Graph forms
for C4 [ 240, 2 ] = C_240(1,31)
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On this page are computer-accessible forms for the graph C4[ 240, 2 ] =
C_240(1,31).
(I) Following is a form readable by MAGMA:
g:=Graph<240|{ {2, 3}, {238, 239}, {236, 237}, {234, 235}, {232, 233}, {230,
231}, {228, 229}, {226, 227}, {224, 225}, {222, 223}, {220, 221}, {218, 219},
{216, 217}, {214, 215}, {212, 213}, {210, 211}, {208, 209}, {206, 207}, {204,
205}, {202, 203}, {200, 201}, {198, 199}, {196, 197}, {194, 195}, {192, 193},
{190, 191}, {188, 189}, {186, 187}, {184, 185}, {182, 183}, {180, 181}, {178,
179}, {176, 177}, {174, 175}, {172, 173}, {170, 171}, {168, 169}, {166, 167},
{164, 165}, {162, 163}, {160, 161}, {158, 159}, {156, 157}, {154, 155}, {84,
85}, {82, 83}, {80, 81}, {78, 79}, {76, 77}, {74, 75}, {72, 73}, {70, 71}, {68,
69}, {66, 67}, {64, 65}, {62, 63}, {60, 61}, {58, 59}, {56, 57}, {54, 55}, {52,
53}, {50, 51}, {48, 49}, {46, 47}, {4, 5}, {6, 7}, {8, 9}, {10, 11}, {12, 13},
{14, 15}, {16, 17}, {18, 19}, {20, 21}, {22, 23}, {24, 25}, {26, 27}, {28, 29},
{30, 31}, {32, 33}, {34, 35}, {36, 37}, {38, 39}, {40, 41}, {42, 43}, {44, 45},
{86, 87}, {88, 89}, {90, 91}, {92, 93}, {94, 95}, {96, 97}, {98, 99}, {100,
101}, {102, 103}, {104, 105}, {106, 107}, {108, 109}, {110, 111}, {112, 113},
{114, 115}, {116, 117}, {118, 119}, {120, 121}, {122, 123}, {124, 125}, {126,
127}, {128, 129}, {130, 131}, {132, 133}, {134, 135}, {136, 137}, {138, 139},
{140, 141}, {142, 143}, {144, 145}, {146, 147}, {148, 149}, {150, 151}, {152,
153}, {1, 2}, {237, 238}, {233, 234}, {229, 230}, {225, 226}, {221, 222}, {217,
218}, {213, 214}, {209, 210}, {205, 206}, {201, 202}, {197, 198}, {193, 194},
{189, 190}, {185, 186}, {181, 182}, {177, 178}, {173, 174}, {169, 170}, {165,
166}, {161, 162}, {157, 158}, {153, 154}, {81, 82}, {77, 78}, {73, 74}, {69,
70}, {65, 66}, {61, 62}, {57, 58}, {53, 54}, {49, 50}, {5, 6}, {9, 10}, {13,
14}, {17, 18}, {21, 22}, {25, 26}, {29, 30}, {33, 34}, {37, 38}, {41, 42}, {45,
46}, {85, 86}, {89, 90}, {93, 94}, {97, 98}, {101, 102}, {105, 106}, {109, 110},
{113, 114}, {117, 118}, {121, 122}, {125, 126}, {129, 130}, {133, 134}, {137,
138}, {141, 142}, {145, 146}, {149, 150}, {3, 4}, {235, 236}, {227, 228}, {219,
220}, {211, 212}, {203, 204}, {195, 196}, {187, 188}, {179, 180}, {171, 172},
{163, 164}, {155, 156}, {83, 84}, {75, 76}, {67, 68}, {59, 60}, {51, 52}, {11,
12}, {19, 20}, {27, 28}, {35, 36}, {43, 44}, {91, 92}, {99, 100}, {107, 108},
{115, 116}, {123, 124}, {131, 132}, {139, 140}, {147, 148}, {7, 8}, {231, 232},
{215, 216}, {199, 200}, {183, 184}, {167, 168}, {71, 72}, {55, 56}, {23, 24},
{39, 40}, {87, 88}, {103, 104}, {119, 120}, {135, 136}, {151, 152}, {15, 16},
{239, 240}, {207, 208}, {192, 223}, {175, 176}, {160, 191}, {79, 80}, {64, 95},
{47, 48}, {32, 63}, {96, 127}, {111, 112}, {128, 159}, {143, 144}, {1, 32},
{209, 240}, {207, 238}, {205, 236}, {203, 234}, {201, 232}, {199, 230}, {197,
228}, {195, 226}, {193, 224}, {159, 190}, {157, 188}, {155, 186}, {153, 184},
{83, 114}, {81, 112}, {79, 110}, {77, 108}, {75, 106}, {73, 104}, {71, 102},
{69, 100}, {67, 98}, {65, 96}, {3, 34}, {5, 36}, {7, 38}, {9, 40}, {11, 42},
{13, 44}, {15, 46}, {17, 48}, {19, 50}, {21, 52}, {23, 54}, {25, 56}, {27, 58},
