# Group 300.40 downloaded from the LMFDB on 26 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 GPC := PcGroupCode(11117729194051009293051959,300); a := GPC.1; b := GPC.2; c := GPC.4; GPerm := Group( (2,3)(4,5)(7,8), (2,3)(4,5)(10,11)(12,13), (6,7,8), (1,2,4,5,3), (9,10,12,13,11) ); GLFp := Group([[[ Z(5)^3, Z(5)^3, Z(5)^0, Z(5)^3 ], [ Z(5)^0, Z(5)^2, 0*Z(5), Z(5)^2 ], [ Z(5)^3, Z(5)^2, Z(5)^0, Z(5) ], [ 0*Z(5), Z(5), Z(5)^0, Z(5)^0 ]], [[ 0*Z(5), Z(5), 0*Z(5), Z(5)^0 ], [ Z(5)^3, Z(5)^0, Z(5)^3, Z(5) ], [ Z(5)^2, 0*Z(5), 0*Z(5), Z(5)^0 ], [ Z(5)^3, Z(5), Z(5)^2, Z(5)^3 ]], [[ Z(5)^3, 0*Z(5), Z(5), Z(5)^3 ], [ Z(5), Z(5)^2, Z(5)^0, Z(5)^3 ], [ Z(5)^0, 0*Z(5), Z(5), Z(5)^2 ], [ 0*Z(5), 0*Z(5), 0*Z(5), Z(5)^0 ]], [[ Z(5), Z(5)^0, Z(5)^3, Z(5) ], [ Z(5)^2, Z(5)^0, Z(5)^2, Z(5)^0 ], [ 0*Z(5), Z(5)^2, Z(5)^3, 0*Z(5) ], [ 0*Z(5), Z(5), 0*Z(5), Z(5)^2 ]], [[ 0*Z(5), Z(5), 0*Z(5), Z(5)^3 ], [ Z(5)^2, 0*Z(5), Z(5)^2, Z(5)^3 ], [ 0*Z(5), Z(5)^0, Z(5)^3, Z(5)^0 ], [ Z(5), Z(5)^0, Z(5)^2, Z(5) ]]]); # Booleans booleans_300_40 := 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_300_40:=rec(); chartbl_300_40.IsFinite:= true; chartbl_300_40.UnderlyingCharacteristic:= 0; chartbl_300_40.UnderlyingGroup:= GPC; chartbl_300_40.Size:= 300; chartbl_300_40.InfoText:= "Character table for group 300.40 downloaded from the LMFDB."; chartbl_300_40.Identifier:= " C15:D10 "; chartbl_300_40.NrConjugacyClasses:= 30; chartbl_300_40.ConjugacyClasses:= [ of ..., f2*f3^2*f4*f5^2, f1*f2, f1*f3^4*f5^3, f4^2*f5, f5, f5^2, f3^3, f3, f3^3*f5, f3*f5^2, f3^3*f5^2, f3*f5^4, f1*f3^4*f4^2*f5^4, f2*f3*f4*f5^2, f2*f3^4*f4*f5^2, f1*f2*f5^3, f1*f2*f5^4, f4, f4^2, f3*f4^2*f5, f3^2*f4^2*f5, f3*f4, f3^4*f4, f3^2*f4^2, f3^3*f4^2, f3*f4^2, f3^4*f4^2, f3^3*f4, f3^2*f4]; chartbl_300_40.