# Group 1728.37589 downloaded from the LMFDB on 10 November 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(76386444621796472778078391062363816277414328911636542431275049,1728); a := GPC.1; b := GPC.2; c := GPC.3; d := GPC.5; e := GPC.7;
GPerm := Group( (11,12)(13,14)(16,17), (1,2)(3,6)(4,5)(7,8)(9,10)(11,13)(12,14), (1,2)(3,5)(4,6)(7,9)(8,10)(11,14)(12,13), (8,9)(11,12,14,13), (7,10)(8,9)(11,14)(12,13), (11,14)(12,13), (1,3,4)(2,5,6), (15,16,17), (1,4,3)(2,5,6) );

 
# Booleans 
booleans_1728_37589 := rec( 
Agroup := false,
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 := true); 

 
# Character Table 
chartbl_1728_37589:=rec(); 
chartbl_1728_37589.IsFinite:= true; 
chartbl_1728_37589.UnderlyingCharacteristic:= 0; 
chartbl_1728_37589.UnderlyingGroup:= GPC;
chartbl_1728_37589.Size:= 1728;
chartbl_1728_37589.InfoText:= "Character table for group 1728.37589 downloaded from the LMFDB."; 
chartbl_1728_37589.Identifier:= " D6^2:D6 "; 
chartbl_1728_37589.NrConjugacyClasses:= 108; 
chartbl_1728_37589.ConjugacyClasses:= [<identity> of ..., f5*f6, f5*f6*f8*f9, f8*f9, f3*f4, f3*f4*f5, f1, f1*f5*f6, f1*f2, f1*f2*f8*f9, f3*f4*f7*f9^2, f2, f2*f5*f6, f1*f3*f4, f1*f3*f4*f8, f1*f2*f3, f1*f2*f3*f8*f9, f2*f3, f2*f3*f8, f2*f3*f5, f2*f3*f5*f8, f2*f7*f8*f9, f4, f6^2, f9^2, f6*f9^2, f4^2*f6, f4^2*f9^2, f4^2*f6*f9^2, f7*f8, f1*f5*f6*f7, f1*f2*f5*f6*f7*f8, f1*f3*f4*f5*f6*f7*f9^2, f1*f2*f3*f5*f7*f8, f2*f3*f4^2*f6^2*f7*f8*f9, f8, f6^2*f8*f9, f4^2*f8*f9, f5, f4^2*f5*f6, f5*f6*f8, f5*f8*f9, f4^2*f5*f6*f8*f9, f5*f6*f9^2, f5*f9, f4*f5*f8*f9, f4*f5*f6*f9, f4*f5*f6*f8, f4^2*f8, f6^2*f8, f4^2*f6^2*f8*f9, f4^2*f5, f5*f8, f4*f5*f9, f4*f5*f8, f4^2*f6^2*f8, f3, f3*f5, f1*f6, f1*f5, f1*f4, f3*f4*f9, f1*f4*f8, f1*f2*f9, f1*f2*f8, f1*f2*f6, f3*f4*f5*f9, f1*f2*f6*f8*f9, f3*f9, f3*f7, f3*f7*f9, f3*f7*f8, f3*f5*f9, f3*f4*f7, f1*f4*f6, f1*f4*f5, f1*f2*f6*f9, f1*f2*f6*f8, f2*f6, f2*f5, f1*f3, f1*f3*f8, f1*f2*f3*f9, f1*f2*f3*f8, f2*f6^2*f7*f8*f9, f7, f4*f7, f4^2*f7, f6*f7*f8, f4*f7*f8, f6*f7, f5*f7, f4*f6*f7, f4*f6^2*f7, f4*f5*f7, f4^2*f6*f7, f4*f6*f7*f8, f4*f6*f7*f9^2, f1*f6*f7, f1*f4*f7, f1*f2*f7, f1*f2*f6*f7*f8, f1*f4*f6*f7, f1*f4*f6^2*f7, f1*f2*f6*f7, f1*f2*f5*f7, f1*f3*f4^2*f7*f8, f1*f2*f3*f6^2*f7*f8*f9];
chartbl_1728_37589.IdentificationOfConjugacyClasses:= [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108];
chartbl_1728_37589.ComputedPowerMaps:= [ , [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 23, 24, 25, 26, 27, 28, 29, 4, 2, 3, 3, 2, 4, 25, 24, 23, 24, 23, 25, 24, 23, 25, 26, 27, 28, 28, 28, 26, 27, 27, 26, 29, 29, 29, 23, 23, 24, 24, 23, 25, 23, 25, 25, 24, 25, 24, 28, 28, 28, 23, 28, 25, 27, 27, 26, 26, 24, 24, 23, 23, 25, 25, 24, 36, 49, 49, 37, 38, 50, 50, 56, 56, 56, 56, 51, 51, 39, 40, 41, 42, 52, 52, 53, 53, 43, 44], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 1, 1, 1, 1, 1, 1, 1, 30, 31, 32, 33, 34, 35, 4, 4, 4, 2, 2, 3, 3, 3, 2, 2, 3, 2, 3, 4, 4, 4, 2, 3, 2, 3, 4, 5, 6, 7, 8, 7, 5, 8, 9, 10, 9, 6, 10, 5, 11, 11, 11, 6, 11, 7, 8, 9, 10, 12, 13, 14, 15, 16, 17, 22, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 31, 31, 32, 32, 31, 31, 32, 32, 33, 34]];
