# Group 448.720 downloaded from the LMFDB on 03 November 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(122963815830230947244470511914059082074629,448); a := GPC.1; b := GPC.2; c := GPC.3; d := GPC.4;
GPerm := Group( (2,3)(4,5)(6,7)(8,9)(10,11), (8,10)(9,11)(12,13,16,19)(14,20,22,27)(15,23,25,18)(17,24,26,21), (9,11)(12,14,16,22)(13,17,19,26)(15,24,25,21)(18,27,23,20), (8,10)(9,11), (12,15,16,25)(13,18,19,23)(14,21,22,24)(17,20,26,27), (12,16)(13,19)(14,22)(15,25)(17,26)(18,23)(20,27)(21,24), (1,2,4,6,7,5,3) );

 
# Booleans 
booleans_448_720 := 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_720:=rec(); 
chartbl_448_720.IsFinite:= true; 
chartbl_448_720.UnderlyingCharacteristic:= 0; 
chartbl_448_720.UnderlyingGroup:= GPC;
chartbl_448_720.Size:= 448;
chartbl_448_720.InfoText:= "Character table for group 448.720 downloaded from the LMFDB."; 
chartbl_448_720.Identifier:= " D14:Q16 "; 
chartbl_448_720.NrConjugacyClasses:= 61; 
chartbl_448_720.ConjugacyClasses:= [<identity> of ..., f2, f2*f6*f7^3, f6*f7^3, f1, f1*f6, f2*f5*f6*f7, f5*f6*f7, f3*f4*f6*f7^2, f2*f3*f4*f6*f7^2, f3*f6*f7^3, f1*f5*f6, f1*f3*f4*f7, f1*f2*f3*f4*f6*f7^5, f1*f2*f3, f7^2, f7^4, f7^6, f4*f5*f6, f4*f6*f7^2, f1*f4*f5*f6, f1*f2*f4*f6*f7^2, f2*f7, f2*f7^3, f2*f7^2, f2*f6, f2*f6*f7, f2*f6*f7^2, f6, f6*f7, f6*f7^2, f2*f5, f2*f5*f6, f2*f5*f7, f5, f5*f6, f5*f7, f3*f4, f3*f4*f5, f3*f4*f7, f2*f3*f4, f2*f3*f4*f5, f2*f3*f4*f7, f3*f7, f3*f7^6, f3*f7^3, f3*f6, f3*f7^5, f3*f5, f4, f2*f4, f4*f5, f4*f5*f7, f4*f6, f2*f4*f6, f4*f7, f4*f7^4, f4*f6*f7, f4*f6*f7^3, f4*f7^2, f4*f7^3];
chartbl_448_720.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];
chartbl_448_720.ComputedPowerMaps:= [ , [1, 1, 1, 1, 1, 1, 4, 4, 4, 4, 4, 4, 4, 4, 3, 17, 18, 16, 8, 8, 7, 7, 16, 18, 17, 18, 17, 16, 18, 17, 16, 29, 30, 31, 29, 30, 31, 30, 31, 29, 30, 31, 29, 30, 30, 31, 31, 29, 29, 35, 35, 36, 36, 37, 37, 37, 37, 35, 35, 36, 36], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 18, 16, 17, 20, 19, 22, 21, 24, 25, 23, 27, 28, 26, 30, 31, 29, 33, 34, 32, 36, 37, 35, 39, 40, 38, 42, 43, 41, 46, 47, 49, 48, 44, 45, 52, 53, 56, 57, 50, 51, 58, 59, 61, 60, 55, 54]];
chartbl_448_720.SizesCentralizers:= [448, 448, 448, 448, 32, 32, 224, 224, 112, 112, 56, 16, 16, 16, 8, 224, 224, 224, 112, 112, 16, 16, 224, 224, 224, 224, 224, 224, 224, 224, 224, 112, 112, 112, 112, 112, 112, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112];
chartbl_448_720.ClassNames:= ["1A", "2A", "2B", "2C", "2D", "2E", "4A", "4B", "4C", "4D", "4E", "4F", "4G", "4H", "4I", "7A1", "7A2", "7A3", "8A1", "8A3", "8B1", "8B3", "14A1", "14A3", "14A5", "14B1", "14B3", "14B5", "14C1", "14C3", "14C5", "28A1", "28A3", "28A5", "28B1", "28B3", "28B5", "28C1", "28C3", "28C5", "28D1", "28D3", "28D5", "28E1", "28E-1", "28E3", "28E-3", "28E5", "28E-5", "56A1", "56A-1", "56A3", "56A-3", "56A5", "56A-5", "56A9", "56A-9", "56A13", "56A-13", "56A17", "56A-17"];
chartbl_448_720.OrderClassRepresentatives:= [1, 2, 2, 2, 2, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 7, 7, 7, 8, 8, 8, 8, 14, 14, 14, 14, 14, 14, 14, 14, 14, 28, 28, 28, 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_720.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], [2, -2, 2, -2, 0, 0, -2, 2, -2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, -2, -2, 2, 2, 2, -2, -2, -2, -2, 2, -2, 2, -2, -2, 2, 0, 2, -2, -2, 2, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, -2, 2, -2, 0, 0, -2, 2, 2, -2, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, -2, -2, 2, 2, 2, -2, -2, -2, -2, 2, -2, 2, -2, -2, 2, 0, -2, 2, 2, -2, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, -2, 2, -2, 0, 0, 2, -2, 0, 0, 0, 0, -2, 2, 0, 2, 2, 2, 0, 0, 0, 0, -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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, -2, 2, -2, 0, 0, 2, -2, 0, 0, 0, 0, 2, -2, 0, 2, 2, 2, 0, 0, 0, 0, -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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, 2, -2, -2, -2, -2, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, 2, 2, 2, -2, -2, 0, 0, 