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