Graph forms
for C4 [ 256, 59 ] = UG(ATD[256,91])
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On this page are computer-accessible forms for the graph C4[ 256, 59 ] =
UG(ATD[256,91]).
(I) Following is a form readable by MAGMA:
g:=Graph<256|{ {36, 38}, {244, 246}, {212, 214}, {176, 178}, {120, 122}, {136,
138}, {16, 19}, {232, 235}, {88, 91}, {1, 5}, {176, 180}, {88, 92}, {59, 63},
{42, 46}, {34, 38}, {112, 116}, {120, 124}, {136, 140}, {120, 125}, {3, 5},
{224, 230}, {192, 198}, {59, 61}, {152, 158}, {42, 45}, {240, 247}, {208, 215},
{1, 9}, {240, 248}, {229, 237}, {208, 216}, {82, 90}, {132, 140}, {150, 158},
{242, 251}, {1, 11}, {226, 232}, {194, 200}, {68, 78}, {50, 56}, {16, 26}, {82,
89}, {230, 237}, {118, 125}, {148, 159}, {1, 13}, {244, 248}, {231, 235}, {228,
232}, {212, 216}, {196, 200}, {66, 78}, {52, 56}, {147, 159}, {243, 254}, {242,
252}, {2, 13}, {132, 139}, {14, 30}, {233, 249}, {99, 115}, {239, 254}, {44,
62}, {239, 253}, {238, 252}, {233, 251}, {236, 255}, {5, 17}, {238, 250}, {229,
241}, {225, 245}, {14, 26}, {9, 29}, {166, 178}, {34, 55}, {43, 62}, {162, 183},
{7, 17}, {231, 241}, {227, 245}, {33, 55}, {161, 183}, {10, 29}, {100, 115},
{166, 177}, {7, 31}, {106, 114}, {102, 126}, {172, 180}, {40, 49}, {40, 50},
{228, 254}, {196, 222}, {110, 116}, {74, 80}, {5, 25}, {234, 246}, {202, 214},
{76, 80}, {15, 19}, {9, 21}, {193, 220}, {227, 254}, {225, 252}, {195, 222}, {9,
23}, {226, 252}, {194, 220}, {108, 114}, {6, 25}, {234, 245}, {202, 213}, {172,
179}, {11, 43}, {218, 250}, {213, 245}, {209, 241}, {206, 238}, {204, 236},
{197, 229}, {195, 227}, {192, 224}, {30, 62}, {66, 99}, {75, 106}, {135, 166},
{11, 41}, {213, 247}, {210, 240}, {199, 229}, {193, 227}, {65, 99}, {156, 190},
{209, 242}, {7, 35}, {217, 253}, {201, 237}, {75, 111}, {17, 53}, {131, 166},
{222, 251}, {207, 234}, {153, 188}, {155, 190}, {73, 111}, {221, 251}, {220,
250}, {219, 253}, {207, 233}, {201, 239}, {88, 126}, {76, 106}, {131, 165},
{154, 188}, {7, 32}, {204, 235}, {18, 53}, {21, 61}, {223, 247}, {215, 255},
{86, 126}, {84, 124}, {68, 108}, {130, 170}, {133, 173}, {146, 186}, {28, 54},
{221, 247}, {215, 253}, {134, 172}, {8, 35}, {92, 119}, {22, 61}, {133, 174},
{13, 33}, {218, 246}, {214, 250}, {65, 109}, {26, 54}, {129, 173}, {145, 189},
{73, 100}, {90, 119}, {87, 122}, {82, 127}, {134, 171}, {150, 187}, {14, 32},
{87, 121}, {81, 127}, {74, 100}, {67, 109}, {15, 33}, {129, 175}, {130, 172},
{147, 189}, {148, 186}, {149, 187}, {67, 108}, {217, 246}, {214, 249}, {84,
123}, {135, 168}, {200, 248}, {216, 232}, {11, 57}, {15, 60}, {6, 50}, {17, 37},
