# Group 448.729 downloaded from the LMFDB on 30 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(61345983602586317507811766492269195195653,448); a := GPC.1; b := GPC.2; c := GPC.5; GPerm := Group( (1,2,6,10)(3,11,12,29)(4,15,19,31)(5,20,17,9)(7,22,23,13)(8,25,27,18)(14,30,21,26)(16,28,32,24)(34,35)(36,37)(38,39), (3,12)(7,23)(11,29)(13,22)(14,21)(16,32)(24,28)(26,30), (1,3)(2,7)(4,16)(5,21)(6,12)(8,26)(9,28)(10,23)(11,15)(13,18)(14,17)(19,32)(20,24)(22,25)(27,30)(29,31), (1,4,17,25,6,19,5,18)(2,8,20,31,10,27,9,15)(3,13,21,32,12,22,14,16)(7,11,28,30,23,29,24,26), (1,5,6,17)(2,9,10,20)(3,14,12,21)(4,18,19,25)(7,24,23,28)(8,15,27,31)(11,26,29,30)(13,16,22,32), (1,6)(2,10)(3,12)(4,19)(5,17)(7,23)(8,27)(9,20)(11,29)(13,22)(14,21)(15,31)(16,32)(18,25)(24,28)(26,30), (33,34,36,38,39,37,35) ); # Booleans booleans_448_729 := rec( Agroup := false, Zgroup := false, abelian := false, almost_simple := false, cyclic := false, metabelian := true, metacyclic := false, monomial := true, nilpotent := false, perfect := false, quasisimple := false, rational := false, solvable := true, supersolvable := true); # Character Table chartbl_448_729:=rec(); chartbl_448_729.IsFinite:= true; chartbl_448_729.UnderlyingCharacteristic:= 0; chartbl_448_729.UnderlyingGroup:= GPC; chartbl_448_729.Size:= 448; chartbl_448_729.InfoText:= "Character table for group 448.729 downloaded from the LMFDB."; chartbl_448_729.Identifier:= " C28.D8 "; chartbl_448_729.NrConjugacyClasses:= 58; chartbl_448_729.ConjugacyClasses:= [ of ..., f6*f7^3, f4*f5*f7^5, f1, f5*f6*f7, f4*f6*f7^3, f1*f5*f6*f7, f1*f2*f7^6, f1*f2*f3*f5*f7^2, f7^4, f7, f7^5, f3*f4*f6*f7^3, f3*f6*f7^3, f3*f4*f5*f7^5, f6, f6*f7, f6*f7^2, f4*f5, f4*f5*f6, f4*f5*f7, f1*f7, f1*f7^6, f1*f7^3, f1*f6, f1*f7^5, f1*f7^2, f2*f7^2, f2*f3*f7^2, f2*f3*f5*f7^4, f2*f5*f6, f5, f5*f6, f5*f7, f5*f7^2, f5*f7^4, f5*f7^3, f4*f7^2, f4*f6*f7^2, f4*f7^3, f1*f5, f1*f3*f5, f1*f5*f6, f1*f5*f7^6, f1*f5*f7, f1*f5*f7^2, f3*f7, f3*f6, f3*f6*f7, f3*f7^2, f3*f4*f7, f3*f7^3, f3*f5, f3*f5*f7^4, f3*f5*f7^2, f3*f5*f6, f3*f4*f5, f3*f5*f7]; chartbl_448_729.