# Group 864.3015 downloaded from the LMFDB on 07 November 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(5339767309491680558191208553894318068721108392048937,864); a := GPC.1; b := GPC.3; c := GPC.4; d := GPC.6; GPerm := Group( (1,2)(3,4)(5,6)(10,11)(12,13,14,15)(17,18), (12,14)(13,15), (3,4,8)(5,6,7)(9,10,11)(16,17,18), (9,10,11)(16,17,18), (16,18,17), (1,3,2,5)(4,8,6,7), (1,4,2,6)(3,7,5,8), (1,2)(3,5)(4,6)(7,8) ); GLZN := Group([[[ZmodnZObj(1,30), ZmodnZObj(20,30)], [ZmodnZObj(20,30), ZmodnZObj(11,30)]],[[ZmodnZObj(1,30), ZmodnZObj(10,30)], [ZmodnZObj(0,30), ZmodnZObj(1,30)]],[[ZmodnZObj(3,30), ZmodnZObj(10,30)], [ZmodnZObj(7,30), ZmodnZObj(7,30)]],[[ZmodnZObj(16,30), ZmodnZObj(15,30)], [ZmodnZObj(15,30), ZmodnZObj(1,30)]],[[ZmodnZObj(11,30), ZmodnZObj(0,30)], [ZmodnZObj(0,30), ZmodnZObj(11,30)]],[[ZmodnZObj(11,30), ZmodnZObj(20,30)], [ZmodnZObj(20,30), ZmodnZObj(1,30)]],[[ZmodnZObj(19,30), ZmodnZObj(0,30)], [ZmodnZObj(0,30), ZmodnZObj(19,30)]],[[ZmodnZObj(13,30), ZmodnZObj(12,30)], [ZmodnZObj(6,30), ZmodnZObj(1,30)]]]); # Booleans booleans_864_3015 := rec( Agroup := false, Zgroup := false, abelian := false, almost_simple := false, cyclic := false, metabelian := false, metacyclic := false, nilpotent := false, perfect := false, quasisimple := false, rational := false, solvable := true, supersolvable := false); # Character Table chartbl_864_3015:=rec(); chartbl_864_3015.IsFinite:= true; chartbl_864_3015.UnderlyingCharacteristic:= 0; chartbl_864_3015.UnderlyingGroup:= GPC; chartbl_864_3015.Size:= 864; chartbl_864_3015.InfoText:= "Character table for group 864.3015 downloaded from the LMFDB."; chartbl_864_3015.Identifier:= " C6^2.S4 "; chartbl_864_3015.NrConjugacyClasses:= 72; chartbl_864_3015.ConjugacyClasses:= [ of ..., f2, f2*f7*f8, f7*f8, f8^2, f5^2, f5^2*f8^2, f5^2*f8, f3^2*f8, f3^2*f4*f5*f7, f3^2*f5^2, f3^2*f4*f5^2*f6*f7, f3^2, f3^2*f5^2*f8^2, f3^2*f4*f5^2*f6*f7*f8^2, f3^2*f5^2*f8, f3^2*f5*f7*f8^2, f6*f7, f2*f6*f7, f1*f8^2, f1*f2*f8^2, f2*f8, f2*f7, f2*f5, f2*f5^2, f2*f5*f8, f2*f5*f7, f2*f5*f8^2, f2*f5^2*f8^2, f7, f5, f5^2*f7, f5*f8^2, f3*f7, f3*f6, f3*f5, f3*f4, f2*f3, f3*f7*f8, f3*f5*f8, f3*f4*f8, f2*f3*f8, f2*f3*f7, f2*f3*f6, f2*f3*f5, f2*f3*f4, f3*f5*f8^2, f3*f5^2*f7, f2*f3*f8^2, f2*f3*f5^2, f2*f3^2*f4, f2*f3*f7*f8, f2*f3*f5*f8, f2*f3*f5*f7, f2*f3*f5*f6, f2*f3*f4*f8, f2*f3*f4*f7, f2*f3*f4*f6, f2*f3*f5*f8^2, f2*f3*f5^2*f7, f1*f2*f4*f5*f6*f8, f1*f4*f5*f7, f1*f4*f5*f8^2, f1*f2*f4*f5*f6*f7*f8^2, f6, f4, f5*f6, f4*f8, f2*f6, f2*f4, f2*f5*f6, f2*f4*f8]; chartbl_864_3015.