Graph forms
for C4 [ 228, 9 ] = Pr_76(1,17,21,37)
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On this page are computer-accessible forms for the graph C4[ 228, 9 ] =
Pr_76(1,17,21,37).
(I) Following is a form readable by MAGMA:
g:=Graph<228|{ {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}, {72, 73}, {74, 75}, {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},
{73, 74}, {3, 4}, {67, 68}, {59, 60}, {51, 52}, {43, 44}, {11, 12}, {19, 20},
{27, 28}, {35, 36}, {75, 76}, {7, 8}, {71, 72}, {55, 56}, {23, 24}, {39, 40},
{136, 157}, {138, 159}, {137, 158}, {135, 156}, {132, 153}, {134, 155}, {15,
16}, {47, 48}, {133, 154}, {154, 191}, {153, 190}, {139, 160}, {143, 164}, {140,
161}, {142, 163}, {141, 162}, {144, 165}, {152, 173}, {146, 167}, {145, 166},
{64, 123}, {151, 172}, {68, 127}, {147, 168}, {65, 124}, {150, 171}, {67, 126},
{148, 169}, {31, 32}, {66, 125}, {149, 170}, {21, 80}, {63, 122}, {61, 120},
{55, 114}, {53, 112}, {47, 106}, {45, 104}, {23, 82}, {29, 88}, {31, 90}, {37,
96}, {39, 98}, {22, 81}, {62, 121}, {54, 113}, {46, 105}, {30, 89}, {38, 97},
{24, 83}, {60, 119}, {56, 115}, {44, 103}, {28, 87}, {40, 99}, {1, 77}, {51,
127}, {50, 126}, {49, 125}, {48, 124}, {2, 78}, {3, 79}, {16, 92}, {17, 93},
{18, 94}, {19, 95}, {32, 108}, {33, 109}, {34, 110}, {35, 111}, {128, 204},
{129, 205}, {130, 206}, {131, 207}, {144, 220}, {145, 221}, {146, 222}, {147,
223}, {1, 76}, {59, 118}, {57, 116}, {43, 102}, {25, 84}, {27, 86}, {41, 100},
{26, 85}, {58, 117}, {42, 101}, {4, 80}, {47, 123}, {46, 122}, {45, 121}, {44,
120}, {5, 81}, {6, 82}, {7, 83}, {12, 88}, {13, 89}, {14, 90}, {15, 91}, {36,
112}, {37, 113}, {38, 114}, {39, 115}, {132, 208}, {133, 209}, {134, 210}, {135,
211}, {140, 216}, {141, 217}, {142, 218}, {143, 219}, {153, 192}, {189, 228},
{187, 226}, {185, 224}, {159, 198}, {157, 196}, {155, 194}, {20, 79}, {191,
228}, {187, 224}, {186, 225}, {159, 196}, {158, 197}, {155, 192}, {154, 193},
{52, 111}, {48, 107}, {8, 84}, {43, 119}, {9, 85}, {10, 86}, {11, 87}, {40,
116}, {41, 117}, {42, 118}, {136, 212}, {137, 213}, {138, 214}, {139, 215}, {19,
78}, {190, 227}, {188, 225}, {158, 195}, {156, 193}, {51, 110}, {49, 108}, {18,
77}, {189, 226}, {188, 227}, {157, 194}, {156, 195}, {50, 109}, {128, 225},
{130, 227}, {129, 226}, {160, 197}, {186, 223}, {184, 221}, {178, 215}, {176,
213}, {170, 207}, {168, 205}, {162, 199}, {131, 228}, {185, 222}, {184, 223},
{177, 214}, {176, 215}, {169, 206}, {168, 207}, {161, 198}, {160, 199}, {161,
200}, {183, 222}, {181, 220}, {179, 218}, {177, 216}, {167, 206}, {165, 204},
{163, 202}, {162, 201}, {183, 220}, {182, 221}, {179, 216}, {178, 217}, {167,
204}, {166, 205}, {163, 200}, {164, 201}, {182, 219}, {180, 217}, {166, 203},
{164, 203}, {181, 218}, {180, 219}, {165, 202}, {20, 96}, {151, 227}, {150,
