# Group 432.610 downloaded from the LMFDB on 15 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(9044686963670919677305272275105045,432); a := GPC.1; b := GPC.2; c := GPC.4; d := GPC.6; GPerm := Group( (2,5)(3,7)(12,13)(14,16)(15,17), (1,2)(3,8)(4,5)(6,7)(12,13)(14,17)(15,16), (1,3)(2,6)(4,7)(5,8)(10,11), (1,4)(2,5)(3,7)(6,8), (9,10,11), (12,14,15)(13,16,17), (12,15,14)(13,16,17) ); # Booleans booleans_432_610 := rec( Agroup := false, 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_432_610:=rec(); chartbl_432_610.IsFinite:= true; chartbl_432_610.UnderlyingCharacteristic:= 0; chartbl_432_610.UnderlyingGroup:= GPC; chartbl_432_610.Size:= 432; chartbl_432_610.InfoText:= "Character table for group 432.610 downloaded from the LMFDB."; chartbl_432_610.Identifier:= " C2.S3^3 "; chartbl_432_610.NrConjugacyClasses:= 39; chartbl_432_610.ConjugacyClasses:= [ of ..., f6*f7, f4*f5, f2*f3, f1, f5, f3, f7^2, f5^2*f7, f3^2*f7, f3^2*f5^2, f3^2*f5^2*f7, f1*f3*f4*f5*f7^2, f1*f2*f3^2, f2*f3*f4*f5*f6, f1*f2*f3*f4*f5*f7, f1*f2*f3*f4*f5*f6*f7^2, f5^2*f6*f7, f6*f7^2, f3*f6*f7, f5*f6, f3*f6, f3*f5*f6*f7, f3*f5*f6, f4, f2, f3*f4, f2*f7, f1*f7, f1*f5, f3^2*f4, f2*f7^2, f3*f4*f5, f2*f3*f7, f1*f5*f7, f1*f5*f7^2, f1*f3*f4*f5^2*f6, f1*f2*f3^2*f6, f2*f4*f5*f7^2]; chartbl_432_610.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]; chartbl_432_610.ComputedPowerMaps:= [ , [1, 1, 1, 1, 1, 6, 7, 8, 9, 10, 11, 12, 2, 2, 2, 2, 2, 6, 8, 7, 9, 10, 11, 12, 6, 7, 11, 10, 8, 6, 11, 10, 7, 8, 9, 9, 18, 19, 20], [1, 2, 3, 4, 5, 1, 1, 1, 1, 1, 1, 1, 13, 14, 15, 17, 16, 2, 2, 2, 2, 2, 2, 2, 3, 4, 3, 4, 5, 5, 3, 4, 3, 4, 5, 5, 13, 14, 15]]; chartbl_432_610.SizesCentralizers:= [432, 432, 72, 72, 72, 216, 216, 216, 108, 108, 108, 54, 24, 24, 24, 16, 16, 216, 216, 216, 108, 108, 108, 54, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 12, 12, 12]; chartbl_432_610.ClassNames:= ["1A", "2A", "2B", "2C", "2D", "3A", "3B", "3C", "3D", "3E", "3F", "3G", "4A", "4B", "4C", "4D1", "4D-1", "6A", "6B", "6C", "6D", "6E", "6F", "6G", "6H", "6I", "6J", "6K", "6L", "6M", "6N", "6O", "6P", "6Q", "6R", "6S", "12A", "12B", "12C"]; chartbl_432_610.OrderClassRepresentatives:= [1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 12, 12, 12]; chartbl_432_610.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, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1, 1, 1, 1, 1, -1, 1, 1, 1, -1, 1, -1], [1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, -1, -1, -1, 1, -1, -1, -1, -1, 1, -1], [1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, -1, 1, 1, 1, -1, -1], [1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -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, 2, 0, 2, 2, -1, 2, 2, -1, 2, -1, -1, 0, 0, 2, 0, 0, -1, 2, 2, 2, -1, -1, -1, 0, -1, 0, 0, 2, -1, -1, -1, 0, -1, 2, -1, 0, -1, 0], [2, 2, 2, 0, 2, 2, -1, 2, 2, -1, -1, -1, 0, 2, 0, 0, 0, 2, 2, -1, -1, -1, 2, -1, -1, 2, -1, -1, 0, 0, 0, -1, 2, 0, -1, -1, -1, 0, 0], [2, 2, 2, 2, 0, 2, 2, -1, -1, -1, 2, -1, 2, 0, 0, 0, 0, 2, -1, 2, -1, 2, -1, -1, -1, 0, -1, 2, -1, 2, -1, 0, -1, -1, 0, 0, 0, 0, -1], [2, 2, -2, -2, 0, 2, 2, -1, -1, -1, 2, -1, 2, 0, 0, 0, 0, 2, -1, 2, -1, 2, -1, -1, 1, 0, 1, -2, 1, -2, 1, 0, 1, 1, 0, 0, 0, 0, -1], [2, 2, -2, 0, -2, 2, -1, 2, 2, -1, -1, -1, 0, 2, 0, 0, 0, 2, 2, -1, -1, -1, 2, -1, 1, -2, 1, 1, 0, 0, 0, 1, -2, 0, 1, 1, -1, 0, 0], [2, 2, -2, 0, 2, 2, -1, 2, 2, -1, -1, -1, 0, -2, 0, 0, 0, 2, 2, -1, -1, -1, 2, -1, 1, 2, 1, 