# Group 64.133 downloaded from the LMFDB on 21 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(1197402799214950,64); a := GPC.1; b := GPC.2; c := GPC.5; d := GPC.6;
GPerm := Group( (1,2,6,10)(3,11,13,16)(4,9,5,8)(7,14,15,12)(19,20), (1,3)(2,7)(4,12)(5,14)(6,13)(8,11)(9,16)(10,15)(17,18)(19,20), (1,4,6,5)(2,8,10,9)(3,12,13,14)(7,11,15,16)(17,19)(18,20), (1,5,6,4)(2,9,10,8)(3,12,13,14)(7,11,15,16), (1,6)(2,10)(3,13)(4,5)(7,15)(8,9)(11,16)(12,14)(17,18)(19,20), (1,6)(2,10)(3,13)(4,5)(7,15)(8,9)(11,16)(12,14) );
GLZN := Group([[[ZmodnZObj(1,48), ZmodnZObj(12,48)], [ZmodnZObj(0,48), ZmodnZObj(1,48)]],[[ZmodnZObj(15,48), ZmodnZObj(38,48)], [ZmodnZObj(32,48), ZmodnZObj(15,48)]],[[ZmodnZObj(17,48), ZmodnZObj(0,48)], [ZmodnZObj(0,48), ZmodnZObj(17,48)]],[[ZmodnZObj(1,48), ZmodnZObj(24,48)], [ZmodnZObj(0,48), ZmodnZObj(1,48)]],[[ZmodnZObj(15,48), ZmodnZObj(41,48)], [ZmodnZObj(32,48), ZmodnZObj(9,48)]],[[ZmodnZObj(33,48), ZmodnZObj(38,48)], [ZmodnZObj(16,48), ZmodnZObj(9,48)]]]);

 
# Booleans 
booleans_64_133 := 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_133:=rec(); 
chartbl_64_133.IsFinite:= true; 
chartbl_64_133.UnderlyingCharacteristic:= 0; 
chartbl_64_133.UnderlyingGroup:= GPC;
chartbl_64_133.Size:= 64;
chartbl_64_133.InfoText:= "Character table for group 64.133 downloaded from the LMFDB."; 
chartbl_64_133.Identifier:= " D4.D4 "; 
chartbl_64_133.NrConjugacyClasses:= 19; 
chartbl_64_133.ConjugacyClasses:= [<identity> of ..., f4*f6, f4, f6, f5, f1, f1*f6, f3, f3*f6, f3*f5, f3*f4*f5, f1*f5, f1*f5*f6, f1*f2, f1*f2*f5, f2, f2*f4, f2*f5, f2*f4*f5];
chartbl_64_133.IdentificationOfConjugacyClasses:= [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19];
chartbl_64_133.ComputedPowerMaps:= [ , [1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 4, 8, 8, 9, 9]];
chartbl_64_133.SizesCentralizers:= [64, 64, 64, 64, 16, 16, 16, 32, 32, 32, 32, 16, 16, 8, 8, 16, 16, 16, 16];
chartbl_64_133.ClassNames:= ["1A", "2A", "2B", "2C", "2D", "2E", "2F", "4A", "4B", "4C1", "4C-1", "4D", "4E", "4F", "4G", "8A1", "8A-1", "8B1", "8B3"];
chartbl_64_133.OrderClassRepresentatives:= [1, 2, 2, 2, 2, 2, 2, 4, 4, 4, 4, 4, 4, 4, 4, 8, 8, 8, 8];
chartbl_64_133.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], [2, -2, 2, -2, 0, -2, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, -2, 2, -2, 0, 0, 0, -2, 2, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0], [2, -2, 2, -2, 0, 0, 0, -2, 2, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0], [2, -2, 2, -2, 0, 2, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, 2, -2, 0, 0, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, 2, 2, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0], [2, -2, -2, 2, 0, 0, 0, 0, 0, -2*E(8)^2, 2*E(8)^2, 0, 0, 0, 0, -1*E(8)-E(8)^-1, E(8)+E(8)^-1, E(8)+E(8)^3, -1*E(8)-E(8)^3], [2, -2, -2, 2, 0, 0, 0, 0, 0, 2*E(8)^2, -2*E(8)^2, 0, 0, 0, 0, -1*E(8)-E(8)^-1, E(8)+E(8)^-1, -1*E(8)-E(8)^3, E(8)+E(8)^3], [2, -2, -2, 2, 0, 0, 0, 0, 0, -2*E(8)^2, 2*E(8)^2, 0, 0, 0, 0, E(8)+E(8)^-1, -1*E(8)-E(8)^-1, -1*E(8)-E(8)^3, E(8)+E(8)^3], [2, -2, -2, 2, 0, 0, 0, 0, 0, 2*E(8)^2, -2*E(8)^2, 0, 0, 0, 0, E(8)+E(8)^-1, -1*E(8)-E(8)^-1, E(8)+E(8)^3, -1*E(8)-E(8)^3], [4, 4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]];
ConvertToLibraryCharacterTableNC(chartbl_64_133);