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