{15, 59}, {12, 57}, {19, 37}, {143, 184}, {200, 255}, {21, 45}, {222, 230},
{199, 255}, {128, 184}, {137, 177}, {143, 183}, {203, 242}, {211, 234}, {6, 60},
{21, 47}, {8, 50}, {137, 179}, {154, 160}, {28, 39}, {220, 231}, {3, 63}, {219,
231}, {205, 241}, {197, 249}, {77, 113}, {27, 39}, {13, 49}, {6, 58}, {156,
160}, {210, 239}, {79, 113}, {216, 230}, {206, 240}, {205, 243}, {198, 248},
{14, 49}, {211, 236}, {203, 244}, {198, 249}, {22, 86}, {180, 244}, {63, 127},
{29, 93}, {139, 203}, {159, 223}, {28, 94}, {63, 125}, {139, 201}, {160, 226},
{3, 64}, {40, 107}, {30, 93}, {22, 85}, {4, 71}, {3, 71}, {37, 97}, {23, 83},
{138, 206}, {157, 217}, {53, 112}, {23, 81}, {54, 112}, {40, 110}, {38, 97},
{180, 243}, {138, 205}, {158, 217}, {38, 110}, {20, 93}, {20, 94}, {39, 107},
{42, 103}, {41, 103}, {19, 67}, {51, 96}, {18, 70}, {54, 98}, {47, 123}, {149,
193}, {25, 76}, {145, 196}, {26, 76}, {47, 121}, {146, 196}, {151, 193}, {20,
67}, {151, 192}, {18, 74}, {179, 235}, {29, 69}, {25, 65}, {140, 212}, {152,
192}, {155, 195}, {157, 197}, {57, 96}, {4, 94}, {179, 233}, {56, 98}, {31, 69},
{27, 65}, {18, 72}, {153, 195}, {159, 197}, {59, 96}, {2, 94}, {189, 225}, {178,
238}, {58, 102}, {53, 105}, {43, 119}, {27, 70}, {185, 228}, {20, 74}, {191,
225}, {186, 228}, {55, 105}, {43, 117}, {30, 64}, {27, 69}, {58, 101}, {191,
224}, {178, 237}, {140, 211}, {24, 120}, {186, 218}, {36, 68}, {171, 202}, {174,
207}, {171, 201}, {36, 71}, {168, 203}, {175, 204}, {2, 102}, {185, 221}, {177,
213}, {168, 204}, {170, 206}, {175, 202}, {190, 219}, {177, 215}, {189, 219},
{188, 218}, {187, 221}, {35, 68}, {33, 73}, {37, 77}, {165, 205}, {2, 104}, {39,
77}, {35, 73}, {165, 207}, {36, 72}, {51, 95}, {24, 119}, {51, 66}, {57, 72},
{52, 69}, {23, 101}, {58, 72}, {49, 66}, {52, 71}, {167, 212}, {10, 126}, {45,
89}, {167, 210}, {45, 91}, {10, 125}, {56, 79}, {31, 104}, {31, 103}, {190,
198}, {55, 79}, {51, 75}, {44, 84}, {169, 209}, {169, 211}, {170, 208}, {188,
199}, {28, 96}, {187, 199}, {41, 85}, {158, 226}, {173, 209}, {24, 101}, {34,
95}, {41, 87}, {174, 208}, {34, 93}, {52, 75}, {44, 83}, {160, 223}, {173, 210},
{16, 144}, {12, 142}, {10, 142}, {8, 141}, {8, 142}, {60, 181}, {60, 183}, {46,
163}, {48, 163}, {32, 182}, {32, 184}, {44, 181}, {16, 142}, {42, 181}, {22,
182}, {12, 164}, {46, 130}, {24, 182}, {12, 163}, {47, 128}, {46, 129}, {48,
128}, {61, 141}, {114, 194}, {4, 181}, {4, 182}, {62, 141}, {116, 194}, {48,
135}, {48, 136}, {80, 151}, {127, 184}, {113, 185}, {70, 143}, {80, 154}, {104,
162}, {70, 141}, {114, 185}, {116, 191}, {123, 176}, {104, 164}, {115, 191},
