# Group 256.26336 downloaded from the LMFDB on 25 September 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(651574923237232375847145550688849,256); a := GPC.1; b := GPC.3; c := GPC.4; d := GPC.5; e := GPC.7; GPerm := Group( (1,11,3,9)(2,12,4,10)(5,16,8,13)(6,15,7,14), (1,2)(3,4)(5,6)(7,8)(9,14)(10,13)(11,16)(12,15), (1,5)(2,6)(3,8)(4,7)(9,13)(10,14)(11,16)(12,15), (1,3)(2,4)(5,7)(6,8)(9,11)(10,12)(13,15)(14,16), (1,5)(2,6)(3,7)(4,8)(9,13)(10,14)(11,15)(12,16), (1,3)(2,4)(5,8)(6,7)(9,11)(10,12)(13,16)(14,15), (9,10)(11,12)(13,14)(15,16), (1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16) ); # Booleans booleans_256_26336 := 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_26336:=rec(); chartbl_256_26336.IsFinite:= true; chartbl_256_26336.UnderlyingCharacteristic:= 0; chartbl_256_26336.UnderlyingGroup:= GPC; chartbl_256_26336.Size:= 256; chartbl_256_26336.InfoText:= "Character table for group 256.26336 downloaded from the LMFDB."; chartbl_256_26336.Identifier:= " (D4*C2^3):C4 "; chartbl_256_26336.NrConjugacyClasses:= 46; chartbl_256_26336.ConjugacyClasses:= [ of ..., f6, f3, f3*f8, f3*f5, f3*f5*f8, f8, f4, f3*f4, f2*f7, f2*f3, f3*f4*f5, f2*f6*f7, f2*f4*f5, f2*f3*f5, f2, f2*f3*f7, f2*f3*f5*f7, f5, f5*f8, f4*f5, f2*f5, f2*f3*f4, f2*f3*f4*f5, f2*f4, f7, f5*f7, f3*f7, f3*f5*f7, f2*f5*f7, f1, f1*f2, f1*f5, f1*f2*f5, f1*f3, f1*f2*f3, f1*f3*f5, f1*f2*f3*f5, f1*f7, f1*f2*f7, f1*f5*f7, f1*f2*f5*f7, f1*f3*f7, f1*f2*f3*f7, f1*f3*f5*f7, f1*f2*f3*f5*f7]; chartbl_256_26336.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, 43, 44, 45, 46]; chartbl_256_26336.ComputedPowerMaps:= [ , [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, 7, 7, 7, 7, 2, 16, 16, 16, 16, 16, 16, 16, 16, 25, 25, 25, 25, 25, 25, 25, 25]]; chartbl_256_26336.SizesCentralizers:= [256, 256, 128, 128, 128, 128, 128, 64, 64, 64, 64, 64, 64, 64, 64, 64, 32, 32, 128, 128, 64, 64, 64, 64, 64, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32]; chartbl_256_26336.ClassNames:= ["1A", "2A", "2B", "2C", "2D", "2E", "2F", "2G", "2H", "2I", "2J", "2K", "2L", "2M", "2N", "2O", "2P", "2Q", "4A", "4B", "4C", "4D", "4E", "4F", "4G", "4H", "4I", "4J", "4K", "4L", "4M1", "4M-1", "4N1", "4N-1", "4O1", "4O-1", "4P1", "4P-1", "8A1", "8A-1", "8B1", "8B-1", "8C1", "8C-1", "8D1", "8D-1"]; chartbl_256_26336.OrderClassRepresentatives:= [1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 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, 8, 8, 8, 8, 8, 8, 8, 8]; chartbl_256_26336.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, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 1, 1, 1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1, -1, -1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [1, 1, -1, -1, 1, -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), E(4), -1*E(4), -1, E(4), -1*E(4), E(4), -1*E(4), E(4), -1*E(4), 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, E(4), -1, -1*E(4), E(4), -1*E(4), -1*E(4), E(4), -1, -1*E(4), E(4), -1*E(4), E(4), -1*E(4), E(4), -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*E(4), 1, E(4), -1*E(4), E(4), E(4), -1*E(4), 1, E(4), -1*E(4), -1*E(4), E(4), -1*E(4), E(4), -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, E(4), 1, -1*E(4), E(4), -1*E(4), -1*E(4), E(4), 1, -1*E(4), E(4), E(4), -1*E(4), E(4), -1*E(4), 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*E(4), 1, E(4), E(4), -1*E(4), -1*E(4), -1*E(4), 1, E(4), E(4), -1*E(4), -1*E(4), E(4), -1*E(4), 