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