# Group 960.2577 downloaded from the LMFDB on 14 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(4505267804488521641799452296159726332614672391,960); a := GPC.1; b := GPC.2; c := GPC.5; d := GPC.6;
GPerm := Group( (1,2)(3,10)(4,8)(5,13)(6,9)(7,11)(12,15)(14,16)(17,18,19,20)(22,23)(24,25), (1,3)(2,7)(4,11)(5,14)(6,12)(8,15)(9,16)(10,13)(17,19)(18,20)(27,28), (1,4,6,5)(2,8,9,13)(3,11,12,14)(7,15,16,10), (17,19)(18,20), (1,5,6,4)(2,8,9,13)(3,11,12,14)(7,10,16,15), (1,6)(2,9)(3,12)(4,5)(7,16)(8,13)(10,15)(11,14), (26,27,28), (21,22,24,25,23) );

 
# Booleans 
booleans_960_2577 := 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_960_2577:=rec(); 
chartbl_960_2577.IsFinite:= true; 
chartbl_960_2577.UnderlyingCharacteristic:= 0; 
chartbl_960_2577.UnderlyingGroup:= GPC;
chartbl_960_2577.Size:= 960;
chartbl_960_2577.InfoText:= "Character table for group 960.2577 downloaded from the LMFDB."; 
chartbl_960_2577.Identifier:= " C20.(C2*D12) "; 
chartbl_960_2577.NrConjugacyClasses:= 120; 
chartbl_960_2577.ConjugacyClasses:= [<identity> of ..., f4, f5, f4*f5, f6*f7*f8^2, f5*f6*f7*f8^2, f1, f1*f5, f7*f8^3, f3*f4*f6*f7*f8^2, f3*f6*f7*f8^2, f3*f4*f5*f6*f7*f8^2, f3*f5*f6*f7*f8^2, f3, f3*f4*f5, f1*f6*f8^4, f1*f5*f6*f8^4, f1*f2*f5*f8^2, f1*f2*f8^2, f1*f2*f4*f5*f6*f7*f8^3, f1*f2*f6*f7*f8^3, f8^2, f8^4, f5*f7^2*f8, f4*f5*f7*f8^3, f4*f7*f8^3, f6*f7^2, f5*f6*f7^2, f2, f2*f5, f2*f3, f2*f4, f2*f6, f2*f4*f5*f6, f2*f5*f6, f2*f4*f6, f4*f8^2, f4*f8, f5*f8, f5*f8^3, f4*f5*f8, f4*f5*f8^3, f6*f7, f6*f7*f8, f5*f6*f7, f5*f6*f7*f8, f1*f8, f1*f7^2, f1*f8^3, f1*f7, f1*f5*f8, f1*f3*f8, f1*f3*f7, f1*f5*f7, f3*f6*f7^2, f3*f4*f6*f8^4, f3*f5*f6*f7^2, f3*f4*f5*f6*f8^4, f3*f7^2*f8, f3*f5*f7^2*f8, f1*f2*f7, f1*f2*f3*f7, f1*f2*f7^2, f1*f2*f5*f7, f1*f2*f6, f1*f2*f3*f6, f1*f2*f6*f7^2, f1*f2*f5*f6, f7^2, f7*f8, f3*f4*f6*f7, f3*f6*f7*f8^4, f3*f6*f7*f8, f3*f4*f6*f7*f8^3, f3*f4*f5*f6*f7, f3*f5*f6*f7*f8^4, f3*f5*f6*f7*f8, f3*f4*f5*f6*f7*f8^3, f3*f4*f8, f3*f8^3, f3*f4*f5*f8, f3*f5*f8^3, f1*f6, f1*f6*f8^3, f1*f6*f7, f1*f6*f8, f1*f5*f6, f1*f3*f6, f1*f5*f6*f7, f1*f5*f6*f8, f5*f7, f5*f7^2, f4*f5*f7, f4*f5*f7^2, f4*f7^2, f4*f7^2*f8^4, f6, f6*f8, f4*f6, f6*f8^2, f5*f6, f5*f6*f8, f4*f5*f6, f5*f6*f8^2, f3*f7, f3*f7*f8, f3*f7^2, f3*f7*f8^2, f3*f6, f3*f4*f6, f3*f4*f6*f8, f3*f6*f8, f3*f5*f7, f3*f5*f7*f8, f3*f5*f7^2, f3*f5*f7*f8^2, f3*f5*f6, f3*f4*f5*f6, f3*f4*f5*f6*f8, f3*f5*f6*f8];
chartbl_960_2577.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];