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, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72]; chartbl_864_3015.ComputedPowerMaps:= [ , [1, 1, 1, 1, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 4, 4, 2, 2, 5, 5, 6, 6, 7, 8, 8, 7, 5, 6, 7, 8, 9, 10, 11, 12, 13, 13, 14, 15, 10, 9, 10, 11, 12, 16, 17, 9, 12, 11, 13, 14, 16, 14, 15, 17, 15, 16, 17, 19, 19, 19, 19, 30, 31, 32, 33, 30, 31, 32, 33], [1, 2, 3, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 18, 19, 21, 20, 2, 3, 3, 2, 3, 2, 3, 2, 4, 4, 4, 4, 4, 4, 4, 4, 2, 4, 4, 4, 2, 3, 3, 3, 3, 4, 4, 2, 2, 2, 3, 3, 2, 2, 3, 2, 2, 3, 3, 63, 64, 61, 62, 18, 18, 18, 18, 19, 19, 19, 19]]; chartbl_864_3015.SizesCentralizers:= [864, 864, 864, 864, 432, 432, 432, 432, 108, 108, 108, 108, 108, 108, 108, 108, 108, 144, 144, 8, 8, 432, 432, 432, 432, 432, 432, 432, 432, 432, 432, 432, 432, 108, 108, 108, 108, 108, 108, 108, 108, 108, 108, 108, 108, 108, 108, 108, 108, 108, 108, 108, 108, 108, 108, 108, 108, 108, 108, 108, 16, 16, 16, 16, 72, 72, 72, 72, 72, 72, 72, 72]; chartbl_864_3015.ClassNames:= ["1A", "2A", "2B", "2C", "3A", "3B", "3C", "3D", "3E", "3F", "3G", "3H", "3I", "3J", "3K", "3L", "3M", "4A", "4B", "4C1", "4C-1", "6A", "6B", "6C", "6D", "6E", "6F", "6G", "6H", "6I", "6J", "6K", "6L", "6M", "6N", "6O", "6P", "6Q", "6R", "6S", "6T", "6U", "6V", "6W", "6X", "6Y", "6Z", "6AA", "6AB", "6AC", "6AD", "6AE", "6AF", "6AG", "6AH", "6AI", "6AJ", "6AK", "6AL", "6AM", "8A1", "8A-1", "8A3", "8A-3", "12A", "12B", "12C", "12D", "12E", "12F", "12G", "12H"]; chartbl_864_3015.OrderClassRepresentatives:= [1, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 8, 8, 8, 8, 12, 12, 12, 12, 12, 12, 12, 12]; chartbl_864_3015.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*E(4), E(4), 1, -1, -1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -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), 1, -1, -1, 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, -1, -1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -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, 1, 1, -1, 1, -1], [2, 2, 2, 2, -1, -1, -1, 2, -1, -1, -1, 2, 2, -1, -1, 2, -1, 2, 2, 0, 0, -1, -1, -1, 2, 2, -1, -1, -1, 2, -1, -1, -1, 2, 2, 2, -1, -1, -1, -1, -1, 2, -1, -1, -1, -1, -1, 2, -1, 2, -1, 2, 2, -1, -1, -1, -1, -1, 2, -1, 0, 0, 0, 0, -1, -1, -1, -1, 2, -1, -1, 2], [2, 2, 2, 2, -1, -1, -1, 2, -1, -1, 2, -1, -1, -1, 2, -1, 2, 2, 2, 0, 0, -1, -1, -1, 2, 2, -1, -1, -1, 2, -1, -1, -1, -1, -1, -1, -1, -1, 2, -1, 2, -1, 2, 2, 2, 2, -1, -1, 2, -1, -1, -1, -1, 2, -1, 2, -1, -1, -1, -1, 0, 0, 0, 0, -1, -1, -1, -1, 2, -1, -1, 2], [2, 2, 2, 2, -1, -1, -1, 2, 2, 2, -1, -1, -1, 