# Group 82944.fs downloaded from the LMFDB on 23 July 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(12992779469462171584828146410725085901074065530937984374933186485544710720071328755857767499984252320869314202356284124205222802433030717884377869057530897660904670463296550621770546048368645233306914845033771785751369167694194088085060086054921156675825196337632477548209164371451688231708264659433544543665253261685709003193893028659541641278307110897493843682693687337566353787282176193393619091479,82944); a := GPC.1; b := GPC.2; c := GPC.4; d := GPC.7; e := GPC.11; f := GPC.13; g := GPC.14;
GPerm := Group( (1,2,4,11)(3,7,5,13)(6,15,12,18)(10,17,16,14)(19,20), (1,3,8,17,15,9,11,13)(2,5)(4,10,18,14,12,7,6,16)(19,20), (2,6)(3,9,17,16)(4,8)(5,14,7,13)(11,15)(19,20), (3,10)(4,12)(6,11)(7,9)(8,18)(14,16)(19,20) );

 
# Booleans 
booleans_82944_fs := rec( 
Agroup := false,
Zgroup := false,
abelian := false,
almost_simple := false,
cyclic := false,
metabelian := false,
metacyclic := false,
nilpotent := false,
perfect := false,
quasisimple := false,
rational := false,
solvable := true,
supersolvable := false); 

 
# Character Table 
chartbl_82944_fs:=rec(); 
chartbl_82944_fs.IsFinite:= true; 
chartbl_82944_fs.UnderlyingCharacteristic:= 0; 
chartbl_82944_fs.UnderlyingGroup:= GPerm;
chartbl_82944_fs.Size:= 82944;
chartbl_82944_fs.InfoText:= "Character table for group 82944.fs downloaded from the LMFDB."; 
chartbl_82944_fs.Identifier:= " S3^4:C2^3.D4 "; 
chartbl_82944_fs.NrConjugacyClasses:= 108; 
chartbl_82944_fs.ConjugacyClasses:= [(), (19,20), (2,15)(4,8)(6,11)(12,18)(19,20), (2,15)(4,8)(6,11)(12,18), (3,17)(5,14)(7,13), (3,17)(5,14)(7,13)(19,20), (2,15)(4,8)(5,9)(6,11)(7,14)(10,17)(12,18)(13,16)(19,20), (1,8)(2,12)(3,14)(5,10)(6,15)(9,13)(11,18)(16,17), (1,6)(2,12)(3,16)(5,7)(8,15)(9,17), (1,10)(2,14)(3,8)(4,17)(5,6)(7,11)(9,12)(13,15)(16,18)(19,20), (1,8)(2,18)(5,13)(7,14)(9,16)(11,12)(19,20), (1,14)(2,9)(3,4)(5,12)(6,10)(7,8)(11,13)(15,17)(16,18), (1,4)(2,11)(5,9)(6,12)(7,17)(10,14)(15,18)(19,20), (1,15)(3,7)(5,16)(6,8)(9,17)(10,13)(11,18), (3,9,5)(7,16,17)(10,13,14), (1,15,2)(3,9,5)(4,11,18)(6,8,12)(7,16,17)(10,13,14), (2,11,15,6)(4,18,8,12)(19,20), (2,11,15,6)(4,18,8,12), (3,16,9,14)(7,13,10,17), (1,8,18,6)(2,11,4,15)(19,20), (1,15,8,6)(2,18,12,11)(3,9,14,13)(5,17,10,16), (1,12,15,4)(3,14)(5,10)(6,8,18,11)(9,13)(16,17), (1,12)(2,6)(3,5,7,16)(4,11)(8,15)(9,10,17,13)(19,20), (2,6,15,11)(3,5,10,13)(4,12,8,18)(7,14