# Group 1024.dih downloaded from the LMFDB on 26 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(237605593520588123342671235491883536806422556954066425666572975069626498067439039,1024); a := GPC.1; b := GPC.3; c := GPC.6; d := GPC.8; GPerm := Group( (1,10,24,14,4,11,21,15,2,9,23,13,3,12,22,16)(5,31,20,26,8,29,18,27,6,32,19,25,7,30,17,28), (1,12,24,32)(2,11,23,31)(3,10,22,30)(4,9,21,29)(5,13,17,27)(6,14,18,28)(7,16,19,25)(8,15,20,26) ); # Booleans booleans_1024_dih := rec( Agroup := false, Zgroup := false, abelian := false, almost_simple := false, cyclic := false, metabelian := true, metacyclic := false, monomial := true, nilpotent := true, perfect := false, quasisimple := false, rational := false, solvable := true, supersolvable := true); # Character Table chartbl_1024_dih:=rec(); chartbl_1024_dih.IsFinite:= true; chartbl_1024_dih.UnderlyingCharacteristic:= 0; chartbl_1024_dih.UnderlyingGroup:= GPC; chartbl_1024_dih.Size:= 1024; chartbl_1024_dih.InfoText:= "Character table for group 1024.dih downloaded from the LMFDB."; chartbl_1024_dih.Identifier:= " C4^2.C2wrC4 "; chartbl_1024_dih.NrConjugacyClasses:= 46; chartbl_1024_dih.ConjugacyClasses:= [ of ..., f7, f7*f10, f5*f6, f2*f5*f8*f9, f2*f3*f6*f8*f9, f2*f3*f5*f7*f8, f6*f10, f6, f6*f9, f6*f9*f10, f5*f10, f9, f2*f8, f1*f2*f3*f5*f6, f1*f3*f4*f5*f6*f7*f8*f9, f1*f3*f5, f1*f2*f3*f8*f10, f4, f4*f5, f4*f7*f10, f4*f5*f7*f10, f4*f9, f4*f9*f10, f8, f8*f10, f7*f8, f4*f8, f5*f8, f5*f8*f10, f5*f8*f9, f5*f7*f8, f2*f4*f6*f7*f10, f2*f4*f7*f10, f3, f3*f5, f3*f10, f3*f8, f3*f9, f3*f5*f9, f3*f9*f10, f3*f4*f9, f1*f6*f8*f9*f10, f1*f2*f4*f8*f10, f1*f2*f4*f6*f8*f10, f1*f8*f9*f10]; chartbl_1024_dih.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]; chartbl_1024_dih.ComputedPowerMaps:= [ , [1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 3, 2, 3, 2, 5, 5, 5, 5, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 13, 13, 9, 9, 19, 20, 19, 20, 21, 22, 21, 22, 33, 34, 34, 33]]; chartbl_1024_dih.SizesCentralizers:= [1024, 1024, 512, 256, 32, 16, 16, 512, 512, 256, 256, 256, 128, 32, 16, 16, 16, 16, 256, 256, 256, 256, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 32, 32, 64, 64, 64, 64, 64, 64, 64, 64, 16, 16, 16, 16]; chartbl_1024_dih.ClassNames:= ["1A", "2A", "2B", "2C", "2D", "2E", "2F", "4A", "4B", "4C", "4D", "4E", "4F", "4G", "4H1", "4H-1", "4I1", "4I-1", "8A1", "8A3", "8B1", "8B3", "8C", "8D", "8E1", "8E3", "8F1", "8F3", "8G1", "8G3", "8H1", "8H3", "8I1", "8I-1", "16A1", "16A3", "16B1", "16B3", "16C1", "16C3", "16D1", "16D3", "16E1", "16E-1", "16E3", "16E-3"]; chartbl_1024_dih.OrderClassRepresentatives:= [1, 2, 2, 2, 2, 2, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16]; chartbl_1024_dih.