2, -1, -1, -1, 2, 2, 0, 0, -1, -1, -1, 2, 2, -1, -1, -1, 2, -1, -1, -1, -1, -1, -1, 2, 2, -1, 2, -1, -1, -1, -1, -1, -1, 2, -1, -1, -1, 2, -1, -1, -1, 2, -1, 2, 2, -1, 2, 0, 0, 0, 0, -1, -1, -1, -1, 2, -1, -1, 2], [2, 2, 2, 2, -1, -1, 2, -1, -1, -1, -1, 2, -1, 2, -1, -1, 2, 2, 2, 0, 0, -1, -1, -1, -1, -1, -1, 2, -1, -1, 2, 2, -1, 2, -1, 2, -1, -1, 2, -1, -1, -1, -1, -1, 2, -1, 2, -1, -1, 2, 2, -1, -1, 2, 2, -1, -1, -1, -1, -1, 0, 0, 0, 0, -1, 2, -1, 2, -1, -1, -1, -1], [2, 2, 2, 2, -1, -1, 2, -1, -1, 2, 2, -1, -1, -1, -1, 2, -1, 2, 2, 0, 0, -1, -1, -1, -1, -1, -1, 2, -1, -1, 2, 2, -1, -1, 2, -1, 2, -1, -1, -1, 2, -1, -1, -1, -1, -1, -1, 2, 2, -1, -1, -1, 2, -1, -1, 2, 2, -1, -1, 2, 0, 0, 0, 0, -1, 2, -1, 2, -1, -1, -1, -1], [2, 2, 2, 2, -1, -1, 2, -1, 2, -1, -1, -1, 2, -1, 2, -1, -1, 2, 2, 0, 0, -1, -1, -1, -1, -1, -1, 2, -1, -1, 2, 2, -1, -1, -1, -1, -1, 2, -1, 2, -1, 2, 2, 2, -1, 2, -1, -1, -1, -1, -1, 2, -1, -1, -1, -1, -1, 2, 2, -1, 0, 0, 0, 0, -1, 2, -1, 2, -1, -1, -1, -1], [2, 2, 2, 2, -1, 2, -1, -1, -1, -1, 2, -1, 2, 2, -1, -1, -1, 2, 2, 0, 0, -1, -1, 2, -1, -1, 2, -1, -1, -1, -1, -1, 2, -1, -1, -1, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, 2, -1, 2, -1, 2, 2, -1, -1, 2, 2, -1, -1, 2, -1, 0, 0, 0, 0, 2, -1, -1, -1, -1, 2, -1, -1], [2, 2, 2, 2, -1, 2, -1, -1, -1, 2, -1, 2, -1, -1, 2, -1, -1, 2, 2, 0, 0, -1, -1, 2, -1, -1, 2, -1, -1, -1, -1, -1, 2, 2, -1, 2, 2, -1, -1, -1, -1, -1, 2, 2, -1, 2, -1, -1, -1, 2, -1, -1, -1, -1, -1, -1, 2, -1, -1, 2, 0, 0, 0, 0, 2, -1, -1, -1, -1, 2, -1, -1], [2, 2, 2, 2, -1, 2, -1, -1, 2, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 0, 0, -1, -1, 2, -1, -1, 2, -1, -1, -1, -1, -1, 2, -1, 2, -1, -1, 2, 2, 2, -1, -1, -1, -1, 2, -1, -1, 2, -1, -1, -1, -1, 2, 2, -1, -1, -1, 2, -1, -1, 0, 0, 0, 0, 2, -1, -1, -1, -1, 2, -1, -1], [2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, -1, 2, 2, 0, 0, 2, 2, -1, -1, -1, -1, -1, 2, -1, -1, -1, -1, -1, 2, -1, -1, -1, -1, -1, -1, -1, 2, 2, -1, 2, 2, 2, -1, -1, 2, -1, 2, -1, 2, -1, -1, -1, -1, -1, 0, 0, 0, 0, -1, -1, 2, -1, -1, -1, 2, -1], [2, 2, 2, 2, 2, -1, -1, -1, -1, 2, -1, -1, 2, -1, -1, -1, 2, 2, 2, 0, 0, 2, 2, -1, -1, -1, -1, -1, 2, -1, -1, -1, -1, -1, -1, -1, 2, -1, 2, -1, -1, 2, -1, -1, 2, -1, -1, -1, -1, -1, -1, 2, -1, 2, -1, -1, 2, -1, 2, 2, 0, 0, 0, 0, -1, -1, 2, -1, -1, -1, 2, -1], [2, 2, 2, 2, 2, -1, -1, -1, 2, -1, 2, 2, -1, -1, -1, -1, -1, 2, 2, 0, 0, 2, 2, -1, -1, -1, -1, -1, 2, -1, -1, -1, -1, 2, -1, 2, -1, 2, -1, 2, 2, -1, -1, -1, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, -1, 2, -1, 2, -1, -1, 0, 0, 0, 0, -1, -1, 