# Group 100.10 downloaded from the LMFDB on 15 June 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 
GPC := PcGroupCode(1970081001743,100); a := GPC.1; b := GPC.3; c := GPC.4;
GPerm := Group( (2,3,4,5)(7,8)(9,10), (2,4)(3,5), (6,7,9,10,8), (1,2,5,3,4) );
GLFp := Group([[[ Z(5)^2, Z(5)^3, Z(5)^2 ], [ 0*Z(5), 0*Z(5), Z(5)^3 ], [ Z(5), Z(5)^0, 0*Z(5) ]], [[ Z(5)^2, Z(5)^0, 0*Z(5) ], [ Z(5)^0, Z(5)^3, 0*Z(5) ], [ Z(5)^3, Z(5)^0, Z(5)^0 ]], [[ Z(5)^2, 0*Z(5), Z(5)^3 ], [ Z(5), Z(5)^3, Z(5)^0 ], [ Z(5)^2, Z(5), Z(5)^2 ]], [[ Z(5)^2, Z(5)^3, Z(5)^0 ], [ Z(5)^0, Z(5), Z(5) ], [ Z(5)^2, 0*Z(5), Z(5) ]]]);

 
# Booleans 
booleans_100_10 := 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_100_10:=rec(); 
chartbl_100_10.IsFinite:= true; 
chartbl_100_10.UnderlyingCharacteristic:= 0; 
chartbl_100_10.UnderlyingGroup:= GPC;
chartbl_100_10.Size:= 100;
chartbl_100_10.InfoText:= "Character table for group 100.10 downloaded from the LMFDB."; 
chartbl_100_10.Identifier:= " C5:F5 "; 
chartbl_100_10.NrConjugacyClasses:= 13; 
chartbl_100_10.ConjugacyClasses:= [<identity> of ..., f2, f1*f3^4*f4^4, f1*f2*f3^3*f4^4, f4^2, f4^4, f3, f3*f4, f3^2*f4, f3*f4^3, f3*f4^2, f2*f4, f2*f4^2];
chartbl_100_10.IdentificationOfConjugacyClasses:= [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13];
chartbl_100_10.ComputedPowerMaps:= [ , [1, 1, 2, 2, 6, 5, 7, 10, 11, 9, 8, 5, 6], [1, 2, 3, 4, 1, 1, 1, 1, 1, 1, 1, 2, 2]];
chartbl_100_10.SizesCentralizers:= [100, 20, 4, 4, 50, 50, 25, 25, 25, 25, 25, 10, 10];
chartbl_100_10.ClassNames:= ["1A", "2A", "4A1", "4A-1", "5A1", "5A2", "5B", "5C1", "5C-1", "5C2", "5C-2", "10A1", "10A3"];
chartbl_100_10.OrderClassRepresentatives:= [1, 2, 4, 4, 5, 5, 5, 5, 5, 5, 5, 10, 10];
chartbl_100_10.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*E(4), E(4), 1, 1, 1, 1, 1, 1, 1, -1, -1], [1, -1, E(4), -1*E(4), 1, 1, 1, 1, 1, 1, 1, -1, -1], [2, 2, 0, 0, E(5)^2+E(5)^-2, E(5)+E(5)^-1, E(5)+E(5)^-1, E(5)^2+E(5)^-2, 2, E(5)^2+E(5)^-2, E(5)+E(5)^-1, E(5)+E(5)^-1, E(5)^2+E(5)^-2], [2, 2, 0, 0, E(5)+E(5)^-1, E(5)^2+E(5)^-2, E(5)^2+E(5)^-2, E(5)+E(5)^-1, 2, E(5)+E(5)^-1, E(5)^2+E(5)^-2, E(5)^2+E(5)^-2, E(5)+E(5)^-1], [2, -2, 0, 0, E(5)^2+E(5)^-2, E(5)+E(5)^-1, E(5)+E(5)^-1, E(5)^2+E(5)^-2, 2, E(5)^2+E(5)^-2, E(5)+E(5)^-1, -1*E(5)-E(5)^-1, -1*E(5)^2-E(5)^-2], [2, -2, 0, 0, E(5)+E(5)^-1, E(5)^2+E(5)^-2, E(5)^2+E(5)^-2, E(5)+E(5)^-1, 2, E(5)+E(5)^-1, E(5)^2+E(5)^-2, -1*E(5)^2-E(5)^-2, -1*E(5)-E(5)^-1], [4, 0, 0, 0, 4, 4, -1, -1, -1, -1, -1, 0, 0], [4, 0, 0, 0, 2*E(5)^2+2*E(5)^-2, 2*E(5)+2*E(5)^-1, -1*E(5)-E(5)^2+E(5)^-2, 1+2*E(5)+E(5)^-2, -1, -1-2*E(5)-E(5)^2-2*E(5)^-2, 1+E(5)+2*E(5)^2, 0, 0], [4, 0, 0, 0, 2*E(5)^2+2*E(5)^-2, 2*E(5)+2*E(5)^-1, 1+E(5)+2*E(5)^2, -1-2*E(5)-E(5)^2-2*E(5)^-2, -1, 1+2*E(5)+E(5)^-2, -1*E(5)-E(5)^2+E(5)^-2, 0, 0], [4, 0, 0, 0, 2*E(5)+2*E(5)^-1, 2*E(5)^2+2*E(5)^-2, -1-2*E(5)-E(5)^2-2*E(5)^-2, -1*E(5)-E(5)^2+E(5)^-2, -1, 1+E(5)+2*E(5)^2, 1+2*E(5)+E(5)^-2, 0, 0], [4, 0, 0, 0, 2*E(5)+2*E(5)^-1, 2*E(5)^2+2*E(5)^-2, 1+2*E(5)+E(5)^-2, 1+E(5)+2*E(5)^2, -1, -1*E(5)-E(5)^2+E(5)^-2, -1-2*E(5)-E(5)^2-2*E(5)^-2, 0, 0]];
ConvertToLibraryCharacterTableNC(chartbl_100_10);