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