# Group 256.11590 downloaded from the LMFDB on 16 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(10675859299953534582720696994568296805,256); a := GPC.1; b := GPC.2; c := GPC.3; d := GPC.5; e := GPC.6; GPerm := Group( (1,2)(3,12)(4,14)(5,10)(6,9)(7,11)(8,16)(13,15)(18,23)(19,21)(24,31)(25,30)(26,28)(27,32), (1,3)(2,4)(5,15)(6,14)(7,8)(9,16)(10,12)(11,13)(17,18)(19,23)(20,27)(21,30)(22,25)(24,29)(26,32)(28,31), (1,4,7,13)(2,8,11,3)(5,16,6,12)(9,14,10,15)(17,19,22,21)(18,23,25,30)(20,26,29,28)(24,31,27,32), (1,2)(3,13)(4,8)(5,9)(6,10)(7,11)(12,15)(14,16)(17,20,22,29)(18,24,25,27)(19,26,21,28)(23,31,30,32), (1,5,7,6)(2,9,11,10)(3,14,8,15)(4,12,13,16)(17,21,22,19)(18,23,25,30)(20,28,29,26)(24,31,27,32), (1,6,7,5)(2,10,11,9)(3,15,8,14)(4,16,13,12)(17,22)(18,25)(19,21)(20,29)(23,30)(24,27)(26,28)(31,32), (1,7)(2,11)(3,8)(4,13)(5,6)(9,10)(12,16)(14,15)(17,22)(18,25)(19,21)(20,29)(23,30)(24,27)(26,28)(31,32), (1,7)(2,11)(3,8)(4,13)(5,6)(9,10)(12,16)(14,15) ); # Booleans booleans_256_11590 := rec( Agroup := false, Zgroup := false, abelian := false, almost_simple := false, cyclic := false, metabelian := true, metacyclic := false, monomial := true, nilpotent := true, perfect := false, quasisimple := false, rational := false, solvable := true, supersolvable := true); # Character Table chartbl_256_11590:=rec(); chartbl_256_11590.IsFinite:= true; chartbl_256_11590.UnderlyingCharacteristic:= 0; chartbl_256_11590.UnderlyingGroup:= GPC; chartbl_256_11590.Size:= 256; chartbl_256_11590.InfoText:= "Character table for group 256.11590 downloaded from the LMFDB."; chartbl_256_11590.Identifier:= " C4^2.C2^4 "; chartbl_256_11590.NrConjugacyClasses:= 40; chartbl_256_11590.ConjugacyClasses:= [ of ..., f4*f8, f8, f4, f5, f2, f2*f3, f2*f6, f3*f8, f3*f4, f3*f4*f7*f8, f3*f4*f7, f3*f5*f7, f3*f4*f5*f7, f5*f7, f3*f5, f7, f1, f1*f8, f1*f5, f1*f5*f8, f2*f5, f1*f7, f1*f2, f2*f3*f5, f1*f5*f7, f1*f2*f7, f1*f2*f5, f1*f2*f5*f7, f2*f5*f6, f6, f4*f6, f5*f6, f5*f6*f7, f1*f2*f6, f1*f2*f6*f8, f1*f2*f5*f6, f1*f2*f5*f6*f8, f1*f6, f1*f5*f6]; chartbl_256_11590.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]; chartbl_256_11590.ComputedPowerMaps:= [ , [1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 2, 2, 2, 2, 3, 4, 3, 3, 3, 3, 3, 4, 4, 3, 4, 4, 2, 2, 3, 2, 17, 17, 17, 17, 9, 9, 10, 10, 11, 12]]; chartbl_256_11590.SizesCentralizers:= [256, 256, 256, 256, 64, 32, 32, 16, 128, 128, 128, 128, 128, 128, 64, 64, 64, 64, 64, 64, 64, 32, 32, 32, 32, 32, 32, 32, 32, 16, 32, 32, 32, 32, 32, 32, 32, 32, 16, 16]; chartbl_256_11590.ClassNames:= ["1A", "2A", "2B", "2C", "2D", "2E", "2F", "2G", "4A", "4B", "4C", "4D", "4E1", "4E-1", "4F", "4G", "4H", "4I1", "4I-1", "4J1", "4J-1", "4K", "4L", "4M", "4N", "4O", "4P", "4Q", "4R", "4S", "8A", "8B", "8C1", "8C-1", "8D1", "8D-1", "8E1", "8E-1", "8F", "8G"]; chartbl_256_11590.OrderClassRepresentatives:= [1, 2, 2, 2, 2, 2, 2, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]; chartbl_256_11590.