# Group 256.5615 downloaded from the LMFDB on 07 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(162905529925418077669625633774677,256); a := GPC.1; b := GPC.3; c := GPC.5; d := GPC.7; GPerm := Group( (1,2)(3,5)(4,13)(6,16)(7,9)(8,11)(10,15)(12,14)(17,18,19,20), (1,3,6,2)(4,12,5,9)(7,16,15,13)(8,10,14,11)(17,19)(18,20), (1,4)(2,9)(3,12)(5,6)(7,8)(10,16)(11,13)(14,15)(17,18,19,20), (1,5,8,15)(2,10,11,3)(4,6,7,14)(9,16,13,12), (17,19)(18,20), (1,6)(2,3)(4,5)(7,15)(8,14)(9,12)(10,11)(13,16), (1,7)(2,9)(3,12)(4,8)(5,14)(6,15)(10,16)(11,13), (1,8)(2,11)(3,10)(4,7)(5,15)(6,14)(9,13)(12,16) ); # Booleans booleans_256_5615 := 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_5615:=rec(); chartbl_256_5615.IsFinite:= true; chartbl_256_5615.UnderlyingCharacteristic:= 0; chartbl_256_5615.UnderlyingGroup:= GPC; chartbl_256_5615.Size:= 256; chartbl_256_5615.InfoText:= "Character table for group 256.5615 downloaded from the LMFDB."; chartbl_256_5615.Identifier:= " C4^2:C4^2 "; chartbl_256_5615.NrConjugacyClasses:= 46; chartbl_256_5615.ConjugacyClasses:= [ of ..., f4, f8, f4*f8, f6, f4*f6*f8, f2, f2*f7, f2*f4, f2*f4*f7*f8, f3, f3*f4, f3*f6, f3*f4*f6, f7, f4*f7, f3*f7, f3*f4*f7, f2*f3, f2*f3*f4, f2*f3*f7, f2*f3*f4*f7, f5, f4*f5, f2*f5, f2*f4*f5, f1, f1*f2, f3*f5, f3*f4*f5, f1*f5, f1*f2*f5, f1*f4, f1*f2*f4, f1*f3, f1*f2*f3*f4, f2*f3*f5, f2*f3*f4*f5, f1*f4*f5, f1*f2*f4*f5, f1*f3*f5, f1*f2*f3*f4*f5, f1*f3*f4, f1*f2*f3, f1*f3*f4*f5, f1*f2*f3*f5]; chartbl_256_5615.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_5615.ComputedPowerMaps:= [ , [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 4, 4, 2, 2, 2, 2, 5, 5, 3, 3, 7, 7, 6, 6, 8, 8, 7, 7, 9, 9, 2, 2, 8, 8, 10, 10, 9, 9, 10, 10]]; chartbl_256_5615.SizesCentralizers:= [256, 256, 256, 256, 128, 128, 64, 64, 64, 64, 128, 128, 128, 128, 64, 64, 64, 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, 32, 32, 32]; chartbl_256_5615.ClassNames:= ["1A", "2A", "2B", "2C", "2D", "2E", "2F", "2G", "2H", "2I", "4A1", "4A-1", "4B1", "4B-1", "4C", "4D", "4E1", "4E-1", "4F1", "4F-1", "4G1", "4G-1", "4H", "4I", "4J", "4K", "4L1", "4L-1", "4M1", "4M-1", "4N1", "4N-1", "4O1", "4O-1", "4P1", "4P-1", "4Q1", "4Q-1", "4R1", "4R-1", "4S1", "4S-1", "4T1", "4T-1", "4U1", "4U-1"]; chartbl_256_5615.OrderClassRepresentatives:= [1, 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, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]; chartbl_256_5615.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*E(4), E(4), -1*E(4), E(4), -1, 1, -1*E(4), E(4), -1*E(4), E(4), -1*E(4), E(4), -1*E(4), -1, E(4), -1, -1*E(4), -1*E(4), -1, E(4), 1, E(4), 1, -1*E(4), 1, E(4), E(4), -1, -1*E(4), -1, E(4), 1, -1, -1*E(4), 1, 1], [1, -1, 1, -1, 1, -1, -1, -1, 1, 1, E(4), -1*E(4), E(4), -1*E(4), -1, 1, E(4), -1*E(4), E(4), -1*E(4), E(4), -1*E(4), E(4), -1, -1*E(4), -1, E(4), E(4), -1, -1*E(4), 1, -1*E(4), 1, E(4), 1, -1*E(4), -1*E(4), -1, E(4), -1, -1*E(4), 1, -1, E(4), 1, 1], [1, -1, 1, -1, 1, -1, -1, -1, 1, 1, -1*E(4), E(4), -1*E(4), E(4), -1, 1, -1*E(4), E(4), -1*E(4), E(4), -1*E(4), E(4), -1*E(4), -1, E(4), 1, E(4), E(4), 1, E(4), -1, -1*E(4), -1, E(4), 1, -1*E(4), -1*E(4), -1, -1*E(4), 1, -1*E(4), -1, 1, E(4), 1, -1], [1, -1, 