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