# Group 480.1197 downloaded from the LMFDB on 22 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(4286144670285320663589309545544917254151,480); a := GPC.1; b := GPC.2; c := GPC.3; d := GPC.5;
GPerm := Group( (4,5)(6,7)(9,10,11,12), (2,3), (4,6)(5,7), (4,7)(5,6), (9,11)(10,12), (1,2,3), (8,9,10,12,11) );
GLZ := Group([[[1, 0, 0, 0, 0, 0], [-1, -1, -1, -1, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1]], [[1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, -1, 0], [0, 0, 0, 0, 0, -1]], [[0, 0, 1, 0, 0, 0], [1, 0, 0, 0, 0, 0], [-1, -1, -1, -1, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]], [[-1, 0, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0], [0, -1, 0, 0, 0, 0], [1, 1, 1, 1, 0, 0], [0, 0, 0, 0, -1, 1], [0, 0, 0, 0, -1, 0]]]);
GLFp := Group([[[ Z(5)^2, 0*Z(5), 0*Z(5), 0*Z(5) ], [ 0*Z(5), Z(5)^2, 0*Z(5), 0*Z(5) ], [ 0*Z(5), 0*Z(5), Z(5)^2, 0*Z(5) ], [ 0*Z(5), 0*Z(5), 0*Z(5), Z(5)^2 ]], [[ Z(5)^2, 0*Z(5), 0*Z(5), 0*Z(5) ], [ Z(5)^2, Z(5)^0, 0*Z(5), Z(5)^0 ], [ Z(5)^3, Z(5)^2, Z(5)^2, Z(5) ], [ 0*Z(5), 0*Z(5), 0*Z(5), Z(5)^2 ]], [[ Z(5)^2, Z(5)^2, Z(5)^3, Z(5)^3 ], [ Z(5)^3, 0*Z(5), Z(5)^3, Z(5)^3 ], [ Z(5)^2, Z(5), 0*Z(5), Z(5)^2 ], [ Z(5), Z(5)^0, Z(5), Z(5)^3 ]], [[ Z(5)^0, Z(5)^0, Z(5), Z(5) ], [ Z(5)^2, Z(5)^0, Z(5)^2, Z(5)^2 ], [ Z(5), Z(5)^0, Z(5)^0, Z(5) ], [ Z(5)^2, Z(5), Z(5)^2, Z(5)^3 ]], [[ 0*Z(5), Z(5)^3, Z(5)^0, 0*Z(5) ], [ 0*Z(5), Z(5)^2, 0*Z(5), Z(5)^3 ], [ 0*Z(5), 0*Z(5), Z(5)^2, Z(5)^2 ], [ Z(5)^0, Z(5)^3, Z(5)^0, Z(5)^3 ]], [[ Z(5)^2, Z(5)^3, Z(5)^3, Z(5)^3 ], [ Z(5)^3, Z(5)^0, Z(5), Z(5)^3 ], [ Z(5)^3, Z(5), Z(5), 0*Z(5) ], [ Z(5)^3, Z(5)^2, Z(5)^3, Z(5) ]], [[ Z(5)^3, Z(5)^0, Z(5), Z(5)^0 ], [ Z(5)^0, Z(5)^2, Z(5)^0, Z(5)^2 ], [ Z(5)^3, Z(5)^2, Z(5)^2, Z(5) ], [ 0*Z(5), 0*Z(5), 0*Z(5), Z(5)^2 ]]]);

 
# Booleans 
booleans_480_1197 := rec( 
Agroup := true,
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_480_1197:=rec(); 
chartbl_480_1197.IsFinite:= true; 
chartbl_480_1197.UnderlyingCharacteristic:= 0; 
chartbl_480_1197.UnderlyingGroup:= GPC;
chartbl_480_1197.Size:= 480;
chartbl_480_1197.InfoText:= "Character table for group 480.1197 downloaded from the LMFDB."; 
chartbl_480_1197.Identifier:= " C2*D6*F5 "; 
chartbl_480_1197.NrConjugacyClasses:= 60; 
chartbl_480_1197.ConjugacyClasses:= [<identity> of ..., f5*f6*f7^2, f1, f1*f5*f6*f7^2, f2, f2*f5*f7^4, f1*f2, f1*f2*f5*f7^4, f4, f4*f5*f6*f7^3, f1*f4*f7^2, f1*f4*f5*f6*f7^3, f2*f4, f2*f4*f5, f1*f2*f4, f1*f2*f4*f5, f6*f7^3, f2*f3*f4*f7, f2*f3*f7^2, f2*f3*f4*f5*f6, f2*f3*f5*f6*f7^3, f1*f2*f3*f4*f7, f1*f2*f3*f7^2, f1*f2*f3*f4*f5*f6, f1*f2*f3*f5*f6*f7^3, f3, f3*f4, f3*f5, f3*f4*f5, f1*f3, f1*f3*f4, f1*f3*f5, f1*f3*f4*f5, f7^2, f5*f6^2, f1*f6^2*f7, f1*f5*f6^2, f4*f5, f1*f4*f6, f1*f4*f5, f4*f6^2*f7^4, f5*f6, f1*f7, f1*f5*f6, f2*f7, f2*f5, f1*f2*f7, f1*f2*f5, f2*f3*f6, f2*f3*f4*f6, f2*f3*f5, f2*f3*f4*f5, f1*f2*f3*f6, f1*f2*f3*f4*f6, f1*f2*f3*f5, f1*f2*f3*f4*f5, f6, f5, f1*f6, f1*f5];
chartbl_480_1197.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];
