# Group 432.251 downloaded from the LMFDB on 31 October 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(251525782316287573359108391294101,432); a := GPC.1; b := GPC.3; c := GPC.4; d := GPC.6; GPerm := Group( (2,4)(3,6)(5,7)(8,9)(11,12)(14,15,16,17), (2,5,9)(4,7,8), (14,16)(15,17), (1,2,4)(3,5,8)(6,9,7)(11,12,13), (1,3,6)(2,5,9)(4,8,7), (10,11)(12,13), (10,12)(11,13) ); GLZN := Group([[[ZmodnZObj(1,36), ZmodnZObj(12,36)], [ZmodnZObj(0,36), ZmodnZObj(1,36)]],[[ZmodnZObj(7,36), ZmodnZObj(29,36)], [ZmodnZObj(3,36), ZmodnZObj(4,36)]],[[ZmodnZObj(17,36), ZmodnZObj(11,36)], [ZmodnZObj(0,36), ZmodnZObj(1,36)]],[[ZmodnZObj(19,36), ZmodnZObj(0,36)], [ZmodnZObj(18,36), ZmodnZObj(19,36)]],[[ZmodnZObj(1,36), ZmodnZObj(0,36)], [ZmodnZObj(0,36), ZmodnZObj(25,36)]],[[ZmodnZObj(1,36), ZmodnZObj(18,36)], [ZmodnZObj(0,36), ZmodnZObj(1,36)]],[[ZmodnZObj(1,36), ZmodnZObj(18,36)], [ZmodnZObj(18,36), ZmodnZObj(1,36)]]]); # Booleans booleans_432_251 := 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_432_251:=rec(); chartbl_432_251.IsFinite:= true; chartbl_432_251.UnderlyingCharacteristic:= 0; chartbl_432_251.UnderlyingGroup:= GPC; chartbl_432_251.Size:= 432; chartbl_432_251.InfoText:= "Character table for group 432.251 downloaded from the LMFDB."; chartbl_432_251.Identifier:= " (C3*A4):C12 "; chartbl_432_251.NrConjugacyClasses:= 38; chartbl_432_251.ConjugacyClasses:= [ of ..., f2, f6*f7, f2*f4*f5, f5^2, f7, f7^2, f3^2*f5^2, f3*f5*f7^2, f3^2*f7, f1*f2, f1, f1*f2*f4*f6*f7, f1*f4, f2*f5, f6, f6*f7^2, f2*f7^2, f2*f7, f2*f6, f2*f6*f7^2, f4, f2*f4, f5*f6, f4*f7, f2*f5*f6, f2*f4*f7, f2*f3*f5, f2*f3^2*f7, f2*f3*f5*f7^2, f1*f7, f1*f2*f6, f1*f6, f1*f2*f7, f1*f4*f7, f1*f2*f4*f6, f1*f4*f6, f1*f2*f4*f7]; chartbl_432_251.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]; chartbl_432_251.ComputedPowerMaps:= [ , [1, 1, 1, 1, 5, 7, 6, 8, 10, 9, 2, 2, 4, 4, 5, 6, 7, 6, 7, 6, 7, 5, 5, 6, 7, 6, 7, 8, 9, 10, 18, 19, 19, 18, 20, 21, 21, 20], [1, 2, 3, 4, 1, 1, 1, 1, 1, 1, 12, 11, 14, 13, 2, 3, 3, 2, 2, 4, 4, 3, 4, 3, 3, 4, 4, 2, 2, 2, 11, 12, 11, 12, 13, 14, 13, 14]]; chartbl_432_251.SizesCentralizers:= [432, 432, 144, 144, 216, 144, 144, 18, 18, 18, 24, 24, 24, 24, 216, 144, 144, 144, 144, 144, 144, 72, 72, 72, 72, 72, 72, 18, 18, 18, 24, 24, 24, 24, 24, 24, 24, 24]; chartbl_432_251.ClassNames:= ["1A", "2A", "2B", "2C", "3A", "3B1", "3B-1", "3C", "3D1", "3D-1", "4A1", "4A-1", "4B1", "4B-1", "6A", "6B1", "6B-1", "6C1", "6C-1", "6D1", "6D-1", "6E", "6F", "6G1", "6G-1", "6H1", "6H-1", "6I", "6J1", "6J-1", "12A1", "12A-1", "12A5", "12A-5", "12B1", "12B-1", "12B5", "12B-5"]; chartbl_432_251.OrderClassRepresentatives:= [1, 2, 2, 2, 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, 12, 12, 12, 12, 12, 12, 12, 12]; chartbl_432_251.