# Group 1728.46310 downloaded from the LMFDB on 28 October 2025. ## Various presentations of this group are stored in this file: # GPC is polycyclic presentation GPerm is permutation group # GLZ, GLFp, GLZA, GLZq, GLFq if they exist are matrix groups # Many characteristics of the group are stored as booleans in a record: # Agroup, Zgroup, abelian, almost_simple,cyclic, metabelian, # metacyclic, monomial, nilpotent, perfect, quasisimple, rational, # solvable, supersolvable # The character table is stored as a record chartbl_n_i where n is the order # of the group and i is which group of that order it is. The record is # converted to a character table using ConvertToLibraryCharacterTableNC # Constructions GPC := PcGroupCode(6107578966063392682036203052788766621036178495933010688613928603852016258621958283849257,1728); a := GPC.1; b := GPC.2; c := GPC.3; d := GPC.5; e := GPC.7; GPerm := Group( (1,2,7,4)(3,8,13,14)(5,9,19,15)(6,10,21,16)(11,22,27,31)(12,23,30,28)(17,18,24,20)(25,29,32,26)(33,34)(35,38)(36,37), (1,3,7,13)(2,8,4,14)(5,11,19,27)(6,12,21,30)(9,22,15,31)(10,23,16,28)(17,32,24,25)(18,26,20,29)(33,34)(35,37)(36,38), (1,4,7,2)(3,8,13,14)(5,17,19,24)(6,10,21,16)(9,18,15,20)(11,25,27,32)(12,28,30,23)(22,29,31,26), (5,6,20)(9,10,17)(11,12,29)(15,16,24)(18,19,21)(22,23,32)(25,31,28)(26,27,30), (33,35,36)(34,37,38), (33,36,35)(34,37,38), (1,5,7,19)(2,9,4,15)(3,11,13,27)(6,20,21,18)(8,22,14,31)(10,17,16,24)(12,29,30,26)(23,32,28,25), (1,6,7,21)(2,10,4,16)(3,12,13,30)(5,18,19,20)(8,23,14,28)(9,24,15,17)(11,26,27,29)(22,25,31,32), (1,7)(2,4)(3,13)(5,19)(6,21)(8,14)(9,15)(10,16)(11,27)(12,30)(17,24)(18,20)(22,31)(23,28)(25,32)(26,29) ); # Booleans booleans_1728_46310 := rec( Agroup := false, Zgroup := false, abelian := false, almost_simple := false, cyclic := false, metabelian := false, metacyclic := false, monomial := false, nilpotent := false, perfect := false, quasisimple := false, rational := false, solvable := true, supersolvable := false); # Character Table chartbl_1728_46310:=rec(); chartbl_1728_46310.IsFinite:= true; chartbl_1728_46310.UnderlyingCharacteristic:= 0; chartbl_1728_46310.UnderlyingGroup:= GPC; chartbl_1728_46310.Size:= 1728; chartbl_1728_46310.InfoText:= "Character table for group 1728.46310 downloaded from the LMFDB."; chartbl_1728_46310.Identifier:= " Q8.S3^3 "; chartbl_1728_46310.NrConjugacyClasses:= 63; chartbl_1728_46310.ConjugacyClasses:= [ of ..., f8*f9, f2*f5*f6*f8*f9, f2*f3*f4*f7*f9^2, f3*f4*f9^2, f1*f2*f3*f6*f8*f9, f1*f3*f4*f7*f8*f9, f6*f8*f9, f9^2, f6*f8, f4, f4^2*f5*f6^2, f4^2*f5*f6*f7*f8*f9, f4^2*f6^2*f9^2, f2*f3*f4*f8*f9, f2*f3*f4, f2, f5*f6, f1*f8*f9, f1*f2*f4^2*f5*f6*f7, f3*f4*f5*f6*f7*f9, f8, f6^2*f8*f9, f6^2*f8*f9^2, f4^2*f8*f9, f4*f6^2*f7*f8, f4*f5*f6*f8, f4*f6*f9, f2*f5, f2*f3*f4*f7, f1*f2*f3*f6*f8, f3*f4^2*f5*f6*f7*f9, f3*f7*f8*f9^2, f1*f4*f5*f6*f7*f9^2, f1*f2*f3*f5*f6*f8*f9, f1*f2*f5*f6*f7*f8*f9, f1*f3*f4*f5*f6^2*f7, f2*f3*f4*f9, f2*f3*f4*f8, f2*f6, f5*f6*f8, f6*f7*f8, f1*f9, f1*f6, f6*f7*f8*f9^2, f2*f4, f2*f4^2, f2*f3, f2*f3*f6, f1*f4^2*f6^2*f8, f2*f4^2*f5*f6^2*f8*f9, f2*f4*f6^2*f7*f8, f2*f3*f5*f7*f8*f9, f2*f3*f4^2*f5*f8, f1*f2*f4^2*f5*f7, f1*f4*f7, f1*f4^2*f7, f1*f5, f1*f5*f9, f1*f5*f7, f1*f2*f3*f7, f1*f2*f3*f7*f9, f1*f2*f5*f6^2*f9]; chartbl_1728_46310.IdentificationOfConjugacyClasses:= [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]; chartbl_1728_46310.ComputedPowerMaps:= [ , [1, 1, 1, 1, 1, 1, 1, 8, 9, 10, 11, 12, 13, 14, 2, 2, 2, 2, 2, 2, 2, 9, 8, 10, 11, 12, 13, 14, 8, 9, 9, 11, 11, 18, 18, 18, 18, 22, 22, 23, 22, 23, 22, 23, 24, 25, 25, 25, 25, 24, 26, 26, 27, 27, 23, 41, 41, 42, 45, 45, 41, 41, 42], [1, 2, 3, 4, 5, 6, 7, 1, 1, 1, 1, 1, 1, 1, 16, 15, 17, 18, 19, 20, 21, 2, 2, 2, 2, 2, 2, 2, 3, 4, 6, 5, 5, 34, 35, 36, 37, 15, 16, 17, 18, 18, 19, 19, 18, 17, 17, 15, 16, 19, 17, 17, 16, 15, 20, 34, 34, 34, 34, 34, 35, 35, 36]]; chartbl_1728_46310.SizesCentralizers:= [1728, 1728, 96, 96, 96, 48, 16, 864, 864, 432, 216, 108, 108, 54, 576, 576, 288, 288, 144, 48, 32, 864, 864, 432, 216, 108, 108, 54, 48, 48, 24, 24, 24, 144, 48, 48, 16, 288, 288, 144, 144, 144, 72, 72, 72, 72, 72, 72, 72, 36, 36, 36, 36, 36, 24, 144, 144, 72, 72, 72, 48, 48, 24]; chartbl_1728_46310.ClassNames:= ["1A", "2A", "2B", "2C", "2D", "2E", "2F", "3A", "3B", "3C", "3D", "3E", "3F", "3G", "4A1", "4A-1", "4B", "4C", "4D", "4E", "4F", "6A", "6B", "6C", "6D", "6E", "6F", "6G", "6H", "6I", "6J", "6K1", "6K-1", "8A", "8B", "8C", "8D", "12A1", "12A-1", "12B", "12C", "12D", "12E", "12F", "12G", "12H1", "12H5", "12I1", "12I-1", "12J", "12K1", "12K5", "12L1", "12L-1", "12M", "24A1", "24A-1", "24B", "24C1", "24C-1", "24D1", "24D7", "24E"]; chartbl_1728_46310.OrderClassRepresentatives:= [1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 8, 8, 8, 8, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 24, 24, 24, 24, 24, 24, 24, 24]; chartbl_1728_46310.Irr:= [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, -1, 1, -1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, 