Graph forms
for C4 [ 240, 97 ] = UG(ATD[240,159])
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On this page are computer-accessible forms for the graph C4[ 240, 97 ] =
UG(ATD[240,159]).
(I) Following is a form readable by MAGMA:
g:=Graph<240|{ {64, 66}, {185, 189}, {74, 79}, {128, 133}, {1, 6}, {75, 76},
{17, 22}, {16, 23}, {105, 110}, {2, 10}, {182, 190}, {165, 173}, {5, 12}, {231,
238}, {162, 171}, {119, 126}, {1, 11}, {211, 217}, {135, 141}, {37, 47}, {82,
88}, {193, 202}, {194, 201}, {103, 107}, {214, 219}, {85, 90}, {112, 127}, {1,
16}, {6, 21}, {98, 113}, {11, 31}, {203, 223}, {193, 213}, {72, 92}, {36, 48},
{100, 114}, {134, 144}, {3, 20}, {205, 218}, {204, 219}, {195, 212}, {99, 116},
{160, 184}, {132, 157}, {71, 93}, {1, 26}, {235, 240}, {97, 122}, {100, 120},
{96, 125}, {175, 178}, {174, 179}, {131, 158}, {7, 25}, {4, 27}, {8, 40}, {202,
234}, {200, 232}, {30, 62}, {13, 45}, {8, 41}, {74, 107}, {6, 36}, {11, 41},
{92, 126}, {203, 232}, {22, 50}, {73, 109}, {68, 97}, {26, 60}, {145, 183}, {69,
99}, {29, 59}, {26, 61}, {159, 181}, {29, 54}, {137, 162}, {136, 163}, {77, 97},
{7, 42}, {205, 224}, {30, 51}, {76, 98}, {199, 233}, {15, 32}, {212, 228}, {12,
62}, {77, 127}, {11, 56}, {214, 229}, {130, 182}, {6, 51}, {213, 224}, {19, 37},
{149, 163}, {133, 179}, {129, 183}, {14, 57}, {214, 225}, {147, 164}, {143,
184}, {134, 177}, {12, 52}, {91, 99}, {20, 45}, {70, 127}, {134, 188}, {14, 53},
{138, 177}, {65, 122}, {27, 32}, {21, 46}, {20, 40}, {136, 180}, {66, 126}, {9,
52}, {210, 239}, {17, 44}, {88, 101}, {28, 34}, {208, 238}, {86, 105}, {132,
187}, {93, 98}, {9, 72}, {59, 122}, {10, 75}, {140, 206}, {178, 240}, {17, 82},
{153, 218}, {18, 81}, {42, 110}, {148, 208}, {61, 121}, {154, 223}, {25, 95},
{154, 220}, {58, 124}, {44, 106}, {23, 80}, {150, 209}, {130, 197}, {165, 237},
{170, 226}, {28, 85}, {173, 228}, {63, 118}, {60, 117}, {59, 114}, {31, 86},
{62, 116}, {170, 224}, {164, 238}, {151, 221}, {26, 81}, {133, 206}, {56, 115},
{47, 100}, {23, 91}, {174, 226}, {169, 229}, {56, 116}, {13, 64}, {46, 96},
{156, 204}, {185, 233}, {189, 236}, {34, 112}, {181, 231}, {7, 84}, {132, 208},
{186, 238}, {2, 87}, {32, 117}, {3, 86}, {33, 119}, {183, 225}, {157, 203}, {16,
71}, {18, 75}, {21, 76}, {33, 123}, {159, 197}, {144, 202}, {34, 121}, {156,
199}, {153, 194}, {152, 195}, {138, 209}, {54, 109}, {145, 205}, {176, 236},
{31, 66}, {55, 106}, {10, 85}, {35, 67}, {55, 87}, {173, 207}, {142, 237}, {184,
219}, {164, 199}, {143, 236}, {63, 90}, {14, 104}, {162, 196}, {4, 108}, {2,
107}, {15, 101}, {61, 87}, {51, 89}, {39, 77}, {181, 222}, {133, 235}, {182,
