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