# Group 64.13 downloaded from the LMFDB on 15 September 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(4976513065026618711,64); a := GPC.1; b := GPC.3; c := GPC.5;
GPerm := Group( (2,5)(3,7)(6,8)(9,10,11,13,12,14,16,15), (1,2,4,6)(3,8,7,5)(9,10)(11,15)(12,14)(13,16), (1,3,4,7)(2,5,6,8)(9,11,12,16)(10,13,14,15), (9,11,12,16)(10,13,14,15), (1,4)(2,6)(3,7)(5,8), (1,4)(2,6)(3,7)(5,8)(9,12)(10,14)(11,16)(13,15) );
GLFp := Group([[[ Z(3), 0*Z(3), 0*Z(3), 0*Z(3) ], [ Z(3)^0, Z(3)^0, 0*Z(3), Z(3) ], [ Z(3), Z(3)^0, Z(3), Z(3)^0 ], [ Z(3), 0*Z(3), Z(3)^0, Z(3) ]], [[ Z(3), 0*Z(3), 0*Z(3), 0*Z(3) ], [ Z(3), 0*Z(3), Z(3)^0, Z(3) ], [ Z(3)^0, Z(3)^0, 0*Z(3), Z(3)^0 ], [ 0*Z(3), Z(3), 0*Z(3), 0*Z(3) ]], [[ Z(3)^0, Z(3)^0, Z(3)^0, 0*Z(3) ], [ Z(3), Z(3)^0, Z(3), 0*Z(3) ], [ Z(3), Z(3)^0, 0*Z(3), 0*Z(3) ], [ 0*Z(3), Z(3)^0, 0*Z(3), Z(3)^0 ]], [[ Z(3), 0*Z(3), 0*Z(3), 0*Z(3) ], [ 0*Z(3), Z(3), 0*Z(3), 0*Z(3) ], [ 0*Z(3), 0*Z(3), Z(3), 0*Z(3) ], [ 0*Z(3), 0*Z(3), 0*Z(3), Z(3) ]], [[ Z(3), 0*Z(3), 0*Z(3), 0*Z(3) ], [ Z(3), Z(3), Z(3)^0, 0*Z(3) ], [ Z(3)^0, 0*Z(3), Z(3)^0, 0*Z(3) ], [ Z(3), Z(3), Z(3), Z(3)^0 ]], [[ 0*Z(3), Z(3), Z(3), 0*Z(3) ], [ Z(3)^0, 0*Z(3), Z(3), Z(3) ], [ 0*Z(3), 0*Z(3), Z(3)^0, Z(3)^0 ], [ 0*Z(3), 0*Z(3), Z(3)^0, Z(3) ]]]);

 
# Booleans 
booleans_64_13 := 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_64_13:=rec(); 
chartbl_64_13.IsFinite:= true; 
chartbl_64_13.UnderlyingCharacteristic:= 0; 
chartbl_64_13.UnderlyingGroup:= GPC;
chartbl_64_13.Size:= 64;
chartbl_64_13.InfoText:= "Character table for group 64.13 downloaded from the LMFDB."; 
chartbl_64_13.Identifier:= " C4.D8 "; 
chartbl_64_13.NrConjugacyClasses:= 19; 
chartbl_64_13.ConjugacyClasses:= [<identity> of ..., f4*f6, f4, f6, f2*f6, f2*f5, f2, f2*f4*f5*f6, f5, f3, f2*f3, f1, f1*f2*f6, f1*f2, f1*f6, f1*f3, f1*f2*f3*f6, f1*f2*f3, f1*f3*f6];
chartbl_64_13.IdentificationOfConjugacyClasses:= [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19];
chartbl_64_13.ComputedPowerMaps:= [ , [1, 1, 1, 1, 2, 3, 2, 3, 4, 3, 3, 7, 7, 7, 7, 8, 8, 8, 8]];
chartbl_64_13.SizesCentralizers:= [64, 64, 64, 64, 32, 32, 32, 32, 16, 8, 8, 16, 16, 16, 16, 16, 16, 16, 16];
chartbl_64_13.ClassNames:= ["1A", "2A", "2B", "2C", "4A", "4B", "4C", "4D", "4E", "4F", "4G", "8A1", "8A-1", "8A3", "8A-3", "8B1", "8B-1", "8B3", "8B-3"];
chartbl_64_13.OrderClassRepresentatives:= [1, 2, 2, 2, 4, 4, 4, 4, 4, 4, 4, 8, 8, 8, 8, 8, 8, 8, 8];
chartbl_64_13.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*E(4), -1*E(4), E(4), E(4), E(4), -1*E(4), E(4), -1*E(4)], [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), E(4)], [1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1*E(4), -1*E(4), -1*E(4), -1*E(4), E(4), E(4), E(4), E(4)], [1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, E(4), E(4), E(4), E(4), -1*E(4), -1*E(4), -1*E(4), -1*E(4)], [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, 0, 0, 0, 0], [2, 2, -2, -2, -2, 0, 2, 0, 0, 0, 0, -1*E(8)-E(8)^-1, E(8)+E(8)^-1, 0, 0, -1*E(8)-E(8)^-1, 0, E(8)+E(8)^-1, 0], [2, 2, -2, -2, -2, 0, 2, 0, 0, 0, 0, E(8)+E(8)^-1, -1*E(8)-E(8)^-1, 0, 0, E(8)+E(8)^-1, 0, -1*E(8)-E(8)^-1, 0], [2, -2, -2, 2, 0, -2, 0, 2, 0, 0, 0, 0, 0, -1*E(8)-E(8)^3, E(8)+E(8)^3, 0, -1*E(8)-E(8)^3, 0, E(8)+E(8)^3], [2, -2, -2, 2, 0, -2, 0, 2, 0, 0, 0, 0, 0, E(8)+E(8)^3, -1*E(8)-E(8)^3, 0, E(8)+E(8)^3, 0, -1*E(8)-E(8)^3], [2, 2, -2, -2, 2, 0, -2, 0, 0, 0, 0, -1*E(8)-E(8)^3, E(8)+E(8)^3, 0, 0, E(8)+E(8)^3, 0, -1*E(8)-E(8)^3, 0], [2, 2, -2, -2, 2, 0, -2, 0, 0, 0, 0, E(8)+E(8)^3, -1*E(8)-E(8)^3, 0, 0, -1*E(8)-E(8)^3, 0, E(8)+E(8)^3, 0], [2, -2, -2, 2, 0, 2, 0, -2, 0, 0, 0, 0, 0, -1*E(8)-E(8)^-1, E(8)+E(8)^-1, 0, E(8)+E(8)^-1, 0, -1*E(8)-E(8)^-1], [2, -2, -2, 2, 0, 2, 0, -2, 0, 0, 0, 0, 0, E(8)+E(8)^-1, -1*E(8)-E(8)^-1, 0, -1*E(8)-E(8)^-1, 0, E(8)+E(8)^-1], [4, -4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]];
ConvertToLibraryCharacterTableNC(chartbl_64_13);