Graph forms
for C4 [ 240, 70 ] = UG(ATD[240,27])
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On this page are computer-accessible forms for the graph C4[ 240, 70 ] =
UG(ATD[240,27]).
(I) Following is a form readable by MAGMA:
g:=Graph<240|{ {80, 81}, {152, 157}, {232, 238}, {1, 9}, {176, 184}, {98, 106},
{2, 11}, {5, 15}, {230, 236}, {101, 110}, {228, 239}, {146, 153}, {97, 109},
{150, 155}, {224, 238}, {3, 12}, {149, 154}, {1, 17}, {35, 51}, {96, 112}, {3,
18}, {7, 21}, {99, 112}, {37, 49}, {33, 55}, {34, 52}, {4, 19}, {231, 240}, {1,
25}, {192, 216}, {170, 178}, {7, 31}, {78, 84}, {132, 158}, {76, 87}, {174,
181}, {173, 182}, {96, 123}, {79, 83}, {135, 154}, {131, 157}, {3, 28}, {4, 27},
{17, 49}, {152, 184}, {31, 63}, {92, 124}, {19, 50}, {194, 227}, {151, 182},
{129, 160}, {94, 127}, {23, 53}, {197, 231}, {150, 181}, {66, 102}, {67, 101},
{148, 178}, {95, 121}, {20, 51}, {198, 225}, {27, 60}, {25, 62}, {69, 98}, {1,
41}, {9, 33}, {5, 45}, {75, 99}, {2, 43}, {140, 165}, {65, 104}, {10, 35}, {3,
42}, {13, 39}, {77, 97}, {200, 228}, {143, 163}, {142, 162}, {80, 125}, {73,
103}, {74, 100}, {11, 36}, {223, 240}, {9, 57}, {192, 240}, {15, 63}, {94, 111},
{220, 237}, {144, 161}, {155, 169}, {212, 230}, {74, 121}, {215, 228}, {153,
170}, {75, 120}, {93, 110}, {211, 231}, {222, 234}, {78, 123}, {136, 189}, {128,
181}, {90, 108}, {157, 171}, {11, 60}, {154, 173}, {143, 184}, {12, 59}, {77,
122}, {209, 232}, {132, 190}, {77, 118}, {140, 183}, {135, 186}, {139, 182},
{137, 180}, {73, 119}, {74, 116}, {57, 121}, {141, 205}, {58, 123}, {139, 202},
{61, 127}, {174, 236}, {134, 196}, {151, 212}, {54, 114}, {130, 199}, {170,
239}, {150, 211}, {148, 209}, {53, 115}, {134, 192}, {56, 126}, {50, 117}, {167,
224}, {137, 206}, {59, 124}, {17, 89}, {41, 97}, {39, 111}, {33, 105}, {21, 93},
{18, 91}, {56, 113}, {43, 98}, {19, 90}, {42, 96}, {54, 124}, {47, 101}, {52,
127}, {60, 112}, {133, 200}, {136, 198}, {35, 108}, {152, 215}, {128, 207}, {44,
99}, {36, 107}, {17, 65}, {153, 201}, {63, 111}, {25, 73}, {23, 71}, {26, 75},
{191, 238}, {155, 202}, {151, 198}, {29, 79}, {159, 205}, {179, 224}, {190,
237}, {145, 197}, {148, 194}, {188, 234}, {19, 68}, {156, 203}, {59, 108}, {57,
110}, {27, 76}, {20, 67}, {9, 81}, {137, 209}, {128, 216}, {47, 119}, {41, 113},
{31, 71}, {13, 85}, {10, 83}, {139, 210}, {135, 222}, {11, 82}, {138, 208},
{143, 213}, {134, 221}, {147, 200}, {28, 64}, {173, 240}, {132, 218}, {176,
238}, {28, 67}, {140, 211}, {44, 115}, {43, 116}, {30, 65}, {168, 200}, {55,
86}, {166, 199}, {48, 82}, {37, 70}, {165, 198}, {16, 116}, {49, 85}, {32, 68},