chartbl_1728_37589.SizesCentralizers:= [1728, 1728, 1728, 1728, 288, 288, 288, 288, 288, 288, 144, 96, 96, 96, 96, 96, 96, 64, 64, 64, 64, 48, 864, 864, 864, 432, 432, 432, 216, 432, 144, 144, 48, 48, 16, 864, 864, 864, 864, 864, 864, 864, 864, 864, 432, 432, 432, 432, 432, 432, 432, 432, 432, 216, 216, 216, 144, 144, 144, 144, 144, 144, 144, 144, 144, 144, 144, 144, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 48, 48, 48, 48, 48, 48, 24, 216, 216, 216, 216, 216, 216, 216, 216, 216, 216, 216, 216, 216, 72, 72, 72, 72, 72, 72, 72, 72, 24, 24];
chartbl_1728_37589.ClassNames:= ["1A", "2A", "2B", "2C", "2D", "2E", "2F", "2G", "2H", "2I", "2J", "2K", "2L", "2M", "2N", "2O", "2P", "2Q", "2R", "2S", "2T", "2U", "3A", "3B", "3C", "3D", "3E", "3F", "3G", "4A", "4B", "4C", "4D", "4E", "4F", "6A", "6B", "6C", "6D", "6E", "6F", "6G", "6H", "6I", "6J", "6K", "6L", "6M", "6N", "6O", "6P", "6Q", "6R", "6S", "6T", "6U", "6V", "6W", "6X", "6Y", "6Z", "6AA", "6AB", "6AC", "6AD", "6AE", "6AF", "6AG", "6AH", "6AI", "6AJ", "6AK", "6AL", "6AM", "6AN", "6AO", "6AP", "6AQ", "6AR", "6AS", "6AT", "6AU", "6AV", "6AW", "6AX", "12A", "12B", "12C", "12D", "12E", "12F1", "12F-1", "12G1", "12G-1", "12H1", "12H-1", "12I1", "12I-1", "12J", "12K", "12L", "12M", "12N1", "12N-1", "12O1", "12O-1", "12P", "12Q"];
chartbl_1728_37589.OrderClassRepresentatives:= [1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12];
chartbl_1728_37589.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, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, 1, -1, 1, -1, -1, -1, -1, -1, -1, 1, -1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, 1, 1, -1, -1, 1], [1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1, 1, 1, 1, -1, 1, -1, -1, 1, -1, -1, -1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, 1, -1, -1, 1, 1, -1], [1, 1, 1, 1, -1, 1, -1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, -1, 1, -1, 1, -1, -1, -1, 1, -1, -1, -1, -1, -1, 1, -1, -1, -1, -1, 1, -1, -1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, -1, 1, -1, 1, -1, -1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, -1, 1, -1, 1, -1, -1, -1, 1, -1, 1, -1, 1, 1, 1, 1, -1, -1, -1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [1, 1, 1, 1, -1, 1, -1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, -1, 1, -1, 1, -1, 1, 1, 1, 1, -1, 1, -1, -1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1], [1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, 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ConvertToLibraryCharacterTableNC(chartbl_1728_37589);