# Group 3528.br downloaded from the LMFDB on 15 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(269543693983666904293044810443180297448527911947133736287605193325836027409495,3528); a := GPC.1; b := GPC.2; c := GPC.4; d := GPC.7; GPerm := Group( (2,4,6,8,10,12,14), (2,12)(4,10)(6,8), (1,8)(2,9)(3,10)(4,11)(5,12)(6,13)(7,14), (2,4,8)(6,12,10) ); # Booleans booleans_3528_br := 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 := false); # Character Table chartbl_3528_br:=rec(); chartbl_3528_br.IsFinite:= true; chartbl_3528_br.UnderlyingCharacteristic:= 0; chartbl_3528_br.UnderlyingGroup:= GPC; chartbl_3528_br.Size:= 3528; chartbl_3528_br.InfoText:= "Character table for group 3528.br downloaded from the LMFDB."; chartbl_3528_br.Identifier:= " F7wrC2 "; chartbl_3528_br.NrConjugacyClasses:= 35; chartbl_3528_br.ConjugacyClasses:= [ of ..., f4*f5*f6^3*f7^6, f1*f3*f6*f7^4, f2*f3*f6^2*f7^2, f3*f5^2*f6^5*f7^2, f3^2*f5*f7^3, f3*f5*f6^3*f7^6, f3^2*f5^2*f6^2*f7^3, f3*f6^6*f7^6, f1*f3^2*f4*f5*f6^4*f7^3, f4*f6*f7^5, f4*f5^2*f6^5*f7^3, f2*f5^2*f7^5, f2*f3^2*f5*f7, f2*f3^2*f6^5*f7^3, f3^2*f4*f6^6*f7^3, f3*f4*f5^2*f6^6, f3^2*f4*f5*f6^5*f7^6, f3*f4*f5*f6^2*f7^4, f3^2*f4*f5^2*f6^3*f7^6, f3*f4*f6^2, f2*f3*f5*f6^4*f7^2, f2*f3*f5^2*f6^6*f7^5, f1*f3^2*f5*f7^3, f1*f5^2*f6^4, f6^4, f6^2*f7, f1*f2*f3*f4*f5^2*f6^6*f7^2, f1*f3*f4*f6^2*f7^2, f4*f5*f6^5*f7^2, f1*f3^2*f7^5, f5*f6*f7^6, f5^2*f6^5*f7^4, f4*f6^4*f7^5, f4*f5^2*f6^2*f7^3]; chartbl_3528_br.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]; chartbl_3528_br.ComputedPowerMaps:= [ , [1, 1, 1, 1, 6, 5, 8, 7, 9, 4, 6, 5, 7, 8, 9, 7, 8, 9, 9, 5, 6, 5, 6, 8, 7, 26, 27, 13, 14, 26, 27, 33, 32, 32, 33], [1, 2, 3, 4, 1, 1, 1, 1, 1, 10, 2, 2, 4, 4, 4, 2, 2, 2, 2, 2, 2, 4, 4, 3, 3, 26, 27, 10, 10, 30, 31, 26, 26, 30, 30], [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, 1, 1, 28, 29, 2, 3, 6, 5, 11, 12]]; chartbl_3528_br.SizesCentralizers:= [3528, 252, 84, 72, 252, 252, 72, 72, 36, 12, 252, 252, 72, 72, 36, 36, 36, 36, 36, 36, 36, 36, 36, 12, 12, 294, 98, 12, 12, 42, 14, 42, 42, 42, 