Graph forms
for C4 [ 213, 1 ] = C_213(1,70)
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On this page are computer-accessible forms for the graph C4[ 213, 1 ] =
C_213(1,70).
(I) Following is a form readable by MAGMA:
g:=Graph<213|{ {2, 3}, {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}, {152,
153}, {150, 151}, {148, 149}, {146, 147}, {144, 145}, {142, 143}, {140, 141},
{138, 139}, {68, 69}, {66, 67}, {64, 65}, {62, 63}, {60, 61}, {58, 59}, {56,
57}, {54, 55}, {52, 53}, {50, 51}, {48, 49}, {46, 47}, {44, 45}, {42, 43}, {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}, {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}, {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}, {153, 154}, {149, 150}, {145, 146}, {141, 142}, {69,
70}, {65, 66}, {61, 62}, {57, 58}, {53, 54}, {49, 50}, {45, 46}, {41, 42}, {5,
6}, {9, 10}, {13, 14}, {17, 18}, {21, 22}, {25, 26}, {29, 30}, {33, 34}, {37,
38}, {73, 74}, {77, 78}, {81, 82}, {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}, {3, 4}, {211, 212}, {203, 204}, {195, 196},
{187, 188}, {179, 180}, {171, 172}, {163, 164}, {155, 156}, {147, 148}, {139,
140}, {67, 68}, {59, 60}, {51, 52}, {43, 44}, {11, 12}, {19, 20}, {27, 28}, {35,
36}, {75, 76}, {83, 84}, {91, 92}, {99, 100}, {107, 108}, {115, 116}, {123,
124}, {131, 132}, {7, 8}, {199, 200}, {183, 184}, {167, 168}, {151, 152}, {55,
56}, {23, 24}, {39, 40}, {71, 72}, {87, 88}, {103, 104}, {119, 120}, {135, 136},
{15, 16}, {207, 208}, {175, 176}, {143, 144}, {47, 48}, {79, 80}, {111, 112},
{31, 32}, {159, 160}, {95, 96}, {1, 71}, {57, 127}, {56, 126}, {49, 119}, {48,
118}, {41, 111}, {8, 78}, {9, 79}, {16, 86}, {17, 87}, {24, 94}, {25, 95}, {32,
102}, {33, 103}, {40, 110}, {128, 198}, {129, 199}, {136, 206}, {137, 207}, {2,
72}, {55, 125}, {54, 124}, {51, 121}, {50, 120}, {3, 73}, {6, 76}, {7, 77}, {18,
88}, {19, 89}, {22, 92}, {23, 93}, {34, 104}, {35, 105}, {38, 108}, {39, 109},
{130, 200}, {131, 201}, {134, 204}, {135, 205}, {4, 74}, {53, 123}, {52, 122},
{5, 75}, {20, 90}, {21, 91}, {36, 106}, {37, 107}, {132, 202}, {133, 203}, {10,
80}, {143, 213}, {142, 212}, {139, 209}, {138, 208}, {47, 117}, {46, 116}, {43,
113}, {42, 112}, {11, 81}, {14, 84}, {15, 85}, {12, 82}, {141, 211}, {140, 210},
{45, 115}, {44, 114}, {13, 83}, {26, 96}, {27, 97}, {30, 100}, {31, 101}, {28,
98}, {29, 99}, {63, 64}, {191, 192}, {16, 159}, {64, 207}, {48, 191}, {32, 175},
{1, 144}, {69, 212}, {67, 210}, {65, 208}, {47, 190}, {45, 188}, {43, 186}, {41,
184}, {3, 146}, {5, 148}, {7, 150}, {9, 152}, {11, 154}, {13, 156}, {15, 158},
{33, 176}, {35, 178}, {37, 180}, {39, 182}, {2, 145}, {66, 209}, {46, 189}, {42,
185}, {6, 149}, {10, 153}, {14, 157}, {34, 177}, {38, 181}, {70, 213}, {4, 147},
{68, 211}, {44, 187}, {12, 155}, {36, 179}, {8, 151}, {40, 183}, {17, 160}, {19,
162}, {21, 164}, {23, 166}, {25, 168}, {27, 170}, {29, 172}, {31, 174}, {18,
161}, {22, 165}, {26, 169}, {30, 173}, {20, 163}, {28, 171}, {58, 128}, {63,
133}, {62, 132}, {59, 129}, {122, 192}, {123, 193}, {126, 196}, {127, 197}, {60,
130}, {61, 131}, {124, 194}, {125, 195}, {24, 167}, {64, 134}, {65, 135}, {72,
142}, {73, 143}, {80, 150}, {81, 151}, {88, 158}, {89, 159}, {96, 166}, {97,