{95, 144}, {81, 129}, {95, 143}, {89, 137}, {85, 133}, {121, 169}, {81, 131},
{89, 139}, {86, 132}, {85, 135}, {121, 171}, {78, 154}, {86, 130}, {118, 162},
{124, 168}, {83, 134}, {123, 174}, {117, 162}, {79, 151}, {83, 136}, {124, 167},
{77, 145}, {78, 145}, {64, 161}, {64, 163}, {102, 128}, {112, 150}, {92, 176},
{113, 157}, {115, 157}, {84, 164}, {105, 153}, {98, 146}, {90, 170}, {118, 134},
{122, 138}, {117, 132}, {107, 153}, {90, 169}, {107, 152}, {92, 175}, {118,
133}, {122, 137}, {97, 149}, {108, 152}, {111, 155}, {101, 144}, {82, 164},
{109, 155}, {100, 146}, {99, 149}, {87, 161}, {117, 131}, {103, 144}, {88, 161},
{111, 150}, {109, 148}, {106, 147}, {105, 147}, {110, 148}, {91, 167}, {97,
156}, {91, 165}, {98, 156}, {223, 256}, {224, 256}, {236, 256}, {243, 256}
}>;
(II) A more general form is to represent the graph as the orbit of {36, 38}
under the group generated by the following permutations:
a: (2, 57, 3, 29)(4, 142)(5, 9, 13, 11)(6, 61, 14, 103)(7, 101, 15, 62)(8, 182,
16, 181)(10, 94, 12, 71)(17, 23, 33, 43)(18, 127, 34, 162)(19, 44, 35, 24)(20,
164, 36, 125)(21, 49, 41, 25)(22, 26, 42, 50)(27, 128, 51, 161)(28, 163, 52,
126)(30, 31, 58, 59)(32, 144, 60, 141)(37, 83, 73, 119)(38, 118, 74, 82)(39, 48,
75, 88)(40, 85, 76, 45)(46, 56, 86, 54)(47, 66, 87, 65)(53, 81, 55, 117)(63, 93,
104, 72)(64, 69, 102, 96)(67, 84, 68, 120)(70, 184, 95, 183)(77, 136, 111,
92)(78, 122, 109, 123)(79, 132, 112, 129)(80, 89, 110, 133)(90, 97, 134,
100)(91, 107, 135, 106)(98, 130)(99, 121)(105, 131)(108, 124)(113, 140, 150,
175)(114, 167, 152, 168)(115, 169, 149, 171)(116, 173, 151, 139)(137, 148, 174,
154)(138, 155, 176, 145)(146, 170, 156, 172)(147, 165, 153, 166)(157, 211, 187,
202)(158, 204, 185, 212)(159, 207, 188, 177)(160, 179, 186, 208)(178, 189, 205,
195)(180, 196, 206, 190)(191, 209, 193, 201)(192, 203, 194, 210)(197, 234, 199,
213)(198, 244, 200, 240)(214, 217, 236, 221)(215, 223, 233, 218)(216, 226, 235,
228)(219, 243, 222, 238)(220, 239, 224, 242)(225, 241, 227, 237)(229, 245)(230,
252, 231, 254)(246, 255, 247, 249)(250, 253, 256, 251) (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, 2, 31, 32, 143, 141, 59, 57)(3, 58, 29, 4, 144, 30, 60, 142)(5, 102, 69,
182, 95, 62, 15, 12)(6, 10, 71, 101, 93, 181, 16, 64)(7, 184, 70, 61, 96, 11,
13, 104)(8, 63, 72, 9, 94, 103, 14, 183)(17, 128, 27, 22, 51, 43, 33, 164)(18,
21, 28, 41, 49, 162, 35, 127)(19, 163, 25, 126, 52, 24, 34, 44)(20, 42, 26, 161,
50, 125, 36, 23)(37, 48, 65, 86, 75, 119, 55, 84)(38, 83, 67, 46, 76, 88, 56,
120)(39, 85, 66, 117, 73, 82, 53, 47)(40, 118, 68, 81, 74, 45, 54, 87)(77, 135,