2, -1, -1, -1, 2, -1], [2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, -2, -2, -1, -1, -1, 2, -1, -1, -1, 2, 2, -1, -1, 2, -1, 2, -2, 0, 0, -1, 1, 1, -2, 2, -1, -1, 1, -2, 1, 1, 1, -2, -2, -2, 1, 1, 1, 1, -1, 2, -1, 1, 1, 1, -1, -2, 1, 2, 1, -2, 2, -1, 1, 1, -1, -1, -2, 1, 0, 0, 0, 0, -1, 1, 1, -1, 2, 1, -1, -2], [2, 2, -2, -2, -1, -1, -1, 2, -1, -1, 2, -1, -1, -1, 2, -1, 2, 2, -2, 0, 0, -1, 1, 1, -2, 2, -1, -1, 1, -2, 1, 1, 1, 1, 1, 1, 1, 1, -2, 1, 2, -1, 2, -2, -2, -2, -1, 1, -2, -1, 1, 1, -1, 2, 1, -2, -1, -1, 1, 1, 0, 0, 0, 0, -1, 1, 1, -1, 2, 1, -1, -2], [2, 2, -2, -2, -1, -1, -1, 2, 2, 2, -1, -1, -1, 2, -1, -1, -1, 2, -2, 0, 0, -1, 1, 1, -2, 2, -1, -1, 1, -2, 1, 1, 1, 1, 1, 1, -2, -2, 1, -2, -1, -1, -1, 1, 1, 1, 2, 1, 1, -1, -2, 1, -1, -1, -2, 1, 2, 2, 1, -2, 0, 0, 0, 0, -1, 1, 1, -1, 2, 1, -1, -2], [2, 2, -2, -2, -1, -1, 2, -1, -1, -1, -1, 2, -1, 2, -1, -1, 2, 2, -2, 0, 0, -1, 1, 1, 1, -1, -1, 2, 1, 1, -2, -2, 1, -2, 1, -2, 1, 1, -2, 1, -1, -1, -1, 1, -2, 1, 2, 1, 1, 2, -2, 1, -1, 2, -2, 1, -1, -1, 1, 1, 0, 0, 0, 0, -1, -2, 1, 2, -1, 1, -1, 1], [2, 2, -2, -2, -1, -1, 2, -1, -1, 2, 2, -1, -1, -1, -1, 2, -1, 2, -2, 0, 0, -1, 1, 1, 1, -1, -1, 2, 1, 1, -2, -2, 1, 1, -2, 1, -2, 1, 1, 1, 2, -1, -1, 1, 1, 1, -1, -2, -2, -1, 1, 1, 2, -1, 1, -2, 2, -1, 1, -2, 0, 0, 0, 0, -1, -2, 1, 2, -1, 1, -1, 1], [2, 2, -2, -2, -1, -1, 2, -1, 2, -1, -1, -1, 2, -1, 2, -1, -1, 2, -2, 0, 0, -1, 1, 1, 1, -1, -1, 2, 1, 1, -2, -2, 1, 1, 1, 1, 1, -2, 1, -2, -1, 2, 2, -2, 1, -2, -1, 1, 1, -1, 1, -2, -1, -1, 1, 1, -1, 2, -2, 1, 0, 0, 0, 0, -1, -2, 1, 2, -1, 1, -1, 1], [2, 2, -2, -2, -1, 2, -1, -1, -1, -1, 2, -1, 2, 2, -1, -1, -1, 2, -2, 0, 0, -1, 1, -2, 1, -1, 2, -1, 1, 1, 1, 1, -2, 1, 1, 1, 1, 1, 1, 1, 2, 2, -1, 1, 1, 1, 2, 1, -2, -1, -2, -2, -1, -1, -2, -2, -1, -1, -2, 1, 0, 0, 0, 0, 2, 1, 1, -1, -1, -2, -1, 1], [2, 2, -2, -2, -1, 2, -1, -1, -1, 2, -1, 2, -1, -1, 2, -1, -1, 2, -2, 0, 0, -1, 1, -2, 1, -1, 2, -1, 1, 1, 1, 1, -2, -2, 1, -2, -2, 1, 1, 1, -1, -1, 2, -2, 1, -2, -1, 1, 1, 2, 1, 1, -1, -1, 1, 1, 2, -1, 1, -2, 0, 0, 0, 0, 2, 1, 1, -1, -1, -2, -1, 1], [2, 2, -2, -2, -1, 2, -1, -1, 2, -1, -1, -1, -1, -1, -1, 2, 2, 2, -2, 0, 0, -1, 1, -2, 1, -1, 2, -1, 1, 1, 1, 1, -2, 1, -2, 1, 1, -2, -2, -2, -1, -1, -1, 1, -2, 1, -1, -2, 1, -1, 1, 1, 2, 2, 1, 1, -1, 2, 1, 1, 0, 0, 0, 0, 2, 1, 1, -1, -1, -2, -1, 1], [2, 2, -2, -2, 2, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, -1, 2, -2, 0, 0, 2, -2, 1, 1, -1, -1, -1, -2, 1, 1, 1, 1, 1, -2, 1, 1, 1, 1, 1, -1, -1, 2, -2, 1, -2, 2, -2, 1, -1, -2, 1, 2, -1, -2, 1, -1, -1, 1, 1, 0, 0, 0, 0, -1, 1, -2, -1, -1, 1, 2, 