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]; chartbl_448_729.ComputedPowerMaps:= [ , [1, 1, 1, 1, 2, 2, 2, 2, 2, 11, 12, 10, 6, 6, 6, 11, 10, 12, 10, 12, 11, 12, 12, 11, 11, 10, 10, 13, 14, 14, 13, 16, 17, 18, 18, 17, 16, 16, 17, 18, 16, 16, 17, 17, 18, 18, 38, 39, 40, 40, 38, 39, 40, 38, 39, 38, 40, 39], [1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 10, 11, 14, 13, 15, 17, 18, 16, 20, 21, 19, 24, 25, 27, 26, 22, 23, 29, 28, 31, 30, 33, 35, 37, 32, 34, 36, 39, 40, 38, 43, 44, 46, 45, 41, 42, 48, 50, 47, 51, 52, 49, 54, 55, 57, 58, 56, 53]]; chartbl_448_729.SizesCentralizers:= [448, 448, 224, 56, 224, 224, 56, 8, 8, 224, 224, 224, 224, 224, 112, 224, 224, 224, 112, 112, 112, 56, 56, 56, 56, 56, 56, 16, 16, 16, 16, 224, 224, 224, 224, 224, 224, 112, 112, 112, 56, 56, 56, 56, 56, 56, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112]; chartbl_448_729.ClassNames:= ["1A", "2A", "2B", "2C", "4A", "4B", "4C", "4D", "4E", "7A1", "7A2", "7A3", "8A1", "8A3", "8B", "14A1", "14A3", "14A5", "14B1", "14B3", "14B5", "14C1", "14C-1", "14C3", "14C-3", "14C5", "14C-5", "16A1", "16A3", "16B1", "16B3", "28A1", "28A3", "28A5", "28A9", "28A11", "28A13", "28B1", "28B3", "28B5", "28C1", "28C-1", "28C3", "28C-3", "28C5", "28C-5", "56A1", "56A3", "56A5", "56A9", "56A13", "56A17", "56B1", "56B3", "56B5", "56B11", "56B15", "56B19"]; chartbl_448_729.OrderClassRepresentatives:= [1, 2, 2, 2, 4, 4, 4, 4, 4, 7, 7, 7, 8, 8, 8, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 16, 16, 16, 16, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56]; chartbl_448_729.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], [2, 2, -2, 0, -2, 2, 0, 0, 0, 2, 2, 2, -2, -2, 2, 2, 2, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, -2, 2, -2, -2, 2, 2, -2, 2, 2, -2, -2], [2, 2, 2, 0, 2, 2, 0, 0, 0, 2, 2, 2, -2, -2, -2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2], [2, 2, -2, 0, 2, -2, 0, 0, 0, 2, 2, 2, 0, 0, 0, 2, 2, 2, -2, -2, -2, 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, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, -2, 0, 2, -2, 0, 0, 0, 2, 2, 2, 0, 0, 0, 2, 2, 