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, E(3)^-1, E(3), 1, E(3), E(3)^-1, 1, 1, 1, 1, 1, E(3)^-1, E(3), E(3), E(3)^-1, E(3), E(3)^-1, E(3)^-1, 1, E(3), E(3)^-1, E(3), 1, 1, E(3)^-1, E(3), E(3), E(3), E(3)^-1, E(3)^-1, E(3)^-1, E(3), E(3)^-1, E(3)], [1, 1, 1, 1, 1, E(3), E(3)^-1, 1, E(3)^-1, E(3), 1, 1, 1, 1, 1, E(3), E(3)^-1, E(3)^-1, E(3), E(3)^-1, E(3), E(3), 1, E(3)^-1, E(3), E(3)^-1, 1, 1, E(3), E(3)^-1, E(3)^-1, E(3)^-1, E(3), E(3), E(3), E(3)^-1, E(3), E(3)^-1], [1, -1, 1, -1, 1, 1, 1, 1, 1, 1, -1*E(4), -1*E(4), E(4), E(4), -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, -1, -1, -1*E(4), -1*E(4), E(4), -1*E(4), E(4), E(4), -1*E(4), E(4)], [1, -1, 1, -1, 1, 1, 1, 1, 1, 1, E(4), E(4), -1*E(4), -1*E(4), -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, -1, -1, E(4), E(4), -1*E(4), E(4), -1*E(4), -1*E(4), E(4), -1*E(4)], [1, 1, 1, 1, 1, E(3)^-1, E(3), 1, E(3), E(3)^-1, -1, -1, -1, -1, 1, E(3)^-1, E(3), E(3), E(3)^-1, E(3), E(3)^-1, E(3)^-1, 1, E(3), E(3)^-1, E(3), 1, 1, E(3)^-1, E(3), -1*E(3), -1*E(3), -1*E(3)^-1, -1*E(3)^-1, -1*E(3)^-1, -1*E(3), -1*E(3)^-1, -1*E(3)], [1, 1, 1, 1, 1, E(3), E(3)^-1, 1, E(3)^-1, E(3), -1, -1, -1, -1, 1, E(3), E(3)^-1, E(3)^-1, E(3), E(3)^-1, E(3), E(3), 1, E(3)^-1, E(3), E(3)^-1, 1, 1, E(3), E(3)^-1, -1*E(3)^-1, -1*E(3)^-1, -1*E(3), -1*E(3), -1*E(3), -1*E(3)^-1, -1*E(3), -1*E(3)^-1], [1, -1, 1, -1, 1, -1*E(12)^2, E(12)^4, 1, E(12)^4, -1*E(12)^2, -1*E(12)^3, -1*E(12)^3, E(12)^3, E(12)^3, -1, -1*E(12)^2, E(12)^4, -1*E(12)^4, E(12)^2, -1*E(12)^4, E(12)^2, E(12)^2, -1, -1*E(12)^4, -1*E(12)^2, E(12)^4, 1, -1, E(12)^2, -1*E(12)^4, E(12), E(12), -1*E(12)^5, E(12)^5, -1*E(12)^5, -1*E(12), E(12)^5, -1*E(12)], [1, -1, 1, -1, 1, E(12)^4, -1*E(12)^2, 1, -1*E(12)^2, E(12)^4, E(12)^3, E(12)^3, -1*E(12)^3, -1*E(12)^3, -1, E(12)^4, -1*E(12)^2, E(12)^2, -1*E(12)^4, E(12)^2, -1*E(12)^4, -1*E(12)^4, -1, E(12)^2, E(12)^4, -1*E(12)^2, 1, -1, -1*E(12)^4, E(12)^2, -1*E(12)^5, -1*E(12)^5, E(12), -1*E(12), E(12), E(12)^5, -1*E(12), E(12)^5], [1, -1, 1, -1, 1, -1*E(12)^2, E(12)^4, 1, E(12)^4, -1*E(12)^2, E(12)^3, E(12)^3, -1*E(12)^3, -1*E(12)^3, -1, -1*E(12)^2, E(12)^4, -1*E(12)^4, E(12)^2, -1*E(12)^4, E(12)^2, E(12)^2, -1, -1*E(12)^4, -1*E(12)^2, E(12)^4, 1, -1, E(12)^2, -1*E(12)^4, -1*E(12), -1*E(12), E(12)^5, -1*E(12)^5, E(12)^5, E(12), -1*E(12)^5, E(12)], [1, -1, 1, -1, 1, E(12)^4, -1*E(12)^2, 1, -1*E(12)^2, E(12)^4, -1*E(12)^3, -1*E(12)^3, E(12)^3, E(12)^3, -1, E(12)^4, -1*E(12)^2, E(12)^2, -1*E(12)^4, E(12)^2, -1*E(12)^4, -1*E(12)^4, -1, E(12)^2, E(12)^4, -1*E(12)^2, 1, -1, -1*E(12)^4, E(12)^2, E(12)^5, E(12)^5, -1*E(12), E(12), -1*E(12), -1*E(12)^5, E(12), -1*E(12)^5], [2, 