Graph forms
for C4 [ 216, 88 ] = BGCG(Pr_12(1,1,5,5),C_3,1)
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On this page are computer-accessible forms for the graph C4[ 216, 88 ] =
BGCG(Pr_12(1,1,5,5),C_3,1).
(I) Following is a form readable by MAGMA:
g:=Graph<216|{ {72, 74}, {144, 146}, {68, 76}, {71, 79}, {68, 77}, {71, 78},
{65, 75}, {65, 74}, {144, 158}, {64, 79}, {66, 82}, {138, 154}, {129, 145}, {69,
84}, {141, 156}, {67, 81}, {139, 153}, {135, 149}, {130, 150}, {70, 83}, {142,
155}, {132, 147}, {134, 145}, {70, 94}, {143, 151}, {140, 148}, {131, 155},
{128, 152}, {128, 153}, {143, 150}, {140, 149}, {131, 154}, {33, 59}, {137,
147}, {134, 156}, {132, 158}, {64, 90}, {137, 146}, {35, 63}, {163, 191}, {161,
189}, {66, 94}, {33, 60}, {161, 188}, {133, 152}, {35, 62}, {98, 127}, {72, 86},
{67, 92}, {136, 151}, {30, 62}, {130, 162}, {23, 54}, {133, 164}, {95, 126},
{23, 53}, {26, 56}, {95, 125}, {19, 48}, {30, 61}, {91, 120}, {1, 37}, {146,
182}, {145, 181}, {74, 110}, {73, 109}, {2, 38}, {15, 42}, {159, 186}, {141,
168}, {69, 96}, {87, 114}, {1, 39}, {159, 185}, {152, 190}, {145, 183}, {80,
118}, {73, 111}, {31, 57}, {28, 58}, {21, 51}, {15, 41}, {8, 46}, {87, 113},
{93, 123}, {2, 37}, {152, 191}, {146, 181}, {135, 160}, {80, 119}, {74, 109},
{31, 56}, {28, 59}, {21, 50}, {8, 47}, {93, 122}, {5, 45}, {149, 189}, {142,
166}, {81, 121}, {82, 122}, {84, 124}, {3, 42}, {151, 190}, {147, 186}, {129,
168}, {7, 46}, {84, 125}, {86, 127}, {6, 44}, {157, 183}, {150, 188}, {136,
162}, {81, 123}, {16, 58}, {13, 39}, {3, 40}, {157, 182}, {147, 184}, {13, 38},
{82, 121}, {4, 40}, {148, 184}, {138, 166}, {16, 60}, {89, 117}, {91, 119}, {4,
41}, {150, 187}, {148, 185}, {26, 55}, {18, 63}, {6, 43}, {83, 126}, {89, 116},
{5, 43}, {149, 187}, {18, 61}, {139, 164}, {83, 124}, {7, 48}, {79, 120}, {14,
57}, {9, 49}, {77, 117}, {12, 52}, {10, 50}, {12, 53}, {79, 118}, {75, 114},
{14, 55}, {9, 51}, {78, 116}, {85, 111}, {10, 49}, {75, 112}, {85, 110}, {17,
45}, {76, 112}, {19, 47}, {11, 54}, {78, 115}, {76, 113}, {17, 44}, {77, 115},
{11, 52}, {43, 107}, {44, 108}, {40, 105}, {37, 103}, {41, 106}, {46, 102}, {37,
108}, {40, 98}, {42, 97}, {39, 107}, {47, 98}, {38, 104}, {45, 99}, {43, 100},
{46, 97}, {24, 72}, {52, 101}, {49, 99}, {22, 69}, {53, 102}, {20, 64}, {51,
103}, {22, 67}, {48, 101}, {20, 66}, {50, 100}, {151, 192}, {158, 201}, {25,
65}, {156, 196}, {154, 194}, {153, 193}, {27, 67}, {25, 64}, {158, 199}, {156,
197}, {57, 96}, {49, 104}, {29, 71}, {153, 195}, {29, 70}, {154, 193}, {155,
198}, {24, 70}, {52, 106}, {27, 68}, {155, 196}, {54, 105}, {53, 85}, {174,