2, -2, -2, -2, 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, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, 0, -2, -2, 0, 0, 0, 2, 2, 2, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, -1*E(8)-E(8)^-1, -1*E(8)-E(8)^-1, E(8)+E(8)^-1, E(8)+E(8)^-1, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, 0, -2, -2, 0, 0, 0, 2, 2, 2, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, E(8)+E(8)^-1, E(8)+E(8)^-1, -1*E(8)-E(8)^-1, -1*E(8)-E(8)^-1, -2, -2, -2, -2, -2, -2, -2, -2, -2, 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, 0, 0, E(7)^3+E(7)^-3, E(7)+E(7)^-1, E(7)^2+E(7)^-2, 2, 2, 2, E(7)+E(7)^-1, E(7)^3+E(7)^-3, E(7)^2+E(7)^-2, E(7)^3+E(7)^-3, E(7)^2+E(7)^-2, E(7)+E(7)^-1, E(7)^2+E(7)^-2, E(7)^2+E(7)^-2, E(7)^3+E(7)^-3, E(7)^3+E(7)^-3, E(7)+E(7)^-1, E(7)+E(7)^-1, 0, 0, 0, 0, E(7)+E(7)^-1, E(7)^3+E(7)^-3, E(7)^2+E(7)^-2, E(7)^2+E(7)^-2, E(7)^3+E(7)^-3, E(7)+E(7)^-1, E(7)^3+E(7)^-3, E(7)^2+E(7)^-2, E(7)+E(7)^-1, E(7)^3+E(7)^-3, E(7)^2+E(7)^-2, E(7)^3+E(7)^-3, E(7)+E(7)^-1, E(7)+E(7)^-1, E(7)^2+E(7)^-2, E(7)^3+E(7)^-3, E(7)^2+E(7)^-2, E(7)^3+E(7)^-3, E(7)^3+E(7)^-3, E(7)+E(7)^-1, E(7)^2+E(7)^-2, E(7)+E(7)^-1, E(7)+E(7)^-1, E(7)^2+E(7)^-2, E(7)+E(7)^-1, E(7)^2+E(7)^-2, E(7)^3+E(7)^-3], [2, 2, 2, 2, 2, 2, 2, 0, 0, E(7)^2+E(7)^-2, E(7)^3+E(7)^-3, E(7)+E(7)^-1, 2, 2, 2, E(7)^3+E(7)^-3, E(7)^2+E(7)^-2, E(7)+E(7)^-1, E(7)^2+E(7)^-2, E(7)+E(7)^-1, E(7)^3+E(7)^-3, E(7)+E(7)^-1, E(7)+E(7)^-1, E(7)^2+E(7)^-2, E(7)^2+E(7)^-2, E(7)^3+E(7)^-3, E(7)^3+E(7)^-3, 0, 0, 0, 0, E(7)^3+E(7)^-3, E(7)^2+E(7)^-2, E(7)+E(7)^-1, E(7)+E(7)^-1, E(7)^2+E(7)^-2, E(7)^3+E(7)^-3, E(7)^2+E(7)^-2, E(7)+E(7)^-1, E(7)^3+E(7)^-3, E(7)^2+E(7)^-2, E(7)+E(7)^-1, E(7)^2+E(7)^-2, E(7)^3+E(7)^-3, E(7)^3+E(7)^-3, E(7)+E(7)^-1, E(7)^2+E(7)^-2, E(7)+E(7)^-1, E(7)^2+E(7)^-2, E(7)^2+E(7)^-2, E(7)^3+E(7)^-3, E(7)+E(7)^-1, E(7)^3+E(7)^-3, E(7)^3+E(7)^-3, E(7)+E(7)^-1, E(7)^3+E(7)^-3, E(7)+E(7)^-1, E(7)^2+E(7)^-2], [2, 2, 2, 2, 2, 2, 2, 0, 0, E(7)+E(7)^-1, E(7)^2+E(7)^-2, E(7)^3+E(7)^-3, 2, 2, 