# Group 512.1824 downloaded from the LMFDB on 22 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(393086652506642482539060828839649338586206857805251897794,512); a := GPC.1; b := GPC.2; c := GPC.4; d := GPC.5; e := GPC.6; f := GPC.7; GPerm := Group( (1,11,3,10,2,12,4,9)(5,15,7,14,6,16,8,13), (1,2)(3,4)(5,8)(6,7)(9,16)(10,15)(11,14)(12,13), (1,7,3,5)(2,8,4,6)(9,14,12,15)(10,13,11,16), (1,3,2,4)(5,7,6,8)(9,11,10,12)(13,15,14,16), (1,3)(2,4)(5,8)(6,7)(9,11)(10,12)(13,15)(14,16), (1,3)(2,4)(5,7)(6,8)(9,12)(10,11)(13,16)(14,15), (5,6)(7,8)(9,10)(11,12), (9,10)(11,12)(13,14)(15,16), (1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16) ); # Booleans booleans_512_1824 := rec( Agroup := false, Zgroup := false, abelian := false, almost_simple := false, cyclic := false, metabelian := false, metacyclic := false, monomial := true, nilpotent := true, perfect := false, quasisimple := false, rational := false, solvable := true, supersolvable := true); # Character Table chartbl_512_1824:=rec(); chartbl_512_1824.IsFinite:= true; chartbl_512_1824.UnderlyingCharacteristic:= 0; chartbl_512_1824.UnderlyingGroup:= GPerm; chartbl_512_1824.Size:= 512; chartbl_512_1824.InfoText:= "Character table for group 512.1824 downloaded from the LMFDB."; chartbl_512_1824.Identifier:= " C2^5.SD16 "; chartbl_512_1824.NrConjugacyClasses:= 29; chartbl_512_1824.ConjugacyClasses:= [(), (1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16), (9,10)(11,12)(13,14)(15,16), (5,6)(7,8)(13,14)(15,16), (1,4)(2,3)(5,8)(6,7)(9,12)(10,11)(13,16)(14,15), (1,4)(2,3)(5,7)(6,8)(9,11)(10,12)(13,16)(14,15), (1,2)(3,4)(5,6)(7,8)(9,10)(11,12), (1,2)(3,4), (1,3)(2,4)(5,7)(6,8)(9,11)(10,12)(13,16)(14,15), (5,7)(6,8)(9,15)(10,16)(11,13)(12,14), (3,4)(7,8)(11,12)(15,16), (1,2)(3,4)(5,7)(6,8)(9,15)(10,16)(11,13)(12,14), (1,3,2,4)(5,7,6,8)(9,11,10,12)(13,15,14,16), (1,3,2,4)(5,8,6,7)(9,11,10,12)(13,15,14,16), (5,7)(6,8)(9,15,10,16)(11,13,12,14), (1,2)(3,4)(5,7)(6,8)(9,15,10,16)(11,13,12,14), (1,6,4,8)(2,5,3,7)(9,16,11,13)(10,15,12,14), (1,8,4,6)(2,7,3,5)(9,13,11,16)(10,14,12,15), (1,5,4,8)(2,6,3,7)(9,16,12,13)(10,15,11,14), (1,6,2,5)(3,7,4,8)(9,12,10,11)(13,14), (1,4,2,3)(5,6)(9,13)(10,14)(11,16)(12,15), (1,11,3,10,2,12,4,9)(5,15,7,14,6,16,8,13), (1,9,4,12,2,10,3,11)(5,13,8,16,6,14,7,15), (1,15,3,14,2,16,4,13)(5,10,8,12,6,9,7,11), (1,13,4,16,2,14,3,15)(5,11,7,9,6,12,8,10), (1,11,6,13,4,9,8,16)(2,12,5,14,3,10,7,15), (1,16,8,9,4,13,6,11)(2,15,7,10,3,14,5,12), (1,13,8,11,4,16,6,9)(2,14,7,12,3,15,5,10), (1,9,6,16,4,11,8,13)(2,10,5,15,3,12,7,14)]; chartbl_512_1824.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]; chartbl_512_1824.ComputedPowerMaps:= [ , [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 3, 6, 6, 5, 7, 8, 13, 13, 14, 14, 17, 18, 18, 17]]; chartbl_512_1824.SizesCentralizers:= [512, 512, 256, 128, 128, 128, 128, 128, 64, 32, 32, 32, 64, 64, 32, 32, 32, 32, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16]; chartbl_512_1824.ClassNames:= ["1A", "2A", "2B", "2C", "2D", "2E", "2F", "2G", "2H", "2I", "2J", "2K", "4A", "4B", "4C", "4D", "4E1", "4E-1", "4F", "4G", "4H", "8A1", "8A-1", "8B1", "8B-1", "8C1", "8C-1", "8C3", "8C-3"]; chartbl_512_1824.OrderClassRepresentatives:= [1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 8, 8, 8, 8, 8, 8, 8, 8]; chartbl_512_1824.