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