# Group 1152.99269 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(347552882444306049056900441586673588912168693187828475405714696201,1152); a := GPC.1; b := GPC.2; c := GPC.3; d := GPC.5; e := GPC.7;
GPerm := Group( (1,2)(3,7)(4,6)(5,8)(9,10)(11,12)(13,14), (4,6)(7,8), (1,3)(2,5)(4,8)(6,7), (11,13)(12,14), (3,5)(7,8), (1,4)(2,6)(3,8)(5,7), (1,2)(3,5)(4,6)(7,8), (9,11,13)(10,12,14), (10,12,14) );

 
# Booleans 
booleans_1152_99269 := 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 := true,
solvable := true,
supersolvable := true); 

 
# Character Table 
chartbl_1152_99269:=rec(); 
chartbl_1152_99269.IsFinite:= true; 
chartbl_1152_99269.UnderlyingCharacteristic:= 0; 
chartbl_1152_99269.UnderlyingGroup:= GPerm;
chartbl_1152_99269.Size:= 1152;
chartbl_1152_99269.InfoText:= "Character table for group 1152.99269 downloaded from the LMFDB."; 
chartbl_1152_99269.Identifier:= " C2^3.D6^2 "; 
chartbl_1152_99269.NrConjugacyClasses:= 81; 
chartbl_1152_99269.ConjugacyClasses:= [(), (1,2)(3,5)(4,6)(7,8), (3,5)(7,8), (1,4)(2,6)(3,7)(5,8), (1,4)(2,6)(3,8)(5,7), (4,6)(7,8), (1,3)(2,5)(4,7)(6,8), (1,3)(2,5)(4,8)(6,7), (11,13)(12,14), (1,2)(3,5)(4,6)(7,8)(11,13)(12,14), (3,7)(5,8)(9,12)(10,13)(11,14), (3,7)(5,8)(9,14)(10,13)(11,12), (1,2)(3,7)(4,6)(5,8)(9,12)(10,13)(11,14), (1,2)(3,7)(4,6)(5,8)(9,14)(10,13)(11,12), (3,5)(7,8)(11,13)(12,14), (1,4)(2,6)(3,7)(5,8)(11,13)(12,14), (1,4)(2,6)(3,8)(5,7)(11,13)(12,14), (1,5)(2,3)(4,8)(6,7)(10,12)(11,13), (1,7)(2,8)(3,6)(4,5)(10,12)(11,13), (4,6)(7,8)(10,14)(11,13), (9,13,11)(10,14,12), (9,13,11)(10,12,14), (10,14,12), (1,5,2,3)(4,8,6,7), (1,5,2,3)(4,7,6,8), (1,6,2,4)(3,8,5,7), (1,8,4,3)(2,7,6,5)(9,10)(11,14)(12,13), (1,8,4,3)(2,7,6,5)(9,12)(10,13)(11,14), (1,5,4,8)(2,3,6,7)(9,14)(10,11)(12,13), (1,2)(3,7,5,8)(9,12)(10,11)(13,14), (1,8,6,3)(2,7,4,5)(9,12)(10,11)(13,14), (3,7,5,8)(4,6)(9,14)(10,11)(12,13), (1,7,2,8)(3,4,5,6)(9,11)(10,14), (1,6,2,4)(3,7,5,8)(10,14)(11,13), (1,8,2,7)(3,4,5,6)(9,11)(10,14), (1,2)(3,5)(4,6)(7,8)(9,13,11)(10,14,12), (1,2)(3,5)(4,6)(7,8)(9,13,11)(10,12,14), (1,2)(3,5)(4,6)(7,8)(10,14,12), (1,4)(2,6)(3,8)(5,7)(9,13,11)(10,12,14), (1,4)(2,6)(3,8)(5,7)(9,13,11)(10,14,12), (1,4)(2,6)(3,7)(5,8)(9,13,11)(10,14,12), (3,5)(7,8)(9,11,13)(10,14,12), (1,6)(2,4)(3,8)(5,7)(9,13,11)(10,12,14), (3,5)(7,8)(9,11,13)(10,12,14), (4,6)(7,8)(10,12,14), (4,6)(7,8)(9,11,13), (4,6)(7,8)(9,11,13)(10,12,14), (4,6)(7,8)(9,11,13)(10,14,12), (3,5)(7,8)(10,12,14), (1,3)(2,5)(4,7)(6,8)(10,12,14), (1,3)(2,5)(4,7)(6,8)(9,11,13), (1,3)(2,5)(4,7)(6,8)(9,11,13)(10,12,14), (1,3)(2,5)(4,7)(6,8)(9,11,13)(10,14,12), (1,3)(2,5)(4,8)(6,7)(10,12,14), (1,3)(2,5)(4,8)(6,7)(9,11,13), (1,3)(2,5)(4,8)(6,7)(9,11,13)(10,12,14), (1,3)(2,5)(4,8)(6,7)(9,11,13)(10,14,12), (1,4)(2,6)(3,7)(5,8)(10,12,14), (1,4)(2,6)(3,8)(5,7)(10,12,14), (3,7)(5,8)(9,10,11,12,13,14), (3,7)(5,8)(9,10,11,14,13,12), (1,2)(3,7)(4,6)(5,8)(9,10,11,12,13,14), (1,2)(3,7)(4,6)(5,8)(9,10,11,14,13,12), (1,3,2,5)(4,7,6,8)(10,12,14), (1,3,2,5)(4,7,6,8)(9,11,13), (1,3,2,5)(4,7,6,8)(