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