2, 2, 2, 2, 2, 2, -1, -1, -1, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0], [2, -2, 2, -2, 2, 2, 2, -1, -1, -1, 0, 0, 0, 0, -2, 2, 2, -2, -2, -2, -2, -2, -2, -2, 2, 2, 2, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, 2, 2, 2*E(3)^-1, 2*E(3), -1, -1*E(3), -1*E(3)^-1, 0, 0, 0, 0, 2, 2*E(3)^-1, 2*E(3), 2*E(3), 2*E(3)^-1, 2*E(3), 2*E(3)^-1, 2*E(3)^-1, 2, 2*E(3), 2*E(3)^-1, 2*E(3), 2, -1, -1*E(3)^-1, -1*E(3), 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, 2, 2, 2*E(3), 2*E(3)^-1, -1, -1*E(3)^-1, -1*E(3), 0, 0, 0, 0, 2, 2*E(3), 2*E(3)^-1, 2*E(3)^-1, 2*E(3), 2*E(3)^-1, 2*E(3), 2*E(3), 2, 2*E(3)^-1, 2*E(3), 2*E(3)^-1, 2, -1, -1*E(3), -1*E(3)^-1, 0, 0, 0, 0, 0, 0, 0, 0], [2, -2, 2, -2, 2, 2*E(3)^-1, 2*E(3), -1, -1*E(3), -1*E(3)^-1, 0, 0, 0, 0, -2, 2*E(3)^-1, 2*E(3), -2*E(3), -2*E(3)^-1, -2*E(3), -2*E(3)^-1, -2*E(3)^-1, -2, -2*E(3), 2*E(3)^-1, 2*E(3), 2, 1, E(3)^-1, E(3), 0, 0, 0, 0, 0, 0, 0, 0], [2, -2, 2, -2, 2, 2*E(3), 2*E(3)^-1, -1, -1*E(3)^-1, -1*E(3), 0, 0, 0, 0, -2, 2*E(3), 2*E(3)^-1, -2*E(3)^-1, -2*E(3), -2*E(3)^-1, -2*E(3), -2*E(3), -2, -2*E(3)^-1, 2*E(3), 2*E(3)^-1, 2, 1, E(3), E(3)^-1, 0, 0, 0, 0, 0, 0, 0, 0], [3, 3, -1, -1, 3, 3, 3, 0, 0, 0, -1, 1, 1, -1, 3, -1, -1, -1, 3, 3, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, -1, 1, -1, 1, 1, 1, -1, -1], [3, 3, -1, -1, 3, 3, 3, 0, 0, 0, 1, -1, -1, 1, 3, -1, -1, -1, 3, 3, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 1, -1, 1, -1, -1, -1, 1, 1], [3, -3, -1, 1, 3, 3, 3, 0, 0, 0, -1*E(4), E(4), -1*E(4), E(4), -3, -1, -1, 1, -3, -3, 1, 1, 1, 1, -1, -1, -1, 0, 0, 0, -1*E(4), E(4), E(4), E(4), -1*E(4), -1*E(4), -1*E(4), E(4)], [3, -3, -1, 1, 3, 3, 3, 0, 0, 0, E(4), -1*E(4), E(4), -1*E(4), -3, -1, -1, 1, -3, -3, 1, 1, 1, 1, -1, -1, -1, 0, 0, 0, E(4), -1*E(4), -1*E(4), -1*E(4), E(4), E(4), E(4), -1*E(4)], [3, 3, -1, -1, 3, 3*E(3)^-1, 3*E(3), 0, 0, 0, -1, 1, 1, -1, 3, -1*E(3)^-1, -1*E(3), -1*E(3), 3*E(3)^-1, 3*E(3), -1*E(3)^-1, -1*E(3)^-1, -1, -1*E(3), -1*E(3)^-1, -1*E(3), -1, 0, 0, 0, -1*E(3), E(3), -1*E(3)^-1, E(3)^-1, E(3)^-1, E(3), -1*E(3)^-1, -1*E(3)], [3, 3, -1, -1, 3, 3*E(3), 3*E(3)^-1, 0, 0, 0, -1, 1, 1, -1, 3, -1*E(3), -1*E(3)^-1, -1*E(3)^-1, 3*E(3), 3*E(3)^-1, -1*E(3), -1*E(3), -1, -1*E(3)^-1, -1*E(3), -1*E(3)^-1, -1, 0, 0, 0, -1*E(3)^-1, E(3)^-1, -1*E(3), E(3), E(3), E(3)^-1, -1*E(3), -1*E(3)^-1], [3, 3, -1, -1, 3, 3*E(3)^-1, 3*E(3), 0, 0, 0, 1, -1, -1, 1, 3, -1*E(3)^-1, -1*E(3), -1*E(3), 3*E(3)^-1, 3*E(3), -1*E(3)^-1, -1*E(3)^-1, -1, -1*E(3), -1*E(3)^-1, -1*E(3), -1, 0, 0, 0, E(3), -1*E(3), E(3)^-1, -1*E(3)^-1, -1*E(3)^-1, -1*E(3), E(3)^-1, E(3)], [3, 3, -1, -1, 3, 3*E(3), 3*E(3)^-1, 0, 0, 0, 1, -1, -1, 1, 3, -1*E(3), -1*E(3)^-1, -1*E(3)^-1, 