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