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On this page are computer-accessible forms for the graph C4[ 164, 3 ] = PS(4,41;3).

(I) Following is a form readable by MAGMA:

g:=Graph<164|{ {41, 42}, {80, 83}, {81, 84}, {82, 85}, {116, 125}, {118, 127}, {117, 126}, {115, 124}, {92, 124}, {93, 125}, {94, 126}, {95, 127}, {64, 102}, {65, 103}, {72, 110}, {73, 111}, {80, 118}, {81, 119}, {2, 42}, {3, 43}, {4, 44}, {5, 45}, {6, 46}, {7, 47}, {16, 56}, {17, 57}, {18, 58}, {19, 59}, {20, 60}, {21, 61}, {22, 62}, {23, 63}, {1, 43}, {4, 46}, {5, 47}, {16, 58}, {17, 59}, {20, 62}, {21, 63}, {66, 104}, {67, 105}, {70, 108}, {71, 109}, {82, 120}, {64, 108}, {65, 109}, {66, 110}, {67, 111}, {2, 44}, {3, 45}, {18, 60}, {19, 61}, {68, 106}, {69, 107}, {68, 112}, {69, 113}, {70, 114}, {71, 115}, {76, 120}, {77, 121}, {78, 122}, {79, 123}, {6, 48}, {7, 49}, {14, 56}, {15, 57}, {8, 48}, {9, 49}, {10, 50}, {11, 51}, {12, 52}, {13, 53}, {14, 54}, {15, 55}, {8, 50}, {9, 51}, {12, 54}, {13, 55}, {74, 112}, {75, 113}, {78, 116}, {79, 117}, {72, 116}, {73, 117}, {74, 118}, {75, 119}, {10, 52}, {11, 53}, {76, 114}, {77, 115}, {43, 122}, {1, 82}, {42, 121}, {52, 96}, {53, 97}, {54, 98}, {55, 99}, {60, 104}, {61, 105}, {62, 106}, {63, 107}, {22, 64}, {31, 73}, {30, 72}, {23, 65}, {44, 123}, {24, 64}, {31, 71}, {30, 70}, {29, 69}, {28, 68}, {25, 65}, {26, 66}, {27, 67}, {24, 66}, {29, 71}, {28, 70}, {25, 67}, {58, 96}, {59, 97}, {62, 100}, {63, 101}, {56, 100}, {57, 101}, {58, 102}, {59, 103}, {26, 68}, {27, 69}, {60, 98}, {61, 99}, {28, 124}, {31, 127}, {30, 126}, {29, 125}, {48, 86}, {49, 87}, {56, 94}, {57, 95}, {32, 72}, {39, 79}, {38, 78}, {37, 77}, {36, 76}, {35, 75}, {34, 74}, {33, 73}, {32, 74}, {51, 89}, {50, 88}, {37, 79}, {36, 78}, {33, 75}, {54, 92}, {55, 93}, {48, 92}, {51, 95}, {50, 94}, {49, 93}, {16, 125}, {18, 127}, {34, 76}, {52, 90}, {35, 77}, {53, 91}, {17, 126}, {15, 124}, {44, 88}, {47, 91}, {46, 90}, {45, 89}, {38, 80}, {39, 81}, {40, 80}, {41, 81}, {40, 82}, {47, 85}, {46, 84}, {42, 86}, {43, 87}, {45, 83}, {2, 139}, {4, 141}, {6, 143}, {16, 153}, {18, 155}, {20, 157}, {22, 159}, {1, 138}, {5, 142}, {17, 154}, {21, 158}, {3, 140}, {19, 156}, {19, 128}, {31, 140}, {23, 132}, {27, 136}, {20, 129}, {30, 139}, {28, 137}, {22, 131}, {1, 151}, {8, 158}, {9, 159}, {7, 144}, {29, 138}, {15, 152}, {21, 130}, {8, 145}, {10, 147}, {12, 149}, {14, 151}, {2, 152}, {3, 153}, {6, 156}, {7, 157}, {9, 146}, {13, 150}, {24, 133}, {26, 135}, {4, 154}, {5, 155}, {11, 148}, {25, 134}, {32, 128}, {41, 137}, {40, 136}, {39, 135}, {38, 134}, {37, 133}, {36, 132}, {35, 131}, {34, 130}, {33, 129}, {10, 160}, {11, 161}, {14, 164}, {32, 141}, {34, 143}, {12, 162}, {13, 163}, {33, 142}, {35, 144}, {39, 148}, {36, 145}, {38, 147}, {23, 160}, {37, 146}, {24, 161}, {26, 163}, {25, 162}, {40, 149}, {27, 164}, {41, 150}, {84, 157}, {86, 159}, {85, 158}, {94, 144}, {95, 145}, {110, 160}, {111, 161}, {83, 156}, {84, 134}, {85, 135}, {88, 138}, {89, 139}, {92, 142}, {93, 143}, {112, 162}, {113, 163}, {83, 133}, {114, 164}, {90, 140}, {91, 141}, {86, 136}, {87, 137}, {96, 128}, {123, 155}, {122, 154}, {121, 153}, {120, 152}, {119, 151}, {118, 150}, {117, 149}, {116, 148}, {115, 147}, {97, 129}, {98, 130}, {99, 131}, {100, 132}, {101, 133}, {102, 134}, {103, 135}, {104, 136}, {105, 137}, {106, 138}, {107, 139}, {108, 140}, {109, 141}, {110, 142}, {111, 143}, {112, 144}, {113, 145}, {114, 146}, {96, 146}, {97, 147}, {100, 150}, {101, 151}, {104, 154}, {105, 155}, {108, 158}, {109, 159}, {98, 148}, {99, 149}, {106, 156}, {107, 157}, {87, 160}, {119, 128}, {88, 161}, {122, 131}, {120, 129}, {90, 163}, {89, 162}, {121, 130}, {102, 152}, {103, 153}, {91, 164}, {123, 132} }>;

