# Group 17496.pw downloaded from the LMFDB on 12 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(224877531997918804637382647183981119506510905947686787289176310179040602485547705981865051524476169487326476084577470254207,17496); a := GPC.1; b := GPC.4; c := GPC.5; d := GPC.6; e := GPC.7; f := GPC.8; g := GPC.9; h := GPC.10; GPerm := Group( (1,18,27,5)(2,16,25,6)(3,17,26,4)(7,24,19,10)(8,22,20,11)(9,23,21,12)(13,29)(14,30)(15,28)(31,36)(32,34)(33,35), (1,8,6,35,26,32,29,11)(2,9,4,36,27,33,30,12)(3,7,5,34,25,31,28,10)(13,19,16,23)(14,20,17,24)(15,21,18,22), (1,33,18,11)(2,31,16,12)(3,32,17,10)(4,22,14,9,29,36,25,20)(5,23,15,7,30,34,26,21)(6,24,13,8,28,35,27,19) ); # Booleans booleans_17496_pw := rec( Agroup := false, Zgroup := false, abelian := false, almost_simple := false, cyclic := false, metabelian := false, metacyclic := false, monomial := true, nilpotent := false, perfect := false, quasisimple := false, rational := false, solvable := true, supersolvable := false); # Character Table chartbl_17496_pw:=rec(); chartbl_17496_pw.IsFinite:= true; chartbl_17496_pw.UnderlyingCharacteristic:= 0; chartbl_17496_pw.UnderlyingGroup:= GPC; chartbl_17496_pw.Size:= 17496; chartbl_17496_pw.InfoText:= "Character table for group 17496.pw downloaded from the LMFDB."; chartbl_17496_pw.Identifier:= " C3^5:F9 "; chartbl_17496_pw.NrConjugacyClasses:= 42; chartbl_17496_pw.ConjugacyClasses:= [ of ..., f3*f5^2*f7^2*f9^2*f10^2, f6^2*f10, f6^2*f8^2, f6^2*f8^2*f10, f8^2, f8, f8*f10, f8^2*f10^2, f9, f5*f7, f4*f7, f4*f5, f9*f10, f9*f10^2, f5*f7*f10, f5*f6*f7, f4*f6*f7, f4*f6^2*f7, f4*f5*f10, f4*f5*f10^2, f5*f6*f7^2*f8^2*f9^2*f10, f4*f5*f6*f7^2*f8*f9^2, f5*f6*f7^2, f4*f5*f6*f7^2*f8*f10, f4*f5^2*f6^2*f7*f8^2*f10, f4*f5*f6*f7*f10, f2*f3*f5^2*f6*f7*f8*f9*f10, f2*f6*f7*f9, f3*f5*f7^2*f8*f9^2, f3*f5^2*f6*f7*f8^2*f9, f3*f5^2*f6*f8^2, f3*f4^2*f5^2*f6^2*f7*f9^2, f3*f4^2*f5^2*f6^2*f7*f8*f9^2, f3*f4^2*f5*f6*f8^2*f9^2, f3*f4^2*f5*f6*f8*f9^2*f10^2, f1*f2*f3*f5^2*f6, f1*f5*f6^2*f7^2*f8^2*f9^2, f1*f3*f5*f6^2*f10^2, f1*f2*f6*f7^2*f8*f9^2, f2*f5^2*f7^2*f9^2*f10^2, f2*f3*f5^2*f8*f10]; chartbl_17496_pw.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]; chartbl_17496_pw.ComputedPowerMaps:= [ , [1, 1, 3, 4, 5, 7, 6, 9, 8, 10, 11, 12, 13, 15, 14, 17, 16, 19, 18, 21, 20, 22, 23, 24, 25, 26, 27, 2, 2, 3, 4, 5, 6, 7, 8, 9, 28, 29, 29, 28, 30, 30], [1, 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, 29, 28, 2, 2, 2, 2, 2, 2, 2, 39, 40, 37, 38, 28, 29]]; chartbl_17496_pw.SizesCentralizers:= [17496, 216, 8748, 4374, 4374, 4374, 4374, 4374, 4374, 243, 243, 243, 243, 243, 243, 243, 243, 243, 243, 243, 243, 81, 81, 81, 81, 81, 81, 24, 24, 108, 54, 54, 54, 54, 54, 54, 8, 8, 8, 8, 12, 12]; chartbl_17496_pw.ClassNames:= ["1A", "2A", "3A", "3B", "3C", "3D1", "3D-1", "3E1", "3E-1", "3F", "3G", "3H", "3I", "3J1", "3J-1", "3K1", "3K-1", "3L1", "3L-1", "3M1", "3M-1", "3N", "3O", "3P", "3Q", "3R", "3S", "4A1", "4A-1", "6A", "6B", "6C", "6D1", "6D-1", "6E1", "6E-1", "8A1", "8A-1", "8A3", "8A-3", "12A1", "12A-1"]; chartbl_17496_pw.OrderClassRepresentatives:= [1, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 6, 6, 6, 6, 6, 6, 6, 8, 8, 8, 8, 12, 12]; chartbl_17496_pw.