Graph forms
for C4 [ 272, 10 ] = PS(16,17;5)
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On this page are computer-accessible forms for the graph C4[ 272, 10 ] =
PS(16,17;5).
(I) Following is a form readable by MAGMA:
g:=Graph<272|{ {17, 18}, {236, 239}, {100, 103}, {153, 154}, {82, 86}, {83, 87},
{218, 222}, {219, 223}, {32, 37}, {34, 39}, {168, 173}, {170, 175}, {64, 70},
{65, 71}, {200, 206}, {201, 207}, {33, 38}, {136, 143}, {169, 174}, {48, 56},
{49, 57}, {50, 58}, {51, 59}, {180, 188}, {181, 189}, {182, 190}, {183, 191},
{48, 57}, {135, 142}, {133, 140}, {131, 138}, {50, 59}, {180, 189}, {182, 191},
{66, 72}, {133, 143}, {132, 142}, {129, 139}, {128, 138}, {67, 73}, {199, 205},
{49, 58}, {134, 141}, {130, 137}, {64, 75}, {68, 79}, {167, 172}, {181, 190},
{196, 207}, {32, 44}, {33, 45}, {34, 46}, {84, 88}, {85, 89}, {160, 172}, {161,
173}, {162, 174}, {163, 175}, {65, 76}, {101, 104}, {67, 78}, {80, 93}, {82,
95}, {166, 171}, {195, 206}, {210, 223}, {68, 74}, {131, 141}, {130, 140}, {119,
121}, {118, 120}, {97, 111}, {96, 110}, {225, 239}, {51, 60}, {132, 139}, {112,
127}, {102, 105}, {66, 77}, {81, 94}, {179, 188}, {194, 205}, {209, 222}, {2,
18}, {143, 159}, {142, 158}, {141, 157}, {140, 156}, {139, 155}, {138, 154}, {3,
19}, {4, 20}, {5, 21}, {6, 22}, {7, 23}, {8, 24}, {9, 25}, {10, 26}, {11, 27},
{12, 28}, {13, 29}, {14, 30}, {15, 31}, {105, 120}, {111, 126}, {109, 124},
{107, 122}, {1, 19}, {238, 252}, {141, 159}, {140, 158}, {137, 155}, {102, 116},
{99, 113}, {98, 112}, {4, 22}, {5, 23}, {8, 26}, {9, 27}, {12, 30}, {13, 31},
{226, 240}, {227, 241}, {230, 244}, {231, 245}, {234, 248}, {235, 249}, {75,
88}, {110, 125}, {108, 127}, {106, 121}, {104, 123}, {79, 92}, {96, 116}, {99,
119}, {98, 118}, {97, 117}, {164, 176}, {165, 177}, {166, 178}, {167, 179},
{224, 244}, {225, 245}, {226, 246}, {227, 247}, {232, 252}, {233, 253}, {234,
254}, {235, 255}, {72, 93}, {107, 126}, {105, 124}, {74, 95}, {76, 89}, {78,
91}, {197, 208}, {199, 210}, {2, 20}, {237, 251}, {236, 250}, {139, 157}, {138,
156}, {135, 145}, {134, 144}, {101, 115}, {100, 114}, {3, 21}, {10, 28}, {11,
29}, {160, 182}, {161, 183}, {228, 242}, {229, 243}, {47, 56}, {108, 123}, {106,
125}, {73, 94}, {77, 90}, {192, 215}, {198, 209}, {44, 52}, {129, 153}, {128,
152}, {45, 53}, {46, 54}, {47, 55}, {36, 61}, {38, 63}, {44, 53}, {46, 55},
{193, 216}, {195, 218}, {197, 220}, {36, 62}, {136, 146}, {37, 63}, {162, 184},
{163, 185}, {202, 208}, {203, 209}, {37, 62}, {45, 54}, {71, 92}, {194, 217},
{198, 221}, {200, 211}, {204, 215}, {168, 180}, {169, 181}, {170, 182}, {192,
220}, {193, 221}, {228, 248}, {229, 249}, {230, 250}, {231, 251}, {70, 91},
{237, 240}, {103, 122}, {74, 87}, {201, 212}, {203, 214}, {6, 24}, {7, 25}, {35,
61}, {164, 186}, {165, 187}, {204, 210}, {232, 246}, {233, 247}, {35, 60}, {238,
241}, {43, 52}, {69, 90}, {73, 86}, {196, 219}, {202, 213}, {224, 255}, {87,