,16,9)(19,20), (1,6,8,15)(2,11,12,18)(3,13)(5,10)(9,14)(19,20), (1,11)(2,4)(3,14,5,17)(7,16,13,10)(15,18), (1,15)(3,13,17,14)(4,12)(5,9,7,16)(6,18)(8,11)(19,20), (1,6,4,12)(2,18,11,15)(3,17)(5,7)(9,16)(13,14), (1,8,6,2)(4,12,18,15)(5,9)(7,17)(10,14)(19,20), (1,12)(3,14,10,9)(4,15)(5,7,13,16)(8,11), (1,4,12,11)(2,15,6,8)(3,17,9,13)(7,16,10,14)(19,20), (1,17,15,10)(2,3)(4,14,12,7)(5,8,9,11)(6,13,18,16), (2,18,15,12)(3,13,17,14)(4,6,8,11)(5,9,7,16), (2,11,15,6)(3,10,5,16)(4,18,8,12)(7,14,13,17)(19,20), (1,13,6,16)(2,10,8,17)(3,11)(4,5,18,9)(7,15,14,12)(19,20), (2,6,15,11)(3,5,13,14)(4,12,8,18)(7,9,17,10), (1,9,6,17)(2,5,12,7)(3,8,16,15)(4,10)(11,14)(13,18), (1,9,18,16)(2,5,8,13)(3,15)(4,7,6,14)(10,12)(11,17)(19,20), (3,5,9)(7,17,16)(10,14,13)(19,20), (3,5,7,17,14,13)(9,10,16), (3,5,7,17,14,13)(9,10,16)(19,20), (1,2,15)(3,5,9)(4,18,11)(6,12,8)(7,17,16)(10,14,13)(19,20), (2,15)(3,5,9)(4,8)(6,11)(7,17,16)(10,14,13)(12,18)(19,20), (2,15)(3,9,5)(4,8)(6,11)(7,16,17)(10,13,14)(12,18), (3,5,9)(4,12)(6,11)(7,17,16)(8,18)(10,14,13), (3,5,9)(4,12)(6,11)(7,17,16)(8,18)(10,14,13)(19,20), (1,12,18)(2,8,11)(3,16,13)(4,15,6)(5,17,10,9,7,14), (1,18,12)(2,15,8,6,11,4)(3,10,17)(5,14,16)(7,9,13)(19,20), (1,4)(2,11)(3,16,13)(5,17,10,9,7,14)(6,12)(15,18)(19,20), (1,18,6,15,11,8)(2,4,12)(3,7)(5,16)(9,17)(10,13), (1,8,2,6,15,12)(3,7,9,16,5,17)(4,11,18)(10,14,13), (1,11,18,8,12,2)(3,17,10)(4,15,6)(5,9,14,13,16,7)(19,20), (1,2,4,18,8,6)(3,13)(5,10)(9,14)(11,15,12), (1,6,8,18,4,2)(3,13)(5,10)(9,14)(11,12,15)(19,20), (1,7,6,10,11,5)(2,17,12,14,4,9)(3,15,16,8,13,18)(19,20), (1,13,6,14,11,10)(2,3,12,9,4,5)(7,15,16,8,17,18), (2,12,11,4,15,18,6,8), (2,8,6,18,15,4,11,12), (2,12,11,4,15,18,6,8)(19,20), (2,8,6,18,15,4,11,12)(19,20), (1,11,15,2,8,18,6,12)(3,16,9,5,14,17,13,10), (1,12,6,18,8,2,15,11)(3,10,13,17,14,5,9,16), (1,2,18,15,6,8,4,12)(3,17)(5,7)(9,16)(13,14)(19,20), (1,12,4,8,6,15,18,2)(3,17)(5,7)(9,16)(13,14)(19,20), (1,15,12,2,11,4,8,18)(3,16)(5,17)(7,9)(10,14), (1,18,8,4,11,2,12,15)(3,16)(5,17)(7,9)(10,14), (1,12,6,18,8,2,15,11)(3,5,14,9,16,17,10,7)(19,20), (1,11,15,2,8,18,6,12)(3,7,10,17,16,9,14,5)(19,20), (1,6)(2,12)(3,13,5,9,7,10,16,17)(8,15)(19,20), (1,6)(2,12)(3,17,16,10,7,9,5,13)(8,15)(19,20), (2,11)(3,9,7,5,13,10,17,14)(6,15)(12,18), (2,11)(3,14,17,10,13,5,7,9)(6,15)(12,18), (1,6,4,11,15,18,12,8)(3,5,13,16,14,10,9,17), (1,8,15,4,18,6,11,2)(3,7,10,17,16,9,14,5)(19,20), (1,8,2,18)(3,10,7,14,13,9,17,5)(4,11,6,12), (1,18,2,8)(3,5,17,9,13