{33, 71}, {162, 196}, {52, 82}, {34, 68}, {136, 224}, {188, 212}, {190, 215},
{191, 214}, {35, 72}, {181, 222}, {51, 88}, {177, 223}, {178, 220}, {45, 93},
{43, 90}, {185, 203}, {191, 204}, {187, 207}, {188, 201}, {168, 222}, {41, 94},
{15, 119}, {45, 85}, {42, 83}, {164, 221}, {166, 218}, {12, 115}, {46, 81}, {14,
113}, {39, 167}, {65, 193}, {61, 189}, {57, 185}, {69, 197}, {58, 187}, {66,
195}, {59, 186}, {67, 194}, {92, 221}, {48, 179}, {94, 218}, {95, 219}, {36,
163}, {38, 161}, {40, 164}, {78, 192}, {21, 133}, {48, 160}, {18, 131}, {117,
228}, {72, 219}, {114, 225}, {88, 203}, {118, 227}, {22, 129}, {25, 129}, {44,
180}, {29, 133}, {82, 202}, {26, 131}, {46, 183}, {27, 130}, {70, 223}, {24,
130}, {86, 205}, {69, 217}, {85, 201}, {47, 177}, {66, 220}, {120, 231}, {113,
208}, {22, 180}, {64, 226}, {38, 132}, {20, 183}, {36, 135}, {8, 172}, {39,
131}, {104, 207}, {7, 175}, {58, 146}, {40, 129}, {126, 215}, {101, 204}, {110,
196}, {62, 149}, {125, 214}, {61, 145}, {98, 206}, {106, 199}, {24, 182}, {122,
212}, {109, 195}, {4, 171}, {23, 184}, {6, 169}, {46, 159}, {112, 193}, {63,
142}, {8, 186}, {84, 230}, {45, 158}, {127, 204}, {62, 141}, {22, 162}, {38,
146}, {87, 226}, {126, 203}, {124, 201}, {109, 216}, {21, 163}, {60, 138}, {42,
156}, {102, 208}, {18, 165}, {55, 128}, {34, 149}, {5, 189}, {53, 141}, {49,
137}, {2, 187}, {117, 204}, {51, 138}, {50, 139}, {24, 161}, {96, 217}, {105,
210}, {114, 206}, {115, 207}, {37, 152}, {88, 229}, {107, 214}, {40, 150}, {86,
232}, {6, 185}, {106, 213}, {76, 140}, {44, 237}, {79, 142}, {34, 230}, {47,
235}, {46, 234}, {16, 214}, {118, 176}, {73, 143}, {37, 226}, {104, 175}, {26,
210}, {89, 145}, {91, 146}, {14, 196}, {90, 144}, {95, 149}, {100, 174}, {12,
199}, {122, 177}, {32, 235}, {30, 213}, {103, 172}, {15, 195}, {29, 209}, {108,
160}, {40, 229}, {126, 179}, {80, 157}, {38, 232}, {92, 147}, {125, 178}, {64,
144}, {93, 141}, {8, 217}, {116, 165}, {31, 206}, {16, 193}, {91, 138}, {76,
158}, {30, 205}, {123, 168}, {64, 147}, {72, 155}, {118, 162}, {13, 216}, {79,
154}, {28, 202}, {102, 176}, {89, 142}, {120, 175}, {61, 229}, {68, 156}, {105,
177}, {48, 233}, {117, 172}, {58, 227}, {70, 159}, {106, 179}, {109, 183}, {75,
144}, {125, 166}, {6, 218}, {114, 174}, {14, 210}, {5, 219}, {122, 164}, {121,
167}, {120, 166}, {71, 153}, {2, 221}, {119, 168}, {62, 225}, {10, 213}, {107,
180}, {103, 134}, {7, 229}, {56, 219}, {14, 234}, {97, 133}, {13, 235}, {100,
130}, {4, 227}, {10, 237}, {6, 225}, {52, 220}, {54, 223}, {8, 226}, {99, 136},
{80, 189}, {55, 217}, {78, 160}, {32, 208}, {111, 159}, {53, 197}, {81, 161},
{87, 167}, {89, 169}, {95, 175}, {30, 239}, {50, 195}, {24, 235}, {32, 211},