42]; chartbl_3528_br.ClassNames:= ["1A", "2A", "2B", "2C", "3A1", "3A-1", "3B1", "3B-1", "3C", "4A", "6A1", "6A-1", "6B1", "6B-1", "6C", "6D1", "6D-1", "6E1", "6E-1", "6F1", "6F-1", "6G1", "6G-1", "6H1", "6H-1", "7A", "7B", "12A1", "12A-1", "14A", "14B", "21A1", "21A-1", "42A1", "42A-1"]; chartbl_3528_br.OrderClassRepresentatives:= [1, 2, 2, 2, 3, 3, 3, 3, 3, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 12, 12, 14, 14, 21, 21, 42, 42]; chartbl_3528_br.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, E(3)^-1, E(3), E(3), E(3)^-1, 1, 1, E(3)^-1, E(3), E(3)^-1, E(3), 1, 1, E(3), E(3)^-1, 1, E(3)^-1, E(3)^-1, E(3), E(3), E(3), E(3)^-1, 1, 1, E(3), E(3)^-1, 1, 1, E(3), E(3)^-1, E(3)^-1, E(3)], [1, 1, 1, 1, E(3), E(3)^-1, E(3)^-1, E(3), 1, 1, E(3), E(3)^-1, E(3), E(3)^-1, 1, 1, E(3)^-1, E(3), 1, E(3), E(3), E(3)^-1, E(3)^-1, E(3)^-1, E(3), 1, 1, E(3)^-1, E(3), 1, 1, E(3)^-1, E(3), E(3), E(3)^-1], [1, -1, -1, 1, E(3)^-1, E(3), E(3), E(3)^-1, 1, 1, -1*E(3)^-1, -1*E(3), E(3)^-1, E(3), 1, -1, -1*E(3), -1*E(3)^-1, -1, -1*E(3)^-1, E(3)^-1, E(3), -1*E(3), -1*E(3), -1*E(3)^-1, 1, 1, E(3), E(3)^-1, -1, -1, E(3), E(3)^-1, -1*E(3)^-1, -1*E(3)], [1, -1, -1, 1, E(3), E(3)^-1, E(3)^-1, E(3), 1, 1, -1*E(3), -1*E(3)^-1, E(3), E(3)^-1, 1, -1, -1*E(3)^-1, -1*E(3), -1, -1*E(3), E(3), E(3)^-1, -1*E(3)^-1, -1*E(3)^-1, -1*E(3), 1, 1, E(3)^-1, E(3), -1, -1, E(3)^-1, E(3), -1*E(3), -1*E(3)^-1], [1, -1, 1, 1, E(3)^-1, E(3), E(3), E(3)^-1, 1, -1, -1*E(3)^-1, -1*E(3), E(3)^-1, E(3), 1, -1, -1*E(3), -1*E(3)^-1, -1, -1*E(3)^-1, E(3)^-1, E(3), -1*E(3), E(3), E(3)^-1, 1, 1, -1*E(3), -1*E(3)^-1, -1, 1, E(3), E(3)^-1, -1*E(3)^-1, -1*E(3)], [1, -1, 1, 1, E(3), E(3)^-1, E(3)^-1, E(3), 1, -1, -1*E(3), -1*E(3)^-1, E(3), E(3)^-1, 1, -1, -1*E(3)^-1, -1*E(3), -1, -1*E(3), E(3), E(3)^-1, -1*E(3)^-1, E(3)^-1, E(3), 1, 1, -1*E(3)^-1, -1*E(3), -1, 1, E(3)^-1, E(3), -1*E(3), -1*E(3)^-1], [1, 1, -1, 1, E(3)^-1, E(3), E(3), E(3)^-1, 1, -1, E(3)^-1, E(3), E(3)^-1, E(3), 1, 1, E(3), E(3)^-1, 1, E(3)^-1, E(3)^-1, E(3), E(3), -1*E(3), -1*E(3)^-1, 1, 1, -1*E(3), -1*E(3)^-1, 1, -1, E(3), E(3)^-1, E(3)^-1, E(3)], [1, 1, -1, 1, E(3), E(3)^-1, E(3)^-1, E(3), 1, -1, E(3), E(3)^-1, E(3), E(3)^-1, 