Graph forms
for C4 [ 240, 64 ] = PL(Br(24,5;2))
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On this page are computer-accessible forms for the graph C4[ 240, 64 ] =
PL(Br(24,5;2)).
(I) Following is a form readable by MAGMA:
g:=Graph<240|{ {117, 121}, {116, 121}, {32, 127}, {31, 127}, {26, 126}, {27,
127}, {26, 127}, {27, 126}, {21, 125}, {22, 126}, {21, 126}, {22, 125}, {16,
124}, {17, 125}, {16, 125}, {17, 124}, {11, 123}, {12, 124}, {11, 124}, {12,
123}, {1, 121}, {2, 122}, {1, 122}, {2, 121}, {6, 122}, {7, 123}, {6, 123}, {7,
122}, {52, 180}, {80, 208}, {81, 209}, {110, 238}, {53, 180}, {113, 240}, {80,
209}, {110, 239}, {48, 178}, {114, 240}, {49, 179}, {48, 179}, {49, 178}, {81,
210}, {17, 149}, {116, 240}, {75, 207}, {85, 209}, {106, 238}, {17, 148}, {104,
237}, {106, 239}, {18, 148}, {53, 179}, {104, 238}, {18, 149}, {52, 179}, {85,
210}, {62, 182}, {120, 240}, {71, 207}, {70, 206}, {90, 210}, {91, 211}, {100,
236}, {63, 182}, {70, 207}, {90, 211}, {100, 237}, {103, 238}, {28, 150}, {69,
207}, {63, 181}, {89, 211}, {103, 237}, {28, 151}, {69, 206}, {62, 181}, {89,
210}, {95, 212}, {25, 149}, {65, 205}, {27, 151}, {95, 211}, {96, 236}, {24,
149}, {27, 150}, {96, 237}, {24, 150}, {59, 181}, {58, 180}, {33, 175}, {25,
150}, {65, 206}, {59, 180}, {58, 181}, {32, 175}, {91, 212}, {32, 176}, {33,
176}, {5, 145}, {7, 147}, {4, 145}, {7, 146}, {4, 146}, {38, 176}, {39, 177},
{5, 146}, {71, 208}, {38, 177}, {39, 176}, {42, 178}, {43, 178}, {8, 146}, {14,
148}, {43, 177}, {8, 147}, {75, 208}, {15, 148}, {42, 177}, {15, 147}, {14,
147}, {114, 239}, {79, 209}, {113, 239}, {31, 128}, {79, 208}, {12, 172}, {120,
216}, {70, 230}, {32, 128}, {13, 172}, {120, 217}, {73, 232}, {70, 231}, {8,
170}, {74, 232}, {9, 171}, {8, 171}, {9, 170}, {36, 128}, {115, 215}, {76, 232},
{66, 230}, {57, 157}, {37, 129}, {36, 129}, {66, 231}, {64, 229}, {57, 156},
{37, 128}, {76, 233}, {13, 171}, {64, 230}, {58, 156}, {12, 171}, {58, 157}, {2,
170}, {41, 129}, {42, 130}, {3, 170}, {3, 169}, {48, 154}, {54, 156}, {2, 169},
{115, 216}, {55, 156}, {41, 130}, {42, 129}, {48, 155}, {46, 130}, {55, 155},
{47, 131}, {46, 131}, {116, 217}, {74, 231}, {47, 130}, {54, 155}, {73, 231},
{119, 216}, {51, 131}, {112, 192}, {52, 132}, {90, 234}, {100, 212}, {101, 213},
{90, 235}, {113, 192}, {93, 236}, {100, 213}, {28, 174}, {29, 175}, {94, 236},
{28, 175}, {29, 174}, {101, 214}, {35, 151}, {45, 153}, {47, 155}, {34, 151},
{44, 153}, {47, 154}, {94, 235}, {44, 154}, {119, 193}, {118, 192}, {93, 235},
{99, 213}, {45, 154}, {119, 192}, {51, 132}, {52, 131}, {99, 212}, {111, 216},
{22, 174}, {62, 134}, {61, 133}, {80, 232}, {110, 214}, {111, 215}, {23, 174},
{120, 193}, {80, 233}, {83, 234}, {110, 215}, {23, 173}, {34, 152}, {83, 233},
{109, 215}, {22, 173}, {62, 133}, {61, 134}, {35, 152}, {109, 214}, {37, 153},
{57, 133}, {56, 132}, {86, 234}, {105, 213}, {37, 152}, {57, 132}, {56, 133},
