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