2, E(7)^2+E(7)^-2, E(7)+E(7)^-1, E(7)^3+E(7)^-3, E(7)+E(7)^-1, E(7)^3+E(7)^-3, E(7)^2+E(7)^-2, E(7)^3+E(7)^-3, E(7)^3+E(7)^-3, E(7)+E(7)^-1, E(7)+E(7)^-1, E(7)^2+E(7)^-2, E(7)^2+E(7)^-2, 0, 0, 0, 0, E(7)^2+E(7)^-2, E(7)+E(7)^-1, E(7)^3+E(7)^-3, E(7)^3+E(7)^-3, E(7)+E(7)^-1, E(7)^2+E(7)^-2, E(7)+E(7)^-1, E(7)^3+E(7)^-3, E(7)^2+E(7)^-2, E(7)+E(7)^-1, E(7)^3+E(7)^-3, E(7)+E(7)^-1, E(7)^2+E(7)^-2, E(7)^2+E(7)^-2, E(7)^3+E(7)^-3, E(7)+E(7)^-1, E(7)^3+E(7)^-3, E(7)+E(7)^-1, E(7)+E(7)^-1, E(7)^2+E(7)^-2, E(7)^3+E(7)^-3, E(7)^2+E(7)^-2, E(7)^2+E(7)^-2, E(7)^3+E(7)^-3, E(7)^2+E(7)^-2, E(7)^3+E(7)^-3, E(7)+E(7)^-1], [2, 2, -2, -2, -2, 2, 2, 0, 0, E(7)^3+E(7)^-3, E(7)+E(7)^-1, E(7)^2+E(7)^-2, 2, 2, -2, E(7)+E(7)^-1, E(7)^3+E(7)^-3, E(7)^2+E(7)^-2, -1*E(7)^3-E(7)^-3, -1*E(7)^2-E(7)^-2, -1*E(7)-E(7)^-1, -1*E(7)^2-E(7)^-2, -1*E(7)^2-E(7)^-2, -1*E(7)^3-E(7)^-3, -1*E(7)^3-E(7)^-3, -1*E(7)-E(7)^-1, -1*E(7)-E(7)^-1, 0, 0, 0, 0, -1*E(7)-E(7)^-1, -1*E(7)^3-E(7)^-3, -1*E(7)^2-E(7)^-2, -1*E(7)^2-E(7)^-2, -1*E(7)^3-E(7)^-3, -1*E(7)-E(7)^-1, E(7)^3+E(7)^-3, E(7)^2+E(7)^-2, E(7)+E(7)^-1, E(7)^3+E(7)^-3, E(7)^2+E(7)^-2, E(7)^3+E(7)^-3, E(7)+E(7)^-1, E(7)+E(7)^-1, E(7)^2+E(7)^-2, -1*E(7)^3-E(7)^-3, E(7)^2+E(7)^-2, -1*E(7)^3-E(7)^-3, E(7)^3+E(7)^-3, E(7)+E(7)^-1, -1*E(7)^2-E(7)^-2, -1*E(7)-E(7)^-1, E(7)+E(7)^-1, -1*E(7)^2-E(7)^-2, -1*E(7)-E(7)^-1, E(7)^2+E(7)^-2, E(7)^3+E(7)^-3], [2, 2, -2, -2, -2, 2, 2, 0, 0, E(7)^2+E(7)^-2, E(7)^3+E(7)^-3, E(7)+E(7)^-1, 2, 2, -2, E(7)^3+E(7)^-3, E(7)^2+E(7)^-2, E(7)+E(7)^-1, -1*E(7)^2-E(7)^-2, -1*E(7)-E(7)^-1, -1*E(7)^3-E(7)^-3, -1*E(7)-E(7)^-1, -1*E(7)-E(7)^-1, -1*E(7)^2-E(7)^-2, -1*E(7)^2-E(7)^-2, -1*E(7)^3-E(7)^-3, -1*E(7)^3-E(7)^-3, 0, 0, 0, 0, -1*E(7)^3-E(7)^-3, -1*E(7)^2-E(7)^-2, -1*E(7)-E(7)^-1, -1*E(7)-E(7)^-1, -1*E(7)^2-E(7)^-2, -1*E(7)^3-E(7)^-3, E(7)^2+E(7)^-2, E(7)+E(7)^-1, E(7)^3+E(7)^-3, E(7)^2+E(7)^-2, E(7)+E(7)^-1, E(7)^2+E(7)^-2, E(7)^3+E(7)^-3, E(7)^3+E(7)^-3, E(7)+E(7)^-1, -1*E(7)^2-E(7)^-2, E(7)+E(7)^-1, -1*E(7)^2-E(7)^-2, E(7)^2+E(7)^-2, E(7)^3+E(7)^-3, -1*E(7)-E(7)^-1, -1*E(7)^3-E(7)^-3, E(7)^3+E(7)^-3, -1*E(7)-E(7)^-1, -1*E(7)^3-E(7)^-3, E(7)+E(7)^-1, E(7)^2+E(7)^-2], [2, 2, -2, -2, -2, 2, 2, 0, 0, E(7)+E(7)^-1, E(7)^2+E(7)^-2, E(7)^3+E(7)^-3, 