# Group 406.2 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(1743145760747,406); a := GPC.1; b := GPC.2; GPerm := Group( (30,31), (2,3,5,8,9,15,20)(4,7,12,19,27,6,10)(11,18,16,24,28,14,17)(13,21,23,26,25,22,29), (1,2,4,7,13,22,21,8,14,23,24,10,17,25,19,28,3,6,11,12,20,27,29,15,5,9,16,18,26) ); GLFp := Group([[[ Z(29)^0, Z(29)^0 ], [ 0*Z(29), Z(29)^0 ]], [[ Z(29)^4, 0*Z(29) ], [ 0*Z(29), Z(29)^0 ]], [[ Z(29)^14, 0*Z(29) ], [ 0*Z(29), Z(29)^14 ]]]); # Booleans booleans_406_2 := rec( Agroup := true, Zgroup := true, abelian := false, almost_simple := false, cyclic := false, metabelian := true, metacyclic := true, monomial := true, nilpotent := false, perfect := false, quasisimple := false, rational := false, solvable := true, supersolvable := true); # Character Table chartbl_406_2:=rec(); chartbl_406_2.IsFinite:= true; chartbl_406_2.UnderlyingCharacteristic:= 0; chartbl_406_2.UnderlyingGroup:= GPC; chartbl_406_2.Size:= 406; chartbl_406_2.InfoText:= "Character table for group 406.2 downloaded from the LMFDB."; chartbl_406_2.Identifier:= " C29:C14 "; chartbl_406_2.NrConjugacyClasses:= 22; chartbl_406_2.ConjugacyClasses:= [ of ..., f2*f3^14, f1*f3^20, f1^6*f3^6, f1^2*f3^21, f1^5*f3^10, f1^3*f3^8, f1^4*f3^3, f1^4*f2*f3^17, f1^3*f2*f3^22, f1^5*f2*f3^24, f1^2*f2*f3^6, f1^6*f2*f3^20, f1*f2*f3^5, f3, f3^28, f3^2, f3^27, f2, f2*f3^2, f2*f3, f2*f3^7]; chartbl_406_2.IdentificationOfConjugacyClasses:= [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22]; chartbl_406_2.ComputedPowerMaps:= [ , [1, 1, 5, 6, 8, 7, 4, 3, 3, 4, 7, 8, 6, 5, 17, 18, 16, 15, 15, 16, 17, 18], [1, 2, 7, 8, 4, 3, 5, 6, 11, 12, 14, 13, 9, 10, 17, 18, 16, 15, 21, 22, 20, 19], [1, 2, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 15, 16, 17, 18, 19, 20, 21, 22]]; chartbl_406_2.SizesCentralizers:= [406, 406, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 58, 58, 58, 58, 58, 58, 58, 58]; chartbl_406_2.ClassNames:= ["1A", "2A", "7A1", "7A-1", "7A2", "7A-2", "7A3", "7A-3", "14A1", "14A-1", "14A3", "14A-3", "14A5", "14A-5", "29A1", "29A-1", "29A2", "29A-2", "58A1", "58A-1", "58A3", "58A-3"]; chartbl_406_2.OrderClassRepresentatives:= [1, 2, 7, 7, 7, 7, 7, 7, 14, 14, 14, 14, 14, 14, 29, 29, 29, 29, 58, 58, 58, 58]; chartbl_406_2.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, E(7)^-3, E(7)^-1, E(7)^3, E(7)^2, E(7), E(7)^-2, E(7)^-1, E(7)^-2, E(7)^-3, E(7)^2, E(7), E(7)^3, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, E(7)^3, E(7), E(7)^-3, E(7)^-2, E(7)^-1, E(7)^2, E(7), E(7)^2, E(7)^3, E(7)^-2, E(7)^-1, E(7)^-3, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, E(7)^-2, E(7)^-3, E(7)^2, E(7)^-1, E(7)^3, E(7), E(7)^-3, E(7), E(7)^-2, E(7)^-1, E(7)^3, E(7)^2, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, E(7)^2, E(7)^3, E(7)^-2, E(7), E(7)^-3, E(7)^-1, E(7)^3, E(7)^-1, E(7)^2, E(7), E(7)^-3, E(7)^-2, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, E(7)^-1, E(7)^2, E(7), E(7)^3, E(7)^-2, E(7)^-3, E(7)^2, E(7)^-3, E(7)^-1, E(7)^3, E(7)^-2, E(7), 