Graph forms
for C4 [ 216, 23 ] = Pr_72(1,61,65,53)
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On this page are computer-accessible forms for the graph C4[ 216, 23 ] =
Pr_72(1,61,65,53).
(I) Following is a form readable by MAGMA:
g:=Graph<216|{ {2, 3}, {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}, {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}, {1, 2}, {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}, {3, 4}, {67, 68},
{59, 60}, {51, 52}, {43, 44}, {11, 12}, {19, 20}, {27, 28}, {35, 36}, {64, 75},
{68, 79}, {65, 76}, {67, 78}, {7, 8}, {66, 77}, {55, 56}, {23, 24}, {39, 40},
{71, 72}, {160, 179}, {196, 215}, {192, 211}, {172, 191}, {168, 187}, {164,
183}, {69, 80}, {195, 214}, {193, 212}, {171, 190}, {169, 188}, {163, 182},
{161, 180}, {71, 82}, {70, 81}, {194, 213}, {170, 189}, {162, 181}, {72, 83},
{165, 184}, {197, 216}, {167, 186}, {15, 16}, {166, 185}, {47, 48}, {157, 176},
{159, 178}, {158, 177}, {148, 167}, {156, 175}, {152, 171}, {145, 164}, {155,
174}, {153, 172}, {147, 166}, {146, 165}, {154, 173}, {149, 168}, {151, 170},
{31, 32}, {150, 169}, {128, 193}, {130, 195}, {132, 197}, {134, 199}, {136,
201}, {138, 203}, {140, 205}, {142, 207}, {144, 209}, {129, 194}, {133, 198},
{137, 202}, {141, 206}, {131, 196}, {139, 204}, {1, 73}, {55, 127}, {54, 126},
{53, 125}, {52, 124}, {51, 123}, {50, 122}, {49, 121}, {48, 120}, {2, 74}, {3,
75}, {4, 76}, {5, 77}, {6, 78}, {7, 79}, {16, 88}, {17, 89}, {18, 90}, {19, 91},
{20, 92}, {21, 93}, {22, 94}, {23, 95}, {32, 104}, {33, 105}, {34, 106}, {35,
107}, {36, 108}, {37, 109}, {38, 110}, {39, 111}, {128, 200}, {129, 201}, {130,
202}, {131, 203}, {132, 204}, {133, 205}, {134, 206}, {135, 207}, {144, 216},
{1, 72}, {155, 208}, {159, 212}, {156, 209}, {158, 211}, {135, 200}, {157, 210},
{4, 87}, {44, 127}, {40, 123}, {8, 91}, {12, 95}, {32, 115}, {36, 119}, {1, 84},
{154, 207}, {152, 205}, {146, 199}, {43, 126}, {41, 124}, {3, 86}, {9, 92}, {11,
94}, {33, 116}, {35, 118}, {2, 85}, {153, 206}, {145, 198}, {42, 125}, {10, 93},
{34, 117}, {8, 80}, {47, 119}, {46, 118}, {45, 117}, {44, 116}, {43, 115}, {42,
114}, {41, 113}, {9, 81}, {10, 82}, {11, 83}, {12, 84}, {13, 85}, {14, 86}, {15,
87}, {40, 112}, {136, 208}, {137, 209}, {138, 210}, {139, 211}, {140, 212},
{141, 213}, {142, 214}, {143, 215}, {147, 200}, {151, 204}, {5, 88}, {150, 203},
{148, 201}, {7, 90}, {37, 120}, {39, 122}, {6, 89}, {149, 202}, {38, 121}, {143,
208}, {13, 96}, {191, 210}, {189, 208}, {175, 194}, {173, 192}, {15, 98}, {29,
112}, {31, 114}, {14, 97}, {190, 209}, {174, 193}, {30, 113}, {16, 99}, {188,
207}, {184, 203}, {180, 199}, {176, 195}, {20, 103}, {24, 107}, {28, 111}, {17,