{84, 233}, {86, 235}, {18, 172}, {19, 173}, {38, 152}, {84, 234}, {18, 173},
{19, 172}, {38, 153}, {105, 214}, {1, 193}, {72, 136}, {71, 135}, {30, 222},
{30, 223}, {33, 224}, {34, 224}, {1, 194}, {5, 193}, {76, 136}, {67, 135}, {66,
134}, {26, 222}, {36, 224}, {77, 137}, {97, 165}, {24, 221}, {76, 137}, {67,
134}, {66, 135}, {26, 223}, {36, 225}, {77, 136}, {97, 164}, {24, 222}, {98,
164}, {5, 194}, {98, 165}, {10, 194}, {11, 195}, {20, 220}, {40, 224}, {10,
195}, {20, 221}, {23, 222}, {40, 225}, {43, 226}, {9, 195}, {23, 221}, {43,
225}, {108, 166}, {9, 194}, {15, 196}, {108, 167}, {15, 195}, {16, 220}, {46,
226}, {105, 165}, {107, 167}, {16, 221}, {44, 225}, {46, 227}, {104, 165}, {107,
166}, {44, 226}, {113, 191}, {104, 166}, {11, 196}, {72, 135}, {71, 136}, {105,
166}, {112, 191}, {10, 218}, {20, 196}, {21, 197}, {50, 226}, {91, 139}, {92,
140}, {10, 219}, {13, 220}, {20, 197}, {50, 227}, {53, 228}, {14, 220}, {54,
228}, {108, 190}, {109, 191}, {21, 198}, {108, 191}, {109, 190}, {75, 159},
{115, 167}, {14, 219}, {114, 167}, {74, 159}, {54, 227}, {13, 219}, {19, 197},
{53, 227}, {19, 196}, {31, 200}, {91, 140}, {92, 139}, {30, 198}, {60, 228},
{31, 199}, {81, 137}, {82, 138}, {102, 190}, {3, 218}, {63, 230}, {60, 229},
{30, 199}, {103, 190}, {3, 217}, {114, 168}, {68, 158}, {63, 229}, {29, 199},
{103, 189}, {29, 198}, {115, 168}, {68, 159}, {81, 138}, {82, 137}, {102, 189},
{6, 218}, {67, 159}, {65, 157}, {56, 228}, {25, 197}, {86, 138}, {87, 139}, {4,
217}, {117, 168}, {67, 158}, {64, 157}, {56, 229}, {6, 219}, {86, 139}, {87,
138}, {4, 218}, {119, 169}, {118, 168}, {64, 158}, {98, 188}, {99, 189}, {25,
198}, {118, 169}, {65, 158}, {98, 189}, {99, 188}, {40, 200}, {41, 201}, {92,
188}, {111, 143}, {112, 144}, {40, 201}, {93, 188}, {88, 186}, {89, 187}, {41,
202}, {88, 187}, {89, 186}, {35, 199}, {117, 145}, {116, 144}, {45, 201}, {106,
142}, {107, 143}, {106, 143}, {117, 144}, {107, 142}, {93, 187}, {45, 202},
{118, 145}, {92, 187}, {82, 186}, {101, 141}, {102, 142}, {83, 186}, {74, 160},
{83, 185}, {35, 200}, {75, 160}, {82, 185}, {101, 142}, {102, 141}, {77, 161},
{96, 140}, {97, 141}, {77, 160}, {96, 141}, {97, 140}, {39, 201}, {78, 160},
{39, 200}, {78, 161}, {60, 204}, {72, 184}, {61, 205}, {60, 205}, {73, 184},
{68, 182}, {69, 183}, {61, 206}, {69, 182}, {68, 183}, {85, 161}, {87, 163},
{84, 161}, {87, 162}, {59, 205}, {78, 184}, {79, 185}, {84, 162}, {59, 204},
{78, 185}, {79, 184}, {85, 162}, {50, 202}, {51, 203}, {50, 203}, {49, 203},
{88, 162}, {94, 164}, {49, 202}, {55, 204}, {88, 163}, {95, 164}, {55, 203},
{95, 163}, {34, 223}, {94, 163}, {33, 223}, {73, 183}, {51, 204}, {72, 183},
{111, 144}, {112, 143} }>;
(II) A more general form is to represent the graph as the orbit of {117, 121}
under the group generated by the following permutations:
a: (1, 2, 3, 4, 5)(6, 8, 10, 7, 9)(11, 12, 13, 14, 15)(16, 18, 20, 17, 19)(21,
