# Group 588.34 downloaded from the LMFDB on 14 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(9398965229125456060021105511,588); a := GPC.1; b := GPC.4; c := GPC.5;
GPerm := Group( (1,8)(2,14,7,9)(3,13,6,10)(4,12,5,11), (2,3,5)(4,7,6)(9,10,12)(11,14,13), (2,7)(3,6)(4,5)(9,14)(10,13)(11,12), (1,7,6,5,4,3,2)(8,11,14,10,13,9,12), (8,11,14,10,13,9,12) );
GLFp := Group([[[ Z(7)^0, 0*Z(7), 0*Z(7) ], [ 0*Z(7), Z(7)^0, 0*Z(7) ], [ Z(7)^5, Z(7)^5, Z(7)^0 ]], [[ 0*Z(7), Z(7), Z(7)^5 ], [ Z(7)^3, Z(7), Z(7)^2 ], [ Z(7)^5, 0*Z(7), Z(7) ]], [[ Z(7)^3, 0*Z(7), 0*Z(7) ], [ Z(7), Z(7)^2, 0*Z(7) ], [ 0*Z(7), 0*Z(7), Z(7)^3 ]], [[ Z(7)^0, 0*Z(7), 0*Z(7) ], [ Z(7), Z(7)^4, 0*Z(7) ], [ 0*Z(7), 0*Z(7), Z(7)^0 ]], [[ Z(7)^5, Z(7)^4, 0*Z(7) ], [ Z(7), Z(7)^4, 0*Z(7) ], [ 0*Z(7), 0*Z(7), Z(7)^0 ]]]);

 
# Booleans 
booleans_588_34 := rec( 
Agroup := true,
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 := false); 

 
# Character Table 
chartbl_588_34:=rec(); 
chartbl_588_34.IsFinite:= true; 
chartbl_588_34.UnderlyingCharacteristic:= 0; 
chartbl_588_34.UnderlyingGroup:= GPC;
chartbl_588_34.Size:= 588;
chartbl_588_34.InfoText:= "Character table for group 588.34 downloaded from the LMFDB."; 
chartbl_588_34.Identifier:= " C7^2:C12 "; 
chartbl_588_34.NrConjugacyClasses:= 16; 
chartbl_588_34.ConjugacyClasses:= [<identity> of ..., f2*f3*f4^6, f3*f4^5, f3^2*f4^4, f1*f3^2*f4^4*f5^2, f1*f2*f4^2*f5^5, f2*f4^2, f2*f3^2*f4, f5, f4, f4*f5, f4^2*f5, f1*f2*f3*f4^6*f5^6, f1*f3*f4^5*f5^4, f1*f2*f3^2*f4*f5^3, f1*f5];
chartbl_588_34.IdentificationOfConjugacyClasses:= [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16];
chartbl_588_34.ComputedPowerMaps:= [ , [1, 1, 4, 3, 2, 2, 3, 4, 9, 10, 11, 12, 7, 8, 8, 7], [1, 2, 1, 1, 6, 5, 2, 2, 9, 10, 11, 12, 5, 6, 5, 6], [1, 2, 3, 4, 6, 5, 7, 8, 1, 1, 1, 1, 16, 15, 14, 13]];
chartbl_588_34.SizesCentralizers:= [588, 12, 12, 12, 12, 12, 12, 12, 49, 49, 49, 49, 12, 12, 12, 12];
chartbl_588_34.ClassNames:= ["1A", "2A", "3A1", "3A-1", "4A1", "4A-1", "6A1", "6A-1", "7A", "7B", "7C", "7D", "12A1", "12A-1", "12A5", "12A-5"];
chartbl_588_34.OrderClassRepresentatives:= [1, 2, 3, 3, 4, 4, 6, 6, 7, 7, 7, 7, 12, 12, 12, 12];
chartbl_588_34.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, E(3)^-1, E(3), 1, 1, E(3), E(3)^-1, 1, 1, 1, 1, E(3), E(3), E(3)^-1, E(3)^-1], [1, 1, E(3), E(3)^-1, 1, 1, E(3)^-1, E(3), 1, 1, 1, 1, E(3)^-1, E(3)^-1, E(3), E(3)], [1, -1, 1, 1, -1*E(4), E(4), -1, -1, 1, 1, 1, 1, E(4), -1*E(4), -1*E(4), E(4)], [1, -1, 1, 1, E(4), -1*E(4), -1, -1, 1, 1, 1, 1, -1*E(4), E(4), E(4), -1*E(4)], [1, 1, E(3)^-1, E(3), -1, -1, E(3), E(3)^-1, 1, 1, 1, 1, -1*E(3), -1*E(3), -1*E(3)^-1, -1*E(3)^-1], [1, 1, E(3), E(3)^-1, -1, -1, E(3)^-1, E(3), 1, 1, 1, 1, -1*E(3)^-1, -1*E(3)^-1, -1*E(3), -1*E(3)], [1, -1, -1*E(12)^2, E(12)^4, -1*E(12)^3, E(12)^3, -1*E(12)^4, E(12)^2, 1, 1, 1, 1, -1*E(12), E(12), E(12)^5, -1*E(12)^5], [1, -1, E(12)^4, -1*E(12)^2, E(12)^3, -1*E(12)^3, E(12)^2, -1*E(12)^4, 1, 1, 1, 1, E(12)^5, -1*E(12)^5, -1*E(12), E(12)], [1, -1, -1*E(12)^2, E(12)^4, E(12)^3, -1*E(12)^3, -1*E(12)^4, E(12)^2, 1, 1, 1, 1, E(12), -1*E(12), -1*E(12)^5, E(12)^5], [1, -1, E(12)^4, -1*E(12)^2, -1*E(12)^3, E(12)^3, E(12)^2, -1*E(12)^4, 1, 1, 1, 1, -1*E(12)^5, E(12)^5, E(12), -1*E(12)], [12, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, 5, 0, 0, 0, 0], [12, 0, 0, 0, 0, 0, 0, 0, -2, -2, 5, -2, 0, 0, 0, 0], [12, 0, 0, 0, 0, 0, 0, 0, -2, 5, -2, -2, 0, 0, 0, 0], [12, 0, 0, 0, 0, 0, 0, 0, 5, -2, -2, -2, 0, 0, 0, 0]];
ConvertToLibraryCharacterTableNC(chartbl_588_34);