167}, {104, 174}, {105, 175}, {112, 182}, {113, 183}, {120, 190}, {121, 191},
{66, 136}, {67, 137}, {70, 140}, {71, 141}, {82, 152}, {83, 153}, {86, 156},
{87, 157}, {98, 168}, {99, 169}, {102, 172}, {103, 173}, {114, 184}, {115, 185},
{118, 188}, {119, 189}, {68, 138}, {69, 139}, {84, 154}, {85, 155}, {100, 170},
{101, 171}, {116, 186}, {117, 187}, {1, 213}, {74, 144}, {75, 145}, {78, 148},
{79, 149}, {106, 176}, {107, 177}, {110, 180}, {111, 181}, {76, 146}, {77, 147},
{108, 178}, {109, 179}, {49, 192}, {63, 206}, {61, 204}, {59, 202}, {57, 200},
{55, 198}, {53, 196}, {51, 194}, {50, 193}, {62, 205}, {58, 201}, {54, 197},
{52, 195}, {60, 203}, {90, 160}, {91, 161}, {94, 164}, {95, 165}, {92, 162},
{93, 163}, {56, 199}, {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) (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, 144)(3, 74)(5, 147)(6, 77)(8, 150)(9, 80)(11, 153)(12, 83)(14, 156)(15,
86)(17, 159)(18, 89)(20, 162)(21, 92)(23, 165)(24, 95)(26, 168)(27, 98)(29,
171)(30, 101)(32, 174)(33, 104)(35, 177)(36, 107)(38, 180)(39, 110)(41, 183)(42,
113)(44, 186)(45, 116)(47, 189)(48, 119)(50, 192)(51, 122)(53, 195)(54, 125)(56,
198)(57, 128)(59, 201)(60, 131)(62, 204)(63, 134)(65, 207)(66, 137)(68, 210)(69,
140)(71, 213)(72, 143)(75, 146)(78, 149)(81, 152)(84, 155)(87, 158)(90, 161)(93,
164)(96, 167)(99, 170)(102, 173)(105, 176)(108, 179)(111, 182)(114, 185)(117,
188)(120, 191)(123, 194)(126, 197)(129, 200)(132, 203)(135, 206)(138, 209)(141,
212)
c: (2, 71)(3, 141)(4, 211)(5, 68)(6, 138)(7, 208)(8, 65)(9, 135)(10, 205)(11,
62)(12, 132)(13, 202)(14, 59)(15, 129)(16, 199)(17, 56)(18, 126)(19, 196)(20,
53)(21, 123)(22, 193)(23, 50)(24, 120)(25, 190)(26, 47)(27, 117)(28, 187)(29,
44)(30, 114)(31, 184)(32, 41)(33, 111)(34, 181)(35, 38)(36, 108)(37, 178)(39,
105)(40, 175)(42, 102)(43, 172)(45, 99)(46, 169)(48, 96)(49, 166)(51, 93)(52,
163)(54, 90)(55, 160)(57, 87)(58, 157)(60, 84)(61, 154)(63, 81)(64, 151)(66,
78)(67, 148)(69, 75)(70, 145)(73, 142)(74, 212)(76, 139)(77, 209)(79, 136)(80,
206)(82, 133)(83, 203)(85, 130)(86, 200)(88, 127)(89, 197)(91, 124)(92, 194)(94,
121)(95, 191)(97, 118)(98, 188)(100, 115)(101, 185)(103, 112)(104, 182)(106,
109)(107, 179)(110, 176)(113, 173)(116, 170)(119, 167)(122, 164)(125, 161)(128,
158)(131, 155)(134, 152)(137, 149)(140, 146)(144, 213)(147, 210)(150, 207)(153,
204)(156, 201)(159, 198)(162, 195)(165, 192)(168, 189)(171, 186)(174, 183)(177,
180)
C4[ 213, 1 ]
213
-1 144 2 213 71
-2 1 145 3 72
-3 2 146 4 73
-4 3 147 5 74
-5 4 148 6 75
-6 5 149 7 76
-7 77 6 150 8
-8 78 7 151 9
-9 79 8 152 10
-10 11 80 9 153
-11 154 12 81 10
-12 11 155 13 82
-13 12 156 14 83
-14 13 157 15 84
-15 14 158 16 85
-16 15 159 17 86
-17 16 160 18 87
-18 88 17 161 19
-19 89 18 162 20
-20 90 19 163 21
-21 22 91 20 164
-22 165 23 92 21
-23 22 166 24 93
-24 23 167 25 94
-25 24 168 26 95
-26 25 169 27 96
-27 26 170 28 97
-28 27 171 29 98
-29 99 28 172 30
-30 100 29 173 31
-31 101 30 174 32
-32 33 102 31 175
-33 176 34 103 32
-34 33 177 35 104
-35 34 178 36 105
-36 35 179 37 106
-37 36 180 38 107
-38 37 181 39 108
-39 38 182 40 109
-40 110 39 183 41
-41 111 40 184 42
-42 112 41 185 43
-43 44 113 42 186
-44 187 45 114 43
