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