Graph forms
for C4 [ 210, 3 ] = C_210(1,41)
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On this page are computer-accessible forms for the graph C4[ 210, 3 ] =
C_210(1,41).
(I) Following is a form readable by MAGMA:
g:=Graph<210|{ {2, 3}, {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}, {86, 87}, {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}, {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}, {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}, {1, 2}, {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}, {85,
86}, {81, 82}, {77, 78}, {73, 74}, {69, 70}, {65, 66}, {61, 62}, {57, 58}, {53,
54}, {5, 6}, {9, 10}, {13, 14}, {17, 18}, {21, 22}, {25, 26}, {29, 30}, {33,
34}, {37, 38}, {41, 42}, {45, 46}, {49, 50}, {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}, {153,
154}, {3, 4}, {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}, {199, 200}, {183,
184}, {167, 168}, {87, 88}, {71, 72}, {55, 56}, {23, 24}, {39, 40}, {103, 104},
{119, 120}, {135, 136}, {151, 152}, {15, 16}, {207, 208}, {175, 176}, {79, 80},
{47, 48}, {111, 112}, {143, 144}, {2, 43}, {86, 127}, {84, 125}, {82, 123}, {80,
121}, {70, 111}, {68, 109}, {66, 107}, {64, 105}, {4, 45}, {6, 47}, {16, 57},
{18, 59}, {20, 61}, {22, 63}, {128, 169}, {130, 171}, {132, 173}, {134, 175},
{144, 185}, {146, 187}, {148, 189}, {150, 191}, {1, 42}, {85, 126}, {81, 122},
{69, 110}, {65, 106}, {5, 46}, {17, 58}, {21, 62}, {129, 170}, {133, 174}, {145,
186}, {149, 190}, {3, 44}, {83, 124}, {67, 108}, {19, 60}, {131, 172}, {147,
188}, {7, 48}, {79, 120}, {71, 112}, {15, 56}, {135, 176}, {143, 184}, {8, 49},
{78, 119}, {76, 117}, {74, 115}, {72, 113}, {10, 51}, {12, 53}, {14, 55}, {136,
177}, {138, 179}, {140, 181}, {142, 183}, {9, 50}, {77, 118}, {73, 114}, {13,
54}, {137, 178}, {141, 182}, {11, 52}, {159, 160}, {75, 116}, {31, 32}, {95,
96}, {139, 180}, {23, 64}, {159, 200}, {63, 104}, {55, 96}, {31, 72}, {151,
192}, {24, 65}, {158, 199}, {156, 197}, {62, 103}, {60, 101}, {58, 99}, {56,
97}, {26, 67}, {28, 69}, {30, 71}, {152, 193}, {154, 195}, {25, 66}, {157, 198},
{61, 102}, {57, 98}, {29, 70}, {153, 194}, {27, 68}, {155, 196}, {59, 100}, {32,
73}, {166, 207}, {164, 205}, {162, 203}, {160, 201}, {54, 95}, {52, 93}, {50,
91}, {34, 75}, {36, 77}, {38, 79}, {48, 89}, {33, 74}, {165, 206}, {161, 202},
{53, 94}, {49, 90}, {37, 78}, {35, 76}, {163, 204}, {51, 92}, {39, 80}, {167,
208}, {47, 88}, {40, 81}, {168, 209}, {42, 83}, {44, 85}, {46, 87}, {41, 82},
{169, 210}, {45, 86}, {43, 84}, {191, 192}, {63, 64}, {2, 171}, {4, 173}, {6,
175}, {16, 185}, {18, 187}, {20, 189}, {22, 191}, {1, 170}, {5, 174}, {17, 186},
{21, 190}, {3, 172}, {19, 188}, {7, 176}, {15, 184}, {8, 177}, {10, 179}, {12,
181}, {14, 183}, {9, 178}, {13, 182}, {11, 180}, {1, 210}, {23, 192}, {87, 128},
{31, 200}, {95, 136}, {119, 160}, {127, 168}, {24, 193}, {26, 195}, {28, 197},
{30, 199}, {88, 129}, {90, 131}, {92, 133}, {94, 135}, {120, 161}, {122, 163},
{124, 165}, {126, 167}, {25, 194}, {29, 198}, {89, 130}, {93, 134}, {121, 162},
