# Group 64.255 downloaded from the LMFDB on 19 September 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(1161363587123228,64); a := GPC.1; b := GPC.2; c := GPC.3; d := GPC.4;
GPerm := Group( (1,2)(3,9)(4,7)(5,13)(6,11)(8,12)(10,16)(14,15)(17,18), (1,3,4,10)(2,6,7,15)(5,14,12,11)(8,16,13,9)(17,18), (2,7)(6,15)(8,13)(9,16)(17,18), (1,4)(2,7)(3,10)(5,12)(6,15)(8,13)(9,16)(11,14)(17,18), (1,5,4,12)(2,8,7,13)(3,11,10,14)(6,9,15,16), (1,4)(2,7)(3,10)(5,12)(6,15)(8,13)(9,16)(11,14) );

 
# Booleans 
booleans_64_255 := 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_255:=rec(); 
chartbl_64_255.IsFinite:= true; 
chartbl_64_255.UnderlyingCharacteristic:= 0; 
chartbl_64_255.UnderlyingGroup:= GPC;
chartbl_64_255.Size:= 64;
chartbl_64_255.InfoText:= "Character table for group 64.255 downloaded from the LMFDB."; 
chartbl_64_255.Identifier:= " Q16:C2^2 "; 
chartbl_64_255.NrConjugacyClasses:= 22; 
chartbl_64_255.ConjugacyClasses:= [<identity> of ..., f1, f1*f6, f6, f2, f1*f2, f3*f4, f1*f3*f4, f2*f5, f1*f5, f1*f2*f5, f5, f3, f2*f3, f1*f3, f2*f3*f4, f1*f2*f3, f1*f2*f3*f4, f4, f2*f4, f1*f4, f1*f2*f4];
chartbl_64_255.IdentificationOfConjugacyClasses:= [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22];
chartbl_64_255.ComputedPowerMaps:= [ , [1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 12, 12, 12, 12]];
chartbl_64_255.SizesCentralizers:= [64, 64, 64, 64, 32, 32, 16, 16, 32, 32, 32, 32, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16];
chartbl_64_255.ClassNames:= ["1A", "2A", "2B", "2C", "2D", "2E", "2F", "2G", "4A", "4B", "4C", "4D", "4E", "4F", "4G", "4H", "4I", "4J", "8A", "8B", "8C", "8D"];
chartbl_64_255.OrderClassRepresentatives:= [1, 2, 2, 2, 2, 2, 2, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 8, 8, 8, 8];
chartbl_64_255.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, -1, -1, 1, -1, 1, -1, 1, -1, -1, 1, 1, -1, 1, -1, -1, 1, -1, -1, 1, 1], [1, 1, 1, 1, -1, -1, -1, -1, -1, 1, -1, 1, -1, -1, 1, 1, 1, 1, 1, -1, 1, -1], [1, 1, 1, 1, -1, -1, -1, -1, -1, 1, -1, 1, 1, 1, -1, 1, -1, 1, -1, 1, -1, 1], [1, 1, 1, 1, -1, -1, 1, 1, -1, 1, -1, 1, -1, -1, 1, -1, 1, -1, -1, 1, -1, 1], [1, 1, 1, 1, -1, -1, 1, 1, -1, 1, -1, 1, 1, 1, -1, -1, -1, -1, 1, -1, 1, -1], [1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1, -1, -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, -2, 2, 0, 0, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, -2, -2, 2, -2, 0, 0, -2, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, 2, -2, -2, 0, 0, 2, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, 2, 2, 2, 0, 0, -2, -2, -2, -2, 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, 0, 0, 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]];
ConvertToLibraryCharacterTableNC(chartbl_64_255);