Graph forms
for C4 [ 240, 44 ] =
PL(MC3(6,20,1,11,9,10,1),[4^30,12^10])
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On this page are computer-accessible forms for the graph C4[ 240, 44 ] =
PL(MC3(6,20,1,11,9,10,1),[4^30,12^10]).
(I) Following is a form readable by MAGMA:
g:=Graph<240|{ {106, 127}, {91, 122}, {89, 127}, {91, 125}, {73, 121}, {73,
124}, {66, 122}, {68, 126}, {66, 125}, {68, 123}, {40, 123}, {45, 126}, {45,
123}, {32, 123}, {25, 121}, {29, 124}, {25, 124}, {20, 121}, {9, 124}, {10,
127}, {15, 121}, {8, 127}, {4, 125}, {2, 126}, {6, 122}, {7, 122}, {3, 125}, {1,
126}, {22, 150}, {71, 199}, {50, 178}, {85, 213}, {10, 139}, {67, 194}, {60,
189}, {42, 171}, {43, 170}, {78, 207}, {82, 211}, {96, 225}, {103, 230}, {8,
138}, {23, 149}, {89, 219}, {108, 238}, {100, 231}, {48, 180}, {86, 210}, {19,
150}, {67, 198}, {62, 187}, {37, 160}, {87, 210}, {100, 225}, {105, 236}, {37,
163}, {77, 203}, {53, 179}, {81, 215}, {4, 131}, {35, 164}, {38, 161}, {92,
219}, {95, 216}, {101, 226}, {76, 196}, {80, 217}, {94, 215}, {109, 228}, {41,
163}, {82, 216}, {88, 210}, {38, 173}, {56, 179}, {93, 214}, {16, 156}, {31,
147}, {51, 191}, {38, 171}, {61, 176}, {21, 155}, {70, 200}, {64, 206}, {57,
182}, {65, 206}, {106, 229}, {37, 181}, {77, 221}, {74, 218}, {26, 139}, {119,
230}, {27, 138}, {30, 143}, {39, 182}, {84, 197}, {14, 156}, {115, 225}, {66,
208}, {62, 173}, {80, 195}, {13, 153}, {118, 226}, {81, 197}, {11, 158}, {69,
208}, {60, 169}, {29, 136}, {114, 231}, {7, 145}, {73, 223}, {63, 169}, {28,
138}, {83, 197}, {6, 145}, {9, 158}, {47, 184}, {52, 172}, {31, 134}, {59, 162},
{81, 200}, {3, 153}, {70, 220}, {18, 137}, {76, 215}, {61, 166}, {24, 131}, {18,
142}, {120, 228}, {21, 137}, {79, 211}, {28, 129}, {33, 188}, {43, 182}, {48,
174}, {116, 234}, {75, 213}, {50, 172}, {93, 195}, {39, 184}, {62, 161}, {45,
178}, {111, 240}, {2, 162}, {8, 168}, {25, 185}, {33, 129}, {46, 142}, {99,
195}, {14, 175}, {12, 174}, {16, 178}, {21, 183}, {27, 185}, {30, 188}, {1,
162}, {72, 235}, {57, 154}, {4, 167}, {13, 174}, {99, 192}, {113, 210}, {3,
167}, {77, 233}, {58, 158}, {32, 132}, {84, 240}, {100, 192}, {15, 170}, {74,
239}, {18, 183}, {46, 139}, {101, 192}, {107, 206}, {52, 146}, {64, 230}, {36,
131}, {116, 211}, {68, 227}, {104, 207}, {79, 231}, {97, 201}, {103, 207}, {112,
216}, {29, 180}, {69, 236}, {34, 136}, {74, 224}, {56, 146}, {49, 155}, {98,
200}, {19, 184}, {60, 151}, {35, 136}, {110, 197}, {40, 132}, {60, 144}, {54,
154}, {111, 195}, {3, 174}, {8, 165}, {23, 186}, {17, 191}, {75, 229}, {33,
