# Group 2304.of downloaded from the LMFDB on 05 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(494284566107313275989506176949012281412490066457931630593000326653936061476546720,2304); a := GPC.1; b := GPC.2; c := GPC.4; d := GPC.6; e := GPC.8; f := GPC.9; g := GPC.10;
GPerm := Group( (5,7,6)(8,13)(9,12)(10,11)(14,15), (4,7)(5,6), (1,2)(5,7), (1,2)(4,6)(8,14)(9,11)(10,12)(13,15), (4,5,7), (1,3,2)(4,5,7)(8,10,14,12)(9,13,11,15), (1,3,2)(4,6,7,5)(8,12)(9,15)(10,14)(11,13), (1,3,2), (1,2,3)(5,7)(8,11)(9,14)(10,15)(12,13), (4,5)(6,7) );

 
# Booleans 
booleans_2304_of := rec( 
Agroup := false,
Zgroup := false,
abelian := false,
almost_simple := false,
cyclic := false,
metabelian := false,
metacyclic := false,
nilpotent := false,
perfect := false,
quasisimple := false,
rational := true,
solvable := true,
supersolvable := false); 

 
# Character Table 
chartbl_2304_of:=rec(); 
chartbl_2304_of.IsFinite:= true; 
chartbl_2304_of.UnderlyingCharacteristic:= 0; 
chartbl_2304_of.UnderlyingGroup:= GPerm;
chartbl_2304_of.Size:= 2304;
chartbl_2304_of.InfoText:= "Character table for group 2304.of downloaded from the LMFDB."; 
chartbl_2304_of.Identifier:= " C2^4.D6^2 "; 
chartbl_2304_of.NrConjugacyClasses:= 129; 
chartbl_2304_of.ConjugacyClasses:= [(), (8,14)(9,11)(10,12)(13,15), (9,11)(10,12), (8,9)(10,15)(11,14)(12,13), (8,10)(9,15)(11,13)(12,14), (8,13)(9,10)(11,12)(14,15), (8,13)(9,12)(10,11)(14,15), (4,6)(5,7), (4,6)(5,7)(8,14)(9,11)(10,12)(13,15), (4,5)(6,7)(9,11)(10,12), (4,5)(6,7)(8,9)(10,15)(11,14)(12,13), (4,5)(6,7)(8,10)(9,15)(11,13)(12,14), (4,5)(6,7)(8,13)(9,10)(11,12)(14,15), (4,5)(6,7)(8,13)(9,12)(10,11)(14,15), (2,3)(10,12)(13,15), (2,3)(9,11)(13,15), (2,3)(8,9)(10,13)(11,14)(12,15), (2,3)(8,10)(9,13)(11,15)(12,14), (6,7)(10,12)(13,15), (6,7)(9,11)(13,15), (6,7)(8,9)(10,13)(11,14)(12,15), (6,7)(8,10)(9,13)(11,15)(12,14), (2,3)(6,7), (2,3)(6,7)(8,14)(9,11)(10,12)(13,15), (2,3)(4,5)(6,7)(10,12)(13,15), (2,3)(4,5)(6,7)(9,11)(13,15), (2,3)(4,5)(6,7)(8,9)(10,13)(11,14)(12,15), (2,3)(4,5)(6,7)(8,10)(9,13)(11,15)(12,14), (2,3)(6,7)(9,11)(10,12), (2,3)(6,7)(8,9)(10,15)(11,14)(12,13), (2,3)(6,7)(8,10)(9,15)(11,13)(12,14), (2,3)(6,7)(8,13)(9,10)(11,12)(14,15), (2,3)(6,7)(8,13)(9,12)(10,11)(14,15), (1,3,2), (5,7,6), (1,3,2)(5,7,6), (8,11,14,9)(10,15,12,13), (8,12,14,10)(9,15,11,13), (4,5)(6,7)(8,11,14,9)(10,15,12,13), (4,5)(6,7)(8,12,14,10)(9,15,11,13), (2,3)(8,11,14,9)(10,13,12,15), (2,3)(8,12,14,10)(9,13,11,15), (2,3)(8,15,14,13)(9,12,11,10), (2,3)(8,15,14,13)(9,10,11,12), (6,7)(8