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