143}, {79, 225}, {10, 165}, {65, 238}, {63, 144}, {24, 168}, {59, 139}, {53,
133}, {34, 147}, {55, 134}, {36, 149}, {41, 152}, {22, 164}, {88, 234}, {12,
191}, {94, 237}, {95, 236}, {28, 168}, {80, 228}, {32, 149}, {117, 192}, {44,
153}, {51, 134}, {90, 239}, {108, 217}, {109, 216}, {43, 157}, {42, 157}, {83,
228}, {97, 217}, {29, 164}, {39, 157}, {61, 135}, {52, 142}, {95, 229}, {96,
218}, {99, 217}, {1, 186}, {17, 170}, {91, 224}, {92, 231}, {5, 185}, {98, 222},
{102, 218}, {2, 191}, {56, 133}, {9, 180}, {37, 152}, {41, 148}, {110, 211}, {7,
185}, {18, 172}, {5, 186}, {63, 128}, {59, 132}, {13, 178}, {16, 175}, {42,
234}, {67, 131}, {87, 151}, {93, 157}, {7, 198}, {11, 202}, {46, 239}, {64,
130}, {84, 150}, {88, 154}, {113, 179}, {66, 129}, {102, 165}, {76, 136}, {117,
177}, {85, 145}, {21, 208}, {26, 223}, {106, 175}, {114, 183}, {43, 237}, {97,
166}, {110, 169}, {112, 183}, {4, 204}, {120, 176}, {118, 190}, {20, 220}, {92,
148}, {5, 204}, {32, 233}, {105, 160}, {22, 220}, {75, 129}, {35, 233}, {108,
166}, {23, 220}, {120, 179}, {77, 134}, {89, 146}, {90, 145}, {92, 151}, {28,
208}, {72, 132}, {38, 234}, {105, 165}, {15, 194}, {36, 233}, {82, 159}, {68,
138}, {115, 189}, {85, 155}, {101, 171}, {17, 222}, {98, 173}, {115, 188}, {20,
196}, {73, 153}, {53, 229}, {15, 222}, {78, 159}, {16, 193}, {86, 135}, {34,
240}, {71, 149}, {65, 147}, {49, 227}, {50, 224}, {23, 196}, {81, 130}, {24,
204}, {119, 163}, {54, 226}, {90, 142}, {104, 188}, {25, 204}, {100, 177}, {107,
190}, {110, 187}, {2, 212}, {117, 163}, {20, 194}, {84, 130}, {97, 182}, {5,
221}, {12, 212}, {19, 203}, {31, 199}, {48, 232}, {6, 223}, {53, 236}, {49,
235}, {87, 141}, {93, 135}, {10, 209}, {61, 230}, {57, 226}, {26, 193}, {1,
221}, {13, 209}, {17, 205}, {80, 140}, {27, 198}, {118, 171}, {116, 169}, {96,
189}, {109, 176}, {69, 155}, {74, 148}, {11, 212}, {83, 140}, {95, 128}, {106,
181}, {72, 168}, {120, 152}, {44, 205}, {55, 214}, {54, 215}, {104, 137}, {36,
198}, {70, 164}, {56, 218}, {40, 202}, {9, 237}, {58, 222}, {12, 232}, {49,
213}, {14, 235}, {69, 160}, {40, 205}, {47, 202}, {114, 151}, {11, 237}, {118,
144}, {34, 196}, {44, 202}, {86, 177}, {103, 128}, {47, 199}, {83, 187}, {101,
141}, {111, 135}, {88, 177}, {107, 130}, {113, 152}, {72, 162}, {87, 189}, {70,
173}, {103, 140}, {39, 203}, {58, 214}, {82, 190}, {14, 227}, {76, 161}, {6,
232}, {116, 154}, {78, 160}, {99, 141}, {31, 240}, {52, 219}, {55, 199}, {117,
133}, {64, 176}, {63, 207}, {62, 206}, {57, 201}, {86, 166}, {112, 128}, {30,
239}, {79, 190}, {26, 232}, {119, 133}, {41, 219}, {48, 194}, {85, 167}, {96,
