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On this page are computer-accessible forms for the graph C4[ 144, 69 ] = SS[144,21].

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {1, 3} under the group generated by the following permutations:

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

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

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