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]; chartbl_300_40.ComputedPowerMaps:= [ , [1, 1, 1, 1, 5, 7, 6, 9, 8, 11, 10, 13, 12, 5, 8, 9, 6, 7, 20, 19, 22, 21, 25, 26, 23, 24, 29, 30, 27, 28], [1, 2, 3, 4, 1, 7, 6, 9, 8, 11, 10, 13, 12, 4, 16, 15, 18, 17, 6, 7, 8, 9, 10, 10, 11, 11, 12, 12, 13, 13], [1, 2, 3, 4, 5, 1, 1, 1, 1, 1, 1, 1, 1, 14, 2, 2, 3, 3, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]]; chartbl_300_40.SizesCentralizers:= [300, 20, 20, 12, 150, 150, 150, 150, 150, 75, 75, 75, 75, 6, 10, 10, 10, 10, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75]; chartbl_300_40.ClassNames:= ["1A", "2A", "2B", "2C", "3A", "5A1", "5A2", "5B1", "5B2", "5C1", "5C2", "5D1", "5D2", "6A", "10A1", "10A3", "10B1", "10B3", "15A1", "15A2", "15B1", "15B2", "15C1", "15C-1", "15C2", "15C-2", "15D1", "15D-1", "15D2", "15D-2"]; chartbl_300_40.OrderClassRepresentatives:= [1, 2, 2, 2, 3, 5, 5, 5, 5, 5, 5, 5, 5, 6, 10, 10, 10, 10, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15]; chartbl_300_40.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], [2, 0, 0, 2, -1, 2, 2, 2, 2, 2, 2, 2, 2, -1, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [2, 0, 0, -2, -1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [2, 0, 2, 0, 2, E(5)^2+E(5)^-2, 2, E(5)+E(5)^-1, 2, E(5)+E(5)^-1, E(5)^2+E(5)^-2, E(5)+E(5)^-1, E(5)^2+E(5)^-2, 0, 0, 0, E(5)^2+E(5)^-2, E(5)+E(5)^-1, E(5)^2+E(5)^-2, E(5)+E(5)^-1, E(5)+E(5)^-1, E(5)^2+E(5)^-2, E(5)+E(5)^-1, E(5)+E(5)^-1, E(5)+E(5)^-1, 2, E(5)^2+E(5)^-2, 2, E(5)^2+E(5)^-2, E(5)^2+E(5)^-2], [2, 0, 2, 0, 2, E(5)+E(5)^-1, 2, E(5)^2+E(5)^-2, 2, E(5)^2+E(5)^-2, E(5)+E(5)^-1, E(5)^2+E(5)^-2, E(5)+E(5)^-1, 0, 0, 0, E(5)+E(5)^-1, E(5)^2+E(5)^-2, E(5)+E(5)^-1, E(5)^2+E(5)^-2, E(5)^2+E(5)^-2, E(5)+E(5)^-1, E(5)^2+E(5)^-2, E(5)^2+E(5)^-2, E(5)^2+E(5)^-2, 2, E(5)+E(5)^-1, 2, E(5)+E(5)^-1, E(5)+E(5)^-1], [2, 2, 0, 0, 2, 2, E(5)^2+E(5)^-2, 2, E(5)+E(5)^-1, E(5)^2+E(5)^-2, E(5)^2+E(5)^-2, E(5)+E(5)^-1, E(5)+E(5)^-1, 0, E(5)+E(5)^-1, E(5)^2+E(5)^-2, 0, 