146}, {102, 148}, {109, 159}, {24, 235}, {58, 201}, {44, 223}, {50, 193}, {33,
213}, {94, 170}, {105, 156}, {89, 175}, {67, 180}, {91, 172}, {104, 159}, {22,
238}, {27, 227}, {51, 203}, {111, 150}, {59, 193}, {65, 187}, {102, 156}, {115,
137}, {47, 212}, {119, 140}, {78, 181}, {107, 144}, {42, 214}, {45, 209}, {98,
158}, {113, 141}, {19, 238}, {71, 186}, {90, 167}, {114, 143}, {30, 224}, {75,
181}, {55, 201}, {35, 221}, {51, 205}, {54, 200}, {46, 209}, {71, 184}, {94,
161}, {108, 147}, {112, 143} }>;
(II) A more general form is to represent the graph as the orbit of {106, 127}
under the group generated by the following permutations:
a: (3, 6)(4, 7)(13, 26)(24, 27)(45, 59)(68, 72)(122, 125)(123, 132)(126,
162)(131, 198)(138, 168)(139, 209)(145, 167)(153, 223)(174, 232)(178, 193)(185,
204)(227, 235) (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, 3)(2, 13)(4, 5)(6, 32)(7, 36)(8, 15, 14, 9)(10, 17, 16, 11)(12, 45)(18,
19, 30, 31)(20, 49, 29, 28)(21, 22, 33, 34)(23, 85, 35, 66)(24, 25)(26, 40)(27,
67)(37, 38)(39, 74, 55, 52)(41, 42)(43, 102, 58, 89)(44, 59)(46, 51, 50, 47)(48,
68)(53, 54)(56, 57)(60, 61)(62, 78)(63, 64)(65, 104)(69, 70, 75, 76)(71, 90, 77,
91)(72, 73)(79, 80)(81, 95)(82, 83)(84, 112)(86, 87)(88, 113)(92, 93)(94, 105,
98, 106)(96, 97)(99, 100)(101, 117)(103, 107)(108, 115)(109, 110)(111, 114)(116,
120)(118, 119)(121, 235, 124, 168)(122, 149, 145, 233)(123, 232)(125, 186, 167,
221)(126, 174)(127, 170, 156, 158)(128, 130)(129, 196, 155, 164)(131, 185)(132,
223)(133, 226)(134, 172, 184, 239)(135, 151)(136, 208, 220, 213)(137, 238, 188,
147)(138, 194, 227, 180)(139, 205, 193, 202)(140, 190)(141, 177)(142, 203, 224,
199)(143, 240, 183, 150)(144, 230)(146, 182, 218, 201)(148, 214, 219, 157)(152,
234)(153, 162)(154, 179)(159, 187)(160, 173, 181, 161)(163, 171)(165, 222, 175,
237)(166, 189)(169, 176)(178, 212, 209, 191)(195, 231)(197, 216)(200, 229, 215,
236)(206, 207)(211, 228)(217, 225)
c: (18, 30)(21, 33)(52, 74)(69, 75)(89, 102)(105, 106)(127, 165)(129, 208)(137,
188)(142, 239)(143, 183)(146, 218)(148, 219)(155, 213)(156, 175)(160, 181)(172,
224)(229, 236)
d: (38, 54)(42, 57)(61, 80)(62, 81)(64, 83)(65, 84)(86, 99)(88, 101)(93,
97)(107, 110)(108, 111)(116, 118)(130, 187)(135, 217)(140, 230)(141, 210)(144,
169)(147, 240)(150, 238)(154, 171)(157, 182)(161, 215)(166, 195)(173, 200)(176,
228)(177, 192)(190, 211)(197, 206)(201, 214)(226, 234)
e: (9, 15)(11, 17)(20, 29)(23, 35)(47, 51)(71, 77)(121, 124)(134, 199)(136,
196)(149, 233)(158, 222)(164, 220)(170, 237)(180, 194)(184, 203)(186, 221)(191,