chartbl_960_2577.ComputedPowerMaps:= [ , [1, 1, 1, 1, 1, 1, 1, 1, 9, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 4, 4, 23, 22, 9, 9, 9, 9, 9, 14, 14, 14, 14, 14, 14, 14, 14, 23, 22, 22, 23, 22, 23, 23, 22, 23, 22, 22, 22, 23, 23, 22, 22, 23, 23, 26, 26, 26, 26, 26, 26, 24, 24, 24, 24, 25, 25, 25, 25, 70, 69, 38, 38, 37, 37, 38, 38, 37, 37, 37, 38, 37, 38, 37, 37, 38, 38, 37, 37, 38, 38, 69, 70, 69, 70, 70, 69, 70, 69, 70, 69, 70, 69, 70, 69, 95, 95, 96, 96, 96, 96, 95, 95, 95, 95, 96, 96, 96, 96, 95, 95], [1, 2, 3, 4, 5, 6, 7, 8, 1, 11, 10, 13, 12, 14, 15, 16, 17, 19, 18, 21, 20, 23, 22, 3, 4, 2, 5, 6, 31, 32, 29, 30, 35, 36, 33, 34, 38, 37, 40, 39, 42, 41, 44, 43, 46, 45, 49, 50, 48, 47, 53, 54, 52, 51, 10, 11, 12, 13, 14, 15, 18, 19, 18, 19, 20, 21, 20, 21, 22, 23, 73, 74, 71, 72, 77, 78, 75, 76, 80, 79, 82, 81, 85, 86, 84, 83, 89, 90, 88, 87, 39, 40, 41, 42, 37, 38, 43, 44, 43, 44, 45, 46, 45, 46, 79, 79, 80, 80, 71, 72, 73, 74, 81, 81, 82, 82, 75, 76, 77, 78], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 1, 1, 24, 25, 26, 27, 28, 32, 31, 30, 29, 36, 35, 34, 33, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 55, 56, 57, 58, 59, 60, 63, 64, 61, 62, 67, 68, 65, 66, 9, 9, 10, 11, 11, 10, 12, 13, 13, 12, 14, 14, 15, 15, 16, 16, 16, 16, 17, 17, 17, 17, 24, 24, 25, 25, 26, 26, 27, 27, 27, 27, 28, 28, 28, 28, 59, 59, 59, 59, 55, 56, 56, 55, 60, 60, 60, 60, 57, 58, 58, 57]];
chartbl_960_2577.SizesCentralizers:= [960, 960, 960, 960, 480, 480, 80, 80, 480, 960, 960, 960, 960, 480, 480, 80, 80, 48, 48, 48, 48, 480, 480, 480, 480, 480, 240, 240, 32, 32, 32, 32, 32, 32, 32, 32, 480, 480, 480, 480, 480, 480, 240, 240, 240, 240, 80, 80, 80, 80, 80, 80, 80, 80, 480, 480, 480, 480, 240, 240, 48, 48, 48, 48, 48, 48, 48, 48, 240, 240, 480, 480, 480, 480, 480, 480, 480, 480, 240, 240, 240, 240, 80, 80, 80, 80, 80, 80, 80, 80, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240, 240];
chartbl_960_2577.ClassNames:= ["1A", "2A", "2B", "2C", "2D", "2E", "2F", "2G", "3A", "4A1", "4A-1", "4B1", "4B-1", "4C", "4D", "4E", "4F", "4G1", "4G-1", "4H1", "4H-1", "5A1", "5A2", "6A", "6B", "6C", "6D", "6E", "8A1", "8A-1", "8A3", "8A-3", "8B1", "8B-1", "8B3", "8B-3", "10A1", "10A3", "10B1", "10B3", "10C1", "10C3", "10D1", "10D3", "10E1", "10E3", "10F1", "10F-1", "10F3", "10F-3", "10G1", "10G-1", "10G3", "10G-3", "12A1", "12A-1", "12B1", "12B-1", "12C", "12D", "12E1", "12E-1", "12E5", "12E-5", "12F1", "12F-1", "12F5", "12F-5", "15A1", "15A2", "20A1", "20A-1", "20A3", "20A-3", "20B1", "20B-1", "20B3", "20B-3", "20C1", "20C3", "20D1", "20D3", "20E1", "20E-1", "20E3", "20E-3", "20F1", "20F-1", "20F3", "20F-3", "30A1", "30A7", "30B1", "30B7", "30C1", "30C7", "30D1", "30D7", "30D11", "30D13", "30E1", "30E7", "30E11", "30E13", "60A1", "60A-1", "60A7", "60A-7", "60B1", "60B-1", "60B7", "60B-7", "60C1", "60C-1", "60C7", "60C-7", "60D1", "60D-1", "60D7", "60D-7"];
