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