# Group 7440.g downloaded from the LMFDB on 30 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(104401002881057110564318274013985132882420018935264789346624919537355060891029,7440); a := GPC.1; b := GPC.2; c := GPC.5;
GPerm := Group( (2,3)(4,7)(5,6)(8,15)(9,14)(10,19)(11,13)(12,23)(16,26)(17,29)(18,20)(21,24)(22,25)(27,28)(30,31)(32,33,34,35), (1,2,4,8,16,27,31,18,19,6,12,24,13,9,17,22,25,29,14,11,21,23,5,10,20,30,28,26,15,7,3), (2,3)(4,7)(5,6)(8,15)(9,14)(10,19)(11,13)(12,23)(16,26)(17,29)(18,20)(21,24)(22,25)(27,28)(30,31)(32,34)(33,35), (2,5,11,22,21,31,19,23,15,26,27,29,4,9,18,3,6,13,25,24,30,10,12,8,16,28,17,7,14,20), (2,3)(4,7)(5,6)(8,15)(9,14)(10,19)(11,13)(12,23)(16,26)(17,29)(18,20)(21,24)(22,25)(27,28)(30,31)(33,35) );

 
# Booleans 
booleans_7440_g := 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_7440_g:=rec(); 
chartbl_7440_g.IsFinite:= true; 
chartbl_7440_g.UnderlyingCharacteristic:= 0; 
chartbl_7440_g.UnderlyingGroup:= GPC;
chartbl_7440_g.Size:= 7440;
chartbl_7440_g.InfoText:= "Character table for group 7440.g downloaded from the LMFDB."; 
chartbl_7440_g.Identifier:= " D4*F31 "; 
chartbl_7440_g.NrConjugacyClasses:= 155; 
chartbl_7440_g.ConjugacyClasses:= [<identity> of ..., f6*f7^15, f1*f2*f3*f4^2, f1*f2*f3*f4^2*f5*f7^23, f2*f3*f4^2, f2*f3*f4^2*f6*f7^19, f1, f1*f5*f7, f3^2*f4, f3*f4^3, f5*f6*f7^7, f2*f3*f4^2*f5*f6*f7^9, f4, f4^4, f4^2, f4^3, f2*f3^2, f2*f4^4, f2*f3^2*f6*f7^27, f2*f4^4*f6*f7^5, f3*f4^3*f6*f7^26, f3^2*f4*f6*f7^19, f1*f3^2*f4, f1*f3*f4^3, f1*f2*f3^2, f1*f2*f4^4, f1*f3^2*f4*f5*f7^16, f1*f3*f4^3*f5*f7^19, f1*f2*f3^2*f5*f7^18, f1*f2*f4^4*f5*f7^24, f2*f3, f2*f3*f4^4, f2*f3*f4, f2*f3*f4^3, f2*f3*f6*f7^21, f2*f3*f4^4*f6*f7^18, f2*f3*f4*f6*f7^2, f2*f3*f4^3*f6*f7^25, f4^2*f6*f7^2, f4^3*f6*f7^10, f4*f6, f4^4*f6*f7^11, f1*f4, f1*f4^4, f1*f4^3, f1*f4^2, f1*f2*f3, f1*f2*f3*f4^4, f1*f2*f3*f4, f1*f2*f3*f4^3, f1*f4*f5*f7^30, f1*f4^4*f5*f7^17, f1*f4^3*f5*f7^21, f1*f4^2*f5*f7^22, f1*f2*f3*f5*f7^14, f1*f2*f3*f4^4*f5*f7^12, f1*f2*f3*f4*f5*f7^22, f1*f2*f3*f4^3*f5*f7^27, f3^2*f4*f5*f7^27, f3*f4^3*f5*f6*f7^18, f2*f3^2*f5*f7^29, f2*f4^4*f5*f6*f7^2, f3, f3^2*f4^4, f3^2, f3*f4^4, f3*f4, f3^2*f4^3, f3*f4^2, f3^2*f4^2, f4*f5*f6*f7^23, f4^4*f5*f7^19, f4^3*f5*f7^18, f4^2*f5*f6*f7^25, f2*f3*f5*f6*f7^10, f2*f3*f4^4*f5*f7^9, f2*f3*f4*f5*f7, f2*f3*f4^3*f5*f6*f7^12, f2, f2*f3^2*f4^4, f2*f4, f2*f3^2*f4^3, f2*f3^2*f4, f2*f4^3, f2*f4^2, f2*f3^2*f4^2, f2*f6, f2*f3^2*f4^4*f6, f2*f4*f6, f2*f3^2*f4^3*f6, f2*f3^2*f4*f6, f2*f4^3*f6, f2*f4^2*f6, f2*f3^2*f4^2*f6, f3^2*f6*f7^12, f3*f4^4*f6*f7^13, f3^2*f4^4*f6*f7^18, f3*f6*f7^