{103, 148}, {29, 233}, {74, 190}, {88, 173}, {100, 145}, {102, 147}, {26, 236},
{54, 193}, {72, 191}, {77, 186}, {83, 164}, {84, 163}, {91, 172}, {92, 171},
{105, 158}, {107, 156}, {20, 236}, {16, 233}, {22, 239}, {69, 188}, {56, 194},
{66, 185}, {70, 187}, {84, 169}, {86, 171}, {87, 170}, {23, 233}, {104, 151}
}>;
(II) A more general form is to represent the graph as the orbit of {80, 81}
under the group generated by the following permutations:
a: (1, 2, 6, 4)(3, 5, 8, 7)(9, 187, 225, 27)(10, 191, 228, 29)(11, 185, 227,
25)(12, 189, 226, 31)(13, 188, 231, 26)(14, 192, 230, 32)(15, 186, 229, 28)(16,
190, 232, 30)(17, 43, 218, 171)(18, 45, 217, 175)(19, 41, 221, 169)(20, 47, 222,
173)(21, 42, 219, 172)(22, 48, 220, 176)(23, 44, 224, 170)(24, 46, 223, 174)(33,
207, 198, 76)(34, 208, 196, 78)(35, 204, 200, 79)(36, 203, 194, 73)(37, 206,
199, 80)(38, 205, 193, 74)(39, 201, 197, 75)(40, 202, 195, 77)(49, 98, 166,
157)(50, 97, 164, 155)(51, 101, 168, 154)(52, 102, 162, 160)(53, 99, 167,
153)(54, 100, 161, 159)(55, 104, 165, 158)(56, 103, 163, 156)(57, 58, 62,
60)(59, 61, 64, 63)(65, 116, 132, 86)(66, 118, 129, 82)(67, 119, 135, 88)(68,
113, 134, 84)(69, 120, 131, 85)(70, 114, 130, 81)(71, 115, 136, 87)(72, 117,
133, 83)(89, 90, 94, 92)(91, 93, 96, 95)(105, 128, 151, 140)(106, 125, 152,
137)(107, 126, 148, 143)(108, 127, 147, 142)(109, 122, 150, 139)(110, 123, 149,
138)(111, 124, 145, 144)(112, 121, 146, 141)(177, 181, 182, 183)(178, 184, 180,
179)(209, 213, 214, 215)(210, 216, 212, 211)(233, 237, 238, 239)(234, 240, 236,
235) (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)(5, 7)(9, 25)(10, 26)(11, 27)(12, 28)(13, 29)(14, 30)(15, 31)(16,
32)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48)(33, 73)(34,
74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80)(49, 97)(50, 98)(51, 99)(52,
100)(53, 101)(54, 102)(55, 103)(56, 104)(57, 62)(59, 64)(65, 113)(66, 114)(67,
115)(68, 116)(69, 117)(70, 118)(71, 119)(72, 120)(81, 129)(82, 130)(83, 131)(84,
132)(85, 133)(86, 134)(87, 135)(88, 136)(89, 94)(91, 96)(105, 143)(106,
139)(107, 140)(108, 144)(109, 137)(110, 141)(111, 142)(112, 138)(121, 149)(122,
152)(123, 146)(124, 147)(125, 150)(126, 151)(127, 145)(128, 148)(153, 168)(154,
167)(155, 166)(156, 165)(157, 164)(158, 163)(159, 162)(160, 161)(169, 218)(170,
222)(171, 221)(172, 217)(173, 224)(174, 220)(175, 219)(176, 223)(177, 184)(178,
181)(179, 182)(180, 183)(185, 225)(186, 226)(187, 227)(188, 228)(189, 229)(190,
230)(191, 231)(192, 232)(193, 208)(194, 207)(195, 206)(196, 205)(197, 204)(198,
203)(199, 202)(200, 201)(209, 216)(210, 213)(211, 214)(212, 215)(233, 235)(234,
