# Group 2916.et downloaded from the LMFDB on 05 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(101670772527364158353411036831507970405043286682837538105567130051752002783044687610687,2916); a := GPC.1; b := GPC.2; c := GPC.4; d := GPC.5; e := GPC.6; f := GPC.7; GPerm := Group( (1,20,17,3,19,16,2,21,18)(4,24,10,6,23,12,5,22,11)(7,25,15,9,27,14,8,26,13), (1,13,8,12,5,16)(2,14,9,10,6,17)(3,15,7,11,4,18)(19,23,26)(20,24,27)(21,22,25), (1,23,2,22,3,24)(4,25,5,27,6,26)(7,21,8,20,9,19)(10,12)(13,14)(17,18) ); # Booleans booleans_2916_et := rec( Agroup := false, Zgroup := false, abelian := false, almost_simple := false, cyclic := false, metabelian := false, metacyclic := false, monomial := true, nilpotent := false, perfect := false, quasisimple := false, rational := false, solvable := true, supersolvable := true); # Character Table chartbl_2916_et:=rec(); chartbl_2916_et.IsFinite:= true; chartbl_2916_et.UnderlyingCharacteristic:= 0; chartbl_2916_et.UnderlyingGroup:= GPC; chartbl_2916_et.Size:= 2916; chartbl_2916_et.InfoText:= "Character table for group 2916.et downloaded from the LMFDB."; chartbl_2916_et.Identifier:= " C3^4:S3^2 "; chartbl_2916_et.NrConjugacyClasses:= 42; chartbl_2916_et.ConjugacyClasses:= [ of ..., f2*f3*f4*f5*f6*f8, f1*f5*f8, f1*f2*f4^2*f5*f6*f7*f8, f8, f4*f6, f4^2*f6^2, f6*f8, f4*f8, f4^2*f8^2, f3*f4^2*f5*f6^2*f7^2, f4*f5*f6^2*f8^2, f3*f5^2*f6*f7*f8, f4*f5^2*f6*f8^2, f4^2*f5*f6^2, f3*f7, f3*f5*f7^2, f3*f5^2*f7, f3*f6*f7, f3*f6^2*f7, f3^2*f8^2, f4^2*f5*f7^2*f8^2, f3*f4^2*f7^2, f2*f3*f5, f2*f3*f4, f1*f5, f1*f2*f5*f6^2*f7*f8^2, f1*f2*f4*f5*f7, f1*f3*f6*f7*f8, f1*f3*f4^2*f7*f8, f2*f4^2*f5^2*f6*f7, f1*f3^2, f2*f4*f7^2, f2*f3^2*f6*f8^2, f2*f3*f5*f6^2*f7*f8^2, f1*f2*f3*f4^2*f6^2*f8, f1*f4*f6^2*f7^2, f1*f5*f6^2*f7^2*f8, f1*f2*f4^2*f6^2*f8, f1*f2*f4*f6^2, f3*f4*f5^2*f8^2, f4*f5^2*f6^2*f7^2*f8]; chartbl_2916_et.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]; chartbl_2916_et.ComputedPowerMaps:= [ , [1, 1, 1, 1, 5, 7, 6, 8, 10, 9, 11, 12, 13, 15, 14, 16, 17, 18, 20, 19, 21, 22, 23, 6, 7, 5, 7, 6, 6, 7, 11, 12, 13, 21, 22, 8, 14, 15, 9, 10, 41, 42], [1, 2, 3, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 4, 4, 3, 3, 2, 3, 2, 2, 2, 4, 3, 3, 4, 4, 5, 5]]; chartbl_2916_et.SizesCentralizers:= [2916, 108, 108, 36, 1458, 972, 972, 486, 486, 486, 162, 162, 162, 162, 162, 81, 81, 81, 81, 81, 54, 54, 27, 108, 108, 