# Group 6496.d downloaded from the LMFDB on 31 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(64477732634971045949145830232570506579603064973809144632044355247064740277467,6496); a := GPC.1; b := GPC.2; c := GPC.5;
GPerm := Group( (2,3)(4,6)(5,9)(7,12)(8,10)(11,17)(13,20)(14,15)(16,25)(18,27)(19,22)(21,28)(23,24)(26,29)(30,31)(32,33), (2,3)(4,6)(5,9)(7,12)(8,10)(11,17)(13,20)(14,15)(16,25)(18,27)(19,22)(21,28)(23,24)(26,29)(30,32,31,33), (2,3)(4,6)(5,9)(7,12)(8,10)(11,17)(13,20)(14,15)(16,25)(18,27)(19,22)(21,28)(23,24)(26,29)(30,32)(31,33), (2,4,7,14,23,16,26,22,27,13,21,9,8,11,3,6,12,15,24,25,29,19,18,20,28,5,10,17), (1,2,5,11,18,24,21,29,25,10,6,13,22,7,15,14,12,19,20,4,8,16,26,28,23,27,17,9,3) );

 
# Booleans 
booleans_6496_d := 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_6496_d:=rec(); 
chartbl_6496_d.IsFinite:= true; 
chartbl_6496_d.UnderlyingCharacteristic:= 0; 
chartbl_6496_d.UnderlyingGroup:= GPC;
chartbl_6496_d.Size:= 6496;
chartbl_6496_d.InfoText:= "Character table for group 6496.d downloaded from the LMFDB."; 
chartbl_6496_d.Identifier:= " D4*F29 "; 
chartbl_6496_d.NrConjugacyClasses:= 145; 
chartbl_6496_d.ConjugacyClasses:= [<identity> of ..., f6*f7^14, f1*f3*f4^3, f1*f3*f4^3*f5*f7^7, f3*f4^3, f3*f4^3*f6*f7^18, f1, f1*f5*f7^25, f5*f6*f7^21, f2*f3*f4, f2*f4^5, f2*f3*f4*f6*f7^28, f2*f4^5*f6*f7^8, f3*f4^3*f5*f6*f7^27, f2*f3*f4*f5*f6*f7^28, f2*f4^5*f5*f7^4, f1*f2*f3*f4, f1*f2*f4^5, f1*f2*f3*f4*f5*f7, f1*f2*f4^5*f5*f7^21, f4^2, f4^5, f4^4, f4^3, f4^6, f4, f3, f3*f4^6, f3*f4, f3*f4^5, f3*f4^2, f3*f4^4, f4^2*f6*f7^13, f4^5*f6*f7^21, f4^6*f6*f7, f4*f6*f7^7, f4^3*f6*f7^12, f4^4*f6*f7^17, f3*f6*f7^19, f3*f4^6*f6*f7^27, f3*f4*f6*f7, f3*f4^5*f6*f7^8, f3*f4^2*f6*f7^4, f3*f4^4*f6*f7^6, f1*f4, f1*f4^6, f1*f4^3, f1*f4^4, f1*f4^5, f1*f4^2, f1*f3, f1*f3*f4^6, f1*f3*f4, f1*f3*f4^5, f1*f3*f4^2, f1*f3*f4^4, f1*f4*f5, f1*f4^6*f5, f1*f4^3*f5, f1*f4^4*f5, f1*f4^5*f5, f1*f4^2*f5, f1*f3*f5, f1*f3*f4^6*f5, f1*f3*f4*f5, f1*f3*f4^5*f5, f1*f3*f4^2*f5, f1*f3*f4^4*f5, f2, f2*f3*f4^6, f2*f3, f2*f4^6, f2*f4, f2*f3*f4^5, f2*f4^2, f2*f3*f4^4, f2*f3*f4^2, f2*f4^4, f2*f4^3, f2*f3*f4^3, f2*f6, f2*f3*f4^6*f6, f2*f3*f6, f2*f4^6*f6, f2*f4*f6, f2*f3*f4^5*f6, f2*f4^2*f6, f2*f3*f4^4*f6, f2*f3*f4^2*f6, f2*f4^4*f6, f2*f4^3*f6, f2*f3*f4^3*f6, f4*f5, f4^6*f5, f4^3*f5, f4^4*f5, f4^5*f5, f4^2*f5, f3*f5, f3*f4^6*f5, f3*f4*f5, f3*f4^5*f5, f3*f4^2*f5, f3*f4^4*f5, f2*f5, f2*f3*f4^6*f5, f2*f3*f5, f2*f4^6*f5, f2*f4*f5, f2*f3*f4^5*f5, f2*f4^2*f5, f2*f3*f4^4*f5, f2*f3*f4^2*f5, f2*f4^4*f5, f2*f4^3*f5, f2*f3*f4^3*f5, f1*f2, f1*f2*f3*f4^6, f1*f2*f3, f1*f2*f4^6, f1*f2*f4, f1*f2*f3*f4^5, f1*f2*f4^2, f1*f2*f3*f4^4, f1*f2*f3*f4^2, f1*f2*f4^4, f1*f2*f4^3, f1*f2*f3*f4^3, f1*f2*f5, f1*f2*f3*f4^6*f5, f1*f2*f3*f5, f1*f2*f4^6*f5, f1*f2*f4*f5, f1*f2*f3*f4^5*f5, f1*f2*f4^2*f5, f1*f2*f3*f4^4*f5, f1*f2*f3*f4^2*f5, f1*f2*f4^4*f5, f1*f2*f4^3*f5, f1*f2*f3*f4^3*f5, f7^2, f6, f1*f3*f4^3*f7, f1*f3*f4^3*f5, f5];
