Graph forms
for C4 [ 192, 158 ] = BGCG(PX(6,4);K1;{3,9})
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On this page are computer-accessible forms for the graph C4[ 192, 158 ] =
BGCG(PX(6,4);K1;{3,9}).
(I) Following is a form readable by MAGMA:
g:=Graph<192|{ {96, 124}, {76, 108}, {84, 117}, {68, 103}, {76, 111}, {80, 115},
{71, 99}, {94, 122}, {79, 106}, {91, 126}, {83, 118}, {86, 112}, {67, 100}, {66,
107}, {91, 114}, {94, 116}, {77, 102}, {85, 121}, {76, 98}, {89, 119}, {70,
105}, {74, 120}, {75, 121}, {86, 100}, {64, 115}, {78, 125}, {69, 113}, {92,
104}, {77, 123}, {86, 97}, {93, 106}, {89, 110}, {88, 111}, {70, 126}, {87,
109}, {79, 116}, {87, 108}, {66, 127}, {84, 107}, {90, 101}, {89, 102}, {36,
100}, {37, 101}, {47, 110}, {46, 108}, {51, 113}, {52, 118}, {46, 109}, {54,
114}, {36, 97}, {50, 119}, {57, 124}, {61, 120}, {45, 106}, {61, 122}, {33,
104}, {60, 117}, {55, 125}, {59, 112}, {55, 123}, {34, 111}, {49, 127}, {36,
107}, {41, 102}, {62, 110}, {32, 113}, {59, 105}, {38, 117}, {42, 121}, {54,
98}, {33, 116}, {50, 103}, {43, 126}, {38, 112}, {55, 97}, {59, 109}, {52, 99},
{37, 124}, {43, 114}, {50, 104}, {42, 118}, {39, 122}, {41, 119}, {58, 101}, {8,
104}, {27, 123}, {13, 109}, {16, 113}, {11, 105}, {29, 121}, {2, 103}, {6, 99},
{3, 101}, {21, 115}, {4, 98}, {24, 127}, {22, 126}, {23, 125}, {12, 97}, {25,
116}, {21, 120}, {1, 110}, {3, 115}, {6, 118}, {11, 122}, {12, 125}, {7, 117},
{11, 120}, {20, 103}, {15, 124}, {12, 127}, {6, 114}, {2, 119}, {31, 106}, {23,
98}, {14, 123}, {18, 107}, {11, 112}, {29, 102}, {23, 108}, {17, 111}, {26,
100}, {22, 105}, {28, 99}, {5, 133}, {48, 176}, {54, 182}, {57, 185}, {10, 139},
{27, 154}, {13, 140}, {42, 168}, {3, 128}, {34, 161}, {10, 137}, {24, 156}, {19,
150}, {48, 181}, {41, 172}, {62, 184}, {37, 162}, {61, 186}, {71, 192}, {15,
135}, {44, 164}, {53, 189}, {18, 155}, {20, 157}, {50, 187}, {58, 179}, {45,
167}, {63, 181}, {28, 151}, {46, 165}, {2, 143}, {20, 153}, {15, 130}, {5, 136},
{26, 148}, {36, 170}, {63, 177}, {17, 158}, {29, 146}, {51, 188}, {5, 148}, {49,
160}, {45, 191}, {56, 170}, {2, 145}, {30, 141}, {12, 159}, {55, 164}, {60,
175}, {7, 147}, {7, 146}, {35, 182}, {52, 161}, {16, 134}, {42, 188}, {26, 140},
{53, 163}, {35, 180}, {37, 178}, {57, 174}, {4, 156}, {13, 149}, {1, 152}, {39,
190}, {24, 129}, {1, 155}, {25, 131}, {32, 187}, {44, 183}, {54, 173}, {18,
142}, {19, 143}, {49, 172}, {93, 192}, {35, 189}, {53, 171}, {56, 166}, {57,
