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