# Group 28.1 downloaded from the LMFDB on 23 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(1018013,28); a := GPC.1; b := GPC.3;
GPerm := Group( (2,3)(4,5)(6,7)(8,9,10,11), (8,10)(9,11), (1,2,4,6,7,5,3) );
GLFp := Group([[[ Z(13)^11, Z(13)^4 ], [ Z(13)^9, Z(13)^5 ]], [[ Z(13)^8, Z(13) ], [ Z(13)^0, Z(13)^8 ]]]);

 
# Booleans 
booleans_28_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_28_1:=rec(); 
chartbl_28_1.IsFinite:= true; 
chartbl_28_1.UnderlyingCharacteristic:= 0; 
chartbl_28_1.UnderlyingGroup:= GPC;
chartbl_28_1.Size:= 28;
chartbl_28_1.InfoText:= "Character table for group 28.1 downloaded from the LMFDB."; 
chartbl_28_1.Identifier:= " C7:C4 "; 
chartbl_28_1.NrConjugacyClasses:= 10; 
chartbl_28_1.ConjugacyClasses:= [<identity> of ..., f2, f1*f2, f1, f3^2, f3^4, f3^6, f2*f3, f2*f3^3, f2*f3^2];
chartbl_28_1.IdentificationOfConjugacyClasses:= [1, 2, 3, 4, 5, 6, 7, 8, 9, 10];
chartbl_28_1.ComputedPowerMaps:= [ , [1, 1, 2, 2, 6, 7, 5, 5, 7, 6], [1, 2, 4, 3, 7, 5, 6, 9, 10, 8]];
chartbl_28_1.SizesCentralizers:= [28, 28, 4, 4, 14, 14, 14, 14, 14, 14];
chartbl_28_1.ClassNames:= ["1A", "2A", "4A1", "4A-1", "7A1", "7A2", "7A3", "14A1", "14A3", "14A5"];
chartbl_28_1.OrderClassRepresentatives:= [1, 2, 4, 4, 7, 7, 7, 14, 14, 14];
chartbl_28_1.Irr:= [[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, E(4), -1*E(4), 1, 1, 1, -1, -1, -1], [2, 2, 0, 0, E(7)^3+E(7)^-3, E(7)+E(7)^-1, E(7)^2+E(7)^-2, E(7)+E(7)^-1, E(7)^3+E(7)^-3, E(7)^2+E(7)^-2], [2, 2, 0, 0, E(7)^2+E(7)^-2, E(7)^3+E(7)^-3, E(7)+E(7)^-1, E(7)^3+E(7)^-3, E(7)^2+E(7)^-2, E(7)+E(7)^-1], [2, 2, 0, 0, E(7)+E(7)^-1, E(7)^2+E(7)^-2, E(7)^3+E(7)^-3, E(7)^2+E(7)^-2, E(7)+E(7)^-1, E(7)^3+E(7)^-3], [2, -2, 0, 0, E(7)^3+E(7)^-3, E(7)+E(7)^-1, E(7)^2+E(7)^-2, -1*E(7)-E(7)^-1, -1*E(7)^3-E(7)^-3, -1*E(7)^2-E(7)^-2], [2, -2, 0, 0, E(7)^2+E(7)^-2, E(7)^3+E(7)^-3, E(7)+E(7)^-1, -1*E(7)^3-E(7)^-3, -1*E(7)^2-E(7)^-2, -1*E(7)-E(7)^-1], [2, -2, 0, 0, E(7)+E(7)^-1, E(7)^2+E(7)^-2, E(7)^3+E(7)^-3, -1*E(7)^2-E(7)^-2, -1*E(7)-E(7)^-1, -1*E(7)^3-E(7)^-3]];
ConvertToLibraryCharacterTableNC(chartbl_28_1);