239)(236, 237)(238, 240)
c: (1, 3)(2, 5)(4, 7)(6, 8)(9, 12)(10, 14)(11, 15)(13, 16)(17, 18)(19, 21)(20,
22)(23, 24)(25, 28)(26, 30)(27, 31)(29, 32)(33, 199)(34, 200)(35, 196)(36,
195)(37, 198)(38, 197)(39, 193)(40, 194)(41, 42)(43, 45)(44, 46)(47, 48)(49,
165)(50, 163)(51, 162)(52, 168)(53, 161)(54, 167)(55, 166)(56, 164)(57, 59)(58,
61)(60, 63)(62, 64)(65, 131)(66, 135)(67, 129)(68, 133)(69, 132)(70, 136)(71,
130)(72, 134)(73, 202)(74, 201)(75, 205)(76, 206)(77, 203)(78, 204)(79, 208)(80,
207)(81, 115)(82, 119)(83, 113)(84, 117)(85, 116)(86, 120)(87, 114)(88, 118)(89,
91)(90, 93)(92, 95)(94, 96)(97, 156)(98, 158)(99, 159)(100, 153)(101, 160)(102,
154)(103, 155)(104, 157)(105, 106)(107, 109)(108, 110)(111, 112)(121, 124)(122,
126)(123, 127)(125, 128)(137, 140)(138, 142)(139, 143)(141, 144)(145, 146)(147,
149)(148, 150)(151, 152)(169, 172)(170, 174)(171, 175)(173, 176)(177, 179)(178,
181)(180, 183)(182, 184)(185, 186)(187, 189)(188, 190)(191, 192)(209, 211)(210,
213)(212, 215)(214, 216)(217, 218)(219, 221)(220, 222)(223, 224)(225, 226)(227,
229)(228, 230)(231, 232)(233, 235)(234, 237)(236, 239)(238, 240)
d: (1, 9, 33, 71, 31, 63, 111, 159, 205, 141, 93, 45, 85, 49, 17)(2, 10, 34, 67,
27, 59, 107, 155, 208, 144, 96, 48, 88, 50, 18)(3, 11, 35, 68, 28, 60, 108, 156,
202, 138, 90, 42, 82, 51, 19)(4, 12, 36, 72, 32, 64, 112, 160, 203, 139, 91, 43,
83, 52, 20)(5, 13, 37, 65, 25, 57, 105, 153, 206, 142, 94, 46, 86, 53, 21)(6,
14, 38, 69, 29, 61, 109, 157, 207, 143, 95, 47, 87, 54, 22)(7, 15, 39, 70, 30,
62, 110, 158, 201, 137, 89, 41, 81, 55, 23)(8, 16, 40, 66, 26, 58, 106, 154,
204, 140, 92, 44, 84, 56, 24)(73, 121, 177, 170, 114, 162, 218, 234, 232, 197,
133, 189, 216, 152, 104)(74, 122, 178, 174, 118, 166, 222, 238, 231, 200, 136,
192, 215, 151, 103)(75, 123, 179, 173, 117, 165, 221, 237, 230, 194, 130, 186,
214, 150, 102)(76, 124, 180, 169, 113, 161, 217, 233, 229, 195, 131, 187, 213,
149, 101)(77, 125, 181, 176, 120, 168, 224, 240, 228, 198, 134, 190, 212, 148,
100)(78, 126, 182, 172, 116, 164, 220, 236, 227, 199, 135, 191, 211, 147,
99)(79, 127, 183, 171, 115, 163, 219, 235, 226, 193, 129, 185, 210, 146, 98)(80,
128, 184, 175, 119, 167, 223, 239, 225, 196, 132, 188, 209, 145, 97)
e: (2, 4)(5, 7)(9, 17)(10, 20)(11, 19)(12, 18)(13, 23)(14, 22)(15, 21)(16,
24)(25, 41)(26, 44)(27, 43)(28, 42)(29, 47)(30, 46)(31, 45)(32, 48)(33, 49)(34,
52)(35, 51)(36, 50)(37, 55)(38, 54)(39, 53)(40, 56)(57, 89)(58, 92)(59, 91)(60,
90)(61, 95)(62, 94)(63, 93)(64, 96)(65, 81)(66, 84)(67, 83)(68, 82)(69, 87)(70,
86)(71, 85)(72, 88)(73, 97)(74, 100)(75, 99)(76, 98)(77, 103)(78, 102)(79,
