# Group 192.1276 downloaded from the LMFDB on 13 November 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(671312538692260912778123777,192); a := GPC.1; b := GPC.2; c := GPC.3; d := GPC.5; GPerm := Group( (1,2)(6,7), (1,2)(9,10), (3,4)(8,9)(10,11), (1,3,2,4)(8,10,11,9), (8,11)(9,10), (1,2)(3,4)(8,11)(9,10), (5,6,7) ); GLZ := Group([[[0, 0, 1, -1, 0, 0], [0, 0, 0, -1, 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]], [[0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0], [0, 0, 1, -1, 0, 0], [0, 0, 0, -1, 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]]]); GLZN := Group([[[ZmodnZObj(1,30), ZmodnZObj(20,30)], [ZmodnZObj(20,30), ZmodnZObj(11,30)]],[[ZmodnZObj(13,30), ZmodnZObj(12,30)], [ZmodnZObj(21,30), ZmodnZObj(7,30)]],[[ZmodnZObj(16,30), ZmodnZObj(15,30)], [ZmodnZObj(15,30), ZmodnZObj(1,30)]],[[ZmodnZObj(11,30), ZmodnZObj(0,30)], [ZmodnZObj(0,30), ZmodnZObj(11,30)]],[[ZmodnZObj(19,30), ZmodnZObj(0,30)], [ZmodnZObj(0,30), ZmodnZObj(19,30)]],[[ZmodnZObj(19,30), ZmodnZObj(21,30)], [ZmodnZObj(0,30), ZmodnZObj(1,30)]],[[ZmodnZObj(29,30), ZmodnZObj(0,30)], [ZmodnZObj(25,30), ZmodnZObj(19,30)]]]); # Booleans booleans_192_1276 := rec( Agroup := false, Zgroup := false, abelian := false, almost_simple := false, cyclic := false, metabelian := true, metacyclic := false, monomial := true, nilpotent := false, perfect := false, quasisimple := false, rational := false, solvable := true, supersolvable := true); # Character Table chartbl_192_1276:=rec(); chartbl_192_1276.IsFinite:= true; chartbl_192_1276.UnderlyingCharacteristic:= 0; chartbl_192_1276.UnderlyingGroup:= GPC; chartbl_192_1276.Size:= 192; chartbl_192_1276.InfoText:= "Character table for group 192.1276 downloaded from the LMFDB."; chartbl_192_1276.Identifier:= " C3:D4^2 "; chartbl_192_1276.NrConjugacyClasses:= 39; chartbl_192_1276.ConjugacyClasses:= [ of ..., f4, f4*f6*f7, f6*f7, f2, f2*f5*f7^2, f2*f3, f2*f3*f5*f7^2, f1, f1*f6, f1*f2, f1*f3*f5, f1*f2*f6, f1*f2*f3, f1*f3*f5*f6, f1*f2*f3*f6, f7^2, f3*f4, f3*f4*f6*f7, f3*f4*f5*f6, f3*f5*f6, f5*f6, f1*f5, f1*f3, f1*f2*f5, f1*f2*f3*f5, f4*f7^2, f4*f6, f6, f2*f7, f2*f5, f2*f3*f7, f2*f3*f5, f3*f7, f3*f6, f3*f5, f3*f4*f5, f5, f5*f7]; chartbl_192_1276.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]; chartbl_192_1276.ComputedPowerMaps:= [ , [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 17, 2, 2, 3, 3, 4, 2, 2, 3, 3, 17, 17, 17, 17, 17, 17, 17, 27, 27, 28, 28, 29, 29], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 1, 18, 19, 20, 21, 22, 23, 24, 25, 26, 2, 3, 4, 5, 6, 7, 8, 18, 19, 20, 21, 22, 22]]; chartbl_192_1276.SizesCentralizers:= [192, 192, 192, 192, 48, 48, 48, 48, 32, 32, 32, 32, 32, 32, 32, 32, 96, 96, 96, 96, 96, 48, 16, 16, 16, 16, 96, 96, 96, 24, 24, 24, 24, 48, 48, 48, 48, 48, 48]; chartbl_192_1276.ClassNames:= ["1A", "2A", "2B", "2C", "2D", "2E", "2F", "2G", "2H", "2I", "2J", "2K", "2L", "2M", "2N", "2O", "3A", "4A", "4B", "4C", "4D", "4E", "4F", "4G", "4H", "4I", "6A", "6B", "6C", "6D", "6E", "6F", "6G", "12A", "12B", "12C", "12D", "12E1", "12E-1"]; chartbl_192_1276.OrderClassRepresentatives:= [1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 6, 6, 6, 6, 6, 6, 6, 12, 12, 12, 12, 12, 12]; chartbl_192_1276.