2, 2, -2, E(7)^2+E(7)^-2, E(7)+E(7)^-1, E(7)^3+E(7)^-3, -1*E(7)-E(7)^-1, -1*E(7)^3-E(7)^-3, -1*E(7)^2-E(7)^-2, -1*E(7)^3-E(7)^-3, -1*E(7)^3-E(7)^-3, -1*E(7)-E(7)^-1, -1*E(7)-E(7)^-1, -1*E(7)^2-E(7)^-2, -1*E(7)^2-E(7)^-2, 0, 0, 0, 0, -1*E(7)^2-E(7)^-2, -1*E(7)-E(7)^-1, -1*E(7)^3-E(7)^-3, -1*E(7)^3-E(7)^-3, -1*E(7)-E(7)^-1, -1*E(7)^2-E(7)^-2, E(7)+E(7)^-1, E(7)^3+E(7)^-3, E(7)^2+E(7)^-2, E(7)+E(7)^-1, E(7)^3+E(7)^-3, E(7)+E(7)^-1, E(7)^2+E(7)^-2, E(7)^2+E(7)^-2, E(7)^3+E(7)^-3, 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-1*E(56)-E(56)^3+E(56)^7-E(56)^11+E(56)^13-E(56)^19+E(56)^23, E(56)^5-E(56)^9+E(56)^19-E(56)^23], [4, -4, 0, 0, 0, 0, 0, 0, 0, -2*E(56)^12-2*E(56)^-12, -2*E(56)^4-2*E(56)^-4, 2*E(56)^8+2*E(56)^-8, 2*E(56)^7+2*E(56)^-7, -2*E(56)^7-2*E(56)^-7, 0, 2*E(56)^4+2*E(56)^-4, 2*E(56)^12+2*E(56)^-12, -2*E(56)^8-2*E(56)^-8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2*E(56)^10+2*E(56)^-10, 2*E(56)^2+2*E(56)^-2, -2*E(56)^6-2*E(56)^-6, 2*E(56)^6+2*E(56)^-6, -2*E(56)^2-2*E(56)^-2, -2*E(56)^10-2*E(56)^-10, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1*E(56)^5-E(56)^9+E(56)^19+E(56)^23, E(56)+E(56)^3-E(56)^7+E(56)^11-E(56)^13+E(56)^19-E(56)^23, E(56)^5+E(56)^9-E(56)^19-E(56)^23, -1*E(56)^5+E(56)^9-E(56)^19+E(56)^23, E(56)+E(56)^3-E(56)^5+E(56)^9+E(56)^11-E(56)^13-E(56)^21, -1*E(56)-E(56)^3+E(56)^7-E(56)^11-E(56)^13+2*E(56)^15-E(56)^19+E(56)^23, E(56)+E(56)^3-E(56)^5+E(56)^9-E(56)^11-E(56)^13+2*E(56)^17-E(56)^21, -1*E(56)-E(56)^3+E(56)^5-E(56)^9-E(56)^11+E(56)^13+E(56)^21, E(56)+E(56)^3-E(56)^7+E(56)^11+E(56)^13-2*E(56)^15+E(56)^19-E(56)^23, -1*E(56)-E(56)^3+E(56)^5-E(56)^9+E(56)^11+E(56)^13-2*E(56)^17+E(56)^21, -1*E(56)-E(56)^3+E(56)^7-E(56)^11+E(56)^13-E(56)^19+E(56)^23, E(56)^5-E(56)^9+E(56)^19-E(56)^23], [4, -4, 0, 0, 0, 0, 0, 0, 0, 2*E(56)^8+2*E(56)^-8, -2*E(56)^12-2*E(56)^-12, -2*E(56)^4-2*E(56)^-4, -2*E(56)^7-2*E(56)^-7, 2*E(56)^7+2*E(56)^-7, 0, 2*E(56)^12+2*E(56)^-12, -2*E(56)^8-2*E(56)^-8, 2*E(56)^4+2*E(56)^-4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2*E(56)^2-2*E(56)^-2, 2*E(56)^6+2*E(56)^-6, 