# Group 1728.47288 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(229070623739173035642210258119991960129674048351237527102925353,1728); a := GPC.1; b := GPC.2; c := GPC.3; d := GPC.5; e := GPC.7;
GPerm := Group( (1,2)(3,8)(4,9)(5,10)(6,14)(7,12)(11,16)(13,15)(17,18), (1,3,7,4)(2,8,12,9)(5,14,15,11)(6,13,16,10)(20,21)(22,25)(23,24), (1,4,7,3)(2,9,12,8)(5,11,15,14)(6,10,16,13)(20,21)(22,24)(23,25), (1,5,7,15)(2,10,12,13)(3,11,4,14)(6,8,16,9), (1,6)(2,11)(3,13)(4,10)(5,8)(7,16)(9,15)(12,14), (1,7)(2,12)(3,4)(5,15)(6,16)(8,9)(10,13)(11,14), (20,22,23)(21,24,25), (17,18,19), (20,23,22)(21,24,25) );

 
# Booleans 
booleans_1728_47288 := 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_47288:=rec(); 
chartbl_1728_47288.IsFinite:= true; 
chartbl_1728_47288.UnderlyingCharacteristic:= 0; 
chartbl_1728_47288.UnderlyingGroup:= GPC;
chartbl_1728_47288.Size:= 1728;
chartbl_1728_47288.InfoText:= "Character table for group 1728.47288 downloaded from the LMFDB."; 
chartbl_1728_47288.Identifier:= " C12.D6^2 "; 
chartbl_1728_47288.NrConjugacyClasses:= 126; 
chartbl_1728_47288.ConjugacyClasses:= [<identity> of ..., f8*f9, f5*f6, f3*f4, f3*f4*f5*f7*f8, f2, f2*f8, f2*f5*f6, f1*f3*f4*f5, f1*f3*f4*f5*f7, f1*f2*f3*f5, f1*f2*f3*f5*f7*f9^2, f2*f3*f4^2*f5*f7, f2*f3*f6*f8*f9, f6, f9^2, f4^2, f6*f9^2, f4^2*f6, f4^2*f9^2, f4^2*f6*f9^2, f7*f8, f5*f6*f7*f9^2, f3*f4*f5*f8*f9, f1*f8*f9, f1*f5*f6*f8*f9, f3*f4*f7*f9^2, f1*f7*f8*f9, f1*f5*f6*f7*f8*f9, f1*f2*f8*f9, f1*f2*f7*f8, f1*f2*f5*f6*f8*f9, f1*f2*f5*f6*f7*f9^2, f1*f3*f4*f8*f9, f2*f7*f8*f9, f2*f5*f6*f7*f8*f9, f1*f3*f4*f7*f8*f9, f1*f2*f3*f8*f9, f1*f2*f3*f7*f8, f2*f3*f4^2*f5*f6, f2*f3*f4*f6^2*f7*f9^2, f8, f6^2*f8*f9, f4^2*f8*f9, f5, f5*f6^2, f5*f6*f9, f4*f5*f6, f4^2*f8, f6^2*f8, f4^2*f6^2*f8*f9, f5*f9, f5*f8, f4*f5, f4*f5*f6^2, f4*f5*f6*f9, f4^2*f6^2*f8, f4*f5*f9, f4*f5*f8, f3, f3*f4*f9, f3*f5*f7*f8, f3*f4*f5*f7, f2*f6, f2*f6*f8, f2*f5, f2*f5*f8, f3*f9, f3*f5*f7, f1*f3*f5, f1*f3*f5*f7, f1*f2*f3*f5*f9, f1*f2*f3*f5*f7, f7, f6*f7*f8, f5*f7*f8, f5*f6*f7, f4*f7*f8, f4*f5*f6*f7*f8, f4*f7, f4^2*f7, f6*f7, f5*f7, f4*f6*f7*f8, f4*f5*f7*f8, f4*f5*f6*f7, f4*f6*f7, f4^2*f6*f7, f4*f5*f7, f4^2*f5*f7, f3*f5, f1*f6, f1*f5, f1*f4, f3*f7*f8, f3*f4*f7, f1*f6*f7, f1*f5*f7, f1*f4*f7, f1*f2*f9, f1*f2*f7, f1*f2*f6, f1*f2*f5, f3*f4*f5*f9, f1*f4*f5*f6, f1*f4*f5*f6*f7, f1*f2*f6*f7*f8, f1*f2*f5*f7*f8, f1*f2*f5*f6*f9, f1*f2*f5*f6*f7, f3*f7, f3*f5*f9, f1*f4*f6, f1*f4*f5, f1*f4*f6*f7, f1*f4*f5*f7, f1*f2*f6*f9, f1*f2*f6*f7, f1*f2*f5*f9, f1*f2*f5*f7, f1*f3, f2*f6*f7, f2*f5*f7, f1*f3*f7, f1*f2*f3*f9, f1*f2*f3*f7];
chartbl_1728_47288.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, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126];
