)(226, 232)(227, 231)(228, 240)(229, 239)(230, 238) (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: (17, 18)(19, 20)(21, 24)(22, 23)(53, 54)(55, 56)(61, 64)(62, 63)(101,
104)(102, 103)(171, 176)(172, 177)(173, 178)(174, 179)(175, 180)
c: (29, 30)(31, 32)(33, 36)(34, 35)(65, 66)(67, 68)(73, 74)(75, 76)(81, 82)(83,
84)(89, 90)(91, 92)(97, 98)(99, 100)(105, 106)(107, 108)(113, 115)(114,
116)(201, 206)(202, 207)(203, 208)(204, 209)(205, 210)(221, 226)(222, 227)(223,
228)(224, 229)(225, 230)
d: (2, 4)(5, 41)(6, 42)(7, 43)(8, 44)(9, 90)(10, 89)(11, 92)(12, 91)(13,
100)(14, 97)(15, 98)(16, 99)(17, 57, 18, 58)(19, 59, 20, 60)(21, 24, 23, 22)(25,
62, 28, 63)(26, 61, 27, 64)(29, 112)(30, 111)(31, 110)(32, 109)(33, 119)(34,
118)(35, 117)(36, 120)(37, 77)(38, 78)(39, 79)(40, 80)(45, 81)(46, 82)(47,
83)(48, 84)(49, 50)(51, 52)(53, 105, 54, 108)(55, 107, 56, 106)(65, 102, 68,
103)(66, 101, 67, 104)(69, 71)(70, 72)(73, 86)(74, 85)(75, 88)(76, 87)(93,
113)(94, 116)(95, 115)(96, 114)(121, 137)(122, 136)(123, 135)(124, 134)(125,
133)(126, 132)(127, 131)(128, 140)(129, 139)(130, 138)(141, 146)(142, 145)(143,
144)(147, 150)(148, 149)(151, 227)(152, 228)(153, 229)(154, 230)(155, 221)(156,
222)(157, 223)(158, 224)(159, 225)(160, 226)(161, 165)(162, 164)(166, 170)(167,
169)(171, 185, 176, 190)(172, 186, 177, 181)(173, 187, 178, 182)(174, 188, 179,
183)(175, 189, 180, 184)(192, 200)(193, 199)(194, 198)(195, 197)(201, 234)(202,
235)(203, 236)(204, 237)(205, 238)(206, 239)(207, 240)(208, 231)(209, 232)(210,
233)(211, 215)(212, 214)(216, 220)(217, 219)
e: (81, 82)(83, 84)(89, 90)(91, 92)(97, 98)(99, 100)(105, 106)(107, 108)(113,
114)(115, 116)(221, 226)(222, 227)(223, 228)(224, 229)(225, 230)
f: (85, 86)(87, 88)(93, 94)(95, 96)(101, 102)(103, 104)(109, 110)(111, 112)(117,
118)(119, 120)(231, 236)(232, 237)(233, 238)(234, 239)(235, 240)
g: (25, 26)(27, 28)(29, 32)(30, 31)(61, 62)(63, 64)(69, 72)(70, 71)(109,
112)(110, 111)(191, 196)(192, 197)(193, 198)(194, 199)(195, 200)
h: (9, 10)(11, 12)(13, 16)(14, 15)(45, 46)(47, 48)(53, 56)(54, 55)(85, 86)(87,
88)(93, 95)(94, 96)(101, 102)(103, 104)(109, 110)(111, 112)(117, 118)(119,
120)(151, 156)(152, 157)(153, 158)(154, 159)(155, 160)(231, 236)(232, 237)(233,
238)(234, 239)(235, 240)
m: (33, 34)(35, 36)(37, 38)(39, 40)(69, 70)(71, 72)(77, 78)(79, 80)(117,
120)(118, 119)(211, 216)(212, 217)(213, 218)(214, 219)(215, 220)
n1: (1, 5, 12, 16, 20, 24, 28, 32, 36, 40)(2, 8, 9, 13, 17, 21, 25, 29, 33,
39)(3, 7, 10, 14, 18, 22, 26, 30, 34, 38)(4, 6, 11, 15, 19, 23, 27, 31, 35,
37)(41, 45, 52, 56, 60, 64, 68, 72, 73, 77)(42, 46, 51, 55, 59, 63, 67, 71, 76,
80)(43, 47, 50, 54, 58, 62, 66, 70, 75, 79)(44, 48, 49, 53, 57, 61, 65, 69, 74,
78)(81, 85, 92, 96, 100, 104, 108, 112, 116, 120, 82, 86, 91, 95, 99, 103, 107,
111, 115, 119)(83, 87, 90, 94, 98, 102, 106, 110, 114, 118, 84, 88, 89, 93, 97,
