Graph forms
for C4 [ 221, 1 ] = C_221(1,21)
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On this page are computer-accessible forms for the graph C4[ 221, 1 ] =
C_221(1,21).
(I) Following is a form readable by MAGMA:
g:=Graph<221|{ {2, 3}, {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}, {90,
91}, {88, 89}, {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}, {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}, {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}, {1, 2}, {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}, {89,
90}, {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}, {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}, {157, 158}, {161, 162}, {3, 4}, {219, 220}, {211, 212}, {203, 204}, {195,
196}, {187, 188}, {179, 180}, {171, 172}, {163, 164}, {91, 92}, {83, 84}, {75,
76}, {67, 68}, {59, 60}, {11, 12}, {19, 20}, {27, 28}, {35, 36}, {43, 44}, {51,
52}, {99, 100}, {107, 108}, {115, 116}, {123, 124}, {131, 132}, {139, 140},
{147, 148}, {155, 156}, {7, 8}, {215, 216}, {199, 200}, {183, 184}, {167, 168},
{87, 88}, {71, 72}, {55, 56}, {23, 24}, {39, 40}, {103, 104}, {119, 120}, {135,
136}, {151, 152}, {2, 23}, {200, 221}, {194, 215}, {192, 213}, {170, 191}, {168,
189}, {162, 183}, {74, 95}, {72, 93}, {66, 87}, {64, 85}, {8, 29}, {10, 31},
{32, 53}, {34, 55}, {40, 61}, {42, 63}, {96, 117}, {98, 119}, {104, 125}, {106,
127}, {128, 149}, {130, 151}, {136, 157}, {138, 159}, {160, 181}, {1, 22}, {193,
214}, {169, 190}, {73, 94}, {65, 86}, {9, 30}, {33, 54}, {41, 62}, {97, 118},
{105, 126}, {129, 150}, {137, 158}, {161, 182}, {3, 24}, {199, 220}, {195, 216},
{167, 188}, {163, 184}, {71, 92}, {67, 88}, {7, 28}, {35, 56}, {39, 60}, {99,
120}, {103, 124}, {131, 152}, {135, 156}, {4, 25}, {198, 219}, {196, 217}, {166,
187}, {164, 185}, {70, 91}, {68, 89}, {6, 27}, {36, 57}, {38, 59}, {100, 121},
{102, 123}, {132, 153}, {134, 155}, {5, 26}, {207, 208}, {197, 218}, {175, 176},
{165, 186}, {79, 80}, {69, 90}, {15, 16}, {37, 58}, {47, 48}, {101, 122}, {111,
112}, {133, 154}, {143, 144}, {11, 32}, {79, 100}, {75, 96}, {15, 36}, {27, 48},
{31, 52}, {91, 112}, {95, 116}, {139, 160}, {143, 164}, {155, 176}, {159, 180},
{12, 33}, {78, 99}, {76, 97}, {14, 35}, {28, 49}, {30, 51}, {92, 113}, {94,
115}, {140, 161}, {142, 163}, {156, 177}, {158, 179}, {13, 34}, {77, 98}, {29,
50}, {93, 114}, {141, 162}, {157, 178}, {16, 37}, {90, 111}, {88, 109}, {82,
103}, {80, 101}, {18, 39}, {24, 45}, {26, 47}, {144, 165}, {146, 167}, {152,
173}, {154, 175}, {17, 38}, {89, 110}, {81, 102}, {25, 46}, {145, 166}, {153,
174}, {19, 40}, {87, 108}, {83, 104}, {23, 44}, {147, 168}, {151, 172}, {20,
41}, {86, 107}, {84, 105}, {22, 43}, {148, 169}, {150, 171}, {21, 42}, {85,
106}, {31, 32}, {95, 96}, {149, 170}, {159, 160}, {43, 64}, {191, 212}, {187,
208}, {175, 196}, {171, 192}, {63, 84}, {59, 80}, {47, 68}, {44, 65}, {190,
211}, {188, 209}, {174, 195}, {172, 193}, {62, 83}, {60, 81}, {46, 67}, {45,
66}, {189, 210}, {173, 194}, {61, 82}, {48, 69}, {186, 207}, {184, 205}, {178,