0, E(5)+E(5)^-1, E(5)+E(5)^-1, E(5)+E(5)^-1, E(5)+E(5)^-1, E(5)^2+E(5)^-2, E(5)^2+E(5)^-2, 2, E(5)+E(5)^-1, 2, E(5)^2+E(5)^-2, E(5)^2+E(5)^-2, E(5)^2+E(5)^-2], [2, 2, 0, 0, 2, 2, E(5)+E(5)^-1, 2, E(5)^2+E(5)^-2, E(5)+E(5)^-1, E(5)+E(5)^-1, E(5)^2+E(5)^-2, E(5)^2+E(5)^-2, 0, E(5)^2+E(5)^-2, E(5)+E(5)^-1, 0, 0, E(5)^2+E(5)^-2, E(5)^2+E(5)^-2, E(5)^2+E(5)^-2, E(5)^2+E(5)^-2, E(5)+E(5)^-1, E(5)+E(5)^-1, 2, E(5)^2+E(5)^-2, 2, E(5)+E(5)^-1, E(5)+E(5)^-1, E(5)+E(5)^-1], [2, -2, 0, 0, 2, 2, E(5)^2+E(5)^-2, 2, E(5)+E(5)^-1, E(5)^2+E(5)^-2, E(5)^2+E(5)^-2, E(5)+E(5)^-1, E(5)+E(5)^-1, 0, -1*E(5)-E(5)^-1, -1*E(5)^2-E(5)^-2, 0, 0, E(5)+E(5)^-1, E(5)+E(5)^-1, E(5)+E(5)^-1, E(5)+E(5)^-1, E(5)^2+E(5)^-2, E(5)^2+E(5)^-2, 2, E(5)+E(5)^-1, 2, E(5)^2+E(5)^-2, E(5)^2+E(5)^-2, E(5)^2+E(5)^-2], [2, -2, 0, 0, 2, 2, E(5)+E(5)^-1, 2, E(5)^2+E(5)^-2, E(5)+E(5)^-1, E(5)+E(5)^-1, E(5)^2+E(5)^-2, E(5)^2+E(5)^-2, 0, -1*E(5)^2-E(5)^-2, -1*E(5)-E(5)^-1, 0, 0, E(5)^2+E(5)^-2, E(5)^2+E(5)^-2, E(5)^2+E(5)^-2, E(5)^2+E(5)^-2, E(5)+E(5)^-1, E(5)+E(5)^-1, 2, E(5)^2+E(5)^-2, 2, E(5)+E(5)^-1, E(5)+E(5)^-1, E(5)+E(5)^-1], [2, 0, -2, 0, 2, E(5)^2+E(5)^-2, 2, E(5)+E(5)^-1, 2, E(5)+E(5)^-1, E(5)^2+E(5)^-2, E(5)+E(5)^-1, E(5)^2+E(5)^-2, 0, 0, 0, -1*E(5)^2-E(5)^-2, -1*E(5)-E(5)^-1, E(5)^2+E(5)^-2, E(5)+E(5)^-1, E(5)+E(5)^-1, E(5)^2+E(5)^-2, E(5)+E(5)^-1, E(5)+E(5)^-1, E(5)+E(5)^-1, 2, E(5)^2+E(5)^-2, 2, E(5)^2+E(5)^-2, E(5)^2+E(5)^-2], [2, 0, -2, 0, 2, E(5)+E(5)^-1, 2, E(5)^2+E(5)^-2, 2, E(5)^2+E(5)^-2, E(5)+E(5)^-1, E(5)^2+E(5)^-2, E(5)+E(5)^-1, 0, 0, 0, -1*E(5)-E(5)^-1, -1*E(5)^2-E(5)^-2, E(5)+E(5)^-1, E(5)^2+E(5)^-2, E(5)^2+E(5)^-2, E(5)+E(5)^-1, E(5)^2+E(5)^-2, E(5)^2+E(5)^-2, E(5)^2+E(5)^-2, 2, E(5)+E(5)^-1, 2, E(5)+E(5)^-1, E(5)+E(5)^-1], [4, 0, 0, 0, 4, 2*E(5)^2+2*E(5)^-2, 2*E(5)^2+2*E(5)^-2, 2*E(5)+2*E(5)^-1, 2*E(5)+2*E(5)^-1, -1, 1-E(5)^2-E(5)^-2, 2+E(5)^2+E(5)^-2, -1, 0, 0, 0, 0, 0, -1, 2+E(5)^2+E(5)^-2, 