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