100}, {187, 206}, {185, 204}, {179, 198}, {177, 196}, {162, 215}, {160, 213},
{63, 74}, {19, 102}, {25, 108}, {27, 110}, {18, 101}, {186, 205}, {178, 197},
{161, 214}, {62, 73}, {26, 109}, {24, 96}, {25, 97}, {26, 98}, {27, 99}, {28,
100}, {29, 101}, {30, 102}, {31, 103}, {163, 216}, {21, 104}, {183, 202}, {181,
200}, {23, 106}, {22, 105}, {182, 201}, {63, 64}, {79, 216}, {74, 211}, {76,
213}, {78, 215}, {73, 210}, {77, 214}, {75, 212}, {45, 128}, {61, 144}, {47,
130}, {46, 129}, {48, 131}, {60, 143}, {56, 139}, {52, 135}, {49, 132}, {59,
142}, {57, 140}, {51, 134}, {50, 133}, {58, 141}, {56, 128}, {63, 135}, {62,
134}, {61, 133}, {60, 132}, {59, 131}, {58, 130}, {57, 129}, {120, 192}, {121,
193}, {122, 194}, {123, 195}, {124, 196}, {125, 197}, {126, 198}, {127, 199},
{53, 136}, {55, 138}, {54, 137}, {127, 192}, {80, 145}, {82, 147}, {84, 149},
{86, 151}, {88, 153}, {90, 155}, {92, 157}, {94, 159}, {96, 161}, {98, 163},
{100, 165}, {102, 167}, {104, 169}, {106, 171}, {108, 173}, {110, 175}, {112,
177}, {114, 179}, {116, 181}, {118, 183}, {120, 185}, {122, 187}, {124, 189},
{126, 191}, {81, 146}, {85, 150}, {89, 154}, {93, 158}, {97, 162}, {101, 166},
{105, 170}, {109, 174}, {113, 178}, {117, 182}, {121, 186}, {125, 190}, {83,
148}, {91, 156}, {99, 164}, {107, 172}, {115, 180}, {123, 188}, {64, 136}, {69,
141}, {68, 140}, {67, 139}, {66, 138}, {65, 137}, {70, 142}, {71, 143}, {80,
152}, {81, 153}, {82, 154}, {83, 155}, {84, 156}, {85, 157}, {86, 158}, {87,
159}, {96, 168}, {97, 169}, {98, 170}, {99, 171}, {100, 172}, {101, 173}, {102,
174}, {103, 175}, {112, 184}, {113, 185}, {114, 186}, {115, 187}, {116, 188},
{117, 189}, {118, 190}, {119, 191}, {87, 152}, {103, 168}, {119, 184}, {72,
144}, {73, 145}, {74, 146}, {75, 147}, {76, 148}, {77, 149}, {78, 150}, {79,
151}, {104, 176}, {105, 177}, {106, 178}, {107, 179}, {108, 180}, {109, 181},
{110, 182}, {111, 183}, {111, 176}, {88, 160}, {89, 161}, {90, 162}, {91, 163},
{92, 164}, {93, 165}, {94, 166}, {95, 167}, {95, 160} }>;
(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) (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, 72)(3, 71)(4, 70)(5, 69)(6, 68)(7, 67)(8, 66)(9, 65)(10, 64)(11, 63)(12,
62)(13, 61)(14, 60)(15, 59)(16, 58)(17, 57)(18, 56)(19, 55)(20, 54)(21, 53)(22,
52)(23, 51)(24, 50)(25, 49)(26, 48)(27, 47)(28, 46)(29, 45)(30, 44)(31, 43)(32,
42)(33, 41)(34, 40)(35, 39)(36, 38)(73, 84)(74, 83)(75, 82)(76, 81)(77, 80)(78,
79)(85, 144)(86, 143)(87, 142)(88, 141)(89, 140)(90, 139)(91, 138)(92, 137)(93,
136)(94, 135)(95, 134)(96, 133)(97, 132)(98, 131)(99, 130)(100, 129)(101,
128)(102, 127)(103, 126)(104, 125)(105, 124)(106, 123)(107, 122)(108, 121)(109,
