Graph forms
for C4 [ 216, 2 ] = C_216(1,53)
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On this page are computer-accessible forms for the graph C4[ 216, 2 ] =
C_216(1,53).
(I) Following is a form readable by MAGMA:
g:=Graph<216|{ {2, 3}, {214, 215}, {212, 213}, {210, 211}, {208, 209}, {206,
207}, {204, 205}, {202, 203}, {200, 201}, {198, 199}, {196, 197}, {194, 195},
{192, 193}, {190, 191}, {188, 189}, {186, 187}, {184, 185}, {182, 183}, {180,
181}, {178, 179}, {176, 177}, {174, 175}, {172, 173}, {170, 171}, {168, 169},
{166, 167}, {164, 165}, {162, 163}, {160, 161}, {158, 159}, {156, 157}, {154,
155}, {84, 85}, {82, 83}, {80, 81}, {78, 79}, {76, 77}, {74, 75}, {72, 73}, {70,
71}, {68, 69}, {66, 67}, {64, 65}, {62, 63}, {60, 61}, {58, 59}, {56, 57}, {54,
55}, {52, 53}, {50, 51}, {48, 49}, {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}, {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}, {1, 2}, {213, 214}, {209, 210}, {205, 206}, {201, 202}, {197, 198},
{193, 194}, {189, 190}, {185, 186}, {181, 182}, {177, 178}, {173, 174}, {169,
170}, {165, 166}, {161, 162}, {157, 158}, {153, 154}, {81, 82}, {77, 78}, {73,
74}, {69, 70}, {65, 66}, {61, 62}, {57, 58}, {53, 54}, {49, 50}, {5, 6}, {9,
10}, {13, 14}, {17, 18}, {21, 22}, {25, 26}, {29, 30}, {33, 34}, {37, 38}, {41,
42}, {45, 46}, {85, 86}, {89, 90}, {93, 94}, {97, 98}, {101, 102}, {105, 106},
{109, 110}, {113, 114}, {117, 118}, {121, 122}, {125, 126}, {129, 130}, {133,
134}, {137, 138}, {141, 142}, {145, 146}, {149, 150}, {3, 4}, {211, 212}, {203,
204}, {195, 196}, {187, 188}, {179, 180}, {171, 172}, {163, 164}, {155, 156},
{83, 84}, {75, 76}, {67, 68}, {59, 60}, {51, 52}, {11, 12}, {19, 20}, {27, 28},
{35, 36}, {43, 44}, {91, 92}, {99, 100}, {107, 108}, {115, 116}, {123, 124},
{131, 132}, {139, 140}, {147, 148}, {7, 8}, {215, 216}, {199, 200}, {183, 184},
{167, 168}, {71, 72}, {55, 56}, {23, 24}, {39, 40}, {87, 88}, {103, 104}, {119,
120}, {135, 136}, {151, 152}, {15, 16}, {207, 208}, {175, 176}, {79, 80}, {47,
48}, {111, 112}, {143, 144}, {2, 55}, {74, 127}, {72, 125}, {66, 119}, {64,
117}, {8, 61}, {10, 63}, {128, 181}, {130, 183}, {136, 189}, {138, 191}, {1,
54}, {73, 126}, {65, 118}, {9, 62}, {129, 182}, {137, 190}, {3, 56}, {71, 124},
{67, 120}, {7, 60}, {131, 184}, {135, 188}, {4, 57}, {70, 123}, {68, 121}, {6,
59}, {132, 185}, {134, 187}, {5, 58}, {159, 160}, {69, 122}, {31, 32}, {95, 96},
{133, 186}, {11, 64}, {159, 212}, {155, 208}, {63, 116}, {59, 112}, {47, 100},
{15, 68}, {27, 80}, {31, 84}, {43, 96}, {139, 192}, {143, 196}, {12, 65}, {158,
211}, {156, 209}, {62, 115}, {60, 113}, {46, 99}, {14, 67}, {28, 81}, {30, 83},
