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