1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1], [1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1, -1, 1, -1, 1, -1, -1, 1, 1, 1, -1, 1, 1, -1, 1, -1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1], [1, 1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, -1, -1, 1, -1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, -1, -1, -1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1, -1], [1, 1, -1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, -1, -1, -1, 1, 1, 1], [1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, 1, 1, 1, -1, 1, -1, -1, 1, -1, 1, -1, -1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, 1], [1, 1, 1, -1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, -1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1], [1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [2, 2, 0, 0, 2, 0, 0, -1, 2, -1, 2, -1, 2, -1, 0, 0, 2, 2, 2, 2, 0, 2, -1, -1, 2, -1, 2, -1, -1, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, -1, 2, -1, 0, 2, -1, 2, 2, 0, -1, 0, -1, -1, 0, -1, -1, 2, 2, -1, -1, -1, 0, 0, -1], [2, 2, 2, 0, 0, 2, 0, 2, -1, -1, 2, 2, -1, -1, 2, 2, 0, 2, 2, 0, 0, -1, 2, -1, 2, 2, -1, -1, 0, -1, -1, 0, 0, 2, 2, 0, 0, -1, -1, 0, -1, 2, 2, 0, -1, -1, 0, 2, 2, -1, 0, 0, -1, -1, 0, -1, -1, 2, -1, -1, -1, -1, 0], [2, 2, 2, 2, 2, 0, 0, 2, 2, 2, -1, -1, -1, -1, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, -1, -1, -1, -1, 2, 2, 0, -1, -1, 0, 0, 0, 0, 2, 2, 2, 2, 2, -1, -1, 2, 0, -1, -1, 0, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, -2, -2, 2, 0, 0, 2, 2, 2, -1, -1, -1, -1, -2, -2, 2, 2, 0, 0, -2, 2, 2, 2, -1, -1, -1, -1, 2, -2, 0, 1, 1, 0, 0, 0, 0, -2, -2, 2, 2, 2, 1, -1, 2, 0, -1, 1, 0, 1, -1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, -2, 0, 0, -2, 0, 2, -1, -1, 2, 2, -1, -1, -2, -2, 0, 2, 2, 0, 0, -1, 2, -1, 2, 2, -1, -1, 0, 1, 1, 0, 0, 2, -2, 0, 0, 1, 1, 0, -1, 2, -2, 0, -1, -1, 0, -2, 2, 1, 0, 0, 1, -1, 0, -1, -1, 2, -1, -1, 1, 1, 0], [2, 2, -2, 0, 0, 2, 0, 2, -1, -1, 2, 2, -1, -1, -2, -2, 0, 2, -2, 0, 0, -1, 2, -1, 2, 2, -1, -1, 0, 1, -1, 0, 0, -2, 2, 0, 0, 1, 1, 0, -1, 2, -2, 0, -1, 1, 0, -2, -2, 1, 0, 0, 1, 1, 0, 1, 1, -2, 1, 1, -1, -1, 0], [2, 2, -2, 2, -2, 0, 0, 2, 2, 2, -1, -1, -1, -1, -2, -2, -2, 2, 0, 0, 2, 2, 2, 2, -1, -1, -1, -1, -2, -2, 0, -1, -1, 0, 0, 0, 0, -2, -2, -2, 2, 2, 1, 1, 2, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 0, 0, -2, 0, 0, -1, 2, -1, 2, -1, 2, -1, 0, 0, -2, 2, -2, 2, 0, 