# Group 144.183 downloaded from the LMFDB on 13 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(17916337004854231243587206281,144); a := GPC.1; b := GPC.2; c := GPC.4; d := GPC.5;
GPerm := Group( (6,7), (2,3), (2,3,4), (5,6,7), (1,2)(3,4), (1,3)(2,4) );
GLZ := Group([[[1, 0, 0, 0, 0], [0, 0, -1, 0, 0], [0, -1, 0, 0, 0], [0, 0, 0, 1, 1], [0, 0, 0, 0, -1]], [[-1, 1, -1, 0, 0], [0, 0, -1, 0, 0], [1, 0, 0, 0, 0], [0, 0, 0, 0, -1], [0, 0, 0, 1, 1]]]);
GLFp := Group([[[ Z(2)^0, 0*Z(2), 0*Z(2), Z(2)^0, 0*Z(2) ], [ 0*Z(2), Z(2)^0, 0*Z(2), 0*Z(2), 0*Z(2) ], [ 0*Z(2), 0*Z(2), Z(2)^0, 0*Z(2), 0*Z(2) ], [ 0*Z(2), 0*Z(2), 0*Z(2), Z(2)^0, 0*Z(2) ], [ 0*Z(2), 0*Z(2), 0*Z(2), Z(2)^0, Z(2)^0 ]], [[ Z(2)^0, Z(2)^0, Z(2)^0, 0*Z(2), 0*Z(2) ], [ 0*Z(2), 0*Z(2), 0*Z(2), Z(2)^0, Z(2)^0 ], [ 0*Z(2), Z(2)^0, Z(2)^0, Z(2)^0, Z(2)^0 ], [ 0*Z(2), 0*Z(2), 0*Z(2), Z(2)^0, 0*Z(2) ], [ 0*Z(2), Z(2)^0, 0*Z(2), 0*Z(2), 0*Z(2) ]], [[ Z(2)^0, 0*Z(2), Z(2)^0, 0*Z(2), 0*Z(2) ], [ 0*Z(2), Z(2)^0, 0*Z(2), Z(2)^0, Z(2)^0 ], [ Z(2)^0, 0*Z(2), 0*Z(2), Z(2)^0, 0*Z(2) ], [ 0*Z(2), 0*Z(2), 0*Z(2), Z(2)^0, 0*Z(2) ], [ 0*Z(2), Z(2)^0, 0*Z(2), 0*Z(2), 0*Z(2) ]], [[ Z(2)^0, Z(2)^0, Z(2)^0, Z(2)^0, Z(2)^0 ], [ 0*Z(2), 0*Z(2), 0*Z(2), Z(2)^0, Z(2)^0 ], [ Z(2)^0, Z(2)^0, 0*Z(2), Z(2)^0, 0*Z(2) ], [ 0*Z(2), 0*Z(2), 0*Z(2), Z(2)^0, 0*Z(2) ], [ 0*Z(2), Z(2)^0, 0*Z(2), Z(2)^0, Z(2)^0 ]], [[ Z(2)^0, 0*Z(2), 0*Z(2), Z(2)^0, 0*Z(2) ], [ 0*Z(2), Z(2)^0, 0*Z(2), Z(2)^0, 0*Z(2) ], [ Z(2)^0, Z(2)^0, Z(2)^0, 0*Z(2), Z(2)^0 ], [ 0*Z(2), 0*Z(2), 0*Z(2), Z(2)^0, 0*Z(2) ], [ 0*Z(2), 0*Z(2), 0*Z(2), 0*Z(2), Z(2)^0 ]], [[ Z(2)^0, 0*Z(2), 0*Z(2), 0*Z(2), 0*Z(2) ], [ 0*Z(2), Z(2)^0, 0*Z(2), Z(2)^0, 0*Z(2) ], [ 0*Z(2), 0*Z(2), Z(2)^0, Z(2)^0, 0*Z(2) ], [ 0*Z(2), 0*Z(2), 0*Z(2), Z(2)^0, 0*Z(2) ], [ 0*Z(2), 0*Z(2), 0*Z(2), Z(2)^0, Z(2)^0 ]]]);

 
# Booleans 
booleans_144_183 := rec( 
Agroup := false,
Zgroup := false,
abelian := false,
almost_simple := false,
cyclic := false,
metabelian := false,
metacyclic := false,
monomial := true,
nilpotent := false,
perfect := false,
quasisimple := false,
rational := true,
solvable := true,
supersolvable := false); 

 
# Character Table 
chartbl_144_183:=rec(); 
chartbl_144_183.IsFinite:= true; 
chartbl_144_183.UnderlyingCharacteristic:= 0; 
chartbl_144_183.UnderlyingGroup:= GPerm;
chartbl_144_183.Size:= 144;
chartbl_144_183.InfoText:= "Character table for group 144.183 downloaded from the LMFDB."; 
chartbl_144_183.Identifier:= " S3*S4 "; 
chartbl_144_183.NrConjugacyClasses:= 15; 
chartbl_144_183.ConjugacyClasses:= [(), (1,3)(2,4), (5,6), (3,4), (1,2)(3,4)(6,7), (1,2)(5,7), (5,7,6), (1,3,4), (1,3,2)(5,6,7), (1,4,3,2), (1,4,3,2)(6,7), (1,3)(2,4)(5,7,6), (3,4)(5,6,7), (1,4,3)(5,6), (1,2,3,4)(5,6,7)];
chartbl_144_183.IdentificationOfConjugacyClasses:= [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15];
chartbl_144_183.ComputedPowerMaps:= [ , [1, 1, 1, 1, 1, 1, 7, 8, 9, 2, 2, 7, 7, 8, 12], [1, 2, 3, 4, 5, 6, 1, 1, 1, 10, 11, 2, 4, 3, 10]];
chartbl_144_183.SizesCentralizers:= [144, 48, 48, 24, 16, 8, 72, 18, 9, 24, 8, 24, 12, 6, 12];
chartbl_144_183.ClassNames:= ["1A", "2A", "2B", "2C", "2D", "2E", "3A", "3B", "3C", "4A", "4B", "6A", "6B", "6C", "12A"];
chartbl_144_183.OrderClassRepresentatives:= [1, 2, 2, 2, 2, 2, 3, 3, 3, 4, 4, 6, 6, 6, 12];
chartbl_144_183.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], [2, 2, 0, 2, 0, 0, -1, 2, -1, 2, 0, -1, -1, 0, -1], [2, 2, 2, 0, 2, 0, 2, -1, -1, 0, 0, 2, 0, -1, 0], [2, 2, -2, 0, -2, 0, 2, -1, -1, 0, 0, 2, 0, 1, 0], [2, 2, 0, -2, 0, 0, -1, 2, -1, -2, 0, -1, 1, 0, 1], [3, -1, 3, 1, -1, 1, 3, 0, 0, -1, -1, -1, 1, 0, -1], [3, -1, 3, -1, -1, -1, 3, 0, 0, 1, 1, -1, -1, 0, 1], [3, -1, -3, -1, 1, 1, 3, 0, 0, 1, -1, -1, -1, 0, 1], [3, -1, -3, 1, 1, -1, 3, 0, 0, -1, 1, -1, 1, 0, -1], [4, 4, 0, 0, 0, 0, -2, -2, 1, 0, 0, -2, 0, 0, 0], [6, -2, 0, 2, 0, 0, -3, 0, 0, -2, 0, 1, -1, 0, 1], [6, -2, 0, -2, 0, 0, -3, 0, 0, 2, 0, 1, 1, 0, -1]];
ConvertToLibraryCharacterTableNC(chartbl_144_183);