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