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