118}, {223, 254}, {70, 100}, {71, 101}, {206, 236}, {207, 237}, {1, 34}, {137,
170}, {19, 48}, {86, 117}, {155, 184}, {222, 253}, {20, 49}, {22, 51}, {156,
185}, {158, 187}, {69, 99}, {205, 235}, {21, 50}, {157, 186}, {26, 48}, {27,
49}, {154, 176}, {155, 177}, {158, 180}, {159, 181}, {75, 96}, {79, 100}, {207,
228}, {92, 112}, {95, 115}, {94, 114}, {93, 113}, {222, 242}, {223, 243}, {76,
97}, {78, 99}, {154, 183}, {206, 227}, {14, 32}, {143, 161}, {142, 160}, {15,
33}, {28, 50}, {29, 51}, {72, 102}, {156, 178}, {157, 179}, {77, 98}, {88, 119},
{205, 226}, {16, 32}, {145, 161}, {144, 160}, {17, 33}, {146, 162}, {147, 163},
{148, 164}, {149, 165}, {150, 166}, {151, 167}, {152, 168}, {153, 169}, {16,
34}, {144, 162}, {95, 109}, {94, 108}, {91, 105}, {90, 104}, {145, 163}, {148,
166}, {149, 167}, {152, 170}, {83, 96}, {211, 224}, {215, 228}, {219, 232}, {23,
35}, {91, 111}, {90, 110}, {89, 109}, {88, 108}, {28, 40}, {29, 41}, {30, 42},
{31, 43}, {159, 171}, {80, 101}, {84, 97}, {208, 229}, {210, 231}, {212, 225},
{214, 227}, {216, 237}, {220, 233}, {24, 46}, {93, 107}, {92, 106}, {25, 47},
{146, 164}, {147, 165}, {81, 102}, {85, 98}, {209, 230}, {213, 226}, {217, 238},
{221, 234}, {18, 40}, {19, 41}, {22, 44}, {23, 45}, {31, 36}, {211, 232}, {215,
236}, {24, 36}, {87, 107}, {25, 37}, {26, 38}, {27, 39}, {86, 106}, {220, 224},
{221, 225}, {18, 47}, {30, 35}, {212, 233}, {214, 235}, {216, 229}, {218, 231},
{20, 42}, {89, 103}, {21, 43}, {150, 168}, {151, 169}, {208, 238}, {213, 234},
{217, 230}, {52, 80}, {53, 81}, {54, 82}, {55, 83}, {188, 216}, {189, 217},
{190, 218}, {191, 219}, {38, 64}, {39, 65}, {174, 200}, {175, 201}, {39, 64},
{175, 200}, {40, 65}, {42, 67}, {57, 80}, {59, 82}, {61, 84}, {172, 197}, {174,
199}, {189, 212}, {191, 214}, {40, 66}, {41, 67}, {172, 198}, {173, 199}, {41,
66}, {58, 81}, {62, 85}, {173, 198}, {190, 213}, {56, 84}, {57, 85}, {42, 68},
{171, 197}, {43, 68}, {60, 83}, {171, 196}, {188, 211}, {61, 72}, {63, 74}, {56,
79}, {62, 73}, {183, 192}, {184, 192}, {185, 193}, {186, 194}, {187, 195}, {53,
76}, {55, 78}, {176, 201}, {178, 203}, {184, 193}, {186, 195}, {63, 69}, {176,
202}, {177, 203}, {54, 77}, {60, 71}, {177, 202}, {185, 194}, {59, 70}, {178,
204}, {52, 75}, {58, 69}, {179, 204}, {187, 196}, {103, 135}, {104, 136}, {125,
152}, {126, 153}, {120, 144}, {127, 151}, {126, 150}, {125, 149}, {124, 148},
{123, 147}, {122, 146}, {121, 145}, {120, 147}, {124, 151}, {109, 128}, {123,
150}, {121, 148}, {111, 130}, {110, 129}, {122, 149}, {113, 128}, {119, 134},
{117, 132}, {115, 130}, {112, 131}, {118, 133}, {116, 135}, {114, 129}, {113,
132}, {115, 134}, {127, 137}, {114, 133}, {116, 131}, {117, 136}, {1, 263}, {8,
270}, {9, 271}, {8, 256}, {9, 257}, {10, 258}, {11, 259}, {12, 260}, {13, 261},
{14, 262}, {15, 263}, {2, 267}, {4, 269}, {6, 271}, {2, 264}, {3, 265}, {6,
