############################################################################# ## #W moufang.tbl Small Moufang loops G. P. Nagy / P. Vojtechovsky ## #H @(#)$Id: moufang.tbl, v 3.1.0 2015/09/23 gap Exp $ ## #Y Copyright (C) 2004, G. P. Nagy (University of Szeged, Hungary), #Y P. Vojtechovsky (University of Denver, USA) ## LOOPS_moufang_data := [ #implemented orders [ 12, 16, 20, 24, 28, 32, 36, 40, 42, 44, 48, 52, 54, 56, 60, 64, 81, 243 ], #number of loops of given order [ 1, 5, 1, 5, 1, 71, 4, 5, 1, 1, 51, 1, 2, 4, 5, 4262, 5, 72 ], # the loops [ # order 12 [ # class 12:01 of Moufang loops [0,['G'],6,1] ], # order 16 [ # class 16:01 of Moufang loops [0,['G'],8,1], [1,['C'],[5,2],9,4], [1,['C'],[2,4,9],3,4], [1,['D'],[5],2,9,4], [2,['D'],[5],9,10,4] ], # order 20 [ # class 20:01 of Moufang loops [0,['G'],10,1] ], # order 24 [ # class 24:01 of Moufang loops [0,['G'],12,1], [1,['C'],[7,2],13,3], [1,['D'],[7],2,13,3], [1,['D'],[7],13,14,3], # class 24:02 of Moufang loops [0,['G'],12,2] ], # order 28 [ # class 28:01 of Moufang loops [0,['G'],14,1] ], # order 32 [ # class 32:01 of Moufang loops [0,['G'],16,1], [1,['C'],[2,6],17,5], [1,['C'],[2,6],17,4], [1,['C'],[2,7,17],3,5], [1,['C'],[2,7,17],3,4], [1,['D'],[2,7],3,17,5], [1,['C'],[2,7,17],3,11], [1,['D'],[3,4,5],2,17,5], [1,['D'],[2,7],3,17,4], [1,['D'],[4,5,17],2,6,4], [1,['C'],[3,4,5,17],2,4], [1,['D'],[3,4],17,18,4], [1,['C'],[3,4,5,17],2,5], [1,['D'],[2,7],17,19,4], [1,['D'],[3,4,5],17,18,5], [2,['D'],[2,7],17,19,4], [2,['D'],[6,12],17,18,4], [2,['C'],[2,7,17],3,4], [2,['C'],[6,12,17],2,11], [2,['D'],[2,7],3,17,4], [2,['C'],[17,19,20],2,4], [2,['D'],[6,12],2,17,11], [2,['C'],[2,7,17],3,11], [2,['D'],[17,20],3,6,11], [2,['D'],[3,4,5],2,17,11], [2,['D'],[3,4,5],17,18,5], [2,['C'],[17,19,20],2,11], [3,['D'],[3,4],17,18,4], [3,['D'],[2,7],17,19,4], [3,['D'],[17,21],2,3,5], [3,['D'],[3,4,5],17,18,5], [4,['D'],[2,7],3,19,4], [4,['D'],[6,13],17,18,11], [4,['C'],[3,9,19],2,4], [4,['D'],[2,7],3,17,4], [5,['D'],[3],17,18,4], [5,['D'],[3,10],17,18,5], [6,['D'],[6,12],2,17,11], [7,['D'],[3,9],2,17,5], [8,['C'],[3,4,17],2,4], [9,['D'],[3,4,5],17,18,11], [10,['D'],[3],17,18,4], [11,['D'],[3,4],17,18,4], [12,['D'],[5,10],17,18,5], [15,['C'],[6,2,17],5,4], [15,['D'],[2,4,17],3,10,4], [15,['D'],[6,2],5,17,4], [15,['D'],[2,4,17],3,5,4], [16,['D'],[3,10],2,17,11], [17,['D'],[3,10],2,17,11], [26,['C'],[6,2],17,4], [27,['D'],[3,4],2,18,4], [28,['D'],[5,10],17,18,5], [29,['D'],[3,10],17,18,11], [31,['D'],[17,24],3,10,4], [31,['D'],[6,17],2,5,4], [31,['D'],[6,17],2,8,4], [31,['D'],[17,24],3,5,4], [38,['C'],[19,3],2,4], [41,['C'],[2,19,3],5,4], # class 32:02 of Moufang loops [0,['G'],16,4], [1,['C'],[6,2],17,5], [1,['C'],[4,2,17],3,5], [1,['D'],[4,2],3,17,5], [1,['D'],[6],2,17,5], [1,['D'],[4,2],17,19,5], [2,['D'],[6],17,18,5], [2,['D'],[4,2],17,19,5], [2,['D'],[4,17],2,6,5], [2,['D'],[4,17],2,3,5], [3,['D'],[6],2,17,5] ], # order 36 [ # class 36:01 of Moufang loops [0,['G'],18,1], # class 36:02 of Moufang loops [0,['G'],18,2], # class 36:03 of Moufang loops [0,['G'],18,3], # 1 Moufang loop of order 36 not accounted for [0,['T'],[12,1,3]] ], # order 40 [ # class 40:01 of Moufang loops [0,['G'],20,1], [1,['C'],[7,2],21,3], [1,['D'],[7],2,21,3], [1,['D'],[7],21,22,3], # class 40:02 of Moufang loops [0,['G'],20,2] ], # order 42 [ # class 42:01 of Moufang loops [0,['G'],21,1] ], # order 44 [ # class 44:01 of Moufang loops [0,['G'],22,1] ], # order 48 [ # class 48:01 of Moufang loops [0,['G'],24,1], [1,['C'],[10,2],25,4], [1,['C'],[10,25],2,4], [1,['D'],[11],25,26,4], [1,['D'],[10],25,26,3], [2,['D'],[11],25,26,4], [2,['D'],[10],25,26,3], [3,['D'],[11],25,26,4], [3,['D'],[10],25,26,3], [4,['C'],[10,11,2],25,9], [4,['D'],[17,2],3,25,9], [4,['D'],[10,11],2,25,9], [4,['C'],[17,2,25],3,9], [4,['D'],[17,25],2,3,9], [4,['D'],[10,11],25,26,9], [5,['D'],[11,6],2,25,4], [6,['D'],[10,11],2,25,9], [6,['C'],[17,2],25,9], [12,['C'],[10,25],2,3], # class 48:02 of Moufang loops [0,['G'],24,2], [1,['C'],[9,13],25,5], # class 48:03 of Moufang loops [0,['G'],24,3], [1,['C'],[10,2],25,4], [1,['D'],[10],2,25,4], [1,['D'],[11,2],3,25,4], [1,['C'],[11,2,25],3,4], [1,['D'],[11,25],2,6,4], [1,['D'],[11,25],2,3,4], [1,['D'],[11,2],25,27,4], [1,['D'],[10],25,26,4], [2,['D'],[11,2],25,27,4], [3,['C'],[11,2,26],3,4], # class 48:08 of Moufang loops [0,['G'],24,8], [1,['C'],[13,7],25,5], [1,['C'],[13,25],2,5], [1,['C'],[7,12,25],3,5], [1,['D'],[13],2,25,5], [1,['D'],[12,25],2,6,5], [1,['D'],[6],25,31,5], [1,['D'],[12,25],2,3,5], [2,['D'],[6],25,31,5], [2,['D'],[12,25],2,6,5], [2,['D'],[12,25],2,3,5], # class 48:10 of Moufang loops [0,['G'],24,10], # class 48:11 of Moufang loops [0,['G'],24,11], [1,['C'],[6,14],25,2], # 5 Moufang loops of order 48 not accounted for [0,['T'],[16,4,3]], #direct product of MoufangLoop(16,4) with cyclic group of order 3. [1,['C'],[11,13],19,4], [1,['D'],[20,21],2,9,4], [1,['C'],[2,4,9],19,4], [2,['D'],[21],9,10,4] ], # order 52 [ # class 52:01 of Moufang loops [0,['G'],26,1] ], # order 54 [ # class 54:01 of Moufang loops [0,['G'],27,1], # class 54:02 of Moufang loops [0,['G'],27,2] ], # order 56 [ # class 56:01 of Moufang loops [0,['G'],28,1], [1,['C'],[7,2],29,3], [1,['D'],[7],2,29,3], [1,['D'],[7],29,30,3] ], # order 60 [ # class 60:01 of Moufang loops [0,['G'],30,1], # class 60:02 of Moufang loops [0,['G'],30,2], # class 60:03 of Moufang loops [0,['G'],30,3], # 2 Moufang loops of order 60 not accounted for (2 classes) [0,['T'],[20,1,3]], [0,['T'],[12,1,5]] ], # order 64 [ # class 64:01 of Moufang loops [0,['G'],32,1], [1,['C'],[2,3],33,4], [1,['C'],[2,3],33,14], [1,['C'],[2,3],33,5], [1,['C'],[2,8,10,33],3,15], [1,['C'],[2,8,10,33],3,4], [1,['C'],[2,8,10,33],3,14], [1,['D'],[2,8,10],3,33,15], [1,['C'],[2,8,10,33],3,5], [1,['D'],[2,8,10],3,33,6], [1,['D'],[4,5,6,33],2,3,16], [1,['D'],[4,5,6,33],2,3,4], [1,['C'],[2,8,10,33],3,6], [1,['D'],[4,5,6,33],2,3,5], [1,['D'],[2,8],33,35,14], [1,['D'],[2,8],33,35,4], [1,['D'],[2,8],33,35,5], [1,['D'],[4,5,6,33],2,3,26], [1,['D'],[2,8,10],33,35,15], [1,['D'],[2,8,10],33,35,6], [2,['D'],[2,8],33,35,14], [2,['D'],[2,8],33,35,4], [2,['D'],[2,8],33,35,5], [2,['C'],[2,8,10,33],3,5], [2,['D'],[2,8,10],3,33,6], [2,['C'],[2,8,10,33],3,14], [2,['D'],[2,8,10],3,33,15], [2,['D'],[2,8,10],33,35,15], [2,['D'],[33,37,38],2,3,5], [2,['C'],[2,8,10,33],3,15], [2,['D'],[33,37,38],2,3,16], [2,['C'],[2,8,10,33],3,6], [2,['D'],[33,37,38