# Group 192.951 downloaded from the LMFDB on 06 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(316318452342688745225486664037861134191295240,192); a := GPC.1; b := GPC.2; c := GPC.5; d := GPC.6; GPerm := Group( (1,2)(3,6)(4,5), (1,2)(3,5)(4,6)(7,8)(9,10,11,12), (9,11)(10,12), (3,6,8)(4,7,5), (1,3,2,5)(4,8,6,7), (1,4,2,6)(3,7,5,8), (1,2)(3,5)(4,6)(7,8) ); GLZ := Group([[[-1, 1, 1, 0, 0, 0], [0, 1, 1, 1, 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, -1, 0, 0, 0], [0, 1, 0, 1, 0, 0], [1, 0, 0, 0, 0, 0], [0, -1, 0, 0, 0, 0], [0, 0, 0, 0, 0, -1], [0, 0, 0, 0, 1, 0]]]); GLFp := Group([[[ Z(3), 0*Z(3), 0*Z(3), Z(3) ], [ Z(3)^0, Z(3), 0*Z(3), Z(3)^0 ], [ Z(3)^0, 0*Z(3), Z(3), 0*Z(3) ], [ Z(3), 0*Z(3), 0*Z(3), Z(3)^0 ]], [[ Z(3)^0, 0*Z(3), 0*Z(3), 0*Z(3) ], [ Z(3)^0, Z(3)^0, Z(3)^0, Z(3)^0 ], [ Z(3)^0, Z(3)^0, Z(3), Z(3) ], [ Z(3)^0, 0*Z(3), 0*Z(3), Z(3)^0 ]], [[ 0*Z(3), 0*Z(3), 0*Z(3), Z(3) ], [ 0*Z(3), Z(3), Z(3), Z(3)^0 ], [ Z(3)^0, Z(3), Z(3)^0, Z(3) ], [ Z(3)^0, 0*Z(3), 0*Z(3), 0*Z(3) ]], [[ Z(3)^0, 0*Z(3), 0*Z(3), 0*Z(3) ], [ Z(3)^0, Z(3), Z(3), 0*Z(3) ], [ 0*Z(3), Z(3), Z(3)^0, Z(3) ], [ 0*Z(3), 0*Z(3), 0*Z(3), Z(3)^0 ]], [[ Z(3)^0, 0*Z(3), 0*Z(3), 0*Z(3) ], [ 0*Z(3), Z(3), 0*Z(3), Z(3)^0 ], [ Z(3), 0*Z(3), Z(3), Z(3)^0 ], [ 0*Z(3), 0*Z(3), 0*Z(3), Z(3)^0 ]], [[ Z(3), 0*Z(3), 0*Z(3), 0*Z(3) ], [ 0*Z(3), Z(3), 0*Z(3), 0*Z(3) ], [ 0*Z(3), 0*Z(3), Z(3), 0*Z(3) ], [ 0*Z(3), 0*Z(3), 0*Z(3), Z(3) ]], [[ Z(3)^0, 0*Z(3), 0*Z(3), 0*Z(3) ], [ Z(3)^0, Z(3)^0, 0*Z(3), Z(3) ], [ Z(3)^0, 0*Z(3), Z(3)^0, Z(3) ], [ Z(3), 0*Z(3), 0*Z(3), Z(3) ]]]); # Booleans booleans_192_951 := rec( Agroup := false, Zgroup := false, abelian := false, almost_simple := false, cyclic := false, metabelian := false, metacyclic := false, monomial := false, nilpotent := false, perfect := false, quasisimple := false, rational := false, solvable := true, supersolvable := false); # Character Table chartbl_192_951:=rec(); chartbl_192_951.IsFinite:= true; chartbl_192_951.UnderlyingCharacteristic:= 0; chartbl_192_951.UnderlyingGroup:= GPC; chartbl_192_951.Size:= 192; chartbl_192_951.InfoText:= "Character table for group 192.951 downloaded from the LMFDB."; chartbl_192_951.Identifier:= " C4*GL(2,3) "; chartbl_192_951.NrConjugacyClasses:= 32; chartbl_192_951.ConjugacyClasses:= [ of ..., f3*f4*f7, f3*f4, f7, f1, f1*f3, f4^2, f2*f3, f2*f4^2, f2*f3*f7, f2*f4^2*f7, f6, f3*f4*f5*f6, f2*f3*f6, f2*f4^2*f6, f1*f2, f1*f2*f3, f4*f7, f3*f7, f3, f1*f5, f1*f5*f7, f1*f3*f6, f1*f3*f6*f7, f1*f2*f6, f1*f2*f3*f5, f1*f2*f3*f5*f7, f1*f2*f6*f7, f2, f2*f3*f4, f2*f7, f2*f3*f4*f7]; chartbl_192_951.