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