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