(II) A more general form is to represent the graph as the orbit of {41, 42} under the group generated by the following permutations:

a: (1, 42, 83, 124)(2, 45, 92, 151, 41, 80, 115, 138)(3, 48, 101, 137, 40, 77, 106, 152)(4, 51, 110, 164, 39, 74, 97, 125)(5, 54, 119, 150, 38, 71, 88, 139)(6, 57, 87, 136, 37, 68, 120, 153)(7, 60, 96, 163, 36, 65, 111, 126)(8, 63, 105, 149, 35, 62, 102, 140)(9, 66, 114, 135, 34, 59, 93, 154)(10, 69, 123, 162, 33, 56, 84, 127)(11, 72, 91, 148, 32, 53, 116, 141)(12, 75, 100, 134, 31, 50, 107, 155)(13, 78, 109, 161, 30, 47, 98, 128)(14, 81, 118, 147, 29, 44, 89, 142)(15, 43, 86, 133, 28, 82, 121, 156)(16, 46, 95, 160, 27, 79, 112, 129)(17, 49, 104, 146, 26, 76, 103, 143)(18, 52, 113, 132, 25, 73, 94, 157)(19, 55, 122, 159, 24, 70, 85, 130)(20, 58, 90, 145, 23, 67, 117, 144)(21, 61, 99, 131, 22, 64, 108, 158)
b: (2, 41)(3, 40)(4, 39)(5, 38)(6, 37)(7, 36)(8, 35)(9, 34)(10, 33)(11, 32)(12, 31)(13, 30)(14, 29)(15, 28)(16, 27)(17, 26)(18, 25)(19, 24)(20, 23)(21, 22)(43, 82)(44, 81)(45, 80)(46, 79)(47, 78)(48, 77)(49, 76)(50, 75)(51, 74)(52, 73)(53, 72)(54, 71)(55, 70)(56, 69)(57, 68)(58, 67)(59, 66)(60, 65)(61, 64)(62, 63)(84, 123)(85, 122)(86, 121)(87, 120)(88, 119)(89, 118)(90, 117)(91, 116)(92, 115)(93, 114)(94, 113)(95, 112)(96, 111)(97, 110)(98, 109)(99, 108)(100, 107)(101, 106)(102, 105)(103, 104)(125, 164)(126, 163)(127, 162)(128, 161)(129, 160)(130, 159)(131, 158)(132, 157)(133, 156)(134, 155)(135, 154)(136, 153)(137, 152)(138, 151)(139, 150)(140, 149)(141, 148)(142, 147)(143, 146)(144, 145)
c: (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, 38, 39, 40, 41)(42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82)(83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123)(124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164)

(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.

