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