,14,7,10)(4,12,6,11), (1,2,12,6)(3,5,17,9,13,14,7,10)(4,8,11,15)(19,20), (1,6,12,2)(3,10,7,14,13,9,17,5)(4,15,11,8)(19,20), (1,8,12,18,15,11,4,6)(3,17,14,16)(5,13,10,9)(19,20), (1,6,4,11,15,18,12,8)(3,16,14,17)(5,9,10,13)(19,20), (1,8,6,4,12,15,2,11)(3,9,7,17)(5,13,16,10), (1,11,2,15,12,4,6,8)(3,17,7,9)(5,10,16,13), (1,13,15,17,18,10,11,9)(2,5,8,3,4,16,6,7)(12,14)(19,20), (1,13,6,16,8,17,15,14)(2,10,11,3,12,7,18,9)(4,5), (1,10)(2,13,18,17,15,14,12,3)(4,16,6,5,8,9,11,7)(19,20), (1,17,12,16,8,9,2,5)(3,15,13,18,7,6,10,11)(4,14), (2,6,15,11)(3,5,9)(4,12,8,18)(7,17,16)(10,14,13)(19,20), (2,6,15,11)(3,9,5)(4,12,8,18)(7,16,17)(10,13,14), (1,11,6)(2,4,12)(3,14,9,16)(7,17,10,13)(8,15,18), (1,6,18,8)(2,15,4,11)(3,5,9)(7,17,16)(10,14,13)(19,20), (1,15,8,6)(2,18,12,11)(3,10,9,13,5,14)(7,17,16)(19,20), (1,18,2,11,15,4)(3,17,5,14)(6,8,12)(7,10,13,16), (1,2,6,8)(3,16,13)(4,15,18,12)(5,17,10,9,7,14)(19,20), (1,11,4,12,8,15)(2,6,18)(3,9,10,14)(5,16,13,7), (1,7,8,9,2,16,6,5,15,17,12,3)(4,13,11,10,18,14), (1,5,6,9,8,14,18,13,4,16,2,7)(3,12,17,15,10,11)(19,20), (1,5,11,14,15,17,2,13,8,10,18,3,6,16,12,9)(4,7), (1,9,12,16,6,3,18,10,8,13,2,17,15,14,11,5)(4,7), (1,9,2,3,8,7,15,5,11,14,18,10,12,16,4,13)(6,17)(19,20), (1,13,4,16,12,10,18,14,11,5,15,7,8,3,2,9)(6,17)(19,20), (2,4,6,12,15,8,11,18)(3,5,9)(7,17,16)(10,14,13), (2,8,6,18,15,4,11,12)(3,5,9)(7,17,16)(10,14,13), (2,4,6,12,15,8,11,18)(3,5,9)(7,17,16)(10,14,13)(19,20), (2,8,6,18,15,4,11,12)(3,5,9)(7,17,16)(10,14,13)(19,20), (1,8,2,6,15,12)(3,9,16,13,7,17,5,10)(4,11,18)(19,20), (1,12,15,6,2,8)(3,10,5,17,7,13,16,9)(4,18,11)(19,20), (1,4,8)(2,12,6,11,18,15)(3,5,17,9,13,14,7,10), (1,8,4)(2,15,18,11,6,12)(3,10,7,14,13,9,17,5)];
chartbl_82944_fs.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_82944_fs.ComputedPowerMaps:= [ , [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 15, 16, 4, 4, 4, 4, 8, 4, 4, 8, 4, 4, 4, 4, 4, 4, 8, 8, 8, 8, 8, 8, 9, 9, 15, 15, 15, 16, 15, 15, 15, 15, 16, 16, 15, 15, 16, 16, 15, 15, 16, 16, 18, 18, 18, 18, 21, 21, 18, 18, 18, 18, 21, 21, 18, 18, 18, 18, 21, 21, 22, 22, 22, 22, 22, 22, 22, 22, 21, 21, 33, 33, 44, 44, 44, 44, 44, 44, 44, 44, 51, 51, 61, 62, 62, 61, 88, 88, 88, 88, 88, 88, 88, 88], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 1, 1, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 2, 5, 6, 2, 3, 4, 5, 6, 5, 6, 13, 14, 9, 11, 9, 11, 10, 12, 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, 17, 18, 19, 20, 25, 26, 29, 30, 37, 38, 97, 98, 99, 100, 57, 58, 59, 60, 69, 70, 71, 72]];