226}, {149, 225}, {21, 97}, {22, 98}, {23, 99}, {28, 104}, {29, 105}, {30, 106},
{31, 107}, {148, 224}, {169, 208}, {175, 214}, {173, 212}, {171, 210}, {32, 91},
{175, 212}, {174, 213}, {171, 208}, {170, 209}, {36, 95}, {24, 100}, {152, 228},
{25, 101}, {26, 102}, {27, 103}, {33, 92}, {174, 211}, {172, 209}, {35, 94},
{34, 93}, {173, 210}, {172, 211}, {63, 64}, {8, 143}, {16, 151}, {1, 136}, {3,
138}, {5, 140}, {7, 142}, {17, 152}, {2, 137}, {6, 141}, {4, 139}, {9, 144},
{11, 146}, {13, 148}, {15, 150}, {10, 145}, {14, 149}, {12, 147}, {95, 192},
{127, 224}, {96, 193}, {98, 195}, {100, 197}, {102, 199}, {104, 201}, {106,
203}, {108, 205}, {110, 207}, {112, 209}, {114, 211}, {116, 213}, {118, 215},
{120, 217}, {122, 219}, {124, 221}, {126, 223}, {97, 194}, {101, 198}, {105,
202}, {109, 206}, {113, 210}, {117, 214}, {121, 218}, {125, 222}, {99, 196},
{107, 204}, {115, 212}, {123, 220}, {103, 200}, {119, 216}, {52, 128}, {63,
139}, {62, 138}, {61, 137}, {60, 136}, {55, 131}, {54, 130}, {53, 129}, {116,
192}, {117, 193}, {118, 194}, {119, 195}, {124, 200}, {125, 201}, {126, 202},
{127, 203}, {56, 132}, {59, 135}, {58, 134}, {57, 133}, {120, 196}, {121, 197},
{122, 198}, {123, 199}, {111, 208}, {69, 128}, {71, 130}, {70, 129}, {72, 131},
{76, 135}, {64, 140}, {67, 143}, {66, 142}, {65, 141}, {80, 156}, {81, 157},
{82, 158}, {83, 159}, {96, 172}, {97, 173}, {98, 174}, {99, 175}, {112, 188},
{113, 189}, {114, 190}, {115, 191}, {73, 132}, {75, 134}, {74, 133}, {68, 144},
{70, 146}, {69, 145}, {71, 147}, {76, 152}, {77, 153}, {78, 154}, {79, 155},
{100, 176}, {101, 177}, {102, 178}, {103, 179}, {108, 184}, {109, 185}, {110,
186}, {111, 187}, {72, 148}, {73, 149}, {74, 150}, {75, 151}, {104, 180}, {105,
181}, {106, 182}, {107, 183}, {78, 175}, {80, 177}, {82, 179}, {84, 181}, {86,
183}, {88, 185}, {90, 187}, {92, 189}, {94, 191}, {77, 174}, {81, 178}, {85,
182}, {89, 186}, {93, 190}, {83, 180}, {91, 188}, {87, 184}, {84, 160}, {85,
161}, {86, 162}, {87, 163}, {92, 168}, {93, 169}, {94, 170}, {95, 171}, {88,
164}, {89, 165}, {90, 166}, {91, 167}, {79, 176} }>;
(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, 222, 223, 224, 225, 226, 227,
228) (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, 136)(3, 157)(4, 81)(6, 140)(7, 161)(8, 85)(10, 144)(11, 165)(12, 89)(14,
148)(15, 169)(16, 93)(18, 152)(19, 173)(20, 97)(22, 80)(23, 177)(24, 101)(26,
84)(27, 181)(28, 105)(30, 88)(31, 185)(32, 109)(34, 92)(35, 189)(36, 113)(38,
96)(39, 193)(40, 117)(42, 100)(43, 197)(44, 121)(46, 104)(47, 201)(48, 125)(50,
108)(51, 205)(52, 129)(54, 112)(55, 209)(56, 133)(58, 116)(59, 213)(60, 137)(62,
120)(63, 217)(64, 141)(66, 124)(67, 221)(68, 145)(70, 128)(71, 225)(72, 149)(74,
132)(75, 153)(76, 77)(78, 212)(79, 194)(82, 216)(83, 198)(86, 220)(87, 202)(90,