2, -1, -1, 2, -1, 2, -1, 1, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 1, 2, -1, 0, -2, -1, -2, -2, 0, 1, 0, 1, 1, 0, 1, -1, -2, -2, 1, 1, 1, 0, 0, -1], [2, 2, 0, 0, -2, 0, 0, -1, 2, -1, 2, -1, 2, -1, 0, 0, -2, 2, 2, -2, 0, 2, -1, -1, 2, -1, 2, -1, 1, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 1, 2, -1, 0, -2, -1, 2, -2, 0, -1, 0, 1, 1, 0, -1, 1, 2, 2, -1, -1, -1, 0, 0, 1], [2, 2, 0, 0, 2, 0, 0, -1, 2, -1, 2, -1, 2, -1, 0, 0, 2, 2, -2, -2, 0, 2, -1, -1, 2, -1, 2, -1, -1, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, -1, 2, -1, 0, 2, -1, -2, 2, 0, 1, 0, -1, -1, 0, 1, 1, -2, -2, 1, 1, 1, 0, 0, 1], [2, 2, 2, -2, -2, 0, 0, 2, 2, 2, -1, -1, -1, -1, 2, 2, -2, 2, 0, 0, -2, 2, 2, 2, -1, -1, -1, -1, -2, 2, 0, 1, 1, 0, 0, 0, 0, 2, 2, -2, 2, 2, -1, 1, 2, 0, 1, -1, 0, -1, 1, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, 0, 0, -2, 0, 2, -1, -1, 2, 2, -1, -1, 2, 2, 0, 2, -2, 0, 0, -1, 2, -1, 2, 2, -1, -1, 0, -1, 1, 0, 0, -2, -2, 0, 0, -1, -1, 0, -1, 2, 2, 0, -1, 1, 0, 2, -2, -1, 0, 0, -1, 1, 0, 1, 1, -2, 1, 1, 1, 1, 0], [3, 3, -1, 3, -1, 1, 1, 3, 3, 3, 0, 0, 0, 0, 3, 3, 3, -1, 1, 1, -1, 3, 3, 3, 0, 0, 0, 0, -1, -1, 1, 0, 0, -1, -1, -1, -1, 3, 3, 3, -1, -1, 0, 0, -1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1], [3, 3, -1, 3, -1, -1, -1, 3, 3, 3, 0, 0, 0, 0, 3, 3, 3, -1, -1, -1, -1, 3, 3, 3, 0, 0, 0, 0, -1, -1, -1, 0, 0, 1, 1, 1, 1, 3, 3, 3, -1, -1, 0, 0, -1, -1, 0, 0, -1, 0, 0, 0, 0, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1], [3, 3, -1, -3, 1, -1, 1, 3, 3, 3, 0, 0, 0, 0, 3, 3, -3, -1, -1, 1, 1, 3, 3, 3, 0, 0, 0, 0, 1, -1, -1, 0, 0, 1, 1, -1, -1, 3, 3, -3, -1, -1, 0, 0, -1, -1, 0, 0, -1, 0, 0, 0, 0, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1], [3, 3, -1, -3, 1, 1, -1, 3, 3, 3, 0, 0, 0, 0, 3, 3, -3, -1, 1, -1, 1, 3, 3, 3, 0, 0, 0, 0, 1, -1, 1, 0, 0, -1, -1, 1, 1, 3, 3, -3, -1, -1, 0, 0, -1, 1, 0, 0, 1, 0, 0, 0, 0, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1], [3, 3, 1, -3, -1, -1, -1, 3, 3, 3, 0, 0, 0, 0, -3, -3, 3, -1, 1, 1, 1, 3, 3, 3, 0, 0, 0, 0, -1, 1, -1, 0, 0, -1, 1, -1, 1, -3, -3, 3, -1, -1, 0, 0, -1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, -1, -1, -1, -1, -1, 1, 1, -1], [3, 3, 1, -3, -1, 1, 1, 3, 3, 3, 0, 0, 0, 0, -3, -3, 3, -1, -1, -1, 1, 3, 3, 3, 0, 0, 0, 0, -1, 1, 1, 0, 0, 1, -1, 1, -1, -3, -3, 3, -1, -1, 0, 0, -1, -1, 0, 0, -1, 0, 0, 0, 0, -1, -1, 1, 1, 1, 1, 1, -1, -1, 1], [3, 3, 1, 3, 1, -1, 1, 3, 3, 3, 0, 0, 0, 0, -3, -3, -3, -1, 1, -1, -1, 3, 3, 