],2,3,4], [2,['D'],[33,37,38],2,3,26], [2,['D'],[2,8,10],33,35,6], [3,['D'],[2,8],33,35,4], [3,['D'],[2,8],33,35,14], [3,['D'],[2,8],33,35,5], [3,['C'],[3,11,12,33],2,15], [3,['D'],[2,8,10],3,33,15], [3,['C'],[2,8,10,33],3,15], [3,['D'],[2,8,10],33,35,15], [3,['D'],[3,11,12],33,34,14], [3,['C'],[2,8,10,33],3,4], [3,['C'],[3,11,12,33],2,4], [3,['C'],[3,11,12,33],2,6], [3,['D'],[33,36,38],2,3,4], [3,['D'],[33,36,38],3,7,6], [3,['D'],[2,8,10],3,33,6], [3,['D'],[3,11,12],2,33,26], [3,['D'],[33,36,38],2,3,16], [3,['D'],[33,36,38],2,3,5], [3,['D'],[33,36,38],2,3,6], [3,['C'],[2,8,10,33],3,6], [3,['C'],[3,11,12,33],2,26], [3,['D'],[33,36,38],2,3,26], [3,['D'],[2,8,10],33,35,6], [3,['D'],[33,36,38],3,7,14], [3,['D'],[33,36,38],3,7,5], [3,['D'],[3,11,12],33,34,5], [4,['D'],[2,8],33,35,14], [4,['D'],[2,8],33,35,5], [4,['C'],[2,8,10,33],3,15], [4,['C'],[3,11,12,33],2,15], [4,['D'],[2,8,10],3,33,15], [4,['D'],[2,8,10],33,35,15], [4,['D'],[33,36,38],3,7,14], [4,['D'],[33,36,38],2,3,5], [4,['D'],[33,36,38],3,7,5], [5,['D'],[2,8,10],3,35,16], [5,['D'],[2,8,10],3,35,6], [5,['D'],[2,8,10],3,35,26], [5,['C'],[7,17,19,39],2,16], [5,['C'],[3,12,13,35],2,4], [5,['C'],[7,17,19,39],2,26], [5,['D'],[4,5,6,33],3,7,4], [5,['D'],[35,43,44],2,7,26], [5,['D'],[7,17,19],2,33,6], [5,['C'],[3,12,13,35],2,16], [5,['C'],[7,17,19,39],2,6], [5,['D'],[3,12,13],2,33,14], [5,['D'],[35,43,44],2,3,16], [5,['D'],[4,5,6,33],3,7,6], [5,['C'],[3,12,13,35],2,14], [5,['D'],[4,5,6,33],3,7,26], [5,['D'],[3,12,13],2,33,5], [5,['D'],[3,13],33,34,6], [5,['D'],[2,8],3,33,4], [5,['D'],[2,8],3,33,14], [5,['D'],[3,13],33,34,15], [5,['D'],[2,8],3,33,5], [5,['D'],[3,13],33,34,4], [5,['C'],[7,17,19,39],2,4], [5,['D'],[4,5,6,33],2,3,4], [5,['D'],[4,5,6,33],2,3,26], [5,['D'],[2,8,10],3,33,16], [5,['D'],[7,17,19],2,33,15], [5,['D'],[2,8,10],3,33,26], [5,['D'],[4,5,6,33],2,3,6], [5,['C'],[7,17,19,39],2,5], [5,['D'],[35,43,44],3,7,14], [5,['D'],[4,5,6,33],2,7,5], [5,['D'],[3,12,13],33,34,14], [5,['D'],[2,8,10],3,33,6], [5,['D'],[35,43,44],3,7,5], [5,['D'],[7,17,19],33,34,5], [5,['D'],[3,12,13],33,34,5], [6,['D'],[35,44,45],2,3,5], [6,['D'],[3,11,12],2,33,5], [6,['D'],[2,8],33,35,14], [6,['D'],[3,11],33,34,6], [6,['D'],[2,8],33,35,4], [6,['D'],[3,11],33,34,4], [6,['D'],[3,11],33,34,15], [6,['D'],[2,8],33,35,5], [6,['D'],[2,8,10],33,35,15], [6,['D'],[3,11,12],33,34,5], [7,['D'],[3,11,12],2,33,16], [7,['D'],[35,43,45],2,3,16], [7,['D'],[35,43,45],2,3,5], [7,['D'],[3,11,12],2,33,26], [7,['D'],[35,43,45],2,3,4], [7,['D'],[2,8],33,35,4], [7,['D'],[2,8],33,35,14], [7,['D'],[2,8],33,35,5], [7,['D'],[4,5,6,33],2,3,26], [7,['D'],[2,8,10],33,35,6], [8,['C'],[2,8,33],3,4], [8,['C'],[2,8,33],3,14], [8,['C'],[2,8,33],3,5], [8,['D'],[3,11,12],2,33,14], [8,['C'],[2,8,10,35],3,6], [8,['C'],[2,8,10,35],3,26], [8,['D'],[3,11,12],2,33,5], [8,['D'],[35,43,44],2,3,5], [8,['D'],[35,43,44],2,3,4], [8,['D'],[3,11],33,34,4], [8,['D'],[3,11],33,34,6], [8,['C'],[7,17,18,39],2,6], [8,['D'],[3,11,12],33,34,14], [8,['D'],[35,43,44],3,7,4], [8,['C'],[2,8,10,33],3,26], [8,['D'],[3,11,12],33,34,5], [9,['D'],[2,8],33,35,14], [9,['D'],[2,8],33,35,5], [10,['C'],[2,8,33],3,14], [10,['C'],[2,8,33],3,4], [10,['C'],[2,8,33],3,5], [10,['C'],[2,8