# Group 432.520 downloaded from the LMFDB on 13 June 2026. 
 
## 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(315743925718442161789025476127419366510060295,432); a := GPC.1; b := GPC.2; c := GPC.5; d := GPC.6; e := GPC.7;
GPerm := Group( (2,3)(4,16,26,21,8,23,14,10)(5,18,27,20,9,22,15,12)(6,17,25,19,7,24,13,11), (2,3)(4,7)(5,9)(6,8)(10,17)(11,16)(12,18)(13,14)(19,23)(20,22)(21,24)(25,26), (4,26,8,14)(5,27,9,15)(6,25,7,13)(10,16,21,23)(11,17,19,24)(12,18,20,22), (4,8)(5,9)(6,7)(10,21)(11,19)(12,20)(13,25)(14,26)(15,27)(16,23)(17,24)(18,22), (1,19,10)(2,20,11)(3,21,12)(4,22,13)(5,23,14)(6,24,15)(7,25,16)(8,26,17)(9,27,18), (1,7,4)(2,8,5)(3,9,6)(10,18,14)(11,16,15)(12,17,13)(19,26,24)(20,27,22)(21,25,23), (1,3,2)(4,6,5)(7,9,8)(10,12,11)(13,15,14)(16,18,17)(19,21,20)(22,24,23)(25,27,26) );
GLZ := Group([[[-1, 0, 0, 0, 0, 0], [0, -1, 0, 0, 0, 0], [-1, 1, 1, 0, 0, 0], [0, 0, -1, -1, -1, 0], [1, -1, 0, 0, 1, 0], [-1, 0, 0, 0, 0, 1]], [[0, -1, 0, 0, 0, 0], [0, -1, 0, -1, 0, 0], [0, 0, 0, 1, 1, 0], [0, 0, -1, 0, -1, 1], [1, 0, 1, 0, 1, -1], [1, -1, 0, 0, 1, -1]]]);
GLFp := Group([[[ Z(3)^0, 0*Z(3), Z(3), Z(3)^0 ], [ Z(3), 0*Z(3), Z(3)^0, 0*Z(3) ], [ Z(3), Z(3), Z(3), Z(3) ], [ Z(3)^0, 0*Z(3), Z(3)^0, Z(3)^0 ]], [[ Z(3)^0, Z(3)^0, 0*Z(3), Z(3) ], [ 0*Z(3), Z(3)^0, 0*Z(3), 0*Z(3) ], [ 0*Z(3), 0*Z(3), Z(3), 0*Z(3) ], [ 0*Z(3), Z(3), 0*Z(3), Z(3) ]], [[ Z(3), Z(3), Z(3), 0*Z(3) ], [ Z(3), Z(3)^0, 0*Z(3), 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), 0*Z(3), Z(3), 0*Z(3) ], [ Z(3), Z(3)^0, 0*Z(3), Z(3) ], [ Z(3)^0, 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), 0*Z(3), 0*Z(3) ], [ Z(3), Z(3)^0, Z(3), Z(3)^0 ], [ 0*Z(3), Z(3)^0, Z(3), Z(3)^0 ], [ 0*Z(3), Z(3)^0, 0*Z(3), Z(3)^0 ]], [[ Z(3), 0*Z(3), Z(3), 0*Z(3) ], [ 0*Z(3), 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), Z(3)^0, Z(3)^0 ]], [[ Z(3), 0*Z(3), 0*Z(3), Z(3)^0 ], [ 0*Z(3), Z(3)^0, 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), 0*Z(3) ]]]);

 
# Booleans 
booleans_432_520 := 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_432_520:=rec(); 
chartbl_432_520.IsFinite:= true; 
chartbl_432_520.UnderlyingCharacteristic:= 0; 
chartbl_432_520.UnderlyingGroup:= GLFp;
chartbl_432_520.Size:= 432;
chartbl_432_520.InfoText:= "Character table for group 432.520 downloaded from the LMFDB."; 
chartbl_432_520.Identifier:= " He3:SD16 "; 
chartbl_432_520.NrConjugacyClasses:= 14; 
chartbl_432_520.ConjugacyClasses:= [[1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1], [0, 1, 0, 2, 2, 2, 0, 2, 0, 1, 2, 1, 1, 2, 0, 2], [2, 2, 1, 1, 0, 2, 0, 0, 1, 0, 2, 1, 2, 1, 2, 0], [2, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 2, 0, 0, 0], [2, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 2, 2, 0, 0], [2, 1, 0, 1, 1, 2, 1, 2, 2, 2, 1, 2, 2, 2, 0, 0], [0, 1, 2, 0, 1, 0, 2, 0, 1, 2, 2, 1, 2, 2, 1, 2], [2, 1, 0, 1, 2, 2, 0, 2, 2, 1, 2, 0, 2, 2, 0, 0], [1, 0, 1, 0, 0, 2, 0, 0, 1, 1, 2, 1, 0, 0, 2, 1], [0, 1, 2, 1, 2, 1, 1, 0, 2, 2, 2, 0, 2, 2, 1, 1], [0, 1, 1, 0, 1, 0, 1, 2, 2, 2, 0, 1, 2, 2, 2, 2], [0, 0, 0, 2, 0, 1, 2, 2, 0, 2, 2, 1, 1, 0, 0, 2], [1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 2, 2, 2], [1, 1, 2, 1, 1, 0, 2, 0, 2, 2, 2, 2, 1, 2, 1, 1]];
chartbl_432_520.IdentificationOfConjugacyClasses:= [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14];
chartbl_432_520.ComputedPowerMaps:= [ , [1, 1, 1, 4, 5, 2, 2, 4, 5, 6, 6, 8, 8, 8], [1, 2, 3, 1, 1, 6, 7, 2, 3, 10, 11, 6, 7, 7]];
chartbl_432_520.SizesCentralizers:= [432, 48, 12, 216, 18, 24, 12, 24, 6, 8, 8, 12, 12, 12];
chartbl_432_520.ClassNames:= ["1A", "2A", "2B", "3A", "3B", "4A", "4B", "6A", "6B", "8A1", "8A-1", "12A", "12B1", "12B-1"];
chartbl_432_520.OrderClassRepresentatives:= [1, 2, 2, 3, 3, 4, 4, 6, 6, 8, 8, 12, 12, 12];
chartbl_432_520.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], [2, 2, 0, 2, 2, -2, 0, 2, 0, 0, 0, 0, 0, -2], [2, -2, 0, 2, 2, 0, 0, -2, 0, -1*E(8)-E(8)^3, E(8)+E(8)^3, 0, 0, 0], [2, -2, 0, 2, 2, 0, 0, -2, 0, E(8)+E(8)^3, -1*E(8)-E(8)^3, 0, 0, 0], [6, -2, 0, -3, 0, 2, 2, 1, 0, 0, 0, -1, -1, -1], [6, -2, 0, -3, 0, 2, -2, 1, 0, 0, 0, 1, 1, -1], [6, -2, 0, -3, 0, -2, 0, 1, 0, 0, 0, -1-2*E(3), 1+2*E(3), 1], [6, -2, 0, -3, 0, -2, 0, 1, 0, 0, 0, 1+2*E(3), -1-2*E(3), 1], [8, 0, 2, 8, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0], [8, 0, -2, 8, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0], [12, 4, 0, -6, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0]];
ConvertToLibraryCharacterTableNC(chartbl_432_520);