# Group 240.90 downloaded from the LMFDB on 14 September 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 
GPerm := Group( (1,30,35,33,22,21,11,6)(2,12,13,19,18,25,14,7)(3,29,38,34,23,26,15,8)(4,36,37,31,24,27,16,9)(5,40,39,32,20,28,17,10), (1,35,22,11)(2,33,18,6)(3,25,23,12)(4,14,24,13)(5,32,20,10)(7,34,19,8)(9,39,31,17)(15,26,38,29)(16,21,37,30)(27,40,36,28) );
GLFp := Group([[[ Z(3), 0*Z(3), Z(3)^0, Z(3) ], [ 0*Z(3), Z(3), Z(3)^0, 0*Z(3) ], [ Z(3), Z(3), Z(3), Z(3)^0 ], [ 0*Z(3), 0*Z(3), Z(3)^0, 0*Z(3) ]], [[ Z(3), 0*Z(3), 0*Z(3), 0*Z(3) ], [ 0*Z(3), Z(3), 0*Z(3), 0*Z(3) ], [ 0*Z(3), 0*Z(3), Z(3), 0*Z(3) ], [ 0*Z(3), 0*Z(3), 0*Z(3), Z(3) ]], [[ Z(3), 0*Z(3), 0*Z(3), 0*Z(3) ], [ Z(3)^0, Z(3)^0, 0*Z(3), 0*Z(3) ], [ 0*Z(3), 0*Z(3), Z(3)^0, 0*Z(3) ], [ Z(3), Z(3)^0, Z(3), Z(3) ]]]);

 
# Booleans 
booleans_240_90 := 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_240_90:=rec(); 
chartbl_240_90.IsFinite:= true; 
chartbl_240_90.UnderlyingCharacteristic:= 0; 
chartbl_240_90.UnderlyingGroup:= GLFp;
chartbl_240_90.Size:= 240;
chartbl_240_90.InfoText:= "Character table for group 240.90 downloaded from the LMFDB."; 
chartbl_240_90.Identifier:= " SL(2,5):C2 "; 
chartbl_240_90.NrConjugacyClasses:= 12; 
chartbl_240_90.ConjugacyClasses:= [[1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1], [2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2], [0, 0, 1, 0, 1, 2, 2, 2, 1, 0, 0, 0, 1, 0, 2, 1], [0, 1, 1, 0, 0, 0, 0, 1, 2, 2, 2, 2, 0, 2, 0, 2], [0, 2, 0, 1, 0, 2, 2, 2, 1, 0, 2, 2, 2, 2, 2, 2], [2, 2, 2, 1, 2, 2, 1, 0, 2, 0, 1, 2, 0, 0, 1, 0], [0, 2, 1, 0, 0, 2, 0, 1, 2, 1, 1, 1, 0, 0, 0, 2], [1, 1, 0, 1, 1, 1, 2, 0, 2, 2, 2, 0, 1, 2, 2, 2], [2, 2, 2, 2, 1, 0, 2, 1, 0, 1, 1, 0, 1, 1, 2, 0], [0, 1, 0, 1, 2, 2, 1, 0, 2, 2, 0, 0, 1, 0, 2, 1], [1, 2, 2, 2, 2, 1, 0, 1, 0, 1, 2, 0, 2, 2, 0, 2], [2, 2, 1, 0, 1, 0, 0, 0, 2, 1, 0, 1, 0, 2, 2, 2]];
chartbl_240_90.IdentificationOfConjugacyClasses:= [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12];
chartbl_240_90.ComputedPowerMaps:= [ , [1, 1, 1, 4, 2, 6, 4, 4, 4, 5, 5, 6], [1, 2, 3, 1, 5, 6, 2, 3, 3, 10, 11, 12], [1, 2, 3, 4, 5, 1, 7, 9, 8, 11, 10, 2]];
chartbl_240_90.SizesCentralizers:= [240, 240, 12, 12, 8, 10, 12, 12, 12, 8, 8, 10];
chartbl_240_90.ClassNames:= ["1A", "2A", "2B", "3A", "4A", "5A", "6A", "6B1", "6B-1", "8A1", "8A-1", "10A"];
chartbl_240_90.OrderClassRepresentatives:= [1, 2, 2, 3, 4, 5, 6, 6, 6, 8, 8, 10];
chartbl_240_90.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], [4, 4, 2, 1, 0, -1, 1, -1, -1, 0, 0, -1], [4, 4, -2, 1, 0, -1, 1, 1, 1, 0, 0, -1], [4, -4, 0, -2, 0, -1, 2, 0, 0, 0, 0, 1], [4, -4, 0, 1, 0, -1, -1, -1-2*E(3), 1+2*E(3), 0, 0, 1], [4, -4, 0, 1, 0, -1, -1, 1+2*E(3), -1-2*E(3), 0, 0, 1], [5, 5, -1, -1, 1, 0, -1, -1, -1, 1, 1, 0], [5, 5, 1, -1, 1, 0, -1, 1, 1, -1, -1, 0], [6, 6, 0, 0, -2, 1, 0, 0, 0, 0, 0, 1], [6, -6, 0, 0, 0, 1, 0, 0, 0, -1*E(8)-E(8)^3, E(8)+E(8)^3, -1], [6, -6, 0, 0, 0, 1, 0, 0, 0, E(8)+E(8)^3, -1*E(8)-E(8)^3, -1]];
ConvertToLibraryCharacterTableNC(chartbl_240_90);