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