{29, 60}, {31, 62}, {85, 116}, {87, 118}, {89, 120}, {91, 122}, {93, 124}, {95,
126}, {129, 160}, {131, 162}, {133, 164}, {135, 166}, {137, 168}, {139, 170},
{141, 172}, {143, 174}, {145, 176}, {147, 178}, {149, 180}, {151, 182}, {2, 33},
{206, 237}, {202, 233}, {198, 229}, {194, 225}, {158, 189}, {154, 185}, {82,
113}, {78, 109}, {74, 105}, {70, 101}, {66, 97}, {6, 37}, {10, 41}, {14, 45},
{18, 49}, {22, 53}, {26, 57}, {30, 61}, {86, 117}, {90, 121}, {94, 125}, {130,
161}, {134, 165}, {138, 169}, {142, 173}, {146, 177}, {150, 181}, {4, 35}, {204,
235}, {196, 227}, {156, 187}, {76, 107}, {68, 99}, {12, 43}, {20, 51}, {28, 59},
{84, 115}, {92, 123}, {132, 163}, {140, 171}, {148, 179}, {8, 39}, {200, 231},
{152, 183}, {72, 103}, {24, 55}, {88, 119}, {136, 167}, {16, 47}, {223, 224},
{208, 239}, {159, 160}, {80, 111}, {31, 32}, {95, 96}, {144, 175}, {33, 64},
{191, 222}, {189, 220}, {187, 218}, {185, 216}, {183, 214}, {181, 212}, {179,
210}, {177, 208}, {175, 206}, {173, 204}, {171, 202}, {169, 200}, {167, 198},
{165, 196}, {163, 194}, {161, 192}, {63, 94}, {61, 92}, {59, 90}, {57, 88}, {55,
86}, {53, 84}, {51, 82}, {49, 80}, {47, 78}, {45, 76}, {35, 66}, {37, 68}, {39,
70}, {41, 72}, {43, 74}, {34, 65}, {190, 221}, {186, 217}, {182, 213}, {178,
209}, {174, 205}, {170, 201}, {166, 197}, {162, 193}, {62, 93}, {58, 89}, {54,
85}, {50, 81}, {46, 77}, {38, 69}, {42, 73}, {36, 67}, {188, 219}, {180, 211},
{172, 203}, {164, 195}, {60, 91}, {52, 83}, {44, 75}, {40, 71}, {184, 215},
{168, 199}, {56, 87}, {48, 79}, {191, 192}, {176, 207}, {63, 64}, {2, 211}, {4,
213}, {6, 215}, {8, 217}, {10, 219}, {12, 221}, {14, 223}, {1, 210}, {5, 214},
{9, 218}, {13, 222}, {3, 212}, {11, 220}, {7, 216}, {97, 128}, {99, 130}, {101,
132}, {103, 134}, {105, 136}, {107, 138}, {109, 140}, {111, 142}, {113, 144},
{115, 146}, {117, 148}, {119, 150}, {121, 152}, {123, 154}, {125, 156}, {127,
158}, {98, 129}, {102, 133}, {106, 137}, {110, 141}, {114, 145}, {118, 149},
{122, 153}, {126, 157}, {100, 131}, {108, 139}, {116, 147}, {124, 155}, {15,
224}, {31, 240}, {104, 135}, {120, 151}, {1, 240}, {16, 225}, {18, 227}, {20,
229}, {22, 231}, {24, 233}, {26, 235}, {28, 237}, {30, 239}, {17, 226}, {21,
230}, {25, 234}, {29, 238}, {19, 228}, {27, 236}, {23, 232}, {112, 143}, {127,
128} }>;
(II) A more general form is to represent the graph as the orbit of {2, 3}
under the group generated by the following permutations:
a: (2, 210)(3, 179)(4, 148)(5, 117)(6, 86)(7, 55)(8, 24)(9, 233)(10, 202)(11,
171)(12, 140)(13, 109)(14, 78)(15, 47)(17, 225)(18, 194)(19, 163)(20, 132)(21,
101)(22, 70)(23, 39)(25, 217)(26, 186)(27, 155)(28, 124)(29, 93)(30, 62)(32,
240)(33, 209)(34, 178)(35, 147)(36, 116)(37, 85)(38, 54)(40, 232)(41, 201)(42,
170)(43, 139)(44, 108)(45, 77)(48, 224)(49, 193)(50, 162)(51, 131)(52, 100)(53,
69)(56, 216)(57, 185)(58, 154)(59, 123)(60, 92)(63, 239)(64, 208)(65, 177)(66,
146)(67, 115)(68, 84)(71, 231)(72, 200)(73, 169)(74, 138)(75, 107)(79, 223)(80,
192)(81, 161)(82, 130)(83, 99)(87, 215)(88, 184)(89, 153)(90, 122)(94, 238)(95,
207)(96, 176)(97, 145)(98, 114)(102, 230)(103, 199)(104, 168)(105, 137)(110,
222)(111, 191)(112, 160)(113, 129)(118, 214)(119, 183)(120, 152)(125, 237)(126,
206)(127, 175)(128, 144)(133, 229)(134, 198)(135, 167)(141, 221)(142, 190)(143,