2*E(56)^10+2*E(56)^-10, -2*E(56)^10-2*E(56)^-10, -2*E(56)^6-2*E(56)^-6, 2*E(56)^2+2*E(56)^-2, 0, 0, 0, 0, 0, 0, 0, 0, 0, E(56)+E(56)^3-E(56)^7+E(56)^11+E(56)^13-2*E(56)^15+E(56)^19-E(56)^23, E(56)+E(56)^3-E(56)^5+E(56)^9+E(56)^11-E(56)^13-E(56)^21, -1*E(56)-E(56)^3+E(56)^7-E(56)^11-E(56)^13+2*E(56)^15-E(56)^19+E(56)^23, -1*E(56)-E(56)^3+E(56)^7-E(56)^11+E(56)^13-E(56)^19+E(56)^23, -1*E(56)^5+E(56)^9-E(56)^19+E(56)^23, -1*E(56)-E(56)^3+E(56)^5-E(56)^9+E(56)^11+E(56)^13-2*E(56)^17+E(56)^21, E(56)^5+E(56)^9-E(56)^19-E(56)^23, E(56)^5-E(56)^9+E(56)^19-E(56)^23, E(56)+E(56)^3-E(56)^5+E(56)^9-E(56)^11-E(56)^13+2*E(56)^17-E(56)^21, -1*E(56)^5-E(56)^9+E(56)^19+E(56)^23, -1*E(56)-E(56)^3+E(56)^5-E(56)^9-E(56)^11+E(56)^13+E(56)^21, E(56)+E(56)^3-E(56)^7+E(56)^11-E(56)^13+E(56)^19-E(56)^23], [4, -4, 0, 0, 0, 0, 0, 0, 0, 2*E(56)^8+2*E(56)^-8, -2*E(56)^12-2*E(56)^-12, -2*E(56)^4-2*E(56)^-4, -2*E(56)^7-2*E(56)^-7, 2*E(56)^7+2*E(56)^-7, 0, 2*E(56)^12+2*E(56)^-12, -2*E(56)^8-2*E(56)^-8, 2*E(56)^4+2*E(56)^-4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2*E(56)^2+2*E(56)^-2, -2*E(56)^6-2*E(56)^-6, -2*E(56)^10-2*E(56)^-10, 2*E(56)^10+2*E(56)^-10, 2*E(56)^6+2*E(56)^-6, -2*E(56)^2-2*E(56)^-2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1*E(56)-E(56)^3+E(56)^7-E(56)^11-E(56)^13+2*E(56)^15-E(56)^19+E(56)^23, E(56)+E(56)^3-E(56)^5+E(56)^9+E(56)^11-E(56)^13-E(56)^21, E(56)+E(56)^3-E(56)^7+E(56)^11+E(56)^13-2*E(56)^15+E(56)^19-E(56)^23, -1*E(56)-E(56)^3+E(56)^7-E(56)^11+E(56)^13-E(56)^19+E(56)^23, -1*E(56)^5+E(56)^9-E(56)^19+E(56)^23, E(56)+E(56)^3-E(56)^5+E(56)^9-E(56)^11-E(56)^13+2*E(56)^17-E(56)^21, -1*E(56)^5-E(56)^9+E(56)^19+E(56)^23, E(56)^5-E(56)^9+E(56)^19-E(56)^23, -1*E(56)-E(56)^3+E(56)^5-E(56)^9+E(56)^11+E(56)^13-2*E(56)^17+E(56)^21, E(56)^5+E(56)^9-E(56)^19-E(56)^23, -1*E(56)-E(56)^3+E(56)^5-E(56)^9-E(56)^11+E(56)^13+E(56)^21, E(56)+E(56)^3-E(56)^7+E(56)^11-E(56)^13+E(56)^19-E(56)^23], [4, -4, 0, 0, 0, 0, 0, 0, 0, 2*E(56)^8+2*E(56)^-8, -2*E(56)^12-2*E(56)^-12, -2*E(56)^4-2*E(56)^-4, 2*E(56)^7+2*E(56)^-7, -2*E(56)^7-2*E(56)^-7, 0, 2*E(56)^12+2*E(56)^-12, -2*E(56)^8-2*E(56)^-8, 