# Group 1152.155984 downloaded from the LMFDB on 27 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(452018924039424194692500408481552684466467316727172572347184137,1152); a := GPC.1; b := GPC.2; c := GPC.4; d := GPC.7; e := GPC.8; GPerm := Group( (5,6)(7,8)(10,11)(12,13,14,15), (2,4)(5,7)(6,8)(12,14)(13,15), (5,8,6,7)(12,14)(13,15), (5,6)(7,8), (12,14)(13,15), (2,3,4), (9,10,11), (1,2)(3,4), (1,3)(2,4) ); # Booleans booleans_1152_155984 := rec( Agroup := false, Zgroup := false, abelian := false, almost_simple := false, cyclic := false, metabelian := false, metacyclic := false, monomial := true, nilpotent := false, perfect := false, quasisimple := false, rational := false, solvable := true, supersolvable := false); # Character Table chartbl_1152_155984:=rec(); chartbl_1152_155984.IsFinite:= true; chartbl_1152_155984.UnderlyingCharacteristic:= 0; chartbl_1152_155984.UnderlyingGroup:= GPC; chartbl_1152_155984.Size:= 1152; chartbl_1152_155984.InfoText:= "Character table for group 1152.155984 downloaded from the LMFDB."; chartbl_1152_155984.Identifier:= " C12:(C4*S4) "; chartbl_1152_155984.NrConjugacyClasses:= 84; chartbl_1152_155984.ConjugacyClasses:= [ of ..., f3, f3*f5*f6, f5*f6, f3*f8*f9, f5*f6*f8*f9, f3*f5*f6*f8*f9, f8*f9, f1, f1*f4, f1*f3, f1*f3*f4, f9^2, f6, f6^2*f9^2, f4*f6^2, f3*f4*f6^2, f2*f3, f2, f2*f3*f5*f6, f2*f5*f6, f4*f6^2*f8*f9, f3*f4*f6^2*f8*f9, f2*f3*f4*f5, f2*f4*f6^2, f2*f8, f2*f3*f8, f2*f5*f6*f8, f2*f3*f5*f6*f8, f1*f7*f8*f9, f1*f4*f7*f8*f9, f1*f3*f7*f8*f9, f1*f3*f4*f7*f8*f9, f2*f4*f5*f8, f2*f3*f4*f5*f8, f1*f2*f3*f6*f7*f9^2, f1*f2*f6*f7*f9^2, f1*f2*f4*f5*f9^2, f1*f2*f3*f4*f5*f9^2, f1*f2*f3*f4*f5*f7*f8*f9, f1*f2*f4*f5*f7, f1*f2*f7, f1*f2*f3*f7*f8*f9, f3*f9, f3*f5*f6*f9, f5*f6*f9^2, f3*f8, f5*f6*f8, f3*f5*f6*f8, f8, f5, f3*f6^2, f3*f5, f3*f6*f9, f3*f5*f9, f5*f9^2, f1*f9, f1*f4*f9, f1*f3*f9, f1*f3*f4*f9, f4*f5*f9, f3*f4*f5*f9, f4, f4*f6, f3*f4, f3*f4*f6, f4*f5*f8, f3*f4*f5*f8, f4*f9, f4*f6*f9, f3*f4*f9, f3*f4*f6*f9, f1*f7*f9, f1*f4*f8, f1*f3*f7*f9, f1*f3*f4*f8, f2*f6, f2*f3*f6, f2*f5, f2*f3*f5, f2*f4, f2*f3*f4, f2*f4*f6, f2*f3*f4*f6]; chartbl_1152_155984.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, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84]; chartbl_1152_155984.ComputedPowerMaps:= [ , [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 13, 14, 15, 4, 4, 2, 2, 2, 2, 4, 4, 3, 3, 2, 2, 2, 2, 8, 8, 8, 8, 3, 3, 2, 2, 2, 2, 5, 5, 5, 5, 13, 13, 13, 13, 13, 13, 13, 14, 14, 14, 15, 15, 15, 13, 13, 13, 13, 46, 46, 51, 51, 51, 51, 46, 46, 56, 56, 56, 56, 50, 50, 50, 50, 52, 52, 52, 52, 53, 53, 53, 53], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 1, 1, 1, 16, 17, 19, 18, 21, 20, 22, 23, 25, 24, 27, 26, 29, 28, 30, 31, 32, 33, 35, 34, 37, 36, 39, 38, 41, 40, 43, 42, 2, 3, 4, 5, 6, 7, 8, 4, 2, 3, 2, 3, 4, 9, 10, 11, 12, 16, 17, 16, 16, 17, 17, 22, 23, 16, 16, 17, 17, 30, 31, 32, 33, 18, 19, 20, 21, 24, 25, 24, 25]]; chartbl_1152_155984.SizesCentralizers:= [1152, 1152, 1152, 1152, 384, 384, 384, 384, 96, 96, 96, 96, 576, 144, 72, 576, 576, 384, 384, 384, 384, 192, 192, 192, 192, 128, 128, 128, 128, 96, 96, 96, 96, 64, 64, 32, 32, 32, 32, 32, 32, 32, 32, 576, 576, 576, 192, 192, 192, 192, 144, 144, 144, 72, 72, 72, 48, 48, 48, 48, 288, 288, 144, 144, 144, 144, 96, 96, 72, 72, 72, 72, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48]; chartbl_1152_155984.ClassNames:= ["1A", "2A", "2B", "2C", "2D", "2E", "2F", "2G", "2H", "2I", "2J", "2K", "3A", "3B", "3C", "4A", "4B", "4C1", "4C-1", "4D1", "4D-1", "4E", "4F", "4G1", "4G-1", "4H1", "4H-1", "4I1", "4I-1", "4J", "4K", "4L", "4M", "4N1", "4N-1", "4O1", "4O-1", "4P1", "4P-1", "4Q1", "4Q-1", "4R1", "4R-1", "6A", "6B", "6C", "6D", "6E", "6F", "6G", "6H", "6I", "6J", "6K", "6L", "6M", "6N", "6O", "6P", "6Q", "12A", "12B", "12C1", "12C5", "12D1", "12D5", "12E", "12F", "12G1", "12G5", "12H1", "12H5", "12I", "12J", "12K", "12L", "12M1", "12M-1", "12N1", "12N-1", "12O1", "12O-1", "12O5", "12O-5"]; chartbl_1152_155984.OrderClassRepresentatives:= [1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12]; chartbl_1152_155984.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], [1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, 1, -1, -1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, -1, -1, 1, 1, -1, 1, -1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, 1], [1, -1, -1, 1, -1, 1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1*E(4), -1*E(4), E(4), E(4), 1, -1, E(4), -1*E(4), -1*E(4), E(4), -1*E(4), E(4), 1, -1, -1, 1, -1*E(4), E(4), E(4), E(4), -1*E(4), E(4), E(4), -1*E(4), -1*E(4), -1*E(4), 1, -1, -1, -1, 1, -1, 1, -1, -1, 1, -1, -1, 1, -1, 1, -1, 1, 1, -1, 1, 1, -1, -1, 1, -1, -1, -1, 1, 1, -1*E(4), -1*E(4), E(4), E(4), E(4), -1*E(4), E(4), 1, -1, -1, -1*E(4), 1], [1, -1, -1, 1, -1, 1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, E(4), E(4), -1*E(4), -1*E(4), 1, -1, -1*E(4), E(4), E(4), -1*E(4), E(4), -1*E(4), 1, -1, -1, 1, E(4), -1*E(4), -1*E(4), -1*E(4), E(4), -1*E(4), -1*E(4), E(4), E(4), E(4), 1, -1, -1, -1, 1, -1, 1, -1, -1, 1, -1, -1, 1, -1, 1, -1, 1, 1, -1, 1, 1, -1, -1, 1, -1, -1, -1, 1, 1, E(4), E(4), -1*E(4), -1*E(4), -1*E(4), E(4), -1*E(4), 1, -1, -1, E(4), 1], [1, -1, -1, 1, -1, 1, -1, 1, -1, 1, 1, -1, 1, 1, 1, -1, 1, -1*E(4), -1*E(4), E(4), E(4), -1, 1, -1*E(4), E(4), -1*E(4), E(4), -1*E(4), E(4), -1, 1, -1, 1, E(4), -1*E(4), E(4), -1*E(4), E(4), E(4), -1*E(4), -1*E(4), E(4), -1*E(4), 1, -1, -1, -1, 1, -1, 1, -1, -1, 1, -1, -1, 1, -1, -1, 1, 1, -1, 1, -1, -1, 1, 1, -1, 1, 1, 1, -1, -1, E(4), -1*E(4), E(4), E(4), -1*E(4), E(4), -1*E(4), 1, -1, 1, -1*E(4), -1], [1, -1, -1, 1, -1, 1, -1, 1, -1, 1, 1, -1, 1, 1, 1, -1, 1, E(4), E(4), -1*E(4), -1*E(4), -1, 1, E(4), -1*E(4), E(4), -1*E(4), E(4), -1*E(4), -1, 1, -1, 1, -1*E(4), E(4), -1*E(4), E(4), -1*E(4), -1*E(4), E(4), E(4), -1*E(4), E(4), 1, -1, -1, -1, 1, -1, 1, -1, -1, 1, -1, -1, 1, -1, -1, 1, 1, -1, 1, -1, -1, 1, 1, -1, 1, 1, 1, -1, -1, -1*E(4), E(4), -1*E(4), -1*E(4), E(4), -1*E(4), E(4), 1, -1, 1, E(4), -1], [1, -1, -1, 1, -1, 1, -1, 1, 1, -1, -1, 1, 1, 1, 1, -1, 1, -1*E(4), -1*E(4), E(4), E(4), -1, 1, -1*E(4), E(4), -1*E(4), E(4), -1*E(4), E(4), 1, -1, 1, -1, E(4), -1*E(4), -1*E(4), E(4), -1*E(4), -1*E(4), E(4), E(4), -1*E(4), E(4), 1, -1, -1, -1, 1, -1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, -1, -1, 1, -1, -1, 1, 1, -1, 1, 1, 1, -1, -1, E(4), -1*E(4), E(4), E(4), -1*E(4), E(4), -1*E(4), -1, 1, -1, -1*E(4), 1], [1, -1, -1, 1, -1, 1, -1, 1, 1, -1, -1, 1, 1, 1, 1, -1, 1, E(4), E(4), -1*E(4), -1*E(4), -1, 1, E(4), -1*E(4), E(4), -1*E(4), E(4), -1*E(4), 1, -1, 