# Group 288.928 downloaded from the LMFDB on 20 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(675383822653342834298487072062714633,288); a := GPC.1; b := GPC.2; c := GPC.5; d := GPC.6; GPerm := Group( (1,2)(3,4)(6,7), (2,4), (9,11,10), (1,3)(2,4), (8,9)(10,11), (8,10)(9,11), (5,6,7) ); GLZN := Group([[[ZmodnZObj(22,28), ZmodnZObj(25,28)], [ZmodnZObj(1,28), ZmodnZObj(5,28)]],[[ZmodnZObj(13,28), ZmodnZObj(0,28)], [ZmodnZObj(0,28), ZmodnZObj(13,28)]],[[ZmodnZObj(1,28), ZmodnZObj(14,28)], [ZmodnZObj(14,28), ZmodnZObj(1,28)]],[[ZmodnZObj(13,28), ZmodnZObj(24,28)], [ZmodnZObj(0,28), ZmodnZObj(1,28)]],[[ZmodnZObj(15,28), ZmodnZObj(0,28)], [ZmodnZObj(14,28), ZmodnZObj(15,28)]],[[ZmodnZObj(9,28), ZmodnZObj(10,28)], [ZmodnZObj(6,28), ZmodnZObj(19,28)]],[[ZmodnZObj(22,28), ZmodnZObj(7,28)], [ZmodnZObj(7,28), ZmodnZObj(1,28)]]]); # Booleans booleans_288_928 := 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 := false); # Character Table chartbl_288_928:=rec(); chartbl_288_928.IsFinite:= true; chartbl_288_928.UnderlyingCharacteristic:= 0; chartbl_288_928.UnderlyingGroup:= GPC; chartbl_288_928.Size:= 288; chartbl_288_928.InfoText:= "Character table for group 288.928 downloaded from the LMFDB."; chartbl_288_928.Identifier:= " A4*C3:D4 "; chartbl_288_928.NrConjugacyClasses:= 36; chartbl_288_928.ConjugacyClasses:= [ of ..., f3*f4, f1, f6*f7, f3*f4*f6*f7, f1*f6*f7, f1*f2*f3, f1*f2*f3*f5*f7^2, f7^2, f4^2, f4, f4*f7^2, f4^2*f7, f2*f3*f7^2, f2*f4^2*f5*f6, f3*f4*f7, f1*f7, f1*f7^2, f3*f6*f7, f3*f4^2*f5, f6, f3*f4*f6, f1*f6, f1*f5*f7, f3*f7, f3*f4^2*f7, f1*f4, f1*f3, f1*f4*f7, f1*f3*f7, f1*f4*f6, f1*f3*f6, f1*f2*f3*f4*f5*f6*f7, f1*f2*f3*f4^2*f5, f2*f5*f7^2, f2*f3*f4^2*f6]; chartbl_288_928.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]; chartbl_288_928.ComputedPowerMaps:= [ , [1, 1, 1, 1, 1, 1, 1, 1, 9, 11, 10, 13, 12, 2, 2, 9, 9, 9, 11, 10, 9, 9, 9, 9, 12, 13, 10, 11, 13, 12, 13, 12, 10, 11, 19, 20], [1, 2, 3, 4, 5, 6, 7, 8, 1, 1, 1, 1, 1, 14, 15, 2, 3, 3, 2, 2, 4, 5, 6, 6, 2, 2, 3, 3, 3, 3, 3, 3, 7, 7, 14, 14]]; chartbl_288_928.SizesCentralizers:= [288, 288, 144, 96, 96, 48, 48, 16, 144, 72, 72, 36, 36, 48, 16, 144, 144, 144, 72, 72, 48, 48, 48, 48, 36, 36, 36, 36, 36, 36, 36, 36, 12, 12, 12, 12]; chartbl_288_928.ClassNames:= ["1A", "2A", "2B", "2C", "2D", "2E", "2F", "2G", "3A", "3B1", "3B-1", "3C1", "3C-1", "4A", "4B", "6A", "6B1", "6B-1", "6C1", "6C-1", "6D", "6E", "6F1", "6F-1", "6G1", "6G-1", "6H1", "6H-1", "6I1", "6I-1", "6J1", "6J-1", "6K1", "6K-1", "12A1", "12A-1"]; chartbl_288_928.OrderClassRepresentatives:= [1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 12, 12]; chartbl_288_928.