54, 36, 36, 36, 36, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 27, 27]; chartbl_2916_et.ClassNames:= ["1A", "2A", "2B", "2C", "3A", "3B1", "3B-1", "3C", "3D1", "3D-1", "3E", "3F", "3G", "3H1", "3H-1", "3I", "3J", "3K", "3L1", "3L-1", "3M", "3N", "3O", "6A1", "6A-1", "6B", "6C1", "6C-1", "6D1", "6D-1", "6E", "6F", "6G", "6H", "6I", "6J", "6K1", "6K-1", "6L1", "6L-1", "9A", "9B"]; chartbl_2916_et.OrderClassRepresentatives:= [1, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 9, 9]; chartbl_2916_et.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], [2, 0, 2, 0, 2, 2, 2, 2, 2, 2, 2, -1, 2, -1, -1, -1, 2, 2, -1, -1, 2, 2, -1, 0, 0, 2, 0, 0, 2, 2, 0, -1, -1, 0, 0, 0, -1, 0, 0, 0, -1, -1], [2, 2, 0, 0, 2, 2, 2, 2, 2, 2, -1, 2, -1, 2, 2, -1, -1, -1, -1, -1, -1, 2, -1, 2, 2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0, -1, 2, 0, -1, 2], [2, 2, 0, 0, 2, 2, 2, 2, 2, 2, -1, 2, -1, 2, 2, -1, -1, -1, -1, -1, 2, -1, -1, 2, 2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 2, 0, -1, -1, 0, 2, -1], [2, 2, 0, 0, 2, 2, 2, 2, 2, 2, -1, 2, 2, 2, 2, 2, -1, 2, 2, 2, -1, -1, -1, 2, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -1, 0, -1, -1, 0, -1, -1], [2, 2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, -1, 2, 2, -1, 2, -1, -1, -1, -1, -1, 2, 2, 2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0, 2, -1, 0, -1, -1], [2, -2, 0, 0, 2, 2, 2, 2, 2, 2, -1, 2, -1, 2, 2, -1, -1, -1, -1, -1, -1, 2, -1, -2, -2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, -2, 0, -1, 2], [2, -2, 0, 0, 2, 2, 2, 2, 2, 2, -1, 2, -1, 2, 2, -1, -1, -1, -1, -1, 2, -1, -1, -2, -2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -2, 0, 1, 1, 0, 2, -1], [2, -2, 0, 0, 2, 2, 2, 2, 2, 2, -1, 2, 2, 2, 2, 2, -1, 2, 2, 2, -1, -1, -1, -2, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 1, 0, 1, 1, 0, -1, -1], [2, -2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, -1, 2, 2, -1, 2, -1, -1, -1, -1, -1, 2, -2, -2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, -2, 1, 0, -1, -1], [2, 0, -2, 0, 2, 2, 2, 2, 2, 2, 2, -1, 2, -1, -1, -1, 2, 2, -1, -1, 2, 2, -1, 0, 0, -2, 0, 0, -2, -2, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, -1, -1], [3, 3, 1, 1, 3, 3*E(3)^-1, 3*E(3), 3, 3*E(3)^-1, 3*E(3), 0, 3, 0, 3*E(3), 3*E(3)^-1, 0, 0, 0, 0, 0, 0, 0, 0, 3*E(3), 3*E(3)^-1, 1, E(3)^-1, E(3), E(3), E(3)^-1, 0, E(3)^-1, E(3), 