199}, {176, 197}, {58, 79}, {56, 77}, {50, 71}, {49, 70}, {185, 206}, {177,
198}, {57, 78}, {51, 72}, {183, 204}, {179, 200}, {55, 76}, {52, 73}, {182,
203}, {180, 201}, {54, 75}, {53, 74}, {191, 192}, {181, 202}, {63, 64}, {1,
201}, {2, 202}, {3, 203}, {4, 204}, {5, 205}, {6, 206}, {7, 207}, {16, 216},
{17, 217}, {18, 218}, {19, 219}, {20, 220}, {21, 221}, {8, 208}, {9, 209}, {10,
210}, {11, 211}, {12, 212}, {13, 213}, {14, 214}, {15, 215}, {1, 221}, {107,
128}, {111, 132}, {123, 144}, {127, 148}, {108, 129}, {110, 131}, {124, 145},
{126, 147}, {109, 130}, {125, 146}, {112, 133}, {114, 135}, {120, 141}, {122,
143}, {113, 134}, {121, 142}, {115, 136}, {119, 140}, {116, 137}, {118, 139},
{117, 138}, {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, 211, 212,
213, 214, 215, 216, 217, 218, 219, 220, 221) (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, 201, 221, 22)(3, 180, 220, 43)(4, 159, 219, 64)(5, 138, 218, 85)(6, 117,
217, 106)(7, 96, 216, 127)(8, 75, 215, 148)(9, 54, 214, 169)(10, 33, 213,
190)(11, 12, 212, 211)(13, 191, 210, 32)(14, 170, 209, 53)(15, 149, 208, 74)(16,
128, 207, 95)(17, 107, 206, 116)(18, 86, 205, 137)(19, 65, 204, 158)(20, 44,
203, 179)(21, 23, 202, 200)(24, 181, 199, 42)(25, 160, 198, 63)(26, 139, 197,
84)(27, 118, 196, 105)(28, 97, 195, 126)(29, 76, 194, 147)(30, 55, 193, 168)(31,
34, 192, 189)(35, 171, 188, 52)(36, 150, 187, 73)(37, 129, 186, 94)(38, 108,
185, 115)(39, 87, 184, 136)(40, 66, 183, 157)(41, 45, 182, 178)(46, 161, 177,
62)(47, 140, 176, 83)(48, 119, 175, 104)(49, 98, 174, 125)(50, 77, 173, 146)(51,
56, 172, 167)(57, 151, 166, 72)(58, 130, 165, 93)(59, 109, 164, 114)(60, 88,
163, 135)(61, 67, 162, 156)(68, 141, 155, 82)(69, 120, 154, 103)(70, 99, 153,
124)(71, 78, 152, 145)(79, 131, 144, 92)(80, 110, 143, 113)(81, 89, 142,
134)(90, 121, 133, 102)(91, 100, 132, 123)(101, 111, 122, 112)
C4[ 221, 1 ]
221
-1 22 221 2 201
-2 1 23 3 202
-3 2 24 4 203
-4 3 25 5 204
-5 4 26 6 205
-6 5 27 7 206
-7 6 28 8 207
-8 7 29 9 208
-9 209 8 30 10
-10 11 210 9 31
-11 12 211 10 32
-12 11 33 13 212
-13 12 34 14 213
-14 13 35 15 214
-15 14 36 16 215
-16 15 37 17 216
-17 16 38 18 217
-18 17 39 19 218
-19 18 40 20 219
-20 220 19 41 21
-21 22 221 20 42
-22 1 23 21 43
-23 22 44 2 24
-24 23 45 3 25
-25 24 46 4 26
-26 25 47 5 27
-27 26 48 6 28
-28 27 49 7 29
-29 28 50 8 30
-30 29 51 9 31
-31 30 52 10 32
-32 11 33 31 53
-33 12 34 32 54
-34 33 55 13 35
-35 34 56 14 36
-36 35 57 15 37
-37 36 58 16 38
-38 37 59 17 39
-39 38 60 18 40
-40 39 61 19 41
-41 40 62 20 42
-42 41 63 21 43
-43 22 44 42 64
-44 23 45 43 65
-45 44 66 24 46
-46 45 67 25 47
-47 46 68 26 48
-48 47 69 27 49
-49 48 70 28 50
-50 49 71 29 51
-51 50 72 30 52
-52 51 73 31 53
-53 52 74 32 54
-54 33 55 53 75
-55 34 56 54 76
-56 55 77 35 57
-57 56 78 36 58
-58 57 79 37 59
-59 58 80 38 60
-60 59 81 39 61
-61 60 82 40 62
-62 61 83 41 63
-63 62 84 42 64
-64 63 85 43 65
-65 44 66 64 86
-66 45 67 65 87
-67 66 88 46 68
-68 67 89 47 69
-69 68 90 48 70
