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