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*E(4), 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, E(4), E(4), -1*E(4), -1*E(4)], [1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, E(4), -1*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*E(4), -1*E(4), E(4), E(4)], [1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1*E(4), 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*E(4), -1*E(4), E(4), E(4)], [1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, E(4), -1*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, E(4), E(4), -1*E(4), -1*E(4)], [2, 2, 2, 2, -2, 0, 0, 2, 2, 2, 2, 2, 2, -2, 0, 0, 0, 0, 2, 2, 2, 2, -2, -2, -2, 2, -2, -2, -2, 2, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, -2, -2, -2, 2, -2, -2, -2, 2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, -2, 2, 0, 0, -2, -2, 2, 2, 2, -2, -2, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1*E(8)-E(8)^-1, E(8)+E(8)^-1, -1*E(8)-E(8)^-1, E(8)+E(8)^-1], [2, 2, 2, -2, 2, 0, 0, -2, -2, 2, 2, 2, -2, -2, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, E(8)+E(8)^-1, -1*E(8)-E(8)^-1, E(8)+E(8)^-1, -1*E(8)-E(8)^-1], [2, 2, 2, -2, -2, 0, 0, -2, -2, 2, 2, 2, -2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1*E(8)-E(8)^3, E(8)+E(8)^3, E(8)+E(8)^3, -1*E(8)-E(8)^3], [2, 2, 2, -2, -2, 0, 0, -2, -2, 2, 2, 2, -2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, E(8)+E(8)^3, -1*E(8)-E(8)^3, -1*E(8)-E(8)^3, E(8)+E(8)^3], [2, 2, 2, -2, 0, 0, 0, -2, -2, 2, 2, 2, -2, 0, -1-E(4), -1+E(4), 1-E(4), 1+E(4), -2, -2, -2, -2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 2*E(4), -2*E(4), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, -2, 0, 0, 0, -2, -2, 2, 2, 2, -2, 0, -1+E(4), -1-E(4), 1+E(4), 1-E(4), -2, -2, -2, -2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, -2*E(4), 2*E(4), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, -2, 0, 0, 0, -2, -2, 2, 2, 2, -2, 0, 1-E(4), 1+E(4), -1-E(4), -1+E(4), -2, -2, -2, -2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, -2*E(4), 2*E(4), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, -2, 0, 0, 0, -2, -2, 2, 2, 2, -2, 0, 1+E(4), 1-E(4), -1+E(4), -1-E(4), -2, -2, -2, -2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 2*E(4), -2*E(4), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, 4, 4, 4, 0, 0, 0, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, -4, -4, -4, -4, 0, 0, 0, -4, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, 4, 4, -4, 0, -2, 2, -4, -4, -4, -4, 4, 4, 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], [4, 4, 4, -4, 0, 2, -2, -4, -4, -4, -4, 4, 4, 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], [4, 4, 4, 4, 0, 0, 0, 4, 4, -4, -4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, -2, -2, 2, -2, 2, 2, 0, 0, 0, 0], [4, 4, 4, 4, 0, 0, 0, 4, 4, -4, -4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 2, 2, -2, 2, -2, -2, 0, 0, 0, 0], [4, 4, 4, -4, 0, 0, 0, 4, 4, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 2, 0, -2, -2, 2, 