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&Graph
C4[ 164, 3 ]
164
-1 82 138 151 43
-2 44 139 42 152
-3 45 140 43 153
-4 44 154 46 141
-5 45 155 47 142
-6 143 46 156 48
-7 144 47 157 49
-8 145 48 158 50
-9 146 49 159 51
-10 147 50 160 52
-11 148 51 161 53
-12 149 52 162 54
-13 55 150 53 163
-14 56 151 54 164
-15 55 57 124 152
-16 56 58 125 153
-17 154 57 59 126
-18 155 58 60 127
-19 156 59 61 128
-20 157 60 62 129
-21 158 61 63 130
-22 159 62 64 131
-23 132 160 63 65
-24 66 133 161 64
-25 67 134 162 65
-26 66 68 135 163
-27 67 69 136 164
-28 68 124 70 137
-29 69 125 71 138
-30 70 126 72 139
-31 71 127 73 140
-32 72 128 74 141
-33 73 129 75 142
-34 143 74 130 76
-35 77 144 75 131
-36 132 78 145 76
-37 77 133 79 146
-38 78 134 80 147
-39 79 135 81 148
-40 80 136 82 149
-41 81 137 150 42
-42 121 2 41 86
-43 1 122 3 87
-44 88 2 123 4
-45 89 3 5 83
-46 90 4 6 84
-47 91 5 7 85
-48 92 6 8 86
-49 93 7 9 87
-50 88 94 8 10
-51 11 89 95 9
-52 12 90 96 10
-53 11 13 91 97
-54 12 14 92 98
-55 99 13 15 93
-56 100 14 16 94
-57 101 15 17 95
-58 102 16 18 96
-59 103 17 19 97
-60 104 18 20 98
-61 99 105 19 21
-62 22 100 106 20
-63 23 101 107 21
-64 22 24 102 108
-65 23 25 103 109
-66 110 24 26 104
-67 111 25 27 105
-68 112 26 28 106
-69 113 27 29 107
-70 114 28 30 108
-71 115 29 31 109
-72 110 116 30 32
-73 33 111 117 31
-74 34 112 118 32
-75 33 35 113 119
-76 34 36 114 120
-77 121 35 37 115
-78 122 36 38 116
-79 123 37 39 117
-80 38 83 40 118
-81 39 84 41 119
-82 1 40 85 120
-83 45 133 156 80
-84 46 134 157 81
-85 47 135 158 82
-86 48 136 159 42
-87 49 137 160 43
-88 44 50 138 161
-89 45 51 139 162
-90 46 52 140 163
-91 47 53 141 164
-92 124 48 54 142
-93 55 143 125 49
-94 56 144 126 50
-95 57 145 127 51
-96 58 146 128 52
-97 59 147 129 53
-98 60 148 130 54
-99 55 61 149 131
-100 132 56 62 150
-101 133 57 63 151
-102 134 58 64 152
-103 135 59 65 153
-104 66 154 136 60
-105 67 155 137 61
-106 68 156 138 62
-107 69 157 139 63
-108 70 158 140 64
-109 71 159 141 65
-110 66 72 160 142
-111 143 67 73 161
-112 144 68 74 162
-113 145 69 75 163
-114 146 70 76 164
-115 77 124 147 71
-116 78 125 148 72
-117 79 126 149 73
-118 80 127 150 74
-119 81 128 151 75
-120 82 129 152 76
-121 77 42 130 153
-122 154 78 43 131
-123 44 132 155 79
-124 15 92 115 28
-125 16 93 116 29
-126 17 94 117 30
-127 18 95 118 31
-128 19 96 119 32
-129 33 20 97 120
-130 121 34 21 98
-131 22 99 122 35
-132 23 100 123 36
-133 24 101 37 83
-134 25 102 38 84
-135 26 103 39 85
-136 27 104 40 86
-137 28 105 41 87
-138 88 1 29 106
-139 89 2 30 107
-140 90 3 31 108
-141 91 4 32 109
-142 33 110 92 5
-143 34 111 93 6
-144 35 112 94 7
-145 36 113 95 8
-146 37 114 96 9
-147 38 115 97 10
-148 11 39 116 98
-149 99 12 40 117
-150 100 13 41 118
-151 1 101 14 119
-152 2 102 15 120
-153 121 3 103 16
-154 122 4 104 17
-155 123 5 105 18
-156 6 83 106 19
-157 7 84 107 20
-158 8 85 108 21
-159 22 9 86 109
-160 110 23 10 87
-161 11 88 111 24
-162 12 89 112 25
-163 13 90 113 26
-164 14 91 114 27
0

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