159)(149, 213)(150, 182)(156, 236)(157, 205)(158, 174)(164, 228)(165, 197)(172,
220)(173, 189)(180, 212)(187, 235)(188, 204)(195, 227)(203, 219)(218, 234) (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, 32)(3, 63)(4, 94)(5, 125)(6, 156)(7, 187)(8, 218)(10, 40)(11, 71)(12,
102)(13, 133)(14, 164)(15, 195)(16, 226)(18, 48)(19, 79)(20, 110)(21, 141)(22,
172)(23, 203)(24, 234)(26, 56)(27, 87)(28, 118)(29, 149)(30, 180)(31, 211)(34,
64)(35, 95)(36, 126)(37, 157)(38, 188)(39, 219)(42, 72)(43, 103)(44, 134)(45,
165)(46, 196)(47, 227)(50, 80)(51, 111)(52, 142)(53, 173)(54, 204)(55, 235)(58,
88)(59, 119)(60, 150)(61, 181)(62, 212)(66, 96)(67, 127)(68, 158)(69, 189)(70,
220)(74, 104)(75, 135)(76, 166)(77, 197)(78, 228)(82, 112)(83, 143)(84, 174)(85,
205)(86, 236)(90, 120)(91, 151)(92, 182)(93, 213)(98, 128)(99, 159)(100,
190)(101, 221)(106, 136)(107, 167)(108, 198)(109, 229)(114, 144)(115, 175)(116,
206)(117, 237)(122, 152)(123, 183)(124, 214)(130, 160)(131, 191)(132, 222)(138,
168)(139, 199)(140, 230)(146, 176)(147, 207)(148, 238)(154, 184)(155, 215)(162,
192)(163, 223)(170, 200)(171, 231)(178, 208)(179, 239)(186, 216)(194, 224)(202,
232)(210, 240)
c: (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21,
22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41,
42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61,
62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81,
82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100,
101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116,
117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132,
133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148,
149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164,
165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180,
181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196,
197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212,
213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228,
229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240)
C4[ 240, 2 ]
240
-1 210 2 240 32
-2 33 1 211 3
-3 34 2 212 4
-4 35 3 213 5
-5 36 4 214 6
-6 37 5 215 7
-7 38 6 216 8
-8 39 7 217 9
-9 40 8 218 10
-10 11 41 9 219
-11 220 12 42 10
-12 11 221 13 43
-13 44 12 222 14
-14 45 13 223 15
-15 46 14 224 16
-16 47 15 225 17
-17 48 16 226 18
-18 49 17 227 19
-19 50 18 228 20
-20 51 19 229 21
-21 22 52 20 230
-22 231 23 53 21
-23 22 232 24 54
-24 55 23 233 25
-25 56 24 234 26
-26 57 25 235 27
-27 58 26 236 28
-28 59 27 237 29
-29 60 28 238 30
-30 61 29 239 31
-31 62 30 240 32
-32 33 1 63 31
-33 34 2 64 32
-34 33 35 3 65
-35 66 34 36 4
-36 67 35 37 5
-37 68 36 38 6
-38 69 37 39 7
-39 70 38 40 8
-40 71 39 41 9
-41 72 40 42 10
-42 11 73 41 43
-43 44 12 74 42
-44 45 13 75 43
-45 44 46 14 76
-46 77 45 47 15
-47 78 46 48 16
-48 79 47 49 17
-49 80 48 50 18
-50 81 49 51 19
-51 82 50 52 20
-52 83 51 53 21
-53 22 84 52 54
-54 55 23 85 53
-55 56 24 86 54
-56 55 57 25 87
-57 88 56 58 26
-58 89 57 59 27
-59 90 58 60 28
-60 91 59 61 29
-61 92 60 62 30
-62 93 61 63 31
-63 94 62 64 32
-64 33 95 63 65
-65 66 34 96 64
-66 67 35 97 65
-67 66 68 36 98
-68 99 67 69 37
-69 100 68 70 38
-70 101 69 71 39
-71 102 70 72 40
-72 103 71 73 41
-73 104 72 74 42
-74 105 73 75 43
-75 44 106 74 76
-76 77 45 107 75
