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