# Group 384.13367 downloaded from the LMFDB on 26 July 2026. ## 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(90891556190173129697174292472040082064602369,384); a := GPC.1; b := GPC.2; c := GPC.3; d := GPC.5; GPerm := Group( (1,2)(3,7)(4,11)(5,14)(6,9)(8,12)(10,16)(13,15)(18,21)(22,24), (1,3,6,5)(2,7,9,14)(4,12,13,10)(8,15,16,11)(17,18)(19,21)(20,22)(23,24), (1,4,5,12,6,13,3,10)(2,8,7,11,9,16,14,15)(17,19)(18,21)(20,23)(22,24), (4,13)(8,16)(10,12)(11,15)(17,20,19,23)(18,22,21,24)(26,27), (17,19)(18,21)(20,23)(22,24), (1,5,6,3)(2,7,9,14)(4,12,13,10)(8,11,16,15), (1,6)(2,9)(3,5)(4,13)(7,14)(8,16)(10,12)(11,15), (25,26,27) ); # Booleans booleans_384_13367 := 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_384_13367:=rec(); chartbl_384_13367.IsFinite:= true; chartbl_384_13367.UnderlyingCharacteristic:= 0; chartbl_384_13367.UnderlyingGroup:= GPC; chartbl_384_13367.Size:= 384; chartbl_384_13367.InfoText:= "Character table for group 384.13367 downloaded from the LMFDB."; chartbl_384_13367.Identifier:= " (C2*C24).C2^3 "; chartbl_384_13367.NrConjugacyClasses:= 48; chartbl_384_13367.ConjugacyClasses:= [ of ..., f4, f4*f7*f8, f7*f8, f1*f6*f8^2, f2, f1*f2*f3*f4*f5*f6*f7*f8, f8^2, f4*f6*f7, f6*f7, f1*f7*f8, f3, f3*f4, f3*f6, f3*f4*f6, f1*f3, f1*f3*f7, f1*f3*f6, f1*f3*f6*f7, f2*f5*f7*f8^2, f1*f2*f4*f7*f8, f1*f2*f4*f5*f7*f8^2, f2*f3*f4*f5*f6*f7*f8^2, f2*f3*f4*f7*f8^2, f1*f2*f3*f7*f8^2, f4*f8, f7, f4*f7, f1*f6, f2*f8, f5*f6, f4*f5*f6, f1*f5*f6, f1*f5*f7*f8^2, f1*f3*f5, f1*f3*f5*f6, f3*f5, f3*f4*f5, f4*f6, f6, f1*f8, f2*f5, f1*f2*f8, f1*f2*f5, f5, f4*f5, f1*f5, f1*f4*f5]; chartbl_384_13367.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, 47, 48]; chartbl_384_13367.ComputedPowerMaps:= [ , [1, 1, 1, 1, 1, 1, 1, 8, 4, 4, 4, 2, 2, 3, 3, 3, 3, 2, 2, 4, 3, 3, 2, 2, 4, 8, 8, 8, 8, 8, 10, 10, 10, 10, 9, 9, 9, 9, 27, 27, 27, 27, 28, 28, 40, 40, 40, 40], [1, 2, 3, 4, 5, 6, 7, 1, 9, 10, 11, 13, 12, 15, 14, 17, 16, 19, 18, 20, 21, 22, 23, 24, 25, 2, 4, 3, 5, 6, 31, 32, 34, 33, 35, 36, 38, 37, 9, 10, 11, 20, 21, 22, 31, 32, 33, 34]]; chartbl_384_13367.SizesCentralizers:= [384, 384, 384, 384, 96, 48, 16, 192, 192, 192, 96, 64, 64, 64, 64, 64, 64, 64, 64, 48, 48, 48, 16, 16, 16, 192, 192, 192, 48, 24, 96, 96, 96, 96, 32, 32, 32, 32, 96, 96, 48, 24, 24, 24, 48, 48, 48, 48]; chartbl_384_13367.ClassNames:= ["1A", "2A", "2B", "2C", "2D", "2E", "2F", "3A", "4A", "4B", "4C", "4D1", "4D-1", "4E1", "4E-1", "4F1", "4F-1", "4G1", "4G-1", "4H", "4I", "4J", "4K", "4L", "4M", "6A", "6B", "6C", "6D", "6E", "8A", "8B", "8C1", "8C-1", "8D", "8E", "8F1", "8F-1", "12A", "12B", "12C", "12D", "12E", "12F", "24A", "24B", "24C1", "24C-1"]; chartbl_384_13367.OrderClassRepresentatives:= [1, 2, 2, 2, 2, 2, 2, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 6, 6, 6, 6, 6, 8, 8, 8, 8, 8, 8, 8, 8, 12, 12, 12, 12, 12, 12, 24, 24, 24, 24]; chartbl_384_13367.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, -1, -1, -1, 1, -1, -1, 1, -1, -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, -1, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, -1, -1, -1, -1, -1, 2, 2, 2, 2, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [2, 2, 2, 2, -2, 0, 0, 2, -2, -2, 2, -2, 2, 2, -2, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, 2, -2, 0, 0, 2, -2, -2, 2, 2, -2, -2, 2, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 2, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, 2, 2, 0, 0, 2, -2, -2, -2, -2, -2, -2, -2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, 2, 2, 0, 0, 2, -2, -2, -2, 2, 2, 2, 2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, 2, -2, -2, 0, -1, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 2, 0, 0, 0, -1, -1, -1, 1, 1, -2, -2, 2, 2, 0, 0, 0, 0, -1, -1, 1, -1, -1, 1, 1, 1, -1, -1], [2, 2, 2, 2, -2, -2, 0, -1, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, 0, 0, 0, -1, -1, -1, 1, 1, 2, 2, -2, -2, 0, 0, 0, 0, -1, -1, 1, 1, -1, -1, -1, -1, 1, 1], [2, 2, 2, 2, -2, 2, 0, -1, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 2, 0, 0, 0, -1, -1, -1, 1, -1, 2, 2, -2, -2, 0, 0, 0, 0, -1, -1, 1, -1, 1, 1, -1, -1, 1, 