224)(91, 206)(94, 228)(95, 210)(98, 156)(99, 214)(102, 160)(103, 218)(106,
164)(107, 222)(110, 168)(111, 226)(114, 172)(115, 154)(118, 176)(119, 158)(122,
180)(123, 162)(126, 184)(127, 166)(130, 188)(131, 170)(134, 192)(135, 174)(138,
196)(139, 178)(142, 200)(143, 182)(146, 204)(147, 186)(150, 208)(151, 190)
c: (2, 76)(3, 75)(4, 74)(5, 73)(6, 72)(7, 71)(8, 70)(9, 69)(10, 68)(11, 67)(12,
66)(13, 65)(14, 64)(15, 63)(16, 62)(17, 61)(18, 60)(19, 59)(20, 58)(21, 57)(22,
56)(23, 55)(24, 54)(25, 53)(26, 52)(27, 51)(28, 50)(29, 49)(30, 48)(31, 47)(32,
46)(33, 45)(34, 44)(35, 43)(36, 42)(37, 41)(38, 40)(77, 136)(78, 135)(79,
134)(80, 133)(81, 132)(82, 131)(83, 130)(84, 129)(85, 128)(86, 127)(87, 126)(88,
125)(89, 124)(90, 123)(91, 122)(92, 121)(93, 120)(94, 119)(95, 118)(96, 117)(97,
116)(98, 115)(99, 114)(100, 113)(101, 112)(102, 111)(103, 110)(104, 109)(105,
108)(106, 107)(137, 152)(138, 151)(139, 150)(140, 149)(141, 148)(142, 147)(143,
146)(144, 145)(153, 157)(154, 156)(158, 228)(159, 227)(160, 226)(161, 225)(162,
224)(163, 223)(164, 222)(165, 221)(166, 220)(167, 219)(168, 218)(169, 217)(170,
216)(171, 215)(172, 214)(173, 213)(174, 212)(175, 211)(176, 210)(177, 209)(178,
208)(179, 207)(180, 206)(181, 205)(182, 204)(183, 203)(184, 202)(185, 201)(186,
200)(187, 199)(188, 198)(189, 197)(190, 196)(191, 195)(192, 194)
C4[ 228, 9 ]
228
-1 77 2 136 76
-2 1 78 3 137
-3 2 79 4 138
-4 3 80 5 139
-5 4 81 6 140
-6 5 82 7 141
-7 6 83 8 142
-8 143 7 84 9
-9 144 8 85 10
-10 11 145 9 86
-11 12 146 10 87
-12 11 88 13 147
-13 12 89 14 148
-14 13 90 15 149
-15 14 91 16 150
-16 15 92 17 151
-17 16 93 18 152
-18 77 17 94 19
-19 78 18 95 20
-20 79 19 96 21
-21 22 80 20 97
-22 23 81 21 98
-23 22 99 24 82
-24 23 100 25 83
-25 24 101 26 84
-26 25 102 27 85
-27 26 103 28 86
-28 27 104 29 87
-29 88 28 105 30
-30 89 29 106 31
-31 90 30 107 32
-32 33 91 31 108
-33 34 92 32 109
-34 33 110 35 93
-35 34 111 36 94
-36 35 112 37 95
-37 36 113 38 96
-38 37 114 39 97
-39 38 115 40 98
-40 99 39 116 41
-41 100 40 117 42
-42 101 41 118 43
-43 44 102 42 119
-44 45 103 43 120
-45 44 121 46 104
-46 45 122 47 105
-47 46 123 48 106
-48 47 124 49 107
-49 48 125 50 108
-50 49 126 51 109
-51 110 50 127 52
-52 111 51 128 53
-53 112 52 129 54
-54 55 113 53 130
-55 56 114 54 131
-56 55 132 57 115
-57 56 133 58 116
-58 57 134 59 117
-59 58 135 60 118
-60 59 136 61 119
-61 60 137 62 120
-62 121 61 138 63
-63 122 62 139 64
-64 123 63 140 65
-65 66 124 64 141
-66 67 125 65 142
-67 66 143 68 126
-68 67 144 69 127
-69 68 145 70 128
-70 69 146 71 129
-71 70 147 72 130
-72 71 148 73 131
-73 132 72 149 74
-74 133 73 150 75
-75 134 74 151 76
-76 1 135 75 152
-77 1 18 174 153
-78 154 2 19 175
-79 176 155 3 20
-80 177 156 4 21
-81 22 178 157 5
-82 23 179 158 6
-83 24 180 159 7
-84 25 181 160 8
-85 26 182 161 9
