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