-70 69 91 49 71
-71 70 92 50 72
-72 71 93 51 73
-73 72 94 52 74
-74 73 95 53 75
-75 74 96 54 76
-76 55 77 75 97
-77 56 78 76 98
-78 77 99 57 79
-79 78 100 58 80
-80 79 101 59 81
-81 80 102 60 82
-82 81 103 61 83
-83 82 104 62 84
-84 83 105 63 85
-85 84 106 64 86
-86 85 107 65 87
-87 66 88 86 108
-88 67 89 87 109
-89 88 110 68 90
-90 89 111 69 91
-91 90 112 70 92
-92 91 113 71 93
-93 92 114 72 94
-94 93 115 73 95
-95 94 116 74 96
-96 95 117 75 97
-97 96 118 76 98
-98 77 99 97 119
-99 78 100 98 120
-100 99 121 79 101
-101 100 122 80 102
-102 101 123 81 103
-103 102 124 82 104
-104 103 125 83 105
-105 104 126 84 106
-106 105 127 85 107
-107 106 128 86 108
-108 107 129 87 109
-109 88 110 108 130
-110 89 111 109 131
-111 110 132 90 112
-112 111 133 91 113
-113 112 134 92 114
-114 113 135 93 115
-115 114 136 94 116
-116 115 137 95 117
-117 116 138 96 118
-118 117 139 97 119
-119 118 140 98 120
-120 99 121 119 141
-121 100 122 120 142
-122 121 143 101 123
-123 122 144 102 124
-124 123 145 103 125
-125 124 146 104 126
-126 125 147 105 127
-127 126 148 106 128
-128 127 149 107 129
-129 128 150 108 130
-130 129 151 109 131
-131 110 132 130 152
-132 111 133 131 153
-133 132 154 112 134
-134 133 155 113 135
-135 134 156 114 136
-136 135 157 115 137
-137 136 158 116 138
-138 137 159 117 139
-139 138 160 118 140
-140 139 161 119 141
-141 140 162 120 142
-142 121 143 141 163
-143 122 144 142 164
-144 143 165 123 145
-145 144 166 124 146
-146 145 167 125 147
-147 146 168 126 148
-148 147 169 127 149
-149 148 170 128 150
-150 149 171 129 151
-151 150 172 130 152
-152 151 173 131 153
-153 132 154 152 174
-154 133 155 153 175
-155 154 176 134 156
-156 155 177 135 157
-157 156 178 136 158
-158 157 179 137 159
-159 158 180 138 160
-160 159 181 139 161
-161 160 182 140 162
-162 161 183 141 163
-163 162 184 142 164
-164 143 165 163 185
-165 144 166 164 186
-166 165 187 145 167
-167 166 188 146 168
-168 167 189 147 169
-169 168 190 148 170
-170 169 191 149 171
-171 170 192 150 172
-172 171 193 151 173
-173 172 194 152 174
-174 173 195 153 175
-175 154 176 174 196
-176 155 177 175 197
-177 176 198 156 178
-178 177 199 157 179
-179 178 200 158 180
-180 179 201 159 181
-181 180 202 160 182
-182 181 203 161 183
-183 182 204 162 184
-184 183 205 163 185
-185 184 206 164 186
-186 165 187 185 207
-187 166 188 186 208
-188 187 209 167 189
-189 188 210 168 190
-190 189 211 169 191
-191 190 212 170 192
-192 191 213 171 193
-193 192 214 172 194
-194 193 215 173 195
-195 194 216 174 196
-196 195 217 175 197
-197 176 198 196 218
-198 177 199 197 219
-199 198 220 178 200
-200 199 221 179 201
-201 1 200 180 202
-202 2 201 181 203
-203 3 202 182 204
-204 4 203 183 205
-205 5 204 184 206
-206 6 205 185 207
-207 7 206 186 208
-208 187 209 8 207
-209 188 210 9 208
-210 209 189 211 10
-211 11 210 190 212
-212 12 211 191 213
-213 13 212 192 214
-214 14 213 193 215
-215 15 214 194 216
-216 16 215 195 217
-217 17 216 196 218
-218 18 217 197 219
-219 198 220 19 218
-220 199 221 20 219
-221 220 1 200 21
0