1, 1, E(3)^-1, E(3), 1, E(3), E(3), E(3)^-1, E(3)^-1, -1*E(3)^-1, -1*E(3), 1, 1, -1*E(3)^-1, -1*E(3), 1, -1, E(3)^-1, E(3), E(3), E(3)^-1], [2, 2, 0, 2, -1, -1, 2, 2, -1, 0, -1, -1, 2, 2, -1, -1, 2, -1, -1, 2, -1, -1, -1, 0, 0, 2, 2, 0, 0, 2, 0, -1, -1, -1, -1], [2, 0, 0, -2, 2, 2, 2, 2, 2, 0, 0, 0, -2, -2, -2, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 2, 0, 0], [2, -2, 0, 2, -1, -1, 2, 2, -1, 0, 1, 1, 2, 2, -1, 1, -2, 1, 1, -2, -1, -1, 1, 0, 0, 2, 2, 0, 0, -2, 0, -1, -1, 1, 1], [2, 2, 0, 2, -1*E(3), -1*E(3)^-1, 2*E(3)^-1, 2*E(3), -1, 0, -1*E(3), -1*E(3)^-1, 2*E(3), 2*E(3)^-1, -1, -1, 2*E(3)^-1, -1*E(3), -1, 2*E(3), -1*E(3), -1*E(3)^-1, -1*E(3)^-1, 0, 0, 2, 2, 0, 0, 2, 0, -1*E(3)^-1, -1*E(3), -1*E(3), -1*E(3)^-1], [2, 2, 0, 2, -1*E(3)^-1, -1*E(3), 2*E(3), 2*E(3)^-1, -1, 0, -1*E(3)^-1, -1*E(3), 2*E(3)^-1, 2*E(3), -1, -1, 2*E(3), -1*E(3)^-1, -1, 2*E(3)^-1, -1*E(3)^-1, -1*E(3), -1*E(3), 0, 0, 2, 2, 0, 0, 2, 0, -1*E(3), -1*E(3)^-1, -1*E(3)^-1, -1*E(3)], [2, 0, 0, -2, -1, -1, 2, 2, -1, 0, -1-2*E(3), 1+2*E(3), -2, -2, 1, 1+2*E(3), 0, 1+2*E(3), -1-2*E(3), 0, 1, 1, -1-2*E(3), 0, 0, 2, 2, 0, 0, 0, 0, -1, -1, -1-2*E(3), 1+2*E(3)], [2, 0, 0, -2, -1, -1, 2, 2, -1, 0, 1+2*E(3), -1-2*E(3), -2, -2, 1, -1-2*E(3), 0, -1-2*E(3), 1+2*E(3), 0, 1, 1, 1+2*E(3), 0, 0, 2, 2, 0, 0, 0, 0, -1, -1, 1+2*E(3), -1-2*E(3)], [2, 0, 0, -2, 2*E(3)^-1, 2*E(3), 2*E(3), 2*E(3)^-1, 2, 0, 0, 0, -2*E(3)^-1, -2*E(3), -2, 0, 0, 0, 0, 0, -2*E(3)^-1, -2*E(3), 0, 0, 0, 2, 2, 0, 0, 0, 0, 2*E(3), 2*E(3)^-1, 0, 0], [2, 0, 0, -2, 2*E(3), 2*E(3)^-1, 2*E(3)^-1, 2*E(3), 2, 0, 0, 0, -2*E(3), -2*E(3)^-1, -2, 0, 0, 0, 0, 0, -2*E(3), -2*E(3)^-1, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2*E(3)^-1, 2*E(3), 0, 0], [2, -2, 0, 2, -1*E(3), -1*E(3)^-1, 2*E(3)^-1, 2*E(3), -1, 0, E(3), E(3)^-1, 2*E(3), 2*E(3)^-1, -1, 1, -2*E(3)^-1, E(3), 1, -2*E(3), -1*E(3), -1*E(3)^-1, E(3)^-1, 0, 0, 2, 2, 0, 0, -2, 0, -1*E(3)^-1, -1*E(3), E(3), E(3)^-1], [2, -2, 0, 2, -1*E(3)^-1, -1*E(3), 2*E(3), 2*E(3)^-1, -1, 0, E(3)^-1, E(3), 2*E(3)^-1, 2*E(3), -1, 1, -2*E(3), E(3)^-1, 1, -2*E(3)^-1, -1*E(3)^-1, -1*E(3), E(3), 0, 0, 2, 