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