Graph forms
for C4 [ 234, 8 ] = PS(6,39;4)
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On this page are computer-accessible forms for the graph C4[ 234, 8 ] =
PS(6,39;4).
(I) Following is a form readable by MAGMA:
g:=Graph<234|{ {75, 79}, {144, 158}, {145, 159}, {39, 40}, {102, 118}, {103,
119}, {104, 120}, {105, 121}, {106, 122}, {107, 123}, {108, 124}, {109, 125},
{110, 126}, {111, 127}, {192, 209}, {194, 211}, {143, 157}, {193, 210}, {192,
214}, {193, 215}, {96, 119}, {195, 212}, {104, 127}, {97, 120}, {99, 122}, {101,
124}, {103, 126}, {132, 157}, {134, 159}, {194, 216}, {195, 217}, {98, 121},
{102, 125}, {133, 158}, {76, 80}, {78, 82}, {77, 81}, {100, 123}, {64, 99}, {76,
111}, {72, 107}, {68, 103}, {65, 100}, {75, 110}, {73, 108}, {67, 102}, {8, 46},
{9, 47}, {16, 54}, {17, 55}, {24, 62}, {25, 63}, {66, 101}, {74, 109}, {135,
160}, {143, 168}, {151, 176}, {1, 41}, {2, 42}, {3, 43}, {4, 44}, {5, 45}, {6,
46}, {7, 47}, {16, 56}, {17, 57}, {18, 58}, {19, 59}, {20, 60}, {21, 61}, {22,
62}, {23, 63}, {95, 118}, {136, 161}, {138, 163}, {140, 165}, {142, 167}, {152,
177}, {154, 179}, {156, 181}, {2, 40}, {3, 41}, {6, 44}, {7, 45}, {18, 56}, {19,
57}, {22, 60}, {23, 61}, {64, 107}, {68, 111}, {137, 162}, {141, 166}, {153,
178}, {65, 108}, {71, 106}, {69, 104}, {67, 110}, {4, 42}, {5, 43}, {20, 58},
{21, 59}, {66, 109}, {70, 105}, {139, 164}, {155, 180}, {146, 160}, {147, 161},
{150, 164}, {151, 165}, {154, 168}, {155, 169}, {69, 112}, {71, 114}, {128,
181}, {130, 183}, {136, 189}, {138, 191}, {148, 162}, {149, 163}, {156, 170},
{70, 113}, {129, 182}, {137, 190}, {8, 48}, {9, 49}, {10, 50}, {11, 51}, {12,
52}, {13, 53}, {14, 54}, {15, 55}, {144, 169}, {146, 171}, {148, 173}, {150,
175}, {10, 48}, {11, 49}, {14, 52}, {15, 53}, {72, 115}, {131, 184}, {135, 188},
{145, 170}, {149, 174}, {73, 116}, {77, 112}, {132, 185}, {134, 187}, {12, 50},
{13, 51}, {152, 166}, {153, 167}, {74, 117}, {78, 113}, {133, 186}, {147, 172},
{128, 192}, {129, 193}, {130, 194}, {131, 195}, {159, 220}, {171, 232}, {167,
228}, {163, 224}, {158, 219}, {172, 233}, {166, 227}, {164, 225}, {157, 218},
{173, 234}, {165, 226}, {157, 213}, {175, 231}, {174, 230}, {173, 229}, {172,
228}, {171, 227}, {170, 226}, {169, 225}, {168, 224}, {158, 214}, {159, 215},
{139, 192}, {140, 193}, {170, 231}, {168, 229}, {142, 195}, {1, 78}, {169, 230},
{141, 194}, {53, 96}, {63, 106}, {61, 104}, {55, 98}, {54, 97}, {62, 105}, {24,
64}, {178, 234}, {177, 233}, {176, 232}, {25, 65}, {26, 66}, {27, 67}, {28, 68},
{29, 69}, {30, 70}, {31, 71}, {26, 64}, {41, 115}, {40, 114}, {27, 65}, {30,
68}, {31, 69}, {56, 99}, {60, 103}, {57, 100}, {63, 98}, {61, 96}, {59, 102},
{28, 66}, {43, 117}, {42, 116}, {29, 67}, {58, 101}, {62, 97}, {44, 79}, {60,
95}, {56, 91}, {52, 87}, {48, 83}, {49, 84}, {59, 94}, {57, 92}, {51, 86}, {32,
70}, {33, 71}, {50, 85}, {58, 93}, {32, 72}, {38, 78}, {37, 77}, {36, 76}, {35,
75}, {33, 73}, {34, 74}, {34, 72}, {191, 213}, {190, 212}, {187, 209}, {186,
208}, {175, 197}, {174, 196}, {39, 77}, {38, 76}, {35, 73}, {48, 91}, {52, 95},