-45 44 188 46 115
-46 45 189 47 116
-47 46 190 48 117
-48 47 191 49 118
-49 48 192 50 119
-50 49 193 51 120
-51 121 50 194 52
-52 122 51 195 53
-53 123 52 196 54
-54 55 124 53 197
-55 198 56 125 54
-56 55 199 57 126
-57 56 200 58 127
-58 57 201 59 128
-59 58 202 60 129
-60 59 203 61 130
-61 60 204 62 131
-62 132 61 205 63
-63 133 62 206 64
-64 134 63 207 65
-65 66 135 64 208
-66 209 67 136 65
-67 66 210 68 137
-68 67 211 69 138
-69 68 212 70 139
-70 69 213 71 140
-71 1 70 72 141
-72 2 71 73 142
-73 143 3 72 74
-74 144 4 73 75
-75 145 5 74 76
-76 77 146 6 75
-77 78 147 7 76
-78 77 79 148 8
-79 78 80 149 9
-80 79 81 150 10
-81 11 80 82 151
-82 12 81 83 152
-83 13 82 84 153
-84 154 14 83 85
-85 155 15 84 86
-86 156 16 85 87
-87 88 157 17 86
-88 89 158 18 87
-89 88 90 159 19
-90 89 91 160 20
-91 90 92 161 21
-92 22 91 93 162
-93 23 92 94 163
-94 24 93 95 164
-95 165 25 94 96
-96 166 26 95 97
-97 167 27 96 98
-98 99 168 28 97
-99 100 169 29 98
-100 99 101 170 30
-101 100 102 171 31
-102 101 103 172 32
-103 33 102 104 173
-104 34 103 105 174
-105 35 104 106 175
-106 176 36 105 107
-107 177 37 106 108
-108 178 38 107 109
-109 110 179 39 108
-110 111 180 40 109
-111 110 112 181 41
-112 111 113 182 42
-113 112 114 183 43
-114 44 113 115 184
-115 45 114 116 185
-116 46 115 117 186
-117 187 47 116 118
-118 188 48 117 119
-119 189 49 118 120
-120 121 190 50 119
-121 122 191 51 120
-122 121 123 192 52
-123 122 124 193 53
-124 123 125 194 54
-125 55 124 126 195
-126 56 125 127 196
-127 57 126 128 197
-128 198 58 127 129
-129 199 59 128 130
-130 200 60 129 131
-131 132 201 61 130
-132 133 202 62 131
-133 132 134 203 63
-134 133 135 204 64
-135 134 136 205 65
-136 66 135 137 206
-137 67 136 138 207
-138 68 137 139 208
-139 209 69 138 140
-140 210 70 139 141
-141 211 71 140 142
-142 143 212 72 141
-143 144 213 73 142
-144 143 1 145 74
-145 144 2 146 75
-146 145 3 147 76
-147 77 146 4 148
-148 78 147 5 149
-149 79 148 6 150
-150 80 149 7 151
-151 81 150 8 152
-152 82 151 9 153
-153 154 83 152 10
-154 11 155 84 153
-155 154 12 156 85
-156 155 13 157 86
-157 156 14 158 87
-158 88 157 15 159
-159 89 158 16 160
-160 90 159 17 161
-161 91 160 18 162
-162 92 161 19 163
-163 93 162 20 164
-164 165 94 163 21
-165 22 166 95 164
-166 165 23 167 96
-167 166 24 168 97
-168 167 25 169 98
-169 99 168 26 170
-170 100 169 27 171
-171 101 170 28 172
-172 102 171 29 173
-173 103 172 30 174
-174 104 173 31 175
-175 176 105 174 32
-176 33 177 106 175
-177 176 34 178 107
-178 177 35 179 108
-179 178 36 180 109
-180 110 179 37 181
-181 111 180 38 182
-182 112 181 39 183
-183 113 182 40 184
-184 114 183 41 185
-185 115 184 42 186
-186 187 116 185 43
-187 44 188 117 186
-188 187 45 189 118
-189 188 46 190 119
-190 189 47 191 120
-191 121 190 48 192
-192 122 191 49 193
-193 123 192 50 194
-194 124 193 51 195
-195 125 194 52 196
-196 126 195 53 197
-197 198 127 196 54
-198 55 199 128 197
-199 198 56 200 129
-200 199 57 201 130
-201 200 58 202 131
-202 132 201 59 203
-203 133 202 60 204
-204 134 203 61 205
-205 135 204 62 206
-206 136 205 63 207
-207 137 206 64 208
-208 209 138 207 65
-209 66 210 139 208
-210 209 67 211 140
-211 210 68 212 141
-212 211 69 213 142
-213 143 1 212 70
0