268}, {7, 269}, {1, 266}, {5, 270}, {11, 256}, {15, 260}, {12, 257}, {14, 259},
{4, 266}, {5, 267}, {3, 268}, {13, 258}, {16, 261}, {7, 272}, {17, 262}, {16,
264}, {17, 265}, {10, 272}, {239, 271}, {240, 272}, {239, 258}, {253, 272},
{241, 256}, {255, 270}, {253, 268}, {251, 266}, {249, 264}, {247, 262}, {245,
260}, {243, 258}, {240, 259}, {254, 269}, {252, 271}, {250, 265}, {248, 267},
{246, 261}, {244, 263}, {242, 257}, {241, 260}, {251, 270}, {249, 268}, {243,
262}, {242, 261}, {252, 267}, {250, 269}, {244, 259}, {245, 264}, {247, 266},
{254, 256}, {255, 257}, {246, 265}, {248, 263} }>;
(II) A more general form is to represent the graph as the orbit of {17, 18}
under the group generated by the following permutations:
a: (2, 17)(3, 16)(4, 15)(5, 14)(6, 13)(7, 12)(8, 11)(9, 10)(19, 34)(20, 33)(21,
32)(22, 31)(23, 30)(24, 29)(25, 28)(26, 27)(36, 51)(37, 50)(38, 49)(39, 48)(40,
47)(41, 46)(42, 45)(43, 44)(53, 68)(54, 67)(55, 66)(56, 65)(57, 64)(58, 63)(59,
62)(60, 61)(70, 85)(71, 84)(72, 83)(73, 82)(74, 81)(75, 80)(76, 79)(77, 78)(87,
102)(88, 101)(89, 100)(90, 99)(91, 98)(92, 97)(93, 96)(94, 95)(104, 119)(105,
118)(106, 117)(107, 116)(108, 115)(109, 114)(110, 113)(111, 112)(121, 136)(122,
135)(123, 134)(124, 133)(125, 132)(126, 131)(127, 130)(128, 129)(138, 153)(139,
152)(140, 151)(141, 150)(142, 149)(143, 148)(144, 147)(145, 146)(155, 170)(156,
169)(157, 168)(158, 167)(159, 166)(160, 165)(161, 164)(162, 163)(172, 187)(173,
186)(174, 185)(175, 184)(176, 183)(177, 182)(178, 181)(179, 180)(189, 204)(190,
203)(191, 202)(192, 201)(193, 200)(194, 199)(195, 198)(196, 197)(206, 221)(207,
220)(208, 219)(209, 218)(210, 217)(211, 216)(212, 215)(213, 214)(223, 238)(224,
237)(225, 236)(226, 235)(227, 234)(228, 233)(229, 232)(230, 231)(240, 255)(241,
254)(242, 253)(243, 252)(244, 251)(245, 250)(246, 249)(247, 248)(257, 272)(258,
271)(259, 270)(260, 269)(261, 268)(262, 267)(263, 266)(264, 265) (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, 18, 35, 52, 69, 86, 103, 120, 137, 154, 171, 188, 205, 222, 239, 256)(2,
23, 43, 58, 82, 100, 105, 130, 153, 166, 180, 199, 209, 225, 254, 263)(3, 28,
51, 64, 78, 97, 107, 123, 152, 161, 172, 193, 213, 228, 252, 270)(4, 33, 42, 53,
74, 94, 109, 133, 151, 156, 181, 204, 217, 231, 250, 260)(5, 21, 50, 59, 70, 91,
111, 126, 150, 168, 173, 198, 221, 234, 248, 267)(6, 26, 41, 65, 83, 88, 113,
136, 149, 163, 182, 192, 208, 237, 246, 257)(7, 31, 49, 54, 79, 102, 115, 129,
148, 158, 174, 203, 212, 223, 244, 264)(8, 19, 40, 60, 75, 99, 117, 122, 147,
170, 183, 197, 216, 226, 242, 271)(9, 24, 48, 66, 71, 96, 119, 132, 146, 165,
175, 191, 220, 229, 240, 261)(10, 29, 39, 55, 84, 93, 104, 125, 145, 160, 184,
202, 207, 232, 255, 268)(11, 34, 47, 61, 80, 90, 106, 135, 144, 155, 176, 196,
211, 235, 253, 258)(12, 22, 38, 67, 76, 87, 108, 128, 143, 167, 185, 190, 215,
238, 251, 265)(13, 27, 46, 56, 72, 101, 110, 121, 142, 162, 177, 201, 219, 224,