1, E(3)^-1, 0, 1, 0, 0, E(3), 0, 0], [3, 3, 1, 1, 3, 3*E(3), 3*E(3)^-1, 3, 3*E(3), 3*E(3)^-1, 0, 3, 0, 3*E(3)^-1, 3*E(3), 0, 0, 0, 0, 0, 0, 0, 0, 3*E(3)^-1, 3*E(3), 1, E(3), E(3)^-1, E(3)^-1, E(3), 0, E(3), E(3)^-1, 1, E(3), 0, 1, 0, 0, E(3)^-1, 0, 0], [3, 3, -1, -1, 3, 3*E(3)^-1, 3*E(3), 3, 3*E(3)^-1, 3*E(3), 0, 3, 0, 3*E(3), 3*E(3)^-1, 0, 0, 0, 0, 0, 0, 0, 0, 3*E(3), 3*E(3)^-1, -1, -1*E(3)^-1, -1*E(3), -1*E(3), -1*E(3)^-1, 0, -1*E(3)^-1, -1*E(3), -1, -1*E(3)^-1, 0, -1, 0, 0, -1*E(3), 0, 0], [3, 3, -1, -1, 3, 3*E(3), 3*E(3)^-1, 3, 3*E(3), 3*E(3)^-1, 0, 3, 0, 3*E(3)^-1, 3*E(3), 0, 0, 0, 0, 0, 0, 0, 0, 3*E(3)^-1, 3*E(3), -1, -1*E(3), -1*E(3)^-1, -1*E(3)^-1, -1*E(3), 0, -1*E(3), -1*E(3)^-1, -1, -1*E(3), 0, -1, 0, 0, -1*E(3)^-1, 0, 0], [3, -3, -1, 1, 3, 3*E(3)^-1, 3*E(3), 3, 3*E(3)^-1, 3*E(3), 0, 3, 0, 3*E(3), 3*E(3)^-1, 0, 0, 0, 0, 0, 0, 0, 0, -3*E(3), -3*E(3)^-1, -1, E(3)^-1, E(3), -1*E(3), -1*E(3)^-1, 0, -1*E(3)^-1, -1*E(3), 1, E(3)^-1, 0, -1, 0, 0, E(3), 0, 0], [3, -3, -1, 1, 3, 3*E(3), 3*E(3)^-1, 3, 3*E(3), 3*E(3)^-1, 0, 3, 0, 3*E(3)^-1, 3*E(3), 0, 0, 0, 0, 0, 0, 0, 0, -3*E(3)^-1, -3*E(3), -1, E(3), E(3)^-1, -1*E(3)^-1, -1*E(3), 0, -1*E(3), -1*E(3)^-1, 1, E(3), 0, -1, 0, 0, E(3)^-1, 0, 0], [3, -3, 1, -1, 3, 3*E(3)^-1, 3*E(3), 3, 3*E(3)^-1, 3*E(3), 0, 3, 0, 3*E(3), 3*E(3)^-1, 0, 0, 0, 0, 0, 0, 0, 0, -3*E(3), -3*E(3)^-1, 1, -1*E(3)^-1, -1*E(3), E(3), E(3)^-1, 0, E(3)^-1, E(3), -1, -1*E(3)^-1, 0, 1, 0, 0, -1*E(3), 0, 0], [3, -3, 1, -1, 3, 3*E(3), 3*E(3)^-1, 3, 3*E(3), 3*E(3)^-1, 0, 3, 0, 3*E(3)^-1, 3*E(3), 0, 0, 0, 0, 0, 0, 0, 0, -3*E(3)^-1, -3*E(3), 1, -1*E(3), -1*E(3)^-1, E(3)^-1, E(3), 0, E(3), E(3)^-1, -1, -1*E(3), 0, 1, 0, 0, -1*E(3)^-1, 0, 0], [4, 0, 0, 0, 4, 4, 4, 4, 4, 4, -2, -2, -2, -2, -2, 1, -2, -2, 1, 1, -2, 4, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2], [4, 0, 0, 0, 4, 4, 4, 4, 4, 4, -2, -2, -2, -2, -2, 1, -2, -2, 1, 1, 4, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1], [4, 0, 0, 0, 4, 4, 4, 4, 4, 4, -2, -2, 4, -2, -2, -2, -2, 4, -2, -2, -2, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1], [4, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, -2, -2, -2, -2, 1, 4, -2, 1, 1, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1], [6, 0, 0, 2, 6, 6, 6, -3, -3, -3, 0, 0, 6, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, -1, 0, 0], [6, 0, 0, -2, 6, 6, 6, -3, -3, -3, 0, 0, 6, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0], [6, 0, 2, 0, 6, 6*E(3)^-1, 6*E(3), 6, 6*E(3)^-1, 6*E(3), 0, -3, 0, -3*E(3), -3*E(3)^-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2*E(3), 2*E(3)^-1, 0, -1*E(3)^-1, -1*E(3), 0, 0, 0, -1, 0, 0, 0, 0, 0], [6, 0, 2, 0, 6, 6*E(3), 6*E(3)^-1, 6, 6*E(3), 6*E(3)^-1, 0, -3, 0, -3*E(3)^-1, -3*E(3), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2*E(3)^-1, 2*E(3), 0, -1*E(3), -1*E(3)^-1, 0, 0, 0, -1, 0, 0, 0, 0, 0], [6, 0, 0, 2, 6, 6*E(3)^-1, 6*E(3), -3, -3*E(3)^-1, -3*E(3), 0, 0, 0, 0, 0, 3, 0, 0, 3*E(3), 3*E(3)^-1, 0, 0, 0, 0, 0, 0, 2*E(3)^-1, 2*E(3), 0, 0, 0, 0, 0, -1, -1*E(3)^-1, 0, 0, 0, 0, -1*E(3), 0, 0], [6, 0, 0, 2, 6, 6*E(3), 6*E(3)^-1, -3, -3*E(3), -3*E(3)^-1, 0, 0, 0, 0, 0, 3, 0, 0, 3*E(3)^-1, 3*E(3), 0, 0, 0, 0, 0, 0, 2*E(3), 2*E(3)^-1, 0, 0, 0, 0, 0, -1, -1*E(3), 0, 0, 0, 0, -1*E(3)^-1, 0, 0], [6, 0, -2, 0, 6, 6*E(3)^-1, 6*E(3), 6, 6*E(3)^-1, 6*E(3), 0, -3, 0, -3*E(3), -3*E(3)^-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2*E(3), -2*E(3)^-1, 0, E(3)^-1, E(3), 0, 0, 0, 1, 0, 0, 0, 0, 0], [6, 0, -2, 0, 6, 6*E(3), 6*E(3)^-1, 6, 6*E(3), 6*E(3)^-1, 0, -3, 0, -3*E(3)^-1, -3*E(3), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2*E(3)^-1, -2*E(3), 0, E(3), E(3)^-1, 0, 0, 0, 1, 0, 0, 0, 0, 0], [6, 0, 0, -2, 6, 6*E(3)^-1, 6*E(3), -3, -3*E(3)^-1, -3*E(3), 0, 0, 0, 0, 0, 3, 0, 0, 3*E(3), 3*E(3)^-1, 0, 0, 0, 0, 0, 0, -2*E(3)^-1, -2*E(3), 0, 0, 0, 0, 0, 1, E(3)^-1, 0, 0, 0, 0, E(3), 0, 0], [6, 0, 0, -2, 6, 6*E(3), 6*E(3)^-1, -3, -3*E(3), -3*E(3)^-1, 0, 0, 0, 0, 0, 3, 0, 0, 3*E(3)^-1, 3*E(3), 0, 0, 0, 0, 0, 0, -2*E(3), -2*E(3)^-1, 0, 0, 0, 0, 0, 1, E(3), 0, 0, 0, 0, E(3)^-1, 0, 0], [12, 0, 0, 0, 12, 12, 12, -6, -6, -6, 0, 0, -6, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [12, 0, 0, 0, 12, 12*E(3)^-1, 12*E(3), -6, -6*E(3)^-1, -6*E(3), 0, 0, 0, 0, 0, -3, 0, 0, -3*E(3), -3*E(3)^-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [12, 0, 0, 0, 12, 12*E(3), 12*E(3)^-1, -6, -6*E(3), -6*E(3)^-1, 0, 0, 0, 0, 0, -3, 0, 0, -3*E(3)^-1, -3*E(3), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [18, 0, 6, 0, -9, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [18, 0, -6, 0, -9, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [36, 0, 0, 0, -18, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 3, 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_2916_et);