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]; chartbl_192_951.ComputedPowerMaps:= [ , [1, 1, 1, 1, 1, 1, 7, 3, 3, 3, 3, 4, 4, 2, 2, 3, 3, 7, 7, 7, 12, 12, 12, 12, 13, 13, 13, 13, 20, 20, 20, 20], [1, 2, 3, 4, 5, 6, 1, 9, 8, 11, 10, 12, 13, 15, 14, 17, 16, 4, 2, 3, 21, 22, 23, 24, 27, 28, 25, 26, 8, 9, 10, 11]]; chartbl_192_951.SizesCentralizers:= [192, 192, 192, 192, 16, 16, 24, 192, 192, 192, 192, 32, 32, 32, 32, 16, 16, 24, 24, 24, 32, 32, 32, 32, 32, 32, 32, 32, 24, 24, 24, 24]; chartbl_192_951.ClassNames:= ["1A", "2A", "2B", "2C", "2D", "2E", "3A", "4A1", "4A-1", "4B1", "4B-1", "4C", "4D", "4E1", "4E-1", "4F1", "4F-1", "6A", "6B", "6C", "8A1", "8A-1", "8B1", "8B-1", "8C1", "8C-1", "8C3", "8C-3", "12A1", "12A-1", "12B1", "12B-1"]; chartbl_192_951.OrderClassRepresentatives:= [1, 2, 2, 2, 2, 2, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 6, 6, 6, 8, 8, 8, 8, 8, 8, 8, 8, 12, 12, 12, 12]; chartbl_192_951.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*E(4), -1*E(4), E(4), E(4), -1*E(4), E(4), -1, 1, E(4), -1*E(4), 1, -1, -1, -1, -1, 1, -1*E(4), -1*E(4), E(4), 1, E(4), -1*E(4), E(4), -1*E(4), E(4)], [1, -1, -1, 1, -1, 1, 1, E(4), E(4), -1*E(4), -1*E(4), E(4), -1*E(4), -1, 1, -1*E(4), E(4), 1, -1, -1, -1, -1, 1, E(4), E(4), -1*E(4), 1, -1*E(4), E(4), -1*E(4), E(4), -1*E(4)], [1, -1, -1, 1, 1, -1, 1, -1*E(4), -1*E(4), E(4), E(4), -1*E(4), E(4), -1, 1, -1*E(4), E(4), 1, -1, -1, 1, 1, -1, E(4), E(4), -1*E(4), -1, -1*E(4), -1*E(4), E(4), -1*E(4), E(4)], [1, -1, -1, 1, 1, -1, 1, E(4), E(4), -1*E(4), -1*E(4), E(4), -1*E(4), -1, 1, E(4), -1*E(4), 1, -1, -1, 1, 1, -1, -1*E(4), -1*E(4), E(4), -1, E(4), E(4), -1*E(4), E(4), -1*E(4)], [2, 2, 2, 2, 0, 0, -1, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1], [2, 2, 2, 2, 0, 0, -1, -2, -2, -2, -2, -2, -2, 2, 2, 0, 0, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1], [2, -2, -2, 2, 0, 0, -1, -2*E(4), -2*E(4), 2*E(4), 2*E(4), -2*E(4), 2*E(4), -2, 2, 0, 0, -1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, E(4), -1*E(4), E(4), -1*E(4)], [2, -2, -2, 2, 0, 0, -1, 2*E(4), 2*E(4), -2*E(4), -2*E(4), 2*E(4), -2*E(4), -2, 2, 0, 0, -1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1*E(4), E(4), -1*E(4), E(4)], [2, -2, 2, -2, 0, 0, -1, -2, 2, 2, -2, 0, 0, 0, 0, 0, 0, 1, 1, -1, -1*E(8)-E(8)^3, E(8)+E(8)^3, E(8)+E(8)^3, -1*E(8)-E(8)^3, E(8)+E(8)^3, E(8)+E(8)^3, -1*E(8)-E(8)^3, -1*E(8)-E(8)^3, -1, -1, 1, 1], [2, -2, 2, -2, 0, 0, -1, -2, 2, 2, -2, 0, 0, 0, 0, 0, 0, 1, 1, -1, E(8)+E(8)^3, -1*E(8)-E(8)^3, -1*E(8)-E(8)^3, E(8)+E(8)^3, -1*E(8)-E(8)^3, -1*E(8)-E(8)^3, E(8)+E(8)^3, E(8)+E(8)^3, -1, -1, 1, 1], [2, -2, 2, -2, 0, 0, -1, 2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 1, 1, -1, -1*E(8)-E(8)^3, E(8)+E(8)^3, E(8)+E(8)^3, E(8)+E(8)^3, -1*E(8)-E(8)^3, -1*E(8)-E(8)^3, -1*E(8)-E(8)^3, E(8)+E(8)^3, 1, 1, -1, -1], [2, -2, 2, -2, 0, 0, -1, 2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 1, 1, -1, E(8)+E(8)^3, -1*E(8)-E(8)^3, -1*E(8)-E(8)^3, -1*E(8)-E(8)^3, E(8)+E(8)^3, E(8)+E(8)^3, E(8)+E(8)^3, -1*E(8)-E(8)^3, 