22, 23, 24, 25)(26, 28, 30, 27, 29)(31, 32, 33, 34, 35)(36, 38, 40, 37, 39)(41,
42, 43, 44, 45)(46, 48, 50, 47, 49)(51, 52, 53, 54, 55)(56, 58, 60, 57, 59)(61,
62, 63, 64, 65)(66, 68, 70, 67, 69)(71, 72, 73, 74, 75)(76, 78, 80, 77, 79)(81,
82, 83, 84, 85)(86, 88, 90, 87, 89)(91, 92, 93, 94, 95)(96, 98, 100, 97,
99)(101, 102, 103, 104, 105)(106, 108, 110, 107, 109)(111, 112, 113, 114,
115)(116, 118, 120, 117, 119)(121, 169, 217, 145, 193)(122, 170, 218, 146,
194)(123, 171, 219, 147, 195)(124, 172, 220, 148, 196)(125, 173, 221, 149,
197)(126, 174, 222, 150, 198)(127, 175, 223, 151, 199)(128, 176, 224, 152,
200)(129, 177, 225, 153, 201)(130, 178, 226, 154, 202)(131, 179, 227, 155,
203)(132, 180, 228, 156, 204)(133, 181, 229, 157, 205)(134, 182, 230, 158,
206)(135, 183, 231, 159, 207)(136, 184, 232, 160, 208)(137, 185, 233, 161,
209)(138, 186, 234, 162, 210)(139, 187, 235, 163, 211)(140, 188, 236, 164,
212)(141, 189, 237, 165, 213)(142, 190, 238, 166, 214)(143, 191, 239, 167,
215)(144, 192, 240, 168, 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, 5)(3, 4)(6, 10)(7, 9)(12, 15)(13, 14)(16, 20)(17, 19)(22, 25)(23, 24)(26,
30)(27, 29)(32, 35)(33, 34)(36, 40)(37, 39)(42, 45)(43, 44)(46, 50)(47, 49)(52,
55)(53, 54)(56, 60)(57, 59)(62, 65)(63, 64)(66, 70)(67, 69)(72, 75)(73, 74)(76,
80)(77, 79)(82, 85)(83, 84)(86, 90)(87, 89)(92, 95)(93, 94)(96, 100)(97,
99)(102, 105)(103, 104)(106, 110)(107, 109)(112, 115)(113, 114)(116, 120)(117,
119)(121, 193)(122, 194)(123, 195)(124, 196)(125, 197)(126, 198)(127, 199)(128,
200)(129, 201)(130, 202)(131, 203)(132, 204)(133, 205)(134, 206)(135, 207)(136,
208)(137, 209)(138, 210)(139, 211)(140, 212)(141, 213)(142, 214)(143, 215)(144,
216)(145, 169)(146, 170)(147, 171)(148, 172)(149, 173)(150, 174)(151, 175)(152,
176)(153, 177)(154, 178)(155, 179)(156, 180)(157, 181)(158, 182)(159, 183)(160,
184)(161, 185)(162, 186)(163, 187)(164, 188)(165, 189)(166, 190)(167, 191)(168,
192)
c: (6, 116)(7, 117)(8, 118)(9, 119)(10, 120)(11, 111)(12, 112)(13, 113)(14,
114)(15, 115)(16, 106)(17, 107)(18, 108)(19, 109)(20, 110)(21, 101)(22, 102)(23,
103)(24, 104)(25, 105)(26, 96)(27, 97)(28, 98)(29, 99)(30, 100)(31, 91)(32,
92)(33, 93)(34, 94)(35, 95)(36, 86)(37, 87)(38, 88)(39, 89)(40, 90)(41, 81)(42,
82)(43, 83)(44, 84)(45, 85)(46, 76)(47, 77)(48, 78)(49, 79)(50, 80)(51, 71)(52,
72)(53, 73)(54, 74)(55, 75)(56, 66)(57, 67)(58, 68)(59, 69)(60, 70)(121,
122)(123, 144)(124, 143)(125, 142)(126, 141)(127, 140)(128, 139)(129, 138)(130,
137)(131, 136)(132, 135)(133, 134)(145, 146)(147, 168)(148, 167)(149, 166)(150,
165)(151, 164)(152, 163)(153, 162)(154, 161)(155, 160)(156, 159)(157, 158)(169,
170)(171, 192)(172, 191)(173, 190)(174, 189)(175, 188)(176, 187)(177, 186)(178,
185)(179, 184)(180, 183)(181, 182)(193, 194)(195, 216)(196, 215)(197, 214)(198,
213)(199, 212)(200, 211)(201, 210)(202, 209)(203, 208)(204, 207)(205, 206)(217,