{44, 97}, {140, 193}, {142, 195}, {13, 66}, {157, 210}, {61, 114}, {29, 82},
{45, 98}, {141, 194}, {16, 69}, {154, 207}, {152, 205}, {58, 111}, {56, 109},
{50, 103}, {48, 101}, {18, 71}, {24, 77}, {26, 79}, {144, 197}, {146, 199}, {17,
70}, {153, 206}, {57, 110}, {49, 102}, {25, 78}, {145, 198}, {19, 72}, {55,
108}, {51, 104}, {23, 76}, {147, 200}, {151, 204}, {20, 73}, {54, 107}, {52,
105}, {22, 75}, {148, 201}, {150, 203}, {21, 74}, {53, 106}, {149, 202}, {32,
85}, {162, 215}, {160, 213}, {34, 87}, {40, 93}, {42, 95}, {33, 86}, {161, 214},
{41, 94}, {35, 88}, {163, 216}, {39, 92}, {36, 89}, {38, 91}, {37, 90}, {191,
192}, {63, 64}, {4, 167}, {8, 171}, {12, 175}, {16, 179}, {20, 183}, {24, 187},
{28, 191}, {1, 164}, {3, 166}, {9, 172}, {11, 174}, {17, 180}, {19, 182}, {25,
188}, {27, 190}, {2, 165}, {10, 173}, {18, 181}, {26, 189}, {5, 168}, {7, 170},
{21, 184}, {23, 186}, {6, 169}, {22, 185}, {13, 176}, {15, 178}, {14, 177}, {75,
128}, {79, 132}, {91, 144}, {95, 148}, {107, 160}, {111, 164}, {123, 176}, {127,
180}, {76, 129}, {78, 131}, {92, 145}, {94, 147}, {108, 161}, {110, 163}, {124,
177}, {126, 179}, {77, 130}, {93, 146}, {109, 162}, {125, 178}, {80, 133}, {82,
135}, {88, 141}, {90, 143}, {112, 165}, {114, 167}, {120, 173}, {122, 175}, {81,
134}, {89, 142}, {113, 166}, {121, 174}, {1, 216}, {83, 136}, {87, 140}, {115,
168}, {119, 172}, {29, 192}, {31, 194}, {84, 137}, {86, 139}, {116, 169}, {118,
171}, {30, 193}, {85, 138}, {117, 170}, {32, 195}, {52, 215}, {48, 211}, {36,
199}, {40, 203}, {44, 207}, {33, 196}, {51, 214}, {49, 212}, {35, 198}, {41,
204}, {43, 206}, {34, 197}, {50, 213}, {42, 205}, {37, 200}, {53, 216}, {39,
202}, {38, 201}, {96, 149}, {98, 151}, {104, 157}, {106, 159}, {97, 150}, {105,
158}, {99, 152}, {103, 156}, {45, 208}, {47, 210}, {100, 153}, {102, 155}, {46,
209}, {101, 154}, {127, 128} }>;
(II) A more general form is to represent the graph as the orbit of {2, 3}
under the group generated by the following permutations:
a: (2, 54)(3, 107)(4, 160)(5, 213)(6, 50)(7, 103)(8, 156)(9, 209)(10, 46)(11,
99)(12, 152)(13, 205)(14, 42)(15, 95)(16, 148)(17, 201)(18, 38)(19, 91)(20,
144)(21, 197)(22, 34)(23, 87)(24, 140)(25, 193)(26, 30)(27, 83)(28, 136)(29,
189)(31, 79)(32, 132)(33, 185)(35, 75)(36, 128)(37, 181)(39, 71)(40, 124)(41,
177)(43, 67)(44, 120)(45, 173)(47, 63)(48, 116)(49, 169)(51, 59)(52, 112)(53,
165)(56, 108)(57, 161)(58, 214)(60, 104)(61, 157)(62, 210)(64, 100)(65, 153)(66,
206)(68, 96)(69, 149)(70, 202)(72, 92)(73, 145)(74, 198)(76, 88)(77, 141)(78,
194)(80, 84)(81, 137)(82, 190)(85, 133)(86, 186)(89, 129)(90, 182)(93, 125)(94,