1, -1, 1, -1, -1, -1, 1, 1, E(4), -1*E(4), E(4), -1*E(4), -1, 1, E(4), -1*E(4), E(4), -1*E(4), E(4), -1*E(4), E(4), -1, -1*E(4), 1, -1*E(4), -1*E(4), 1, -1*E(4), -1, E(4), -1, -1*E(4), 1, E(4), E(4), -1, E(4), 1, E(4), -1, 1, -1*E(4), 1, -1], [1, -1, 1, -1, 1, -1, -1, -1, 1, 1, -1*E(4), E(4), -1*E(4), E(4), -1, 1, -1*E(4), E(4), -1*E(4), E(4), -1*E(4), E(4), E(4), 1, -1*E(4), -1, -1*E(4), E(4), 1, -1*E(4), -1, -1*E(4), -1, E(4), -1, E(4), E(4), 1, E(4), 1, -1*E(4), 1, -1, -1*E(4), -1, 1], [1, -1, 1, -1, 1, -1, -1, -1, 1, 1, E(4), -1*E(4), E(4), -1*E(4), -1, 1, E(4), -1*E(4), E(4), -1*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), -1, -1*E(4), -1, -1*E(4), -1*E(4), 1, -1*E(4), 1, E(4), 1, -1, E(4), -1, 1], [1, -1, 1, -1, 1, -1, -1, -1, 1, 1, -1*E(4), E(4), -1*E(4), E(4), -1, 1, -1*E(4), E(4), -1*E(4), E(4), -1*E(4), E(4), E(4), 1, -1*E(4), 1, E(4), -1*E(4), -1, -1*E(4), 1, E(4), 1, -1*E(4), -1, -1*E(4), -1*E(4), 1, E(4), -1, E(4), -1, 1, E(4), -1, -1], [1, -1, 1, -1, 1, -1, -1, -1, 1, 1, E(4), -1*E(4), E(4), -1*E(4), -1, 1, E(4), -1*E(4), E(4), -1*E(4), E(4), -1*E(4), -1*E(4), 1, E(4), 1, -1*E(4), E(4), -1, E(4), 1, -1*E(4), 1, E(4), -1, E(4), E(4), 1, -1*E(4), -1, -1*E(4), -1, 1, -1*E(4), -1, -1], [1, -1, 1, -1, 1, -1, 1, 1, -1, -1, -1*E(4), E(4), -1*E(4), E(4), -1, 1, -1*E(4), E(4), E(4), -1*E(4), E(4), -1*E(4), -1*E(4), -1, -1*E(4), E(4), -1, -1, -1*E(4), E(4), E(4), -1, -1*E(4), 1, -1, -1, 1, 1, E(4), E(4), 1, -1*E(4), -1*E(4), 1, 1, E(4)], [1, -1, 1, -1, 1, -1, 1, 1, -1, -1, E(4), -1*E(4), E(4), -1*E(4), -1, 1, E(4), -1*E(4), -1*E(4), E(4), -1*E(4), E(4), E(4), -1, E(4), -1*E(4), -1, -1, E(4), -1*E(4), -1*E(4), -1, E(4), 1, -1, -1, 1, 1, -1*E(4), -1*E(4), 1, E(4), E(4), 1, 1, -1*E(4)], [1, -1, 1, -1, 1, -1, 1, 1, -1, -1, -1*E(4), E(4), -1*E(4), E(4), -1, 1, -1*E(4), E(4), E(4), -1*E(4), E(4), -1*E(4), -1*E(4), -1, -1*E(4), -1*E(4), 1, 1, E(4), E(4), -1*E(4), 1, E(4), -1, -1, 1, -1, 1, E(4), -1*E(4), -1, E(4), E(4), -1, 1, -1*E(4)], [1, -1, 1, -1, 1, -1, 1, 1, -1, -1, E(4), -1*E(4), E(4), -1*E(4), -1, 1, E(4), -1*E(4), -1*E(4), E(4), -1*E(4), E(4), E(4), -1, E(4), E(4), 1, 1, -1*E(4), -1*E(4), E(4), 1, -1*E(4), -1, -1, 1, -1, 1, -1*E(4), E(4), -1, -1*E(4), -1*E(4), -1, 1, E(4)], [1, -1, 1, -1, 1, -1, 1, 1, -1, -1, -1*E(4), E(4), -1*E(4), E(4), -1, 1, -1*E(4), E(4), E(4), -1*E(4), E(4), -1*E(4), E(4), 1, E(4), E(4), -1, 1, E(4), -1*E(4), -1*E(4), 1, E(4), -1, 1, -1, 1, -1, -1*E(4), -1*E(4), -1, -1*E(4), -1*E(4), 1, -1, E(4)], [1, -1, 1, -1, 1, -1, 1, 1, -1, -1, E(4), -1*E(4), E(4), -1*E(4), -1, 1, E(4), -1*E(4), -1*E(4), E(4), -1*E(4), E(4), -1*E(4), 1, -1*E(4), -1*E(4), -1, 1, -1*E(4), E(4), E(4), 1, -1*E(4), -1, 1, -1, 1, -1, E(4), E(4), -1, E(4), E(4), 1, -1, -1*E(4)], [1, -1, 1, -1, 1, -1, 1, 1, -1, -1, -1*E(4), E(4), -1*E(4), E(4), -1, 1, -1*E(4), E(4), E(4), -1*E(4), E(4), -1*E(4), E(4), 1, E(4), -1*E(4), 1, -1, -1*E(4), -1*E(4), E(4), -1, -1*E(4), 1, 1, 1, -1, -1, -1*E(4), E(4), 1, E(4), E(4), -1, -1, -1*E(4)], [1, -1, 1, -1, 1, -1, 1, 1, -1, -1, E(4), -1*E(4), E(4), -1*E(4), -1, 1, E(4), -1*E(4), -1*E(4), E(4), -1*E(4), E(4), -1*E(4), 1, -1*E(4), E(4), 1, -1, E(4), E(4), -1*E(4), -1, E(4), 1, 1, 1, -1, -1, E(4), -1*E(4), 