101)(80, 104)(105, 137)(106, 140)(107, 139)(108, 138)(109, 143)(110, 142)(111,
141)(112, 144)(113, 129)(114, 132)(115, 131)(116, 130)(117, 135)(118, 134)(119,
133)(120, 136)(121, 145)(122, 148)(123, 147)(124, 146)(125, 151)(126, 150)(127,
149)(128, 152)(153, 201)(154, 204)(155, 203)(156, 202)(157, 207)(158, 206)(159,
205)(160, 208)(161, 193)(162, 196)(163, 195)(164, 194)(165, 199)(166, 198)(167,
197)(168, 200)(169, 185)(170, 188)(171, 187)(172, 186)(173, 191)(174, 190)(175,
189)(176, 192)(177, 209)(178, 212)(179, 211)(180, 210)(181, 215)(182, 214)(183,
213)(184, 216)(217, 226)(218, 225)(219, 229)(220, 230)(221, 227)(222, 228)(223,
232)(224, 231)(233, 235)(234, 239)(236, 237)(238, 240)
C4[ 240, 70 ]
240
-1 25 17 41 9
-2 11 187 221 43
-3 12 28 18 42
-4 27 171 227 19
-5 45 189 15 219
-6 169 225 185 218
-7 31 229 21 175
-8 226 172 217 186
-9 33 1 57 81
-10 35 213 83 237
-11 2 36 60 82
-12 199 3 59 115
-13 235 39 216 85
-14 210 113 234 196
-15 5 63 195 119
-16 233 214 116 193
-17 1 89 49 65
-18 165 3 91 131
-19 68 90 4 50
-20 67 236 51 183
-21 133 93 7 163
-22 180 129 162 239
-23 233 71 184 53
-24 235 182 161 130
-25 1 62 73 129
-26 210 236 75 131
-27 4 60 130 76
-28 67 3 202 64
-29 209 133 79 233
-30 213 205 239 65
-31 71 7 63 206
-32 68 211 235 208
-33 55 71 105 9
-34 68 149 52 230
-35 72 51 108 10
-36 11 135 107 163
-37 70 49 226 152
-38 132 232 146 161
-39 111 13 167 131
-40 150 129 229 164
-41 1 113 94 97
-42 156 3 83 96
-43 2 90 116 98
-44 99 180 115 237
-45 158 5 93 85
-46 234 81 159 183
-47 177 101 235 119
-48 233 179 82 160
-49 37 137 17 85
-50 117 139 19 195
-51 88 35 138 20
-52 220 34 82 127
-53 23 115 141 197
-54 124 223 114 193
-55 33 128 217 86
-56 113 126 194 219
-57 110 121 9 185
-58 187 123 146 227
-59 12 124 108 186
-60 11 112 27 138
-61 145 189 127 229
-62 25 225 149 141
-63 111 15 31 142
-64 144 147 28 226
-65 104 17 193 30
-66 220 102 195 185
-67 101 28 194 20
-68 34 156 19 32
-69 188 217 98 197
-70 187 223 37 159
-71 33 23 31 153
-72 155 35 191 219
-73 143 25 103 119
-74 121 100 190 116
-75 99 144 26 120
-76 158 27 140 87
-77 122 118 97 186
-78 123 192 160 84
-79 154 83 29 142
-80 189 157 81 125
-81 46 80 161 9
-82 11 48 202 52
-83 79 42 10 164
-84 78 169 163 230
-85 45 13 201 49
-86 55 232 171 205
-87 167 170 226 76
-88 203 51 173 229
-89 145 169 17 142
-90 144 19 108 43
-91 146 138 18 172
-92 221 124 147 171
-93 110 45 141 21
-94 111 127 41 218
-95 121 149 175 219
-96 112 123 217 42
-97 77 133 41 109
-98 69 106 206 43
-99 44 112 136 75
-100 145 74 130 174
-101 110 67 47 204
-102 66 176 147 208
-103 134 148 73 172
-104 151 207 65 175
