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