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, E(3)^-1, E(3), E(3), E(3)^-1, 1, 1, 1, 1, 1, E(3)^-1, E(3), 1, 1, 1, 1, E(3)^-1, E(3), E(3), E(3), E(3)^-1, E(3), E(3)^-1, E(3)^-1, E(3), E(3)^-1, E(3), E(3)^-1], [1, 1, 1, 1, 1, 1, 1, 1, 1, E(3), E(3)^-1, E(3)^-1, E(3), 1, 1, 1, 1, 1, E(3), E(3)^-1, 1, 1, 1, 1, E(3), E(3)^-1, E(3)^-1, E(3)^-1, E(3), E(3)^-1, E(3), E(3), E(3)^-1, E(3), E(3)^-1, E(3)], [1, 1, -1, 1, 1, -1, -1, -1, 1, E(3)^-1, E(3), E(3), E(3)^-1, 1, 1, 1, -1, -1, E(3)^-1, E(3), 1, -1, 1, -1, E(3)^-1, E(3), -1*E(3), -1*E(3), -1*E(3)^-1, -1*E(3), -1*E(3)^-1, -1*E(3)^-1, -1*E(3), -1*E(3)^-1, E(3), E(3)^-1], [1, 1, -1, 1, 1, -1, -1, -1, 1, E(3), E(3)^-1, E(3)^-1, E(3), 1, 1, 1, -1, -1, E(3), E(3)^-1, 1, -1, 1, -1, E(3), E(3)^-1, -1*E(3)^-1, -1*E(3)^-1, -1*E(3), -1*E(3)^-1, -1*E(3), -1*E(3), -1*E(3)^-1, -1*E(3), E(3)^-1, E(3)], [1, 1, -1, 1, 1, -1, 1, 1, 1, E(3)^-1, E(3), E(3), E(3)^-1, -1, -1, 1, -1, -1, E(3)^-1, E(3), 1, -1, 1, -1, E(3)^-1, E(3), -1*E(3), -1*E(3), -1*E(3)^-1, -1*E(3), -1*E(3)^-1, -1*E(3)^-1, E(3), E(3)^-1, -1*E(3), -1*E(3)^-1], [1, 1, -1, 1, 1, -1, 1, 1, 1, E(3), E(3)^-1, E(3)^-1, E(3), -1, -1, 1, -1, -1, E(3), E(3)^-1, 1, -1, 1, -1, E(3), E(3)^-1, -1*E(3)^-1, -1*E(3)^-1, -1*E(3), -1*E(3)^-1, -1*E(3), -1*E(3), E(3)^-1, E(3), -1*E(3)^-1, -1*E(3)], [1, 1, 1, 1, 1, 1, -1, -1, 1, E(3)^-1, E(3), E(3), E(3)^-1, -1, -1, 1, 1, 1, E(3)^-1, E(3), 1, 1, 1, 1, E(3)^-1, E(3), E(3), E(3), E(3)^-1, E(3), E(3)^-1, E(3)^-1, -1*E(3), -1*E(3)^-1, -1*E(3), -1*E(3)^-1], [1, 1, 1, 1, 1, 1, -1, -1, 1, E(3), E(3)^-1, E(3)^-1, E(3), -1, -1, 1, 1, 1, E(3), E(3)^-1, 1, 1, 1, 1, E(3), E(3)^-1, E(3)^-1, E(3)^-1, E(3), E(3)^-1, E(3), E(3), -1*E(3)^-1, -1*E(3), -1*E(3)^-1, -1*E(3)], [2, 2, 2, 2, 2, 2, 0, 0, -1, 2, 2, -1, -1, 0, 0, -1, -1, -1, 2, 2, -1, -1, -1, -1, -1, -1, 2, -1, -1, -1, -1, 2, 0, 0, 0, 0], [2, -2, 0, 2, -2, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0, -2, 0, 0, -2, -2, -2, 0, 2, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, -2, 2, 2, -2, 0, 0, -1, 2, 2, -1, -1, 0, 0, -1, 1, 1, 2, 2, -1, 1, -1, 1, -1, -1, -2, 1, 1, 1, 1, -2, 0, 0, 0, 0], [2, 2, 2, 2, 2, 2, 0, 0, -1, 2*E(3)^-1, 2*E(3), -1*E(3), -1*E(3)^-1, 0, 0, -1, -1, -1, 2*E(3)^-1, 2*E(3), -1, -1, -1, -1, -1*E(3)^-1, -1*E(3), 2*E(3), -1*E(3), -1*E(3)^-1, -1*E(3), -1*E(3)^-1, 2*E(3)^-1, 0, 0, 0, 0], [2, 2, 2, 2, 2, 2, 0, 0, -1, 2*E(3), 2*E(3)^-1, -1*E(3)^-1, -1*E(3), 0, 0, -1, -1, -1, 2*E(3), 2*E(3)^-1, -1, -1, -1, -1, -1*E(3), -1*E(3)^-1, 2*E(3)^-1, -1*E(3)^-1, -1*E(3), -1*E(3)^-1, -1*E(3), 2*E(3), 0, 0, 0, 0], [2, -2, 0, 2, -2, 0, 0, 0, -1, 2, 2, -1, -1, 0, 0, 1, -1-2*E(3), 1+2*E(3), -2, -2, 1, 1+2*E(3), -1, -1-2*E(3), 1, 1, 0, 1+2*E(3), -1-2*E(3), -1-2*E(3), 1+2*E(3), 0, 0, 0, 0, 0], [2, -2, 0, 2, -2, 0, 0, 0, -1, 2, 2, -1, -1, 0, 0, 1, 1+2*E(3), -1-2*E(3), -2, -2, 1, -1-2*E(3), -1, 1+2*E(3), 1, 1, 0, -1-2*E(3), 1+2*E(3), 1+2*E(3), -1-2*E(3), 0, 0, 0, 0, 0], [2, -2, 0, 2, -2, 0, 0, 0, 2, 2*E(3)^-1, 2*E(3), 2*E(3), 