chartbl_960_2577.OrderClassRepresentatives:= [1, 2, 2, 2, 2, 2, 2, 2, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 6, 6, 6, 6, 6, 8, 8, 8, 8, 8, 8, 8, 8, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 15, 15, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60];
chartbl_960_2577.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, 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2*E(60)^15, -2*E(60)^15, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, E(60)^6+E(60)^-6, -1*E(60)^12-E(60)^-12, 2*E(60)-2*E(60)^9-2*E(60)^11+2*E(60)^15, -2*E(60)+2*E(60)^9+2*E(60)^11, -2*E(60)+2*E(60)^9+2*E(60)^11-2*E(60)^15, -2*E(60)+2*E(60)^9+2*E(60)^11-2*E(60)^15, 2*E(60)-2*E(60)^9-2*E(60)^11, 2*E(60)-2*E(60)^9-2*E(60)^11+2*E(60)^15, -2*E(60)+2*E(60)^9+2*E(60)^11, 2*E(60)-2*E(60)^9-2*E(60)^11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2+2*E(60)^2+E(60)^4-E(60)^6-2*E(60)^8-2*E(60)^10+3*E(60)^14, E(60)^12+E(60)^-12, -1+2*E(60)^2+E(60)^4+E(60)^6+2*E(60)^8-2*E(60)^12-E(60)^14, 1-2*E(60)^2-E(60)^4-E(60)^6-2*E(60)^8+2*E(60)^12+E(60)^14, -1*E(60)^6-E(60)^-6, -2-2*E(60)^2-E(60)^4+E(60)^6+2*E(60)^8+2*E(60)^10-3*E(60)^14, E(60)^6+E(60)^-6, -1*E(60)^12-E(60)^-12, 1-2*E(60)^2-E(60)^4-E(60)^6-2*E(60)^8+2*E(60)^12+E(60)^14, -1*E(60)^6-E(60)^-6, E(60)^12+E(60)^-12, -1+2*E(60)^2+E(60)^4+E(60)^6+2*E(60)^8-2*E(60)^12-E(60)^14, -2-2*E(60)^2-E(60)^4+E(60)^6+2*E(60)^8+2*E(60)^10-3*E(60)^14, 2+2*E(60)^2+E(60)^4-E(60)^6-2*E(60)^8-2*E(60)^10+3*E(60)^14, E(60)+2*E(60)^3-2*E(60)^7-E(60)^9-E(60)^11-2*E(60)^13+E(60)^15, -3*E(60)+2*E(60)^5+2*E(60)^7+E(60)^9-E(60)^11-2*E(60)^13-2*E(60)^15, E(60)-E(60)^9-E(60)^11+E(60)^15, -1*E(60)+E(60)^9+E(60)^11, E(60)-E(60)^9-E(60)^11, -1*E(60)-2*E(60)^3+2*E(60)^7+E(60)^9+E(60)^11+2*E(60)^13-E(60)^15, E(60)-E(60)^9-E(60)^11+E(60)^15, E(60)+2*E(60)^3-2*E(60)^7-E(60)^9-E(60)^11-2*E(60)^13+E(60)^15, 3*E(60)-2*E(60)^5-2*E(60)^7-E(60)^9+E(60)^11+2*E(60)^13+2*E(60)^15, -1*E(60)+E(60)^9+E(60)^11, -1*E(60)+E(60)^9+E(60)^11-E(60)^15, -3*E(60)+2*E(60)^5+2*E(60)^7+E(60)^9-E(60)^11-2*E(60)^13-2*E(60)^15, -1*E(60)-2*E(60)^3+2*E(60)^7+E(60)^9+E(60)^11+2*E(60)^13-E(60)^15, E(60)-E(60)^9-E(60)^11, -1*E(60)+E(60)^9+E(60)^11-E(60)^15, 3*E(60)-2*E(60)^5-2*E(60)^7-E(60)^9+E(60)^11+2*E(60)^13+2*E(60)^15]];
ConvertToLibraryCharacterTableNC(chartbl_960_2577);