0, -2, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, -2, -2, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, -1*E(8)-E(8)^-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, E(8)+E(8)^-1, -1*E(8)-E(8)^-1, -1*E(8)-E(8)^-1, -1*E(8)-E(8)^-1, E(8)+E(8)^-1, -1*E(8)-E(8)^-1, E(8)+E(8)^-1, -1*E(8)-E(8)^-1, -1*E(8)-E(8)^-1, E(8)+E(8)^-1, E(8)+E(8)^-1, E(8)+E(8)^-1], [2, -2, -2, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, E(8)+E(8)^-1, -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, -1*E(8)-E(8)^-1, E(8)+E(8)^-1, E(8)+E(8)^-1, E(8)+E(8)^-1, -1*E(8)-E(8)^-1, E(8)+E(8)^-1, -1*E(8)-E(8)^-1, E(8)+E(8)^-1, E(8)+E(8)^-1, -1*E(8)-E(8)^-1, -1*E(8)-E(8)^-1, -1*E(8)-E(8)^-1], [2, -2, -2, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, -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, E(8)+E(8)^-1, -1*E(8)-E(8)^-1, -1*E(8)-E(8)^-1, -1*E(8)-E(8)^-1, E(8)+E(8)^-1, -1*E(8)-E(8)^-1, E(8)+E(8)^-1, -1*E(8)-E(8)^-1, -1*E(8)-E(8)^-1, E(8)+E(8)^-1, E(8)+E(8)^-1, E(8)+E(8)^-1], [2, -2, -2, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 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, -1*E(8)-E(8)^-1, E(8)+E(8)^-1, E(8)+E(8)^-1, E(8)+E(8)^-1, -1*E(8)-E(8)^-1, E(8)+E(8)^-1, -1*E(8)-E(8)^-1, E(8)+E(8)^-1, E(8)+E(8)^-1, -1*E(8)-E(8)^-1, -1*E(8)-E(8)^-1, -1*E(8)-E(8)^-1], [2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0, E(7)^3+E(7)^-3, E(7)+E(7)^-1, E(7)^2+E(7)^-2, 2, 2, 0, 0, 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)+E(7)^-1, E(7)^3+E(7)^-3, 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)+E(7)^-1, E(7)^2+E(7)^-2, E(7)+E(7)^-1, E(7)+E(7)^-1, E(7)^3+E(7)^-3, E(7)^3+E(7)^-3, E(7)^2+E(7)^-2, 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, E(7)^3+E(7)^-3, E(7)^3+E(7)^-3, 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)^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], [2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0, E(7)^2+E(7)^-2, E(7)^3+E(7)^-3, E(7)+E(7)^-1, 2, 2, 0, 0, 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)^3+E(7)^-3, E(7)^2+E(7)^-2, 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)^3+E(7)^-3, E(7)+E(7)^-1, E(7)^3+E(7)^-3, E(7)^3+E(7)^-3, E(7)^2+E(7)^-2, E(7)^2+E(7)^-2, E(7)+E(7)^-1, 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, E(7)^2+E(7)^-2, E(7)^2+E(7)^-2, 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)+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], [2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0, E(7)+E(7)^-1, E(7)^2+E(7)^-2, E(7)^3+E(7)^-3, 2, 2, 0, 0, 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)^2+E(7)^-2, E(7)+E(7)^-1, 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)^2+E(7)^-2, E(7)^3+E(7)^-3, E(7)^2+E(7)^-2, E(7)^2+E(7)^-2, E(7)+E(7)^-1, E(7)+E(7)^-1, E(7)^3+E(7)^-3, 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, E(7)+E(7)^-1, E(7)+E(7)^-1, 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)^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], [2, 2, 2, 2, 0, 0, 2, 2, -2, -2, -2, 0, 0, 0, 0, E(7)^3+E(7)^-3, E(7)+E(7)^-1, E(7)^2+E(7)^-2, 2, 2, 0, 0, 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)+E(7)^-1, E(7)^3+E(7)^-3, 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)+E(7)^-1, -1*E(7)^2-E(7)^-2, -1*E(7)-E(7)^-1, -1*E(7)-E(7)^-1, -1*E(7)^3-E(7)^-3, -1*E(7)^3-E(7)^-3, -1*E(7)^2-E(7)^-2, 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-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-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)^5-E(56)^9+E(56)^19-E(56)^23], [4, -4, -4, 4, 0, 0, 0, 0, 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, 0, -2*E(56)^8-2*E(56)^-8, 2*E(56)^4+2*E(56)^-4, 2*E(56)^12+2*E(56)^-12, -2*E(56)^8-2*E(56)^-8, 2*E(56)^4+2*E(56)^-4, -2*E(56)^12-2*E(56)^-12, -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, 0, 0, 0, 0, 0, E(56)+E(56)^3-E(56)^7+E(56)^11-E(56)^13+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)-E(56)^3+E(56)^7-E(56)^11+E(56)^13-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)^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+E(56)^21, E(56)+E(56)^3-E(56)^5+E(56)^9+E(56)^11-E(56)^13-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, -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], [4, -4, -4, 4, 0, 0, 0, 0, 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, 0, -2*E(56)^8-2*E(56)^-8, 2*E(56)^4+2*E(56)^-4, 2*E(56)^12+2*E(56)^-12, -2*E(56)^8-2*E(56)^-8, 2*E(56)^4+2*E(56)^-4, -2*E(56)^12-2*E(56)^-12, -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, 0, 0, 0, 0, 0, -1*E(56)-E(56)^3+E(56)^7-E(56)^11+E(56)^13-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)+E(56)^3-E(56)^7+E(56)^11-E(56)^13+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)^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)^5-E(56)^9-E(56)^11+E(56)^13+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, E(56)^5-E(56)^9+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], [4, 