{49, 92}, {55, 90}, {53, 88}, {51, 94}, {36, 74}, {189, 211}, {188, 210}, {37,
75}, {50, 93}, {191, 208}, {54, 89}, {180, 197}, {190, 207}, {188, 205}, {186,
203}, {184, 201}, {182, 199}, {181, 198}, {189, 206}, {185, 202}, {45, 88}, {47,
90}, {176, 198}, {185, 207}, {184, 206}, {177, 199}, {46, 89}, {187, 204}, {179,
196}, {160, 216}, {167, 223}, {166, 222}, {165, 221}, {161, 217}, {162, 218},
{163, 219}, {164, 220}, {178, 200}, {183, 205}, {182, 204}, {179, 201}, {40,
83}, {44, 87}, {41, 84}, {47, 82}, {45, 80}, {43, 86}, {160, 221}, {162, 223},
{180, 202}, {181, 203}, {42, 85}, {183, 200}, {46, 81}, {161, 222}, {118, 182},
{119, 183}, {120, 184}, {121, 185}, {122, 186}, {123, 187}, {124, 188}, {125,
189}, {126, 190}, {127, 191}, {79, 141}, {83, 145}, {82, 144}, {86, 148}, {87,
149}, {90, 152}, {91, 153}, {94, 156}, {84, 146}, {85, 147}, {92, 154}, {93,
155}, {15, 200}, {39, 224}, {23, 208}, {31, 216}, {12, 197}, {79, 134}, {14,
199}, {24, 209}, {26, 211}, {28, 213}, {30, 215}, {89, 144}, {91, 146}, {93,
148}, {95, 150}, {13, 198}, {25, 210}, {29, 214}, {90, 145}, {94, 149}, {123,
176}, {127, 180}, {2, 207}, {16, 221}, {18, 223}, {124, 177}, {126, 179}, {88,
150}, {89, 151}, {1, 206}, {11, 196}, {17, 222}, {27, 212}, {92, 147}, {125,
178}, {3, 208}, {7, 212}, {11, 216}, {15, 220}, {4, 209}, {6, 211}, {12, 217},
{14, 219}, {120, 173}, {122, 175}, {5, 210}, {80, 135}, {13, 218}, {88, 143},
{121, 174}, {16, 201}, {85, 140}, {83, 138}, {81, 136}, {18, 203}, {20, 205},
{22, 207}, {87, 142}, {30, 196}, {31, 197}, {17, 202}, {82, 137}, {21, 206},
{86, 141}, {119, 172}, {8, 213}, {10, 215}, {118, 171}, {80, 142}, {81, 143},
{9, 214}, {84, 139}, {19, 204}, {1, 225}, {2, 226}, {3, 227}, {4, 228}, {5,
229}, {6, 230}, {7, 231}, {8, 232}, {9, 233}, {10, 234}, {32, 198}, {33, 199},
{105, 128}, {107, 130}, {109, 132}, {111, 134}, {34, 200}, {39, 205}, {38, 204},
{35, 201}, {106, 129}, {110, 133}, {36, 202}, {37, 203}, {108, 131}, {112, 128},
{113, 129}, {114, 130}, {115, 131}, {116, 132}, {117, 133}, {19, 224}, {23,
228}, {27, 232}, {20, 225}, {22, 227}, {28, 233}, {21, 226}, {29, 234}, {96,
151}, {112, 135}, {32, 217}, {38, 223}, {36, 221}, {34, 219}, {97, 152}, {99,
154}, {101, 156}, {113, 136}, {115, 138}, {117, 140}, {33, 218}, {37, 222}, {98,
153}, {114, 137}, {24, 229}, {26, 231}, {25, 230}, {35, 220}, {100, 155}, {116,
139} }>;
(II) A more general form is to represent the graph as the orbit of {75, 79}
under the group generated by the following permutations:
a: (2, 39)(3, 38)(4, 37)(5, 36)(6, 35)(7, 34)(8, 33)(9, 32)(10, 31)(11, 30)(12,
29)(13, 28)(14, 27)(15, 26)(16, 25)(17, 24)(18, 23)(19, 22)(20, 21)(41, 78)(42,
77)(43, 76)(44, 75)(45, 74)(46, 73)(47, 72)(48, 71)(49, 70)(50, 69)(51, 68)(52,
67)(53, 66)(54, 65)(55, 64)(56, 63)(57, 62)(58, 61)(59, 60)(80, 117)(81,
116)(82, 115)(83, 114)(84, 113)(85, 112)(86, 111)(87, 110)(88, 109)(89, 108)(90,
107)(91, 106)(92, 105)(93, 104)(94, 103)(95, 102)(96, 101)(97, 100)(98, 99)(119,
156)(120, 155)(121, 154)(122, 153)(123, 152)(124, 151)(125, 150)(126, 149)(127,
