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