{125, 166}, {27, 196}, {91, 132}, {123, 164}, {32, 201}, {34, 203}, {36, 205},
{38, 207}, {96, 137}, {98, 139}, {100, 141}, {102, 143}, {112, 153}, {114, 155},
{116, 157}, {118, 159}, {33, 202}, {37, 206}, {97, 138}, {101, 142}, {113, 154},
{117, 158}, {35, 204}, {99, 140}, {115, 156}, {39, 208}, {103, 144}, {111, 152},
{40, 209}, {104, 145}, {106, 147}, {108, 149}, {110, 151}, {41, 210}, {105,
146}, {109, 150}, {107, 148}, {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: (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) (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, 42)(3, 83)(4, 124)(5, 165)(6, 206)(7, 37)(8, 78)(9, 119)(10, 160)(11,
201)(12, 32)(13, 73)(14, 114)(15, 155)(16, 196)(17, 27)(18, 68)(19, 109)(20,
150)(21, 191)(23, 63)(24, 104)(25, 145)(26, 186)(28, 58)(29, 99)(30, 140)(31,
181)(33, 53)(34, 94)(35, 135)(36, 176)(38, 48)(39, 89)(40, 130)(41, 171)(44,
84)(45, 125)(46, 166)(47, 207)(49, 79)(50, 120)(51, 161)(52, 202)(54, 74)(55,
115)(56, 156)(57, 197)(59, 69)(60, 110)(61, 151)(62, 192)(65, 105)(66, 146)(67,
187)(70, 100)(71, 141)(72, 182)(75, 95)(76, 136)(77, 177)(80, 90)(81, 131)(82,
172)(86, 126)(87, 167)(88, 208)(91, 121)(92, 162)(93, 203)(96, 116)(97, 157)(98,
198)(101, 111)(102, 152)(103, 193)(107, 147)(108, 188)(112, 142)(113, 183)(117,
137)(118, 178)(122, 132)(123, 173)(128, 168)(129, 209)(133, 163)(134, 204)(138,
158)(139, 199)(143, 153)(144, 194)(149, 189)(154, 184)(159, 179)(164, 174)(170,
210)(175, 205)(180, 200)(185, 195)
c: (2, 170)(3, 129)(4, 88)(5, 47)(7, 175)(8, 134)(9, 93)(10, 52)(12, 180)(13,
139)(14, 98)(15, 57)(17, 185)(18, 144)(19, 103)(20, 62)(22, 190)(23, 149)(24,
108)(25, 67)(27, 195)(28, 154)(29, 113)(30, 72)(32, 200)(33, 159)(34, 118)(35,
77)(37, 205)(38, 164)(39, 123)(40, 82)(42, 210)(43, 169)(44, 128)(45, 87)(48,
174)(49, 133)(50, 92)(53, 179)(54, 138)(55, 97)(58, 184)(59, 143)(60, 102)(63,
189)(64, 148)(65, 107)(68, 194)(69, 153)(70, 112)(73, 199)(74, 158)(75, 117)(78,
204)(79, 163)(80, 122)(83, 209)(84, 168)(85, 127)(89, 173)(90, 132)(94, 178)(95,
137)(99, 183)(100, 142)(104, 188)(105, 147)(109, 193)(110, 152)(114, 198)(115,
157)(119, 203)(120, 162)(124, 208)(125, 167)(130, 172)(135, 177)(140, 182)(145,
187)(150, 192)(155, 197)(160, 202)(165, 207)
C4[ 210, 3 ]
210
-1 210 2 170 42
-2 1 3 171 43
-3 44 2 4 172
-4 45 3 5 173
-5 46 4 6 174
-6 47 5 7 175
-7 176 48 6 8
-8 177 49 7 9
-9 178 50 8 10
-10 11 179 51 9
-11 12 180 52 10
-12 11 13 181 53
-13 12 14 182 54
-14 55 13 15 183
-15 56 14 16 184
-16 57 15 17 185
-17 58 16 18 186
-18 187 59 17 19
-19 188 60 18 20
-20 189 61 19 21
-21 22 190 62 20
-22 23 191 63 21
-23 22 24 192 64
-24 23 25 193 65
-25 66 24 26 194
-26 67 25 27 195
-27 68 26 28 196
-28 69 27 29 197
-29 198 70 28 30
-30 199 71 29 31
-31 200 72 30 32
-32 33 201 73 31
-33 34 202 74 32
-34 33 35 203 75
-35 34 36 204 76
-36 77 35 37 205
-37 78 36 38 206
-38 79 37 39 207
-39 80 38 40 208
-40 209 81 39 41
-41 210 82 40 42
-42 1 83 41 43
-43 44 2 84 42
-44 45 3 85 43
-45 44 46 4 86
-46 45 47 5 87
-47 88 46 48 6
-48 89 47 49 7
-49 90 48 50 8
-50 91 49 51 9
