# Group 96.202 downloaded from the LMFDB on 16 November 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(519523785079220879101576,96); a := GPC.1; b := GPC.2; c := GPC.4; d := GPC.5;
GPerm := Group( (9,10)(11,12)(13,14)(15,16), (1,9)(2,10)(3,11)(4,12)(5,13)(6,14)(7,15)(8,16), (3,7,5)(4,8,6)(11,15,13)(12,16,14), (1,6,2,5)(3,8,4,7)(9,14,10,13)(11,16,12,15), (1,4,2,3)(5,7,6,8)(9,12,10,11)(13,15,14,16), (1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16) );
GLFp := Group([[[ Z(3)^0, 0*Z(3), Z(3), 0*Z(3) ], [ Z(3), Z(3), 0*Z(3), Z(3)^0 ], [ Z(3), 0*Z(3), Z(3), 0*Z(3) ], [ 0*Z(3), Z(3)^0, Z(3), Z(3)^0 ]], [[ Z(3)^0, Z(3), Z(3), Z(3)^0 ], [ Z(3), Z(3), 0*Z(3), Z(3)^0 ], [ Z(3), 0*Z(3), 0*Z(3), Z(3) ], [ Z(3)^0, Z(3)^0, Z(3), Z(3)^0 ]], [[ 0*Z(3), Z(3), 0*Z(3), Z(3)^0 ], [ Z(3), Z(3), Z(3)^0, 0*Z(3) ], [ Z(3), 0*Z(3), Z(3)^0, Z(3)^0 ], [ Z(3)^0, Z(3), Z(3)^0, 0*Z(3) ]], [[ Z(3), 0*Z(3), 0*Z(3), 0*Z(3) ], [ 0*Z(3), Z(3), 0*Z(3), 0*Z(3) ], [ 0*Z(3), 0*Z(3), Z(3), 0*Z(3) ], [ 0*Z(3), 0*Z(3), 0*Z(3), Z(3) ]], [[ 0*Z(3), 0*Z(3), Z(3)^0, 0*Z(3) ], [ 0*Z(3), Z(3), Z(3), Z(3) ], [ Z(3), 0*Z(3), 0*Z(3), 0*Z(3) ], [ Z(3)^0, Z(3), Z(3)^0, Z(3)^0 ]], [[ Z(3), 0*Z(3), Z(3), 0*Z(3) ], [ Z(3)^0, 0*Z(3), 0*Z(3), Z(3) ], [ Z(3), 0*Z(3), Z(3)^0, 0*Z(3) ], [ Z(3), Z(3)^0, Z(3), 0*Z(3) ]]]);

 
# Booleans 
booleans_96_202 := rec( 
Agroup := false,
Zgroup := false,
abelian := false,
almost_simple := false,
cyclic := false,
metabelian := false,
metacyclic := false,
monomial := false,
nilpotent := false,
perfect := false,
quasisimple := false,
rational := false,
solvable := true,
supersolvable := false); 

 
# Character Table 
chartbl_96_202:=rec(); 
chartbl_96_202.IsFinite:= true; 
chartbl_96_202.UnderlyingCharacteristic:= 0; 
chartbl_96_202.UnderlyingGroup:= GPC;
chartbl_96_202.Size:= 96;
chartbl_96_202.InfoText:= "Character table for group 96.202 downloaded from the LMFDB."; 
chartbl_96_202.Identifier:= " D4.A4 "; 
chartbl_96_202.NrConjugacyClasses:= 19; 
chartbl_96_202.ConjugacyClasses:= [<identity> of ..., f6, f2*f3, f1, f1*f2*f3*f5, f3, f3^2, f1*f2*f3*f6, f5, f1*f5, f2*f3*f5, f3*f6, f3^2*f6, f2, f2*f3^2, f1*f3, f1*f3^2, f1*f2, f1*f2*f3^2];
chartbl_96_202.IdentificationOfConjugacyClasses:= [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19];
chartbl_96_202.ComputedPowerMaps:= [ , [1, 1, 1, 1, 1, 7, 6, 2, 2, 2, 2, 7, 6, 6, 7, 7, 6, 12, 13], [1, 2, 3, 4, 5, 1, 1, 8, 9, 10, 11, 2, 2, 3, 3, 4, 4, 8, 8]];
chartbl_96_202.SizesCentralizers:= [96, 96, 48, 48, 16, 24, 24, 48, 16, 16, 16, 24, 24, 12, 12, 12, 12, 12, 12];
chartbl_96_202.ClassNames:= ["1A", "2A", "2B", "2C", "2D", "3A1", "3A-1", "4A", "4B", "4C", "4D", "6A1", "6A-1", "6B1", "6B-1", "6C1", "6C-1", "12A1", "12A-1"];
chartbl_96_202.OrderClassRepresentatives:= [1, 2, 2, 2, 2, 3, 3, 4, 4, 4, 4, 6, 6, 6, 6, 6, 6, 12, 12];
chartbl_96_202.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, E(3)^-1, E(3), 1, 1, 1, 1, E(3)^-1, E(3), E(3), E(3)^-1, E(3)^-1, E(3), E(3), E(3)^-1], [1, 1, 1, 1, 1, E(3), E(3)^-1, 1, 1, 1, 1, E(3), E(3)^-1, E(3)^-1, E(3), E(3), E(3)^-1, E(3)^-1, E(3)], [1, 1, -1, -1, 1, E(3)^-1, E(3), 1, -1, -1, 1, E(3)^-1, E(3), -1*E(3), -1*E(3)^-1, -1*E(3)^-1, -1*E(3), E(3), E(3)^-1], [1, 1, -1, -1, 1, E(3), E(3)^-1, 1, -1, -1, 1, E(3), E(3)^-1, -1*E(3)^-1, -1*E(3), -1*E(3), -1*E(3)^-1, E(3)^-1, E(3)], [1, 1, -1, 1, -1, E(3)^-1, E(3), -1, 1, -1, 1, E(3)^-1, E(3), -1*E(3), -1*E(3)^-1, E(3)^-1, E(3), -1*E(3), -1*E(3)^-1], [1, 1, -1, 1, -1, E(3), E(3)^-1, -1, 1, -1, 1, E(3), E(3)^-1, -1*E(3)^-1, -1*E(3), E(3), E(3)^-1, -1*E(3)^-1, -1*E(3)], [1, 1, 1, -1, -1, E(3)^-1, E(3), -1, -1, 1, 1, E(3)^-1, E(3), E(3), E(3)^-1, -1*E(3)^-1, -1*E(3), -1*E(3), -1*E(3)^-1], [1, 1, 1, -1, -1, E(3), E(3)^-1, -1, -1, 1, 1, E(3), E(3)^-1, E(3)^-1, E(3), -1*E(3), -1*E(3)^-1, -1*E(3)^-1, -1*E(3)], [3, 3, 3, 3, -1, 0, 0, 3, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0], [3, 3, -3, -3, -1, 0, 0, 3, 1, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0], [3, 3, -3, 3, 1, 0, 0, -3, -1, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0], [3, 3, 3, -3, 1, 0, 0, -3, 1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0], [4, -4, 0, 0, 0, -2, -2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0], [4, -4, 0, 0, 0, -2*E(3), -2*E(3)^-1, 0, 0, 0, 0, 2*E(3), 2*E(3)^-1, 0, 0, 0, 0, 0, 0], [4, -4, 0, 0, 0, -2*E(3)^-1, -2*E(3), 0, 0, 0, 0, 2*E(3)^-1, 2*E(3), 0, 0, 0, 0, 0, 0]];
ConvertToLibraryCharacterTableNC(chartbl_96_202);