chartbl_6496_d.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, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145];
chartbl_6496_d.ComputedPowerMaps:= [ , [1, 1, 1, 1, 1, 1, 1, 1, 2, 5, 5, 5, 5, 2, 6, 6, 5, 5, 5, 5, 23, 24, 26, 25, 22, 21, 26, 25, 24, 23, 22, 21, 23, 24, 22, 21, 25, 26, 26, 25, 24, 23, 22, 21, 21, 22, 25, 26, 24, 23, 26, 25, 24, 23, 22, 21, 21, 22, 25, 26, 24, 23, 26, 25, 24, 23, 22, 21, 27, 28, 29, 30, 31, 32, 32, 31, 30, 29, 28, 27, 27, 28, 29, 30, 31, 32, 32, 31, 30, 29, 28, 27, 33, 34, 35, 36, 37, 38, 36, 35, 37, 38, 34, 33, 39, 40, 41, 42, 43, 44, 44, 43, 42, 41, 40, 39, 27, 28, 29, 30, 31, 32, 32, 31, 30, 29, 28, 27, 27, 28, 29, 30, 31, 32, 32, 31, 30, 29, 28, 27, 141, 141, 141, 141, 142], [1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 10, 13, 12, 14, 16, 15, 18, 17, 20, 19, 25, 26, 22, 21, 23, 24, 29, 30, 32, 31, 27, 28, 35, 36, 38, 37, 33, 34, 41, 42, 44, 43, 39, 40, 47, 48, 50, 49, 45, 46, 53, 54, 56, 55, 51, 52, 59, 60, 62, 61, 57, 58, 65, 66, 68, 67, 63, 64, 71, 72, 75, 76, 80, 79, 70, 69, 73, 74, 77, 78, 83, 84, 87, 88, 92, 91, 82, 81, 85, 86, 89, 90, 95, 96, 98, 97, 93, 94, 101, 102, 104, 103, 99, 100, 107, 108, 111, 112, 116, 115, 106, 105, 109, 110, 113, 114, 119, 120, 123, 124, 128, 127, 118, 117, 121, 122, 125, 126, 131, 132, 135, 136, 140, 139, 130, 129, 133, 134, 137, 138, 141, 142, 143, 144, 145], [1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 10, 13, 12, 14, 16, 15, 18, 17, 20, 19, 1, 1, 1, 1, 1, 1, 5, 5, 5, 5, 5, 5, 2, 2, 2, 2, 2, 2, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 3, 3, 3, 3, 3, 3, 8, 8, 8, 8, 8, 8, 4, 4, 4, 4, 4, 4, 10, 11, 11, 10, 10, 11, 10, 11, 11, 10, 10, 11, 12, 13, 13, 12, 12, 13, 12, 13, 13, 12, 12, 13, 9, 9, 9, 9, 9, 9, 14, 14, 14, 14, 14, 14, 15, 16, 16, 15, 15, 16, 15, 16, 16, 15, 15, 16, 17, 18, 18, 17, 17, 18, 17, 18, 18, 17, 17, 18, 19, 20, 20, 19, 19, 20, 19, 20, 20, 19, 19, 20, 141, 142, 143, 144, 145]];
chartbl_6496_d.SizesCentralizers:= [6496, 6496, 3248, 3248, 224, 224, 112, 112, 3248, 224, 224, 224, 224, 112, 112, 112, 112, 112, 112, 112, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 232, 232, 116, 116, 116];