101, 105, 109, 113, 117)(121, 146, 156, 166, 176, 186, 196, 206, 216, 138)(122,
147, 157, 167, 177, 187, 197, 207, 217, 137)(123, 148, 158, 168, 178, 188, 198,
208, 218, 136)(124, 149, 159, 169, 179, 189, 199, 209, 219, 135)(125, 150, 160,
170, 180, 190, 200, 210, 220, 134)(126, 141, 151, 161, 171, 181, 191, 201, 211,
133)(127, 142, 152, 162, 172, 182, 192, 202, 212, 132)(128, 143, 153, 163, 173,
183, 193, 203, 213, 131)(129, 144, 154, 164, 174, 184, 194, 204, 214, 140)(130,
145, 155, 165, 175, 185, 195, 205, 215, 139)(221, 231, 222, 232, 223, 233, 224,
234, 225, 235, 226, 236, 227, 237, 228, 238, 229, 239, 230, 240)
a1: (13, 14)(15, 16)(17, 19)(18, 20)(21, 24)(22, 23)(49, 50)(51, 52)(53, 54)(55,
56)(57, 60)(58, 59)(61, 64)(62, 63)(97, 100)(98, 99)(101, 104)(102, 103)(161,
166)(162, 167)(163, 168)(164, 169)(165, 170)(171, 176)(172, 177)(173, 178)(174,
179)(175, 180)
b1: (1, 2)(3, 4)(37, 40)(38, 39)(41, 44)(42, 43)(73, 76)(74, 75)(81, 84)(82,
83)(131, 136)(132, 137)(133, 138)(134, 139)(135, 140)
c1: (5, 6)(7, 8)(9, 12)(10, 11)(41, 42)(43, 44)(49, 52)(50, 51)(89, 92)(90,
91)(141, 146)(142, 147)(143, 148)(144, 149)(145, 150)
d1: (21, 22)(23, 24)(25, 28)(26, 27)(57, 58)(59, 60)(65, 68)(66, 67)(105,
108)(106, 107)(181, 186)(182, 187)(183, 188)(184, 189)(185, 190)
C4[ 240, 139 ]
240
-1 121 122 136 137
-2 121 132 122 131
-3 132 126 127 131
-4 136 126 137 127
-5 122 123 146 147
-6 122 123 141 142
-7 127 128 141 142
-8 146 147 127 128
-9 143 156 157 142
-10 143 151 152 142
-11 147 148 151 152
-12 156 157 147 148
-13 166 167 152 153
-14 161 162 152 153
-15 157 158 161 162
-16 166 167 157 158
-17 176 177 162 163
-18 171 172 162 163
-19 167 168 171 172
-20 176 177 167 168
-21 187 172 173 186
-22 181 182 172 173
-23 177 178 181 182
-24 187 177 178 186
-25 182 183 196 197
-26 191 192 182 183
-27 187 188 191 192
-28 187 188 196 197
-29 192 193 206 207
-30 201 202 192 193
-31 198 201 202 197
-32 198 206 207 197
-33 202 203 216 217
-34 211 212 202 203
-35 211 212 207 208
-36 216 217 207 208
-37 132 133 217 218
-38 132 133 212 213
-39 212 213 137 138
-40 137 138 217 218
-41 135 136 150 141
-42 145 135 146 136
-43 145 146 140 131
-44 150 140 141 131
-45 123 124 160 151
-46 155 123 156 124
-47 155 156 128 129
-48 160 128 129 151
-49 143 144 170 161
-50 143 165 144 166
-51 165 166 148 149
-52 148 170 149 161
-53 154 180 171 153
-54 154 176 153 175
-55 176 158 159 175
-56 158 180 159 171
-57 190 181 163 164
-58 163 185 164 186
-59 168 169 185 186
-60 168 190 169 181
-61 200 191 173 174
-62 173 195 174 196
-63 178 179 195 196
-64 178 200 179 191
-65 210 201 183 184
-66 183 205 184 206
-67 188 189 205 206
-68 188 210 189 201
-69 220 211 193 194
-70 193 215 194 216
-71 198 199 215 216
-72 198 220 199 211
-73 209 133 134 208
-74 133 134 203 204
-75 203 138 204 139
-76 209 138 139 208
-77 125 126 218 219
-78 125 213 126 214
-79 121 213 214 130
-80 121 130 218 219
-81 134 135 226 227