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, -1, -1, 1, -1, 1, -1, -1, 1], [1, 1, 1, 1, -1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, -1, 1, -1, 1, 1, -1, -1, 1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 1, 1, 1, -1], [1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, -1, -1, -1, -1, 1, 1, -1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1], [1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, -1, 1, -1, 1, 1], [1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, -1, -1, -1, -1, 1, 1, -1, 1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1], [1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, 1, 1, -1, 1, -1, -1], [1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, -1, -1, -1, -1, -1, -1, 1, -1, 1, -1, -1, 1, -1, -1, -1, 1, 1, -1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -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, 2, 2, -2, -2, 2, 0, -2, -2, 2, 2, -2, -2, 0, -2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, 2, -2, 0, 0, 0, -2, -2, 2, 2, 2, 2, -2, 2, 2, -2, -2, 2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, 2, -2, 0, 0, 0, -2, -2, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, 2, -2, 0, 0, 0, 2, 2, -2, -2, -2, -2, 0, 2, 0, -2, 2, 0, 0, 0, 0, -2, 2, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, 2, -2, 0, 0, 0, 2, 2, -2, -2, -2, -2, 0, 2, 0, -2, 2, 0, 0, 0, 0, 2, -2, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, 2, -2, 2, -2, 0, -2, -2, 2, 2, -2, -2, 0, -2, 0, 2, 2, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, 2, 2, -2, 2, 0, -2, -2, -2, -2, -2, -2, 0, 2, 0, 2, -2, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, 2, 2, 0, 0, 0, -2, -2, -2, -2, 2, 2, -2, -2, -2, -2, 2, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, 2, 2, 0, 0, 0, -2, -2, -2, -2, 2, 2, 2, -2, 2, -2, 2, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, 2, 2, 0, 0, 0, 2, 2, 2, 2, -2, -2, 0, -2, 0, -2, -2, 0, 0, 0, 0, -2, -2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, 2, 2, 0, 0, 0, 2, 2, 2, 2, -2, -2, 0, -2, 0, -2, -2, 0, 0, 0, 0, 2, 2, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, 2, 2, 2, -2, 0, -2, -2, -2, -2, -2, -2, 0, 2, 0, 2, -2, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, -4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, -4*E(4), 0, 0, 0, 0, 0, 4*E(4), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, -4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, 4*E(4), 0, 0, 0, 0, 0, -4*E(4), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, -4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, 0, 0, -4*E(4), 0, 0, 4*E(4), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, -4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, 0, 0, 4*E(4), 0, 0, -4*E(4), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, 4, -4, -4, 0, 0, 0, 0, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2*E(8)-2*E(8)^3, 0, 0, 0, 2*E(8)+2*E(8)^3, 0, 0, 0, 0, 0], [4, 4, -4, -4, 0, 0, 0, 0, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2*E(8)+2*E(8)^3, 0, 0, 0, -2*E(8)-2*E(8)^3, 0, 0, 0, 0, 0], [4, 4, -4, -4, 0, 0, 0, 0, 4, -4, 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*E(8)-2*E(8)^3, 0, 2*E(8)+2*E(8)^3, 0, 0], [4, 4, -4, -4, 0, 0, 0, 0, 4, -4, 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*E(8)+2*E(8)^3, 0, -2*E(8)-2*E(8)^3, 0, 0], [4, -4, 4, -4, 0, 0, 0, 0, 0, 0, -4*E(4), 4*E(4), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2*E(4), 2*E(4), 0, 0, 2, 0, 0, 0], [4, -4, 4, -4, 0, 0, 0, 0, 0, 0, 4*E(4), -4*E(4), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2*E(4), -2*E(4), 0, 0, 2, 0, 0, 0], [4, -4, 4, -4, 0, 0, 0, 0, 0, 0, -4*E(4), 4*E(4), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2*E(4), -2*E(4), 0, 0, -2, 0, 0, 0], [4, -4, 4, -4, 0, 0, 0, 0, 0, 0, 4*E(4), -4*E(4), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2*E(4), 2*E(4), 0, 0, -2, 0, 0, 0]]; ConvertToLibraryCharacterTableNC(chartbl_256_11590);