,10,35],3,26], [10,['D'],[3,11],33,34,6], [10,['D'],[35,43,44],3,7,14], [10,['D'],[3,11,12],33,34,14], [11,['D'],[4,5,34],2,7,5], [11,['D'],[4,5,34],2,7,4], [11,['D'],[4,5,34],2,7,14], [11,['D'],[4,5,6,34],3,7,26], [11,['D'],[7,29],33,34,26], [11,['D'],[7,29],33,34,16], [11,['D'],[7,29],33,34,4], [11,['D'],[4,5,6,34],2,7,26], [12,['D'],[2,8],33,35,14], [12,['D'],[2,8],33,35,4], [12,['D'],[2,8],33,35,5], [13,['D'],[2,8],3,33,4], [13,['D'],[2,8],3,33,5], [14,['D'],[4,6,35],3,7,6], [14,['D'],[4,6,35],3,7,4], [14,['D'],[2,8],33,35,5], [15,['D'],[10],33,35,4], [15,['D'],[2,6],33,35,15], [15,['D'],[10,22],33,35,5], [15,['D'],[2,6],33,35,6], [16,['D'],[2,6],33,35,6], [19,['C'],[2,3,33],6,14], [19,['D'],[2,3],6,33,5], [19,['D'],[2,3],6,33,4], [19,['D'],[2,3],6,33,14], [19,['C'],[2,3,33],6,4], [19,['D'],[2,8,33],3,13,4], [19,['D'],[3,12,33],2,10,14], [19,['D'],[2,8,33],3,13,14], [19,['D'],[3,12,33],2,10,5], [19,['C'],[2,3,33],6,5], [19,['D'],[2,8,33],3,13,5], [19,['D'],[3,12,33],2,10,4], [19,['D'],[3,12,33],2,6,14], [19,['D'],[2,8,33],3,6,14], [19,['D'],[3,12,33],2,6,4], [19,['D'],[2,8,33],3,6,4], [19,['D'],[2,8,33],3,6,5], 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[731,['D'],[2,10,38],3,5,4], [737,['D'],[38,54,6],3,12,4], [737,['D'],[38,54,6],3,5,4], [761,['D'],[3,33],6,10,4], [762,['D'],[3,35],2,6,4], [770,['D'],[38,13],3,7,4], [771,['D'],[3,33],6,10,4], [774,['D'],[3,2,33],6,16,4], [774,['D'],[19,35,50],3,12,4], [774,['D'],[6,10,38],3,5,4], [775,['D'],[2,3,33],6,16,4], [777,['D'],[3,38],2,6,4], [831,['D'],[4,7,33],2,10,4], [847,['D'],[7,33],2,10,4], [892,['D'],[3,4,33],6,10,4], [898,['D'],[3,4,33],2,6,4], [916,['D'],[3,4,33],2,10,4], [939,['C'],[10,3,33],2,4], [945,['D'],[2,33],3,6,4], [945,['D'],[5,12,33],2,6,4], [945,['D'],[6,33],2,3,4], [949,['D'],[10,16],3,33,4], [987,['D'],[39,61],2,7,4], [1237,['D'],[3,13],33,34,4], [1237,['D'],[4,6,12],33,34,4], # class 64:04 of Moufang loops [0,['G'],32,4], [1,['C'],[2,7],33,6], [1,['C'],[2,8,33],3,6], [1,['C'],[12,23,3,33],2,6], [1,['D'],[12,23],33,34,6], [1,['D'],[4,5,6,33],2,3,6], [1,['D'],[3,4,6],33,34,6], [2,['D'],[12,23],33,34,6], [2,['D'],[3,4,6],33,34,6], [2,['D'],[33,36,37],2,3,6], [3,['D'],[3,11],33,34,6], [3,['D'],[4,6,12],33,34,6], [4,['D'],[12,23],33,34,6], [4,['D'],[3,4,6],33,34,6], [5,['D'],[5,14,33],2,3,6], [5,['D'],[5,14,33],2,7,6], [8,['D'],[5,14,33],2,3,6], [8,['D'],[5,14,33],2,7,6], # class 64:07 of Moufang loops [0,['G'],32,7], [1,['C'],[7,17,2],33,5], [1,['C'],[7,17,2],33,6], [1,['C'],[7,17,2],33,16], [1,['C'],[2,4,33],3,5], [1,['C'],[2,4,33],3,6], [1,['C'],[7,17,33],2,6], [1,['C'],[7,17,33],2,16], [1,['C'],[2,4,33],3,16], [1,['C'],[7,17,33],2,5], [1,['D'],[2,4],3,33,5], [1,['D'],[4,14,3],2,33,5], [1,['D'],[4,14,33],2,7,6], [1,['C'],[4,14,3,33],2,6], [1,['D'],[2,4],3,33,6], [1,['D'],[7,17],2,33,6], [1,['C'],[4,14,3,33],2,16], [1,['D'],[4,14,33],2,7,16], [1,['D'],[4,14,3],2,33,16], [1,['D'],[2,4],3,33,16], [1,['D'],[7,17],2,33,16], [1,['C'],[4,14,3,33],2,5], [1,['D'],[2,4],33,35,5], [1,['D'],[4,14,33],2,3,6], [1,['D'],[2,4],33,35,6], [1,['D'],[4,14,33],2,3,16], [1,['D'],[2,4],33,35,16], [1,['D'],[4,3],33,34,6], [1,['D'],[4,14,3],33,34,16], [1,['D'],[4,14,3],33,34,5], [2,['D'