chartbl_6496_d.ClassNames:= ["1A", "2A", "2B", "2C", "2D", "2E", "2F", "2G", "4A", "4B1", "4B-1", "4C1", "4C-1", "4D", "4E1", "4E-1", "4F1", "4F-1", "4G1", "4G-1", "7A1", "7A-1", "7A2", "7A-2", "7A3", "7A-3", "14A1", "14A-1", "14A3", "14A-3", "14A5", "14A-5", "14B1", "14B-1", "14B3", "14B-3", "14B5", "14B-5", "14C1", "14C-1", "14C3", "14C-3", "14C5", "14C-5", "14D1", "14D-1", "14D3", "14D-3", "14D5", "14D-5", "14E1", "14E-1", "14E3", "14E-3", "14E5", "14E-5", "14F1", "14F-1", "14F3", "14F-3", "14F5", "14F-5", "14G1", "14G-1", "14G3", "14G-3", "14G5", "14G-5", "28A1", "28A-1", "28A3", "28A-3", "28A5", "28A-5", "28A9", "28A-9", "28A11", "28A-11", "28A13", "28A-13", "28B1", "28B-1", "28B3", "28B-3", "28B5", "28B-5", "28B9", "28B-9", "28B11", "28B-11", "28B13", "28B-13", "28C1", "28C-1", "28C3", "28C-3", "28C5", "28C-5", "28D1", "28D-1", "28D3", "28D-3", "28D5", "28D-5", "28E1", "28E-1", "28E3", "28E-3", "28E5", "28E-5", "28E9", "28E-9", "28E11", "28E-11", "28E13", "28E-13", "28F1", "28F-1", "28F3", "28F-3", "28F5", "28F-5", "28F9", "28F-9", "28F11", "28F-11", "28F13", "28F-13", "28G1", "28G-1", "28G3", "28G-3", "28G5", "28G-5", "28G9", "28G-9", "28G11", "28G-11", "28G13", "28G-13", "29A", "58A", "58B", "58C", "116A"];
chartbl_6496_d.OrderClassRepresentatives:= [1, 2, 2, 2, 2, 2, 2, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 7, 7, 7, 7, 7, 7, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 29, 58, 58, 58, 116];
chartbl_6496_d.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, 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E(28)^9, E(28)^3, E(28)^13, -1*E(28)^8, 1, 1, 1, 1, 1], [1, 1, 1, 1, -1, -1, -1, -1, 1, -1*E(28)^7, E(28)^7, -1*E(28)^7, E(28)^7, E(28)^7, E(28)^7, -1*E(28)^7, -1, E(28)^7, -1*E(28)^7, -1*E(28)^7, -1*E(28)^10, -1*E(28)^2, E(28)^8, E(28)^4, E(28)^12, -1*E(28)^6, E(28)^2, E(28)^2, -1*E(28)^12, E(28)^10, E(28)^4, E(28)^6, -1*E(28)^2, -1*E(28)^6, -1*E(28)^12, -1*E(28)^8, E(28)^6, -1*E(28)^4, -1*E(28)^10, -1*E(28)^8, E(28)^8, -1*E(28)^4, E(28)^10, E(28)^12, E(28)^6, E(28)^2, -1*E(28)^6, E(28)^2, -1*E(28)^6, E(28)^10, E(28)^6, -1*E(28)^8, E(28)^12, -1*E(28)^10, E(28)^4, -1*E(28)^2, -1*E(28)^12, -1*E(28)^4, E(28)^8, E(28)^8, -1*E(28)^4, -1*E(28)^2, -1*E(28)^12, -1*E(28)^10, E(28)^4, -1*E(28)^8, E(28)^12, E(28)^10, -1*E(28)^5, -1*E(28)^9, E(28), -1*E(28)^13, E(28)^5, E(28)^11, -1*E(28)^11, E(28)^3, -1*E(28), -1*E(28)^5, E(28)^5, E(28)^9, E(28), -1*E(28), -1*E(28)^9, E(28)^13, E(28)^11, E(28)^13, -1*E(28)^13, E(28)^3, -1*E(28)^3, -1*E(28)^3, E(28)^9, -1*E(28)^11, E(28)^3, -1*E(28)^8, E(28)^6, 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ConvertToLibraryCharacterTableNC(chartbl_6496_d);