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