167}, {20, 139}, {29, 130}, {21, 138}, {17, 177}, {48, 144}, {15, 174}, {44,
141}, {34, 131}, {22, 183}, {19, 178}, {8, 170}, {43, 137}, {28, 190}, {14,
172}, {25, 186}, {41, 138}, {32, 132}, {34, 134}, {60, 152}, {4, 161}, {22,
179}, {60, 155}, {7, 175}, {45, 133}, {40, 128}, {24, 176}, {23, 191}, {52,
156}, {61, 149}, {10, 163}, {17, 184}, {56, 145}, {14, 164}, {6, 173}, {47,
132}, {18, 185}, {5, 169}, {62, 146}, {16, 189}, {35, 142}, {62, 147}, {8, 166},
{49, 159}, {47, 129}, {26, 180}, {14, 160}, {9, 167}, {58, 148}, {40, 135}, {3,
179}, {38, 150}, {32, 144}, {30, 174}, {25, 169}, {19, 163}, {9, 185}, {30,
175}, {40, 153}, {4, 182}, {8, 187}, {31, 171}, {39, 147}, {51, 134}, {10, 188},
{46, 152}, {27, 173}, {13, 186}, {56, 143}, {59, 140}, {9, 177}, {48, 136}, {51,
139}, {63, 135}, {1, 184}, {31, 166}, {27, 162}, {31, 165}, {47, 149}, {39,
157}, {16, 171}, {9, 181}, {38, 154}, {28, 160}, {53, 137}, {21, 168}, {44,
145}, {63, 130}, {33, 159}, {33, 158}, {40, 151}, {58, 133}, {64, 128}, {81,
145}, {69, 132}, {94, 159}, {92, 157}, {88, 153}, {84, 150}, {92, 158}, {82,
151}, {85, 144}, {72, 142}, {64, 136}, {69, 140}, {72, 129}, {81, 152}, {73,
131}, {95, 149}, {65, 141}, {86, 154}, {70, 139}, {77, 130}, {92, 147}, {78,
158}, {75, 154}, {82, 131}, {82, 128}, {96, 178}, {67, 144}, {72, 155}, {72,
156}, {93, 137}, {95, 138}, {65, 151}, {67, 148}, {75, 146}, {80, 138}, {70,
157}, {83, 136}, {74, 150}, {81, 141}, {68, 153}, {96, 189}, {89, 132}, {30,
192}, {95, 129}, {91, 133}, {88, 134}, {80, 143}, {88, 135}, {85, 181}, {94,
190}, {87, 183}, {65, 160}, {73, 171}, {74, 168}, {80, 178}, {83, 176}, {91,
191}, {75, 173}, {79, 169}, {71, 175}, {64, 169}, {74, 163}, {79, 166}, {85,
188}, {43, 192}, {73, 165}, {90, 182}, {90, 180}, {96, 142}, {65, 174}, {77,
162}, {69, 180}, {78, 191}, {66, 176}, {68, 183}, {95, 172}, {73, 186}, {82,
161}, {87, 164}, {76, 184}, {81, 165}, {68, 179}, {67, 187}, {90, 162}, {71,
190}, {93, 167}, {66, 185}, {83, 168}, {84, 170}, {78, 177} }>;
(II) A more general form is to represent the graph as the orbit of {96, 124}
under the group generated by the following permutations:
a: (1, 17, 34, 51, 69, 89)(2, 18, 33, 52, 70, 90)(3, 19, 36, 49, 71, 91)(4, 20,
35, 50, 72, 92)(5, 21, 38, 55, 65, 93)(6, 22, 37, 56, 66, 94)(7, 23, 40, 53, 67,
95)(8, 24, 39, 54, 68, 96)(9, 25, 42, 59, 77, 81)(10, 26, 41, 60, 78, 82)(11,
27, 44, 57, 79, 83)(12, 28, 43, 58, 80, 84)(13, 29, 46, 63, 73, 85)(14, 30, 45,