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], [2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -1, 2, 2, 2, 2, 2, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [2, -2, -2, 2, 0, 0, 0, 0, -2, 2, 0, 0, -2, 0, 0, 2, 2, -2, 0, 2, 0, 0, 0, 0, 0, 0, 2, -2, -2, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2], [2, -2, -2, 2, 0, 0, 0, 0, -2, 2, 0, 0, 2, 0, 0, -2, 2, 2, 0, -2, 0, 0, 0, 0, 0, 0, 2, -2, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2], [2, -2, -2, 2, 0, 0, 0, 0, 2, -2, 0, 0, -2, 0, 0, 2, 2, 2, 0, -2, 0, 0, 0, 0, 0, 0, 2, -2, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2], [2, -2, -2, 2, 0, 0, 0, 0, 2, -2, 0, 0, 2, 0, 0, -2, 2, -2, 0, 2, 0, 0, 0, 0, 0, 0, 2, -2, -2, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2], [2, 2, -2, -2, 0, 0, 0, 0, 0, 0, -2, -2, 0, 2, 2, 0, 2, 0, -2, 0, 2, 0, 0, 0, 0, 0, -2, 2, -2, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0], [2, 2, -2, -2, 0, 0, 0, 0, 0, 0, -2, 2, 0, 2, -2, 0, 2, 0, 2, 0, -2, 0, 0, 0, 0, 0, -2, 2, -2, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0], [2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 2, -2, 0, -2, 2, 0, 2, 0, 2, 0, -2, 0, 0, 0, 0, 0, -2, 2, -2, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0], [2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 2, 2, 0, -2, -2, 0, 2, 0, -2, 0, 2, 0, 0, 0, 0, 0, -2, 2, -2, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0], [2, 2, 2, 2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -1, 2, 2, 2, 2, 2, 0, 0, 0, 0, -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, 0, 0, 0, -1, -2, -2, -2, -2, 2, 0, 0, 0, 0, -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, 0, 0, 0, -1, 2, -2, 2, -2, -2, 0, 0, 0, 0, -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, 0, 0, 0, -1, -2, 2, -2, 2, -2, 0, 0, 0, 0, -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, 0, 0, 0, -1, -2, 2, -2, 2, -2, 0, 0, 0, 0, -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, 0, 0, 0, -1, 2, -2, 2, -2, -2, 0, 0, 0, 0, -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, 0, 0, 0, -1, -2, -2, -2, -2, 2, 0, 0, 0, 0, -1, -1, -1, 1, 1, -1, -1, 1, -1, 1, -1, 1, 1], [4, -4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 4, 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, -2, -4, 0, 4, 0, 0, 0, 0, 0, 0, -2, 2, 2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2], [4, -4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 4, 0, -4, 0, 0, 0, 0, 0, 0, -2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2], [4, 4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -4, 0, 4, 0, 0, 0, 0, 0, 2, -2, 2, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0], [4, 4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 4, 0, -4, 0, 0, 0, 0, 0, 2, -2, 2, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0], [4, -4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, 0, 0, 0, 0, 0, -2-4*E(3), 0, 2+4*E(3), 0, 0], [4, -4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, 0, 0, 0, 0, 0, 2+4*E(3), 0, -2-4*E(3), 0, 0]]; ConvertToLibraryCharacterTableNC(chartbl_192_1276);