216}, {135, 232}, {31, 111}, {188, 204}, {168, 216}, {158, 239}, {148, 230},
{159, 237}, {24, 107}, {169, 218}, {42, 89}, {16, 101}, {19, 102}, {45, 90},
{190, 201}, {183, 192}, {179, 196}, {147, 228}, {40, 80}, {185, 193}, {154,
226}, {167, 222}, {189, 196}, {29, 103}, {188, 198}, {57, 67}, {33, 90}, {63,
68}, {180, 200}, {27, 102}, {152, 230}, {21, 106}, {175, 208}, {58, 69}, {49,
177}, {78, 206}, {83, 211}, {88, 216}, {57, 184}, {71, 197}, {77, 207}, {22,
149}, {35, 166}, {70, 195}, {60, 185}, {82, 212}, {89, 222}, {38, 174}, {61,
181}, {109, 229}, {5, 140}, {65, 203}, {108, 230}, {34, 169}, {49, 186}, {44,
167}, {39, 172}, {86, 221}, {50, 190}, {93, 209}, {4, 137}, {87, 217}, {97,
239}, {25, 150}, {73, 198}, {41, 166}, {49, 161}, {123, 235}, {94, 207}, {50,
160}, {48, 163}, {59, 168}, {116, 231}, {122, 233}, {100, 240}, {119, 225}, {2,
154}, {55, 175}, {88, 192}, {115, 235}, {53, 172}, {112, 234}, {70, 221}, {24,
132}, {52, 168}, {55, 170}, {5, 155}, {57, 167}, {46, 176}, {25, 135}, {119,
232}, {38, 135}, {58, 155}, {51, 146}, {48, 145}, {41, 136}, {120, 217}, {19,
176}, {53, 150}, {46, 141}, {63, 155}, {125, 217}, {78, 234}, {106, 206}, {17,
180}, {69, 224}, {99, 198}, {120, 221}, {73, 239}, {124, 218}, {36, 131}, {75,
236}, {43, 140}, {5, 173}, {36, 140}, {96, 200}, {8, 161}, {96, 201}, {118,
220}, {39, 139}, {48, 156}, {113, 220}, {114, 223}, {112, 222}, {3, 172}, {56,
151}, {47, 128}, {10, 165}, {98, 205}, {49, 129}, {14, 191}, {115, 194}, {42,
152}, {24, 172}, {38, 146}, {95, 234}, {7, 177}, {37, 147}, {111, 216}, {43,
147}, {80, 233}, {94, 231}, {126, 196}, {9, 178}, {45, 150}, {123, 192}, {23,
171}, {54, 138}, {43, 151}, {108, 210}, {125, 195}, {52, 139}, {85, 149}, {93,
157}, {105, 169}, {74, 139}, {79, 142}, {80, 145}, {102, 167}, {105, 171}, {27,
223}, {20, 210}, {104, 174}, {83, 148}, {115, 187}, {83, 153}, {110, 164}, {118,
188}, {38, 237}, {72, 131}, {91, 144}, {13, 193}, {74, 134}, {67, 142}, {79,
130}, {108, 161}, {71, 137}, {113, 191}, {84, 155}, {117, 186}, {22, 198}, {114,
160}, {4, 215}, {15, 220}, {92, 143}, {3, 214}, {111, 186}, {70, 144}, {12,
219}, {40, 240}, {65, 152}, {69, 159}, {83, 137}, {73, 146}, {81, 138}, {72,
148}, {18, 207}, {29, 192}, {28, 194}, {109, 179}, {110, 176}, {24, 199}, {66,
157}, {94, 129}, {37, 197}, {50, 210}, {104, 136}, {124, 158}, {54, 213}, {121,
156}, {53, 211}, {89, 191}, {65, 166}, {91, 178}, {8, 226}, {64, 170}, {32,
202}, {9, 227}, {94, 180}, {15, 228}, {78, 162}, {58, 215}, {102, 139}, {13,
227}, {79, 161}, {35, 204}, {60, 211}, {39, 200}, {19, 227}, {78, 190}, {103,