64, 74, 86)(15, 31, 48, 61, 75, 87)(16, 32, 47, 62, 76, 88)(97, 160, 192, 133,
115, 150)(98, 153, 189, 187, 129, 147)(99, 126, 101, 143, 107, 159)(100, 172,
175, 191, 128, 163)(102, 152, 177, 131, 188, 140)(103, 142, 104, 156, 157,
182)(105, 162, 145, 185, 116, 118)(106, 136, 120, 154, 164, 174)(108, 135, 171,
144, 149, 146)(109, 130, 165, 181, 186, 121)(110, 184, 111, 134, 113, 132)(112,
123, 141, 167, 169, 168)(114, 179, 178, 170, 127, 190)(117, 125, 151, 137, 148,
138)(119, 155, 158, 161, 139, 180)(122, 173, 183, 124, 166, 176) (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: (17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)(33, 36)(34,
35)(37, 40)(38, 39)(41, 44)(42, 43)(45, 48)(46, 47)(49, 55)(50, 56)(51, 53)(52,
54)(57, 63)(58, 64)(59, 61)(60, 62)(65, 77)(66, 78)(67, 79)(68, 80)(69, 73)(70,
74)(71, 75)(72, 76)(81, 89)(82, 90)(83, 91)(84, 92)(85, 93)(86, 94)(87, 95)(88,
96)(97, 159)(98, 156)(99, 173)(100, 116)(101, 128)(102, 141)(103, 143)(104,
170)(105, 120)(106, 144)(107, 158)(108, 129)(109, 149)(110, 152)(111, 142)(112,
122)(113, 171)(114, 118)(115, 179)(117, 147)(119, 145)(121, 192)(123, 160)(124,
135)(125, 127)(126, 168)(130, 174)(131, 180)(132, 165)(133, 136)(134, 189)(137,
188)(138, 183)(139, 163)(140, 186)(146, 175)(148, 169)(150, 157)(151, 162)(153,
178)(154, 190)(155, 184)(161, 182)(164, 172)(166, 187)(167, 181)(176, 191)(177,
185)
c: (2, 9)(3, 5)(4, 13)(6, 11)(8, 15)(12, 14)(17, 81)(18, 89)(19, 85)(20, 93)(21,
83)(22, 91)(23, 87)(24, 95)(25, 82)(26, 90)(27, 86)(28, 94)(29, 84)(30, 92)(31,
88)(32, 96)(33, 65)(34, 73)(35, 69)(36, 77)(37, 67)(38, 75)(39, 71)(40, 79)(41,
66)(42, 74)(43, 70)(44, 78)(45, 68)(46, 76)(47, 72)(48, 80)(50, 57)(51, 53)(52,
61)(54, 59)(56, 63)(60, 62)(97, 123)(98, 109)(99, 122)(100, 162)(101, 148)(102,
107)(103, 167)(104, 174)(105, 114)(106, 153)(110, 155)(111, 165)(112, 173)(113,
189)(115, 136)(116, 151)(117, 146)(118, 120)(119, 185)(121, 150)(124, 187)(125,
164)(127, 172)(128, 169)(130, 170)(132, 142)(133, 179)(134, 171)(135, 166)(137,
139)(138, 176)(140, 182)(141, 158)(143, 181)(144, 178)(145, 177)(147, 175)(149,
156)(152, 184)(157, 192)(159, 160)(161, 186)(163, 188)(183, 191)
d: (1, 2, 10, 9)(3, 6, 12, 13)(4, 14, 11, 5)(7, 8, 16, 15)(17, 81, 20, 93)(18,
89, 19, 85)(21, 83, 24, 95)(22, 91, 23, 87)(25, 82, 28, 94)(26, 90, 27, 86)(29,
84, 32, 96)(30, 92, 31, 88)(33, 73, 40, 71)(34, 65, 39, 79)(35, 77, 38, 67)(36,
69, 37, 75)(41, 74, 48, 72)(42, 66, 47, 80)(43, 78, 46, 68)(44, 70, 45, 76)(49,