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*E(4), E(4), 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, 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, 1, 1, -1*E(8)^2, E(8)^2, -1, -1, -1, -1, -1, -1, -1, E(8)^3, -1*E(8), E(8), -1*E(8)^3, E(8)^2, -1*E(8)^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)^2, -1*E(8)^2, -1, -1, -1, -1, -1, -1, -1, -1*E(8), E(8)^3, -1*E(8)^3, E(8), -1*E(8)^2, E(8)^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)^2, E(8)^2, -1, -1, -1, -1, -1, -1, -1, -1*E(8)^3, E(8), -1*E(8), E(8)^3, E(8)^2, -1*E(8)^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)^2, -1*E(8)^2, -1, -1, -1, -1, -1, -1, -1, E(8), -1*E(8)^3, E(8)^3, -1*E(8), -1*E(8)^2, E(8)^2], [8, 0, 8, 8, 8, 8, 8, 8, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [8, 0, 8, 8, 8, 8, 8, 8, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 8, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [8, 0, 8, 8, 8, 8, 8, 8, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 8, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [8, 0, 8, 8, 8, 8, 8, 8, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 8, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [8, 0, 8, 8, 8, 8, 8, 8, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 8, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [8, 0, 8, 8, 8, 8, 8, 8, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 8, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [8, 0, 8, 8, 8, 8, 8, 8, 8, -1, -1, -1, 8, -1, -1, -1, -1, -1, -1, 8, 8, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [8, 0, 8, 8, 8, 8, 8, 8, 8, -1, -1, 8, -1, -1, -1, -1, -1, 8, 8, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [8, 0, 8, 8, 8, 8, 8, 8, 8, -1, 8, -1, -1, -1, -1, 8, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [8, 0, 8, 8, 8, 8, 8, 8, 8, 8, -1, -1, -1, 8, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [12, 4, -6, 3, -6, 3, 3, -6-9*E(3), 3+9*E(3), 3, 3, 3, 3, 3*E(3)^-1, 3*E(3), 3*E(3), 3*E(3)^-1, 3*E(3)^-1, 3*E(3), 3*E(3)^-1, 3*E(3), 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, -2, 1, 1, 1+3*E(3), -2-3*E(3), 0, 0, 0, 0, 0, 0], [12, 4, -6, 3, -6, 3, 3, 3+9*E(3), -6-9*E(3), 3, 3, 3, 3, 3*E(3), 3*E(3)^-1, 3*E(3)^-1, 3*E(3), 3*E(3), 3*E(3)^-1, 3*E(3), 3*E(3)^-1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, -2, 1, 1, -2-3*E(3), 1+3*E(3), 0, 0, 0, 0, 0, 0], [12, -4, -6, 3, -6, 3, 3, -6-9*E(3), 3+9*E(3), 3, 3, 3, 3, 3*E(3)^-1, 3*E(3), 3*E(3), 3*E(3)^-1, 3*E(3)^-1, 3*E(3), 3*E(3)^-1, 3*E(3), 0, 0, 0, 0, 0, 0, 0, 0, 2, -1, 2, -1, -1, -1-3*E(3), 2+3*E(3), 0, 0, 0, 0, 0, 0], [12, -4, -6, 3, -6, 3, 3, 3+9*E(3), -6-9*E(3), 3, 3, 3, 3, 3*E(3), 3*E(3)^-1, 3*E(3)^-1, 3*E(3), 3*E(3), 3*E(3)^-1, 3*E(3), 3*E(3)^-1, 0, 0, 0, 0, 0, 0, 0, 0, 2, -1, 2, -1, -1, 2+3*E(3), -1-3*E(3), 0, 0, 0, 0, 0, 0], [18, 2, -9, 18, 18, -9, -9, -9, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -1, 2, 2, -1, -1, -1, -1, 0, 0, 0, 0, -1, -1], [18, 2, -9, 18, 18, -9, -9, -9, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -1, 