# Group 480.218 downloaded from the LMFDB on 26 August 2026. 
 
## 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 
GPerm := Group( (1,17,16,14)(2,13,24,23)(4,9,6,15)(5,22,18,20)(8,12,11,21), (1,7,21,14,17,9,24,19,8,13,23,22,15,3,12,6,4,16,20,10,11,18,5,2) );
GLFp := Group([[[ Z(5)^0, Z(5)^0 ], [ 0*Z(5), Z(5)^0 ]], [[ Z(5)^0, 0*Z(5) ], [ 0*Z(5), Z(5) ]], [[ Z(5)^0, 0*Z(5) ], [ Z(5)^0, Z(5)^0 ]]]);

 
# Booleans 
booleans_480_218 := rec( 
Agroup := false,
Zgroup := false,
abelian := false,
almost_simple := false,
cyclic := false,
metabelian := false,
metacyclic := false,
monomial := false,
nilpotent := false,
perfect := false,
quasisimple := false,
rational := false,
solvable := false,
supersolvable := false); 

 
# Character Table 
chartbl_480_218:=rec(); 
chartbl_480_218.IsFinite:= true; 
chartbl_480_218.UnderlyingCharacteristic:= 0; 
chartbl_480_218.Size:= 480;
chartbl_480_218.InfoText:= "Character table for group 480.218 downloaded from the LMFDB."; 
chartbl_480_218.Identifier:= " GL(2,5) "; 
chartbl_480_218.NrConjugacyClasses:= 24; 
chartbl_480_218.ConjugacyClasses:= [[1, 0, 0, 1], [4, 0, 0, 4], [1, 3, 0, 4], [1, 1, 2, 3], [3, 0, 0, 3], [2, 0, 0, 2], [2, 0, 0, 3], [1, 2, 0, 3], [1, 1, 0, 2], [2, 0, 1, 4], [3, 0, 3, 4], [1, 0, 2, 1], [2, 1, 2, 4], [4, 1, 2, 1], [3, 2, 4, 2], [4, 0, 4, 4], [2, 2, 4, 1], [4, 2, 4, 3], [2, 0, 1, 2], [3, 0, 1, 3], [0, 1, 2, 2], [0, 1, 3, 4], [0, 1, 3, 1], [0, 1, 2, 3]];
chartbl_480_218.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];
chartbl_480_218.ComputedPowerMaps:= [ , [1, 1, 1, 4, 2, 2, 2, 3, 3, 3, 3, 12, 4, 5, 6, 12, 13, 13, 16, 16, 17, 18, 18, 17], [1, 2, 3, 1, 6, 5, 7, 9, 8, 11, 10, 12, 2, 15, 14, 16, 5, 6, 20, 19, 14, 15, 15, 14], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 1, 13, 14, 15, 2, 17, 18, 6, 5, 21, 22, 23, 24]];
chartbl_480_218.SizesCentralizers:= [480, 480, 16, 24, 480, 480, 16, 16, 16, 16, 16, 20, 24, 24, 24, 20, 24, 24, 20, 20, 24, 24, 24, 24];
chartbl_480_218.ClassNames:= ["1A", "2A", "2B", "3A", "4A1", "4A-1", "4B", "4C1", "4C-1", "4D1", "4D-1", "5A", "6A", "8A1", "8A-1", "10A", "12A1", "12A-1", "20A1", "20A-1", "24A1", "24A-1", "24A7", "24A-7"];
chartbl_480_218.OrderClassRepresentatives:= [1, 2, 2, 3, 4, 4, 4, 4, 4, 4, 4, 5, 6, 8, 8, 10, 12, 12, 20, 20, 24, 24, 24, 24];
