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