],[2,4],33,35,5], [2,['D'],[2,4],33,35,6], [2,['D'],[2,4],33,35,16], [2,['D'],[7,17],33,34,6], [2,['D'],[4,14,33],2,7,6], [2,['C'],[7,17,33],2,16], [2,['C'],[2,4,33],3,16], [2,['C'],[2,4,33],3,6], [2,['C'],[7,17,33],2,6], [2,['D'],[4,14,33],2,3,16], [2,['D'],[4,14,3],33,34,16], [2,['C'],[4,14,33,35],2,16], [2,['D'],[2,4],3,33,16], [2,['D'],[7,17],2,33,16], [2,['D'],[4,14,33],3,7,16], [2,['D'],[4,14,3],2,33,16], [2,['D'],[4,14,33],2,3,6], [2,['D'],[2,4],3,33,6], [2,['D'],[7,17],2,33,6], [2,['D'],[4,14,33],3,7,6], [2,['C'],[4,14,33,35],2,6], [2,['D'],[4,14,3],33,34,5], [3,['D'],[2,4],33,35,6], [3,['D'],[2,4],33,35,5], [3,['D'],[4,14,33],2,7,16], [3,['C'],[2,4,33],3,5], [3,['D'],[2,4],33,35,16], [3,['D'],[4,3],33,34,6], [3,['D'],[4,14,33],2,7,6], [3,['D'],[4,14,33],2,3,16], [3,['C'],[7,17,33],2,5], [3,['D'],[2,4],3,33,5], [3,['D'],[4,14,3],2,33,5], [3,['D'],[4,14,33],2,3,5], [3,['D'],[4,14,3],33,34,16], [3,['D'],[4,14,33],2,3,6], [3,['C'],[4,14,33,35],2,5], [3,['D'],[4,14,3],33,34,5], [4,['D'],[2,4],33,35,5], [4,['D'],[4,14,33],2,7,6], [4,['D'],[4,14,33],2,3,5], [4,['D'],[4,14,33],3,7,16], [4,['D'],[4,14,33],2,3,16], [5,['D'],[2,4],3,35,6], [5,['D'],[2,4],3,35,16], [5,['D'],[7,18],2,33,6], [5,['D'],[4,14,35],2,7,6], [5,['D'],[3,4],2,33,16], [5,['D'],[4,14,33],3,7,6], [5,['C'],[3,4,35],2,16], [5,['C'],[3,4,35],2,6], [5,['D'],[3,4],33,34,16], [5,['D'],[2,4],33,35,16], [5,['D'],[4,14,33],2,7,16], [5,['D'],[4,14,35],3,7,16], [5,['D'],[2,4],3,33,16], [5,['D'],[7,18],33,34,16], [5,['D'],[2,4],33,35,6], [5,['D'],[4,14,33],2,7,6], [5,['D'],[2,4],3,33,6], [6,['D'],[2,4],3,35,5], [6,['D'],[2,4],3,35,16], [6,['D'],[7,17],2,33,16], [6,['D'],[4,14,35],2,7,16], [6,['D'],[3,4,12],2,33,16], [6,['D'],[4,14,35],2,3,16], [6,['D'],[7,17],2,33,6], [6,['C'],[7,17,39],2,5], [6,['D'],[2,4],3,33,5], [6,['C'],[3,4,12,35],2,5], [6,['D'],[2,4],33,35,5], [6,['D'],[3,4,12],33,34,16], [6,['D'],[3,4],33,34,6], [6,['D'],[3,4,12],33,34,5], [7,['D'],[7,17],2,34,16], [7,['D'],[2,4],3,33,16], [7,['D'],[4,14,34],2,7,16], [7,['D'],[2,4],33,35,5], [7,['D'],[4,14,33],2,7,16], [7,['D'],[7,17],2,33,16], [7,['D'],[4,14,34],2,3,16], [7,['D'],[2,4],33,35,16], [7,['D'],[3,4],33,34,6], [7,['D'],[3,4,12],33,34,16], [8,['D'],[3,4],33,34,16], [8,['D'],[4,14,34],2,3,16], [8,['D'],[2,4,9],33,35,16], [9,['D'],[2,4],3,35,5], [9,['D'],[2,4],3,35,6], [9,['D'],[7,18],2,33,6], [9,['D'],[4,14,35],2,7,6], [9,['D'],[3,4],2,33,5], [9,['D'],[7,18],33,34,16], [10,['D'],[3,4],2,33,16], [10,['D'],[4,14,34],2,7,6], [10,['D'],[4,14,2],3,33,6], [10,['D'],[4,14,2],3,33,16], [11,['D'],[7,17],2,33,16], [12,['C'],[4,3,33],2,6], [13,['C'],[3,4,12,34],2,16], [13,['D'],[4,14,39],2,3,16], [13,['D'],[2,4],33,35,5], [13,['D'],[4,14,34],2,3,5], [13,['C'],[3,4,12,34],2,5], [13,['D'],[3,4],33,34,6], [13,['D'],[3,4,12],33,34,5], [14,['D'],[4,3],33,34,6], [14,['D'],[4,14,33],2,3,16], [15,['D'],[4,14,3],33,34,16], [16,['D'],[4,14,3],33,34,5], [17,['D'],[4,3],2,33,6], [18,['D'],[4,14,35],2,3,5], [19,['C'],[4,3,33],2,6], [21,['D'],[2,4],33,35,5], [22,['D'],[4,3],2,33,6], [23,['D'],[7],33,34,6], [26,['D'],[4,35],3,7,6], [28,['D'],[4,5,12],33,34,5], [29,['C'],[7,2,33],5,6], [29,['D'],[7,2],5,33,6], [29,['D'],[2,4,33],3,5,6], [29,['D'