3, 0, 0, 0, 0, 1, 1, -1, 0, 0, -1, 1, 1, -1, -3, -3, -3, -1, -1, 0, 0, -1, 1, 0, 0, 1, 0, 0, 0, 0, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1], [3, 3, 1, 3, 1, 1, -1, 3, 3, 3, 0, 0, 0, 0, -3, -3, -3, -1, -1, 1, -1, 3, 3, 3, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, -1, -1, 1, -3, -3, -3, -1, -1, 0, 0, -1, -1, 0, 0, -1, 0, 0, 0, 0, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1], [4, 4, 0, 0, 0, 0, 0, -2, -2, 1, 4, -2, -2, 1, 0, 0, 0, 4, 4, 0, 0, -2, -2, 1, 4, -2, -2, 1, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 1, -2, 0, 0, -2, 0, 0, 0, 0, 1, 0, -2, -2, -2, 1, 1, 0, 0, 0], [4, 4, 0, 0, 4, 0, 0, -2, 4, -2, -2, 1, -2, 1, 0, 0, 4, 4, 0, 0, 0, 4, -2, -2, -2, 1, -2, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 4, -2, 0, -2, -2, 0, -2, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, 4, 4, 0, 0, 0, 0, 4, -2, -2, -2, -2, 1, 1, 4, 4, 0, 4, 0, 0, 0, -2, 4, -2, -2, -2, 1, 1, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, -2, 4, -2, 0, -2, 0, 0, -2, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, 4, -4, 0, 0, 0, 0, 4, -2, -2, -2, -2, 1, 1, -4, -4, 0, 4, 0, 0, 0, -2, 4, -2, -2, -2, 1, 1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, -2, 4, 2, 0, -2, 0, 0, 2, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, 4, 0, 0, -4, 0, 0, -2, 4, -2, -2, 1, -2, 1, 0, 0, -4, 4, 0, 0, 0, 4, -2, -2, -2, 1, -2, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, -2, 0, 2, -2, 0, 2, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, 4, 0, 0, 0, 0, 0, -2, -2, 1, 4, -2, -2, 1, 0, 0, 0, 4, -4, 0, 0, -2, -2, 1, 4, -2, -2, 1, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 1, 2, 0, 0, 2, 0, 0, 0, 0, -1, 0, 2, 2, 2, -1, -1, 0, 0, 0], [4, -4, 0, 0, 0, 0, 0, 4, 4, 4, -2, -2, -2, -2, -4*E(4), 4*E(4), 0, 0, 0, 0, 0, -4, -4, -4, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4*E(4), -4*E(4), 0, 0, 0, -2*E(4), 0, 0, 0, 0, 2*E(4), 0, -2*E(4), 0, 0, 2*E(4), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, -4, 0, 0, 0, 0, 0, 4, 4, 4, -2, -2, -2, -2, 4*E(4), -4*E(4), 0, 0, 0, 0, 0, -4, -4, -4, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4*E(4), 4*E(4), 0, 0, 0, 2*E(4), 0, 0, 0, 0, -2*E(4), 0, 2*E(4), 0, 0, -2*E(4), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, -4, 0, 0, 0, 0, 0, 4, 4, 4, 1, 1, 1, 1, -4*E(12)^3, 4*E(12)^3, 0, 0, 0, 0, 0, -4, -4, -4, -1, -1, -1, -1, 0, 0, 0, 1-2*E(12)^2, -1+2*E(12)^2, 0, 0, 0, 0, 4*E(12)^3, -4*E(12)^3, 0, 0, 0, E(12)^3, E(12)+E(12)^-1, 0, 