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