1], [2, 2, 2, 2, -2, 2, 0, -1, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, -2, 0, 0, 0, -1, -1, -1, 1, -1, -2, -2, 2, 2, 0, 0, 0, 0, -1, -1, 1, 1, 1, -1, 1, 1, -1, -1], [2, 2, 2, 2, 2, -2, 0, -1, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, 0, 0, 0, -1, -1, -1, -1, 1, 2, 2, 2, 2, 0, 0, 0, 0, -1, -1, -1, 1, 1, 1, -1, -1, -1, -1], [2, 2, 2, 2, 2, -2, 0, -1, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 2, 0, 0, 0, -1, -1, -1, -1, 1, -2, -2, -2, -2, 0, 0, 0, 0, -1, -1, -1, -1, 1, -1, 1, 1, 1, 1], [2, 2, 2, 2, 2, 2, 0, -1, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, -2, 0, 0, 0, -1, -1, -1, -1, -1, -2, -2, -2, -2, 0, 0, 0, 0, -1, -1, -1, 1, -1, 1, 1, 1, 1, 1], [2, -2, -2, 2, 0, 0, 0, 2, -2, 2, 0, 0, -2*E(4), 2*E(4), 0, -2*E(4), 2*E(4), 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 2, 0, 0, -2, 2, 0, 0, 2*E(4), 0, -2*E(4), 0, -2, 2, 0, 0, 0, 0, -2, 2, 0, 0], [2, -2, -2, 2, 0, 0, 0, 2, -2, 2, 0, 0, 2*E(4), -2*E(4), 0, 2*E(4), -2*E(4), 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 2, 0, 0, -2, 2, 0, 0, -2*E(4), 0, 2*E(4), 0, -2, 2, 0, 0, 0, 0, -2, 2, 0, 0], [2, -2, -2, 2, 0, 0, 0, 2, -2, 2, 0, 0, -2*E(4), 2*E(4), 0, -2*E(4), 2*E(4), 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 2, 0, 0, 2, -2, 0, 0, -2*E(4), 0, 2*E(4), 0, -2, 2, 0, 0, 0, 0, 2, -2, 0, 0], [2, -2, -2, 2, 0, 0, 0, 2, -2, 2, 0, 0, 2*E(4), -2*E(4), 0, 2*E(4), -2*E(4), 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 2, 0, 0, 2, -2, 0, 0, 2*E(4), 0, -2*E(4), 0, -2, 2, 0, 0, 0, 0, 2, -2, 0, 0], [2, -2, -2, 2, 0, 0, 0, 2, 2, -2, 0, 0, -2*E(4), 2*E(4), 0, 2*E(4), -2*E(4), 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 2, 0, 0, 0, 0, -2*E(4), 2*E(4), 0, -2, 0, 2, 2, -2, 0, 0, 0, 0, 0, 0, 2*E(4), -2*E(4)], [2, -2, -2, 2, 0, 0, 0, 2, 2, -2, 0, 0, 2*E(4), -2*E(4), 0, -2*E(4), 2*E(4), 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 2, 0, 0, 0, 0, 2*E(4), -2*E(4), 0, -2, 0, 2, 2, -2, 0, 0, 0, 0, 0, 0, -2*E(4), 2*E(4)], [2, -2, -2, 2, 0, 0, 0, 2, 2, -2, 0, 0, -2*E(4), 2*E(4), 0, 2*E(4), -2*E(4), 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 2, 0, 0, 0, 0, 2*E(4), -2*E(4), 0, 2, 0, -2, 2, -2, 0, 0, 0, 0, 0, 0, -2*E(4), 2*E(4)], [2, -2, -2, 2, 0, 0, 0, 2, 2, -2, 0, 0, 2*E(4), -2*E(4), 0, -2*E(4), 2*E(4), 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 2, 0, 0, 0, 0, -2*E(4), 2*E(4), 0, 2, 0, -2, 2, -2, 0, 0, 0, 0, 0, 0, 2*E(4), -2*E(4)], [4, 4, 4, 4, -4, 0, 0, -2, -4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0], [4, 4, 4, 4, 4, 0, 0, -2, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0], [4, -4, -4, 4, 0, 0, 0, -2, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, 0, 0, -4, 4, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 2, -2, 0, 0], [4, -4, -4, 4, 0, 0, 0, -2, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, 0, 0, 4, -4, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, -2, 2, 0, 0], [4, -4, 4, -4, 0, 0, 0, 4, 0, 0, 0, -4*E(4), 0, 0, 4*E(4), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, -4, 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, 4, 0, 0, 0, 4*E(4), 0, 0, -4*E(4), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, -4, 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, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4*E(4), 4*E(4), 0, 0, 0, 0, 0, 0, -4, 4, -4, 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, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4*E(4), -4*E(4), 0, 0, 0, 0, 0, 0, -4, 4, -4, 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, -2, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, 0, 0, 0, 0, -4*E(4), 4*E(4), 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, -2*E(4), 2*E(4)], [4, -4, -4, 4, 0, 0, 0, -2, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, 0, 0, 0, 0, 4*E(4), -4*E(4), 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 2*E(4), -2*E(4)], [8, -8, 8, -8, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, 4, 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, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]; ConvertToLibraryCharacterTableNC(chartbl_384_13367);