0, -1*E(12)-E(12)^-1, -1*E(12)^3, 0, E(12)^3, -1*E(12)-E(12)^-1, E(12)+E(12)^-1, -1*E(12)^3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, -4, 0, 0, 0, 0, 0, 4, 4, 4, 1, 1, 1, 1, 4*E(12)^3, -4*E(12)^3, 0, 0, 0, 0, 0, -4, -4, -4, -1, -1, -1, -1, 0, 0, 0, -1+2*E(12)^2, 1-2*E(12)^2, 0, 0, 0, 0, -4*E(12)^3, 4*E(12)^3, 0, 0, 0, -1*E(12)^3, E(12)+E(12)^-1, 0, 0, -1*E(12)-E(12)^-1, E(12)^3, 0, -1*E(12)^3, -1*E(12)-E(12)^-1, E(12)+E(12)^-1, E(12)^3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, -4, 0, 0, 0, 0, 0, 4, 4, 4, 1, 1, 1, 1, -4*E(12)^3, 4*E(12)^3, 0, 0, 0, 0, 0, -4, -4, -4, -1, -1, -1, -1, 0, 0, 0, -1+2*E(12)^2, 1-2*E(12)^2, 0, 0, 0, 0, 4*E(12)^3, -4*E(12)^3, 0, 0, 0, E(12)^3, -1*E(12)-E(12)^-1, 0, 0, E(12)+E(12)^-1, -1*E(12)^3, 0, E(12)^3, E(12)+E(12)^-1, -1*E(12)-E(12)^-1, -1*E(12)^3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, -4, 0, 0, 0, 0, 0, 4, 4, 4, 1, 1, 1, 1, 4*E(12)^3, -4*E(12)^3, 0, 0, 0, 0, 0, -4, -4, -4, -1, -1, -1, -1, 0, 0, 0, 1-2*E(12)^2, -1+2*E(12)^2, 0, 0, 0, 0, -4*E(12)^3, 4*E(12)^3, 0, 0, 0, -1*E(12)^3, -1*E(12)-E(12)^-1, 0, 0, E(12)+E(12)^-1, E(12)^3, 0, -1*E(12)^3, E(12)+E(12)^-1, -1*E(12)-E(12)^-1, E(12)^3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, -4, 0, 0, 0, 0, 0, 4, -2, -2, -2, -2, 1, 1, -4*E(24)^6, 4*E(24)^6, 0, 0, 0, 0, 0, 2, -4, 2, 2, 2, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2*E(24)^6, 2*E(24)^6, 0, 0, 0, -2*E(24)^6, 0, 0, 0, 0, 2*E(24)^6, 0, E(24)^6, 0, 0, -1*E(24)^6, 0, 0, -1*E(24)+E(24)^3-E(24)^5-2*E(24)^7, E(24)-E(24)^3+E(24)^5+2*E(24)^7, 0, -1*E(24)+E(24)^3-E(24)^5-2*E(24)^7, E(24)-E(24)^3+E(24)^5+2*E(24)^7, -1*E(24)-E(24)^3-E(24)^5+2*E(24)^7, E(24)+E(24)^3+E(24)^5-2*E(24)^7, 0], [4, -4, 0, 0, 0, 0, 0, 4, -2, -2, -2, -2, 1, 1, 4*E(24)^6, -4*E(24)^6, 0, 0, 0, 0, 0, 2, -4, 2, 2, 2, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2*E(24)^6, -2*E(24)^6, 0, 0, 0, 2*E(24)^6, 0, 0, 0, 0, -2*E(24)^6, 0, -1*E(24)^6, 0, 0, E(24)^6, 0, 0, E(24)-E(24)^3+E(24)^5+2*E(24)^7, -1*E(24)+E(24)^3-E(24)^5-2*E(24)^7, 0, E(24)-E(24)^3+E(24)^5+2*E(24)^7, -1*E(24)+E(24)^3-E(24)^5-2*E(24)^7, -1*E(24)-E(24)^3-E(24)^5+2*E(24)^7, E(24)+E(24)^3+E(24)^5-2*E(24)^7, 0], [4, -4, 0, 0, 0, 0, 0, 4, -2, -2, -2, -2, 1, 1, -4*E(24)^6, 4*E(24)^6, 0, 0, 0, 0, 0, 2, -4, 2, 2, 2, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2*E(24)^6, 2*E(24)^6, 0, 0, 0, -2*E(24)^6, 0, 0, 0, 0, 2*E(24)^6, 0, E(24)^6, 0, 0, -1*E(24)^6, 0, 0, E(24)-E(24)^3+E(24)^5+2*E(24)^7, -1*E(24)+E(24)^3-E(24)^5-2*E(24)^7, 