151}, {113, 129}, {104, 153}, {124, 141}, {111, 158}, {103, 149}, {123, 142},
{33, 215}, {64, 182}, {118, 128}, {18, 229}, {62, 201}, {35, 212}, {76, 187},
{81, 166}, {101, 146}, {120, 143}, {30, 230}, {67, 187}, {117, 141}, {68, 189},
{121, 128}, {95, 165}, {44, 215}, {68, 191}, {84, 168}, {127, 131}, {82, 175},
{43, 213}, {47, 209}, {28, 227}, {125, 130}, {30, 225}, {84, 171}, {92, 163},
{95, 160} }>;
(II) A more general form is to represent the graph as the orbit of {64, 66}
under the group generated by the following permutations:
a: (1, 6, 21, 46, 96, 125, 195, 212, 228, 173, 165, 95, 160, 114, 59, 29, 54,
109, 179, 196, 126, 66, 31, 11)(2, 7, 22, 47, 97, 123, 193, 214, 226, 171, 163,
93, 158, 115, 60, 30, 55, 110, 180, 197, 127, 67, 32, 12)(3, 8, 23, 48, 98, 124,
194, 211, 230, 175, 164, 94, 159, 112, 57, 27, 52, 107, 177, 198, 128, 68, 33,
13)(4, 9, 24, 49, 99, 121, 191, 215, 227, 172, 161, 91, 156, 113, 58, 28, 53,
108, 178, 199, 129, 69, 34, 14)(5, 10, 25, 50, 100, 122, 192, 213, 229, 174,
162, 92, 157, 111, 56, 26, 51, 106, 176, 200, 130, 70, 35, 15)(16, 36, 76, 141,
201, 217, 152, 82, 147, 207, 237, 234, 184, 223, 168, 103, 138, 73, 133, 189,
119, 64, 86, 41)(17, 37, 77, 142, 202, 219, 154, 84, 149, 209, 239, 235, 185,
225, 170, 105, 136, 71, 131, 187, 117, 62, 87, 42)(18, 38, 78, 143, 203, 216,
151, 81, 146, 206, 236, 232, 182, 221, 166, 101, 140, 75, 135, 190, 120, 65, 88,
43)(19, 39, 79, 144, 204, 220, 155, 85, 150, 210, 240, 233, 183, 224, 169, 104,
137, 72, 132, 186, 116, 61, 89, 44)(20, 40, 80, 145, 205, 218, 153, 83, 148,
208, 238, 231, 181, 222, 167, 102, 139, 74, 134, 188, 118, 63, 90, 45) (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, 4, 3, 5)(6, 26, 16, 11)(7, 29, 17, 14)(8, 30, 18, 15)(9, 28, 19, 13)(10,
27, 20, 12)(21, 60, 23, 56)(22, 57, 25, 59)(24, 58)(31, 36, 61, 71)(32, 40, 62,
75)(33, 39, 63, 74)(34, 37, 64, 72)(35, 38, 65, 73)(41, 51, 81, 101)(42, 54, 82,
104)(43, 55, 83, 105)(44, 53, 84, 103)(45, 52, 85, 102)(46, 185, 91, 115)(47,
182, 92, 112)(48, 181, 93, 111)(49, 183, 94, 113)(50, 184, 95, 114)(66, 131,
121, 197)(67, 135, 122, 198)(68, 134, 123, 200)(69, 132, 124, 199)(70, 133, 125,
196)(76, 117, 80, 116)(77, 118, 79, 119)(78, 120)(86, 140, 87, 137)(88, 136, 89,
138)(90, 139)(96, 189, 144, 235)(97, 188, 142, 232)(98, 186, 145, 231)(99, 187,
141, 233)(100, 190, 143, 234)(106, 211, 171, 151)(107, 215, 172, 155)(108, 214,
173, 154)(109, 212, 174, 152)(110, 213, 175, 153)(126, 127, 128, 130)(146,
166)(147, 170, 148, 169)(149, 167, 150, 168)(156, 159, 157, 158)(161, 225, 207,