99, 132, 111, 90, 105, 123)(78, 131, 100, 89, 112, 121, 107, 133)(79, 124, 97,
136, 109, 130, 106, 92)(80, 91, 98, 122, 110, 134, 108, 129)(113, 168, 149, 140,
155, 170, 147, 176)(114, 175, 151, 167, 156, 138, 148, 172)(115, 139, 150, 169,
153, 174, 145, 166)(116, 171, 152, 173, 154, 165, 146, 137)(157, 203, 187, 211,
195, 208, 189, 178)(158, 209, 188, 207, 196, 177, 191, 201)(159, 180, 185, 204,
193, 212, 190, 206)(160, 205, 186, 179, 194, 202, 192, 210)(197, 244, 221, 236,
227, 216, 219, 238)(198, 240, 223, 243, 228, 235, 220, 214)(199, 234, 222, 215,
225, 237, 217, 242)(200, 213, 224, 239, 226, 241, 218, 233)(229, 246, 251, 255,
245, 230, 253, 252)(231, 250, 249, 248, 247, 256, 254, 232)
c: (1, 5, 17, 37, 77, 113, 157, 197, 229, 241, 209, 173, 133, 118, 162, 183,
143, 95, 51, 75, 111, 155, 195, 227, 245, 213, 177, 137, 89, 45, 21, 9)(2, 6,
18, 38, 78, 114, 158, 198, 230, 243, 211, 175, 135, 120, 164, 181, 141, 93, 49,
76, 112, 156, 196, 228, 246, 214, 178, 138, 90, 46, 22, 10)(3, 7, 19, 39, 79,
115, 159, 199, 231, 242, 210, 174, 134, 117, 161, 184, 144, 96, 52, 73, 109,
153, 193, 225, 247, 215, 179, 139, 91, 47, 23, 11)(4, 8, 20, 40, 80, 116, 160,
200, 232, 244, 212, 176, 136, 119, 163, 182, 142, 94, 50, 74, 110, 154, 194,
226, 248, 216, 180, 140, 92, 48, 24, 12)(13, 25, 53, 97, 145, 185, 217, 249,
237, 205, 169, 129, 85, 125, 104, 60, 70, 34, 66, 106, 150, 190, 222, 254, 234,
202, 166, 122, 82, 42, 61, 29)(14, 26, 54, 98, 146, 186, 218, 250, 238, 206,
170, 130, 86, 126, 102, 58, 72, 36, 68, 108, 152, 192, 224, 256, 236, 204, 168,
124, 84, 44, 62, 30)(15, 27, 55, 99, 147, 187, 219, 251, 239, 207, 171, 131, 87,
127, 103, 59, 69, 33, 65, 105, 149, 189, 221, 253, 233, 201, 165, 121, 81, 41,
63, 31)(16, 28, 56, 100, 148, 188, 220, 252, 240, 208, 172, 132, 88, 128, 101,
57, 71, 35, 67, 107, 151, 191, 223, 255, 235, 203, 167, 123, 83, 43, 64, 32)
d: (6, 7)(9, 11)(10, 12)(14, 15)(17, 25)(18, 27)(19, 26)(20, 28)(21, 43)(22,
44)(23, 41)(24, 42)(29, 57)(30, 59)(31, 58)(32, 60)(33, 49)(34, 51)(35, 50)(36,
52)(37, 76)(38, 75)(39, 74)(40, 73)(45, 119)(46, 120)(47, 117)(48, 118)(53,
65)(54, 67)(55, 66)(56, 68)(61, 62)(63, 64)(69, 72)(77, 80)(78, 79)(81, 87)(82,
88)(83, 85)(84, 86)(89, 92)(90, 91)(93, 96)(97, 106)(98, 108)(99, 105)(100,
107)(101, 103)(102, 104)(109, 112)(110, 111)(113, 154)(114, 156)(115, 153)(116,
155)(121, 131)(122, 129)(123, 132)(124, 130)(125, 163)(126, 164)(127, 161)(128,
162)(133, 136)(134, 135)(137, 175)(138, 173)(139, 176)(140, 174)(145, 151)(146,
152)(147, 149)(148, 150)(157, 188)(158, 186)(159, 187)(160, 185)(165, 169)(166,