206}, {58, 90}, {32, 65}, {176, 209}, {167, 198}, {61, 92}, {32, 66}, {176,
210}, {170, 200}, {167, 197}, {36, 71}, {180, 215}, {174, 205}, {163, 192}, {34,
68}, {178, 212}, {175, 201}, {172, 202}, {165, 195}, {34, 69}, {178, 213}, {175,
200}, {172, 203}, {165, 194}, {63, 88}, {51, 91}, {59, 83}, {56, 80}, {48, 89},
{59, 82}, {56, 81}, {60, 86}, {160, 202}, {62, 84}, {54, 93}, {36, 72}, {180,
216}, {160, 204}, {50, 95}, {170, 199}, {162, 207}, {61, 80}, {55, 88}, {162,
205}, {41, 89}, {168, 216}, {57, 73}, {38, 87}, {47, 93}, {63, 77}, {166, 213},
{58, 78}, {164, 208}, {166, 211}, {164, 210}, {44, 91}, {62, 73}, {60, 75}, {39,
95}, {171, 211}, {169, 209}, {169, 208}, {45, 87}, {177, 203}, {173, 215}, {55,
76}, {173, 214}, {179, 207}, {177, 204}, {179, 206}, {168, 214}, {42, 85}, {171,
212}, {36, 181}, {35, 183}, {32, 182}, {35, 187}, {36, 188}, {33, 184}, {34,
185}, {23, 183}, {30, 190}, {26, 184}, {25, 186}, {26, 191}, {27, 189}, {25,
190}, {28, 187}, {17, 185}, {21, 191}, {31, 181}, {19, 188}, {15, 189}, {13,
186}, {15, 182}, {8, 200}, {22, 214}, {11, 203}, {115, 179}, {116, 180}, {9,
200}, {10, 203}, {112, 177}, {12, 206}, {18, 208}, {14, 204}, {109, 175}, {4,
199}, {113, 178}, {22, 210}, {8, 205}, {20, 211}, {1, 201}, {13, 197}, {111,
167}, {121, 176}, {5, 207}, {6, 202}, {24, 213}, {124, 178}, {1, 206}, {3, 204},
{126, 177}, {4, 212}, {19, 195}, {7, 215}, {113, 161}, {5, 212}, {24, 201}, {17,
192}, {6, 215}, {124, 173}, {3, 209}, {119, 165}, {121, 171}, {2, 209}, {21,
198}, {94, 141}, {125, 174}, {92, 136}, {123, 175}, {23, 194}, {94, 139}, {120,
173}, {14, 216}, {92, 138}, {122, 172}, {7, 208}, {16, 199}, {86, 129}, {116,
163}, {10, 210}, {18, 202}, {118, 174}, {123, 163}, {12, 213}, {29, 196}, {20,
205}, {109, 180}, {120, 161}, {2, 216}, {27, 193}, {9, 211}, {88, 130}, {112,
170}, {30, 197}, {114, 169}, {126, 165}, {31, 195}, {88, 132}, {111, 179}, {11,
214}, {29, 192}, {90, 135}, {119, 170}, {122, 167}, {28, 194}, {110, 176}, {117,
171}, {16, 207}, {90, 133}, {115, 172}, {118, 169}, {127, 160}, {102, 134},
{125, 157}, {32, 193}, {104, 137}, {98, 128}, {104, 138}, {102, 133}, {108,
143}, {34, 196}, {100, 130}, {103, 129}, {106, 140}, {33, 198}, {100, 131},
{103, 128}, {106, 141}, {97, 137}, {99, 139}, {97, 136}, {101, 143}, {105, 131},
{117, 159}, {101, 142}, {127, 148}, {107, 135}, {105, 132}, {107, 134}, {96,
142}, {99, 140}, {114, 157}, {96, 144}, {110, 159}, {108, 144} }>;
(II) A more general form is to represent the graph as the orbit of {72, 74}
under the group generated by the following permutations:
a: (2, 13)(3, 25)(4, 20)(5, 9)(6, 21)(7, 33)(8, 16)(10, 17)(11, 29)(12, 24)(14,
30)(15, 32)(18, 26)(19, 28)(22, 34)(23, 36)(31, 35)(37, 39)(40, 64)(41, 66)(42,
65)(43, 51)(44, 50)(45, 49)(46, 60)(47, 58)(48, 59)(52, 70)(53, 72)(54, 71)(55,
61)(56, 63)(57, 62)(67, 68)(74, 85)(75, 97)(76, 92)(77, 81)(78, 93)(79, 105)(80,
88)(82, 89)(83, 101)(84, 96)(86, 102)(87, 104)(90, 98)(91, 100)(94, 106)(95,
108)(103, 107)(109, 111)(112, 136)(113, 138)(114, 137)(115, 123)(116, 122)(117,
121)(118, 132)(119, 130)(120, 131)(124, 142)(125, 144)(126, 143)(127, 133)(128,
135)(129, 134)(139, 140)(146, 157)(147, 169)(148, 164)(149, 153)(150, 165)(151,
177)(152, 160)(154, 161)(155, 173)(156, 168)(158, 174)(159, 176)(162, 170)(163,
172)(166, 178)(167, 180)(175, 179)(181, 183)(184, 208)(185, 210)(186, 209)(187,
195)(188, 194)(189, 193)(190, 204)(191, 202)(192, 203)(196, 214)(197, 216)(198,
215)(199, 205)(200, 207)(201, 206)(211, 212) (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, 209, 40, 212,
43, 215, 46, 200, 49, 203, 52, 206)(38, 204, 41, 207, 44, 208, 47, 211, 50, 214,
53, 201)(39, 216, 42, 199, 45, 202, 48, 205, 51, 210, 54, 213)(55, 189, 58, 192,
61, 195, 66, 198, 69, 183, 72, 186)(56, 193, 59, 196, 62, 181, 65, 184, 68, 187,
71, 190)(57, 182, 60, 185, 63, 188, 64, 191, 67, 194, 70, 197)(73, 146, 75, 148,
77, 150, 79, 152, 81, 154, 83, 156)(74, 147, 76, 149, 78, 151, 80, 153, 82, 155,
84, 145)(85, 158, 87, 160, 89, 162, 91, 164, 93, 166, 95, 168)(86, 159, 88, 161,
90, 163, 92, 165, 94, 167, 96, 157)(97, 170, 99, 172, 101, 174, 103, 176, 105,
178, 107, 180)(98, 171, 100, 173, 102, 175, 104, 177, 106, 179, 108, 169)(109,
137, 112, 140, 115, 143, 118, 128, 121, 131, 124, 134)(110, 132, 113, 135, 116,
136, 119, 139, 122, 142, 125, 129)(111, 144, 114, 127, 117, 130, 120, 133, 123,
138, 126, 141)
c: (2, 95, 12, 158)(3, 177, 11, 105)(4, 14, 10, 23)(5, 73, 9, 145)(6, 167, 8,
86)(7, 33)(13, 174, 24, 108)(15, 76, 22, 154)(16, 180, 21, 102)(17, 30, 20,
36)(18, 82, 19, 148)(25, 79, 29, 151)(26, 164, 28, 89)(31, 99, 35, 171)(32, 161,
34, 92)(37, 39, 206, 201)(38, 125, 213, 144)(40, 204, 203, 54)(41, 55, 210,
194)(42, 112, 214, 131)(43, 111, 200, 129)(44, 197, 205, 72)(45, 62, 211,
181)(46, 60, 215, 198)(47, 127, 202, 122)(48, 184, 208, 59)(49, 183, 212,
57)(50, 53, 199, 216)(51, 134, 207, 109)(52, 132, 209, 126)(56, 139, 187,
117)(58, 116, 191, 133)(61, 66, 188, 185)(63, 121, 195, 140)(64, 71, 192,
190)(65, 120, 196, 136)(67, 193, 189, 68)(69, 138, 182, 113)(70, 143, 186,
118)(74, 91, 156, 162)(75, 173, 155, 97)(77, 81, 153, 149)(78, 163, 152, 90)(80,