1], [2, 2, -2, -2, 2, -1, -1, -1, -1, 2, -1, -1, 2, -1, -1, -1, 2, 2, -2, 0, 0, 2, -2, 1, 1, -1, -1, -1, -2, 1, 1, 1, 1, 1, 1, 1, -2, 1, -2, 1, -1, 2, -1, 1, -2, 1, -1, 1, 1, -1, 1, -2, -1, 2, 1, 1, 2, -1, -2, -2, 0, 0, 0, 0, -1, 1, -2, -1, -1, 1, 2, 1], [2, 2, -2, -2, 2, -1, -1, -1, 2, -1, 2, 2, -1, -1, -1, -1, -1, 2, -2, 0, 0, 2, -2, 1, 1, -1, -1, -1, -2, 1, 1, 1, 1, -2, 1, -2, 1, -2, 1, -2, 2, -1, -1, 1, 1, 1, -1, 1, -2, 2, 1, 1, -1, -1, 1, -2, -1, 2, 1, 1, 0, 0, 0, 0, -1, 1, -2, -1, -1, 1, 2, 1], [2, 2, -2, -2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, -2, 0, 0, 2, -2, -2, -2, 2, 2, 2, -2, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, -1, 1, 1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 0, 0, 0, 0, 2, -2, -2, 2, 2, -2, 2, -2], [2, -2, 2, -2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, -2, -2, 2, 2, -2, -2, -2, 2, -2, 2, -2, -2, 1, -1, -1, -1, -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(8)-E(8)^3, E(8)+E(8)^3, -1*E(8)-E(8)^3, E(8)+E(8)^3, 0, 0, 0, 0, 0, 0, 0, 0], [2, -2, 2, -2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, -2, -2, 2, 2, -2, -2, -2, 2, -2, 2, -2, -2, 1, -1, -1, -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(8)+E(8)^3, -1*E(8)-E(8)^3, E(8)+E(8)^3, -1*E(8)-E(8)^3, 0, 0, 0, 0, 0, 0, 0, 0], [2, -2, -2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, -2, 2, -2, -2, -2, -2, -2, -2, 2, -2, 2, 2, -1, 1, 1, 1, 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(8)-E(8)^-1, -1*E(8)-E(8)^-1, E(8)+E(8)^-1, E(8)+E(8)^-1, 0, 0, 0, 0, 0, 0, 0, 0], [2, -2, -2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, -2, 2, -2, -2, -2, -2, -2, -2, 2, -2, 2, 2, -1, 1, 1, 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(8)+E(8)^-1, E(8)+E(8)^-1, -1*E(8)-E(8)^-1, -1*E(8)-E(8)^-1, 0, 0, 0, 0, 0, 0, 0, 0], [3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1], [3, 3, -3, -3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, -1*E(4), E(4), 3, -3, -3, -3, 3, 3, 3, -3, -3, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1*E(4), E(4), E(4), -1*E(4), -1, 1, 1, -1, -1, 1, -1, 1], [3, 3, -3, -3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, E(4), -1*E(4), 3, -3, -3, -3, 3, 3, 3, -3, -3, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, E(4), -1*E(4), -1*E(4), E(4), -1, 1, 1, -1, -1, 1, -1, 1], [4, -4, 4, -4, 4, 4, 4, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, -4, -4, 4, 4, -4, -4, -4, 4, -4, 4, -4, -4, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, -4, -4, 4, 4, 4, 4, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, -4, 4, -4, -4, -4, -4, -4, -4, 