-77 78 46 108 76
-78 77 79 47 109
-79 110 78 80 48
-80 111 79 81 49
-81 112 80 82 50
-82 113 81 83 51
-83 114 82 84 52
-84 115 83 85 53
-85 116 84 86 54
-86 55 117 85 87
-87 88 56 118 86
-88 89 57 119 87
-89 88 90 58 120
-90 121 89 91 59
-91 122 90 92 60
-92 123 91 93 61
-93 124 92 94 62
-94 125 93 95 63
-95 126 94 96 64
-96 127 95 97 65
-97 66 128 96 98
-98 99 67 129 97
-99 100 68 130 98
-100 99 101 69 131
-101 132 100 102 70
-102 133 101 103 71
-103 134 102 104 72
-104 135 103 105 73
-105 136 104 106 74
-106 137 105 107 75
-107 138 106 108 76
-108 77 139 107 109
-109 110 78 140 108
-110 111 79 141 109
-111 110 112 80 142
-112 143 111 113 81
-113 144 112 114 82
-114 145 113 115 83
-115 146 114 116 84
-116 147 115 117 85
-117 148 116 118 86
-118 149 117 119 87
-119 88 150 118 120
-120 121 89 151 119
-121 122 90 152 120
-122 121 123 91 153
-123 154 122 124 92
-124 155 123 125 93
-125 156 124 126 94
-126 157 125 127 95
-127 158 126 128 96
-128 159 127 129 97
-129 160 128 130 98
-130 99 161 129 131
-131 132 100 162 130
-132 133 101 163 131
-133 132 134 102 164
-134 165 133 135 103
-135 166 134 136 104
-136 167 135 137 105
-137 168 136 138 106
-138 169 137 139 107
-139 170 138 140 108
-140 171 139 141 109
-141 110 172 140 142
-142 143 111 173 141
-143 144 112 174 142
-144 143 145 113 175
-145 176 144 146 114
-146 177 145 147 115
-147 178 146 148 116
-148 179 147 149 117
-149 180 148 150 118
-150 181 149 151 119
-151 182 150 152 120
-152 121 183 151 153
-153 154 122 184 152
-154 155 123 185 153
-155 154 156 124 186
-156 187 155 157 125
-157 188 156 158 126
-158 189 157 159 127
-159 190 158 160 128
-160 191 159 161 129
-161 192 160 162 130
-162 193 161 163 131
-163 132 194 162 164
-164 165 133 195 163
-165 166 134 196 164
-166 165 167 135 197
-167 198 166 168 136
-168 199 167 169 137
-169 200 168 170 138
-170 201 169 171 139
-171 202 170 172 140
-172 203 171 173 141
-173 204 172 174 142
-174 143 205 173 175
-175 176 144 206 174
-176 177 145 207 175
-177 176 178 146 208
-178 209 177 179 147
-179 210 178 180 148
-180 211 179 181 149
-181 212 180 182 150
-182 213 181 183 151
-183 214 182 184 152
-184 215 183 185 153
-185 154 216 184 186
-186 187 155 217 185
-187 188 156 218 186
-188 187 189 157 219
-189 220 188 190 158
-190 221 189 191 159
-191 222 190 192 160
-192 223 191 193 161
-193 224 192 194 162
-194 225 193 195 163
-195 226 194 196 164
-196 165 227 195 197
-197 198 166 228 196
-198 199 167 229 197
-199 198 200 168 230
-200 231 199 201 169
-201 232 200 202 170
-202 233 201 203 171
-203 234 202 204 172
-204 235 203 205 173
-205 236 204 206 174
-206 237 205 207 175
-207 176 238 206 208
-208 209 177 239 207
-209 210 178 240 208
-210 209 1 211 179
-211 210 2 212 180
-212 211 3 213 181
-213 212 4 214 182
-214 213 5 215 183
-215 214 6 216 184
-216 215 7 217 185
-217 216 8 218 186
-218 187 217 9 219
-219 220 188 218 10
-220 11 221 189 219
-221 220 12 222 190
-222 221 13 223 191
-223 222 14 224 192
-224 223 15 225 193
-225 224 16 226 194
-226 225 17 227 195
-227 226 18 228 196
-228 227 19 229 197
-229 198 228 20 230
-230 231 199 229 21
-231 22 232 200 230
-232 231 23 233 201
-233 232 24 234 202
-234 233 25 235 203
-235 234 26 236 204
-236 235 27 237 205
-237 236 28 238 206
-238 237 29 239 207
-239 238 30 240 208
-240 209 1 239 31
0