61, 64, 52)(50, 53, 63, 60)(51, 57, 62, 56)(54, 55, 59, 58)(97, 140, 101,
173)(98, 164, 105, 133)(99, 159, 186, 128)(100, 180, 162, 154)(102, 150, 144,
142)(103, 137, 177, 152)(104, 171, 135, 175)(106, 111, 141, 157)(107, 132, 178,
121)(108, 183, 126, 191)(109, 179, 114, 125)(110, 143, 188, 185)(112, 148, 182,
123)(113, 124, 146, 170)(115, 118, 127, 149)(116, 131, 151, 190)(117, 187, 189,
130)(119, 163, 181, 155)(120, 136, 156, 172)(122, 169, 161, 160)(129, 138, 168,
176)(134, 174, 147, 166)(139, 167, 184, 145)(153, 192, 158, 165)
e: (1, 3, 7, 5)(2, 11, 8, 13)(4, 15, 6, 9)(10, 12, 16, 14)(17, 82, 30, 91)(18,
90, 29, 83)(19, 86, 32, 95)(20, 94, 31, 87)(21, 84, 26, 89)(22, 92, 25, 81)(23,
88, 28, 93)(24, 96, 27, 85)(33, 73, 44, 70)(34, 65, 43, 78)(35, 77, 42, 66)(36,
69, 41, 74)(37, 75, 48, 72)(38, 67, 47, 80)(39, 79, 46, 68)(40, 71, 45, 76)(49,
53, 55, 51)(50, 61, 56, 59)(52, 57, 54, 63)(58, 62, 64, 60)(97, 113, 172,
163)(98, 135, 99, 167)(100, 132, 138, 150)(101, 146, 136, 155)(102, 168, 107,
180)(103, 122, 166, 109)(104, 186, 145, 105)(106, 108, 153, 190)(110, 115, 117,
148)(111, 151, 192, 191)(112, 187, 149, 143)(114, 177, 161, 174)(116, 165, 183,
157)(118, 185, 182, 130)(119, 120, 170, 140)(121, 176, 142, 162)(123, 188, 127,
189)(124, 173, 181, 156)(125, 134, 160, 137)(126, 158, 131, 141)(128, 175, 133,
184)(129, 178, 154, 144)(139, 159, 171, 164)(147, 169, 152, 179)
C4[ 192, 158 ]
192
-1 110 155 184 152
-2 143 145 103 119
-3 101 179 115 128
-4 156 182 161 98
-5 133 136 169 148
-6 99 114 118 173
-7 146 147 117 175
-8 187 166 104 170
-9 177 167 181 185
-10 188 137 139 163
-11 122 112 105 120
-12 125 159 127 97
-13 149 140 109 186
-14 123 160 172 164
-15 124 135 130 174
-16 134 189 113 171
-17 111 177 158 184
-18 155 107 185 142
-19 143 178 150 163
-20 157 103 139 153
-21 168 115 138 120
-22 179 126 105 183
-23 125 191 108 98
-24 176 156 127 129
-25 169 116 131 186
-26 100 180 148 140
-27 154 123 162 173
-28 99 190 160 151
-29 121 102 146 130
-30 192 141 174 175
-31 165 166 171 106
-32 132 187 144 113
-33 158 104 159 116
-34 111 134 161 131
-35 189 180 182 142
-36 100 170 107 97
-37 101 178 124 162
-38 154 112 117 150
-39 122 157 190 147
-40 135 128 151 153
-41 102 138 172 119
-42 121 188 168 118
-43 114 126 137 192
-44 145 183 141 164
-45 133 167 191 106
-46 165 108 152 109
-47 110 132 149 129
-48 176 144 136 181
-49 159 127 160 172
-50 187 103 104 119
-51 188 134 113 139
-52 99 156 161 118
-53 189 137 171 163
