# Group 256.18790 downloaded from the LMFDB on 10 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(41863552016730566467276331461034981,256); a := GPC.1; b := GPC.2; c := GPC.3; d := GPC.5; e := GPC.6; GPerm := Group( (1,2)(3,6)(4,12)(5,10)(7,9)(8,13)(11,15)(14,16)(18,19), (1,2,7,10,6,3,5,9)(4,8,15,16,14,11,13,12)(17,18,20,19), (1,3,6,2)(4,11,14,8)(5,10,7,9)(12,13,16,15)(17,18,20,19), (1,4,5,13,6,14,7,15)(2,8,9,12,3,11,10,16)(17,19,20,18), (1,5,6,7)(2,9,3,10)(4,13,14,15)(8,12,11,16)(17,20)(18,19), (1,6)(2,3)(4,14)(5,7)(8,11)(9,10)(12,16)(13,15)(17,20)(18,19), (1,5,6,7)(2,10,3,9)(4,13,14,15)(8,16,11,12), (1,6)(2,3)(4,14)(5,7)(8,11)(9,10)(12,16)(13,15) ); # Booleans booleans_256_18790 := 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_18790:=rec(); chartbl_256_18790.IsFinite:= true; chartbl_256_18790.UnderlyingCharacteristic:= 0; chartbl_256_18790.UnderlyingGroup:= GPC; chartbl_256_18790.Size:= 256; chartbl_256_18790.InfoText:= "Character table for group 256.18790 downloaded from the LMFDB."; chartbl_256_18790.Identifier:= " C4.D4^2 "; chartbl_256_18790.NrConjugacyClasses:= 46; chartbl_256_18790.ConjugacyClasses:= [ of ..., f8, f5, f5*f8, f4*f5, f4, f1*f3*f6, f1*f3*f5*f6, f2, f2*f4*f6, f1*f2*f3, f1*f2*f3*f5, f1*f2, f7, f4*f7, f5*f7, f4*f5*f7, f3, f3*f8, f3*f7, f3*f7*f8, f1*f3*f6*f7, f1*f3*f4*f6, f1, f2*f6, f2*f4, f1*f7, f1*f2*f3*f6, f1*f2*f3*f5*f6, f1*f2*f6, f6, f6*f8, f5*f6, f5*f6*f8, f4*f6, f4*f5*f6, f3*f6, f3*f6*f8, f3*f6*f7, f3*f6*f7*f8, f1*f6, f1*f3, f1*f6*f7, f1*f3*f5, f2*f3, f2*f3*f6]; chartbl_256_18790.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_18790.ComputedPowerMaps:= [ , [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 6, 6, 6, 6, 2, 2, 3, 2, 2, 4, 2, 2, 2, 14, 14, 14, 14, 14, 14, 15, 15, 15, 15, 16, 14, 16, 14, 17, 17]]; chartbl_256_18790.SizesCentralizers:= [256, 256, 256, 256, 128, 128, 64, 64, 32, 32, 32, 32, 16, 128, 128, 128, 128, 64, 64, 64, 64, 64, 64, 32, 32, 32, 32, 32, 32, 16, 128, 128, 128, 128, 64, 64, 64, 64, 64, 64, 32, 32, 32, 32, 16, 16]; chartbl_256_18790.ClassNames:= ["1A", "2A", "2B", "2C", "2D", "2E", "2F", "2G", "2H", "2I", "2J", "2K", "2L", "4A", "4B", "4C", "4D", "4E", "4F", "4G", "4H", "4I", "4J", "4K", "4L", "4M", "4N", "4O", "4P", "4Q", "8A1", "8A-1", "8B1", "8B-1", "8C", "8D", "8E1", "8E-1", "8F1", "8F-1", "8G", "8H", "8I", "8J", "8K", "8L"]; chartbl_256_18790.OrderClassRepresentatives:= [1, 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, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]; chartbl_256_18790.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], [2, 2, -2, -2, -2, 2, -2, 2, 0, 0, 0, 0, 0, 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, 0, -2, 0, 0, 0], [2, 2, -2, -2, -2, 2, -2, 2, 0, 0, 0, 0, 0, 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, 0, 2, 0, 0, 0], [2, 2, -2, -2, -2, 2, 0, 0, 0, 0, -2, 2, 0, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 2, -2, -2, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, -2, -2, -2, 2, 0, 0, 0, 0, -2, 2, 0, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, -2, 2, 2, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, -2, -2, -2, 2, 0, 0, 0, 0, 2, -2, 0, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, -2, 2, 2, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, -2, -2, -2, 2, 0, 0, 0, 0, 2, -2, 0, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 2, -2, -2, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, -2, -2, -2, 2, 2, -2, 0, 0, 0, 0, 0, 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, 0, 2, 0, 0, 0], [2, 2, -2, -2, -2, 2, 2, -2, 0, 0, 0, 0, 0, 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, 0, -2, 0, 0, 0], [2, 2, -2, -2, 2, -2, -2, 2, 0, 0, 0, 0, 0, 2, -2, -2, 2, 0, -2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 