1, 1, -1, -1], [2, 2, -2, -2, 0, 0, -1, -2*E(8)^2, 2*E(8)^2, -2*E(8)^2, 2*E(8)^2, 0, 0, 0, 0, 0, 0, 1, -1, 1, -1*E(8)-E(8)^3, E(8)+E(8)^3, -1*E(8)-E(8)^3, -1*E(8)-E(8)^-1, E(8)+E(8)^-1, -1*E(8)-E(8)^-1, E(8)+E(8)^3, E(8)+E(8)^-1, -1*E(8)^2, E(8)^2, E(8)^2, -1*E(8)^2], [2, 2, -2, -2, 0, 0, -1, 2*E(8)^2, -2*E(8)^2, 2*E(8)^2, -2*E(8)^2, 0, 0, 0, 0, 0, 0, 1, -1, 1, E(8)+E(8)^3, -1*E(8)-E(8)^3, E(8)+E(8)^3, -1*E(8)-E(8)^-1, E(8)+E(8)^-1, -1*E(8)-E(8)^-1, -1*E(8)-E(8)^3, E(8)+E(8)^-1, E(8)^2, -1*E(8)^2, -1*E(8)^2, E(8)^2], [2, 2, -2, -2, 0, 0, -1, -2*E(8)^2, 2*E(8)^2, -2*E(8)^2, 2*E(8)^2, 0, 0, 0, 0, 0, 0, 1, -1, 1, E(8)+E(8)^3, -1*E(8)-E(8)^3, E(8)+E(8)^3, E(8)+E(8)^-1, -1*E(8)-E(8)^-1, E(8)+E(8)^-1, -1*E(8)-E(8)^3, -1*E(8)-E(8)^-1, -1*E(8)^2, E(8)^2, E(8)^2, -1*E(8)^2], [2, 2, -2, -2, 0, 0, -1, 2*E(8)^2, -2*E(8)^2, 2*E(8)^2, -2*E(8)^2, 0, 0, 0, 0, 0, 0, 1, -1, 1, -1*E(8)-E(8)^3, E(8)+E(8)^3, -1*E(8)-E(8)^3, E(8)+E(8)^-1, -1*E(8)-E(8)^-1, E(8)+E(8)^-1, E(8)+E(8)^3, -1*E(8)-E(8)^-1, E(8)^2, -1*E(8)^2, -1*E(8)^2, E(8)^2], [3, 3, 3, 3, 1, 1, 0, 3, 3, 3, 3, -1, -1, -1, -1, 1, 1, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0], [3, 3, 3, 3, -1, -1, 0, 3, 3, 3, 3, -1, -1, -1, -1, -1, -1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0], [3, 3, 3, 3, -1, -1, 0, -3, -3, -3, -3, 1, 1, -1, -1, 1, 1, 0, 0, 0, 1, 1, 1, -1, -1, -1, 1, -1, 0, 0, 0, 0], [3, 3, 3, 3, 1, 1, 0, -3, -3, -3, -3, 1, 1, -1, -1, -1, -1, 0, 0, 0, -1, -1, -1, 1, 1, 1, -1, 1, 0, 0, 0, 0], [3, -3, -3, 3, -1, 1, 0, -3*E(4), -3*E(4), 3*E(4), 3*E(4), E(4), -1*E(4), 1, -1, E(4), -1*E(4), 0, 0, 0, 1, 1, -1, E(4), E(4), -1*E(4), -1, -1*E(4), 0, 0, 0, 0], [3, -3, -3, 3, -1, 1, 0, 3*E(4), 3*E(4), -3*E(4), -3*E(4), -1*E(4), E(4), 1, -1, -1*E(4), E(4), 0, 0, 0, 1, 1, -1, -1*E(4), -1*E(4), E(4), -1, E(4), 0, 0, 0, 0], [3, -3, -3, 3, 1, -1, 0, -3*E(4), -3*E(4), 3*E(4), 3*E(4), E(4), -1*E(4), 1, -1, -1*E(4), E(4), 0, 0, 0, -1, -1, 1, -1*E(4), -1*E(4), E(4), 1, E(4), 0, 0, 0, 0], [3, -3, -3, 3, 1, -1, 0, 3*E(4), 3*E(4), -3*E(4), -3*E(4), -1*E(4), E(4), 1, -1, E(4), -1*E(4), 0, 0, 0, -1, -1, 1, E(4), E(4), -1*E(4), 1, -1*E(4), 0, 0, 0, 0], [4, -4, 4, -4, 0, 0, 1, -4, 4, 4, -4, 0, 0, 0, 0, 0, 0, -1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, -1, -1], [4, -4, 4, -4, 0, 0, 1, 4, -4, -4, 4, 0, 0, 0, 0, 0, 0, -1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 1, 1], [4, 4, -4, -4, 0, 0, 1, -4*E(4), 4*E(4), -4*E(4), 4*E(4), 0, 0, 0, 0, 0, 0, -1, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, E(4), -1*E(4), -1*E(4), E(4)], [4, 4, -4, -4, 0, 0, 1, 4*E(4), -4*E(4), 4*E(4), -4*E(4), 0, 0, 0, 0, 0, 0, -1, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1*E(4), E(4), E(4), -1*E(4)]]; ConvertToLibraryCharacterTableNC(chartbl_192_951);