chartbl_82944_fs.SizesCentralizers:= [82944, 82944, 4608, 4608, 3456, 3456, 1024, 1024, 576, 576, 576, 576, 384, 384, 5184, 1296, 2304, 2304, 1152, 1152, 256, 256, 256, 256, 192, 192, 128, 128, 96, 96, 64, 64, 64, 64, 64, 64, 48, 48, 5184, 1728, 1728, 1296, 576, 576, 432, 432, 216, 216, 192, 192, 144, 144, 144, 144, 72, 72, 2304, 2304, 2304, 2304, 256, 256, 256, 256, 256, 256, 256, 256, 192, 192, 192, 192, 128, 128, 128, 128, 128, 128, 64, 64, 64, 64, 32, 32, 16, 16, 288, 288, 144, 144, 96, 96, 48, 48, 24, 24, 32, 32, 32, 32, 288, 288, 288, 288, 96, 96, 96, 96];
chartbl_82944_fs.ClassNames:= ["1A", "2A", "2B", "2C", "2D", "2E", "2F", "2G", "2H", "2I", "2J", "2K", "2L", "2M", "3A", "3B", "4A", "4B", "4C", "4D", "4E", "4F", "4G", "4H", "4I", "4J", "4K", "4L", "4M", "4N", "4O", "4P", "4Q", "4R", "4S", "4T", "4U", "4V", "6A", "6B", "6C", "6D", "6E", "6F", "6G", "6H", "6I", "6J", "6K", "6L", "6M", "6N", "6O", "6P", "6Q", "6R", "8A1", "8A-1", "8B1", "8B-1", "8C1", "8C-1", "8D1", "8D-1", "8E1", "8E-1", "8F1", "8F-1", "8G1", "8G-1", "8H1", "8H-1", "8I", "8J", "8K1", "8K-1", "8L1", "8L-1", "8M1", "8M-1", "8N1", "8N-1", "8O", "8P", "8Q", "8R", "12A", "12B", "12C", "12D", "12E", "12F", "12G", "12H", "12I", "12J", "16A1", "16A-1", "16B1", "16B-1", "24A1", "24A-1", "24B1", "24B-1", "24C1", "24C-1", "24D1", "24D-1"];
chartbl_82944_fs.OrderClassRepresentatives:= [1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 4, 4, 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, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 16, 16, 16, 16, 24, 24, 24, 24, 24, 24, 24, 24];
chartbl_82944_fs.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, 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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [64, 64, 0, 0, -16, -16, 0, 0, 4, -8, 4, -8, 0, 0, -8, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -8, 8, 8, 1, 0, 0, 2, 2, -1, -1, 0, 0, 1, 1, -2, -2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [64, 64, 0, 0, 16, 16, 0, 0, 4, -8, 4, -8, 0, 0, -8, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -8, -8, -8, 1, 0, 0, -2, -2, 1, 1, 0, 0, 1, 1, -2, -2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [128, -128, 0, 0, 0, 0, 0, 0, -8, 0, 8, 0, 0, 0, -16, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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ConvertToLibraryCharacterTableNC(chartbl_82944_fs);