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