,11,14,9)(10,13,12,15), (6,7)(8,12,14,10)(9,13,11,15), (6,7)(8,15,14,13)(9,12,11,10), (6,7)(8,15,14,13)(9,10,11,12), (4,7,6,5)(10,12)(13,15), (4,7,6,5)(9,11)(13,15), (4,7,6,5)(8,9)(10,13)(11,14)(12,15), (4,7,6,5)(8,11,14,9)(10,13,12,15), (4,7,6,5)(8,10)(9,13)(11,15)(12,14), (4,7,6,5)(8,12,14,10)(9,13,11,15), (4,7,6,5)(8,15,14,13)(9,12,11,10), (4,7,6,5)(8,15,14,13)(9,10,11,12), (2,3)(4,5)(6,7)(8,9,14,11)(10,15,12,13), (2,3)(4,5)(6,7)(8,10,14,12)(9,15,11,13), (2,3)(4,5)(6,7)(8,13,14,15)(9,10,11,12), (2,3)(4,5)(6,7)(8,13,14,15)(9,12,11,10), (2,3)(4,5,6,7), (2,3)(4,5,6,7)(8,14)(9,11)(10,12)(13,15), (2,3)(6,7)(8,9,14,11)(10,13,12,15), (2,3)(6,7)(8,10,14,12)(9,13,11,15), (2,3)(4,5,6,7)(9,11)(10,12), (2,3)(4,5,6,7)(8,9)(10,15)(11,14)(12,13), (2,3)(4,5,6,7)(8,9,14,11)(10,13,12,15), (2,3)(4,5,6,7)(8,10,14,12)(9,13,11,15), (2,3)(4,5,6,7)(8,10)(9,15)(11,13)(12,14), (2,3)(4,5,6,7)(8,13)(9,10)(11,12)(14,15), (2,3)(4,5,6,7)(8,13)(9,12)(10,11)(14,15), (1,3,2)(8,14)(9,11)(10,12)(13,15), (1,2,3)(9,11)(10,12), (1,2,3)(8,9)(10,15)(11,14)(12,13), (1,2,3)(8,10)(9,15)(11,13)(12,14), (1,2,3)(8,13)(9,10)(11,12)(14,15), (1,2,3)(8,13)(9,12)(10,11)(14,15), (1,3,2)(4,6)(5,7), (1,3,2)(4,6)(5,7)(8,14)(9,11)(10,12)(13,15), (5,7,6)(8,14)(9,11)(10,12)(13,15), (1,2,3)(4,5)(6,7)(9,11)(10,12), (1,2,3)(4,5)(6,7)(8,9)(10,15)(11,14)(12,13), (1,2,3)(4,5)(6,7)(8,10)(9,15)(11,13)(12,14), (1,2,3)(4,5)(6,7)(8,13)(9,10)(11,12)(14,15), (1,2,3)(4,5)(6,7)(8,13)(9,12)(10,11)(14,15), (5,6,7)(9,11)(10,12), (5,6,7)(8,9)(10,15)(11,14)(12,13), (5,6,7)(8,10)(9,15)(11,13)(12,14), (5,6,7)(8,13)(9,10)(11,12)(14,15), (5,6,7)(8,13)(9,12)(10,11)(14,15), (1,2,3)(5,6,7)(8,13)(9,12)(10,11)(14,15), (1,2,3)(5,6,7)(8,15)(9,10)(11,12)(13,14), (1,3,2)(5,7,6)(8,14)(9,11)(10,12)(13,15), (1,2,3)(6,7)(10,12)(13,15), (1,2,3)(6,7)(9,11)(13,15), (1,2,3)(6,7)(8,9)(10,13)(11,14)(12,15), (1,2,3)(6,7)(8,10)(9,13)(11,15)(12,14), (1,2,3)(5,6,7)(9,11)(10,12), (1,2,3)(5,6,7)(8,9)(10,15)(11,14)(12,13), (1,2,3)(5,6,7)(8,10)(9,15)(11,13)(12,14), (1,2,3)(5,6,7)(8,13)(9,10)(11,12)(14,15), (2,3)(5,6,7)(10,12)(13,15), (2,3)(5,6,7)(9,11)(13,15), (2,3)(5,6,7)(8,9)(10,13)(11,14)(12,15), (2,3)(5,6,7)(8,10)(9,13)(11,15)(12,14), (1,2,3)(8,9,14,11)(10,13,12,15), (1,2,3)(8,10,14,12)(9,13,11,15), (1,2,3)(4,5)(6,7)(8,9,14,11)(10,13,12,15), (1,2,3)(4,5)(6,7)(8,10,14,12)(9,13,11,15), (5,6,7)(8,9,14,11)(10,13,12,15), (5,6,7)(8,10,14,12)(9,13,11,15), (1,2,3)(6,7)(8,9,14,11)(10,15,12,13), (1,2,3)(6,7)(8,10,14,12)(9,15,11,13), (1,2,3)(6,7)(8,13,14,15)(9,10,11,12), (1,2,3)(6,7)(8,13