# Group 1944.3473 downloaded from the LMFDB on 13 June 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(99702897758858508457332253025251313008553975453765731103,1944); a := GPC.1; b := GPC.4; c := GPC.5; d := GPC.6; e := GPC.7; f := GPC.8; GPerm := Group( (2,5,6,16,7,17,20,8)(3,10,11,23,12,22,18,9)(4,15)(13,25,19,26,21,27,14,24)(28,29)(30,31,32,33), (2,6,7,20)(3,11,12,18)(5,16,17,8)(9,10,23,22)(13,19,21,14)(24,25,26,27)(30,32)(31,33), (2,7)(3,12)(5,17)(6,20)(8,16)(9,23)(10,22)(11,18)(13,21)(14,19)(24,26)(25,27), (1,2,7)(3,13,20)(4,9,23)(5,18,22)(6,21,12)(8,24,19)(10,11,17)(14,26,16)(15,25,27), (1,3,14)(2,8,6)(4,5,12)(7,22,11)(9,13,10)(15,19,17)(16,23,24)(18,26,25)(20,21,27), (29,31,33), (28,30,32)(29,31,33), (1,4,15)(2,9,25)(3,5,19)(6,10,26)(7,23,27)(8,13,18)(11,16,21)(12,17,14)(20,22,24) ); # Booleans booleans_1944_3473 := rec( Agroup := false, Zgroup := false, abelian := false, almost_simple := false, cyclic := false, metabelian := false, metacyclic := false, nilpotent := false, perfect := false, quasisimple := false, rational := false, solvable := true, supersolvable := false); # Character Table chartbl_1944_3473:=rec(); chartbl_1944_3473.IsFinite:= true; chartbl_1944_3473.UnderlyingCharacteristic:= 0; chartbl_1944_3473.UnderlyingGroup:= GPC; chartbl_1944_3473.Size:= 1944; chartbl_1944_3473.InfoText:= "Character table for group 1944.3473 downloaded from the LMFDB."; chartbl_1944_3473.Identifier:= " C3^3.F9 "; chartbl_1944_3473.NrConjugacyClasses:= 33; chartbl_1944_3473.ConjugacyClasses:= [ of ..., f3, f8, f6^2, f4^2, f6^2*f8^2, f6*f8, f4^2*f8^2, f4*f8, f7, f6*f7, f6^2*f7, f5*f6, f5*f6^2, f4*f7, f4^2*f7, f4*f5, f4^2*f5, f2*f5, f2*f3*f5*f7^2*f8, f3*f7^2*f8^2, f3*f6, f3*f4, f3*f6*f8, f3*f5*f6, f3*f4*f8, f3*f4*f5, f1*f7*f8, f1*f2*f3*f5^2, f1*f2*f7^2*f8^2, f1*f3*f5^2*f7, f2*f3*f4^2*f5^2*f6*f8, f2*f4^2*f5*f6*f7^2*f8]; chartbl_1944_3473.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]; chartbl_1944_3473.ComputedPowerMaps:= [ , [1, 1, 3, 4, 5, 7, 6, 9, 8, 10, 12, 11, 14, 13, 16, 15, 18, 17, 2, 2, 3, 4, 5, 6, 7, 8, 9, 19, 20, 20, 19, 21, 21], [1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 20, 19, 2, 2, 2, 2, 2, 2, 2, 30, 31, 28, 29, 19, 20]]; chartbl_1944_3473.SizesCentralizers:= [1944, 216, 972, 486, 486, 486, 486, 486, 486, 81, 81, 81, 81, 81, 81, 81, 81, 81, 24, 24, 108, 54, 54, 54, 54, 54, 54, 8, 8, 8, 8, 12, 12]; chartbl_1944_3473.ClassNames:= ["1A", "2A", "3A", "3B", "3C", "3D1", "3D-1", "3E1", "3E-1", "3F", "3G1", "3G-1", "3H1", "3H-1", "3I1", "3I-1", "3J1", "3J-1", "4A1", "4A-1", "6A", "6B", "6C", "6D1", "6D-1", "6E1", "6E-1", "8A1", "8A-1", "8A3", "8A-3", "12A1", "12A-1"]; chartbl_1944_3473.OrderClassRepresentatives:= [1, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 6, 6, 6, 6, 6, 6, 6, 8, 8, 8, 8, 12, 12]; chartbl_1944_3473.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*E(4), E(4), E(4), -1*E(4), -1, -1], [1, 1, 1, 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), -1*E(4), E(4), -1, -1], [1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1*E(8)^2, E(8)^2, -1, -1, -1, -1, -1, -1, -1, E(8)^3, -1*E(8), E(8), -1*E(8)^3, E(8)^2, -1*E(8)^2], [1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, E(8)^2, -1*E(8)^2, -1, -1, -1, -1, -1, -1, -1, -1*E(8), E(8)^3, -1*E(8)^3, E(8), -1*E(8)^2, E(8)^2], [1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1*E(8)^2, E(8)^2, -1, -1, -1, -1, -1, -1, -1, -1*E(8)^3, E(8), -1*E(8), E(8)^3, E(8)^2, -1*E(8)^2], [1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, E(8)^2, -1*E(8)^2, -1, -1, -1, -1, -1, -1, -1, E(8), -1*E(8)^3, E(8)^3, -1*E(8), -1*E(8)^2, E(8)^2], [4, 