],[4,3,33],2,9,6], [29,['D'],[7,33],2,5,6], [29,['D'],[7,33],2,9,6], [29,['D'],[4,3,33],2,5,6], [29,['D'],[2,4,33],3,12,6], [30,['C'],[7,2,33],5,6], [30,['D'],[7,2],5,33,6], [30,['D'],[4,2,33],3,12,6], [31,['D'],[7,18],2,33,16], [32,['C'],[3,4,12,33],2,16], [32,['D'],[3,4,12],2,33,16], [32,['C'],[3,4,12,33],2,6], [33,['C'],[7,18,33],2,6], [33,['D'],[7,18],2,33,16], [33,['D'],[4,14,33],3,7,16], [33,['C'],[7,18,33],2,16], [34,['D'],[3,4,12],2,33,16], [34,['C'],[3,4,12,33],2,16], [35,['C'],[3,4,12,33],2,16], [36,['D'],[3,4],33,34,5], [37,['D'],[4,14,35],2,3,6], [38,['D'],[3,4,12],33,34,16], [39,['D'],[3,4,12],33,34,16], [41,['C'],[7,2],33,6], [41,['D'],[2,4,9],3,33,6], [42,['D'],[4,3],2,34,6], [52,['C'],[7,2],33,6], [53,['D'],[3,4,12],33,34,16], [54,['D'],[7],33,34,6], [54,['D'],[4,14,33],2,7,6], [56,['D'],[4,14,35],3,7,16], [58,['D'],[4,5,12],33,34,5], [58,['D'],[4,5,33],2,3,6], [60,['D'],[4,35],3,7,6], [64,['D'],[4,35],3,7,6], [65,['D'],[2,4,33],3,5,6], [65,['D'],[4,33,35],2,9,6], [65,['D'],[7,33],2,5,6], [65,['D'],[7,33],2,9,6], [65,['D'],[4,33,35],2,5,6], [65,['D'],[2,4,33],3,12,6], [67,['D'],[4,3],2,33,6], [68,['D'],[7,33],2,5,6], [68,['D'],[4,33,41],3,12,6], [68,['D'],[7,33],2,9,6], [78,['C'],[7,39],2,6], [82,['C'],[2,4,33],3,6], [84,['D'],[4,35],3,7,6], [86,['D'],[7],33,34,6], [87,['D'],[2,4],3,33,6], [96,['D'],[4,33],3,7,6], [100,['D'],[3,4],2,33,6], [102,['D'],[2,4,33],3,12,6], [102,['D'],[7,50],2,5,6], [102,['D'],[7,2],33,34,6], [102,['D'],[2,4,35],3,12,6], [108,['D'],[7],33,34,6], [111,['D'],[4,39],3,7,6], [117,['D'],[7],2,33,6], [128,['C'],[4,35,3],2,6], [139,['C'],[7,2,35],5,6], [144,['C'],[7,33],2,6], [167,['D'],[7],2,34,6], # class 64:15 of Moufang loops [0,['G'],32,15], [1,['C'],[7,2],33,6], [1,['C'],[4,2,33],3,6], [1,['D'],[4,2],3,33,6], [1,['D'],[7],2,33,6], [1,['D'],[4,2],33,35,6], [2,['D'],[7],33,34,6], [2,['D'],[4,2],33,35,6], [2,['D'],[4,33],2,7,6], [2,['D'],[4,33],2,3,6], [3,['D'],[7],2,33,6], # class 64:23 of Moufang loops [0,['G'],32,23], [1,['C'],[7,8,17],33,5], [1,['C'],[8,17,33],2,6], [1,['C'],[8,17,33],2,5], [1,['C'],[7,19,2,33],4,5], [1,['C'],[7,19,2,33],4,6], [1,['D'],[8,17],2,33,6], [1,['D'],[8,17],2,33,5], [1,['C'],[3,4,5,6,33],2,5], [1,['D'],[7,19,33],4,8,6], [1,['D'],[7,19,2],4,33,5], [1,['D'],[7,19,2],4,33,6], [1,['D'],[3,5,6,33],2,8,5], [1,['D'],[3,5,6,33],2,8,6], [1,['D'],[7,19,33],4,8,5], [1,['D'],[7,19,33],2,4,16], [1,['D'],[7,19,33],2,4,5], [1,['D'],[3,5,6,33],4,8,6], [1,['D'],[8,17],33,34,6], [1,['D'],[2,5,6,33],3,4,5], [1,['D'],[7,19,2],33,36,5], [1,['D'],[3,5,6,33],2,4,5], [1,['D'],[7,19,33],2,4,6], [1,['D'],[2,5,6,33],3,4,16], [1,['D'],[7,19,2],33,36,6], [1,['D'],[3,5,6,33],2,4,6], [2,['D'],[7,17],33,34,5], 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[266,['D'],[11,23,43],2,7,16], [267,['D'],[36,43],2,8,5], [269,['D'],[4,14,2],33,35,5], [271,['D'],[3,12,17],2,33,6], [271,['D'],[3,12,17],2,34,6], [271,['D'],[4,15,2],33,35,5], [279,['D'],[4,14,2],33,35,5], [377,['D'],[11,23,43],2,7,6], [381,['D'],[3,12,34],4,8,16], [386,['D'],[2,9,17],33,35,6], [397,['D'],[3,8],33,34,16], [397,['D'],[2,3],33,36,16], [406,['D'],[7,8],33,34,16], [422,['D'],[17,27,35],2,3,6], [704,['C'],[3,4,33],2,6], [704,['D'],