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