# Group 42.1 downloaded from the LMFDB on 27 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(37793315,42); a := GPC.1; b := GPC.3;
GPerm := Group( (2,7)(3,6)(4,5), (2,3,5)(4,7,6), (1,7,6,5,4,3,2) );
GLZ := Group([[[0, 0, 0, 0, 0, 1], [0, -1, 0, 0, 0, 1], [1, -1, 0, -1, 0, 1], [0, 1, -1, 0, -1, 0], [0, 0, 0, 1, 0, 0], [0, 0, -1, 0, 0, 0]], [[0, -1, 0, 0, 0, 1], [0, -1, 0, 0, 1, 0], [-1, 0, 1, 1, 1, 0], [1, 0, -1, 0, -1, 0], [0, -1, 0, 0, 0, 0], [1, -1, 0, 0, 0, 0]]]);
GLFp := Group([[[ Z(7)^0, Z(7)^0 ], [ 0*Z(7), Z(7)^0 ]], [[ Z(7)^0, 0*Z(7) ], [ 0*Z(7), Z(7) ]]]);

 
# Booleans 
booleans_42_1 := rec( 
Agroup := true,
Zgroup := true,
abelian := false,
almost_simple := false,
cyclic := false,
metabelian := true,
metacyclic := true,
monomial := true,
nilpotent := false,
perfect := false,
quasisimple := false,
rational := false,
solvable := true,
supersolvable := true); 

 
# Character Table 
chartbl_42_1:=rec(); 
chartbl_42_1.IsFinite:= true; 
chartbl_42_1.UnderlyingCharacteristic:= 0; 
chartbl_42_1.UnderlyingGroup:= GPC;
chartbl_42_1.Size:= 42;
chartbl_42_1.InfoText:= "Character table for group 42.1 downloaded from the LMFDB."; 
chartbl_42_1.Identifier:= " F7 "; 
chartbl_42_1.NrConjugacyClasses:= 7; 
chartbl_42_1.ConjugacyClasses:= [<identity> of ..., f1*f2*f3^6, f2*f3^5, f2^2*f3^4, f1*f3^2, f1*f2^2*f3, f3];
chartbl_42_1.IdentificationOfConjugacyClasses:= [1, 2, 3, 4, 5, 6, 7];
chartbl_42_1.ComputedPowerMaps:= [ , [1, 1, 4, 3, 3, 4, 7], [1, 2, 1, 1, 2, 2, 7], [1, 2, 3, 4, 5, 6, 1]];
chartbl_42_1.SizesCentralizers:= [42, 6, 6, 6, 6, 6, 7];
chartbl_42_1.ClassNames:= ["1A", "2A", "3A1", "3A-1", "6A1", "6A-1", "7A"];
chartbl_42_1.OrderClassRepresentatives:= [1, 2, 3, 3, 6, 6, 7];
chartbl_42_1.Irr:= [[1, 1, 1, 1, 1, 1, 1], [1, -1, 1, 1, -1, -1, 1], [1, 1, E(3)^-1, E(3), E(3), E(3)^-1, 1], [1, 1, E(3), E(3)^-1, E(3)^-1, E(3), 1], [1, -1, E(3)^-1, E(3), -1*E(3), -1*E(3)^-1, 1], [1, -1, E(3), E(3)^-1, -1*E(3)^-1, -1*E(3), 1], [6, 0, 0, 0, 0, 0, -1]];
ConvertToLibraryCharacterTableNC(chartbl_42_1);