# Group 7.1 downloaded from the LMFDB on 08 December 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(0,7); a := GPC.1;
GPerm := Group( (1,7,6,5,4,3,2) );
GLZ := Group([[[0, 0, 0, 0, 0, 1], [0, 0, -1, 1, -1, 1], [-1, 0, 0, 0, 0, 0], [0, 0, -1, 0, 0, 1], [1, 0, -1, 0, -1, 1], [0, -1, 0, 0, 0, 0]]]);
GLFp := Group([[[ Z(7)^0, Z(7)^0 ], [ 0*Z(7), Z(7)^0 ]]]);

 
# Booleans 
booleans_7_1 := 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_7_1:=rec(); 
chartbl_7_1.IsFinite:= true; 
chartbl_7_1.UnderlyingCharacteristic:= 0; 
chartbl_7_1.UnderlyingGroup:= GPC;
chartbl_7_1.Size:= 7;
chartbl_7_1.InfoText:= "Character table for group 7.1 downloaded from the LMFDB."; 
chartbl_7_1.Identifier:= " C7 "; 
chartbl_7_1.NrConjugacyClasses:= 7; 
chartbl_7_1.ConjugacyClasses:= [<identity> of ..., f1, f1^6, f1^2, f1^5, f1^3, f1^4];
chartbl_7_1.IdentificationOfConjugacyClasses:= [1, 2, 3, 4, 5, 6, 7];
chartbl_7_1.ComputedPowerMaps:= [ , [1, 4, 5, 7, 6, 3, 2]];
chartbl_7_1.SizesCentralizers:= [7, 7, 7, 7, 7, 7, 7];
chartbl_7_1.ClassNames:= ["1A", "7A1", "7A-1", "7A2", "7A-2", "7A3", "7A-3"];
chartbl_7_1.OrderClassRepresentatives:= [1, 7, 7, 7, 7, 7, 7];
chartbl_7_1.Irr:= [[1, 1, 1, 1, 1, 1, 1], [1, E(7)^-3, E(7)^-1, E(7)^3, E(7)^2, E(7), E(7)^-2], [1, E(7)^3, E(7), E(7)^-3, E(7)^-2, E(7)^-1, E(7)^2], [1, E(7)^-2, E(7)^-3, E(7)^2, E(7)^-1, E(7)^3, E(7)], [1, E(7)^2, E(7)^3, E(7)^-2, E(7), E(7)^-3, E(7)^-1], [1, E(7)^-1, E(7)^2, E(7), E(7)^3, E(7)^-2, E(7)^-3], [1, E(7), E(7)^-2, E(7)^-1, E(7)^-3, E(7)^2, E(7)^3]];
ConvertToLibraryCharacterTableNC(chartbl_7_1);