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