# Group 32.26 downloaded from the LMFDB on 25 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(555827723,32); a := GPC.1; b := GPC.2; c := GPC.4;
GPerm := Group( (1,2,4,6)(3,7,8,5)(9,10,11,12), (1,3,4,8)(2,5,6,7)(9,11)(10,12), (9,10,11,12), (1,4)(2,6)(3,8)(5,7), (1,4)(2,6)(3,8)(5,7)(9,11)(10,12) );
GLZ := Group([[[0, 1, 0, 1, 0, 0], [-1, 1, 1, 1, 0, 0], [1, 0, 0, 1, 0, 0], [0, -1, -1, -1, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1]], [[0, 0, -1, -1, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0], [-1, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, -1], [0, 0, 0, 0, 1, 0]], [[-1, 1, 1, 0, 0, 0], [-1, 0, 0, -1, 0, 0], [-1, 1, 1, 1, 0, 0], [1, 0, -1, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1]]]);
GLFp := Group([[[ Z(5)^3, 0*Z(5), 0*Z(5) ], [ 0*Z(5), Z(5)^3, 0*Z(5) ], [ 0*Z(5), 0*Z(5), Z(5)^3 ]], [[ Z(5)^0, 0*Z(5), 0*Z(5) ], [ Z(5)^2, Z(5)^0, Z(5)^0 ], [ Z(5)^0, Z(5)^3, Z(5)^2 ]], [[ Z(5)^2, 0*Z(5), 0*Z(5) ], [ Z(5)^0, Z(5)^0, 0*Z(5) ], [ Z(5)^3, 0*Z(5), Z(5)^0 ]], [[ Z(5)^2, 0*Z(5), 0*Z(5) ], [ 0*Z(5), Z(5)^2, 0*Z(5) ], [ 0*Z(5), 0*Z(5), Z(5)^2 ]], [[ Z(5)^3, 0*Z(5), 0*Z(5) ], [ Z(5)^3, Z(5)^2, 0*Z(5) ], [ Z(5)^3, Z(5), Z(5)^0 ]]]);

 
# Booleans 
booleans_32_26 := 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_32_26:=rec(); 
chartbl_32_26.IsFinite:= true; 
chartbl_32_26.UnderlyingCharacteristic:= 0; 
chartbl_32_26.UnderlyingGroup:= GPC;
chartbl_32_26.Size:= 32;
chartbl_32_26.InfoText:= "Character table for group 32.26 downloaded from the LMFDB."; 
chartbl_32_26.Identifier:= " C4*Q8 "; 
chartbl_32_26.NrConjugacyClasses:= 20; 
chartbl_32_26.ConjugacyClasses:= [<identity> of ..., f3*f5, f5, f3, f1, f1*f3*f5, f1*f5, f1*f3, f4, f3*f4, f1*f2, f1*f2*f4, f1*f2*f3, f1*f2*f3*f4, f2, f2*f3, f2*f4, f2*f3*f4, f1*f4, f1*f3*f4];
chartbl_32_26.IdentificationOfConjugacyClasses:= [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20];
chartbl_32_26.ComputedPowerMaps:= [ , [1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4]];
chartbl_32_26.SizesCentralizers:= [32, 32, 32, 32, 32, 32, 32, 32, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16];
chartbl_32_26.ClassNames:= ["1A", "2A", "2B", "2C", "4A1", "4A-1", "4B1", "4B-1", "4C", "4D", "4E", "4F", "4G", "4H", "4I1", "4I-1", "4J1", "4J-1", "4K1", "4K-1"];
chartbl_32_26.OrderClassRepresentatives:= [1, 2, 2, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4];
chartbl_32_26.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, -1, -1, -1, 1, -1, -1, -1, 1], [1, 1, -1, -1, -1*E(4), E(4), -1*E(4), E(4), E(4), -1*E(4), -1, -1*E(4), -1, E(4), 1, -1*E(4), -1, 1, E(4), 1], [1, 1, -1, -1, E(4), -1*E(4), E(4), -1*E(4), -1*E(4), E(4), -1, E(4), -1, -1*E(4), 1, E(4), -1, 1, -1*E(4), 1], [1, 1, -1, -1, -1*E(4), E(4), -1*E(4), E(4), E(4), E(4), -1, E(4), 1, -1*E(4), -1, -1*E(4), 1, -1, -1*E(4), 1], [1, 1, -1, -1, E(4), -1*E(4), E(4), -1*E(4), -1*E(4), -1*E(4), -1, -1*E(4), 1, E(4), -1, E(4), 1, -1, E(4), 1], [1, 1, -1, -1, -1*E(4), E(4), -1*E(4), E(4), -1*E(4), E(4), 1, -1*E(4), -1, -1*E(4), 1, E(4), 1, -1, E(4), -1], [1, 1, -1, -1, E(4), -1*E(4), E(4), -1*E(4), E(4), -1*E(4), 1, E(4), -1, E(4), 1, -1*E(4), 1, -1, -1*E(4), -1], [1, 1, -1, -1, -1*E(4), E(4), -1*E(4), E(4), -1*E(4), -1*E(4), 1, E(4), 1, E(4), -1, E(4), -1, 1, -1*E(4), -1], [1, 1, -1, -1, E(4), -1*E(4), E(4), -1*E(4), E(4), E(4), 1, -1*E(4), 1, -1*E(4), -1, -1*E(4), -1, 1, E(4), -1], [2, -2, -2, 2, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, -2, -2, 2, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, -2, 2, -2, -2*E(4), 2*E(4), 2*E(4), -2*E(4), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, -2, 2, -2, 2*E(4), -2*E(4), -2*E(4), 2*E(4), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]];
ConvertToLibraryCharacterTableNC(chartbl_32_26);