23, f3*f4^2*f6*f7^6, f3^2*f4^2*f6*f7^16, f3^2*f4^3*f6*f7^4, f3*f4*f6*f7, f1*f3, f1*f3^2*f4^4, f1*f3*f4^2, f1*f3^2*f4^2, f1*f3^2*f4^3, f1*f3*f4, f1*f3*f4^4, f1*f3^2, f1*f2, f1*f2*f3^2*f4^4, f1*f2*f4, f1*f2*f3^2*f4^3, f1*f2*f3^2*f4, f1*f2*f4^3, f1*f2*f4^2, f1*f2*f3^2*f4^2, f1*f3*f5, f1*f3^2*f4^4*f5, f1*f3*f4^2*f5, f1*f3^2*f4^2*f5, f1*f3^2*f4^3*f5, f1*f3*f4*f5, f1*f3*f4^4*f5, f1*f3^2*f5, f1*f2*f5, f1*f2*f3^2*f4^4*f5, f1*f2*f4*f5, f1*f2*f3^2*f4^3*f5, f1*f2*f3^2*f4*f5, f1*f2*f4^3*f5, f1*f2*f4^2*f5, f1*f2*f3^2*f4^2*f5, f7^2, f3*f5, f3^2*f4^4*f5, f3*f4^2*f5, f3^2*f4^2*f5, f3^2*f4^3*f5, f3*f4*f5, f3*f4^4*f5, f3^2*f5, f2*f5, f2*f3^2*f4^4*f5, f2*f4*f5, f2*f3^2*f4^3*f5, f2*f3^2*f4*f5, f2*f4^3*f5, f2*f4^2*f5, f2*f3^2*f4^2*f5, f6, f1*f2*f3*f4^2*f7, f1*f2*f3*f4^2*f5, f5];
chartbl_7440_g.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, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155];
chartbl_7440_g.ComputedPowerMaps:= [ , [1, 1, 1, 1, 1, 1, 1, 1, 10, 9, 2, 2, 15, 16, 14, 13, 9, 10, 9, 10, 9, 10, 10, 9, 9, 10, 10, 9, 9, 10, 13, 14, 16, 15, 13, 14, 16, 15, 14, 13, 15, 16, 15, 16, 13, 14, 13, 14, 16, 15, 15, 16, 13, 14, 13, 14, 16, 15, 21, 22, 22, 21, 65, 66, 67, 68, 70, 69, 64, 63, 39, 40, 41, 42, 41, 42, 40, 39, 63, 64, 69, 70, 68, 67, 66, 65, 63, 64, 69, 70, 68, 67, 66, 65, 67, 68, 66, 65, 64, 63, 69, 70, 65, 66, 64, 63, 69, 70, 68, 67, 63, 64, 69, 70, 68, 67, 66, 65, 65, 66, 64, 63, 69, 70, 68, 67, 63, 64, 69, 70, 68, 67, 66, 65, 135, 95, 96, 97, 98, 99, 100, 101, 102, 98, 97, 99, 100, 101, 102, 96, 95, 135, 135, 135, 152], [1, 2, 3, 4, 5, 6, 7, 8, 1, 1, 11, 12, 16, 15, 13, 14, 5, 5, 6, 6, 2, 2, 7, 7, 3, 3, 8, 8, 4, 4, 33, 34, 32, 31, 37, 38, 36, 35, 41, 42, 40, 39, 45, 46, 44, 43, 49, 50, 48, 47, 53, 54, 52, 51, 57, 58, 56, 55, 11, 11, 12, 12, 13, 14, 15, 16, 14, 13, 15, 16, 73, 74, 72, 71, 77, 78, 76, 75, 31, 32, 34, 33, 31, 32, 33, 34, 35, 36, 38, 37, 35, 36, 37, 38, 39, 40, 42, 41, 39, 40, 41, 42, 43, 44, 46, 45, 43, 44, 45, 46, 47, 48, 50, 49, 47, 48, 49, 50, 51, 52, 54, 53, 51, 52, 53, 54, 55, 56, 58, 57, 55, 56, 57, 58, 135, 71, 72, 74, 73, 71, 72, 73, 74, 75, 76, 78, 77, 75, 76, 77, 78, 152, 153, 154, 155], [1, 2, 3, 4, 5, 6, 7, 8, 10, 9, 11, 12, 1, 1, 1, 1, 18, 17, 20, 19, 22, 21, 24, 23, 26, 25, 28, 27, 30, 29, 5, 5, 5, 5, 6, 6, 6, 6, 2, 2, 2, 2, 7, 7, 7, 7, 3, 3, 3, 3, 8, 8, 8, 8, 4, 4, 4, 4, 60, 59, 62, 61, 9, 10, 10, 9, 9, 10, 9, 10, 11, 11, 11, 11, 12, 12, 12, 12, 17, 18, 17, 18, 18, 17, 17, 18, 19, 20, 19, 20, 20, 19, 19, 20, 21, 22, 21, 22, 22, 21, 21, 22, 23, 24, 23, 24, 24, 23, 23, 24, 25, 26, 25, 26, 26, 25, 25, 26, 27, 28, 27, 28, 28, 27, 27, 28, 29, 30, 29, 30, 30, 29, 29, 30, 135, 59, 60, 59, 60, 60, 59, 59, 60, 61, 62, 61, 62, 62, 61, 61, 62, 152, 153, 154, 155], [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, 1, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 2, 3, 4, 11]];
