# Group 1024.dfb downloaded from the LMFDB on 01 October 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(29759160622346366286547587349104150709157016332178734886503269069516847867099215,1024); a := GPC.1; b := GPC.4; c := GPC.6; d := GPC.7; e := GPC.9; f := GPC.10;
GPerm := Group( (1,9,3,11,6,13,8,16,2,10,4,12,5,14,7,15), (1,3,6,7)(2,4,5,8)(9,16,14,11)(10,15,13,12), (1,10,4,11,6,14,7,16,2,9,3,12,5,13,8,15) );

 
# Booleans 
booleans_1024_dfb := rec( 
Agroup := false,
Zgroup := false,
abelian := false,
almost_simple := false,
cyclic := false,
metabelian := false,
metacyclic := false,
monomial := true,
nilpotent := true,
perfect := false,
quasisimple := false,
rational := false,
solvable := true,
supersolvable := true); 

 
# Character Table 
chartbl_1024_dfb:=rec(); 
chartbl_1024_dfb.IsFinite:= true; 
chartbl_1024_dfb.UnderlyingCharacteristic:= 0; 
chartbl_1024_dfb.UnderlyingGroup:= GPerm;
chartbl_1024_dfb.Size:= 1024;
chartbl_1024_dfb.InfoText:= "Character table for group 1024.dfb downloaded from the LMFDB."; 
chartbl_1024_dfb.Identifier:= " C2^6.OD16 "; 
chartbl_1024_dfb.NrConjugacyClasses:= 37; 
chartbl_1024_dfb.ConjugacyClasses:= [(), (1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16), (9,10)(11,12)(13,14)(15,16), (3,4)(7,8)(11,12)(15,16), (3,4)(7,8)(9,10)(11,12)(13,14)(15,16), (11,12)(15,16), (13,14)(15,16), (5,6)(7,8)(11,12)(15,16), (5,6)(7,8)(9,10)(13,14), (5,6)(7,8)(9,10)(11,12)(13,14)(15,16), (5,6)(7,8)(13,14)(15,16), (1,5)(2,6)(3,8)(4,7)(9,14)(10,13)(11,16)(12,15), (1,5,2,6)(3,8,4,7)(9,14,10,13)(11,16,12,15), (1,5,2,6)(3,8,4,7)(9,13,10,14)(11,16,12,15), (7,8)(9,13)(10,14)(11,15,12,16), (7,8)(9,13)(10,14)(11,16,12,15), (7,8)(9,13,10,14)(11,15)(12,16), (7,8)(9,13,10,14)(11,16)(12,15), (3,4)(5,6)(7,8)(9,13)(10,14)(11,15,12,16), (3,4)(5,6)(7,8)(9,13)(10,14)(11,16,12,15), (3,4)(5,6)(7,8)(9,13,10,14)(11,15)(12,16), (3,4)(5,6)(7,8)(9,13,10,14)(11,16)(12,15), (1,5)(2,6)(3,7)(4,8)(9,13,10,14)(11,15,12,16), (1,8,5,3)(2,7,6,4)(9,11,14,16)(10,12,13,15), (1,3,5,8)(2,4,6,7)(9,16,14,11)(10,15,13,12), (1,8,5,4,2,7,6,3)(9,15,14,11,10,16,13,12), (1,3,6,7,2,4,5,8)(9,12,13,16,10,11,14,15), (1,4,5,7,2,3,6,8)(9,12,13,15,10,11,14,16), (1,8,6,3,2,7,5,4)(9,16,14,11,10,15,13,12), (1,16,8,13,5,12,4,9,2,15,7,14,6,11,3,10), (1,10,3,11,6,14,7,15,2,9,4,12,5,13,8,16), (1,13,4,15,6,10,8,12,2,14,3,16,5,9,7,11), (1,11,7,9,5,16,3,14,2,12,8,10,6,15,4,13), (1,12,4,13,5,15,7,10,2,11,3,14,6,16,8,9), (1,9,8,16,6,14,3,11,2,10,7,15,5,13,4,12), (1,13,7,11,6,9,4,15,2,14,8,12,5,10,3,16), (1,16,3,10,5,12,8,14,2,15,4,9,6,11,7,13)];
chartbl_1024_dfb.IdentificationOfConjugacyClasses:= [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37];
chartbl_1024_dfb.ComputedPowerMaps:= [ , [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 6, 6, 6, 6, 6, 6, 6, 6, 3, 12, 12, 13, 13, 14, 14, 26, 27, 27, 26, 28, 29, 29, 28]];
chartbl_1024_dfb.SizesCentralizers:= [1024, 1024, 512, 256, 256, 256, 128, 128, 128, 128, 64, 64, 128, 128, 64, 64, 64, 64, 64, 64, 64, 64, 32, 16, 16, 32, 32, 32, 32, 16, 16, 16, 16, 16, 16, 16, 16];
chartbl_1024_dfb.ClassNames:= ["1A", "2A", "2B", "2C", "2D", "2E", "2F", "2G", "2H", "2I", "2J", "2K", "4A", "4B", "4C1", "4C-1", "4D1", "4D-1", "4E1", "4E-1", "4F1", "4F-1", "4G", "4H1", "4H-1", "8A1", "8A-1", "8B1", "8B-1", "16A1", "16A-1", "16A3", "16A-3", "16B1", "16B-1", "16B3", "16B-3"];
chartbl_1024_dfb.OrderClassRepresentatives:= [1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 8, 8, 8, 8, 16, 16, 16, 16, 16, 16, 16, 16];