4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2*E(56)^4-2*E(56)^-4, 2*E(56)^8+2*E(56)^-8, -2*E(56)^12-2*E(56)^-12, 0, 0, 0, 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, 2*E(56)^4+2*E(56)^-4, 2*E(56)^12+2*E(56)^-12, -2*E(56)^8-2*E(56)^-8, 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, 0, 0, 0, 0, 0, -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)^5-E(56)^9-E(56)^11+E(56)^13-2*E(56)^17+E(56)^21, 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)^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+2*E(56)^15-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, -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)^5-E(56)^9-E(56)^19-E(56)^23, 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], [4, 4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2*E(56)^4-2*E(56)^-4, 2*E(56)^8+2*E(56)^-8, -2*E(56)^12-2*E(56)^-12, 0, 0, 0, 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, 2*E(56)^4+2*E(56)^-4, 2*E(56)^12+2*E(56)^-12, -2*E(56)^8-2*E(56)^-8, 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, 0, 0, 0, 0, 0, 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)-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)^13-2*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)^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)^13-2*E(56)^15+E(56)^19-E(56)^23, -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, 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)^5+E(56)^9+E(56)^19+E(56)^23, -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)^13-2*E(56)^17+E(56)^21], [4, 4, -4, -4, 0, 0, 0, 0, 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, 0, 0, 0, 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, 2*E(56)^12+2*E(56)^-12, -2*E(56)^8-2*E(56)^-8, 2*E(56)^4+2*E(56)^-4, -2*E(56)^8-2*E(56)^-8, -2*E(56)^4-2*E(56)^-4, 2*E(56)^12+2*E(56)^-12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -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, E(56)^5+E(56)^9+E(56)^19+E(56)^23, -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)^13-2*E(56)^17+E(56)^21, 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)^13-2*E(56)^15+E(56)^19-E(56)^23, 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, 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, E(56)^5+E(56)^9+E(56)^19+E(56)^23], [4, 4, -4, -4, 0, 0, 0, 0, 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, 0, 0, 0, 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, 2*E(56)^12+2*E(56)^-12, -2*E(56)^8-2*E(56)^-8, 2*E(56)^4+2*E(56)^-4, -2*E(56)^8-2*E(56)^-8, -2*E(56)^4-2*E(56)^-4, 2*E(56)^12+2*E(56)^-12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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)^5-E(56)^9-E(56)^19-E(56)^23, 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)^13-2*E(56)^17+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)^13-2*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)^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)^5-E(56)^9-E(56)^19-E(56)^23], [4, 4, -4, -4, 0, 0, 0, 0, 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, 0, 0, 0, 0, 2*E(56)^8+2*E(56)^-8, -2*E(56)^4-2*E(56)^-4, 2*E(56)^12+2*E(56)^-12, -2*E(56)^8-2*E(56)^-8, 2*E(56)^4+2*E(56)^-4, 2*E(56)^12+2*E(56)^-12, 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, 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)^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+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, 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)+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)^13-2*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)^7-E(56)^11+E(56)^13+2*E(56)^15-E(56)^19+E(56)^23], [4, 4, -4, -4, 0, 0, 0, 0, 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, 0, 0, 0, 0, 2*E(56)^8+2*E(56)^-8, -2*E(56)^4-2*E(56)^-4, 2*E(56)^12+2*E(56)^-12, -2*E(56)^8-2*E(56)^-8, 2*E(56)^4+2*E(56)^-4, 2*E(56)^12+2*E(56)^-12, 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, 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)^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)^13-2*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)^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)-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+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)^7+E(56)^11-E(56)^13-2*E(56)^15+E(56)^19-E(56)^23]];
ConvertToLibraryCharacterTableNC(chartbl_448_720);