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