# Group 64.216 downloaded from the LMFDB on 28 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(18970941854804,64); a := GPC.1; b := GPC.2; c := GPC.3; d := GPC.5; GPerm := Group( (1,2)(3,5)(4,6)(7,8)(10,12), (1,3,5,2)(4,6,8,7), (1,4)(2,6)(3,7)(5,8)(9,10)(11,12), (1,4)(2,7)(3,6)(5,8), (1,5)(2,3)(4,8)(6,7), (9,11)(10,12) ); GLZ := Group([[[0, 1, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, -1, 0, 0, 0], [0, 0, 0, 0, -1, 0], [0, 0, 0, 0, 0, -1]], [[1, 0, 0, 0, 0, 0], [0, -1, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, -1, 0, 0], [0, 0, 0, 0, 0, -1], [0, 0, 0, 0, -1, 0]], [[0, 0, 0, -1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0], [0, 0, 0, 0, -1, 0], [0, 0, 0, 0, 0, 1]], [[-1, 0, 0, 0, 0, 0], [0, -1, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, -1, 0], [0, 0, 0, 0, 0, -1]]]); GLFp := Group([[[ Z(2)^0, Z(2)^0, 0*Z(2), 0*Z(2), 0*Z(2) ], [ 0*Z(2), Z(2)^0, 0*Z(2), 0*Z(2), 0*Z(2) ], [ Z(2)^0, 0*Z(2), 0*Z(2), Z(2)^0, 0*Z(2) ], [ 0*Z(2), 0*Z(2), Z(2)^0, 0*Z(2), 0*Z(2) ], [ Z(2)^0, Z(2)^0, Z(2)^0, Z(2)^0, Z(2)^0 ]], [[ Z(2)^0, Z(2)^0, 0*Z(2), 0*Z(2), 0*Z(2) ], [ 0*Z(2), Z(2)^0, 0*Z(2), 0*Z(2), 0*Z(2) ], [ Z(2)^0, Z(2)^0, 0*Z(2), Z(2)^0, 0*Z(2) ], [ Z(2)^0, 0*Z(2), Z(2)^0, 0*Z(2), 0*Z(2) ], [ Z(2)^0, Z(2)^0, Z(2)^0, Z(2)^0, Z(2)^0 ]], [[ Z(2)^0, 0*Z(2), 0*Z(2), 0*Z(2), 0*Z(2) ], [ 0*Z(2), Z(2)^0, 0*Z(2), 0*Z(2), 0*Z(2) ], [ 0*Z(2), 0*Z(2), 0*Z(2), 0*Z(2), Z(2)^0 ], [ Z(2)^0, Z(2)^0, Z(2)^0, Z(2)^0, Z(2)^0 ], [ 0*Z(2), 0*Z(2), Z(2)^0, 0*Z(2), 0*Z(2) ]], [[ Z(2)^0, 0*Z(2), 0*Z(2), 0*Z(2), 0*Z(2) ], [ 0*Z(2), Z(2)^0, 0*Z(2), 0*Z(2), 0*Z(2) ], [ Z(2)^0, Z(2)^0, Z(2)^0, 0*Z(2), 0*Z(2) ], [ Z(2)^0, Z(2)^0, 0*Z(2), Z(2)^0, 0*Z(2) ], [ Z(2)^0, Z(2)^0, 0*Z(2), 0*Z(2), Z(2)^0 ]], [[ Z(2)^0, 0*Z(2), 0*Z(2), 0*Z(2), 0*Z(2) ], [ 0*Z(2), Z(2)^0, 0*Z(2), 0*Z(2), 0*Z(2) ], [ Z(2)^0, 0*Z(2), Z(2)^0, 0*Z(2), 0*Z(2) ], [ Z(2)^0, 0*Z(2), 0*Z(2), Z(2)^0, 0*Z(2) ], [ Z(2)^0, 0*Z(2), 0*Z(2), 0*Z(2), Z(2)^0 ]], [[ Z(2)^0, 0*Z(2), 0*Z(2), 0*Z(2), 0*Z(2) ], [ 0*Z(2), Z(2)^0, 0*Z(2), 0*Z(2), 0*Z(2) ], [ Z(2)^0, 0*Z(2), Z(2)^0, 0*Z(2), 0*Z(2) ], [ Z(2)^0, Z(2)^0, 0*Z(2), Z(2)^0, 0*Z(2) ], [ Z(2)^0, 0*Z(2), 0*Z(2), 0*Z(2), Z(2)^0 ]]]); GLZq := Group([[[ZmodnZObj(1,16), ZmodnZObj(8,16)], [ZmodnZObj(0,16), ZmodnZObj(1,16)]],[[ZmodnZObj(15,16), ZmodnZObj(0,16)], [ZmodnZObj(8,16), ZmodnZObj(15,16)]],[[ZmodnZObj(9,16), ZmodnZObj(8,16)], [ZmodnZObj(8,16), ZmodnZObj(9,16)]],[[ZmodnZObj(7,16), ZmodnZObj(2,16)], [ZmodnZObj(3,16), ZmodnZObj(9,16)]],[[ZmodnZObj(5,16), ZmodnZObj(0,16)], [ZmodnZObj(4,16), ZmodnZObj(13,16)]],[[ZmodnZObj(15,16), ZmodnZObj(0,16)], [ZmodnZObj(3,16), ZmodnZObj(1,16)]]]); # Booleans booleans_64_216 := 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 := true, solvable := true, supersolvable := true); # Character Table chartbl_64_216:=rec(); chartbl_64_216.IsFinite:= true; chartbl_64_216.UnderlyingCharacteristic:= 0; chartbl_64_216.UnderlyingGroup:= GLZq; chartbl_64_216.Size:= 64; chartbl_64_216.InfoText:= "Character table for group 64.216 downloaded from the LMFDB."; chartbl_64_216.Identifier:= " C4^2:C2^2 "; chartbl_64_216.NrConjugacyClasses:= 22; chartbl_64_216.ConjugacyClasses:= [[1, 0, 0, 1], [9, 0, 8, 9], [15, 0, 8, 15], [7, 0, 0, 7], [9, 8, 8, 9], [7, 8, 0, 7], [15, 10, 8, 9], [11, 10, 4, 13], [7, 2, 0, 1], [3, 2, 12, 5], [13, 8, 5, 3], [9, 0, 5, 7], [13, 8, 12, 5], [3, 8, 12, 11], [5, 0, 4, 13], [11, 0, 4, 3], [5, 14, 5, 3], [9, 14, 5, 7], [13, 0, 5, 11], [5, 6, 5, 11], [9, 8, 5, 15], [9, 6, 5, 15]]; chartbl_64_216.IdentificationOfConjugacyClasses:= [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22]; chartbl_64_216.ComputedPowerMaps:= [ , [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 4, 2, 4, 2, 3]]; chartbl_64_216.SizesCentralizers:= [64, 64, 64, 64, 32, 32, 16, 16, 16, 16, 16, 16, 32, 32, 32, 32, 16, 16, 16, 16, 16, 16]; chartbl_64_216.ClassNames:= ["1A", "2A", "2B", "2C", "2D", "2E", "2F", "2G", "2H", "2I", "2J", "2K", "4A", "4B", "4C", "4D", "4E", "4F", "4G", "4H", "4I", "4J"]; chartbl_64_216.OrderClassRepresentatives:= [1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]; chartbl_64_216.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], [2, 2, -2, -2, -2, 2, 0, 0, 0, 0, 0, 0, -2, 2, 2, -2, 0, 0, 0, 0, 0, 0], [2, 2, -2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 2, -2, -2, 2, 0, 0, 0, 0, 0, 0], [2, 2, -2, -2, 2, -2, 0, 0, 0, 0, 0, 0, -2, 2, -2, 2, 0, 0, 0, 0, 0, 0], [2, 2, -2, -2, 2, -2, 0, 0, 0, 0, 0, 0, 2, -2, 2, -2, 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], [4, -4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]; ConvertToLibraryCharacterTableNC(chartbl_64_216);