2+E(5)^2+E(5)^-2, -1, -1, -1, 2*E(5)+2*E(5)^-1, 2*E(5)+2*E(5)^-1, 2*E(5)^2+2*E(5)^-2, 2*E(5)^2+2*E(5)^-2, 1-E(5)^2-E(5)^-2, 1-E(5)^2-E(5)^-2], [4, 0, 0, 0, 4, 2*E(5)+2*E(5)^-1, 2*E(5)+2*E(5)^-1, 2*E(5)^2+2*E(5)^-2, 2*E(5)^2+2*E(5)^-2, -1, 2+E(5)^2+E(5)^-2, 1-E(5)^2-E(5)^-2, -1, 0, 0, 0, 0, 0, -1, 1-E(5)^2-E(5)^-2, 1-E(5)^2-E(5)^-2, -1, -1, -1, 2*E(5)^2+2*E(5)^-2, 2*E(5)^2+2*E(5)^-2, 2*E(5)+2*E(5)^-1, 2*E(5)+2*E(5)^-1, 2+E(5)^2+E(5)^-2, 2+E(5)^2+E(5)^-2], [4, 0, 0, 0, 4, 2*E(5)^2+2*E(5)^-2, 2*E(5)+2*E(5)^-1, 2*E(5)+2*E(5)^-1, 2*E(5)^2+2*E(5)^-2, 2+E(5)^2+E(5)^-2, -1, -1, 1-E(5)^2-E(5)^-2, 0, 0, 0, 0, 0, 1-E(5)^2-E(5)^-2, -1, -1, 1-E(5)^2-E(5)^-2, 2+E(5)^2+E(5)^-2, 2+E(5)^2+E(5)^-2, 2*E(5)+2*E(5)^-1, 2*E(5)^2+2*E(5)^-2, 2*E(5)^2+2*E(5)^-2, 2*E(5)+2*E(5)^-1, -1, -1], [4, 0, 0, 0, 4, 2*E(5)+2*E(5)^-1, 2*E(5)^2+2*E(5)^-2, 2*E(5)^2+2*E(5)^-2, 2*E(5)+2*E(5)^-1, 1-E(5)^2-E(5)^-2, -1, -1, 2+E(5)^2+E(5)^-2, 0, 0, 0, 0, 0, 2+E(5)^2+E(5)^-2, -1, -1, 2+E(5)^2+E(5)^-2, 1-E(5)^2-E(5)^-2, 1-E(5)^2-E(5)^-2, 2*E(5)^2+2*E(5)^-2, 2*E(5)+2*E(5)^-1, 2*E(5)+2*E(5)^-1, 2*E(5)^2+2*E(5)^-2, -1, -1], [4, 0, 0, 0, -2, 2*E(5)^2+2*E(5)^-2, 4, 2*E(5)+2*E(5)^-1, 4, 2*E(5)+2*E(5)^-1, 2*E(5)^2+2*E(5)^-2, 2*E(5)+2*E(5)^-1, 2*E(5)^2+2*E(5)^-2, 0, 0, 0, 0, 0, -1*E(5)^2-E(5)^-2, -1*E(5)-E(5)^-1, -1*E(5)-E(5)^-1, -1*E(5)^2-E(5)^-2, -1*E(5)-E(5)^-1, -1*E(5)-E(5)^-1, -1*E(5)-E(5)^-1, -2, -1*E(5)^2-E(5)^-2, -2, -1*E(5)^2-E(5)^-2, -1*E(5)^2-E(5)^-2], [4, 0, 0, 0, -2, 2*E(5)+2*E(5)^-1, 4, 2*E(5)^2+2*E(5)^-2, 4, 2*E(5)^2+2*E(5)^-2, 2*E(5)+2*E(5)^-1, 2*E(5)^2+2*E(5)^-2, 2*E(5)+2*E(5)^-1, 0, 0, 0, 0, 0, -1*E(5)-E(5)^-1, -1*E(5)^2-E(5)^-2, -1*E(5)^2-E(5)^-2, -1*E(5)-E(5)^-1, -1*E(5)^2-E(5)^-2, -1*E(5)^2-E(5)^-2, -1*E(5)^2-E(5)^-2, -2, -1*E(5)-E(5)^-1, -2, -1*E(5)-E(5)^-1, -1*E(5)-E(5)^-1], [4, 0, 0, 0, -2, 4, 2*E(5)^2+2*E(5)^-2, 4, 2*E(5)+2*E(5)^-1, 2*E(5)^2+2*E(5)^-2, 2*E(5)^2+2*E(5)^-2, 2*E(5)+2*E(5)^-1, 2*E(5)+2*E(5)^-1, 