212)(202, 205)
f: (8, 14)(10, 16)(28, 49)(46, 50)(66, 85)(90, 91)(122, 145)(125, 167)(127,
175)(129, 213)(138, 227)(139, 193)(142, 172)(155, 208)(156, 165)(168, 235)(178,
209)(224, 239)
g: (2, 5)(3, 15)(4, 17)(6, 9)(7, 11)(8, 31)(10, 34)(12, 25)(13, 20)(14, 19)(16,
22)(18, 38, 30, 54)(21, 42, 33, 57)(23, 45)(24, 51)(26, 29)(27, 47)(28, 55)(35,
59)(36, 40)(37, 61, 53, 80)(39, 49)(41, 64, 56, 83)(43, 85)(44, 67)(46, 76)(48,
73)(50, 70)(52, 62, 74, 81)(58, 66)(63, 87)(65, 102, 84, 89)(68, 71)(69, 93, 75,
97)(72, 77)(78, 86, 95, 99)(82, 100)(88, 112, 101, 104)(90, 94)(91, 98)(92, 107,
96, 110)(103, 113)(105, 111, 106, 108)(109, 117)(114, 118, 115, 116)(119,
120)(121, 174)(122, 158)(123, 149)(124, 232)(125, 222)(126, 186)(127, 147, 165,
240)(128, 141, 207, 210)(129, 201, 208, 214)(130, 146, 187, 148)(131, 205)(132,
233)(133, 228, 163, 176)(134, 168)(135, 229, 217, 160)(136, 139)(137, 234, 143,
226)(138, 199)(140, 152, 230, 179)(142, 161, 239, 215)(144, 189, 169, 151)(145,
237)(150, 175, 238, 156)(153, 194)(154, 183, 171, 188)(155, 157, 213, 182)(159,
177, 216, 192)(162, 221)(164, 193)(166, 236, 195, 181)(167, 170)(172, 173, 224,
200)(178, 220)(180, 223)(184, 227)(185, 212)(190, 225, 211, 231)(191, 204)(196,
209)(197, 219, 206, 218)(198, 202)(203, 235)
h: (9, 15)(11, 17)(19, 31)(20, 29)(22, 34)(23, 35)(39, 55)(43, 58)(47, 51)(70,
76)(71, 77)(94, 98)(121, 124)(134, 184)(136, 220)(147, 238)(149, 233)(150,
240)(157, 214)(158, 170)(161, 173)(164, 196)(180, 194)(182, 201)(186, 221)(191,
212)(199, 203)(200, 215)(202, 205)(222, 237)
m: (37, 53)(41, 56)(60, 79)(63, 82)(78, 95)(87, 100)(92, 96)(103, 109)(104,
112)(113, 117)(114, 115)(119, 120)(128, 159)(133, 152)(137, 183)(140, 228)(141,
192)(143, 188)(144, 190)(146, 219)(148, 218)(151, 225)(160, 236)(163, 179)(169,
211)(176, 230)(177, 210)(181, 229)(189, 231)(207, 216)
n1: (1, 2, 12, 48, 67, 36, 32, 40, 44, 73, 25, 5)(3, 20, 24, 71, 59, 11, 6, 29,
27, 77, 45, 17)(4, 23, 72, 47, 26, 9, 7, 35, 68, 51, 13, 15)(8, 55, 50, 94, 85,
22)(10, 58, 91, 76, 49, 19)(14, 39, 46, 98, 66, 34)(16, 43, 90, 70, 28, 31)(18,
62, 75, 111, 102, 57)(21, 65, 106, 93, 74, 54)(30, 81, 69, 108, 89, 42)(33, 84,
105, 97, 52, 38)(37, 86, 92, 116, 112, 83, 53, 99, 96, 118, 104, 64)(41, 88,
114, 110, 95, 80, 56, 101, 115, 107, 78, 61)(60, 63, 103, 119, 117, 100, 79, 82,
109, 120, 113, 87)(121, 204, 186, 162, 212, 232, 180, 198, 233, 123, 205,
153)(122, 136, 227, 203, 209, 222, 125, 196, 235, 184, 139, 158)(124, 185, 221,
126, 191, 174, 194, 131, 149, 132, 202, 223)(127, 214, 224, 215, 155, 238)(128,