1, -1, -1*E(4), E(4), E(4), -1*E(4), E(4), E(4), -1*E(4), -1*E(4), E(4), -1*E(4), 1, -1, -1, -1, 1, -1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, -1, -1, 1, -1, -1, 1, 1, -1, 1, 1, 1, -1, -1, -1*E(4), E(4), -1*E(4), -1*E(4), E(4), -1*E(4), E(4), -1, 1, -1, E(4), 1], [1, -1, -1, 1, -1, 1, -1, 1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1*E(4), -1*E(4), E(4), E(4), 1, -1, E(4), -1*E(4), -1*E(4), E(4), -1*E(4), E(4), -1, 1, 1, -1, -1*E(4), E(4), -1*E(4), -1*E(4), E(4), -1*E(4), -1*E(4), E(4), E(4), E(4), 1, -1, -1, -1, 1, -1, 1, -1, -1, 1, -1, -1, 1, 1, -1, 1, -1, 1, -1, 1, 1, -1, -1, 1, -1, -1, -1, 1, 1, -1*E(4), -1*E(4), E(4), E(4), E(4), -1*E(4), E(4), -1, 1, 1, -1*E(4), -1], [1, -1, -1, 1, -1, 1, -1, 1, 1, 1, -1, -1, 1, 1, 1, 1, -1, E(4), E(4), -1*E(4), -1*E(4), 1, -1, -1*E(4), E(4), E(4), -1*E(4), E(4), -1*E(4), -1, 1, 1, -1, E(4), -1*E(4), E(4), E(4), -1*E(4), E(4), E(4), -1*E(4), -1*E(4), -1*E(4), 1, -1, -1, -1, 1, -1, 1, -1, -1, 1, -1, -1, 1, 1, -1, 1, -1, 1, -1, 1, 1, -1, -1, 1, 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-3, -3, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, -1, 1, 1, -1, 3, 3, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, -1, 0, -1], [6, -6, -6, 6, 2, -2, 2, -2, -2, -2, 2, 2, -3, 0, 0, 6, -6, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, -2, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 3, 3, -1, 1, -1, 1, 0, 0, 0, 0, 0, 0, 1, -1, 1, -1, -3, 3, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, -1, 0, 1], [6, -6, -6, 6, 2, -2, 2, -2, -2, 2, 2, -2, -3, 0, 0, -6, 6, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 2, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 3, 3, -1, 1, -1, 1, 0, 0, 0, 0, 0, 0, 1, 1, -1, -1, 3, -3, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 1, 0, -1], [6, -6, -6, 6, 2, -2, 2, -2, 2, -2, -2, 2, -3, 0, 0, -6, 6, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, -2, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 3, 3, -1, 1, -1, 1, 0, 0, 0, 0, 0, 0, -1, -1, 1, 1, 3, -3, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, -1, 0, 1], [6, -6, -6, 6, 2, -2, 2, -2, 2, 2, -2, -2, -3, 0, 0, 6, -6, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 3, 3, -1, 1, -1, 1, 0, 0, 0, 0, 0, 0, -1, 1, -1, 1, -3, 3, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 1, 0, -1], [6, -6, 6, -6, -2, -2, 2, 2, 0, 0, 0, 0, 6, 0, 0, 0, 0, -6*E(4), 6*E(4), -6*E(4), 6*E(4), 0, 0, 0, 0, 2*E(4), -2*E(4), -2*E(4), 2*E(4), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, -6, 6, 2, 2, -2, -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], [6, -6, 6, -6, -2, -2, 2, 2, 0, 0, 0, 0, 6, 0, 0, 0, 0, 6*E(4), -6*E(4), 6*E(4), -6*E(4), 0, 0, 0, 0, -2*E(4), 2*E(4), 2*E(4), -2*E(4), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, -6, 6, 2, 2, -2, -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], [12, 12, -12, -12, 4, -4, -4, 4, 0, 0, 0, 0, -6, 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, 6, -6, 6, 2, -2, -2, 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], [12, -12, 12, -12, -4, -4, 4, 4, 0, 0, 0, 0, -6, 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, 6, 6, -6, -2, -2, 2, 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]]; ConvertToLibraryCharacterTableNC(chartbl_1152_155984);