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