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*E(4), E(4), E(4), -1*E(4), E(4), -1*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, E(4), -1*E(4), -1*E(4), E(4), -1*E(4), 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, -1*E(4), E(4), -1*E(4), -1*E(4), E(4), 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(4), -1*E(4), E(4), E(4), -1*E(4), -1*E(4), E(4), -1*E(4)], [2, 2, 2, 2, 2, 2, 2, 2, 2, -2, 0, 0, -2, -2, 0, 0, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 2, 2, 0, 0, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, -2, 2, -2, 2, 2, -2, -2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1*E(8)-E(8)^-1, 0, 0, E(8)+E(8)^-1, E(8)+E(8)^-1, -1*E(8)-E(8)^-1], [2, 2, 2, -2, 2, -2, 2, 2, -2, -2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, E(8)+E(8)^-1, 0, 0, -1*E(8)-E(8)^-1, -1*E(8)-E(8)^-1, E(8)+E(8)^-1], [2, 2, 2, -2, 2, -2, 2, 2, -2, 2, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1*E(8)-E(8)^3, 0, 0, -1*E(8)-E(8)^3, E(8)+E(8)^3, E(8)+E(8)^3], [2, 2, 2, -2, 2, -2, 2, 2, -2, 2, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, E(8)+E(8)^3, 0, 0, E(8)+E(8)^3, -1*E(8)-E(8)^3, -1*E(8)-E(8)^3], [2, 2, 2, -2, 2, -2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0, -2*E(4), 2*E(4), 0, 0, 0, -1-E(4), -1+E(4), 0, 1+E(4), 1-E(4), 0, 0, 0], [2, 2, 2, -2, 2, -2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 2*E(4), -2*E(4), 0, 0, 0, -1+E(4), -1-E(4), 0, 1-E(4), 1+E(4), 0, 0, 0], [2, 2, 2, -2, 2, -2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0, -2*E(4), 2*E(4), 0, 0, 0, 1+E(4), 1-E(4), 0, -1-E(4), -1+E(4), 0, 0, 0], [2, 2, 2, -2, 2, -2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 2*E(4), -2*E(4), 0, 0, 0, 1-E(4), 1+E(4), 0, -1+E(4), -1-E(4), 0, 0, 0], [4, 4, 4, 4, 4, 4, -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, -4, 4, 0, 0, 0, 0, -2, -2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, 4, 4, -4, -4, 4, 0, 0, 0, 0, 2, 2, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, 4, 4, 4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0], [4, 4, 4, 4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0], [8, 8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [8, 8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [8, -8, 0, 0, 0, 0, -4, 4, 0, 0, -2, 2, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [8, -8, 0, 0, 0, 0, -4, 4, 0, 0, 2, -2, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [8, -8, 0, 0, 0, 0, 4, -4, 0, 0, -2, 2, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [8, -8, 0, 0, 0, 0, 4, -4, 0, 0, 2, -2, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]; ConvertToLibraryCharacterTableNC(chartbl_512_1824);