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