4, -4, 4, 4, 1, -1, -1, -1, -1, 1, 1, -1, -1, -1, 1, -1, -1, -1, 1, -1, -1, -1, 1, -1, -1, 1, 1, -1, -1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, -4, 4, -4, -2, -2, -2, 4, -2, -2, 1, 1, 1, -2, 1, 1, 1, 0, 0, 0, 0, 2, 2, -2, 4, -4, 2, 2, -2, -4, -2, 2, 2, -1, 1, 1, -2, -2, -1, 2, -1, -1, -1, -1, 1, 1, 2, -1, 1, -1, -2, -1, -1, -1, 2, -1, 2, 2, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, -4, 4, -4, -2, -2, -2, 4, 1, 1, -2, 1, 1, 1, -2, 1, -2, 0, 0, 0, 0, 2, 2, -2, 4, -4, 2, 2, -2, -4, -2, 2, 2, -1, 1, 1, 1, 1, 2, -1, 2, -1, 2, 2, -2, -2, -1, -1, -2, -1, 1, -1, -1, 2, -1, 2, -1, -1, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, -4, 4, -4, -2, -2, -2, 4, 1, 1, 1, -2, -2, 1, 1, -2, 1, 0, 0, 0, 0, 2, 2, -2, 4, -4, 2, 2, -2, -4, -2, 2, 2, 2, -2, -2, 1, 1, -1, -1, -1, 2, -1, -1, 1, 1, -1, 2, 1, 2, 1, 2, 2, -1, -1, -1, -1, -1, -2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, -4, 4, -4, -2, -2, 4, -2, -2, 1, 1, 1, -2, 1, -2, 1, 1, 0, 0, 0, 0, 2, 2, -2, -2, 2, 2, -4, -2, 2, 4, -4, 2, -1, 1, 1, 1, -2, -1, 2, -1, 2, 2, 2, 1, -2, -1, -1, 1, -1, 1, 2, -1, -1, -1, -1, -1, 2, -2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, -4, 4, -4, -2, -2, 4, -2, 1, -2, -2, 1, 1, 1, 1, -2, 1, 0, 0, 0, 0, 2, 2, -2, -2, 2, 2, -4, -2, 2, 4, -4, 2, -1, -2, 1, -2, 1, -1, -1, 2, -1, -1, -1, 1, 1, -1, 2, -2, -1, 1, -1, 2, -1, -1, 2, 2, -1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, -4, 4, -4, -2, -2, 4, -2, 1, 1, 1, -2, 1, -2, 1, 1, -2, 0, 0, 0, 0, 2, 2, -2, -2, 2, 2, -4, -2, 2, 4, -4, 2, 2, 1, -2, 1, 1, 2, -1, -1, -1, -1, -1, -2, 1, 2, -1, 1, 2, -2, -1, -1, 2, 2, -1, -1, -1, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, -4, 4, -4, -2, 4, -2, -2, -2, 1, 1, 1, 1, 1, 1, -2, -2, 0, 0, 0, 0, 2, 2, 4, -2, 2, -4, 2, -2, 2, -2, 2, -4, -1, -2, 1, 1, -2, 2, 2, -1, -1, -1, -1, -2, 1, -1, 2, 1, -1, 1, -1, 2, 2, -1, -1, -1, 2, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, -4, 4, -4, -2, 4, -2, -2, 1, -2, 1, -2, 1, 1, -2, 1, 1, 0, 0, 0, 0, 2, 2, 4, -2, 2, -4, 2, -2, 2, -2, 2, -4, 2, 1, -2, -2, 1, -1, -1, -1, -1, 2, 2, 1, -2, -1, -1, 1, 2, 1, -1, -1, -1, -1, -1, 2, -1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, -4, 4, -4, -2, 4, -2, -2, 1, 1, -2, 1, -2, -2, 1, 1, 1, 0, 0, 0, 0, 2, 2, 4, -2, 2, -4, 2, -2, 2, -2, 2, -4, -1, 1, 1, 1, 1, -1, -1, 2, 2, -1, -1, 1, 1, 2, -1, -2, -1, -2, 2, -1, -1, 2, 2, -1, -1, -2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, -4, 4, -4, 4, -2, -2, -2, -2, 1, -2, -2, 1, 1, 1, 1, 1, 0, 0, 0, 0, -4, -4, -2, -2, 2, 2, 2, 4, 2, -2, 2, 2, 2, 1, -2, 1, -2, -1, 2, 2, -1, -1, -1, 