-105 33 177 210 158
-106 199 179 213 98
-107 156 36 180 214
-108 35 90 59 160
-109 183 216 195 97
-110 57 101 93 196
-111 159 39 94 63
-112 99 60 193 96
-113 56 14 41 208
-114 225 206 174 54
-115 44 12 53 207
-116 165 16 74 43
-117 50 204 172 228
-118 77 176 227 162
-119 47 168 15 73
-120 231 166 75 175
-121 57 167 95 74
-122 77 177 212 164
-123 78 58 168 96
-124 201 59 92 54
-125 166 178 80 214
-126 56 179 203 215
-127 61 94 204 52
-128 55 181 216 207
-129 22 25 160 40
-130 100 199 24 27
-131 157 26 39 18
-132 190 158 38 218
-133 200 29 97 21
-134 221 103 192 196
-135 154 222 36 186
-136 99 198 189 224
-137 209 180 49 206
-138 91 60 51 208
-139 210 202 50 182
-140 165 211 183 76
-141 93 62 205 53
-142 89 79 63 162
-143 213 73 184 163
-144 90 161 64 75
-145 89 100 61 197
-146 58 91 38 153
-147 200 102 92 64
-148 209 178 103 194
-149 154 34 62 95
-150 155 211 181 40
-151 198 212 104 182
-152 157 37 215 184
-153 146 201 71 170
-154 79 135 149 173
-155 169 202 72 150
-156 68 203 107 42
-157 80 171 152 131
-158 132 45 105 76
-159 111 46 70 205
-160 78 48 129 108
-161 144 24 81 38
-162 22 118 196 142
-163 143 36 84 21
-164 122 221 83 40
-165 198 116 18 140
-166 199 125 218 120
-167 121 224 39 87
-168 123 200 222 119
-169 89 155 6 84
-170 178 239 87 153
-171 157 4 92 86
-172 91 103 117 8
-173 88 154 182 240
-174 100 114 181 236
-175 104 7 95 120
-176 102 238 118 184
-177 122 47 223 105
-178 220 125 148 170
-179 48 224 126 106
-180 22 44 137 107
-181 222 128 150 174
-182 24 139 151 173
-183 46 140 20 109
-184 143 176 23 152
-185 66 57 203 6
-186 77 135 59 8
-187 2 58 70 207
-188 69 212 234 201
-189 80 136 5 61
-190 132 215 237 74
-191 214 72 204 238
-192 78 134 216 240
-193 112 16 54 65
-194 56 67 148 227
-195 66 15 50 109
-196 110 134 14 162
-197 231 145 69 53
-198 165 136 225 151
-199 12 166 106 130
-200 133 168 147 228
-201 188 124 85 153
-202 155 82 28 139
-203 88 156 126 185
-204 101 191 127 117
-205 159 30 86 141
-206 114 137 31 98
-207 187 104 115 128
-208 102 113 138 32
-209 232 137 148 29
-210 14 26 105 139
-211 231 150 140 32
-212 122 188 151 230
-213 143 106 30 10
-214 125 191 16 107
-215 190 126 228 152
-216 13 192 128 109
-217 55 69 8 96
-218 132 166 6 94
-219 56 5 72 95
-220 66 178 237 52
-221 2 134 92 164
-222 135 168 234 181
-223 177 70 240 54
-224 167 179 136 238
-225 198 114 6 62
-226 37 8 64 87
-227 58 4 194 118
-228 200 215 117 239
-229 88 61 7 40
-230 34 212 236 84
-231 211 240 120 197
-232 209 38 238 86
-233 23 48 16 29
-234 188 46 222 14
-235 13 24 47 32
-236 26 20 174 230
-237 44 220 190 10
-238 176 232 191 224
-239 22 170 30 228
-240 231 223 192 173
0