120)(110, 119)(111, 118)(112, 117)(113, 116)(114, 115)(145, 149)(146, 148)(150,
216)(151, 215)(152, 214)(153, 213)(154, 212)(155, 211)(156, 210)(157, 209)(158,
208)(159, 207)(160, 206)(161, 205)(162, 204)(163, 203)(164, 202)(165, 201)(166,
200)(167, 199)(168, 198)(169, 197)(170, 196)(171, 195)(172, 194)(173, 193)(174,
192)(175, 191)(176, 190)(177, 189)(178, 188)(179, 187)(180, 186)(181, 185)(182,
184)
c: (2, 84)(3, 149)(4, 77)(6, 88)(7, 153)(8, 81)(10, 92)(11, 157)(12, 85)(14,
96)(15, 161)(16, 89)(18, 100)(19, 165)(20, 93)(22, 104)(23, 169)(24, 97)(26,
108)(27, 173)(28, 101)(30, 112)(31, 177)(32, 105)(34, 116)(35, 181)(36, 109)(38,
120)(39, 185)(40, 113)(42, 124)(43, 189)(44, 117)(46, 128)(47, 193)(48, 121)(50,
132)(51, 197)(52, 125)(54, 136)(55, 201)(56, 129)(58, 140)(59, 205)(60, 133)(62,
144)(63, 209)(64, 137)(66, 76)(67, 213)(68, 141)(70, 80)(71, 145)(72, 73)(74,
156)(75, 202)(78, 160)(79, 206)(82, 164)(83, 210)(86, 168)(87, 214)(90, 172)(91,
146)(94, 176)(95, 150)(98, 180)(99, 154)(102, 184)(103, 158)(106, 188)(107,
162)(110, 192)(111, 166)(114, 196)(115, 170)(118, 200)(119, 174)(122, 204)(123,
178)(126, 208)(127, 182)(130, 212)(131, 186)(134, 216)(135, 190)(138, 148)(139,
194)(142, 152)(143, 198)(147, 183)(151, 187)(155, 191)(159, 195)(163, 199)(167,
203)(171, 207)(175, 211)(179, 215)
C4[ 216, 23 ]
216
-1 2 72 73 84
-2 1 3 74 85
-3 2 4 75 86
-4 3 5 76 87
-5 77 88 4 6
-6 78 89 5 7
-7 79 90 6 8
-8 80 91 7 9
-9 81 92 8 10
-10 11 82 93 9
-11 12 83 94 10
-12 11 13 84 95
-13 12 14 85 96
-14 13 15 86 97
-15 14 16 87 98
-16 88 99 15 17
-17 89 100 16 18
-18 90 101 17 19
-19 91 102 18 20
-20 92 103 19 21
-21 22 93 104 20
-22 23 94 105 21
-23 22 24 95 106
-24 23 25 96 107
-25 24 26 97 108
-26 25 27 98 109
-27 99 110 26 28
-28 100 111 27 29
-29 101 112 28 30
-30 102 113 29 31
-31 103 114 30 32
-32 33 104 115 31
-33 34 105 116 32
-34 33 35 106 117
-35 34 36 107 118
-36 35 37 108 119
-37 36 38 109 120
-38 110 121 37 39
-39 111 122 38 40
-40 112 123 39 41
-41 113 124 40 42
-42 114 125 41 43
-43 44 115 126 42
-44 45 116 127 43
-45 44 46 117 128
-46 45 47 118 129
-47 46 48 119 130
-48 47 49 120 131
-49 121 132 48 50
-50 122 133 49 51
-51 123 134 50 52
-52 124 135 51 53
-53 125 136 52 54
-54 55 126 137 53
-55 56 127 138 54
-56 55 57 128 139
-57 56 58 129 140
-58 57 59 130 141
-59 58 60 131 142
-60 132 143 59 61
-61 133 144 60 62
-62 134 61 73 63
-63 135 62 74 64
-64 136 63 75 65
-65 66 137 64 76
-66 77 67 138 65
-67 66 78 68 139
-68 67 79 69 140
-69 68 80 70 141
-70 69 81 71 142
-71 143 70 82 72
-72 1 144 71 83
-73 1 210 145 62
-74 2 211 146 63
-75 3 212 147 64
-76 4 213 148 65
-77 66 5 214 149
-78 67 6 215 150
-79 68 7 216 151
