# Group 96.16 downloaded from the LMFDB on 17 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(20225168039707146382977,96); a := GPC.1; b := GPC.2; c := GPC.4;
GPerm := Group( (1,2)(3,4)(6,7)(9,12)(11,14)(13,15), (1,3,4,2)(8,9,10,13)(11,15,14,12), (1,4)(2,3)(8,10)(9,13)(11,14)(12,15), (1,4)(2,3)(8,11,10,14)(9,12,13,15), (8,10)(9,13)(11,14)(12,15), (5,6,7) );
GLZ := Group([[[-1, 1, 1, 1, 0, 0], [0, 1, 0, 1, 0, 0], [0, 0, 1, 1, 0, 0], [0, 0, 0, -1, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1]], [[-1, 0, 1, 0, 0, 0], [0, 0, 1, 0, 0, 0], [-1, 1, 1, 1, 0, 0], [0, -1, 0, 0, 0, 0], [0, 0, 0, 0, 0, -1], [0, 0, 0, 0, 1, 0]]]);
GLZN := Group([[[ZmodnZObj(9,15), ZmodnZObj(14,15)], [ZmodnZObj(2,15), ZmodnZObj(1,15)]],[[ZmodnZObj(13,15), ZmodnZObj(3,15)], [ZmodnZObj(9,15), ZmodnZObj(1,15)]],[[ZmodnZObj(13,15), ZmodnZObj(10,15)], [ZmodnZObj(10,15), ZmodnZObj(8,15)]],[[ZmodnZObj(4,15), ZmodnZObj(0,15)], [ZmodnZObj(0,15), ZmodnZObj(4,15)]],[[ZmodnZObj(11,15), ZmodnZObj(0,15)], [ZmodnZObj(0,15), ZmodnZObj(11,15)]],[[ZmodnZObj(1,15), ZmodnZObj(5,15)], [ZmodnZObj(5,15), ZmodnZObj(11,15)]]]);

 
# Booleans 
booleans_96_16 := rec( 
Agroup := false,
Zgroup := false,
abelian := false,
almost_simple := false,
cyclic := false,
metabelian := true,
metacyclic := false,
monomial := true,
nilpotent := false,
perfect := false,
quasisimple := false,
rational := false,
solvable := true,
supersolvable := true); 

 
# Character Table 
chartbl_96_16:=rec(); 
chartbl_96_16.IsFinite:= true; 
chartbl_96_16.UnderlyingCharacteristic:= 0; 
chartbl_96_16.UnderlyingGroup:= GPC;
chartbl_96_16.Size:= 96;
chartbl_96_16.InfoText:= "Character table for group 96.16 downloaded from the LMFDB."; 
chartbl_96_16.Identifier:= " D12:C4 "; 
chartbl_96_16.NrConjugacyClasses:= 24; 
chartbl_96_16.ConjugacyClasses:= [<identity> of ..., f3*f5*f6, f5*f6, f3, f1*f4*f5*f6^2, f1*f3*f4*f5*f6^2, f6, f3*f4*f6^2, f4*f5, f2*f3, f2, f3*f5, f5, f3*f6^2, f1*f2, f1*f2*f3, f1*f2*f3*f5, f1*f2*f5, f4, f3*f4, f2*f6, f2*f3*f5, f2*f5, f2*f3*f6];
chartbl_96_16.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];
chartbl_96_16.ComputedPowerMaps:= [ , [1, 1, 1, 1, 1, 1, 7, 3, 3, 4, 4, 7, 7, 7, 8, 8, 8, 8, 13, 13, 14, 14, 14, 14], [1, 2, 3, 4, 5, 6, 1, 8, 9, 11, 10, 2, 3, 4, 17, 18, 15, 16, 9, 8, 10, 11, 10, 11]];
chartbl_96_16.SizesCentralizers:= [96, 96, 96, 96, 8, 8, 48, 48, 48, 24, 24, 48, 48, 48, 16, 16, 16, 16, 24, 24, 24, 24, 24, 24];
chartbl_96_16.ClassNames:= ["1A", "2A", "2B", "2C", "2D", "2E", "3A", "4A", "4B", "4C1", "4C-1", "6A", "6B", "6C", "8A1", "8A-1", "8A3", "8A-3", "12A", "12B", "12C1", "12C-1", "12C5", "12C-5"];