171)(167, 170)(168, 172)(177, 202)(178, 201)(179, 204)(180, 203)(181, 182)(183,
184)(189, 193)(190, 194)(191, 195)(192, 196)(197, 199)(198, 200)(205, 209)(206,
210)(207, 211)(208, 212)(214, 215)(217, 218)(219, 220)(221, 223)(222, 224)(225,
227)(226, 228)(233, 236)(238, 239)(242, 243)(249, 255)(250, 253)(251, 256)(252,
254)
C4[ 256, 59 ]
256
-1 11 13 5 9
-2 13 102 104 94
-3 5 71 63 64
-4 71 181 94 182
-5 1 3 25 17
-6 25 58 60 50
-7 35 17 31 32
-8 35 50 141 142
-9 1 23 29 21
-10 125 126 29 142
-11 1 57 41 43
-12 57 163 142 164
-13 33 1 2 49
-14 26 49 30 32
-15 33 59 60 19
-16 144 26 19 142
-17 37 5 7 53
-18 70 72 74 53
-19 67 15 37 16
-20 67 93 94 74
-21 45 47 61 9
-22 61 182 85 86
-23 101 81 83 9
-24 101 182 119 120
-25 5 6 65 76
-26 14 16 54 76
-27 69 70 39 65
-28 39 94 96 54
-29 69 93 9 10
-30 14 93 62 64
-31 69 103 104 7
-32 14 182 7 184
-33 55 13 15 73
-34 55 38 93 95
-35 68 7 73 8
-36 68 38 71 72
-37 77 17 19 97
-38 110 34 36 97
-39 77 27 28 107
-40 110 49 50 107
-41 11 103 85 87
-42 45 46 103 181
-43 11 62 117 119
-44 181 83 62 84
-45 89 91 42 21
-46 129 42 130 163
-47 121 123 128 21
-48 135 136 128 163
-49 66 13 14 40
-50 56 6 40 8
-51 66 95 96 75
-52 56 69 71 75
-53 112 17 105 18
-54 112 26 28 98
-55 33 34 79 105
-56 79 50 52 98
-57 11 12 72 96
-58 101 102 6 72
-59 15 61 63 96
-60 15 181 6 183
-61 22 59 141 21
-62 44 30 141 43
-63 3 59 125 127
-64 3 161 30 163
-65 99 25 27 109
-66 99 78 49 51
-67 19 20 108 109
-68 78 35 36 108
-69 27 29 52 31
-70 143 27 18 141
-71 3 36 4 52
-72 57 36 58 18
-73 33 100 111 35
-74 100 80 18 20
-75 111 51 106 52
-76 25 80 26 106
-77 145 113 37 39
-78 66 154 68 145
-79 55 56 113 151
-80 154 74 151 76
-81 23 127 129 131
-82 89 90 127 164
-83 44 23 134 136
-84 44 123 124 164
-85 22 133 135 41
-86 22 132 126 130
-87 121 122 161 41
-88 91 92 126 161
-89 45 82 137 139
-90 169 82 170 119
-91 88 165 45 167
-92 88 176 119 175
-93 34 29 30 20
-94 2 4 28 20
-95 143 34 144 51
-96 57 59 28 51
-97 156 37 38 149
-98 56 156 146 54
-99 66 115 149 65
-100 146 115 73 74
-101 23 144 24 58
-102 2 58 126 128
-103 144 41 31 42
-104 2 162 31 164
-105 55 147 53 153
-106 114 147 75 76
-107 39 40 152 153
-108 67 68 114 152
-109 67 155 148 65
-110 38 148 116 40
-111 155 73 150 75
-112 116 150 53 54
-113 77 79 157 185
-114 106 194 108 185
-115 99 100 157 191
-116 110 112 191 194
-117 132 162 43 131
-118 133 134 125 162
-119 24 90 92 43
-120 122 24 124 125
-121 47 169 171 87
-122 137 138 87 120
-123 176 47 84 174
-124 167 168 84 120
-125 63 118 10 120
-126 88 102 86 10
-127 81 82 63 184
-128 47 102 48 184
-129 46 81 173 175
-130 46 170 172 86