-51 92 50 52 10
-52 11 93 51 53
-53 12 94 52 54
-54 55 13 95 53
-55 56 14 96 54
-56 55 57 15 97
-57 56 58 16 98
-58 99 57 59 17
-59 100 58 60 18
-60 101 59 61 19
-61 102 60 62 20
-62 103 61 63 21
-63 22 104 62 64
-64 23 105 63 65
-65 66 24 106 64
-66 67 25 107 65
-67 66 68 26 108
-68 67 69 27 109
-69 110 68 70 28
-70 111 69 71 29
-71 112 70 72 30
-72 113 71 73 31
-73 114 72 74 32
-74 33 115 73 75
-75 34 116 74 76
-76 77 35 117 75
-77 78 36 118 76
-78 77 79 37 119
-79 78 80 38 120
-80 121 79 81 39
-81 122 80 82 40
-82 123 81 83 41
-83 124 82 84 42
-84 125 83 85 43
-85 44 126 84 86
-86 45 127 85 87
-87 88 46 128 86
-88 89 47 129 87
-89 88 90 48 130
-90 89 91 49 131
-91 132 90 92 50
-92 133 91 93 51
-93 134 92 94 52
-94 135 93 95 53
-95 136 94 96 54
-96 55 137 95 97
-97 56 138 96 98
-98 99 57 139 97
-99 100 58 140 98
-100 99 101 59 141
-101 100 102 60 142
-102 143 101 103 61
-103 144 102 104 62
-104 145 103 105 63
-105 146 104 106 64
-106 147 105 107 65
-107 66 148 106 108
-108 67 149 107 109
-109 110 68 150 108
-110 111 69 151 109
-111 110 112 70 152
-112 111 113 71 153
-113 154 112 114 72
-114 155 113 115 73
-115 156 114 116 74
-116 157 115 117 75
-117 158 116 118 76
-118 77 159 117 119
-119 78 160 118 120
-120 121 79 161 119
-121 122 80 162 120
-122 121 123 81 163
-123 122 124 82 164
-124 165 123 125 83
-125 166 124 126 84
-126 167 125 127 85
-127 168 126 128 86
-128 169 127 129 87
-129 88 170 128 130
-130 89 171 129 131
-131 132 90 172 130
-132 133 91 173 131
-133 132 134 92 174
-134 133 135 93 175
-135 176 134 136 94
-136 177 135 137 95
-137 178 136 138 96
-138 179 137 139 97
-139 180 138 140 98
-140 99 181 139 141
-141 100 182 140 142
-142 143 101 183 141
-143 144 102 184 142
-144 143 145 103 185
-145 144 146 104 186
-146 187 145 147 105
-147 188 146 148 106
-148 189 147 149 107
-149 190 148 150 108
-150 191 149 151 109
-151 110 192 150 152
-152 111 193 151 153
-153 154 112 194 152
-154 155 113 195 153
-155 154 156 114 196
-156 155 157 115 197
-157 198 156 158 116
-158 199 157 159 117
-159 200 158 160 118
-160 201 159 161 119
-161 202 160 162 120
-162 121 203 161 163
-163 122 204 162 164
-164 165 123 205 163
-165 166 124 206 164
-166 165 167 125 207
-167 166 168 126 208
-168 209 167 169 127
-169 210 168 170 128
-170 1 169 171 129
-171 2 170 172 130
-172 3 171 173 131
-173 132 4 172 174
-174 133 5 173 175
-175 176 134 6 174
-176 177 135 7 175
-177 176 178 136 8
-178 177 179 137 9
-179 178 180 138 10
-180 11 179 181 139
-181 12 180 182 140
-182 13 181 183 141
-183 14 182 184 142
-184 143 15 183 185
-185 144 16 184 186
-186 187 145 17 185
-187 188 146 18 186
-188 187 189 147 19
-189 188 190 148 20
-190 189 191 149 21
-191 22 190 192 150
-192 23 191 193 151
-193 24 192 194 152
-194 25 193 195 153
-195 154 26 194 196
-196 155 27 195 197
-197 198 156 28 196
-198 199 157 29 197
-199 198 200 158 30
-200 199 201 159 31
-201 200 202 160 32
-202 33 201 203 161
-203 34 202 204 162
-204 35 203 205 163
-205 36 204 206 164
-206 165 37 205 207
-207 166 38 206 208
-208 209 167 39 207
-209 210 168 40 208
-210 209 1 169 41
0