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