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