# Group 20.2 downloaded from the LMFDB on 07 June 2026. 
 
## 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(51395,20); a := GPC.1;
GPerm := Group( (1,4,2,3), (5,9,8,7,6), (1,2)(3,4) );
GLZ := Group([[[0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [-1, -1, -1, -1, 0, 0], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, -1, 0]]]);
GLFp := Group([[[ Z(5)^0, Z(5)^0 ], [ 0*Z(5), Z(5)^0 ]], [[ Z(5)^2, 0*Z(5) ], [ 0*Z(5), Z(5)^2 ]], [[ Z(5), 0*Z(5) ], [ 0*Z(5), Z(5) ]]]);

 
# Booleans 
booleans_20_2 := rec( 
Agroup := true,
Zgroup := true,
abelian := true,
almost_simple := false,
cyclic := true,
metabelian := true,
metacyclic := true,
monomial := true,
nilpotent := true,
perfect := false,
quasisimple := false,
rational := false,
solvable := true,
supersolvable := true); 

 
# Character Table 
chartbl_20_2:=rec(); 
chartbl_20_2.IsFinite:= true; 
chartbl_20_2.UnderlyingCharacteristic:= 0; 
chartbl_20_2.UnderlyingGroup:= GPC;
chartbl_20_2.Size:= 20;
chartbl_20_2.InfoText:= "Character table for group 20.2 downloaded from the LMFDB."; 
chartbl_20_2.Identifier:= " C20 "; 
chartbl_20_2.NrConjugacyClasses:= 20; 
chartbl_20_2.ConjugacyClasses:= [<identity> of ..., f2*f3^2, f1*f3, f1*f2*f3^3, f3, f3^4, f3^2, f3^3, f2, f2*f3^4, f2*f3, f2*f3^3, f1, f1*f2*f3^4, f1*f2, f1*f3^4, f1*f2*f3, f1*f3^3, f1*f3^2, f1*f2*f3^2];
chartbl_20_2.IdentificationOfConjugacyClasses:= [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20];
chartbl_20_2.ComputedPowerMaps:= [ , [1, 1, 2, 2, 7, 8, 6, 5, 5, 6, 8, 7, 9, 10, 11, 12, 12, 11, 10, 9], [1, 2, 3, 4, 1, 1, 1, 1, 2, 2, 2, 2, 3, 4, 4, 3, 4, 3, 3, 4]];
chartbl_20_2.SizesCentralizers:= [20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20];
chartbl_20_2.ClassNames:= ["1A", "2A", "4A1", "4A-1", "5A1", "5A-1", "5A2", "5A-2", "10A1", "10A-1", "10A3", "10A-3", "20A1", "20A-1", "20A3", "20A-3", "20A7", "20A-7", "20A9", "20A-9"];
chartbl_20_2.OrderClassRepresentatives:= [1, 2, 4, 4, 5, 5, 5, 5, 10, 10, 10, 10, 20, 20, 20, 20, 20, 20, 20, 20];
chartbl_20_2.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*E(4), E(4), 1, 1, 1, 1, -1, -1, -1, -1, -1*E(4), E(4), E(4), -1*E(4), E(4), -1*E(4), -1*E(4), E(4)], [1, -1, E(4), -1*E(4), 1, 1, 1, 1, -1, -1, -1, -1, E(4), -1*E(4), -1*E(4), E(4), -1*E(4), E(4), E(4), -1*E(4)], [1, 1, 1, 1, E(5)^-2, E(5)^2, E(5), E(5)^-1, E(5)^-1, E(5), E(5)^2, E(5)^-2, E(5)^2, E(5)^-2, E(5), E(5)^-1, E(5)^-1, E(5), E(5)^-2, E(5)^2], [1, 1, 1, 1, E(5)^2, E(5)^-2, E(5)^-1, E(5), E(5), E(5)^-1, E(5)^-2, E(5)^2, E(5)^-2, E(5)^2, E(5)^-1, E(5), E(5), E(5)^-1, E(5)^2, E(5)^-2], [1, 