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