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