0, 0, 0, 0, 0, -1*E(5)-E(5)^-1, -1*E(5)-E(5)^-1, -1*E(5)-E(5)^-1, -1*E(5)-E(5)^-1, -1*E(5)^2-E(5)^-2, -1*E(5)^2-E(5)^-2, -2, -1*E(5)-E(5)^-1, -2, -1*E(5)^2-E(5)^-2, -1*E(5)^2-E(5)^-2, -1*E(5)^2-E(5)^-2], [4, 0, 0, 0, -2, 4, 2*E(5)+2*E(5)^-1, 4, 2*E(5)^2+2*E(5)^-2, 2*E(5)+2*E(5)^-1, 2*E(5)+2*E(5)^-1, 2*E(5)^2+2*E(5)^-2, 2*E(5)^2+2*E(5)^-2, 0, 0, 0, 0, 0, -1*E(5)^2-E(5)^-2, -1*E(5)^2-E(5)^-2, -1*E(5)^2-E(5)^-2, -1*E(5)^2-E(5)^-2, -1*E(5)-E(5)^-1, -1*E(5)-E(5)^-1, -2, -1*E(5)^2-E(5)^-2, -2, -1*E(5)-E(5)^-1, -1*E(5)-E(5)^-1, -1*E(5)-E(5)^-1], [4, 0, 0, 0, -2, 2*E(15)^6+2*E(15)^-6, 2*E(15)^6+2*E(15)^-6, 2*E(15)^3+2*E(15)^-3, 2*E(15)^3+2*E(15)^-3, -1, 2-E(15)^2+E(15)^3-E(15)^7, 1+E(15)^2-E(15)^3+E(15)^7, -1, 0, 0, 0, 0, 0, 2-2*E(15)-E(15)^2+E(15)^3-2*E(15)^4+E(15)^5-E(15)^7, -1-E(15)-E(15)^2+E(15)^3-E(15)^4-2*E(15)^5-E(15)^7, E(15)+E(15)^4+2*E(15)^5, -1+2*E(15)+E(15)^2-E(15)^3+2*E(15)^4-E(15)^5+E(15)^7, -1+2*E(15)+E(15)^2-E(15)^3+2*E(15)^4-E(15)^5+E(15)^7, 2-2*E(15)-E(15)^2+E(15)^3-2*E(15)^4+E(15)^5-E(15)^7, -1*E(15)^3-E(15)^-3, -1*E(15)^3-E(15)^-3, -1*E(15)^6-E(15)^-6, -1*E(15)^6-E(15)^-6, -3+E(15)+E(15)^2-E(15)^3+E(15)^4-3*E(15)^5+E(15)^7, 1-E(15)-E(15)^4+3*E(15)^5], [4, 0, 0, 0, -2, 2*E(15)^6+2*E(15)^-6, 2*E(15)^6+2*E(15)^-6, 2*E(15)^3+2*E(15)^-3, 2*E(15)^3+2*E(15)^-3, -1, 2-E(15)^2+E(15)^3-E(15)^7, 1+E(15)^2-E(15)^3+E(15)^7, -1, 0, 0, 0, 0, 0, -1+2*E(15)+E(15)^2-E(15)^3+2*E(15)^4-E(15)^5+E(15)^7, E(15)+E(15)^4+2*E(15)^5, -1-E(15)-E(15)^2+E(15)^3-E(15)^4-2*E(15)^5-E(15)^7, 2-2*E(15)-E(15)^2+E(15)^3-2*E(15)^4+E(15)^5-E(15)^7, 2-2*E(15)-E(15)^2+E(15)^3-2*E(15)^4+E(15)^5-E(15)^7, -1+2*E(15)+E(15)^2-E(15)^3+2*E(15)^4-E(15)^5+E(15)^7, -1*E(15)^3-E(15)^-3, -1*E(15)^3-E(15)^-3, -1*E(15)^6-E(15)^-6, -1*E(15)^6-E(15)^-6, 1-E(15)-E(15)^4+3*E(15)^5, -3+E(15)+E(15)^2-E(15)^3+E(15)^4-3*E(15)^5+E(15)^7], [4, 0, 0, 0, -2, 2*E(15)^3+2*E(15)^-3, 2*E(15)^3+2*E(15)^-3, 2*E(15)^6+2*E(15)^-6, 