,14,15)(9,12,11,10), (1,2,3)(4,5,6,7)(10,12)(13,15), (1,2,3)(4,5,6,7)(9,11)(13,15), (1,2,3)(4,5,6,7)(8,9)(10,13)(11,14)(12,15), (1,2,3)(4,5,6,7)(8,9,14,11)(10,15,12,13), (1,2,3)(4,5,6,7)(8,10)(9,13)(11,15)(12,14), (1,2,3)(4,5,6,7)(8,10,14,12)(9,15,11,13), (1,2,3)(4,5,6,7)(8,13,14,15)(9,10,11,12), (1,2,3)(4,5,6,7)(8,13,14,15)(9,12,11,10), (1,2,3)(5,6,7)(8,9,14,11)(10,13,12,15), (1,2,3)(5,6,7)(8,10,14,12)(9,13,11,15), (2,3)(5,6,7)(8,9,14,11)(10,15,12,13), (2,3)(5,6,7)(8,10,14,12)(9,15,11,13), (2,3)(5,6,7)(8,13,14,15)(9,10,11,12), (2,3)(5,6,7)(8,13,14,15)(9,12,11,10)];
chartbl_2304_of.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, 127, 128, 129];
chartbl_2304_of.ComputedPowerMaps:= [ , [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 34, 35, 36, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8, 8, 8, 9, 8, 9, 9, 9, 2, 2, 2, 2, 8, 8, 2, 2, 8, 8, 9, 9, 8, 8, 8, 34, 34, 34, 34, 34, 34, 34, 34, 35, 34, 34, 34, 34, 34, 35, 35, 35, 35, 35, 36, 36, 36, 34, 34, 34, 34, 36, 36, 36, 36, 35, 35, 35, 35, 72, 72, 72, 72, 80, 80, 72, 72, 72, 72, 78, 78, 78, 79, 78, 79, 79, 79, 93, 93, 80, 80, 80, 80], [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, 1, 1, 1, 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, 2, 3, 4, 5, 6, 7, 8, 9, 2, 10, 11, 12, 13, 14, 3, 4, 5, 6, 7, 7, 7, 2, 19, 20, 21, 22, 3, 4, 5, 6, 15, 16, 17, 18, 37, 38, 39, 40, 37, 38, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 37, 38, 41, 42, 43, 44]];
chartbl_2304_of.SizesCentralizers:= [2304, 2304, 1152, 1152, 1152, 1152, 1152, 768, 768, 384, 384, 384, 384, 384, 384, 384, 384, 384, 192, 192, 192, 192, 128, 128, 128, 128, 128, 128, 64, 64, 64, 64, 64, 1152, 288, 144, 1152, 1152, 384, 384, 384, 384, 384, 384, 192, 192, 192, 192, 192, 192, 192, 192, 192, 192, 192, 192, 128, 128, 128, 128, 128, 128, 64, 64, 64, 64, 64, 64, 64, 64, 64, 1152, 576, 576, 576, 576, 576, 384, 384, 288, 192, 192, 192, 192, 192, 144, 144, 144, 144, 144, 144, 144, 144, 96, 96, 96, 96, 72, 72, 72, 72, 48, 48, 48, 48, 576, 576, 192, 192, 144, 144, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 72, 72, 48, 48, 48, 48];
chartbl_2304_of.ClassNames:= ["1A", "2A", "2B", "2C", "2D", "2E", "2F", "2G", "2H", "2I", "2J", "2K", "2L", "2M", "2N", "2O", "2P", "2Q", "2R", "2S", "2T", "2U", "2V", "2W", "2X", "2Y", "2Z", "2AA", "2AB", "2AC", "2AD", "2AE", "2AF", "3A", "3B", "3C", "4A", "4B", "4C", "4D", "4E", "4F", "4G", "4H", "4I", "4J", "4K", "4L", "4M", "4N", "4O", "4P", "4Q", "4R", "4S", "4T", "4U", "4V", "4W", "4X", "4Y", "4Z", "4AA", "4AB", "4AC", "4AD", "4AE", "4AF", "4AG", "4AH", "4AI", "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", "12A", "12B", "12C", "12D", "12E", "12F", "12G", "12H", "12I", "12J", "12K", "12L", "12M", "12N", "12O", "12P", "12Q", "12R", "12S", "12T", "12U", "12V", "12W", "12X"];
