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