# Group 128.144 downloaded from the LMFDB on 22 February 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(20454561330425315986176559339445,128); a := GPC.1; b := GPC.3; c := GPC.5;
GPerm := Group( (1,9)(2,10)(3,12,4,11)(5,15,7,13)(6,16,8,14), (1,6,2,5)(3,8,4,7)(9,13)(10,14)(11,15)(12,16), (5,6)(7,8)(9,12,10,11)(13,16,14,15), (3,4)(5,7)(6,8)(11,12)(13,15)(14,16), (1,4,2,3)(5,7,6,8)(9,11,10,12)(13,16,14,15), (1,2)(3,4)(5,6)(7,8), (1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16) );

 
# Booleans 
booleans_128_144 := 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_128_144:=rec(); 
chartbl_128_144.IsFinite:= true; 
chartbl_128_144.UnderlyingCharacteristic:= 0; 
chartbl_128_144.UnderlyingGroup:= GPC;
chartbl_128_144.Size:= 128;
chartbl_128_144.InfoText:= "Character table for group 128.144 downloaded from the LMFDB."; 
chartbl_128_144.Identifier:= " C4^2.(C2*C4) "; 
chartbl_128_144.NrConjugacyClasses:= 14; 
chartbl_128_144.ConjugacyClasses:= [<identity> of ..., f7, f4, f2*f3*f7, f2*f4*f6*f7, f6, f3, f2*f3*f5*f7, f1*f2*f4*f5*f7, f1*f3*f5*f6, f1*f3, f1*f2*f3*f6*f7, f5, f5*f6];
chartbl_128_144.IdentificationOfConjugacyClasses:= [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14];
chartbl_128_144.ComputedPowerMaps:= [ , [1, 1, 1, 1, 1, 2, 3, 3, 4, 4, 5, 5, 6, 6]];
chartbl_128_144.SizesCentralizers:= [128, 128, 64, 16, 16, 32, 16, 8, 8, 8, 8, 8, 16, 16];
chartbl_128_144.ClassNames:= ["1A", "2A", "2B", "2C", "2D", "4A", "4B", "4C", "4D1", "4D-1", "4E1", "4E-1", "8A1", "8A-1"];
chartbl_128_144.OrderClassRepresentatives:= [1, 2, 2, 2, 2, 4, 4, 4, 4, 4, 4, 4, 8, 8];
chartbl_128_144.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*E(4), -1, E(4), E(4), -1*E(4), 1, 1], [1, 1, 1, -1, -1, 1, 1, E(4), -1, -1*E(4), -1*E(4), E(4), 1, 1], [1, 1, 1, -1, -1, 1, 1, -1*E(4), 1, -1*E(4), E(4), E(4), -1, -1], [1, 1, 1, -1, -1, 1, 1, E(4), 1, E(4), -1*E(4), -1*E(4), -1, -1], [2, 2, 2, -2, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, 2, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0], [4, 4, 4, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0], [4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2*E(4), 2*E(4)], [4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2*E(4), -2*E(4)], [8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]];
ConvertToLibraryCharacterTableNC(chartbl_128_144);