chartbl_2304_of.OrderClassRepresentatives:= [1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 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, 4, 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, 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];
chartbl_2304_of.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, 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1, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, -1, -1, 0, 0, -1, 1, -1, -1, -1, 1, 1, -1, 1, 1, -1, 1, 0, 0, 0, 0, 0, 0], [6, 6, -6, 6, 6, -6, 6, -2, -2, 2, -2, 0, -2, 2, 0, -2, 0, 0, 2, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, -6, -6, 2, 2, 0, 0, 0, 0, -2, -2, -2, -2, -2, 2, 2, 2, 2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 3, -3, -3, 3, -3, 1, 1, 0, -1, 1, 1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, -1, -1, 0, 0, 1, -1, 1, 1, 1, -1, -1, 1, -1, -1, 1, -1, 0, 0, 0, 0, 0, 0], [6, 6, 6, -6, -6, 6, 6, -2, -2, -2, 2, 0, 2, -2, 0, -2, 0, 0, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, -6, -6, 2, 2, 0, 0, 0, 0, -2, 2, -2, -2, 2, -2, 2, -2, -2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, -3, 3, 3, -3, -3, 1, 1, 0, 1, -1, -1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, -1, -1, 0, 0, 1, 1, 1, 1, -1, 1, 1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0], [6, 6, 6, -6, -6, 6, 6, -2, -2, -2, 2, 0, 2, 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-1, 0, 0, -1, 1, 1, 1, -1, 1, -1, -1, 1, 1, 1, -1, 0, 0, 0, 0, 0, 0], [8, -8, 0, 0, 0, 0, 0, 8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 8, -4, 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, 4, 0, 0, 0, 0, 0, -4, 4, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 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], [8, -8, 0, 0, 0, 0, 0, 8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, -4, -4, 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, -8, 0, 0, 0, 0, 0, 8, -8, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 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], [8, -8, 0, 0, 0, 0, 0, 8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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ConvertToLibraryCharacterTableNC(chartbl_2304_of);