chartbl_480_218.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*E(4), E(4), E(4), -1*E(4), 1, 1, 1, E(4), -1*E(4), 1, -1, -1, -1, -1, E(4), -1*E(4), -1*E(4), E(4)], [1, 1, -1, 1, -1, -1, E(4), -1*E(4), -1*E(4), E(4), 1, 1, 1, -1*E(4), E(4), 1, -1, -1, -1, -1, -1*E(4), E(4), E(4), -1*E(4)], [4, 4, 0, 1, 4, 4, 0, 0, 0, 0, 0, -1, 1, 2, 2, -1, 1, 1, -1, -1, -1, -1, -1, -1], [4, 4, 0, 1, 4, 4, 0, 0, 0, 0, 0, -1, 1, -2, -2, -1, 1, 1, -1, -1, 1, 1, 1, 1], [4, 4, 0, 1, -4, -4, 0, 0, 0, 0, 0, -1, 1, -2*E(4), 2*E(4), -1, -1, -1, 1, 1, E(4), -1*E(4), -1*E(4), E(4)], [4, 4, 0, 1, -4, -4, 0, 0, 0, 0, 0, -1, 1, 2*E(4), -2*E(4), -1, -1, -1, 1, 1, -1*E(4), E(4), E(4), -1*E(4)], [4, -4, 0, -2, -4*E(4), 4*E(4), 0, 0, 0, 0, 0, -1, 2, 0, 0, 1, -2*E(4), 2*E(4), -1*E(4), E(4), 0, 0, 0, 0], [4, -4, 0, -2, 4*E(4), -4*E(4), 0, 0, 0, 0, 0, -1, 2, 0, 0, 1, 2*E(4), -2*E(4), E(4), -1*E(4), 0, 0, 0, 0], [4, -4, 0, 1, -4*E(24)^6, 4*E(24)^6, 0, 0, 0, 0, 0, -1, -1, 0, 0, 1, E(24)^6, -1*E(24)^6, -1*E(24)^6, E(24)^6, -1*E(24)-E(24)^5, -1*E(24)^3+2*E(24)^7, E(24)^3-2*E(24)^7, E(24)+E(24)^5], [4, -4, 0, 1, 4*E(24)^6, -4*E(24)^6, 0, 0, 0, 0, 0, -1, -1, 0, 0, 1, -1*E(24)^6, E(24)^6, E(24)^6, -1*E(24)^6, -1*E(24)^3+2*E(24)^7, -1*E(24)-E(24)^5, E(24)+E(24)^5, E(24)^3-2*E(24)^7], [4, -4, 0, 1, -4*E(24)^6, 4*E(24)^6, 0, 0, 0, 0, 0, -1, -1, 0, 0, 1, E(24)^6, -1*E(24)^6, -1*E(24)^6, E(24)^6, E(24)+E(24)^5, E(24)^3-2*E(24)^7, -1*E(24)^3+2*E(24)^7, -1*E(24)-E(24)^5], [4, -4, 0, 1, 4*E(24)^6, -4*E(24)^6, 0, 0, 0, 0, 0, -1, -1, 0, 0, 1, -1*E(24)^6, E(24)^6, E(24)^6, -1*E(24)^6, E(24)^3-2*E(24)^7, E(24)+E(24)^5, -1*E(24)-E(24)^5, -1*E(24)^3+2*E(24)^7], [5, 5, 1, -1, 5, 5, 1, 1, 1, 1, 1, 0, -1, -1, -1, 0, -1, -1, 0, 0, -1, -1, -1, -1], [5, 5, 1, -1, 5, 5, -1, -1, -1, -1, 1, 0, -1, 1, 1, 0, -1, -1, 0, 0, 1, 1, 1, 1], [5, 5, -1, -1, -5, -5, -1*E(4), E(4), E(4), -1*E(4), 1, 0, -1, -1*E(4), E(4), 0, 1, 1, 0, 0, -1*E(4), E(4), E(4), -1*E(4)], [5, 5, -1, -1, -5, -5, E(4), -1*E(4), -1*E(4), E(4), 1, 0, -1, E(4), -1*E(4), 0, 1, 1, 0, 0, E(4), -1*E(4), -1*E(4), E(4)], [6, 6, 2, 0, -6, -6, 0, 0, 0, 0, -2, 1, 0, 0, 0, 1, 0, 0, -1, -1, 0, 0, 0, 0], [6, 6, -2, 0, 6, 6, 0, 0, 0, 0, -2, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0], [6, -6, 0, 0, -6*E(4), 6*E(4), -1+E(4), 1+E(4), -1-E(4), 1-E(4), 0, 1, 0, 0, 0, -1, 0, 0, E(4), -1*E(4), 0, 0, 0, 0], [6, -6, 0, 0, 6*E(4), -6*E(4), -1-E(4), 1-E(4), -1+E(4), 1+E(4), 0, 1, 0, 0, 0, -1, 0, 0, -1*E(4), E(4), 0, 0, 0, 0], [6, -6, 0, 0, -6*E(4), 6*E(4), 1-E(4), -1-E(4), 1+E(4), -1+E(4), 0, 1, 0, 0, 0, -1, 0, 0, E(4), -1*E(4), 0, 0, 0, 0], [6, -6, 0, 0, 6*E(4), -6*E(4), 1+E(4), -1+E(4), 1-E(4), -1-E(4), 0, 1, 0, 0, 0, -1, 0, 0, -1*E(4), E(4), 0, 0, 0, 0]];
ConvertToLibraryCharacterTableNC(chartbl_480_218);