4, 4, -2, 1, -2, -2, 1, 1, 4, -2, -2, -2, -2, 1, 1, 1, 1, 0, 0, 4, -2, 1, -2, -2, 1, 1, 0, 0, 0, 0, 0, 0], [4, 4, 4, 1, -2, 1, 1, -2, -2, 4, 1, 1, 1, 1, -2, -2, -2, -2, 0, 0, 4, 1, -2, 1, 1, -2, -2, 0, 0, 0, 0, 0, 0], [4, -4, 4, -2, 1, -2, -2, 1, 1, 4, -2, -2, -2, -2, 1, 1, 1, 1, 0, 0, -4, 2, -1, 2, 2, -1, -1, 0, 0, 0, 0, 0, 0], [4, -4, 4, 1, -2, 1, 1, -2, -2, 4, 1, 1, 1, 1, -2, -2, -2, -2, 0, 0, -4, -1, 2, -1, -1, 2, 2, 0, 0, 0, 0, 0, 0], [6, -2, -3, 6, 6, -3, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 1, -2, -2, 1, 1, 1, 1, 0, 0, 0, 0, -1, -1], [6, -2, -3, 6, 6, -3, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 1, -2, -2, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1], [6, 2, -3, 6, 6, -3, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2*E(4), 2*E(4), -1, 2, 2, -1, -1, -1, -1, 0, 0, 0, 0, -1*E(4), E(4)], [6, 2, -3, 6, 6, -3, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2*E(4), -2*E(4), -1, 2, 2, -1, -1, -1, -1, 0, 0, 0, 0, E(4), -1*E(4)], [8, 0, 8, 8, 8, 8, 8, 8, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [8, 0, 8, -4, 2, -4, -4, 2, 2, -1, -1-3*E(3), 2+3*E(3), 2+3*E(3), -1-3*E(3), -1+3*E(3), -4-3*E(3), 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [8, 0, 8, -4, 2, -4, -4, 2, 2, -1, 2+3*E(3), -1-3*E(3), -1-3*E(3), 2+3*E(3), -4-3*E(3), -1+3*E(3), 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [8, 0, 8, -4, 2, -4, -4, 2, 2, -1, -1-3*E(3), 2+3*E(3), -1-3*E(3), 2+3*E(3), 2, 2, -1+3*E(3), -4-3*E(3), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [8, 0, 8, -4, 2, -4, -4, 2, 2, -1, 2+3*E(3), -1-3*E(3), 2+3*E(3), -1-3*E(3), 2, 2, -4-3*E(3), -1+3*E(3), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [8, 0, 8, 2, -4, 2, 2, -4, -4, -1, -4-3*E(3), -1+3*E(3), 2, 2, -1-3*E(3), 2+3*E(3), -1-3*E(3), 2+3*E(3), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [8, 0, 8, 2, -4, 2, 2, -4, -4, -1, -1+3*E(3), -4-3*E(3), 2, 2, 2+3*E(3), -1-3*E(3), 2+3*E(3), -1-3*E(3), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [8, 0, 8, 2, -4, 2, 2, -4, -4, -1, 2, 2, -4-3*E(3), -1+3*E(3), 2+3*E(3), -1-3*E(3), -1-3*E(3), 2+3*E(3), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [8, 0, 8, 2, -4, 2, 2, -4, -4, -1, 2, 2, -1+3*E(3), -4-3*E(3), -1-3*E(3), 2+3*E(3), 2+3*E(3), -1-3*E(3), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [12, 4, -6, -6, 3, 3, 3, -6-9*E(3), 3+9*E(3), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 1, 1, 1, 1+3*E(3), -2-3*E(3), 0, 0, 0, 0, 0, 0], [12, 4, -6, -6, 3, 3, 3, 3+9*E(3), -6-9*E(3), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 1, 1, 1, -2-3*E(3), 1+3*E(3), 0, 0, 0, 0, 0, 0], [12, 4, -6, 3, -6, -6-9*E(3), 3+9*E(3), 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, -2, 1+3*E(3), -2-3*E(3), 1, 1, 0, 0, 0, 0, 0, 0], [12, 4, -6, 3, -6, 3+9*E(3), -6-9*E(3), 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, -2, -2-3*E(3), 1+3*E(3), 1, 1, 0, 0, 0, 0, 0, 0], [12, -4, -6, -6, 3, 3, 3, -6-9*E(3), 3+9*E(3), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -1, -1, -1, -1-3*E(3), 2+3*E(3), 0, 0, 0, 0, 0, 0], [12, -4, -6, -6, 3, 3, 3, 3+9*E(3), -6-9*E(3), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -1, -1, -1, 2+3*E(3), -1-3*E(3), 0, 0, 0, 0, 0, 0], [12, -4, -6, 3, -6, -6-9*E(3), 3+9*E(3), 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -1, 2, -1-3*E(3), 2+3*E(3), -1, -1, 0, 0, 0, 0, 0, 0], [12, -4, -6, 3, -6, 3+9*E(3), -6-9*E(3), 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -1, 2, 2+3*E(3), -1-3*E(3), -1, -1, 0, 0, 0, 0, 0, 0]]; ConvertToLibraryCharacterTableNC(chartbl_1944_3473);