178)(97, 121)(98, 174)(101, 117)(102, 170)(105, 113)(106, 166)(110, 162)(111,
215)(114, 158)(115, 211)(118, 154)(119, 207)(122, 150)(123, 203)(126, 146)(127,
199)(130, 142)(131, 195)(134, 138)(135, 191)(139, 187)(143, 183)(147, 179)(151,
175)(155, 171)(159, 167)(164, 216)(168, 212)(172, 208)(176, 204)(180, 200)(184,
196)(188, 192) (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, 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)
c: (2, 164)(3, 111)(4, 58)(6, 168)(7, 115)(8, 62)(10, 172)(11, 119)(12, 66)(14,
176)(15, 123)(16, 70)(18, 180)(19, 127)(20, 74)(22, 184)(23, 131)(24, 78)(26,
188)(27, 135)(28, 82)(30, 192)(31, 139)(32, 86)(34, 196)(35, 143)(36, 90)(38,
200)(39, 147)(40, 94)(42, 204)(43, 151)(44, 98)(46, 208)(47, 155)(48, 102)(50,
212)(51, 159)(52, 106)(54, 216)(55, 163)(56, 110)(59, 167)(60, 114)(63, 171)(64,
118)(67, 175)(68, 122)(71, 179)(72, 126)(75, 183)(76, 130)(79, 187)(80, 134)(83,
191)(84, 138)(87, 195)(88, 142)(91, 199)(92, 146)(95, 203)(96, 150)(99,
207)(100, 154)(103, 211)(104, 158)(107, 215)(108, 162)(112, 166)(116, 170)(120,
174)(124, 178)(128, 182)(132, 186)(136, 190)(140, 194)(144, 198)(148, 202)(152,
206)(156, 210)(160, 214)
C4[ 216, 2 ]
216
-1 2 216 54 164
-2 55 165 1 3
-3 56 166 2 4
-4 57 167 3 5
-5 58 168 4 6
-6 59 169 5 7
-7 60 170 6 8
-8 61 171 7 9
-9 62 172 8 10
-10 11 63 173 9
-11 12 64 174 10
-12 11 13 65 175
-13 66 176 12 14
-14 67 177 13 15
-15 68 178 14 16
-16 69 179 15 17
-17 70 180 16 18
-18 71 181 17 19
-19 72 182 18 20
-20 73 183 19 21
-21 22 74 184 20
-22 23 75 185 21
-23 22 24 76 186
-24 77 187 23 25
-25 78 188 24 26
-26 79 189 25 27
-27 80 190 26 28
-28 81 191 27 29
-29 82 192 28 30
-30 83 193 29 31
-31 84 194 30 32
-32 33 85 195 31
-33 34 86 196 32
-34 33 35 87 197
-35 88 198 34 36
-36 89 199 35 37
-37 90 200 36 38
-38 91 201 37 39
-39 92 202 38 40
-40 93 203 39 41
-41 94 204 40 42
-42 95 205 41 43
-43 44 96 206 42
-44 45 97 207 43
-45 44 46 98 208
-46 99 209 45 47
-47 100 210 46 48
-48 101 211 47 49
-49 102 212 48 50
-50 103 213 49 51
-51 104 214 50 52
-52 105 215 51 53
-53 106 216 52 54
-54 55 1 107 53
-55 56 2 108 54
-56 55 57 3 109
-57 110 56 58 4
-58 111 57 59 5
-59 112 58 60 6
-60 113 59 61 7
-61 114 60 62 8
-62 115 61 63 9
-63 116 62 64 10
-64 11 117 63 65
-65 66 12 118 64
-66 67 13 119 65
-67 66 68 14 120
-68 121 67 69 15
-69 122 68 70 16
-70 123 69 71 17
-71 124 70 72 18
-72 125 71 73 19
-73 126 72 74 20
-74 127 73 75 21
-75 22 128 74 76
-76 77 23 129 75
-77 78 24 130 76
-78 77 79 25 131
-79 132 78 80 26
-80 133 79 81 27
-81 134 80 82 28
-82 135 81 83 29
-83 136 82 84 30