140, 133, 192, 225, 190, 159, 176, 152, 210, 151, 169)(129, 240, 156, 182, 142,
173)(130, 160, 166, 219, 234, 143, 197, 236, 217, 146, 171, 188)(134, 178, 170,
167, 220, 168, 199, 193, 237, 145, 164, 138)(135, 148, 154, 183, 187, 229, 195,
218, 226, 137, 206, 181)(141, 189, 144, 207, 230, 163, 177, 231, 211, 216, 228,
179)(147, 175, 157, 239, 200, 208)(150, 165, 201, 172, 161, 213)
a1: (61, 80)(64, 83)(86, 99)(88, 101)(107, 110)(116, 118)(130, 197)(135,
195)(140, 230)(141, 210)(144, 169)(154, 226)(166, 217)(171, 234)(176, 228)(177,
192)(187, 206)(190, 211)
C4[ 240, 44 ]
240
-1 221 126 162 186
-2 212 191 126 162
-3 167 125 174 153
-4 167 125 204 131
-5 221 204 185 186
-6 122 232 145 223
-7 198 122 145 185
-8 165 168 127 138
-9 124 158 180 237
-10 165 209 127 139
-11 212 158 202 237
-12 232 212 191 174
-13 209 178 174 153
-14 156 235 227 175
-15 121 222 170 194
-16 156 178 193 175
-17 222 191 170 205
-18 137 172 183 142
-19 203 150 238 184
-20 121 220 194 196
-21 155 137 183 208
-22 220 150 238 164
-23 220 149 196 186
-24 168 235 204 131
-25 121 124 204 185
-26 232 223 193 139
-27 198 138 227 185
-28 168 138 129 208
-29 124 136 180 164
-30 143 188 224 239
-31 199 134 147 240
-32 132 123 233 149
-33 143 188 213 129
-34 136 147 196 240
-35 221 233 136 164
-36 198 233 149 131
-37 181 160 152 163
-38 234 171 161 173
-39 157 203 182 184
-40 132 123 202 205
-41 148 152 163 219
-42 157 234 214 171
-43 157 170 182 237
-44 223 202 205 153
-45 209 123 178 126
-46 209 139 239 142
-47 199 212 202 184
-48 232 180 194 174
-49 155 213 235 227
-50 178 224 193 172
-51 134 191 203 205
-52 146 172 142 219
-53 133 179 236 229
-54 154 200 215 226
-55 199 134 201 214
-56 133 146 179 218
-57 154 201 182 226
-58 222 201 158 214
-59 132 193 139 162
-60 144 189 169 151
-61 176 166 135 230
-62 187 161 173 206
-63 144 169 128 207
-64 176 206 130 230
-65 187 147 238 206
-66 122 125 129 208
-67 198 180 194 131
-68 123 126 138 227
-69 155 236 160 208
-70 220 200 173 164
-71 199 149 184 186
-72 132 168 235 162
-73 121 124 223 153
-74 224 148 239 218
-75 213 181 129 229
-76 136 215 161 196
-77 221 134 233 203
-78 159 181 160 207
-79 231 211 190 225
-80 140 228 195 217
-81 200 215 130 197
-82 211 190 159 216
-83 187 140 228 197
-84 150 130 240 197
-85 155 145 167 213
-86 166 177 210 135
-87 210 189 151 141
-88 154 177 210 234
-89 146 127 175 219
-90 145 167 239 142
-91 122 125 224 172
-92 231 148 151 219
-93 135 157 214 195
-94 170 215 237 161
-95 236 128 216 229
-96 189 146 225 218
-97 166 201 182 217
-98 200 222 158 173