2, 0, 0, -2, 0, -1*E(3), -1*E(3)^-1, E(3)^-1, E(3)], [2, 0, 0, -2, -1*E(3), -1*E(3)^-1, 2*E(3)^-1, 2*E(3), -1, 0, -2-E(3), -1+E(3), -2*E(3), -2*E(3)^-1, 1, -1-2*E(3), 0, 2+E(3), 1+2*E(3), 0, E(3), E(3)^-1, 1-E(3), 0, 0, 2, 2, 0, 0, 0, 0, -1*E(3)^-1, -1*E(3), -2-E(3), -1+E(3)], [2, 0, 0, -2, -1*E(3)^-1, -1*E(3), 2*E(3), 2*E(3)^-1, -1, 0, -1+E(3), -2-E(3), -2*E(3)^-1, -2*E(3), 1, 1+2*E(3), 0, 1-E(3), -1-2*E(3), 0, E(3)^-1, E(3), 2+E(3), 0, 0, 2, 2, 0, 0, 0, 0, -1*E(3), -1*E(3)^-1, -1+E(3), -2-E(3)], [2, 0, 0, -2, -1*E(3), -1*E(3)^-1, 2*E(3)^-1, 2*E(3), -1, 0, 2+E(3), 1-E(3), -2*E(3), -2*E(3)^-1, 1, 1+2*E(3), 0, -2-E(3), -1-2*E(3), 0, E(3), E(3)^-1, -1+E(3), 0, 0, 2, 2, 0, 0, 0, 0, -1*E(3)^-1, -1*E(3), 2+E(3), 1-E(3)], [2, 0, 0, -2, -1*E(3)^-1, -1*E(3), 2*E(3), 2*E(3)^-1, -1, 0, 1-E(3), 2+E(3), -2*E(3)^-1, -2*E(3), 1, -1-2*E(3), 0, -1+E(3), 1+2*E(3), 0, E(3)^-1, E(3), -2-E(3), 0, 0, 2, 2, 0, 0, 0, 0, -1*E(3), -1*E(3)^-1, 1-E(3), 2+E(3)], [12, 6, 0, 0, 6, 6, 0, 0, 0, 0, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, -2, 0, 0, -1, 0, -1, -1, -1, -1], [12, -6, 0, 0, 6, 6, 0, 0, 0, 0, -6, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, -2, 0, 0, 1, 0, -1, -1, 1, 1], [12, 6, 0, 0, 6*E(3)^-1, 6*E(3), 0, 0, 0, 0, 6*E(3)^-1, 6*E(3), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, -2, 0, 0, -1, 0, -1*E(3), -1*E(3)^-1, -1*E(3)^-1, -1*E(3)], [12, 6, 0, 0, 6*E(3), 6*E(3)^-1, 0, 0, 0, 0, 6*E(3), 6*E(3)^-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, -2, 0, 0, -1, 0, -1*E(3)^-1, -1*E(3), -1*E(3), -1*E(3)^-1], [12, -6, 0, 0, 6*E(3)^-1, 6*E(3), 0, 0, 0, 0, -6*E(3)^-1, -6*E(3), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, -2, 0, 0, 1, 0, -1*E(3), -1*E(3)^-1, E(3)^-1, E(3)], [12, -6, 0, 0, 6*E(3), 6*E(3)^-1, 0, 0, 0, 0, -6*E(3), -6*E(3)^-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, -2, 0, 0, 1, 0, -1*E(3)^-1, -1*E(3), E(3), E(3)^-1], [36, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 1, 0, 0, 0, -1, 0, 0, 0, 0], [36, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 1, 0, 0, 0, 1, 0, 0, 0, 0]]; ConvertToLibraryCharacterTableNC(chartbl_3528_br);