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