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, E(7), E(7)^-2, E(7)^-1, E(7)^-3, E(7)^2, E(7)^3, E(7)^-2, E(7)^3, E(7), E(7)^-3, E(7)^2, E(7)^-1, 1, 1, 1, 1, 1, 1, 1, 1], [1, -1, E(7)^-3, E(7)^-1, E(7)^3, E(7)^2, E(7), E(7)^-2, -1*E(7)^-1, -1*E(7)^-2, -1*E(7)^-3, -1*E(7)^2, -1*E(7), -1*E(7)^3, 1, 1, 1, 1, -1, -1, -1, -1], [1, -1, E(7)^3, E(7), E(7)^-3, E(7)^-2, E(7)^-1, E(7)^2, -1*E(7), -1*E(7)^2, -1*E(7)^3, -1*E(7)^-2, -1*E(7)^-1, -1*E(7)^-3, 1, 1, 1, 1, -1, -1, -1, -1], [1, -1, E(7)^-2, E(7)^-3, E(7)^2, E(7)^-1, E(7)^3, E(7), -1*E(7)^-3, -1*E(7), -1*E(7)^-2, -1*E(7)^-1, -1*E(7)^3, -1*E(7)^2, 1, 1, 1, 1, -1, -1, -1, -1], [1, -1, E(7)^2, E(7)^3, E(7)^-2, E(7), E(7)^-3, E(7)^-1, -1*E(7)^3, -1*E(7)^-1, -1*E(7)^2, -1*E(7), -1*E(7)^-3, -1*E(7)^-2, 1, 1, 1, 1, -1, -1, -1, -1], [1, -1, E(7)^-1, E(7)^2, E(7), E(7)^3, E(7)^-2, E(7)^-3, -1*E(7)^2, -1*E(7)^-3, -1*E(7)^-1, -1*E(7)^3, -1*E(7)^-2, -1*E(7), 1, 1, 1, 1, -1, -1, -1, -1], [1, -1, E(7), E(7)^-2, E(7)^-1, E(7)^-3, E(7)^2, E(7)^3, -1*E(7)^-2, -1*E(7)^3, -1*E(7), -1*E(7)^-3, -1*E(7)^2, -1*E(7)^-1, 1, 1, 1, 1, -1, -1, -1, -1], [7, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, E(29)^2+E(29)^3+E(29)^11+E(29)^14+E(29)^-12+E(29)^-10+E(29)^-8, E(29)^4+E(29)^5+E(29)^6+E(29)^9+E(29)^13+E(29)^-7+E(29)^-1, E(29)+E(29)^7+E(29)^-13+E(29)^-9+E(29)^-6+E(29)^-5+E(29)^-4, E(29)^8+E(29)^10+E(29)^12+E(29)^-14+E(29)^-11+E(29)^-3+E(29)^-2, E(29)^2+E(29)^3+E(29)^11+E(29)^14+E(29)^-12+E(29)^-10+E(29)^-8, E(29)+E(29)^7+E(29)^-13+E(29)^-9+E(29)^-6+E(29)^-5+E(29)^-4, E(29)^4+E(29)^5+E(29)^6+E(29)^9+E(29)^13+E(29)^-7+E(29)^-1, E(29)^8+E(29)^10+E(29)^12+E(29)^-14+E(29)^-11+E(29)^-3+E(29)^-2], [7, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, E(29)^8+E(29)^10+E(29)^12+E(29)^-14+E(29)^-11+E(29)^-3+E(29)^-2, E(29)+E(29)^7+E(29)^-13+E(29)^-9+E(29)^-6+E(29)^-5+E(29)^-4, E(29)^4+E(29)^5+E(29)^6+E(29)^9+E(29)^13+E(29)^-7+E(29)^-1, E(29)^2+E(29)^3+E(29)^11+E(29)^14+E(29)^-12+E(29)^-10+E(29)^-8, E(29)^8+E(29)^10+E(29)^12+E(29)^-14+E(29)^-11+E(29)^-3+E(29)^-2, E(29)^4+E(29)^5+E(29)^6+E(29)^9+E(29)^13+E(29)^-7+E(29)^-1, E(29)+E(29)^7+E(29)^-13+E(29)^-9+E(29)^-6+E(29)^-5+E(29)^-4, E(29)^2+E(29)^3+E(29)^11+E(29)^14+E(29)^-12+E(29)^-10+E(29)^-8], [7, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, E(29)+E(29)^7+E(29)^-13+E(29)^-9+E(29)^-6+E(29)^-5+E(29)^-4, E(29)^2+E(29)^3+E(29)^11+E(29)^14+E(29)^-12+E(29)^-10+E(29)^-8, E(29)^8+E(29)^10+E(29)^12+E(29)^-14+E(29)^-11+E(29)^-3+E(29)^-2, E(29)^4+E(29)^5+E(29)^6+E(29)^9+E(29)^13+E(29)^-7+E(29)^-1, E(29)+E(29)^7+E(29)^-13+E(29)^-9+E(29)^-6+E(29)^-5+E(29)^-4, E(29)^8+E(29)^10+E(29)^12+E(29)^-14+E(29)^-11+E(29)^-3+E(29)^-2, E(29)^2+E(29)^3+E(29)^11+E(29)^14+E(29)^-12+E(29)^-10+E(29)^-8, E(29)^4+E(29)^5+E(29)^6+E(29)^9+E(29)^13+E(29)^-7+E(29)^-1], [7, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, E(29)^4+E(29)^5+E(29)^6+E(29)^9+E(29)^13+E(29)^-7+E(29)^-1, E(29)^8+E(29)^10+E(29)^12+E(29)^-14+E(29)^-11+E(29)^-3+E(29)^-2, E(29)^2+E(29)^3+E(29)^11+E(29)^14+E(29)^-12+E(29)^-10+E(29)^-8, E(29)+E(29)^7+E(29)^-13+E(29)^-9+E(29)^-6+E(29)^-5+E(29)^-4, E(29)^4+E(29)^5+E(29)^6+E(29)^9+E(29)^13+E(29)^-7+E(29)^-1, E(29)^2+E(29)^3+E(29)^11+E(29)^14+E(29)^-12+E(29)^-10+E(29)^-8, E(29)^8+E(29)^10+E(29)^12+E(29)^-14+E(29)^-11+E(29)^-3+E(29)^-2, E(29)+E(29)^7+E(29)^-13+E(29)^-9+E(29)^-6+E(29)^-5+E(29)^-4], [7, -7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, E(29)^2+E(29)^3+E(29)^11+E(29)^14+E(29)^-12+E(29)^-10+E(29)^-8, E(29)^4+E(29)^5+E(29)^6+E(29)^9+E(29)^13+E(29)^-7+E(29)^-1, E(29)+E(29)^7+E(29)^-13+E(29)^-9+E(29)^-6+E(29)^-5+E(29)^-4, E(29)^8+E(29)^10+E(29)^12+E(29)^-14+E(29)^-11+E(29)^-3+E(29)^-2, -1*E(29)^2-E(29)^3-E(29)^11-E(29)^14-E(29)^-12-E(29)^-10-E(29)^-8, -1*E(29)-E(29)^7-E(29)^-13-E(29)^-9-E(29)^-6-E(29)^-5-E(29)^-4, -1*E(29)^4-E(29)^5-E(29)^6-E(29)^9-E(29)^13-E(29)^-7-E(29)^-1, -1*E(29)^8-E(29)^10-E(29)^12-E(29)^-14-E(29)^-11-E(29)^-3-E(29)^-2], [7, -7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, E(29)^8+E(29)^10+E(29)^12+E(29)^-14+E(29)^-11+E(29)^-3+E(29)^-2, E(29)+E(29)^7+E(29)^-13+E(29)^-9+E(29)^-6+E(29)^-5+E(29)^-4, E(29)^4+E(29)^5+E(29)^6+E(29)^9+E(29)^13+E(29)^-7+E(29)^-1, E(29)^2+E(29)^3+E(29)^11+E(29)^14+E(29)^-12+E(29)^-10+E(29)^-8, -1*E(29)^8-E(29)^10-E(29)^12-E(29)^-14-E(29)^-11-E(29)^-3-E(29)^-2, -1*E(29)^4-E(29)^5-E(29)^6-E(29)^9-E(29)^13-E(29)^-7-E(29)^-1, -1*E(29)-E(29)^7-E(29)^-13-E(29)^-9-E(29)^-6-E(29)^-5-E(29)^-4, -1*E(29)^2-E(29)^3-E(29)^11-E(29)^14-E(29)^-12-E(29)^-10-E(29)^-8], [7, -7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, E(29)+E(29)^7+E(29)^-13+E(29)^-9+E(29)^-6+E(29)^-5+E(29)^-4, E(29)^2+E(29)^3+E(29)^11+E(29)^14+E(29)^-12+E(29)^-10+E(29)^-8, E(29)^8+E(29)^10+E(29)^12+E(29)^-14+E(29)^-11+E(29)^-3+E(29)^-2, E(29)^4+E(29)^5+E(29)^6+E(29)^9+E(29)^13+E(29)^-7+E(29)^-1, -1*E(29)-E(29)^7-E(29)^-13-E(29)^-9-E(29)^-6-E(29)^-5-E(29)^-4, -1*E(29)^8-E(29)^10-E(29)^12-E(29)^-14-E(29)^-11-E(29)^-3-E(29)^-2, -1*E(29)^2-E(29)^3-E(29)^11-E(29)^14-E(29)^-12-E(29)^-10-E(29)^-8, -1*E(29)^4-E(29)^5-E(29)^6-E(29)^9-E(29)^13-E(29)^-7-E(29)^-1], [7, -7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, E(29)^4+E(29)^5+E(29)^6+E(29)^9+E(29)^13+E(29)^-7+E(29)^-1, E(29)^8+E(29)^10+E(29)^12+E(29)^-14+E(29)^-11+E(29)^-3+E(29)^-2, E(29)^2+E(29)^3+E(29)^11+E(29)^14+E(29)^-12+E(29)^-10+E(29)^-8, E(29)+E(29)^7+E(29)^-13+E(29)^-9+E(29)^-6+E(29)^-5+E(29)^-4, -1*E(29)^4-E(29)^5-E(29)^6-E(29)^9-E(29)^13-E(29)^-7-E(29)^-1, -1*E(29)^2-E(29)^3-E(29)^11-E(29)^14-E(29)^-12-E(29)^-10-E(29)^-8, -1*E(29)^8-E(29)^10-E(29)^12-E(29)^-14-E(29)^-11-E(29)^-3-E(29)^-2, -1*E(29)-E(29)^7-E(29)^-13-E(29)^-9-E(29)^-6-E(29)^-5-E(29)^-4]]; ConvertToLibraryCharacterTableNC(chartbl_406_2);