-99 192 195 217 141
-100 231 177 192 225
-101 192 171 226 141
-102 165 156 148 218
-103 128 140 207 230
-104 188 137 159 207
-105 165 156 236 160
-106 181 127 229 175
-107 144 190 206 130
-108 166 147 238 217
-109 176 159 216 228
-110 187 211 169 197
-111 135 150 195 240
-112 143 128 183 216
-113 210 179 141 152
-114 143 231 183 151
-115 188 189 137 225
-116 154 211 234 169
-117 133 177 192 163
-118 144 190 171 226
-119 133 140 163 230
-120 176 179 228 152
-121 25 15 73 20
-122 66 91 6 7
-123 45 68 40 32
-124 25 29 73 9
-125 66 3 91 4
-126 1 45 2 68
-127 89 106 8 10
-128 112 103 95 63
-129 33 66 28 75
-130 81 84 107 64
-131 67 24 36 4
-132 59 72 40 32
-133 56 117 53 119
-134 55 77 51 31
-135 111 93 61 86
-136 34 35 29 76
-137 104 115 18 21
-138 68 27 28 8
-139 46 26 59 10
-140 80 103 83 119
-141 99 101 113 87
-142 46 90 18 52
-143 33 112 114 30
-144 60 63 107 118
-145 90 6 7 85
-146 56 89 52 96
-147 34 31 108 65
-148 102 92 41 74
-149 23 36 71 32
-150 22 111 84 19
-151 92 114 60 87
-152 113 37 41 120
-153 44 13 3 73
-154 88 57 116 54
-155 69 49 85 21
-156 14 102 16 105
-157 93 39 42 43
-158 11 58 9 98
-159 78 82 104 109
-160 78 69 37 105
-161 38 94 62 76
-162 1 2 59 72
-163 37 117 41 119
-164 22 35 70 29
-165 102 105 8 10
-166 61 86 97 108
-167 90 3 4 85
-168 24 28 72 8
-169 110 60 116 63
-170 15 17 94 43
-171 101 38 118 42
-172 91 50 18 52
-173 70 38 62 98
-174 12 13 3 48
-175 89 14 16 106
-176 61 64 109 120
-177 88 100 117 86
-178 45 13 16 50
-179 56 113 53 120
-180 67 48 29 9
-181 78 37 106 75
-182 57 39 97 43
-183 112 114 18 21
-184 47 71 39 19
-185 25 5 27 7
-186 1 23 5 71
-187 110 83 62 65
-188 33 104 115 30
-189 60 115 96 87
-190 79 82 107 118
-191 12 2 17 51
-192 99 100 101 117
-193 26 59 16 50
-194 67 15 48 20
-195 99 111 80 93
-196 23 34 20 76
-197 110 81 83 84
-198 67 36 27 7
-199 55 47 71 31
-200 70 81 54 98
-201 55 57 58 97
-202 11 44 47 40
-203 77 39 51 19
-204 24 25 4 5
-205 44 17 40 51
-206 62 107 64 65
-207 78 103 104 63
-208 66 69 28 21
-209 45 13 46 10
-210 88 113 86 87
-211 110 79 82 116
-212 11 12 2 47
-213 33 49 85 75
-214 55 58 93 42
-215 81 94 54 76
-216 112 82 95 109
-217 99 80 97 108
-218 56 102 74 96
-219 89 92 41 52
-220 22 23 70 20
-221 77 1 35 5
-222 58 15 17 98
-223 44 26 6 73
-224 91 50 30 74
-225 100 79 115 96
-226 57 101 118 54
-227 68 14 27 49
-228 80 83 109 120
-229 95 106 53 75
-230 103 61 64 119
-231 100 79 92 114
-232 12 26 48 6
-233 77 35 36 32
-234 88 38 116 42
-235 24 14 49 72
-236 69 105 95 53
-237 11 94 9 43
-238 22 19 108 65
-239 46 90 30 74
-240 34 111 84 31
0