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