chartbl_480_1197.ComputedPowerMaps:= [ , [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 17, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 34, 17, 17, 17, 17, 17, 17, 17, 34, 34, 34, 34, 34, 34, 34, 41, 41, 41, 41, 41, 41, 41, 41, 57, 57, 57, 57], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 1, 19, 18, 21, 20, 23, 22, 25, 24, 27, 26, 29, 28, 31, 30, 33, 32, 34, 2, 3, 4, 10, 11, 12, 9, 42, 43, 44, 45, 46, 47, 48, 18, 19, 20, 21, 22, 23, 24, 25, 34, 42, 43, 44], [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, 35, 36, 37, 38, 39, 40, 41, 2, 3, 4, 5, 6, 7, 8, 49, 50, 51, 52, 53, 54, 55, 56, 17, 35, 36, 37]];
chartbl_480_1197.SizesCentralizers:= [480, 480, 480, 480, 160, 160, 160, 160, 96, 96, 96, 96, 32, 32, 32, 32, 240, 96, 96, 96, 96, 96, 96, 96, 96, 32, 32, 32, 32, 32, 32, 32, 32, 120, 240, 240, 240, 48, 48, 48, 48, 120, 120, 120, 40, 40, 40, 40, 48, 48, 48, 48, 48, 48, 48, 48, 60, 60, 60, 60];
chartbl_480_1197.ClassNames:= ["1A", "2A", "2B", "2C", "2D", "2E", "2F", "2G", "2H", "2I", "2J", "2K", "2L", "2M", "2N", "2O", "3A", "4A1", "4A-1", "4B1", "4B-1", "4C1", "4C-1", "4D1", "4D-1", "4E1", "4E-1", "4F1", "4F-1", "4G1", "4G-1", "4H1", "4H-1", "5A", "6A", "6B", "6C", "6D", "6E", "6F", "6G", "10A", "10B", "10C", "10D", "10E", "10F", "10G", "12A1", "12A-1", "12B1", "12B-1", "12C1", "12C-1", "12D1", "12D-1", "15A", "30A", "30B", "30C"];
chartbl_480_1197.OrderClassRepresentatives:= [1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 6, 6, 6, 6, 6, 6, 6, 10, 10, 10, 10, 10, 10, 10, 12, 12, 12, 12, 12, 12, 12, 12, 15, 30, 30, 30];
chartbl_480_1197.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, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1], [1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1*E(4), -1*E(4), -1*E(4), E(4), E(4), E(4), -1*E(4), E(4), -1*E(4), -1*E(4), -1*E(4), -1*E(4), E(4), E(4), E(4), E(4), 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, 1, -1, 1, 1, -1, -1*E(4), E(4), E(4), -1*E(4), E(4), -1*E(4), E(4), -1*E(4), 1, 1, -1, -1], [1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, 1, -1, -1, 1, 1, E(4), E(4), E(4), -1*E(4), -1*E(4), -1*E(4), E(4), -1*E(4), E(4), E(4), E(4), E(4), -1*E(4), -1*E(4), -1*E(4), -1*E(4), 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, 1, -1, 1, 1, -1, E(4), -1*E(4), -1*E(4), E(4), -1*E(4), E(4), -1*E(4), E(4), 1, 1, -1, -1], [1, -1, -1, 1, 1, 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1, -1, 1, -1, 1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 1, -1], [4, 4, -4, -4, -4, -4, 4, 4, 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, -1, -4, 4, -4, 0, 0, 0, 0, -1, 1, 1, 1, 1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, -1, 1], [4, 4, -4, -4, 4, 4, -4, -4, 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, -1, -4, 4, -4, 0, 0, 0, 0, -1, 1, 1, -1, -1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, -1, 1], [4, 4, 4, 4, -4, -4, -4, -4, 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, -1, 4, 4, 4, 0, 0, 0, 0, -1, -1, -1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1], [8, 8, 8, 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, -2, -4, -4, -4, 0, 0, 0, 0, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1], [8, -8, -8, 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, -2, -4, 4, 4, 0, 0, 0, 0, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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ConvertToLibraryCharacterTableNC(chartbl_480_1197);