1, 0, 0, 0, -1, -2, 0, -1, -1, 1, 0, 0], [2, 2, -2, 2, 0, 2, 2, -1, -1, -1, 2, -1, -2, 0, 0, 0, 0, 2, -1, 2, -1, 2, -1, -1, 1, 0, 1, -2, -1, 2, -1, 0, 1, -1, 0, 0, 0, 0, 1], [2, 2, 0, -2, -2, -1, 2, 2, -1, 2, -1, -1, 0, 0, 2, 0, 0, -1, 2, 2, 2, -1, -1, -1, 0, 1, 0, 0, -2, 1, 1, 1, 0, 1, -2, 1, 0, -1, 0], [2, 2, 0, -2, 2, -1, 2, 2, -1, 2, -1, -1, 0, 0, -2, 0, 0, -1, 2, 2, 2, -1, -1, -1, 0, -1, 0, 0, -2, 1, 1, -1, 0, 1, 2, -1, 0, 1, 0], [2, 2, 0, 2, -2, -1, 2, 2, -1, 2, -1, -1, 0, 0, -2, 0, 0, -1, 2, 2, 2, -1, -1, -1, 0, 1, 0, 0, 2, -1, -1, 1, 0, -1, -2, 1, 0, 1, 0], [2, 2, 2, -2, 0, 2, 2, -1, -1, -1, 2, -1, -2, 0, 0, 0, 0, 2, -1, 2, -1, 2, -1, -1, -1, 0, -1, 2, 1, -2, 1, 0, -1, 1, 0, 0, 0, 0, 1], [2, 2, 2, 0, -2, 2, -1, 2, 2, -1, -1, -1, 0, -2, 0, 0, 0, 2, 2, -1, -1, -1, 2, -1, -1, -2, -1, -1, 0, 0, 0, 1, 2, 0, 1, 1, 1, 0, 0], [2, -2, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, -2*E(4), 2*E(4), -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, -2, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 2*E(4), -2*E(4), -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, 4, 0, 0, 4, -2, -2, 4, -2, -2, 1, 1, 0, 0, 0, 0, 0, -2, 4, -2, -2, 1, -2, 1, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, -2, 1, 0, 0, 0], [4, 4, 0, 4, 0, -2, 4, -2, 1, -2, -2, 1, 0, 0, 0, 0, 0, -2, -2, 4, -2, -2, 1, 1, 0, 0, 0, 0, -2, -2, 1, 0, 0, 1, 0, 0, 0, 0, 0], [4, 4, 4, 0, 0, 4, -2, -2, -2, 1, -2, 1, 0, 0, 0, 0, 0, 4, -2, -2, 1, -2, -2, 1, 1, 0, 1, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0], [4, 4, -4, 0, 0, 4, -2, -2, -2, 1, -2, 1, 0, 0, 0, 0, 0, 4, -2, -2, 1, -2, -2, 1, -1, 0, -1, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0], [4, 4, 0, -4, 0, -2, 4, -2, 1, -2, -2, 1, 0, 0, 0, 0, 0, -2, -2, 4, -2, -2, 1, 1, 0, 0, 0, 0, 2, 2, -1, 0, 0, -1, 0, 0, 0, 0, 0], [4, 4, 0, 0, -4, -2, -2, 4, -2, -2, 1, 1, 0, 0, 0, 0, 0, -2, 4, -2, -2, 1, -2, 1, 0, 2, 0, 0, 0, 0, 0, -1, 0, 0, 2, -1, 0, 0, 0], [4, -4, 0, 0, 0, -2, 4, 4, -2, 4, -2, -2, 0, 0, 0, 0, 0, 2, -4, -4, -4, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, -4, 0, 0, 0, 4, -2, 4, 4, -2, -2, -2, 0, 0, 0, 0, 0, -4, -4, 2, 2, 2, -4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, -4, 0, 0, 0, 4, 4, -2, -2, -2, 4, -2, 0, 0, 0, 0, 0, -4, 2, -4, 2, -4, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, -4, 0, 0, 0, -2, -2, 4, -2, -2, 1, 1, 0, 0, 0, 0, 0, 2, -4, 2, 2, -1, 2, -1, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 3, 0, 0, 0], [4, -4, 0, 0, 0, -2, -2, 4, -2, -2, 1, 1, 0, 0, 0, 0, 0, 2, -4, 2, 2, -1, 2, -1, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, -3, 0, 0, 0], [4, -4, 0, 0, 0, -2, 4, -2, 1, -2, -2, 1, 0, 0, 0, 0, 0, 2, 2, -4, 2, 2, -1, -1, 0, 0, 0, 0, 0, 0, -3, 0, 0, 3, 0, 0, 0, 0, 0], [4, -4, 0, 0, 0, -2, 4, -2, 1, -2, -2, 1, 0, 0, 0, 0, 0, 2, 2, -4, 2, 2, -1, -1, 0, 0, 0, 0, 0, 0, 3, 0, 0, -3, 0, 0, 0, 0, 0], [4, -4, 0, 0, 0, 4, -2, -2, -2, 1, -2, 1, 0, 0, 0, 0, 0, -4, 2, 2, -1, 2, 2, -1, -3, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, -4, 0, 0, 0, 4, -2, -2, -2, 1, -2, 1, 0, 0, 0, 0, 0, -4, 2, 2, -1, 2, 2, -1, 3, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [8, 8, 0, 0, 0, -4, -4, -4, 2, 2, 2, -1, 0, 0, 0, 0, 0, -4, -4, -4, 2, 2, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [8, -8, 0, 0, 0, -4, -4, -4, 2, 2, 2, -1, 0, 0, 0, 0, 0, 4, 4, 4, -2, -2, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]; ConvertToLibraryCharacterTableNC(chartbl_432_610);