249, 272)(14, 32, 37, 62, 85, 98, 112, 131, 141, 157, 186, 195, 206, 227, 247,
262)(15, 20, 45, 68, 81, 95, 114, 124, 140, 169, 178, 189, 210, 230, 245,
269)(16, 25, 36, 57, 77, 92, 116, 134, 139, 164, 187, 200, 214, 233, 243,
259)(17, 30, 44, 63, 73, 89, 118, 127, 138, 159, 179, 194, 218, 236, 241,
266)
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, 241, 242, 243, 244,
245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255)(256, 257, 258, 259, 260,
261, 262, 263, 264, 265, 266, 267, 268, 269, 270, 271, 272)
C4[ 272, 10 ]
272
-1 34 266 19 263
-2 264 267 18 20
-3 265 268 19 21
-4 22 266 269 20
-5 23 267 270 21
-6 22 24 268 271
-7 23 25 269 272
-8 24 256 26 270
-9 25 257 27 271
-10 26 258 28 272
-11 256 27 259 29
-12 257 28 260 30
-13 258 29 261 31
-14 259 30 262 32
-15 33 260 31 263
-16 264 34 261 32
-17 33 265 18 262
-18 2 47 17 40
-19 1 3 48 41
-20 2 4 49 42
-21 3 5 50 43
-22 44 4 6 51
-23 45 35 5 7
-24 46 36 6 8
-25 47 37 7 9
-26 48 38 8 10
-27 11 49 39 9
-28 12 50 40 10
-29 11 13 51 41
-30 12 35 14 42
-31 13 36 15 43
-32 44 14 37 16
-33 45 15 38 17
-34 1 46 16 39
-35 23 60 61 30
-36 24 61 62 31
-37 25 62 63 32
-38 33 26 63 64
-39 34 27 64 65
-40 66 28 18 65
-41 66 67 29 19
-42 67 68 30 20
-43 68 52 31 21
-44 22 52 53 32
-45 33 23 53 54
-46 55 34 24 54
-47 55 56 25 18
-48 56 57 26 19
-49 57 58 27 20
-50 58 59 28 21
-51 22 59 60 29
-52 44 80 75 43
-53 44 45 81 76
-54 77 45 46 82
-55 78 46 47 83
-56 79 47 48 84
-57 80 48 49 85
-58 69 81 49 50
-59 70 82 50 51
-60 35 71 83 51
-61 35 36 72 84
-62 36 37 73 85
-63 69 37 38 74
-64 70 38 39 75
-65 71 39 40 76
-66 77 72 40 41
-67 78 73 41 42
-68 79 74 42 43
-69 99 90 58 63
-70 100 91 59 64
-71 101 92 60 65
-72 66 102 93 61
-73 67 94 62 86
-74 68 95 63 87
-75 88 52 96 64
-76 89 53 97 65
-77 66 90 54 98
-78 55 99 67 91
-79 56 100 68 92
-80 57 101 93 52
-81 58 102 94 53
-82 59 95 86 54
-83 55 60 96 87
-84 88 56 61 97
-85 89 57 62 98
-86 82 73 106 117
-87 83 74 107 118
-88 84 75 108 119
-89 103 85 76 109
-90 77 110 69 104
-91 78 111 70 105
-92 79 112 71 106
-93 80 113 72 107
-94 81 114 73 108
-95 82 115 74 109
-96 110 83 116 75
-97 111 84 117 76
-98 77 112 85 118
-99 78 69 113 119
-100 79 70 103 114
-101 80 71 104 115
-102 81 72 105 116
-103 89 100 122 135
-104 90 101 123 136
-105 91 102 124 120
-106 121 92 125 86
-107 122 93 126 87
-108 88 123 94 127
-109 89 124 95 128
-110 90 125 96 129
-111 91 126 97 130
-112 92 127 98 131
-113 99 132 93 128
-114 100 133 94 129
-115 101 134 95 130
-116 102 135 96 131
-117 132 136 86 97
-118 133 87 98 120
-119 88 99 121 134
-120 144 147 105 118
-121 145 148 106 119
-122 146 103 149 107
-123 147 104 150 108
-124 148 105 151 109
-125 110 149 106 152
-126 111 150 107 153
-127 112 137 151 108
-128 113 138 152 109
-129 110 114 139 153
-130 111 115 137 140
-131 112 116 138 141
-132 113 117 139 142
-133 143 114 118 140