2, 2, -1, -1, -1, -1, 0, 0, 0, 0, 1, 1], [18, -2, -9, 18, 18, -9, -9, -9, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2*E(4), 2*E(4), 1, -2, -2, 1, 1, 1, 1, 0, 0, 0, 0, -1*E(4), E(4)], [18, -2, -9, 18, 18, -9, -9, -9, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2*E(4), -2*E(4), 1, -2, -2, 1, 1, 1, 1, 0, 0, 0, 0, E(4), -1*E(4)], [24, 0, -12, 6, -12, 6, 6, -12-18*E(3), 6+18*E(3), -3, -3, -3, 6, -3*E(3)^-1, -3*E(3), -3*E(3), -3*E(3)^-1, -3*E(3)^-1, -3*E(3), 6*E(3)^-1, 6*E(3), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [24, 0, -12, 6, -12, 6, 6, 6+18*E(3), -12-18*E(3), -3, -3, -3, 6, -3*E(3), -3*E(3)^-1, -3*E(3)^-1, -3*E(3), -3*E(3), -3*E(3)^-1, 6*E(3), 6*E(3)^-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [24, 0, -12, 6, -12, 6, 6, -12-18*E(3), 6+18*E(3), -3, -3, 6, -3, -3*E(3)^-1, -3*E(3), -3*E(3), -3*E(3)^-1, 6*E(3)^-1, 6*E(3), -3*E(3)^-1, -3*E(3), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [24, 0, -12, 6, -12, 6, 6, 6+18*E(3), -12-18*E(3), -3, -3, 6, -3, -3*E(3), -3*E(3)^-1, -3*E(3)^-1, -3*E(3), 6*E(3), 6*E(3)^-1, -3*E(3), -3*E(3)^-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [24, 0, -12, 6, -12, 6, 6, -12-18*E(3), 6+18*E(3), -3, 6, -3, -3, -3*E(3)^-1, -3*E(3), 6*E(3), 6*E(3)^-1, -3*E(3)^-1, -3*E(3), -3*E(3)^-1, -3*E(3), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [24, 0, -12, 6, -12, 6, 6, 6+18*E(3), -12-18*E(3), -3, 6, -3, -3, -3*E(3), -3*E(3)^-1, 6*E(3)^-1, 6*E(3), -3*E(3), -3*E(3)^-1, -3*E(3), -3*E(3)^-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [24, 0, -12, 6, -12, 6, 6, -12-18*E(3), 6+18*E(3), 6, -3, -3, -3, 6*E(3)^-1, 6*E(3), -3*E(3), -3*E(3)^-1, -3*E(3)^-1, -3*E(3), -3*E(3)^-1, -3*E(3), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [24, 0, -12, 6, -12, 6, 6, 6+18*E(3), -12-18*E(3), 6, -3, -3, -3, 6*E(3), 6*E(3)^-1, -3*E(3)^-1, -3*E(3), -3*E(3), -3*E(3)^-1, -3*E(3), -3*E(3)^-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [36, 4, 36, -18, 9, 9, 9, -18, -18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -2, 1, 1, 1, -2, -2, 0, 0, 0, 0, 0, 0], [36, 4, 36, 9, -18, -18, -18, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 1, -2, -2, -2, 1, 1, 0, 0, 0, 0, 0, 0], [36, -4, 36, -18, 9, 9, 9, -18, -18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 2, -1, -1, -1, 2, 2, 0, 0, 0, 0, 0, 0], [36, -4, 36, 9, -18, -18, -18, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -1, 2, 2, 2, -1, -1, 0, 0, 0, 0, 0, 0], [36, 4, -18, -18, 9, -18-27*E(3), 9+27*E(3), 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 1, 1+3*E(3), -2-3*E(3), 1, 1, 0, 0, 0, 0, 0, 0], [36, 4, -18, -18, 9, 9+27*E(3), -18-27*E(3), 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 1, -2-3*E(3), 1+3*E(3), 1, 1, 0, 0, 0, 0, 0, 0], [36, -4, -18, -18, 9, -18-27*E(3), 9+27*E(3), 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -1, -1-3*E(3), 2+3*E(3), -1, -1, 0, 0, 0, 0, 0, 0], [36, -4, -18, -18, 9, 9+27*E(3), -18-27*E(3), 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -1, 2+3*E(3), -1-3*E(3), -1, -1, 0, 0, 0, 0, 0, 0]]; ConvertToLibraryCharacterTableNC(chartbl_17496_pw);