220)(162, 221, 206, 217)(163, 222, 209, 216)(164, 224, 208, 218)(165, 223, 210,
219)(176, 193, 178, 194)(177, 192, 180, 191)(179, 195)(201, 236, 202, 240)(203,
239, 204, 237)(205, 238)(226, 230, 229, 228)
c: (2, 3)(4, 5)(6, 16)(7, 17)(8, 18)(9, 19)(10, 20)(11, 26)(12, 27)(13, 28)(14,
29)(15, 30)(21, 23)(22, 25)(31, 61)(32, 62)(33, 63)(34, 64)(35, 65)(36, 71)(37,
72)(38, 73)(39, 74)(40, 75)(41, 81)(42, 82)(43, 83)(44, 84)(45, 85)(46, 91)(47,
92)(48, 93)(49, 94)(50, 95)(51, 101)(52, 102)(53, 103)(54, 104)(55, 105)(56,
60)(57, 59)(66, 121)(67, 122)(68, 123)(69, 124)(70, 125)(76, 80)(77, 79)(86,
87)(88, 89)(96, 144)(97, 142)(98, 145)(99, 141)(100, 143)(106, 171)(107,
172)(108, 173)(109, 174)(110, 175)(111, 181)(112, 182)(113, 183)(114, 184)(115,
185)(116, 117)(118, 119)(126, 128)(127, 130)(131, 197)(132, 199)(133, 196)(134,
200)(135, 198)(136, 138)(137, 140)(147, 148)(149, 150)(151, 211)(152, 212)(153,
213)(154, 214)(155, 215)(156, 157)(158, 159)(161, 207)(162, 206)(163, 209)(164,
208)(165, 210)(167, 168)(169, 170)(176, 178)(177, 180)(186, 231)(187, 233)(188,
232)(189, 235)(190, 234)(191, 192)(193, 194)(201, 202)(203, 204)(216, 222)(217,
221)(218, 224)(219, 223)(220, 225)(226, 229)(228, 230)(236, 240)(237, 239)
d: (1, 2, 229, 227, 42, 44)(3, 52, 230, 82, 41, 103)(4, 101, 226, 54, 45, 84)(5,
83, 228, 104, 43, 53)(6, 87, 18, 28, 110, 167)(7, 215, 16, 154, 109, 13)(8, 29,
20, 168, 108, 88)(9, 152, 17, 11, 107, 214)(10, 169, 19, 89, 106, 26)(12, 148,
212, 136, 151, 172)(14, 140, 211, 173, 153, 147)(15, 174, 213, 150, 155,
137)(21, 61, 75, 34, 176, 222)(22, 31, 74, 225, 178, 65)(23, 223, 73, 64, 177,
33)(24, 219, 72, 195, 180, 56)(25, 58, 71, 220, 179, 193)(27, 146, 170, 138, 90,
171)(30, 175, 166, 149, 86, 139)(32, 38, 224, 209, 63, 162)(35, 163, 221, 39,
62, 208)(36, 217, 207, 194, 164, 57)(37, 191, 206, 60, 165, 218)(40, 59, 210,
216, 161, 192)(46, 181, 76, 121, 236, 112)(47, 68, 78, 117, 237, 205)(48, 120,
77, 201, 238, 67)(49, 123, 80, 114, 239, 182)(50, 111, 79, 183, 240, 122)(51,
55, 81, 85, 105, 102)(66, 134, 119, 91, 203, 198)(69, 93, 118, 196, 202,
135)(70, 200, 116, 132, 204, 92)(94, 115, 199, 184, 131, 125)(95, 124, 197, 113,
133, 185)(96, 231, 187, 156, 143, 127)(97, 190, 186, 142, 145, 100)(98, 128,
189, 234, 141, 159)(99, 157, 188, 126, 144, 232)(129, 235, 233, 160, 158,
130)
e: (2, 53)(3, 103)(4, 44)(5, 84)(6, 16)(7, 173)(8, 136)(10, 150)(12, 168)(13,
28)(14, 154)(15, 89)(17, 108)(18, 138)(20, 149)(21, 71)(22, 210)(23, 36)(25,
165)(27, 167)(29, 214)(30, 88)(31, 56)(32, 222)(34, 193)(35, 65)(37, 176)(39,