1, 1, -1, -1, -2, 2, 1, -1, -1, -1, -1, 2, -1, 2, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, -4, 4, -4, 4, -2, -2, -2, 1, -2, 1, 1, -2, 1, 1, 1, -2, 0, 0, 0, 0, -4, -4, -2, -2, 2, 2, 2, 4, 2, -2, 2, 2, -1, 1, 1, -2, 1, 2, -1, -1, 2, -1, -1, -2, 1, -1, -1, 1, -1, 1, 2, -1, 2, -1, -1, 2, -1, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, -4, 4, -4, 4, -2, -2, -2, 1, 1, 1, 1, 1, -2, -2, -2, 1, 0, 0, 0, 0, -4, -4, -2, -2, 2, 2, 2, 4, 2, -2, 2, 2, -1, -2, 1, 1, 1, -1, -1, -1, -1, 2, 2, 1, -2, 2, 2, 1, -1, -2, -1, 2, -1, 2, -1, -1, -1, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, -4, -4, 4, -2, -2, -2, 4, -2, -2, 1, 1, 1, -2, 1, 1, 1, 0, 0, 0, 0, 2, -2, 2, -4, -4, 2, 2, 2, 4, 2, -2, -2, 1, -1, -1, 2, 2, 1, -2, -1, -1, -1, 1, -1, -1, 2, 1, -1, -1, 2, 1, -1, -1, -2, 1, 2, 2, -1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, -4, -4, 4, -2, -2, -2, 4, 1, 1, -2, 1, 1, 1, -2, 1, -2, 0, 0, 0, 0, 2, -2, 2, -4, -4, 2, 2, 2, 4, 2, -2, -2, 1, -1, -1, -1, -1, -2, 1, 2, -1, 2, -2, 2, 2, -1, 1, 2, -1, -1, 1, -1, 2, 1, -2, -1, -1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, -4, -4, 4, -2, -2, -2, 4, 1, 1, 1, -2, -2, 1, 1, -2, 1, 0, 0, 0, 0, 2, -2, 2, -4, -4, 2, 2, 2, 4, 2, -2, -2, -2, 2, 2, -1, -1, 1, 1, -1, 2, -1, 1, -1, -1, -1, -2, -1, 2, -1, -2, 2, -1, 1, 1, -1, -1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, -4, -4, 4, -2, -2, 4, -2, -2, 1, 1, 1, -2, 1, -2, 1, 1, 0, 0, 0, 0, 2, -2, 2, 2, 2, 2, -4, 2, -2, -4, 4, -2, 1, -1, -1, -1, 2, 1, -2, -1, 2, 2, -2, -1, 2, -1, 1, -1, -1, -1, -2, -1, -1, 1, 1, -1, 2, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, -4, -4, 4, -2, -2, 4, -2, 1, -2, -2, 1, 1, 1, 1, -2, 1, 0, 0, 0, 0, 2, -2, 2, 2, 2, 2, -4, 2, -2, -4, 4, -2, 1, 2, -1, 2, -1, 1, 1, 2, -1, -1, 1, -1, -1, -1, -2, 2, -1, -1, 1, 2, -1, 1, -2, 2, -1, -1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, -4, -4, 4, -2, -2, 4, -2, 1, 1, 1, -2, 1, -2, 1, 1, -2, 0, 0, 0, 0, 2, -2, 2, 2, 2, 2, -4, 2, -2, -4, 4, -2, -2, -1, 2, -1, -1, -2, 1, -1, -1, -1, 1, 2, -1, 2, 1, -1, 2, 2, 1, -1, 2, -2, 1, -1, -1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, -4, -4, 4, -2, 4, -2, -2, -2, 1, 1, 1, 1, 1, 1, -2, -2, 0, 0, 0, 0, 2, -2, -4, 2, 2, -4, 2, 2, -2, 2, -2, 4, 1, 2, -1, -1, 2, -2, -2, -1, -1, -1, 1, 2, -1, -1, -2, -1, -1, -1, 1, 2, 2, 1, 1, -1, 2, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, -4, -4, 4, -2, 4, -2, -2, 1, -2, 1, -2, 1, 1, -2, 1, 1, 0, 0, 0, 0, 2, -2, -4, 2, 2, -4, 2, 2, -2, 2, -2, 4, -2, -1, 2, 2, -1, 1, 1, -1, -1, 2, -2, -1, 2, -1, 1, -1, 2, -1, 1, -1, -1, 1, 1, 