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