-80 145 69 8 152
-81 146 70 9 153
-82 154 147 71 10
-83 11 155 148 72
-84 1 12 156 149
-85 2 13 157 150
-86 3 14 158 151
-87 4 15 159 152
-88 5 16 160 153
-89 154 6 17 161
-90 155 7 18 162
-91 156 8 19 163
-92 157 9 20 164
-93 165 158 10 21
-94 11 22 166 159
-95 12 23 167 160
-96 13 24 168 161
-97 14 25 169 162
-98 15 26 170 163
-99 16 27 171 164
-100 165 17 28 172
-101 166 18 29 173
-102 167 19 30 174
-103 168 20 31 175
-104 176 169 21 32
-105 22 33 177 170
-106 23 34 178 171
-107 24 35 179 172
-108 25 36 180 173
-109 26 37 181 174
-110 27 38 182 175
-111 176 28 39 183
-112 177 29 40 184
-113 178 30 41 185
-114 179 31 42 186
-115 187 180 32 43
-116 33 44 188 181
-117 34 45 189 182
-118 35 46 190 183
-119 36 47 191 184
-120 37 48 192 185
-121 38 49 193 186
-122 187 39 50 194
-123 188 40 51 195
-124 189 41 52 196
-125 190 42 53 197
-126 198 191 43 54
-127 44 55 199 192
-128 45 56 200 193
-129 46 57 201 194
-130 47 58 202 195
-131 48 59 203 196
-132 49 60 204 197
-133 198 50 61 205
-134 199 51 62 206
-135 200 52 63 207
-136 201 53 64 208
-137 209 202 54 65
-138 55 66 210 203
-139 56 67 211 204
-140 57 68 212 205
-141 58 69 213 206
-142 59 70 214 207
-143 60 71 215 208
-144 209 61 72 216
-145 198 80 73 164
-146 165 199 81 74
-147 166 200 82 75
-148 167 201 83 76
-149 77 168 202 84
-150 78 169 203 85
-151 79 170 204 86
-152 80 171 205 87
-153 88 81 172 206
-154 89 82 173 207
-155 90 83 174 208
-156 209 91 84 175
-157 176 210 92 85
-158 177 211 93 86
-159 178 212 94 87
-160 88 179 213 95
-161 89 180 214 96
-162 90 181 215 97
-163 91 182 216 98
-164 99 145 92 183
-165 100 146 93 184
-166 101 147 94 185
-167 102 148 95 186
-168 187 103 149 96
-169 188 104 150 97
-170 189 105 151 98
-171 99 190 106 152
-172 100 191 107 153
-173 154 101 192 108
-174 155 102 193 109
-175 110 156 103 194
-176 111 157 104 195
-177 112 158 105 196
-178 113 159 106 197
-179 198 114 160 107
-180 199 115 161 108
-181 200 116 162 109
-182 110 201 117 163
-183 111 202 118 164
-184 165 112 203 119
-185 166 113 204 120
-186 121 167 114 205
-187 122 168 115 206
-188 123 169 116 207
-189 124 170 117 208
-190 209 125 171 118
-191 210 126 172 119
-192 211 127 173 120
-193 121 212 128 174
-194 122 213 129 175
-195 176 123 214 130
-196 177 124 215 131
-197 132 178 125 216
-198 133 145 179 126
-199 134 146 180 127
-200 135 147 181 128
-201 136 148 182 129
-202 137 149 183 130
-203 138 150 184 131
-204 132 139 151 185
-205 133 140 152 186
-206 187 134 141 153
-207 154 188 135 142
-208 143 155 189 136
-209 144 156 190 137
-210 157 191 138 73
-211 158 192 139 74
-212 159 193 140 75
-213 160 194 141 76
-214 77 161 195 142
-215 143 78 162 196
-216 144 79 163 197
0