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