# Group 64.177 downloaded from the LMFDB on 23 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(73220881777691066,64); a := GPC.1; b := GPC.2; c := GPC.4;
GPerm := Group( (2,5)(3,8)(6,7)(10,11), (1,2,3,5,4,7,8,6)(9,10,12,11), (1,3,4,8)(2,6,7,5)(9,11,12,10), (1,3,4,8)(2,5,7,6)(9,12)(10,11), (1,4)(2,7)(3,8)(5,6)(9,12)(10,11), (1,4)(2,7)(3,8)(5,6) );
GLZ := Group([[[1, 0, 0, 0, 0, 0], [0, -1, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, -1], [0, 0, 0, 0, 1, 0]], [[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 0, -1, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, -1]], [[0, 1, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, -1, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, -1]]]);
GLZN := Group([[[ZmodnZObj(1,24), ZmodnZObj(12,24)], [ZmodnZObj(0,24), ZmodnZObj(1,24)]],[[ZmodnZObj(17,24), ZmodnZObj(0,24)], [ZmodnZObj(0,24), ZmodnZObj(17,24)]],[[ZmodnZObj(17,24), ZmodnZObj(21,24)], [ZmodnZObj(8,24), ZmodnZObj(7,24)]],[[ZmodnZObj(11,24), ZmodnZObj(5,24)], [ZmodnZObj(0,24), ZmodnZObj(1,24)]],[[ZmodnZObj(17,24), ZmodnZObj(5,24)], [ZmodnZObj(8,24), ZmodnZObj(1,24)]],[[ZmodnZObj(1,24), ZmodnZObj(6,24)], [ZmodnZObj(0,24), ZmodnZObj(1,24)]]]);
GLZq := Group([[[ZmodnZObj(12,32), ZmodnZObj(9,32)], [ZmodnZObj(9,32), ZmodnZObj(4,32)]],[[ZmodnZObj(31,32), ZmodnZObj(0,32)], [ZmodnZObj(0,32), ZmodnZObj(31,32)]],[[ZmodnZObj(0,32), ZmodnZObj(1,32)], [ZmodnZObj(1,32), ZmodnZObj(0,32)]],[[ZmodnZObj(1,32), ZmodnZObj(24,32)], [ZmodnZObj(8,32), ZmodnZObj(1,32)]],[[ZmodnZObj(28,32), ZmodnZObj(23,32)], [ZmodnZObj(9,32), ZmodnZObj(4,32)]],[[ZmodnZObj(1,32), ZmodnZObj(16,32)], [ZmodnZObj(16,32), ZmodnZObj(1,32)]]]);

 
# Booleans 
booleans_64_177 := 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 := true,
solvable := true,
supersolvable := true); 

 
# Character Table 
chartbl_64_177:=rec(); 
chartbl_64_177.IsFinite:= true; 
chartbl_64_177.UnderlyingCharacteristic:= 0; 
chartbl_64_177.UnderlyingGroup:= GPC;
chartbl_64_177.Size:= 64;
chartbl_64_177.InfoText:= "Character table for group 64.177 downloaded from the LMFDB."; 
chartbl_64_177.Identifier:= " C8:D4 "; 
chartbl_64_177.NrConjugacyClasses:= 16; 
chartbl_64_177.ConjugacyClasses:= [<identity> of ..., f3, f3*f6, f6, f1, f1*f2, f1*f2*f4, f5, f3*f5*f6, f2, f2*f5, f1*f4, f4, f3*f4, f2*f4, f2*f4*f5];
chartbl_64_177.IdentificationOfConjugacyClasses:= [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16];
chartbl_64_177.ComputedPowerMaps:= [ , [1, 1, 1, 1, 1, 1, 1, 4, 4, 2, 3, 4, 8, 8, 9, 9]];
chartbl_64_177.SizesCentralizers:= [64, 64, 64, 64, 8, 8, 8, 32, 32, 16, 16, 8, 16, 16, 16, 16];
chartbl_64_177.ClassNames:= ["1A", "2A", "2B", "2C", "2D", "2E", "2F", "4A", "4B", "4C", "4D", "4E", "8A", "8B", "8C", "8D"];
chartbl_64_177.OrderClassRepresentatives:= [1, 2, 2, 2, 2, 2, 2, 4, 4, 4, 4, 4, 8, 8, 8, 8];
chartbl_64_177.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], [2, 2, -2, -2, 0, 0, 0, -2, 2, 0, 0, 0, 0, -2, 2, 0], [2, 2, -2, -2, 0, 0, 0, -2, 2, 0, 0, 0, 0, 2, -2, 0], [2, 2, -2, -2, 0, 0, 0, 2, -2, 0, 0, 0, -2, 0, 0, 2], [2, 2, -2, -2, 0, 0, 0, 2, -2, 0, 0, 0, 2, 0, 0, -2], [2, 2, 2, 2, 0, 0, 0, -2, -2, -2, 2, 0, 0, 0, 0, 0], [2, 2, 2, 2, 0, 0, 0, -2, -2, 2, -2, 0, 0, 0, 0, 0], [4, -4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, -4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]];
ConvertToLibraryCharacterTableNC(chartbl_64_177);