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