2*E(56)^4+2*E(56)^-4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2*E(56)^2-2*E(56)^-2, 2*E(56)^6+2*E(56)^-6, 2*E(56)^10+2*E(56)^-10, -2*E(56)^10-2*E(56)^-10, -2*E(56)^6-2*E(56)^-6, 2*E(56)^2+2*E(56)^-2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1*E(56)-E(56)^3+E(56)^7-E(56)^11-E(56)^13+2*E(56)^15-E(56)^19+E(56)^23, -1*E(56)-E(56)^3+E(56)^5-E(56)^9-E(56)^11+E(56)^13+E(56)^21, E(56)+E(56)^3-E(56)^7+E(56)^11+E(56)^13-2*E(56)^15+E(56)^19-E(56)^23, E(56)+E(56)^3-E(56)^7+E(56)^11-E(56)^13+E(56)^19-E(56)^23, E(56)^5-E(56)^9+E(56)^19-E(56)^23, E(56)+E(56)^3-E(56)^5+E(56)^9-E(56)^11-E(56)^13+2*E(56)^17-E(56)^21, -1*E(56)^5-E(56)^9+E(56)^19+E(56)^23, -1*E(56)^5+E(56)^9-E(56)^19+E(56)^23, -1*E(56)-E(56)^3+E(56)^5-E(56)^9+E(56)^11+E(56)^13-2*E(56)^17+E(56)^21, E(56)^5+E(56)^9-E(56)^19-E(56)^23, E(56)+E(56)^3-E(56)^5+E(56)^9+E(56)^11-E(56)^13-E(56)^21, -1*E(56)-E(56)^3+E(56)^7-E(56)^11+E(56)^13-E(56)^19+E(56)^23], [4, -4, 0, 0, 0, 0, 0, 0, 0, 2*E(56)^8+2*E(56)^-8, -2*E(56)^12-2*E(56)^-12, -2*E(56)^4-2*E(56)^-4, 2*E(56)^7+2*E(56)^-7, -2*E(56)^7-2*E(56)^-7, 0, 2*E(56)^12+2*E(56)^-12, -2*E(56)^8-2*E(56)^-8, 2*E(56)^4+2*E(56)^-4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2*E(56)^2+2*E(56)^-2, -2*E(56)^6-2*E(56)^-6, -2*E(56)^10-2*E(56)^-10, 2*E(56)^10+2*E(56)^-10, 2*E(56)^6+2*E(56)^-6, -2*E(56)^2-2*E(56)^-2, 0, 0, 0, 0, 0, 0, 0, 0, 0, E(56)+E(56)^3-E(56)^7+E(56)^11+E(56)^13-2*E(56)^15+E(56)^19-E(56)^23, -1*E(56)-E(56)^3+E(56)^5-E(56)^9-E(56)^11+E(56)^13+E(56)^21, -1*E(56)-E(56)^3+E(56)^7-E(56)^11-E(56)^13+2*E(56)^15-E(56)^19+E(56)^23, E(56)+E(56)^3-E(56)^7+E(56)^11-E(56)^13+E(56)^19-E(56)^23, E(56)^5-E(56)^9+E(56)^19-E(56)^23, -1*E(56)-E(56)^3+E(56)^5-E(56)^9+E(56)^11+E(56)^13-2*E(56)^17+E(56)^21, E(56)^5+E(56)^9-E(56)^19-E(56)^23, -1*E(56)^5+E(56)^9-E(56)^19+E(56)^23, E(56)+E(56)^3-E(56)^5+E(56)^9-E(56)^11-E(56)^13+2*E(56)^17-E(56)^21, -1*E(56)^5-E(56)^9+E(56)^19+E(56)^23, E(56)+E(56)^3-E(56)^5+E(56)^9+E(56)^11-E(56)^13-E(56)^21, -1*E(56)-E(56)^3+E(56)^7-E(56)^11+E(56)^13-E(56)^19+E(56)^23]]; ConvertToLibraryCharacterTableNC(chartbl_448_729);