3*E(3), 3*E(3)^-1, -1*E(3), -1*E(3), -1, -1*E(3)^-1, -1*E(3), -1*E(3)^-1, -1, 0, 0, 0, E(3)^-1, -1*E(3)^-1, E(3), -1*E(3), -1*E(3), -1*E(3)^-1, E(3), E(3)^-1], [3, -3, -1, 1, 3, -3*E(12)^2, 3*E(12)^4, 0, 0, 0, -1*E(12)^3, E(12)^3, -1*E(12)^3, E(12)^3, -3, E(12)^2, -1*E(12)^4, E(12)^4, 3*E(12)^2, -3*E(12)^4, -1*E(12)^2, -1*E(12)^2, 1, E(12)^4, E(12)^2, -1*E(12)^4, -1, 0, 0, 0, E(12), -1*E(12), -1*E(12)^5, -1*E(12)^5, E(12)^5, E(12), E(12)^5, -1*E(12)], [3, -3, -1, 1, 3, 3*E(12)^4, -3*E(12)^2, 0, 0, 0, E(12)^3, -1*E(12)^3, E(12)^3, -1*E(12)^3, -3, -1*E(12)^4, E(12)^2, -1*E(12)^2, -3*E(12)^4, 3*E(12)^2, E(12)^4, E(12)^4, 1, -1*E(12)^2, -1*E(12)^4, E(12)^2, -1, 0, 0, 0, -1*E(12)^5, E(12)^5, E(12), E(12), -1*E(12), -1*E(12)^5, -1*E(12), E(12)^5], [3, -3, -1, 1, 3, -3*E(12)^2, 3*E(12)^4, 0, 0, 0, E(12)^3, -1*E(12)^3, E(12)^3, -1*E(12)^3, -3, E(12)^2, -1*E(12)^4, E(12)^4, 3*E(12)^2, -3*E(12)^4, -1*E(12)^2, -1*E(12)^2, 1, E(12)^4, E(12)^2, -1*E(12)^4, -1, 0, 0, 0, -1*E(12), E(12), E(12)^5, E(12)^5, -1*E(12)^5, -1*E(12), -1*E(12)^5, E(12)], [3, -3, -1, 1, 3, 3*E(12)^4, -3*E(12)^2, 0, 0, 0, -1*E(12)^3, E(12)^3, -1*E(12)^3, E(12)^3, -3, -1*E(12)^4, E(12)^2, -1*E(12)^2, -3*E(12)^4, 3*E(12)^2, E(12)^4, E(12)^4, 1, -1*E(12)^2, -1*E(12)^4, E(12)^2, -1, 0, 0, 0, E(12)^5, -1*E(12)^5, -1*E(12), -1*E(12), E(12), E(12)^5, E(12), -1*E(12)^5], [6, 6, 6, 6, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [6, 6, -2, -2, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 4, 4, 4, 0, 0, 4, -2, 1, -2, -2, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [6, -6, 6, -6, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [6, -6, -2, 2, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 4, 4, -4, 0, 0, -4, 2, -1, 2, -2, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [6, 6, -2, -2, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 4*E(3)^-1, 4*E(3), 4*E(3), 0, 0, 4*E(3)^-1, -2*E(3)^-1, 1, -2*E(3), -2*E(3)^-1, -2*E(3), 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [6, 6, -2, -2, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 4*E(3), 4*E(3)^-1, 4*E(3)^-1, 0, 0, 4*E(3), -2*E(3), 1, -2*E(3)^-1, -2*E(3), -2*E(3)^-1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [6, -6, -2, 2, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 4*E(3)^-1, 4*E(3), -4*E(3), 0, 0, -4*E(3)^-1, 2*E(3)^-1, -1, 2*E(3), -2*E(3)^-1, -2*E(3), 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [6, -6, -2, 2, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 4*E(3), 4*E(3)^-1, -4*E(3)^-1, 0, 0, -4*E(3), 2*E(3), -1, 2*E(3)^-1, -2*E(3), -2*E(3)^-1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]; ConvertToLibraryCharacterTableNC(chartbl_432_251);