0, 2, 2, 0, 0, 0, -2*E(8)-2*E(8)^-1, 0, 0, -2*E(8)-2*E(8)^-1, 0, 2*E(8)+2*E(8)^-1, 2*E(8)+2*E(8)^-1, 0, 0, 0, 0], [4, 4, 4, -4, 0, 0, 0, 4, 4, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 2, 0, -2, -2, 2, 0, 2, 2, 0, 0, 0, 2*E(8)+2*E(8)^-1, 0, 0, 2*E(8)+2*E(8)^-1, 0, -2*E(8)-2*E(8)^-1, -2*E(8)-2*E(8)^-1, 0, 0, 0, 0], [4, 4, 4, -4, 0, 0, 0, 4, 4, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, 0, 2, 2, -2, 0, -2, -2, 0, 0, -2*E(8)-2*E(8)^-1, 0, 2*E(8)+2*E(8)^-1, 2*E(8)+2*E(8)^-1, 0, -2*E(8)-2*E(8)^-1, 0, 0, 0, 0, 0, 0], [4, 4, 4, -4, 0, 0, 0, 4, 4, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, 0, 2, 2, -2, 0, -2, -2, 0, 0, 2*E(8)+2*E(8)^-1, 0, -2*E(8)-2*E(8)^-1, -2*E(8)-2*E(8)^-1, 0, 2*E(8)+2*E(8)^-1, 0, 0, 0, 0, 0, 0], [4, 4, -4, 0, 0, 0, 0, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 2, 2, 0, 0, -2*E(8)-2*E(8)^-1, -2, 0, 0, 2*E(8)+2*E(8)^-1, 2, 2*E(8)+2*E(8)^-1, -2*E(8)-2*E(8)^-1, 0, 0, -1*E(8)-E(8)^-1, -2-E(8)+E(8)^3, -1*E(8)-E(8)^-1, E(8)+E(8)^-1, 2+E(8)-E(8)^3, E(8)+E(8)^-1, 2-E(8)+E(8)^3, -2+E(8)-E(8)^3, 0, 0, 0, 0], [4, 4, -4, 0, 0, 0, 0, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 2, 2, 0, 0, 2*E(8)+2*E(8)^-1, -2, 0, 0, -2*E(8)-2*E(8)^-1, 2, -2*E(8)-2*E(8)^-1, 2*E(8)+2*E(8)^-1, 0, 0, E(8)+E(8)^-1, -2+E(8)-E(8)^3, E(8)+E(8)^-1, -1*E(8)-E(8)^-1, 2-E(8)+E(8)^3, -1*E(8)-E(8)^-1, 2+E(8)-E(8)^3, -2-E(8)+E(8)^3, 0, 0, 0, 0], [4, 4, -4, 0, 0, 0, 0, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 2, 2, 0, 0, -2*E(8)-2*E(8)^-1, -2, 0, 0, 2*E(8)+2*E(8)^-1, 2, 2*E(8)+2*E(8)^-1, -2*E(8)-2*E(8)^-1, 0, 0, E(8)+E(8)^-1, 2+E(8)-E(8)^3, E(8)+E(8)^-1, -1*E(8)-E(8)^-1, -2-E(8)+E(8)^3, -1*E(8)-E(8)^-1, -2+E(8)-E(8)^3, 2-E(8)+E(8)^3, 0, 0, 0, 0], [4, 4, -4, 0, 0, 0, 0, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 2, 2, 0, 0, 2*E(8)+2*E(8)^-1, -2, 0, 0, -2*E(8)-2*E(8)^-1, 2, -2*E(8)-2*E(8)^-1, 2*E(8)+2*E(8)^-1, 0, 0, -1*E(8)-E(8)^-1, 2-E(8)+E(8)^3, -1*E(8)-E(8)^-1, E(8)+E(8)^-1, -2+E(8)-E(8)^3, E(8)+E(8)^-1, -2-E(8)+E(8)^3, 2+E(8)-E(8)^3, 0, 0, 0, 0], [4, 4, -4, 0, 0, 0, 0, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, -2, -2*E(8)-2*E(8)^-1, -2*E(8)-2*E(8)^-1, 0, 2, 2*E(8)+2*E(8)^-1, 2*E(8)+2*E(8)^-1, 0, -2, 0, 0, 0, 0, -2+E(8)-E(8)^3, -1*E(8)-E(8)^-1, 2+E(8)-E(8)^3, -2-E(8)+E(8)^3, E(8)+E(8)^-1, 2-E(8)+E(8)^3, -1*E(8)-E(8)^-1, E(8)+E(8)^-1, 0, 0, 0, 0], [4, 4, -4, 0, 0, 0, 0, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, -2, 2*E(8)+2*E(8)^-1, 2*E(8)+2*E(8)^-1, 0, 2, -2*E(8)-2*E(8)^-1, -2*E(8)-2*E(8)^-1, 0, -2, 0, 0, 0, 0, -2-E(8)+E(8)^3, E(8)+E(8)^-1, 2-E(8)+E(8)^3, -2+E(8)-E(8)^3, -1*E(8)-E(8)^-1, 2+E(8)-E(8)^3, E(8)+E(8)^-1, -1*E(8)-E(8)^-1, 0, 0, 0, 0], [4, 4, -4, 0, 0, 0, 0, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, -2, -2*E(8)-2*E(8)^-1, -2*E(8)-2*E(8)^-1, 0, 2, 2*E(8)+2*E(8)^-1, 2*E(8)+2*E(8)^-1, 0, -2, 0, 0, 0, 0, 