[3,4],2,33,16], [704,['D'],[3,12,33],2,4,16], [704,['C'],[3,4,33],2,16], [705,['D'],[7,19,36],2,4,16], [706,['D'],[3,4],2,33,16], [707,['D'],[17,27,34],2,3,16], [708,['D'],[3,13,33],4,8,16], [708,['D'],[11,23,33],2,3,16], [709,['D'],[11,23,33],2,7,16], [710,['D'],[3,8,12],33,34,16], [710,['D'],[8,20,34],3,7,16], [710,['D'],[2,10,11],3,35,16], [710,['D'],[3,4],2,33,16], [710,['D'],[2,3],4,33,16], [710,['D'],[3,12,34],4,8,16], [710,['D'],[11,24,34],3,7,16], [710,['D'],[3,8,12],2,33,16], [711,['D'],[11,24,33],2,7,5], [711,['D'],[11,24,35],2,7,16], [714,['D'],[3,12,34],4,8,6], [716,['D'],[4,14,33],2,3,6], [720,['D'],[11,24,34],3,7,16], [726,['D'],[11,24,34],2,3,16], [758,['D'],[3,12,34],2,8,5], [759,['D'],[2,9,11],33,35,5], [763,['C'],[3,4,34],2,16], [783,['D'],[11,24,34],2,7,6], [856,['D'],[3,13,33],2,8,5], # class 64:38 of Moufang loops [0,['G'],32,38], [1,['C'],[7,17,8],33,6], [1,['C'],[17,8,33],2,6], [1,['C'],[7,17,33],2,6], [1,['C'],[5,8,14,33],3,6], [1,['C'],[7,2,33],4,6], [1,['D'],[7,33],4,8,6], [1,['C'],[5,14,3,33],2,6], [1,['D'],[5,14,33],2,7,6], [1,['D'],[7,17],2,33,6], [1,['D'],[5,8,14],3,33,6], [1,['D'],[17,8],2,33,6], [1,['D'],[5,2,33],3,4,6], [1,['D'],[5,8,33],2,3,6], [1,['D'],[5,3,33],4,8,6], [1,['D'],[5,8,33],3,7,6], [1,['D'],[5,8,14],33,35,6], [1,['D'],[5,14,33],2,3,6], [1,['D'],[7,33],2,4,6], [1,['D'],[5,2,33],3,11,6], [2,['D'],[5,8,14],33,35,6], [2,['D'],[5,14,33],2,7,6], [2,['D'],[7,33],4,8,6], [2,['D'],[5,33,34],3,4,6], [2,['D'],[5,8,33],2,3,6], [2,['D'],[5,33,35],4,8,6], [2,['D'],[5,8,33],3,7,6], [2,['D'],[7,33],2,4,6], [2,['D'],[5,14,33],2,3,6], [2,['D'],[5,33,34],3,11,6], [3,['D'],[5,8,33],2,7,6], [3,['D'],[2,5,34],4,11,6], [3,['D'],[7,8],2,33,6], [3,['D'],[2,4,5],3,33,6], [3,['D'],[4,5,36],2,3,6], [3,['D'],[7,39],2,8,6], [3,['D'],[2,5,34],3,11,6], [3,['D'],[2,5,34],3,4,6], [3,['D'],[5,8,34],2,7,6], [3,['D'],[4,5,36],3,7,6], [3,['D'],[7,39],2,4,6], [4,['D'],[5,40,8],2,3,6], [4,['D'],[5,40,8],3,7,6], [6,['D'],[5,40,8],2,3,6], # class 64:43 of Moufang loops [0,['G'],32,43], [1,['C'],[7,9,11,20],33,6], [1,['C'],[7,20,27,33],4,6], [1,['D'],[23,27,33],3,5,6], [1,['C'],[7,11,2,33],5,6], [1,['D'],[7,20,27],4,33,6], [1,['D'],[7,20,33],2,4,6], [1,['D'],[7,2,33],4,14,6], [1,['D'],[7,20,27],33,36,6], [1,['D'],[23,27,33],3,4,6], [1,['D'],[2,4,6,33],3,5,6], [1,['D'],[7,2,33],4,5,6], [2,['D'],[7,20,27],33,36,6], [2,['D'],[23,27,33],3,5,6], [2,['D'],[7,20,33],2,4,6], [2,['D'],[7,33,34],4,14,6], [2,['D'],[33,34,36],3,5,6], [2,['D'],[23,27,33],3,4,6], [2,['D'],[7,33,34],4,5,6], [3,['D'],[7,20,33],4,5,6], [3,['D'],[4,7,36],5,9,6], [3,['D'],[4,20,36],2,7,6], [3,['D'],[5,17,23],3,33,6], [3,['D'],[4,8,36],3,12,6], [3,['D'],[5,37,41],3,4,6], [3,['D'],[27,41,9],2,3,6], [3,['D'],[4,7,36],2,5,6], [3,['D'],[7,20,36],4,5,6], [3,['D'],[4,20,36],2,3,6], [3,['D'],[4,8,36],3,5,6], [4,['D'],[4,9,36],3,7,6], [4,['D'],[4,11,36],2,9,6], [4,['C'],[4,7,8,36],5,6], [4,['D'],[12,44,3],2,4,6], [4,['D'],[4,11,36],2,5,6], [5,['D'],[5,37,41],4,11,6], [5,['D'],[7,52,20],2,4,6], [7,['D'],[9,27,43],2,3,6], [7,['D'],[43,2,11],3,12,6], [12,['D'],[59,8,12],2,3,6], [14,['D'],[4,9,33],3,7,6], [14,['D'],[4,11,33],2,9,6], [14,['D'],[12,33,35],2,4,6], [14,['D'],[4,11,33],2,5,6], [15,['D'],[9,27,33],2,3,6], [15,['D'],[33,34,49],3,12,6], [19,['D'],[33,40,44],2,3,6] ], # order 81 [ [ 3, 1, 27, 5, "M%eojo4?WT0S)H{KXP=o7y$NeW(z^i`m/?