-131 165 166 81 117
-132 117 139 140 86
-133 85 118 173 174
-134 83 171 172 118
-135 166 168 48 85
-136 48 83 138 140
-137 89 122 177 179
-138 122 136 205 206
-139 132 89 201 203
-140 132 211 212 136
-141 70 61 62 8
-142 12 16 8 10
-143 70 95 183 184
-144 101 103 16 95
-145 77 78 189 196
-146 100 196 98 186
-147 189 159 105 106
-148 110 159 109 186
-149 99 187 193 97
-150 187 111 112 158
-151 79 80 192 193
-152 158 192 107 108
-153 188 105 107 195
-154 78 188 80 160
-155 111 190 195 109
-156 190 160 97 98
-157 113 115 217 197
-158 226 150 217 152
-159 223 147 148 197
-160 154 156 223 226
-161 88 183 64 87
-162 104 117 183 118
-163 12 46 48 64
-164 12 82 104 84
-165 91 205 207 131
-166 177 178 135 131
-167 210 91 124 212
-168 124 135 203 204
-169 121 209 90 211
-170 90 206 130 208
-171 121 134 201 202
-172 134 179 180 130
-173 209 133 210 129
-174 133 123 207 208
-175 92 202 204 129
-176 123 178 92 180
-177 166 213 137 215
-178 176 166 237 238
-179 233 235 137 172
-180 176 243 244 172
-181 44 4 60 42
-182 22 24 4 32
-183 143 60 161 162
-184 143 127 128 32
-185 221 113 114 228
-186 146 148 228 218
-187 199 221 149 150
-188 154 199 218 153
-189 145 147 225 219
-190 198 155 156 219
-191 224 115 225 116
-192 198 224 151 152
-193 220 149 227 151
-194 220 200 114 116
-195 155 222 227 153
-196 145 200 222 146
-197 157 159 249 229
-198 190 192 248 249
-199 187 188 255 229
-200 255 248 194 196
-201 171 237 139 239
-202 213 214 171 175
-203 242 244 168 139
-204 168 235 236 175
-205 165 243 138 241
-206 170 138 238 240
-207 165 233 234 174
-208 170 215 216 174
-209 242 169 173 241
-210 167 173 239 240
-211 234 169 236 140
-212 167 214 216 140
-213 177 245 202 247
-214 212 202 249 250
-215 253 177 255 208
-216 232 212 208 230
-217 253 157 158 246
-218 188 246 250 186
-219 231 253 189 190
-220 231 193 194 250
-221 187 247 185 251
-222 195 196 251 230
-223 256 159 247 160
-224 256 191 192 230
-225 189 245 191 252
-226 232 158 160 252
-227 254 245 193 195
-228 232 254 185 186
-229 199 237 197 241
-230 222 224 237 216
-231 220 235 219 241
-232 235 226 216 228
-233 179 249 207 251
-234 211 245 246 207
-235 231 232 179 204
-236 211 255 256 204
-237 178 201 229 230
-238 178 206 250 252
-239 253 210 254 201
-240 210 247 248 206
-241 209 231 205 229
-242 209 203 251 252
-243 254 256 180 205
-244 180 246 203 248
-245 234 213 225 227
-246 244 234 217 218
-247 221 223 213 240
-248 198 200 244 240
-249 198 233 214 197
-250 220 214 238 218
-251 242 221 222 233
-252 242 225 226 238
-253 215 217 239 219
-254 243 227 228 239
-255 199 200 236 215
-256 243 223 224 236
0