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, E(4), 1, -1*E(4), -1*E(4), E(4), E(4), E(4), 1, -1*E(4), -1*E(4), E(4), E(4), -1*E(4), E(4), -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*E(4), -1, E(4), E(4), -1*E(4), -1*E(4), -1*E(4), -1, E(4), E(4), E(4), E(4), -1*E(4), E(4), -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, E(4), -1, -1*E(4), -1*E(4), E(4), E(4), E(4), -1, -1*E(4), -1*E(4), -1*E(4), -1*E(4), E(4), -1*E(4), 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*E(4), 1, E(4), E(4), E(4), -1*E(4), E(4), -1, -1*E(4), -1*E(4), -1*E(4), E(4), E(4), -1*E(4), -1*E(4), 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, E(4), 1, -1*E(4), -1*E(4), -1*E(4), E(4), -1*E(4), -1, E(4), E(4), E(4), -1*E(4), -1*E(4), E(4), E(4), -1*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*E(4), -1, E(4), E(4), E(4), -1*E(4), E(4), 1, -1*E(4), -1*E(4), E(4), -1*E(4), -1*E(4), E(4), E(4), -1*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, E(4), -1, -1*E(4), -1*E(4), -1*E(4), E(4), -1*E(4), 1, E(4), E(4), -1*E(4), E(4), E(4), -1*E(4), -1*E(4), 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*E(4), -1, E(4), -1*E(4), -1*E(4), E(4), E(4), 1, -1*E(4), E(4), E(4), E(4), E(4), -1*E(4), -1*E(4), -1*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, E(4), -1, -1*E(4), E(4), E(4), -1*E(4), -1*E(4), 1, E(4), -1*E(4), -1*E(4), -1*E(4), -1*E(4), E(4), E(4), 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*E(4), 1, E(4), -1*E(4), -1*E(4), E(4), E(4), -1, -1*E(4), E(4), -1*E(4), -1*E(4), -1*E(4), E(4), E(4), 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, E(4), 1, -1*E(4), E(4), E(4), -1*E(4), -1*E(4), -1, E(4), -1*E(4), E(4), E(4), E(4), -1*E(4), -1*E(4), -1*E(4), E(4), -1*E(4)], [2, 2, -2, -2, 2, -2, -2, -2, 2, -2, 2, 0, 2, 2, 0, 2, 0, 0, 2, 2, -2, -2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, -2, -2, 2, -2, -2, 2, -2, -2, -2, 0, 2, 2, 0, -2, 0, 0, 2, 2, 2, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, -2, -2, 2, 2, 2, -2, -2, -2, -2, 0, 2, -2, 0, 2, 0, 0, -2, -2, 2, 2, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, -2, -2, 2, 2, 2, 2, 2, -2, 2, 0, 2, -2, 0, -2, 0, 0, -2, -2, -2, 2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, 2, 2, -2, -2, -2, 2, -2, -2, 0, -2, 2, 0, -2, 0, 0, -2, -2, 2, 2, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, 2, 2, -2, -2, 2, -2, -2, 2, 0, -2, 2, 0, 2, 0, 0, -2, -2, -2, 2, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, 2, 2, 2, 2, -2, -2, -2, 2, 0, -2, -2, 0, -2, 0, 0, 2, 2, -2, -2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, 0, -2, -2, 0, 2, 0, 0, 2, 2, 2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, 4, -4, 4, -4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 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, 0], [4, 4, -4, 4, -4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 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, 0], [4, 4, 4, -4, -4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 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, 0], [4, 4, 4, -4, -4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 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, 0], [8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 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, 0, 0, 0, 0, 0, 0], [8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, -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, 0, 0, 0, 0, 0, 0]]; ConvertToLibraryCharacterTableNC(chartbl_256_26336);