-82 221 134 222 135
-83 221 222 139 140
-84 226 139 227 140
-85 124 125 236 237
-86 231 232 124 125
-87 231 232 129 130
-88 236 237 129 130
-89 144 145 227 228
-90 144 145 222 223
-91 222 223 149 150
-92 149 150 227 228
-93 154 155 237 238
-94 154 155 232 233
-95 232 233 159 160
-96 159 160 237 238
-97 165 228 229 164
-98 165 223 224 164
-99 223 169 224 170
-100 169 170 228 229
-101 238 239 174 175
-102 233 234 174 175
-103 233 179 234 180
-104 179 180 238 239
-105 184 185 229 230
-106 224 225 184 185
-107 189 190 224 225
-108 189 190 229 230
-109 194 195 239 240
-110 234 235 194 195
-111 199 200 234 235
-112 199 200 239 240
-113 221 204 205 230
-114 225 204 226 205
-115 209 210 225 226
-116 209 210 221 230
-117 231 214 215 240
-118 235 214 236 215
-119 220 235 236 219
-120 220 231 240 219
-121 1 2 79 80
-122 1 2 5 6
-123 45 46 5 6
-124 45 46 85 86
-125 77 78 85 86
-126 77 78 3 4
-127 3 4 7 8
-128 47 48 7 8
-129 88 47 48 87
-130 88 79 80 87
-131 44 2 3 43
-132 2 3 37 38
-133 37 38 73 74
-134 81 82 73 74
-135 81 82 41 42
-136 1 4 41 42
-137 1 4 39 40
-138 39 40 75 76
-139 83 84 75 76
-140 44 83 84 43
-141 44 6 7 41
-142 6 7 9 10
-143 49 50 9 10
-144 89 90 49 50
-145 89 90 42 43
-146 5 8 42 43
-147 11 12 5 8
-148 11 12 51 52
-149 91 92 51 52
-150 44 91 92 41
-151 11 45 48 10
-152 11 13 14 10
-153 13 14 53 54
-154 93 94 53 54
-155 46 47 93 94
-156 12 46 47 9
-157 12 15 16 9
-158 55 56 15 16
-159 55 56 95 96
-160 45 48 95 96
-161 14 15 49 52
-162 14 15 17 18
-163 57 58 17 18
-164 57 58 97 98
-165 50 51 97 98
-166 13 16 50 51
-167 13 16 19 20
-168 59 60 19 20
-169 99 100 59 60
-170 99 100 49 52
-171 56 18 19 53
-172 22 18 19 21
-173 22 61 62 21
-174 101 102 61 62
-175 55 101 102 54
-176 55 17 20 54
-177 23 24 17 20
-178 23 24 63 64
-179 103 104 63 64
-180 56 103 104 53
-181 22 23 57 60
-182 22 23 25 26
-183 66 25 26 65
-184 66 105 106 65
-185 58 59 105 106
-186 24 58 59 21
-187 24 27 28 21
-188 67 68 27 28
-189 67 68 107 108
-190 57 60 107 108
-191 26 27 61 64
-192 26 27 29 30
-193 69 70 29 30
-194 110 69 70 109
-195 110 62 63 109
-196 25 28 62 63
-197 25 28 31 32
-198 71 72 31 32
-199 111 112 71 72
-200 111 112 61 64
-201 68 30 31 65
-202 33 34 30 31
-203 33 34 74 75
-204 113 114 74 75
-205 66 67 113 114
-206 66 67 29 32
-207 35 36 29 32
-208 35 36 73 76
-209 115 116 73 76
-210 68 115 116 65
-211 34 35 69 72
-212 34 35 38 39
-213 78 79 38 39
-214 78 79 117 118
-215 70 71 117 118
-216 33 36 70 71
-217 33 36 37 40
-218 77 80 37 40
-219 77 80 119 120
-220 69 72 119 120
-221 113 82 83 116
-222 90 91 82 83
-223 99 90 91 98
-224 99 106 107 98
-225 114 115 106 107
-226 81 114 115 84
-227 89 81 92 84
-228 89 100 92 97
-229 100 105 97 108
-230 113 105 116 108
-231 117 86 87 120
-232 94 95 86 87
-233 102 103 94 95
-234 110 111 102 103
-235 110 111 118 119
-236 88 85 118 119
-237 88 93 85 96
-238 101 93 104 96
-239 101 112 104 109
-240 112 117 109 120
0