94, 150, 159)(83, 101, 147, 169)(84, 166, 146, 87)(85, 170, 168, 100)(88, 176,
165, 106)(93, 98, 160, 172)(96, 104, 157, 178)(103, 107, 179, 175)(110, 119,
141, 130)(114, 124, 142, 137)(115, 123, 128, 135)
d: (2, 12)(3, 11)(4, 10)(5, 9)(6, 8)(13, 24)(14, 23)(15, 22)(16, 21)(17, 20)(18,
19)(25, 29)(26, 28)(30, 36)(31, 35)(32, 34)(37, 206)(38, 213)(39, 201)(40,
203)(41, 210)(42, 214)(43, 200)(44, 205)(45, 211)(46, 215)(47, 202)(48, 208)(49,
212)(50, 199)(51, 207)(52, 209)(53, 216)(54, 204)(55, 194)(56, 187)(57, 183)(58,
191)(59, 184)(60, 198)(61, 188)(62, 181)(63, 195)(64, 192)(65, 196)(66, 185)(67,
189)(68, 193)(69, 182)(70, 186)(71, 190)(72, 197)(73, 145)(74, 156)(75, 155)(76,
154)(77, 153)(78, 152)(79, 151)(80, 150)(81, 149)(82, 148)(83, 147)(84, 146)(85,
168)(86, 167)(87, 166)(88, 165)(89, 164)(90, 163)(91, 162)(92, 161)(93, 160)(94,
159)(95, 158)(96, 157)(97, 173)(98, 172)(99, 171)(100, 170)(101, 169)(102,
180)(103, 179)(104, 178)(105, 177)(106, 176)(107, 175)(108, 174)(109, 134)(110,
141)(111, 129)(112, 131)(113, 138)(114, 142)(115, 128)(116, 133)(117, 139)(118,
143)(119, 130)(120, 136)(121, 140)(122, 127)(123, 135)(124, 137)(125, 144)(126,
132)
C4[ 216, 88 ]
216
-1 201 37 39 206
-2 209 37 38 216
-3 209 204 40 42
-4 199 212 40 41
-5 45 212 207 43
-6 44 202 215 43
-7 46 48 215 208
-8 46 200 47 205
-9 200 211 49 51
-10 210 49 203 50
-11 203 214 52 54
-12 213 52 206 53
-13 38 39 186 197
-14 55 57 204 216
-15 189 182 41 42
-16 199 58 60 207
-17 44 45 192 185
-18 202 61 63 208
-19 188 47 48 195
-20 66 211 205 64
-21 198 191 50 51
-22 67 210 69 214
-23 183 194 53 54
-24 201 70 213 72
-25 190 64 65 186
-26 55 56 191 184
-27 67 68 189 193
-28 187 58 59 194
-29 70 71 192 196
-30 190 61 62 197
-31 56 57 181 195
-32 66 182 193 65
-33 198 59 60 184
-34 68 69 185 196
-35 187 62 183 63
-36 188 71 181 72
-37 1 2 103 108
-38 2 13 104 87
-39 1 13 95 107
-40 3 4 105 98
-41 89 4 15 106
-42 3 15 85 97
-43 100 5 6 107
-44 91 6 17 108
-45 99 5 17 87
-46 102 7 8 97
-47 93 8 19 98
-48 89 101 7 19
-49 99 104 9 10
-50 100 95 10 21
-51 91 103 9 21
-52 11 12 101 106
-53 12 23 102 85
-54 11 23 93 105
-55 88 14 26 76
-56 80 26 81 31
-57 14 73 96 31
-58 78 90 16 28
-59 33 82 28 83
-60 33 16 75 86
-61 80 92 18 30
-62 35 73 84 30
-63 77 88 35 18
-64 79 90 25 20
-65 25 74 75 32
-66 82 94 20 32
-67 22 81 92 27
-68 77 34 27 76
-69 22 34 84 96
-70 24 83 94 29
-71 78 79 36 29
-72 24 36 74 86
-73 111 57 62 109
-74 110 72 65 109
-75 112 114 60 65
-76 55 68 112 113
-77 68 115 117 63
-78 58 71 115 116
-79 71 118 64 120
-80 56 61 118 119
-81 121 56 67 123
-82 66 121 122 59
-83 124 59 70 126