2*E(3)^-1, 0, 0, -2, 0, 0, -2*E(3)^-1, -2*E(3), -2, 0, 2, 0, -2*E(3)^-1, -2*E(3), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, -2, 0, 2, -2, 0, 0, 0, 2, 2*E(3), 2*E(3)^-1, 2*E(3)^-1, 2*E(3), 0, 0, -2, 0, 0, -2*E(3), -2*E(3)^-1, -2, 0, 2, 0, -2*E(3), -2*E(3)^-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, -2, 2, 2, -2, 0, 0, -1, 2*E(3)^-1, 2*E(3), -1*E(3), -1*E(3)^-1, 0, 0, -1, 1, 1, 2*E(3)^-1, 2*E(3), -1, 1, -1, 1, -1*E(3)^-1, -1*E(3), -2*E(3), E(3), E(3)^-1, E(3), E(3)^-1, -2*E(3)^-1, 0, 0, 0, 0], [2, 2, -2, 2, 2, -2, 0, 0, -1, 2*E(3), 2*E(3)^-1, -1*E(3)^-1, -1*E(3), 0, 0, -1, 1, 1, 2*E(3), 2*E(3)^-1, -1, 1, -1, 1, -1*E(3), -1*E(3)^-1, -2*E(3)^-1, E(3)^-1, E(3), E(3)^-1, E(3), -2*E(3), 0, 0, 0, 0], [2, -2, 0, 2, -2, 0, 0, 0, -1, 2*E(3)^-1, 2*E(3), -1*E(3), -1*E(3)^-1, 0, 0, 1, -1-2*E(3), 1+2*E(3), -2*E(3)^-1, -2*E(3), 1, 1+2*E(3), -1, -1-2*E(3), E(3)^-1, E(3), 0, -2-E(3), -1+E(3), 2+E(3), 1-E(3), 0, 0, 0, 0, 0], [2, -2, 0, 2, -2, 0, 0, 0, -1, 2*E(3), 2*E(3)^-1, -1*E(3)^-1, -1*E(3), 0, 0, 1, 1+2*E(3), -1-2*E(3), -2*E(3), -2*E(3)^-1, 1, -1-2*E(3), -1, 1+2*E(3), E(3), E(3)^-1, 0, -1+E(3), -2-E(3), 1-E(3), 2+E(3), 0, 0, 0, 0, 0], [2, -2, 0, 2, -2, 0, 0, 0, -1, 2*E(3)^-1, 2*E(3), -1*E(3), -1*E(3)^-1, 0, 0, 1, 1+2*E(3), -1-2*E(3), -2*E(3)^-1, -2*E(3), 1, -1-2*E(3), -1, 1+2*E(3), E(3)^-1, E(3), 0, 2+E(3), 1-E(3), -2-E(3), -1+E(3), 0, 0, 0, 0, 0], [2, -2, 0, 2, -2, 0, 0, 0, -1, 2*E(3), 2*E(3)^-1, -1*E(3)^-1, -1*E(3), 0, 0, 1, -1-2*E(3), 1+2*E(3), -2*E(3), -2*E(3)^-1, 1, 1+2*E(3), -1, -1-2*E(3), E(3), E(3)^-1, 0, 1-E(3), 2+E(3), -1+E(3), -2-E(3), 0, 0, 0, 0, 0], [3, 3, 3, -1, -1, -1, 3, -1, 3, 0, 0, 0, 0, 3, -1, 3, 3, 3, 0, 0, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, 3, -3, -1, -1, 1, -3, 1, 3, 0, 0, 0, 0, 3, -1, 3, -3, -3, 0, 0, -1, 1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, 3, -3, -1, -1, 1, 3, -1, 3, 0, 0, 0, 0, -3, 1, 3, -3, -3, 0, 0, -1, 1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, 3, 3, -1, -1, -1, -3, 1, 3, 0, 0, 0, 0, -3, 1, 3, 3, 3, 0, 0, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [6, 6, 6, -2, -2, -2, 0, 0, -3, 0, 0, 0, 0, 0, 0, -3, -3, -3, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [6, -6, 0, -2, 2, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [6, 6, -6, -2, -2, 2, 0, 0, -3, 0, 0, 0, 0, 0, 0, -3, 3, 3, 0, 0, 1, -1, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [6, -6, 0, -2, 2, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 3, -3-6*E(3), 3+6*E(3), 0, 0, -1, -1-2*E(3), 1, 1+2*E(3), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [6, -6, 0, -2, 2, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 3, 3+6*E(3), -3-6*E(3), 0, 0, -1, 1+2*E(3), 1, -1-2*E(3), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]; ConvertToLibraryCharacterTableNC(chartbl_288_928);