148)(128, 147)(129, 146)(130, 145)(131, 144)(132, 143)(133, 142)(134, 141)(135,
140)(136, 139)(137, 138)(158, 195)(159, 194)(160, 193)(161, 192)(162, 191)(163,
190)(164, 189)(165, 188)(166, 187)(167, 186)(168, 185)(169, 184)(170, 183)(171,
182)(172, 181)(173, 180)(174, 179)(175, 178)(176, 177)(197, 234)(198, 233)(199,
232)(200, 231)(201, 230)(202, 229)(203, 228)(204, 227)(205, 226)(206, 225)(207,
224)(208, 223)(209, 222)(210, 221)(211, 220)(212, 219)(213, 218)(214, 217)(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: (1, 40, 79, 118, 157, 196)(2, 44, 95, 143, 179, 206)(3, 48, 111, 129, 162,
216)(4, 52, 88, 154, 184, 226)(5, 56, 104, 140, 167, 197)(6, 60, 81, 126, 189,
207)(7, 64, 97, 151, 172, 217)(8, 68, 113, 137, 194, 227)(9, 72, 90, 123, 177,
198)(10, 76, 106, 148, 160, 208)(11, 41, 83, 134, 182, 218)(12, 45, 99, 120,
165, 228)(13, 49, 115, 145, 187, 199)(14, 53, 92, 131, 170, 209)(15, 57, 108,
156, 192, 219)(16, 61, 85, 142, 175, 229)(17, 65, 101, 128, 158, 200)(18, 69,
117, 153, 180, 210)(19, 73, 94, 139, 163, 220)(20, 77, 110, 125, 185, 230)(21,
42, 87, 150, 168, 201)(22, 46, 103, 136, 190, 211)(23, 50, 80, 122, 173,
221)(24, 54, 96, 147, 195, 231)(25, 58, 112, 133, 178, 202)(26, 62, 89, 119,
161, 212)(27, 66, 105, 144, 183, 222)(28, 70, 82, 130, 166, 232)(29, 74, 98,
155, 188, 203)(30, 78, 114, 141, 171, 213)(31, 43, 91, 127, 193, 223)(32, 47,
107, 152, 176, 233)(33, 51, 84, 138, 159, 204)(34, 55, 100, 124, 181, 214)(35,
59, 116, 149, 164, 224)(36, 63, 93, 135, 186, 234)(37, 67, 109, 121, 169,
205)(38, 71, 86, 146, 191, 215)(39, 75, 102, 132, 174, 225)
c: (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,
229, 230, 231, 232, 233, 234)
C4[ 234, 8 ]
234
-1 78 225 41 206
-2 226 40 42 207
-3 227 41 43 208
-4 44 209 228 42
-5 45 210 229 43
-6 44 46 211 230
-7 231 45 47 212
-8 232 46 48 213
-9 233 47 49 214
-10 234 48 50 215
-11 49 51 216 196
-12 50 52 217 197
-13 198 51 53 218
-14 199 52 54 219
-15 55 220 200 53
-16 56 221 201 54
-17 55 57 222 202
-18 56 58 223 203
-19 57 59 224 204
-20 58 60 225 205
-21 59 61 226 206
-22 60 62 227 207
-23 61 63 228 208
-24 209 62 64 229
-25 210 63 65 230
-26 66 231 211 64
-27 67 232 212 65
-28 66 68 233 213
-29 67 69 234 214
-30 68 70 215 196
-31 69 71 216 197
-32 198 70 72 217
-33 199 71 73 218
-34 200 72 74 219
-35 220 201 73 75
-36 221 202 74 76
-37 77 222 203 75
-38 78 223 204 76
-39 77 224 40 205
-40 2 114 39 83
-41 1 3 115 84
-42 2 4 116 85
-43 3 5 117 86
-44 79 4 6 87
-45 88 80 5 7
-46 89 81 6 8
-47 90 82 7 9
-48 91 83 8 10
-49 11 92 84 9
-50 12 93 85 10
-51 11 13 94 86
-52 12 14 95 87
-53 88 13 15 96
-54 89 14 16 97
-55 90 15 17 98
-56 99 91 16 18
-57 100 92 17 19
-58 101 93 18 20
-59 102 94 19 21
-60 22 103 95 20
-61 23 104 96 21
-62 22 24 105 97
-63 23 25 106 98
-64 99 24 26 107
-65 100 25 27 108
-66 101 26 28 109
-67 110 102 27 29
-68 111 103 28 30
-69 112 104 29 31
-70 113 105 30 32
-71 33 114 106 31
-72 34 115 107 32
-73 33 35 116 108
-74 34 36 117 109
-75 110 35 79 37
-76 111 36 80 38
-77 112 37 81 39
-78 1 113 38 82