-84 69 124 125 62
-85 110 111 42 53
-86 60 72 127 129
-87 45 113 114 38
-88 55 132 63 130
-89 48 116 117 41
-90 133 58 135 64
-91 44 51 119 120
-92 67 136 61 138
-93 122 123 47 54
-94 66 70 139 141
-95 125 126 39 50
-96 144 57 69 142
-97 46 136 137 42
-98 47 127 40 128
-99 45 49 139 140
-100 50 130 43 131
-101 143 48 52 142
-102 133 46 134 53
-103 37 51 128 129
-104 38 49 137 138
-105 132 40 54 131
-106 41 52 140 141
-107 134 135 39 43
-108 44 143 144 37
-109 180 73 74 175
-110 176 159 74 85
-111 167 179 73 85
-112 177 170 75 76
-113 178 161 76 87
-114 157 169 75 87
-115 77 78 179 172
-116 78 89 180 163
-117 77 89 159 171
-118 79 80 169 174
-119 165 80 91 170
-120 79 91 161 173
-121 176 81 82 171
-122 167 82 93 172
-123 81 93 163 175
-124 178 83 84 173
-125 157 84 95 174
-126 165 177 83 95
-127 148 160 86 98
-128 103 152 98 153
-129 145 168 103 86
-130 88 100 150 162
-131 154 100 155 105
-132 88 147 158 105
-133 90 102 152 164
-134 145 156 102 107
-135 90 149 160 107
-136 92 151 162 97
-137 146 147 104 97
-138 154 166 92 104
-139 99 94 153 164
-140 99 148 149 106
-141 156 168 94 106
-142 155 166 101 96
-143 101 150 151 108
-144 146 158 96 108
-145 134 181 183 129
-146 144 137 181 182
-147 132 137 184 186
-148 127 140 184 185
-149 187 189 135 140
-150 143 187 188 130
-151 143 190 136 192
-152 133 190 191 128
-153 193 128 139 195
-154 138 193 194 131
-155 198 196 131 142
-156 134 141 196 197
-157 114 125 182 183
-158 132 144 199 201
-159 110 117 185 186
-160 135 202 127 204
-161 188 189 113 120
-162 136 205 130 207
-163 123 191 192 116
-164 133 210 139 208
-165 126 194 195 119
-166 211 213 138 142
-167 198 111 122 197
-168 214 216 129 141
-169 209 114 118 208
-170 199 112 200 119
-171 121 211 212 117
-172 122 202 115 203
-173 124 214 215 120
-174 125 205 118 206
-175 123 200 201 109
-176 110 121 209 210
-177 112 126 203 204
-178 113 124 212 213
-179 111 115 206 207
-180 116 215 216 109
-181 145 36 146 31
-182 146 157 15 32
-183 23 35 145 157
-184 33 26 147 148
-185 34 148 159 17
-186 13 25 147 159
-187 35 28 149 150
-188 36 150 161 19
-189 15 27 149 161
-190 25 30 151 152
-191 26 152 163 21
-192 17 29 151 163
-193 154 27 32 153
-194 154 165 23 28
-195 165 19 31 153
-196 34 155 156 29
-197 13 156 167 30
-198 33 155 167 21
-199 4 158 16 170
-200 170 8 9 175
-201 1 24 158 175
-202 6 160 18 172
-203 11 177 172 10
-204 177 3 14 160
-205 8 162 20 174
-206 1 12 179 174
-207 179 5 16 162
-208 169 7 18 164
-209 176 2 3 169
-210 22 176 10 164
-211 166 171 9 20
-212 178 4 5 171
-213 12 166 24 178
-214 11 22 168 173
-215 180 6 7 173
-216 2 14 168 180
0