74)(40, 163)(42, 228)(43, 105)(45, 85)(46, 197)(47, 236)(48, 80)(49, 94)(51,
101)(54, 229)(55, 83)(57, 223)(59, 219)(60, 61)(62, 216)(64, 194)(66, 115)(67,
203)(68, 118)(69, 124)(72, 178)(75, 209)(76, 93)(77, 134)(79, 200)(82, 230)(86,
151)(87, 211)(91, 131)(92, 240)(96, 130)(97, 188)(99, 158)(100, 143)(104,
226)(106, 137)(107, 172)(110, 147)(111, 116)(112, 202)(114, 184)(117, 181)(119,
123)(121, 185)(122, 204)(126, 235)(127, 144)(128, 189)(133, 196)(135, 237)(140,
171)(141, 159)(142, 232)(148, 175)(152, 212)(153, 170)(156, 233)(157, 187)(161,
180)(162, 206)(169, 213)(177, 207)(182, 201)(186, 231)(191, 220)(192, 225)(198,
239)(218, 224)
C4[ 240, 97 ]
240
-1 11 26 16 6
-2 154 107 10 87
-3 214 172 20 86
-4 27 137 215 108
-5 12 155 140 173
-6 1 36 51 21
-7 177 25 84 42
-8 226 40 161 41
-9 178 72 227 52
-10 165 2 85 75
-11 1 56 41 31
-12 5 62 52 219
-13 45 193 227 64
-14 57 191 104 53
-15 220 101 228 32
-16 1 23 101 71
-17 22 44 180 82
-18 81 75 207 229
-19 176 102 37 227
-20 45 210 3 40
-21 46 6 106 76
-22 198 17 50 149
-23 80 91 16 171
-24 132 199 172 107
-25 135 7 95 150
-26 1 81 60 61
-27 102 223 4 32
-28 34 194 227 85
-29 59 103 192 54
-30 225 51 62 230
-31 11 66 111 86
-32 15 202 27 117
-33 90 123 215 119
-34 121 112 169 28
-35 67 166 212 204
-36 48 6 140 131
-37 47 147 19 197
-38 135 146 237 174
-39 77 200 139 172
-40 80 8 20 240
-41 11 166 136 8
-42 110 89 7 152
-43 147 213 140 151
-44 167 17 215 106
-45 13 90 150 20
-46 176 96 141 21
-47 209 100 37 128
-48 145 156 36 163
-49 177 161 129 186
-50 22 210 190 160
-51 89 146 6 30
-52 12 168 139 9
-53 211 14 150 172
-54 213 138 29 109
-55 170 106 87 175
-56 11 115 116 151
-57 67 167 14 184
-58 155 69 124 215
-59 122 168 114 29
-60 211 26 117 185
-61 121 26 181 87
-62 12 201 116 30
-63 155 68 90 118
-64 66 13 170 182
-65 122 166 203 152
-66 157 126 31 64
-67 187 35 57 142
-68 189 191 63 97
-69 99 58 224 159
-70 144 221 127 195
-71 16 93 137 197
-72 92 148 9 131
-73 198 146 239 109
-74 79 134 139 107
-75 236 18 10 76
-76 187 75 21 98
-77 39 127 97 207
-78 190 234 162 206
-79 161 74 130 142
-80 23 145 233 40
-81 166 26 138 18
-82 88 212 17 175
-83 211 137 148 153
-84 155 168 171 7
-85 90 28 149 10
-86 221 3 105 31
-87 55 2 61 217
-88 101 82 192 216
-89 222 191 51 42
-90 33 45 63 85
-91 99 23 144 178
-92 143 126 72 163
-93 209 157 71 98
-94 231 180 129 207
-95 165 25 234 160
-96 46 200 201 125
-97 77 122 68 239
-98 113 93 205 76
-99 198 69 91 116
-100 47 114 240 120
-101 88 146 15 16
-102 167 27 139 19
-103 149 29 107 151
-104 14 136 174 153
-105 110 169 171 86
-106 44 55 206 21
-107 2 24 103 74