218)(219, 240)(220, 239)(221, 238)(222, 237)(223, 236)(224, 235)(225, 234)(226,
233)(227, 232)(228, 231)(229, 230)
d: (1, 6, 13, 19, 21, 26, 33, 39, 41, 46, 53, 59, 61, 66, 73, 79, 81, 86, 93,
99, 101, 106, 113, 119)(2, 10, 12, 20, 22, 30, 32, 40, 42, 50, 52, 60, 62, 70,
72, 80, 82, 90, 92, 100, 102, 110, 112, 120)(3, 9, 11, 16, 23, 29, 31, 36, 43,
49, 51, 56, 63, 69, 71, 76, 83, 89, 91, 96, 103, 109, 111, 116)(4, 8, 15, 17,
24, 28, 35, 37, 44, 48, 55, 57, 64, 68, 75, 77, 84, 88, 95, 97, 104, 108, 115,
117)(5, 7, 14, 18, 25, 27, 34, 38, 45, 47, 54, 58, 65, 67, 74, 78, 85, 87, 94,
98, 105, 107, 114, 118)(121, 218, 171, 196, 125, 222, 175, 200, 129, 226, 179,
204, 133, 230, 183, 208, 137, 234, 187, 212, 141, 238, 191, 216)(122, 219, 172,
197, 126, 223, 176, 201, 130, 227, 180, 205, 134, 231, 184, 209, 138, 235, 188,
213, 142, 239, 192, 193)(123, 220, 173, 198, 127, 224, 177, 202, 131, 228, 181,
206, 135, 232, 185, 210, 139, 236, 189, 214, 143, 240, 169, 194)(124, 221, 174,
199, 128, 225, 178, 203, 132, 229, 182, 207, 136, 233, 186, 211, 140, 237, 190,
215, 144, 217, 170, 195)(145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155,
156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168)
C4[ 240, 64 ]
240
-1 121 122 193 194
-2 121 122 169 170
-3 169 170 217 218
-4 145 146 217 218
-5 145 146 193 194
-6 122 123 218 219
-7 122 123 146 147
-8 146 147 170 171
-9 170 171 194 195
-10 194 195 218 219
-11 123 124 195 196
-12 123 124 171 172
-13 220 171 172 219
-14 220 147 148 219
-15 147 148 195 196
-16 220 221 124 125
-17 124 125 148 149
-18 148 149 172 173
-19 172 173 196 197
-20 220 221 196 197
-21 198 125 126 197
-22 125 126 173 174
-23 221 222 173 174
-24 221 222 149 150
-25 198 149 150 197
-26 222 223 126 127
-27 126 127 150 151
-28 150 151 174 175
-29 198 199 174 175
-30 198 199 222 223
-31 199 200 127 128
-32 176 127 128 175
-33 176 223 224 175
-34 223 224 151 152
-35 199 200 151 152
-36 224 225 128 129
-37 128 129 152 153
-38 176 177 152 153
-39 176 177 200 201
-40 200 201 224 225
-41 201 202 129 130
-42 177 178 129 130
-43 177 178 225 226
-44 154 225 226 153
-45 154 201 202 153
-46 226 227 130 131
-47 154 155 130 131
-48 154 155 178 179
-49 178 179 202 203
-50 202 203 226 227
-51 132 203 204 131
-52 132 179 180 131
-53 179 180 227 228
-54 155 156 227 228
-55 155 156 203 204
-56 132 133 228 229
-57 132 133 156 157
-58 156 157 180 181
-59 180 181 204 205
-60 204 205 228 229
-61 133 134 205 206
-62 133 134 181 182
-63 181 182 229 230
-64 157 158 229 230
-65 157 158 205 206
-66 231 134 135 230
-67 134 135 158 159
-68 158 159 182 183
-69 182 183 206 207
-70 231 206 207 230
-71 135 136 207 208
-72 135 136 183 184
-73 231 232 183 184
-74 231 232 159 160
-75 159 160 207 208
-76 232 233 136 137
-77 136 137 160 161
-78 160 161 184 185
-79 209 184 185 208
-80 209 232 233 208
-81 209 210 137 138