2*E(15)^6+2*E(15)^-6, -1, 1+E(15)^2-E(15)^3+E(15)^7, 2-E(15)^2+E(15)^3-E(15)^7, -1, 0, 0, 0, 0, 0, 2-2*E(15)-E(15)^2+E(15)^3-2*E(15)^4+E(15)^5-E(15)^7, 1-E(15)-E(15)^4+3*E(15)^5, -3+E(15)+E(15)^2-E(15)^3+E(15)^4-3*E(15)^5+E(15)^7, -1+2*E(15)+E(15)^2-E(15)^3+2*E(15)^4-E(15)^5+E(15)^7, -1+2*E(15)+E(15)^2-E(15)^3+2*E(15)^4-E(15)^5+E(15)^7, 2-2*E(15)-E(15)^2+E(15)^3-2*E(15)^4+E(15)^5-E(15)^7, -1*E(15)^6-E(15)^-6, -1*E(15)^6-E(15)^-6, -1*E(15)^3-E(15)^-3, -1*E(15)^3-E(15)^-3, E(15)+E(15)^4+2*E(15)^5, -1-E(15)-E(15)^2+E(15)^3-E(15)^4-2*E(15)^5-E(15)^7], [4, 0, 0, 0, -2, 2*E(15)^3+2*E(15)^-3, 2*E(15)^3+2*E(15)^-3, 2*E(15)^6+2*E(15)^-6, 2*E(15)^6+2*E(15)^-6, -1, 1+E(15)^2-E(15)^3+E(15)^7, 2-E(15)^2+E(15)^3-E(15)^7, -1, 0, 0, 0, 0, 0, -1+2*E(15)+E(15)^2-E(15)^3+2*E(15)^4-E(15)^5+E(15)^7, -3+E(15)+E(15)^2-E(15)^3+E(15)^4-3*E(15)^5+E(15)^7, 1-E(15)-E(15)^4+3*E(15)^5, 2-2*E(15)-E(15)^2+E(15)^3-2*E(15)^4+E(15)^5-E(15)^7, 2-2*E(15)-E(15)^2+E(15)^3-2*E(15)^4+E(15)^5-E(15)^7, -1+2*E(15)+E(15)^2-E(15)^3+2*E(15)^4-E(15)^5+E(15)^7, -1*E(15)^6-E(15)^-6, -1*E(15)^6-E(15)^-6, -1*E(15)^3-E(15)^-3, -1*E(15)^3-E(15)^-3, -1-E(15)-E(15)^2+E(15)^3-E(15)^4-2*E(15)^5-E(15)^7, E(15)+E(15)^4+2*E(15)^5], [4, 0, 0, 0, -2, 2*E(15)^6+2*E(15)^-6, 2*E(15)^3+2*E(15)^-3, 2*E(15)^3+2*E(15)^-3, 2*E(15)^6+2*E(15)^-6, 1+E(15)^2-E(15)^3+E(15)^7, -1, -1, 2-E(15)^2+E(15)^3-E(15)^7, 0, 0, 0, 0, 0, -3+E(15)+E(15)^2-E(15)^3+E(15)^4-3*E(15)^5+E(15)^7, 2-2*E(15)-E(15)^2+E(15)^3-2*E(15)^4+E(15)^5-E(15)^7, -1+2*E(15)+E(15)^2-E(15)^3+2*E(15)^4-E(15)^5+E(15)^7, 1-E(15)-E(15)^4+3*E(15)^5, -1-E(15)-E(15)^2+E(15)^3-E(15)^4-2*E(15)^5-E(15)^7, E(15)+E(15)^4+2*E(15)^5, -1*E(15)^3-E(15)^-3, -1*E(15)^6-E(15)^-6, -1*E(15)^6-E(15)^-6, -1*E(15)^3-E(15)^-3, -1+2*E(15)+E(15)^2-E(15)^3+2*E(15)^4-E(15)^5+E(15)^7, 2-2*E(15)-E(15)^2+E(15)^3-2*E(15)^4+E(15)^5-E(15)^7], [4, 0, 0, 0, -2, 2*E(15)^6+2*E(15)^-6, 2*E(15)^3+2*E(15)^-3, 