-86 27 183 162 10
-87 11 28 184 163
-88 12 29 185 164
-89 165 13 30 186
-90 187 166 14 31
-91 188 167 15 32
-92 33 189 168 16
-93 34 190 169 17
-94 35 191 170 18
-95 36 192 171 19
-96 37 193 172 20
-97 38 194 173 21
-98 22 39 195 174
-99 23 40 196 175
-100 176 24 41 197
-101 198 177 25 42
-102 199 178 26 43
-103 44 200 179 27
-104 45 201 180 28
-105 46 202 181 29
-106 47 203 182 30
-107 48 204 183 31
-108 49 205 184 32
-109 33 50 206 185
-110 34 51 207 186
-111 187 35 52 208
-112 209 188 36 53
-113 210 189 37 54
-114 55 211 190 38
-115 56 212 191 39
-116 57 213 192 40
-117 58 214 193 41
-118 59 215 194 42
-119 60 216 195 43
-120 44 61 217 196
-121 45 62 218 197
-122 198 46 63 219
-123 220 199 47 64
-124 221 200 48 65
-125 66 222 201 49
-126 67 223 202 50
-127 68 224 203 51
-128 69 225 204 52
-129 70 226 205 53
-130 71 227 206 54
-131 55 72 228 207
-132 56 73 153 208
-133 154 209 57 74
-134 155 210 58 75
-135 156 211 59 76
-136 1 157 212 60
-137 2 158 213 61
-138 3 159 214 62
-139 4 160 215 63
-140 5 161 216 64
-141 6 162 217 65
-142 66 7 163 218
-143 67 8 164 219
-144 165 220 68 9
-145 166 221 69 10
-146 11 167 222 70
-147 12 168 223 71
-148 13 169 224 72
-149 14 170 225 73
-150 15 171 226 74
-151 16 172 227 75
-152 17 173 228 76
-153 77 132 190 192
-154 78 133 191 193
-155 79 134 192 194
-156 80 135 193 195
-157 81 136 194 196
-158 82 137 195 197
-159 198 83 138 196
-160 199 84 139 197
-161 198 200 85 140
-162 199 201 86 141
-163 200 202 87 142
-164 88 143 201 203
-165 89 144 202 204
-166 90 145 203 205
-167 91 146 204 206
-168 92 147 205 207
-169 93 148 206 208
-170 209 94 149 207
-171 210 95 150 208
-172 209 211 96 151
-173 210 212 97 152
-174 77 211 213 98
-175 99 78 212 214
-176 100 79 213 215
-177 101 80 214 216
-178 102 81 215 217
-179 103 82 216 218
-180 104 83 217 219
-181 220 105 84 218
-182 221 106 85 219
-183 220 222 107 86
-184 221 223 108 87
-185 88 222 224 109
-186 110 89 223 225
-187 111 90 224 226
-188 112 91 225 227
-189 113 92 226 228
-190 114 93 227 153
-191 154 115 94 228
-192 155 116 95 153
-193 154 156 117 96
-194 155 157 118 97
-195 156 158 119 98
-196 99 157 159 120
-197 121 100 158 160
-198 122 101 159 161
-199 123 102 160 162
-200 124 103 161 163
-201 125 104 162 164
-202 165 126 105 163
-203 166 127 106 164
-204 165 167 128 107
-205 166 168 129 108
-206 167 169 130 109
-207 110 168 170 131
-208 132 111 169 171
-209 133 112 170 172
-210 134 113 171 173
-211 135 114 172 174
-212 136 115 173 175
-213 176 137 116 174
-214 177 138 117 175
-215 176 178 139 118
-216 177 179 140 119
-217 178 180 141 120
-218 121 179 181 142
-219 143 122 180 182
-220 144 123 181 183
-221 145 124 182 184
-222 146 125 183 185
-223 147 126 184 186
-224 187 148 127 185
-225 188 149 128 186
-226 187 189 150 129
-227 188 190 151 130
-228 189 191 152 131
0