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