2*E(15)^3+2*E(15)^-3, 2*E(15)^6+2*E(15)^-6, 1+E(15)^2-E(15)^3+E(15)^7, -1, -1, 2-E(15)^2+E(15)^3-E(15)^7, 0, 0, 0, 0, 0, 1-E(15)-E(15)^4+3*E(15)^5, -1+2*E(15)+E(15)^2-E(15)^3+2*E(15)^4-E(15)^5+E(15)^7, 2-2*E(15)-E(15)^2+E(15)^3-2*E(15)^4+E(15)^5-E(15)^7, -3+E(15)+E(15)^2-E(15)^3+E(15)^4-3*E(15)^5+E(15)^7, E(15)+E(15)^4+2*E(15)^5, -1-E(15)-E(15)^2+E(15)^3-E(15)^4-2*E(15)^5-E(15)^7, -1*E(15)^3-E(15)^-3, -1*E(15)^6-E(15)^-6, -1*E(15)^6-E(15)^-6, -1*E(15)^3-E(15)^-3, 2-2*E(15)-E(15)^2+E(15)^3-2*E(15)^4+E(15)^5-E(15)^7, -1+2*E(15)+E(15)^2-E(15)^3+2*E(15)^4-E(15)^5+E(15)^7], [4, 0, 0, 0, -2, 2*E(15)^3+2*E(15)^-3, 2*E(15)^6+2*E(15)^-6, 2*E(15)^6+2*E(15)^-6, 2*E(15)^3+2*E(15)^-3, 2-E(15)^2+E(15)^3-E(15)^7, -1, -1, 1+E(15)^2-E(15)^3+E(15)^7, 0, 0, 0, 0, 0, -1-E(15)-E(15)^2+E(15)^3-E(15)^4-2*E(15)^5-E(15)^7, -1+2*E(15)+E(15)^2-E(15)^3+2*E(15)^4-E(15)^5+E(15)^7, 2-2*E(15)-E(15)^2+E(15)^3-2*E(15)^4+E(15)^5-E(15)^7, E(15)+E(15)^4+2*E(15)^5, -3+E(15)+E(15)^2-E(15)^3+E(15)^4-3*E(15)^5+E(15)^7, 1-E(15)-E(15)^4+3*E(15)^5, -1*E(15)^6-E(15)^-6, -1*E(15)^3-E(15)^-3, -1*E(15)^3-E(15)^-3, -1*E(15)^6-E(15)^-6, 2-2*E(15)-E(15)^2+E(15)^3-2*E(15)^4+E(15)^5-E(15)^7, -1+2*E(15)+E(15)^2-E(15)^3+2*E(15)^4-E(15)^5+E(15)^7], [4, 0, 0, 0, -2, 2*E(15)^3+2*E(15)^-3, 2*E(15)^6+2*E(15)^-6, 2*E(15)^6+2*E(15)^-6, 2*E(15)^3+2*E(15)^-3, 2-E(15)^2+E(15)^3-E(15)^7, -1, -1, 1+E(15)^2-E(15)^3+E(15)^7, 0, 0, 0, 0, 0, E(15)+E(15)^4+2*E(15)^5, 2-2*E(15)-E(15)^2+E(15)^3-2*E(15)^4+E(15)^5-E(15)^7, -1+2*E(15)+E(15)^2-E(15)^3+2*E(15)^4-E(15)^5+E(15)^7, -1-E(15)-E(15)^2+E(15)^3-E(15)^4-2*E(15)^5-E(15)^7, 1-E(15)-E(15)^4+3*E(15)^5, -3+E(15)+E(15)^2-E(15)^3+E(15)^4-3*E(15)^5+E(15)^7, -1*E(15)^6-E(15)^-6, -1*E(15)^3-E(15)^-3, -1*E(15)^3-E(15)^-3, -1*E(15)^6-E(15)^-6, -1+2*E(15)+E(15)^2-E(15)^3+2*E(15)^4-E(15)^5+E(15)^7, 2-2*E(15)-E(15)^2+E(15)^3-2*E(15)^4+E(15)^5-E(15)^7]]; ConvertToLibraryCharacterTableNC(chartbl_300_40);