chartbl_7440_g.SizesCentralizers:= [7440, 7440, 3720, 3720, 240, 240, 120, 120, 240, 240, 3720, 120, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 120, 120, 120, 120, 120, 120, 120, 120, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 240, 240, 240, 240, 240, 240, 240, 240, 120, 120, 120, 120, 120, 120, 120, 120, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 248, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 248, 124, 124, 124];
chartbl_7440_g.ClassNames:= ["1A", "2A", "2B", "2C", "2D", "2E", "2F", "2G", "3A1", "3A-1", "4A", "4B", "5A1", "5A-1", "5A2", "5A-2", "6A1", "6A-1", "6B1", "6B-1", "6C1", "6C-1", "6D1", "6D-1", "6E1", "6E-1", "6F1", "6F-1", "6G1", "6G-1", "10A1", "10A-1", "10A3", "10A-3", "10B1", "10B-1", "10B3", "10B-3", "10C1", "10C-1", "10C3", "10C-3", "10D1", "10D-1", "10D3", "10D-3", "10E1", "10E-1", "10E3", "10E-3", "10F1", "10F-1", "10F3", "10F-3", "10G1", "10G-1", "10G3", "10G-3", "12A1", "12A-1", "12B1", "12B-1", "15A1", "15A-1", "15A2", "15A-2", "15A4", "15A-4", "15A7", "15A-7", "20A1", "20A-1", "20A3", "20A-3", "20B1", "20B-1", "20B3", "20B-3", "30A1", "30A-1", "30A7", "30A-7", "30A11", "30A-11", "30A13", "30A-13", "30B1", "30B-1", "30B7", "30B-7", "30B11", "30B-11", "30B13", "30B-13", "30C1", "30C-1", "30C7", "30C-7", "30C11", "30C-11", "30C13", "30C-13", "30D1", "30D-1", "30D7", "30D-7", "30D11", "30D-11", "30D13", "30D-13", "30E1", "30E-1", "30E7", "30E-7", "30E11", "30E-11", "30E13", "30E-13", "30F1", "30F-1", "30F7", "30F-7", "30F11", "30F-11", "30F13", "30F-13", "30G1", "30G-1", "30G7", "30G-7", "30G11", "30G-11", "30G13", "30G-13", "31A", "60A1", "60A-1", "60A7", "60A-7", "60A11", "60A-11", "60A13", "60A-13", "60B1", "60B-1", "60B7", "60B-7", "60B11", "60B-11", "60B13", "60B-13", "62A", "62B", "62C", "124A"];
chartbl_7440_g.OrderClassRepresentatives:= [1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 12, 12, 12, 12, 15, 15, 15, 15, 15, 15, 15, 15, 20, 20, 20, 20, 20, 20, 20, 20, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 31, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 62, 62, 62, 124];
chartbl_7440_g.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, 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ConvertToLibraryCharacterTableNC(chartbl_7440_g);