2, -2, -2, 2, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0], [2, 2, -2, -2, 2, -2, -2, 2, 0, 0, 0, 0, 0, 2, -2, -2, 2, 0, -2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, -2, 2, 2, -2, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0], [2, 2, -2, -2, 2, -2, 2, -2, 0, 0, 0, 0, 0, 2, -2, -2, 2, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 2, -2, -2, 2, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0], [2, 2, -2, -2, 2, -2, 2, -2, 0, 0, 0, 0, 0, 2, -2, -2, 2, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, -2, 2, 2, -2, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0], [2, 2, 2, 2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 2, -2, 2, -2, 0, 2, 0, 0, 2, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0], [2, 2, 2, 2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 2, -2, 2, -2, 0, 2, 0, 0, 2, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0], [2, 2, 2, 2, -2, -2, 0, 0, -2, -2, 0, 0, 0, -2, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, -2, -2, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, 2, -2, -2, 0, 0, -2, 2, 0, 0, 0, -2, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 2, 2, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, 2, -2, -2, 0, 0, 2, -2, 0, 0, 0, -2, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 2, 2, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, 2, -2, -2, 0, 0, 2, 2, 0, 0, 0, -2, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, -2, -2, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, 2, -2, -2, 2, 2, 0, 0, 0, 0, 0, 2, -2, 2, -2, 0, -2, 0, 0, -2, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0], [2, 2, 2, 2, -2, -2, 2, 2, 0, 0, 0, 0, 0, 2, -2, 2, -2, 0, -2, 0, 0, -2, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0], [4, 4, -4, -4, 4, -4, 0, 0, 0, 0, 0, 0, 0, -4, 4, 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, 0, 0, 0], [4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, -4, -4, -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, 0, 0, 0], [4, -4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2*E(8)-2*E(8)^3, 2*E(8)+2*E(8)^3, -2*E(8)-2*E(8)^3, 2*E(8)+2*E(8)^3, 0, 0, 2*E(8)+2*E(8)^3, -2*E(8)-2*E(8)^3, 0, 0, 0, 0, 0, 0, 0, 0], [4, -4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2*E(8)+2*E(8)^3, -2*E(8)-2*E(8)^3, 2*E(8)+2*E(8)^3, -2*E(8)-2*E(8)^3, 0, 0, -2*E(8)-2*E(8)^3, 2*E(8)+2*E(8)^3, 0, 0, 0, 0, 0, 0, 0, 0], [4, -4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2*E(8)-2*E(8)^3, 2*E(8)+2*E(8)^3, -2*E(8)-2*E(8)^3, 2*E(8)+2*E(8)^3, 0, 0, -2*E(8)-2*E(8)^3, 2*E(8)+2*E(8)^3, 0, 0, 0, 0, 0, 0, 0, 0], [4, -4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2*E(8)+2*E(8)^3, -2*E(8)-2*E(8)^3, 2*E(8)+2*E(8)^3, -2*E(8)-2*E(8)^3, 0, 0, 2*E(8)+2*E(8)^3, -2*E(8)-2*E(8)^3, 0, 0, 0, 0, 0, 0, 0, 0], [4, -4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 2, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2*E(8)-2*E(8)^3, -2*E(8)-2*E(8)^3, 2*E(8)+2*E(8)^3, 2*E(8)+2*E(8)^3, 0, 0, 0, 0, -2*E(8)-2*E(8)^3, 2*E(8)+2*E(8)^3, 0, 0, 0, 0, 0, 0], [4, -4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 2, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2*E(8)+2*E(8)^3, 2*E(8)+2*E(8)^3, -2*E(8)-2*E(8)^3, -2*E(8)-2*E(8)^3, 0, 0, 0, 0, 2*E(8)+2*E(8)^3, -2*E(8)-2*E(8)^3, 0, 0, 0, 0, 0, 0], [4, -4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2*E(8)-2*E(8)^3, -2*E(8)-2*E(8)^3, 2*E(8)+2*E(8)^3, 2*E(8)+2*E(8)^3, 0, 0, 0, 0, 2*E(8)+2*E(8)^3, -2*E(8)-2*E(8)^3, 0, 0, 0, 0, 0, 0], [4, -4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2*E(8)+2*E(8)^3, 2*E(8)+2*E(8)^3, -2*E(8)-2*E(8)^3, -2*E(8)-2*E(8)^3, 0, 0, 0, 0, -2*E(8)-2*E(8)^3, 2*E(8)+2*E(8)^3, 0, 0, 0, 0, 0, 0]]; ConvertToLibraryCharacterTableNC(chartbl_256_18790);