-79 44 134 75 141
-80 45 135 76 142
-81 77 143 46 136
-82 78 144 47 137
-83 145 48 138 40
-84 146 49 139 41
-85 147 50 140 42
-86 148 51 141 43
-87 44 149 52 142
-88 143 45 150 53
-89 144 46 151 54
-90 55 145 47 152
-91 56 146 48 153
-92 154 57 147 49
-93 155 58 148 50
-94 156 59 149 51
-95 60 150 52 118
-96 61 151 53 119
-97 62 152 54 120
-98 55 121 63 153
-99 154 56 122 64
-100 155 57 123 65
-101 66 156 58 124
-102 67 59 125 118
-103 68 60 126 119
-104 69 61 127 120
-105 121 70 62 128
-106 122 71 63 129
-107 123 72 64 130
-108 124 73 65 131
-109 66 132 125 74
-110 67 133 126 75
-111 68 134 127 76
-112 77 69 135 128
-113 78 70 136 129
-114 71 137 40 130
-115 72 138 41 131
-116 132 73 139 42
-117 133 74 140 43
-118 102 171 182 95
-119 103 172 183 96
-120 104 173 184 97
-121 105 174 185 98
-122 99 106 175 186
-123 176 187 100 107
-124 177 188 101 108
-125 178 189 102 109
-126 110 179 190 103
-127 111 180 191 104
-128 112 181 192 105
-129 113 182 193 106
-130 114 183 194 107
-131 115 184 195 108
-132 157 116 185 109
-133 110 158 117 186
-134 187 111 79 159
-135 188 112 80 160
-136 189 113 81 161
-137 190 114 82 162
-138 191 115 83 163
-139 192 116 84 164
-140 165 193 117 85
-141 166 79 194 86
-142 167 80 195 87
-143 88 157 168 81
-144 89 158 169 82
-145 90 159 170 83
-146 91 160 171 84
-147 92 161 172 85
-148 93 162 173 86
-149 94 163 174 87
-150 88 95 164 175
-151 165 176 89 96
-152 166 177 90 97
-153 167 178 91 98
-154 99 168 179 92
-155 100 169 180 93
-156 101 170 181 94
-157 132 143 213 218
-158 133 144 214 219
-159 220 134 145 215
-160 221 135 146 216
-161 222 136 147 217
-162 223 137 148 218
-163 224 138 149 219
-164 220 225 139 150
-165 221 226 140 151
-166 222 227 141 152
-167 223 228 142 153
-168 143 154 224 229
-169 144 155 225 230
-170 231 145 156 226
-171 232 146 227 118
-172 233 147 228 119
-173 234 148 229 120
-174 121 149 196 230
-175 231 122 150 197
-176 198 232 123 151
-177 199 233 124 152
-178 200 234 125 153
-179 154 201 126 196
-180 155 202 127 197
-181 198 156 203 128
-182 199 204 118 129
-183 200 205 119 130
-184 201 206 120 131
-185 121 132 202 207
-186 122 133 203 208
-187 209 123 134 204
-188 210 124 135 205
-189 211 125 136 206
-190 212 126 137 207
-191 213 127 138 208
-192 209 214 128 139
-193 210 215 129 140
-194 211 216 130 141
-195 212 217 131 142
-196 11 179 30 174
-197 12 180 31 175
-198 176 13 181 32
-199 33 177 14 182
-200 34 178 15 183
-201 35 179 16 184
-202 36 180 17 185
-203 37 181 18 186
-204 187 38 182 19
-205 188 39 183 20
-206 1 189 184 21
-207 22 2 190 185
-208 23 3 191 186
-209 187 24 4 192
-210 188 25 5 193
-211 189 26 6 194
-212 190 27 7 195
-213 157 191 28 8
-214 158 192 29 9
-215 159 193 30 10
-216 11 160 194 31
-217 12 161 195 32
-218 33 13 157 162
-219 34 14 158 163
-220 35 15 159 164
-221 165 36 16 160
-222 166 37 17 161
-223 167 38 18 162
-224 168 39 19 163
-225 1 169 20 164
-226 165 2 170 21
-227 22 166 3 171
-228 23 167 4 172
-229 24 168 5 173
-230 25 169 6 174
-231 26 170 7 175
-232 176 27 171 8
-233 177 28 172 9
-234 178 29 173 10
0