-6-\ QJw>86'IY;F`IRnZHaE}mWiV5hI(pr`Hq;j9#L8U=(W+p@{]M{PE%rA,p>a[L5^fZc|xs4Qc#Z3wo<\ HYKTNtOg" ], [ 3, 1, 27, 5, "M%eojo4`2%11|5jm4>F+N+(,h*xxiw7U(GxF9*{k)A|1lp_TJdDmgV>qiY:A[,SUQ@^Z~(q&8R/F:\ Xx-avt)H^6enpJ%R1T/7r4FnI)~X7hb3}7{,t1Wbn:*9jf6mcTYriVx@.yLVD/dl%'=wm@vIvz#GF{\ Y?Ub/-V>" ], [ 3, 1, 27, 5, "M%eojs*^QmOJq@e&mrUgjw_u)G7e-MPR#WGMXka`&Q9{<08p#G`UCvX_pg~:UWbpD99ul93lr7~s{\ x6oK/UFTAeWQ^Zu820yrv@>c,)$~v-U_3C/0bK{A@;JSt8-Pt.iabG$BR#DhZF^d's9_9Ak.W02yxA\ .sp0.(T[" ], [ 3, 1, 27, 5, "M%eojs*}{@Ei&Ag%E{F{=j$*-vsN0iB'X/fpy^~Snajg/0Q}3*:W+Jhc(J|*:tt(MLn/SvaI`W.,,\ vpq5HgMd8E}4gb@UjS.A0R7(`iGc}pb`3lQPBg5K9'4j(%&ghi$C(V|/@_Ukzu'aWV4cWzQGWPr]~;\ tK#4{bsF" ], [ 3, 1, 27, 5, "T_^JN3r_P,Pfj{x3+>t0,keL^=FKzpJk?tBQs4*KOR+x2FqJF+}:Z{02goFR0Bx/83/;{OGrW1kXq\ dI_'SGalw\ [;n+1L[,=;uBd&l" ] ], # order 243 (in the same order as on Slattery+Zenisek list) [ [ 9, 2, 27, 5, "Jv+VAkF]^3&-k(S(?K2(;pX~(e3-kI0vnO9(sUqZ<>w}P2(djosF=d\ >p4L0I*WLwApLc>=_f]$rn-=?J;fNv=xyM;aa>LGDDb9XfJ&Gl:~SPbM&&L=@f53UV^*S#)zo{uv)NU]1,Le6Ah9kae+&1/&%PA~#)i]ahXFqqcFxv)F+}\ ,4d'n}PF$9vApFNSg/^ShKcMkv6t{rW;NYx>i]AJ=3/^ac9|~KeXk(]}v5Im4koprpD3D;qZfP3T9]\ UOvYO'Sfos_r7BoMf]msK0K$R$u.EG#-Gj/$3TF@qnF.+iy-eel2UqZtNj|LP}r=KL,eeX>PWWxzCV\ >&)YbKEtj`?oF{;jC?4q{wJ)MpL:p{|g>dlu$9<=-QMMc1LA]SMLEZ4H&WB=+tn}~a)s5s4?Xs]_`C\ '@fDhB^Lvq$a7qStXTb4@5;=$F6o2" ], [ 9, 2, 27, 5, "Jv+VAkF]^3&-k(S($tuCoX%|i,=VY4?Ls%='PX\ cmDNXN-&U}MFVIVywA_rQE(yOWA)qt{X~h_}oxYJQT'WP4HYDLg3?2#Ukcz$&Se2mpQvWhLQ/Hz1JZuqY0O\ zk+2'rJ,78XlIV3E*UpmWz?1enI5W" ], [ 9, 1, 27, 5, "9/ZFo)rf{lW@)>M&&L=@f53UWX_.V:r|/:352h9Q~~g1F:(9bFeeO2df]K)6Mzvb1*$^^@G.>w]@l\ Ma1r;cM}-A5r^|TsZ~M&MHf[YHax8mCF}@*P~F:>.e_V@G|@%h^TIg7mZ>Vn9WgsQ}9?AZLEDzcc]T\ cD)$pW>/GS/+JTGktlkZ?,hy+e&T2%fU|DM'g=m/a&DBF+Y=()7DN}vL.*OLfZ1RS=}@p:)IjhDP#f08h,=#q98Bg{li_xf'8Tr3w>W;p)Ad%z#WY-T;Ojb4LVN:6|d3&o@v`*\ [f]bhcq9'(XyT_V-$OaF?BV}[:C2l/a9S8E-p02|?s3y]qXl%|PR3.7s8XC`r8bHDjf~i}Js:)^I@A<$0\ dAn1X{$>Wy@]ZU:t@pjP}w_g@g,$E" ], [ 9, 2, 27, 5, "Jv+VAkF]^3&-k(S({}pm,F'unDWT^u5N6TCmA_7'ToM9PX{=jc]>9[[;8:l8IZEoU}kM7('8rr#B=7:'" ], [ 9, 2, 27, 5, "Jv+VAkF]^3&-k(S(v<)xjtXIoepU_0>h;\ w*4|WTrjj%+eH(2w{A5A*]>%@*N-\ 1{>%5HGbFw'h]DU:KjDP9SDzbH4sf;qU,V,s/'6Nz(+]4=K4*vnV+zI@qxNm'8|oRP[+;l#j@suCe+\ %X>14qAp{ta1/6U'q/|~S-~&ulkMP+nPmBokj^9k/+A5M%<~d|;Wcj2HWk/dIT##/#bxr09#`|782'\ )?=t^L1NDCs345W+HZ=Wfo[pA9;ys" ], [ 9, 1, 27, 5, "9/ZFo)rf{lW@)>M&&L=@f53UV}H}BeKfZ1Ek(+#{DohSP;q32l*.EWNC|uS$wj)PwXx&ST>G~3L%8\ QxWV~QE`D9:1gH=$7Ah)B:{20rpJ9}g2;edBA8jYJ~_GAixvEKj?{[2E3fT?-/.N'B8yM+WE[,9M.)U+?r9X+/\ SZwO%zCnQW-3BELsT{4h/)OTzkWHaa+D8W;\ LL(%Q$z^Ti4=a{=Y[URe9}z`K@v^;" ], [ 9, 2, 27, 5, "Jv+VAkF]^3&-k(S(veuI6=D;HxmwLVika<2NJ1/b-/ah46[qus24bZl`G~ZHaq$S;Y(s/{Kc2?i]7czA{u749|=_IM\ -(00.I;=5FX'2-BN^~C'j'd1J-k:PK|q/w.NYdo\ RLc+Yx_A`E{*4S#U-G|zA<6v(hfR(" ], [ 9, 2, 27, 5, ">y$H^p[ck=k7q%rGG5vU$}QSZ=i>#>9kPhAh?9[Izl?W<.w4BDPd2qyMN}&s?5j%vEDjko]DP6P3:\ o|0>m3/#}fSqr4:8mFu9i%8u3+'i&P%b.yC{+_kt/P?5%kD,#(uQ1B{~|cUz(SV)f4fLmf+}$zH|TW\ Abp.%h-aQY[+c+NiLp~#Ob@i'AFju$6k,,XJiQ,Z.KW'DSXe%f1hFwI>f6(B}:d0t5c788&P1{3&#_\ 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