1, -1*E(4), -1*E(4), -1, -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*E(4), E(4), E(4), E(4), -1, E(4), -1*E(4), -1*E(4), -1*E(4), -1, -1*E(4), E(4), -1, 1, -1*E(4), E(4), -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, -1, -1, 1, 1, 1, 1, -1, 1, 1, E(4), -1*E(4), -1*E(4), -1*E(4), -1, -1*E(4), E(4), E(4), E(4), -1, E(4), -1*E(4), -1, 1, E(4), -1*E(4), E(4), -1*E(4), E(4), 1, -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*E(4), E(4), -1*E(4), -1*E(4), 1, -1*E(4), E(4), E(4), E(4), 1, -1*E(4), E(4), 1, -1, E(4), -1*E(4), -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, -1, -1, 1, 1, 1, 1, 1, -1, -1, E(4), -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, -1, -1*E(4), E(4), E(4), -1*E(4), E(4), -1, -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*E(4), -1*E(4), E(4), -1*E(4), -1, -1*E(4), -1*E(4), E(4), -1*E(4), 1, E(4), -1*E(4), 1, 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, E(4), E(4), -1*E(4), E(4), -1, E(4), E(4), -1*E(4), E(4), 1, -1*E(4), E(4), 1, 1, -1*E(4), -1*E(4), E(4), -1*E(4), -1*E(4), -1, -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*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), -1, -1, -1*E(4), -1*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, E(4), E(4), E(4), -1*E(4), 1, -1*E(4), -1*E(4), E(4), -1*E(4), -1, -1*E(4), E(4), -1, -1, E(4), E(4), E(4), -1*E(4), -1*E(4), 1, -1*E(4)], [2, 2, 2, 2, 2, 2, -2, 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, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, 2, 2, 2, -2, 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, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, 2, 2, 2, 2, -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, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, 2, 2, 2, 2, -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, 0, 0, 0, 0, 0, 0, 0], [2, -2, 2, -2, 2, -2, -2, 2, 2, -2, -2*E(4), 2*E(4), -2*E(4), 2*E(4), 2, -2, 2*E(4), -2*E(4), 2*E(4), 2*E(4), -2*E(4), -2*E(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], [2, -2, 2, -2, 2, -2, -2, 2, 2, -2, 2*E(4), -2*E(4), 2*E(4), -2*E(4), 2, -2, -2*E(4), 2*E(4), -2*E(4), -2*E(4), 2*E(4), 2*E(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], [2, -2, 2, -2, 2, -2, 2, -2, -2, 2, -2*E(4), 2*E(4), -2*E(4), 2*E(4), 2, -2, 2*E(4), -2*E(4), -2*E(4), -2*E(4), 2*E(4), 2*E(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], [2, -2, 2, -2, 2, -2, 2, -2, -2, 2, 2*E(4), -2*E(4), 2*E(4), -2*E(4), 2, -2, -2*E(4), 2*E(4), 2*E(4), 2*E(4), -2*E(4), -2*E(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], [4, 4, 4, 4, -4, -4, 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, 0, 0, 0], [4, 4, 4, 4, -4, -4, 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, 0, 0, 0], [4, -4, 4, -4, -4, 4, 0, 0, 0, 0, -4*E(4), 4*E(4), 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, -4, 4, -4, -4, 4, 0, 0, 0, 0, 4*E(4), -4*E(4), -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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [8, 8, -8, -8, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [8, -8, -8, 8, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]; ConvertToLibraryCharacterTableNC(chartbl_256_5615);