-134 144 115 119 141
-135 145 103 116 142
-136 143 146 104 117
-137 155 170 127 130
-138 154 156 128 131
-139 132 155 157 129
-140 133 156 158 130
-141 134 157 159 131
-142 132 135 158 160
-143 133 136 159 161
-144 134 160 162 120
-145 121 135 161 163
-146 122 136 162 164
-147 165 123 163 120
-148 121 166 124 164
-149 165 122 167 125
-150 166 123 168 126
-151 167 124 169 127
-152 168 125 170 128
-153 154 169 126 129
-154 176 138 183 153
-155 177 137 139 184
-156 178 138 140 185
-157 179 139 141 186
-158 187 180 140 142
-159 143 181 171 141
-160 144 182 172 142
-161 143 145 183 173
-162 144 146 184 174
-163 145 147 185 175
-164 176 146 148 186
-165 187 177 147 149
-166 178 148 171 150
-167 179 149 172 151
-168 180 150 173 152
-169 181 151 174 153
-170 137 182 152 175
-171 166 159 196 197
-172 198 167 160 197
-173 198 199 168 161
-174 199 200 169 162
-175 200 201 170 163
-176 154 201 202 164
-177 165 155 202 203
-178 166 156 203 204
-179 188 167 157 204
-180 188 189 168 158
-181 189 190 169 159
-182 190 191 170 160
-183 154 191 192 161
-184 155 192 193 162
-185 156 193 194 163
-186 157 194 195 164
-187 165 158 195 196
-188 211 179 180 216
-189 212 180 181 217
-190 213 181 182 218
-191 214 182 183 219
-192 220 215 183 184
-193 221 216 184 185
-194 205 217 185 186
-195 187 206 218 186
-196 187 171 207 219
-197 220 171 172 208
-198 209 221 172 173
-199 210 205 173 174
-200 211 206 174 175
-201 176 212 207 175
-202 176 177 213 208
-203 209 177 178 214
-204 210 178 179 215
-205 199 235 226 194
-206 200 236 227 195
-207 201 237 228 196
-208 202 238 229 197
-209 198 222 203 230
-210 231 199 223 204
-211 188 232 200 224
-212 189 233 201 225
-213 190 234 202 226
-214 191 235 203 227
-215 192 236 204 228
-216 188 193 237 229
-217 189 194 238 230
-218 231 222 190 195
-219 232 223 191 196
-220 233 224 192 197
-221 198 234 225 193
-222 209 242 253 218
-223 210 243 254 219
-224 220 211 244 255
-225 221 212 245 239
-226 213 246 205 240
-227 214 247 206 241
-228 242 215 248 207
-229 243 216 249 208
-230 209 244 217 250
-231 210 245 218 251
-232 211 246 219 252
-233 220 253 212 247
-234 221 254 213 248
-235 255 214 205 249
-236 215 206 239 250
-237 216 207 240 251
-238 217 208 241 252
-239 225 236 258 271
-240 226 237 259 272
-241 256 227 238 260
-242 222 257 228 261
-243 223 258 229 262
-244 224 259 230 263
-245 231 264 225 260
-246 232 265 226 261
-247 233 266 227 262
-248 234 267 228 263
-249 264 235 268 229
-250 265 236 269 230
-251 231 266 237 270
-252 232 267 238 271
-253 222 233 268 272
-254 223 234 256 269
-255 224 235 257 270
-256 11 254 8 241
-257 242 12 255 9
-258 243 13 239 10
-259 11 244 14 240
-260 12 245 15 241
-261 242 13 246 16
-262 243 14 247 17
-263 1 244 15 248
-264 2 245 16 249
-265 3 246 17 250
-266 1 4 247 251
-267 2 5 248 252
-268 253 3 6 249
-269 254 4 7 250
-270 255 5 8 251
-271 6 239 9 252
-272 253 7 240 10
0