chartbl_96_16.OrderClassRepresentatives:= [1, 2, 2, 2, 2, 2, 3, 4, 4, 4, 4, 6, 6, 6, 8, 8, 8, 8, 12, 12, 12, 12, 12, 12];
chartbl_96_16.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*E(4), E(4), -1, -1, 1, -1*E(4), E(4), E(4), -1*E(4), -1*E(4), -1, E(4), E(4), -1*E(4), 1], [1, -1, -1, 1, -1, 1, 1, -1, 1, E(4), -1*E(4), -1, -1, 1, E(4), -1*E(4), -1*E(4), E(4), E(4), -1, -1*E(4), -1*E(4), E(4), 1], [1, -1, -1, 1, 1, -1, 1, -1, 1, -1*E(4), E(4), -1, -1, 1, E(4), -1*E(4), -1*E(4), E(4), -1*E(4), -1, E(4), E(4), -1*E(4), 1], [1, -1, -1, 1, 1, -1, 1, -1, 1, E(4), -1*E(4), -1, -1, 1, -1*E(4), E(4), E(4), -1*E(4), E(4), -1, -1*E(4), -1*E(4), E(4), 1], [2, 2, 2, 2, 0, 0, -1, 2, 2, 2, 2, -1, -1, -1, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1], [2, -2, -2, 2, 0, 0, 2, 2, -2, 0, 0, -2, -2, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2], [2, 2, 2, 2, 0, 0, 2, -2, -2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2], [2, 2, 2, 2, 0, 0, -1, 2, 2, -2, -2, -1, -1, -1, 0, 0, 0, 0, 1, -1, 1, 1, 1, -1], [2, 2, -2, -2, 0, 0, 2, 0, 0, 0, 0, 2, -2, -2, -1*E(8)-E(8)^-1, -1*E(8)-E(8)^-1, E(8)+E(8)^-1, E(8)+E(8)^-1, 0, 0, 0, 0, 0, 0], [2, 2, -2, -2, 0, 0, 2, 0, 0, 0, 0, 2, -2, -2, E(8)+E(8)^-1, E(8)+E(8)^-1, -1*E(8)-E(8)^-1, -1*E(8)-E(8)^-1, 0, 0, 0, 0, 0, 0], [2, -2, 2, -2, 0, 0, 2, 0, 0, 0, 0, -2, 2, -2, -1*E(8)-E(8)^3, E(8)+E(8)^3, -1*E(8)-E(8)^3, E(8)+E(8)^3, 0, 0, 0, 0, 0, 0], [2, -2, 2, -2, 0, 0, 2, 0, 0, 0, 0, -2, 2, -2, E(8)+E(8)^3, -1*E(8)-E(8)^3, E(8)+E(8)^3, -1*E(8)-E(8)^3, 0, 0, 0, 0, 0, 0], [2, -2, -2, 2, 0, 0, -1, -2, 2, -2*E(4), 2*E(4), 1, 1, -1, 0, 0, 0, 0, E(4), 1, -1*E(4), -1*E(4), E(4), -1], [2, -2, -2, 2, 0, 0, -1, -2, 2, 2*E(4), -2*E(4), 1, 1, -1, 0, 0, 0, 0, -1*E(4), 1, E(4), E(4), -1*E(4), -1], [2, -2, -2, 2, 0, 0, -1, 2, -2, 0, 0, 1, 1, -1, 0, 0, 0, 0, -1*E(12)-E(12)^-1, -1, E(12)+E(12)^-1, -1*E(12)-E(12)^-1, E(12)+E(12)^-1, 1], [2, -2, -2, 2, 0, 0, -1, 2, -2, 0, 0, 1, 1, -1, 0, 0, 0, 0, E(12)+E(12)^-1, -1, -1*E(12)-E(12)^-1, E(12)+E(12)^-1, -1*E(12)-E(12)^-1, 1], [2, 2, 2, 2, 0, 0, -1, -2, -2, 0, 0, -1, -1, -1, 0, 0, 0, 0, -1-2*E(3), 1, -1-2*E(3), 1+2*E(3), 1+2*E(3), 1], [2, 2, 2, 2, 0, 0, -1, -2, -2, 0, 0, -1, -1, -1, 0, 0, 0, 0, 1+2*E(3), 1, 1+2*E(3), -1-2*E(3), -1-2*E(3), 1], [4, -4, 4, -4, 0, 0, -2, 0, 0, 0, 0, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, 4, -4, -4, 0, 0, -2, 0, 0, 0, 0, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]];
ConvertToLibraryCharacterTableNC(chartbl_96_16);