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