-82 137 138 185 186
-83 233 234 185 186
-84 233 234 161 162
-85 209 210 161 162
-86 234 235 138 139
-87 138 139 162 163
-88 187 162 163 186
-89 187 210 211 186
-90 210 211 234 235
-91 211 212 139 140
-92 187 188 139 140
-93 187 188 235 236
-94 235 236 163 164
-95 211 212 163 164
-96 236 237 140 141
-97 165 140 141 164
-98 165 188 189 164
-99 188 189 212 213
-100 212 213 236 237
-101 213 214 141 142
-102 189 190 141 142
-103 189 190 237 238
-104 165 166 237 238
-105 165 166 213 214
-106 143 238 239 142
-107 143 166 167 142
-108 166 167 190 191
-109 190 191 214 215
-110 214 215 238 239
-111 143 144 215 216
-112 143 144 191 192
-113 191 192 239 240
-114 167 168 239 240
-115 167 168 215 216
-116 121 144 217 240
-117 121 144 145 168
-118 145 168 169 192
-119 169 192 193 216
-120 193 216 217 240
-121 1 2 116 117
-122 1 2 6 7
-123 11 12 6 7
-124 11 12 16 17
-125 22 16 17 21
-126 22 26 27 21
-127 26 27 31 32
-128 36 37 31 32
-129 36 37 41 42
-130 46 47 41 42
-131 46 47 51 52
-132 56 57 51 52
-133 56 57 61 62
-134 66 67 61 62
-135 66 67 71 72
-136 77 71 72 76
-137 77 81 82 76
-138 81 82 86 87
-139 91 92 86 87
-140 91 92 96 97
-141 101 102 96 97
-142 101 102 106 107
-143 111 112 106 107
-144 111 112 116 117
-145 4 5 117 118
-146 4 5 7 8
-147 14 15 7 8
-148 14 15 17 18
-149 24 25 17 18
-150 24 25 27 28
-151 34 35 27 28
-152 34 35 37 38
-153 44 45 37 38
-154 44 45 47 48
-155 55 47 48 54
-156 55 57 58 54
-157 57 58 64 65
-158 67 68 64 65
-159 67 68 74 75
-160 77 78 74 75
-161 77 78 84 85
-162 88 84 85 87
-163 88 94 95 87
-164 94 95 97 98
-165 104 105 97 98
-166 104 105 107 108
-167 114 115 107 108
-168 114 115 117 118
-169 2 3 118 119
-170 2 3 8 9
-171 12 13 8 9
-172 12 13 18 19
-173 22 23 18 19
-174 22 23 28 29
-175 33 28 29 32
-176 33 38 39 32
-177 38 39 42 43
-178 48 49 42 43
-179 48 49 52 53
-180 58 59 52 53
-181 58 59 62 63
-182 68 69 62 63
-183 68 69 72 73
-184 78 79 72 73
-185 78 79 82 83
-186 88 89 82 83
-187 88 89 92 93
-188 99 92 93 98
-189 99 102 103 98
-190 102 103 108 109
-191 112 113 108 109
-192 112 113 118 119
-193 1 5 119 120
-194 1 5 9 10
-195 11 15 9 10
-196 11 15 19 20
-197 25 19 20 21
-198 25 29 30 21
-199 35 29 30 31
-200 35 39 40 31
-201 45 39 40 41
-202 45 49 50 41
-203 55 49 50 51
-204 55 59 60 51
-205 59 60 61 65
-206 69 70 61 65
-207 69 70 71 75
-208 79 80 71 75
-209 79 80 81 85
-210 89 90 81 85
-211 89 90 91 95
-212 99 100 91 95
-213 99 100 101 105
-214 110 101 105 109
-215 110 111 115 109
-216 111 115 119 120
-217 3 4 116 120
-218 3 4 6 10
-219 13 14 6 10
-220 13 14 16 20
-221 23 24 16 20
-222 23 24 26 30
-223 33 34 26 30
-224 33 34 36 40
-225 44 36 40 43
-226 44 46 50 43
-227 46 50 53 54
-228 56 60 53 54
-229 56 60 63 64
-230 66 70 63 64
-231 66 70 73 74
-232 80 73 74 76
-233 80 83 84 76
-234 90 83 84 86
-235 90 93 94 86
-236 100 93 94 96
-237 100 103 104 96
-238 110 103 104 106
-239 110 113 114 106
-240 113 114 116 120
0