-84 137 83 85 31
-85 138 84 86 32
-86 33 139 85 87
-87 88 34 140 86
-88 89 35 141 87
-89 88 90 36 142
-90 143 89 91 37
-91 144 90 92 38
-92 145 91 93 39
-93 146 92 94 40
-94 147 93 95 41
-95 148 94 96 42
-96 149 95 97 43
-97 44 150 96 98
-98 99 45 151 97
-99 100 46 152 98
-100 99 101 47 153
-101 154 100 102 48
-102 155 101 103 49
-103 156 102 104 50
-104 157 103 105 51
-105 158 104 106 52
-106 159 105 107 53
-107 160 106 108 54
-108 55 161 107 109
-109 110 56 162 108
-110 111 57 163 109
-111 110 112 58 164
-112 165 111 113 59
-113 166 112 114 60
-114 167 113 115 61
-115 168 114 116 62
-116 169 115 117 63
-117 170 116 118 64
-118 171 117 119 65
-119 66 172 118 120
-120 121 67 173 119
-121 122 68 174 120
-122 121 123 69 175
-123 176 122 124 70
-124 177 123 125 71
-125 178 124 126 72
-126 179 125 127 73
-127 180 126 128 74
-128 181 127 129 75
-129 182 128 130 76
-130 77 183 129 131
-131 132 78 184 130
-132 133 79 185 131
-133 132 134 80 186
-134 187 133 135 81
-135 188 134 136 82
-136 189 135 137 83
-137 190 136 138 84
-138 191 137 139 85
-139 192 138 140 86
-140 193 139 141 87
-141 88 194 140 142
-142 143 89 195 141
-143 144 90 196 142
-144 143 145 91 197
-145 198 144 146 92
-146 199 145 147 93
-147 200 146 148 94
-148 201 147 149 95
-149 202 148 150 96
-150 203 149 151 97
-151 204 150 152 98
-152 99 205 151 153
-153 154 100 206 152
-154 155 101 207 153
-155 154 156 102 208
-156 209 155 157 103
-157 210 156 158 104
-158 211 157 159 105
-159 212 158 160 106
-160 213 159 161 107
-161 214 160 162 108
-162 215 161 163 109
-163 110 216 162 164
-164 165 1 111 163
-165 166 2 112 164
-166 165 167 3 113
-167 166 168 4 114
-168 167 169 5 115
-169 168 170 6 116
-170 169 171 7 117
-171 170 172 8 118
-172 171 173 9 119
-173 172 174 10 120
-174 11 121 173 175
-175 176 12 122 174
-176 177 13 123 175
-177 176 178 14 124
-178 177 179 15 125
-179 178 180 16 126
-180 179 181 17 127
-181 180 182 18 128
-182 181 183 19 129
-183 182 184 20 130
-184 183 185 21 131
-185 22 132 184 186
-186 187 23 133 185
-187 188 24 134 186
-188 187 189 25 135
-189 188 190 26 136
-190 189 191 27 137
-191 190 192 28 138
-192 191 193 29 139
-193 192 194 30 140
-194 193 195 31 141
-195 194 196 32 142
-196 33 143 195 197
-197 198 34 144 196
-198 199 35 145 197
-199 198 200 36 146
-200 199 201 37 147
-201 200 202 38 148
-202 201 203 39 149
-203 202 204 40 150
-204 203 205 41 151
-205 204 206 42 152
-206 205 207 43 153
-207 44 154 206 208
-208 209 45 155 207
-209 210 46 156 208
-210 209 211 47 157
-211 210 212 48 158
-212 211 213 49 159
-213 212 214 50 160
-214 213 215 51 161
-215 214 216 52 162
-216 1 215 53 163
0