9,11,13)(10,12,14), (1,3,2,5)(4,7,6,8)(9,11,13)(10,14,12), (1,3,2,5)(4,8,6,7)(10,12,14), (1,3,2,5)(4,8,6,7)(9,11,13), (1,3,2,5)(4,8,6,7)(9,11,13)(10,12,14), (1,3,2,5)(4,8,6,7)(9,11,13)(10,14,12), (1,4,2,6)(3,7,5,8)(10,12,14), (1,4,2,6)(3,7,5,8)(9,11,13), (1,4,2,6)(3,7,5,8)(9,11,13)(10,12,14), (1,4,2,6)(3,7,5,8)(9,11,13)(10,14,12), (1,3,4,8)(2,5,6,7)(9,14,13,10,11,12), (1,3,4,8)(2,5,6,7)(9,14,13,12,11,10), (1,8,4,5)(2,7,6,3)(9,10,13,14,11,12), (1,2)(3,8,5,7)(9,14,11,12,13,10), (1,3,6,8)(2,5,4,7)(9,10,13,12,11,14), (3,8,5,7)(4,6)(9,12,11,14,13,10)];
chartbl_1152_99269.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];
chartbl_1152_99269.ComputedPowerMaps:= [ , [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 21, 22, 23, 2, 2, 2, 5, 5, 4, 3, 4, 3, 2, 2, 2, 21, 22, 23, 22, 21, 21, 22, 22, 21, 23, 23, 21, 22, 23, 23, 23, 21, 22, 23, 23, 21, 22, 23, 23, 21, 22, 21, 22, 38, 38, 36, 37, 38, 38, 36, 37, 38, 38, 36, 37, 39, 40, 41, 42, 43, 44], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 1, 1, 1, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 2, 2, 2, 5, 5, 4, 3, 4, 3, 6, 6, 6, 6, 3, 7, 7, 7, 7, 8, 8, 8, 8, 4, 5, 11, 12, 13, 14, 24, 24, 24, 24, 25, 25, 25, 25, 26, 26, 26, 26, 27, 28, 29, 30, 31, 32]];
chartbl_1152_99269.SizesCentralizers:= [1152, 1152, 576, 576, 576, 288, 288, 288, 128, 128, 96, 96, 96, 96, 64, 64, 64, 32, 32, 32, 576, 576, 288, 288, 288, 288, 48, 48, 48, 48, 48, 48, 32, 32, 32, 576, 576, 288, 288, 288, 288, 288, 288, 288, 144, 144, 144, 144, 144, 144, 144, 144, 144, 144, 144, 144, 144, 144, 144, 48, 48, 48, 48, 144, 144, 144, 144, 144, 144, 144, 144, 144, 144, 144, 144, 24, 24, 24, 24, 24, 24];
chartbl_1152_99269.ClassNames:= ["1A", "2A", "2B", "2C", "2D", "2E", "2F", "2G", "2H", "2I", "2J", "2K", "2L", "2M", "2N", "2O", "2P", "2Q", "2R", "2S", "3A", "3B", "3C", "4A", "4B", "4C", "4D", "4E", "4F", "4G", "4H", "4I", "4J", "4K", "4L", "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", "12A", "12B", "12C", "12D", "12E", "12F", "12G", "12H", "12I", "12J", "12K", "12L", "12M", "12N", "12O", "12P", "12Q", "12R"];
chartbl_1152_99269.OrderClassRepresentatives:= [1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 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, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12];
chartbl_1152_99269.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, -1, -1, -1, 1, -1, -1, 1, -1, 1], [1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, 1, 1, 1, -1, 1, -1, 1, 1, 1, -1, 1, -1, 1, 1, -1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, 1, -1, -1, -1, -1, -1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, 1, 1, -1], [1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, 1, -1, 1, -1, -1, -1, 1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, 1, -1, -1, -1, -1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, -1, -1, 1], [1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, -1], [1, 1, 1, 1, 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_1152_99269);