-108 210 4 161 230
-109 179 73 229 54
-110 176 105 42 164
-111 158 216 31 186
-112 34 222 234 127
-113 220 191 129 98
-114 100 223 59 160
-115 187 56 235 194
-116 99 231 56 62
-117 60 141 32 186
-118 220 188 128 63
-119 33 232 126 225
-120 143 100 221 217
-121 34 156 61 128
-122 233 59 97 65
-123 33 235 192 142
-124 58 158 141 218
-125 96 195 217 130
-126 66 92 119 196
-127 77 112 70 131
-128 121 133 47 118
-129 113 49 94 183
-130 79 125 182 197
-131 36 158 72 127
-132 187 24 157 208
-133 179 235 128 206
-134 144 177 188 74
-135 232 25 38 141
-136 180 104 41 163
-137 4 71 83 162
-138 209 177 81 54
-139 102 39 52 74
-140 36 5 206 43
-141 46 124 135 117
-142 67 79 123 237
-143 92 236 184 120
-144 134 91 70 202
-145 80 48 183 205
-146 101 38 51 73
-147 37 228 43 164
-148 72 83 208 230
-149 22 103 85 163
-150 209 45 25 53
-151 56 221 103 43
-152 195 42 65 230
-153 104 83 194 218
-154 220 2 223 226
-155 58 5 84 63
-156 121 199 48 204
-157 66 132 93 203
-158 111 124 239 131
-159 69 181 237 197
-160 114 50 95 184
-161 79 49 8 108
-162 78 137 171 196
-163 48 92 136 149
-164 110 199 147 238
-165 237 95 173 10
-166 35 81 41 65
-167 44 57 222 102
-168 59 84 216 52
-169 34 105 218 229
-170 55 224 226 64
-171 23 105 84 162
-172 24 3 39 53
-173 165 5 228 207
-174 179 38 104 226
-175 55 178 82 208
-176 110 46 236 19
-177 134 49 138 7
-178 91 9 240 175
-179 133 174 196 109
-180 200 136 17 94
-181 231 222 159 61
-182 190 216 64 130
-183 145 192 225 129
-184 143 57 160 219
-185 189 233 60 193
-186 111 49 117 238
-187 132 67 115 76
-188 198 134 204 118
-189 68 236 185 196
-190 78 201 50 182
-191 89 68 14 113
-192 88 123 29 183
-193 13 202 213 185
-194 201 115 28 153
-195 212 70 125 152
-196 189 179 126 162
-197 37 71 159 130
-198 22 99 188 73
-199 24 156 233 164
-200 232 180 39 96
-201 190 62 194 96
-202 144 234 193 32
-203 232 157 223 65
-204 188 35 156 219
-205 145 224 218 98
-206 78 133 106 140
-207 77 94 18 173
-208 132 148 238 175
-209 47 93 138 150
-210 50 239 20 108
-211 60 83 217 53
-212 35 82 195 228
-213 224 193 43 54
-214 3 225 229 219
-215 33 44 58 4
-216 88 111 168 182
-217 211 125 87 120
-218 124 169 205 153
-219 12 214 204 184
-220 154 113 15 118
-221 70 151 86 120
-222 89 112 167 181
-223 154 114 27 203
-224 69 213 170 205
-225 214 183 30 119
-226 154 170 8 174
-227 13 28 19 9
-228 212 15 147 173
-229 169 214 18 109
-230 148 30 108 152
-231 181 94 116 238
-232 200 135 203 119
-233 122 199 80 185
-234 78 112 202 95
-235 133 123 115 240
-236 143 176 189 75
-237 165 38 159 142
-238 231 164 186 208
-239 210 158 73 97
-240 100 178 235 40
0