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