2-E(8)+E(8)^3, E(8)+E(8)^-1, -2-E(8)+E(8)^3, 2+E(8)-E(8)^3, -1*E(8)-E(8)^-1, -2+E(8)-E(8)^3, E(8)+E(8)^-1, -1*E(8)-E(8)^-1, 0, 0, 0, 0], [4, 4, -4, 0, 0, 0, 0, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, -2, 2*E(8)+2*E(8)^-1, 2*E(8)+2*E(8)^-1, 0, 2, -2*E(8)-2*E(8)^-1, -2*E(8)-2*E(8)^-1, 0, -2, 0, 0, 0, 0, 2+E(8)-E(8)^3, -1*E(8)-E(8)^-1, -2+E(8)-E(8)^3, 2-E(8)+E(8)^3, E(8)+E(8)^-1, -2-E(8)+E(8)^3, -1*E(8)-E(8)^-1, E(8)+E(8)^-1, 0, 0, 0, 0], [8, 8, 8, 8, 0, 0, 0, -8, -8, 0, 0, -8, 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, -8, 0, 0, 0, 0, 8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 4, 4, 0, 0, 0, 4, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [8, 8, -8, 0, 0, 0, 0, 8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, -4, -4, 0, 0, 0, -4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [8, -8, 0, 0, 0, 0, 0, 0, 0, -4, 4, 0, 0, 0, 0, 0, 0, 0, -4*E(8)-4*E(8)^-1, 4*E(8)+4*E(8)^-1, 0, 0, -2-2*E(8)+2*E(8)^3, 2+2*E(8)-2*E(8)^3, 2, 0, -2+2*E(8)-2*E(8)^3, 2-2*E(8)+2*E(8)^3, 2, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [8, -8, 0, 0, 0, 0, 0, 0, 0, -4, 4, 0, 0, 0, 0, 0, 0, 0, 4*E(8)+4*E(8)^-1, -4*E(8)-4*E(8)^-1, 0, 0, -2+2*E(8)-2*E(8)^3, 2-2*E(8)+2*E(8)^3, 2, 0, -2-2*E(8)+2*E(8)^3, 2+2*E(8)-2*E(8)^3, 2, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [8, -8, 0, 0, 0, 0, 0, 0, 0, -4, 4, 0, 0, 0, 0, 0, 0, 0, -4*E(8)-4*E(8)^-1, 4*E(8)+4*E(8)^-1, 0, 0, 2+2*E(8)-2*E(8)^3, -2-2*E(8)+2*E(8)^3, -2, 0, 2-2*E(8)+2*E(8)^3, -2+2*E(8)-2*E(8)^3, -2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [8, -8, 0, 0, 0, 0, 0, 0, 0, -4, 4, 0, 0, 0, 0, 0, 0, 0, 4*E(8)+4*E(8)^-1, -4*E(8)-4*E(8)^-1, 0, 0, 2-2*E(8)+2*E(8)^3, -2+2*E(8)-2*E(8)^3, -2, 0, 2+2*E(8)-2*E(8)^3, -2-2*E(8)+2*E(8)^3, -2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [8, -8, 0, 0, 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4*E(8)-4*E(8)^-1, 4*E(8)+4*E(8)^-1, -2, 2, -2-2*E(8)+2*E(8)^3, 0, -2, 2, -2+2*E(8)-2*E(8)^3, 0, 2-2*E(8)+2*E(8)^3, 2+2*E(8)-2*E(8)^3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [8, -8, 0, 0, 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4*E(8)+4*E(8)^-1, -4*E(8)-4*E(8)^-1, -2, 2, -2+2*E(8)-2*E(8)^3, 0, -2, 2, -2-2*E(8)+2*E(8)^3, 0, 2+2*E(8)-2*E(8)^3, 2-2*E(8)+2*E(8)^3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [8, -8, 0, 0, 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4*E(8)-4*E(8)^-1, 4*E(8)+4*E(8)^-1, 2, -2, 2+2*E(8)-2*E(8)^3, 0, 2, -2, 2-2*E(8)+2*E(8)^3, 0, -2+2*E(8)-2*E(8)^3, -2-2*E(8)+2*E(8)^3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [8, -8, 0, 0, 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4*E(8)+4*E(8)^-1, -4*E(8)-4*E(8)^-1, 2, -2, 2-2*E(8)+2*E(8)^3, 0, 2, -2, 2+2*E(8)-2*E(8)^3, 0, -2-2*E(8)+2*E(8)^3, -2+2*E(8)-2*E(8)^3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]; ConvertToLibraryCharacterTableNC(chartbl_1024_dih);