chartbl_1024_dfb.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, -1, -1, -1, -1, -1, 1, 1, 1, -1, -1, -1, -1, -1*E(4), -1*E(4), E(4), E(4), -1*E(4), -1*E(4), E(4), E(4)], [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), -1*E(4), E(4), E(4), -1*E(4), -1*E(4)], [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), E(4), E(4), E(4), -1*E(4), -1*E(4)], [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), -1*E(4), -1*E(4), -1*E(4), E(4), E(4)], [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(8)^2, E(8)^2, E(8)^2, -1*E(8)^2, E(8)^2, -1*E(8)^2, E(8)^3, -1*E(8)^3, -1*E(8), E(8), E(8), -1*E(8), -1*E(8)^3, E(8)^3], [1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, E(8)^2, -1*E(8)^2, -1*E(8)^2, E(8)^2, -1*E(8)^2, E(8)^2, -1*E(8), E(8), E(8)^3, -1*E(8)^3, -1*E(8)^3, E(8)^3, E(8), -1*E(8)], [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(8)^2, E(8)^2, E(8)^2, -1*E(8)^2, E(8)^2, -1*E(8)^2, -1*E(8)^3, E(8)^3, E(8), -1*E(8), -1*E(8), E(8), E(8)^3, -1*E(8)^3], [1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, E(8)^2, -1*E(8)^2, -1*E(8)^2, E(8)^2, -1*E(8)^2, E(8)^2, E(8), -1*E(8), -1*E(8)^3, E(8)^3, E(8)^3, -1*E(8)^3, -1*E(8), E(8)], [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(8)^2, E(8)^2, -1*E(8)^2, E(8)^2, -1*E(8)^2, E(8)^2, -1*E(8), E(8), E(8)^3, -1*E(8)^3, E(8)^3, -1*E(8)^3, -1*E(8), E(8)], [1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, 1, 1, E(8)^2, -1*E(8)^2, E(8)^2, -1*E(8)^2, E(8)^2, -1*E(8)^2, E(8)^3, -1*E(8)^3, -1*E(8), E(8), -1*E(8), E(8), E(8)^3, -1*E(8)^3], [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(8)^2, E(8)^2, -1*E(8)^2, E(8)^2, -1*E(8)^2, E(8)^2, E(8), -1*E(8), -1*E(8)^3, E(8)^3, -1*E(8)^3, E(8)^3, E(8), -1*E(8)], [1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, 1, 1, E(8)^2, -1*E(8)^2, E(8)^2, -1*E(8)^2, E(8)^2, -1*E(8)^2, -1*E(8)^3, E(8)^3, E(8), -1*E(8), E(8), -1*E(8), -1*E(8)^3, E(8)^3], [2, 2, 2, 2, 2, 2, -2, -2, -2, -2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, 2, 2, 2, -2, -2, -2, -2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2*E(4), 2*E(4), 2*E(4), -2*E(4), 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2*E(4), -2*E(4), -2*E(4), 2*E(4), 0, 0, 0, 0, 0, 0, 0, 0], [4, 4, 4, 4, 4, 4, 0, 0, 0, 0, -4, 4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, 4, 4, 4, 4, 4, 0, 0, 0, 0, -4, -4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, 4, 4, -4, -4, 4, 0, 0, 0, 0, 0, 0, -4, 4, -2*E(4), 2*E(4), 2*E(4), -2*E(4), -2*E(4), 2*E(4), -2*E(4), 2*E(4), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, 4, 4, -4, -4, 4, 0, 0, 0, 0, 0, 0, -4, 4, 2*E(4), -2*E(4), -2*E(4), 2*E(4), 2*E(4), -2*E(4), 2*E(4), -2*E(4), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, 4, 4, -4, -4, 4, 0, 0, 0, 0, 0, 0, 4, -4, -2*E(4), 2*E(4), -2*E(4), 2*E(4), 2*E(4), -2*E(4), -2*E(4), 2*E(4), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, 4, 4, -4, -4, 4, 0, 0, 0, 0, 0, 0, 4, -4, 2*E(4), -2*E(4), 2*E(4), -2*E(4), -2*E(4), 2*E(4), 2*E(4), -2*E(4), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [8, 8, 8, 0, 0, -8, -4, 4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [8, 8, 8, 0, 0, -8, 4, -4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [8, -8, 0, -4, 4, 0, -4, 0, 4, 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, 0, 0, 0], [8, -8, 0, -4, 4, 0, -4, 0, 4, 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, 0, 0, 0], [8, -8, 0, -4, 4, 0, 4, 0, -4, 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, 0, 0, 0], [8, -8, 0, -4, 4, 0, 4, 0, -4, 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, 0, 0, 0], [8, -8, 0, 4, -4, 0, 0, -4, 0, 4, 0, 0, 0, 0, -2*E(4), 2*E(4), -2*E(4), 2*E(4), -2*E(4), 2*E(4), 2*E(4), -2*E(4), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [8, -8, 0, 4, -4, 0, 0, -4, 0, 4, 0, 0, 0, 0, 2*E(4), -2*E(4), 2*E(4), -2*E(4), 2*E(4), -2*E(4), -2*E(4), 2*E(4), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [8, -8, 0, 4, -4, 0, 0, 4, 0, -4, 0, 0, 0, 0, -2*E(4), 2*E(4), 2*E(4), -2*E(4), 2*E(4), -2*E(4), 2*E(4), -2*E(4), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [8, -8, 0, 4, -4, 0, 0, 4, 0, -4, 0, 0, 0, 0, 2*E(4), -2*E(4), -2*E(4), 2*E(4), -2*E(4), 2*E(4), -2*E(4), 2*E(4), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [16, 16, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]];
ConvertToLibraryCharacterTableNC(chartbl_1024_dfb);