-54 114 182 173 98
-55 123 125 97 164
-56 143 166 145 170
-57 167 124 174 185
-58 133 101 179 148
-59 112 105 140 109
-60 155 117 152 175
-61 122 149 120 186
-62 110 146 147 184
-63 177 135 181 130
-64 136 169 115 128
-65 160 151 141 174
-66 176 127 107 185
-67 187 100 144 148
-68 179 103 183 153
-69 132 113 180 140
-70 157 126 105 139
-71 99 190 192 175
-72 155 156 129 142
-73 165 171 131 186
-74 168 150 163 120
-75 121 154 146 173
-76 111 184 108 98
-77 123 102 162 130
-78 177 125 158 191
-79 166 169 116 106
-80 143 178 115 138
-81 165 145 141 152
-82 128 161 151 131
-83 176 168 136 118
-84 170 117 150 107
-85 121 144 188 181
-86 154 100 112 97
-87 183 108 109 164
-88 111 134 135 153
-89 110 132 102 119
-90 101 180 182 162
-91 133 114 191 126
-92 157 147 158 104
-93 167 137 192 106
-94 122 190 159 116
-95 138 149 172 129
-96 178 189 124 142
-97 55 12 36 86
-98 23 4 54 76
-99 71 6 28 52
-100 67 36 26 86
-101 90 3 58 37
-102 77 89 29 41
-103 2 68 50 20
-104 33 92 50 8
-105 11 22 59 70
-106 45 79 93 31
-107 66 36 18 84
-108 23 46 76 87
-109 13 46 59 87
-110 1 89 47 62
-111 88 34 17 76
-112 11 59 38 86
-113 69 16 51 32
-114 91 6 43 54
-115 3 80 64 21
-116 33 79 25 94
-117 38 60 7 84
-118 6 83 52 42
-119 89 2 50 41
-120 11 61 74 21
-121 29 85 42 75
-122 11 39 61 94
-123 55 77 14 27
-124 57 15 37 96
-125 55 12 23 78
-126 22 91 70 43
-127 66 12 24 49
-128 3 82 40 64
-129 24 47 72 95
-130 77 15 29 63
-131 34 25 82 73
-132 89 47 69 32
-133 45 58 91 5
-134 88 34 16 51
-135 88 15 40 63
-136 48 5 83 64
-137 93 53 10 43
-138 80 95 41 21
-139 70 51 20 10
-140 13 69 26 59
-141 44 81 30 65
-142 35 72 18 96
-143 56 2 80 19
-144 67 48 85 32
-145 44 56 2 81
-146 7 29 62 75
-147 92 39 7 62
-148 67 58 26 5
-149 13 47 61 95
-150 38 84 19 74
-151 82 28 40 65
-152 1 46 81 60
-153 88 68 40 20
-154 27 38 75 86
-155 1 60 72 18
-156 24 4 72 52
-157 70 92 39 20
-158 33 78 92 17
-159 33 12 49 94
-160 14 49 28 65
-161 34 4 82 52
-162 77 90 37 27
-163 19 74 53 10
-164 44 55 14 87
-165 46 81 73 31
-166 56 79 8 31
-167 45 57 93 9
-168 83 74 42 21
-169 79 25 5 64
-170 56 36 84 8
-171 16 73 31 53
-172 14 49 95 41
-173 27 6 75 54
-174 57 15 30 65
-175 60 71 7 30
-176 66 24 48 83
-177 78 17 63 9
-178 80 37 19 96
-179 22 68 3 58
-180 35 90 69 26
-181 48 63 85 9
-182 35 90 4 54
-183 22 44 68 87
-184 1 17 62 76
-185 66 57 18 9
-186 13 25 61 73
-187 67 50 8 32
-188 51 85 42 10
-189 35 16 96 53
-190 71 28 39 94
-191 23 45 78 91
-192 71 93 30 43
0