0, E(24)-E(24)^3+E(24)^5+2*E(24)^7, -1*E(24)+E(24)^3-E(24)^5-2*E(24)^7, E(24)+E(24)^3+E(24)^5-2*E(24)^7, -1*E(24)-E(24)^3-E(24)^5+2*E(24)^7, 0], [4, -4, 0, 0, 0, 0, 0, 4, -2, -2, -2, -2, 1, 1, 4*E(24)^6, -4*E(24)^6, 0, 0, 0, 0, 0, 2, -4, 2, 2, 2, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2*E(24)^6, -2*E(24)^6, 0, 0, 0, 2*E(24)^6, 0, 0, 0, 0, -2*E(24)^6, 0, -1*E(24)^6, 0, 0, E(24)^6, 0, 0, -1*E(24)+E(24)^3-E(24)^5-2*E(24)^7, E(24)-E(24)^3+E(24)^5+2*E(24)^7, 0, -1*E(24)+E(24)^3-E(24)^5-2*E(24)^7, E(24)-E(24)^3+E(24)^5+2*E(24)^7, E(24)+E(24)^3+E(24)^5-2*E(24)^7, -1*E(24)-E(24)^3-E(24)^5+2*E(24)^7, 0], [6, 6, -2, 0, 0, 2, 0, 6, -3, -3, 0, 0, 0, 0, 6, 6, 0, -2, 2, 0, 0, -3, 6, -3, 0, 0, 0, 0, 0, 1, -1, 0, 0, -2, -2, 0, 0, -3, -3, 0, 1, -2, 0, 0, 1, -1, 0, 0, 2, 0, 0, 0, 0, -1, 0, 1, 1, -2, 1, 1, 1, 1, 0], [6, 6, 0, 0, -2, 0, 0, -3, 6, -3, 0, 0, 0, 0, 0, 0, 6, -2, 2, 2, 0, 6, -3, -3, 0, 0, 0, 0, 1, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, -3, -2, 1, 0, 0, 1, 2, 0, 0, -1, 0, 0, 0, 0, -1, -1, -2, -2, 1, 1, 1, 0, 0, 1], [6, 6, -2, 0, 0, -2, 0, 6, -3, -3, 0, 0, 0, 0, 6, 6, 0, -2, -2, 0, 0, -3, 6, -3, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 2, 0, 0, -3, -3, 0, 1, -2, 0, 0, 1, 1, 0, 0, -2, 0, 0, 0, 0, 1, 0, -1, -1, 2, -1, -1, -1, -1, 0], [6, 6, 0, 0, -2, 0, 0, -3, 6, -3, 0, 0, 0, 0, 0, 0, 6, -2, -2, -2, 0, 6, -3, -3, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, -3, -2, 1, 0, 0, 1, -2, 0, 0, 1, 0, 0, 0, 0, 1, 1, 2, 2, -1, -1, -1, 0, 0, -1], [6, 6, 0, 0, 2, 0, 0, -3, 6, -3, 0, 0, 0, 0, 0, 0, -6, -2, -2, 2, 0, 6, -3, -3, 0, 0, 0, 0, -1, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 3, -2, 1, 0, 0, 1, -2, 0, 0, 1, 0, 0, 0, 0, 1, -1, 2, 2, -1, -1, -1, 0, 0, 1], [6, 6, 0, 0, 2, 0, 0, -3, 6, -3, 0, 0, 0, 0, 0, 0, -6, -2, 2, -2, 0, 6, -3, -3, 0, 0, 0, 0, -1, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 3, -2, 1, 0, 0, 1, 2, 0, 0, -1, 0, 0, 0, 0, -1, 1, -2, -2, 1, 1, 1, 0, 0, -1], [6, 6, 2, 0, 0, -2, 0, 6, -3, -3, 0, 0, 0, 0, -6, -6, 0, -2, 2, 0, 0, -3, 6, -3, 0, 0, 0, 0, 0, -1, 1, 0, 0, -2, 2, 0, 0, 3, 3, 0, 1, -2, 0, 0, 1, -1, 0, 0, 2, 0, 0, 0, 0, -1, 0, 1, 1, -2, 1, 1, -1, -1, 0], [6, 6, 2, 0, 0, 2, 0, 6, -3, -3, 0, 0, 0, 0, -6, -6, 0, -2, -2, 0, 0, -3, 6, -3, 0, 0, 0, 0, 0, -1, -1, 0, 0, 2, -2, 0, 0, 3, 3, 0, 1, -2, 0, 0, 1, 1, 0, 0, -2, 0, 0, 0, 0, 1, 0, -1, -1, 2, -1, -1, 1, 1, 0], [8, 8, 0, 0, 0, 0, 0, -4, -4, 2, -4, 2, 2, -1, 0, 0, 0, 8, 0, 0, 0, -4, -4, 2, -4, 2, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [8, -8, 0, 0, 0, 0, 0, -4, 8, -4, -4, 2, -4, 2, 0, 0, 0, 0, 0, 0, 0, -8, 4, 4, 4, -2, 4, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [8, -8, 0, 0, 0, 0, 0, -4, -4, 2, -4, 2, 2, -1, 0, 0, 0, 0, 0, 0, 0, 4, 4, -2, 4, -2, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2*E(24)+2*E(24)^3-2*E(24)^5-4*E(24)^7, 2*E(24)-2*E(24)^3+2*E(24)^5+4*E(24)^7, 0, E(24)-E(24)^3+E(24)^5+2*E(24)^7, -1*E(24)+E(24)^3-E(24)^5-2*E(24)^7, 0, 0, 0], [8, -8, 0, 0, 0, 0, 0, -4, -4, 2, -4, 2, 2, -1, 0, 0, 0, 0, 0, 0, 0, 4, 4, -2, 4, -2, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2*E(24)-2*E(24)^3+2*E(24)^5+4*E(24)^7, -2*E(24)+2*E(24)^3-2*E(24)^5-4*E(24)^7, 0, -1*E(24)+E(24)^3-E(24)^5-2*E(24)^7, E(24)-E(24)^3+E(24)^5+2*E(24)^7, 0, 0, 0], [8, -8, 0, 0, 0, 0, 0, -4, 8, -4, 2, -1, 2, -1, 0, 0, 0, 0, 0, 0, 0, -8, 4, 4, -2, 1, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2*E(12)-2*E(12)^-1, 0, 0, 2*E(12)+2*E(12)^-1, 0, 0, 0, -1*E(12)-E(12)^-1, E(12)+E(12)^-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [8, -8, 0, 0, 0, 0, 0, -4, 8, -4, 2, -1, 2, -1, 0, 0, 0, 0, 0, 0, 0, -8, 4, 4, -2, 1, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2*E(12)+2*E(12)^-1, 0, 0, -2*E(12)-2*E(12)^-1, 0, 0, 0, E(12)+E(12)^-1, -1*E(12)-E(12)^-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [8, -8, 0, 0, 0, 0, 0, 8, -4, -4, 2, 2, -1, -1, -8*E(4), 8*E(4), 0, 0, 0, 0, 0, 4, -8, 4, -2, -2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4*E(4), 4*E(4), 0, 0, 0, 2*E(4), 0, 0, 0, 0, -2*E(4), 0, -1*E(4), 0, 0, E(4), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [8, -8, 0, 0, 0, 0, 0, 8, -4, -4, 2, 2, -1, -1, 8*E(4), -8*E(4), 0, 0, 0, 0, 0, 4, -8, 4, -2, -2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4*E(4), -4*E(4), 0, 0, 0, -2*E(4), 0, 0, 0, 0, 2*E(4), 0, E(4), 0, 0, -1*E(4), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [12, 12, 0, 0, 0, 0, 0, -6, -6, 3, 0, 0, 0, 0, 0, 0, 0, -4, 4, 0, 0, -6, -6, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, -1, -2, 0, 0, -2, 0, 0, 0, 0, 1, 0, 2, 2, 2, -1, -1, 0, 0, 0], [12, 12, 0, 0, 0, 0, 0, -6, -6, 3, 0, 0, 0, 0, 0, 0, 0, -4, -4, 0, 0, -6, -6, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, -1, 2, 0, 0, 2, 0, 0, 0, 0, -1, 0, -2, -2, -2, 1, 1, 0, 0, 0], [16, -16, 0, 0, 0, 0, 0, -8, -8, 4, 4, -2, -2, 1, 0, 0, 0, 0, 0, 0, 0, 8, 8, -4, -4, 2, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]; ConvertToLibraryCharacterTableNC(chartbl_1728_46310);