2, -1, -1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, -4, -4, 4, -2, 4, -2, -2, 1, 1, -2, 1, -2, -2, 1, 1, 1, 0, 0, 0, 0, 2, -2, -4, 2, 2, -4, 2, 2, -2, 2, -2, 4, 1, -1, -1, -1, -1, 1, 1, 2, 2, -1, 1, -1, -1, 2, 1, 2, -1, 2, -2, -1, -1, -2, -2, -1, -1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, -4, -4, 4, 4, -2, -2, -2, -2, 1, -2, -2, 1, 1, 1, 1, 1, 0, 0, 0, 0, -4, 4, 2, 2, 2, 2, 2, -4, -2, 2, -2, -2, -2, -1, 2, -1, 2, 1, -2, 2, -1, -1, 1, -1, -1, -1, 1, 2, 2, -1, 1, -1, -1, 1, -2, -1, 2, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, -4, -4, 4, 4, -2, -2, -2, 1, -2, 1, 1, -2, 1, 1, 1, -2, 0, 0, 0, 0, -4, 4, 2, 2, 2, 2, 2, -4, -2, 2, -2, -2, 1, -1, -1, 2, -1, -2, 1, -1, 2, -1, 1, 2, -1, -1, 1, -1, -1, -1, -2, -1, 2, 1, 1, 2, -1, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, -4, -4, 4, 4, -2, -2, -2, 1, 1, 1, 1, 1, -2, -2, -2, 1, 0, 0, 0, 0, -4, 4, 2, 2, 2, 2, 2, -4, -2, 2, -2, -2, 1, 2, -1, -1, -1, 1, 1, -1, -1, 2, -2, -1, 2, 2, -2, -1, -1, 2, 1, 2, -1, -2, 1, -1, -1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [6, 6, 6, 6, -3, -3, -3, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, -3, -3, -3, 6, 6, -3, -3, -3, 6, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, -2, 1, 1, -2], [6, 6, 6, 6, -3, -3, 6, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, -3, -3, -3, -3, -3, -3, 6, -3, -3, 6, 6, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 1, -2, 1, 1, 1, 1], [6, 6, 6, 6, -3, 6, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, -3, -3, 6, -3, -3, 6, -3, -3, -3, -3, -3, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, 1, 1, 1, -2, 1, 1], [6, 6, 6, 6, 6, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 6, 6, -3, -3, -3, -3, -3, 6, -3, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, -2, 1, 1, 1, -2, 1], [6, 6, -6, -6, -3, -3, -3, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, -3, 3, 3, -6, 6, -3, -3, 3, -6, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, -1, 1, -2, -1, 1, 2], [6, 6, -6, -6, -3, -3, 6, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, -3, 3, 3, 3, -3, -3, 6, 3, 3, -6, -6, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, -1, -2, 1, -1, 1, -1], [6, 6, -6, -6, -3, 6, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, -3, 3, -6, 3, -3, 6, -3, 3, 3, 3, 3, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -1, -1, 1, 1, 2, 1, -1], [6, 6, -6, -6, 6, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 6, -6, 3, 3, -3, -3, -3, -6, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 2, 1, 1, -1, -2, -1]]; ConvertToLibraryCharacterTableNC(chartbl_864_3015);