1, 1, 1, E(5)^-1, E(5), E(5)^-2, E(5)^2, E(5)^2, E(5)^-2, E(5), E(5)^-1, E(5), E(5)^-1, E(5)^-2, E(5)^2, E(5)^2, E(5)^-2, E(5)^-1, E(5)], [1, 1, 1, 1, E(5), E(5)^-1, E(5)^2, E(5)^-2, E(5)^-2, E(5)^2, E(5)^-1, E(5), E(5)^-1, E(5), E(5)^2, E(5)^-2, E(5)^-2, E(5)^2, E(5), E(5)^-1], [1, 1, -1, -1, E(5)^-2, E(5)^2, E(5), E(5)^-1, E(5)^-1, E(5), E(5)^2, E(5)^-2, -1*E(5)^2, -1*E(5)^-2, -1*E(5), -1*E(5)^-1, -1*E(5)^-1, -1*E(5), -1*E(5)^-2, -1*E(5)^2], [1, 1, -1, -1, E(5)^2, E(5)^-2, E(5)^-1, E(5), E(5), E(5)^-1, E(5)^-2, E(5)^2, -1*E(5)^-2, -1*E(5)^2, -1*E(5)^-1, -1*E(5), -1*E(5), -1*E(5)^-1, -1*E(5)^2, -1*E(5)^-2], [1, 1, -1, -1, E(5)^-1, E(5), E(5)^-2, E(5)^2, E(5)^2, E(5)^-2, E(5), E(5)^-1, -1*E(5), -1*E(5)^-1, -1*E(5)^-2, -1*E(5)^2, -1*E(5)^2, -1*E(5)^-2, -1*E(5)^-1, -1*E(5)], [1, 1, -1, -1, E(5), E(5)^-1, E(5)^2, E(5)^-2, E(5)^-2, E(5)^2, E(5)^-1, E(5), -1*E(5)^-1, -1*E(5), -1*E(5)^2, -1*E(5)^-2, -1*E(5)^-2, -1*E(5)^2, -1*E(5), -1*E(5)^-1], [1, -1, -1*E(20)^5, E(20)^5, -1*E(20)^2, E(20)^8, E(20)^4, -1*E(20)^6, E(20)^6, -1*E(20)^4, -1*E(20)^8, E(20)^2, E(20)^3, -1*E(20)^7, E(20)^9, -1*E(20), E(20), -1*E(20)^9, E(20)^7, -1*E(20)^3], [1, -1, E(20)^5, -1*E(20)^5, E(20)^8, -1*E(20)^2, -1*E(20)^6, E(20)^4, -1*E(20)^4, E(20)^6, E(20)^2, -1*E(20)^8, -1*E(20)^7, E(20)^3, -1*E(20), E(20)^9, -1*E(20)^9, E(20), -1*E(20)^3, E(20)^7], [1, -1, -1*E(20)^5, E(20)^5, E(20)^8, -1*E(20)^2, -1*E(20)^6, E(20)^4, -1*E(20)^4, E(20)^6, E(20)^2, -1*E(20)^8, E(20)^7, -1*E(20)^3, E(20), -1*E(20)^9, E(20)^9, -1*E(20), E(20)^3, -1*E(20)^7], [1, -1, E(20)^5, -1*E(20)^5, -1*E(20)^2, E(20)^8, E(20)^4, -1*E(20)^6, E(20)^6, -1*E(20)^4, -1*E(20)^8, E(20)^2, -1*E(20)^3, E(20)^7, -1*E(20)^9, E(20), -1*E(20), E(20)^9, -1*E(20)^7, E(20)^3], [1, -1, -1*E(20)^5, E(20)^5, -1*E(20)^6, E(20)^4, -1*E(20)^2, E(20)^8, -1*E(20)^8, E(20)^2, -1*E(20)^4, E(20)^6, -1*E(20)^9, E(20), -1*E(20)^7, E(20)^3, -1*E(20)^3, E(20)^7, -1*E(20), E(20)^9], [1, -1, E(20)^5, -1*E(20)^5, E(20)^4, -1*E(20)^6, E(20)^8, -1*E(20)^2, E(20)^2, -1*E(20)^8, E(20)^6, -1*E(20)^4, E(20), -1*E(20)^9, E(20)^3, -1*E(20)^7, E(20)^7, -1*E(20)^3, E(20)^9, -1*E(20)], [1, -1, -1*E(20)^5, E(20)^5, E(20)^4, -1*E(20)^6, E(20)^8, -1*E(20)^2, E(20)^2, -1*E(20)^8, E(20)^6, -1*E(20)^4, -1*E(20), E(20)^9, -1*E(20)^3, E(20)^7, -1*E(20)^7, E(20)^3, -1*E(20)^9, E(20)], [1, -1, E(20)^5, -1*E(20)^5, -1*E(20)^6, E(20)^4, -1*E(20)^2, E(20)^8, -1*E(20)^8, E(20)^2, -1*E(20)^4, E(20)^6, E(20)^9, -1*E(20), E(20)^7, -1*E(20)^3, E(20)^3, -1*E(20)^7, E(20), -1*E(20)^9]];
ConvertToLibraryCharacterTableNC(chartbl_20_2);