chartbl_1728_47288.ComputedPowerMaps:= [ , [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 15, 16, 17, 18, 19, 20, 21, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 16, 15, 17, 15, 15, 16, 17, 20, 18, 19, 18, 18, 19, 19, 20, 21, 21, 21, 17, 16, 17, 16, 15, 15, 15, 15, 20, 20, 17, 17, 16, 16, 42, 43, 43, 42, 44, 44, 49, 49, 50, 50, 51, 51, 49, 57, 57, 57, 57, 44, 43, 43, 44, 44, 42, 43, 43, 44, 42, 42, 43, 43, 42, 44, 44, 43, 43, 42, 42, 49, 49, 51, 51, 51, 51, 50, 50, 50, 50, 44, 43, 43, 44, 42, 42], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 1, 1, 1, 1, 1, 1, 1, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 2, 2, 2, 3, 3, 3, 3, 2, 2, 2, 3, 3, 3, 3, 3, 2, 3, 3, 4, 4, 5, 5, 6, 7, 8, 8, 4, 5, 9, 10, 11, 12, 22, 22, 23, 23, 22, 23, 22, 22, 22, 23, 22, 23, 23, 22, 22, 23, 23, 24, 25, 26, 25, 27, 27, 28, 29, 28, 30, 31, 30, 32, 24, 26, 29, 31, 33, 32, 33, 27, 24, 25, 26, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39]];
chartbl_1728_47288.SizesCentralizers:= [1728, 1728, 864, 288, 288, 192, 192, 96, 96, 96, 96, 96, 32, 32, 864, 864, 864, 432, 432, 432, 216, 864, 864, 288, 288, 288, 288, 288, 288, 288, 288, 288, 288, 96, 96, 96, 96, 96, 96, 32, 32, 864, 864, 864, 864, 864, 432, 432, 432, 432, 432, 432, 432, 432, 432, 216, 216, 216, 216, 144, 144, 144, 144, 96, 96, 96, 96, 72, 72, 48, 48, 48, 48, 432, 432, 432, 432, 432, 432, 432, 432, 216, 216, 216, 216, 216, 216, 216, 216, 216, 144, 144, 144, 144, 144, 144, 144, 144, 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];
chartbl_1728_47288.ClassNames:= ["1A", "2A", "2B", "2C", "2D", "2E", "2F", "2G", "2H", "2I", "2J", "2K", "2L", "2M", "3A", "3B", "3C", "3D", "3E", "3F", "3G", "4A", "4B", "4C", "4D", "4E", "4F", "4G", "4H", "4I", "4J", "4K", "4L", "4M", "4N", "4O", "4P", "4Q", "4R", "4S", "4T", "6A", "6B", "6C", "6D1", "6D-1", "6E", "6F", "6G", "6H", "6I", "6J1", "6J-1", "6K1", "6K-1", "6L", "6M", "6N1", "6N-1", "6O", "6P", "6Q", "6R", "6S", "6T", "6U1", "6U-1", "6V", "6W", "6X", "6Y", "6Z", "6AA", "12A", "12B", "12C", "12D", "12E", "12F", "12G1", "12G-1", "12H", "12I", "12J", "12K", "12L", "12M1", "12M-1", "12N1", "12N5", "12O", "12P", "12Q", "12R", "12S", "12T", "12U", "12V", "12W", "12X", "12Y", "12Z", "12AA", "12AB", "12AC", "12AD", "12AE", "12AF", "12AG", "12AH", "12AI", "12AJ", "12AK", "12AL", "12AM", "12AN", "12AO", "12AP", "12AQ", "12AR", "12AS", "12AT", "12AU", "12AV", "12AW", "12AX"];
chartbl_1728_47288.OrderClassRepresentatives:= [1, 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, 4, 4, 4, 4, 4, 4, 4, 4, 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, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 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_47288.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, 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ConvertToLibraryCharacterTableNC(chartbl_1728_47288);