# Group 70.3 downloaded from the LMFDB on 10 September 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(182417639,70); a := GPC.1; b := GPC.2; GPerm := Group( (2,3)(4,5)(6,7)(9,10)(11,12), (8,9,11,12,10), (1,2,4,6,7,5,3) ); GLFp := Group([[[ Z(71)^2, 0*Z(71) ], [ 0*Z(71), Z(71)^68 ]], [[ 0*Z(71), Z(71)^0 ], [ Z(71)^0, 0*Z(71) ]]]); # Booleans booleans_70_3 := 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_70_3:=rec(); chartbl_70_3.IsFinite:= true; chartbl_70_3.UnderlyingCharacteristic:= 0; chartbl_70_3.UnderlyingGroup:= GPC; chartbl_70_3.Size:= 70; chartbl_70_3.InfoText:= "Character table for group 70.3 downloaded from the LMFDB."; chartbl_70_3.Identifier:= " D35 "; chartbl_70_3.NrConjugacyClasses:= 19; chartbl_70_3.ConjugacyClasses:= [ of ..., f1, f2^2*f3, f2^4*f3^2, f3, f3^2, f3^3, f2, f2^2, f2^3, f2^4, f2*f3, f2^3*f3, f2^4*f3, f2*f3^2, f2^2*f3^2, f2^3*f3^2, f2*f3^3, f2^2*f3^3]; chartbl_70_3.IdentificationOfConjugacyClasses:= [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]; chartbl_70_3.ComputedPowerMaps:= [ , [1, 1, 4, 3, 6, 7, 5, 9, 11, 12, 13, 16, 18, 19, 17, 15, 14, 10, 8], [1, 2, 4, 3, 7, 5, 6, 10, 12, 14, 16, 19, 15, 13, 9, 8, 11, 17, 18], [1, 2, 1, 1, 6, 7, 5, 5, 6, 7, 7, 5, 5, 6, 7, 6, 5, 6, 7]]; chartbl_70_3.SizesCentralizers:= [70, 2, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35]; chartbl_70_3.ClassNames:= ["1A", "2A", "5A1", "5A2", "7A1", "7A2", "7A3", "35A1", "35A2", "35A3", "35A4", "35A6", "35A8", "35A9", "35A11", "35A12", "35A13", "35A16", "35A17"]; chartbl_70_3.OrderClassRepresentatives:= [1, 2, 5, 5, 7, 7, 7, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35]; chartbl_70_3.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], [2, 0, E(5)^2+E(5)^-2, E(5)+E(5)^-1, 2, 2, 2, E(5)^2+E(5)^-2, E(5)+E(5)^-1, E(5)^2+E(5)^-2, E(5)+E(5)^-1, E(5)+E(5)^-1, E(5)^2+E(5)^-2, E(5)^2+E(5)^-2, E(5)+E(5)^-1, E(5)^2+E(5)^-2, E(5)+E(5)^-1, E(5)+E(5)^-1, E(5)^2+E(5)^-2], [2, 0, E(5)+E(5)^-1, E(5)^2+E(5)^-2, 2, 2, 2, E(5)+E(5)^-1, E(5)^2+E(5)^-2, E(5)+E(5)^-1, E(5)^2+E(5)^-2, E(5)^2+E(5)^-2, E(5)+E(5)^-1, E(5)+E(5)^-1, E(5)^2+E(5)^-2, E(5)+E(5)^-1, E(5)^2+E(5)^-2, E(5)^2+E(5)^-2, E(5)+E(5)^-1], [2, 0, 2, 2, E(7)^3+E(7)^-3, E(7)+E(7)^-1, E(7)^2+E(7)^-2, E(7)^2+E(7)^-2, E(7)+E(7)^-1, E(7)+E(7)^-1, E(7)^2+E(7)^-2, E(7)^3+E(7)^-3, E(7)+E(7)^-1, E(7)^3+E(7)^-3, E(7)^2+E(7)^-2, E(7)^3+E(7)^-3, E(7)^3+E(7)^-3, E(7)+E(7)^-1, E(7)^2+E(7)^-2], [2, 0, 2, 2, E(7)^2+E(7)^-2, E(7)^3+E(7)^-3, E(7)+E(7)^-1, E(7)+E(7)^-1, E(7)^3+E(7)^-3, E(7)^3+E(7)^-3, E(7)+E(7)^-1, E(7)^2+E(7)^-2, E(7)^3+E(7)^-3, E(7)^2+E(7)^-2, E(7)+E(7)^-1, E(7)^2+E(7)^-2, E(7)^2+E(7)^-2, E(7)^3+E(7)^-3, E(7)+E(7)^-1], [2, 0, 2, 2, E(7)+E(7)^-1, E(7)^2+E(7)^-2, E(7)^3+E(7)^-3, E(7)^3+E(7)^-3, E(7)^2+E(7)^-2, E(7)^2+E(7)^-2, E(7)^3+E(7)^-3, E(7)+E(7)^-1, E(7)^2+E(7)^-2, E(7)+E(7)^-1, E(7)^3+E(7)^-3, E(7)+E(7)^-1, E(7)+E(7)^-1, E(7)^2+E(7)^-2, E(7)^3+E(7)^-3], [2, 0, E(35)^14+E(35)^-14, E(35)^7+E(35)^-7, E(35)^15+E(35)^-15, E(35)^5+E(35)^-5, E(35)^10+E(35)^-10, E(35)^11+E(35)^-11, E(35)^12+E(35)^-12, E(35)^9+E(35)^-9, E(35)^3+E(35)^-3, E(35)^8+E(35)^-8, E(35)^16+E(35)^-16, E(35)+E(35)^-1, E(35)^17+E(35)^-17, E(35)^6+E(35)^-6, E(35)^13+E(35)^-13, E(35)^2+E(35)^-2, E(35)^4+E(35)^-4], [2, 0, E(35)^14+E(35)^-14, E(35)^7+E(35)^-7, E(35)^15+E(35)^-15, E(35)^5+E(35)^-5, E(35)^10+E(35)^-10, E(35)^4+E(35)^-4, E(35)^2+E(35)^-2, E(35)^16+E(35)^-16, E(35)^17+E(35)^-17, E(35)^13+E(35)^-13, E(35)^9+E(35)^-9, E(35)^6+E(35)^-6, E(35)^3+E(35)^-3, E(35)+E(35)^-1, E(35)^8+E(35)^-8, E(35)^12+E(35)^-12, E(35)^11+E(35)^-11], [2, 0, E(35)^14+E(35)^-14, E(35)^7+E(35)^-7, E(35)^10+E(35)^-10, E(35)^15+E(35)^-15, E(35)^5+E(35)^-5, E(35)^16+E(35)^-16, E(35)^8+E(35)^-8, E(35)^6+E(35)^-6, E(35)^2+E(35)^-2, E(35)^17+E(35)^-17, E(35)+E(35)^-1, E(35)^11+E(35)^-11, E(35)^12+E(35)^-12, E(35)^4+E(35)^-4, E(35)^3+E(35)^-3, E(35)^13+E(35)^-13, E(35)^9+E(35)^-9], [2, 0, E(35)^14+E(35)^-14, E(35)^7+E(35)^-7, E(35)^10+E(35)^-10, E(35)^15+E(35)^-15, E(35)^5+E(35)^-5, E(35)^9+E(35)^-9, E(35)^13+E(35)^-13, E(35)+E(35)^-1, E(35)^12+E(35)^-12, E(35)^3+E(35)^-3, E(35)^6+E(35)^-6, E(35)^4+E(35)^-4, E(35)^2+E(35)^-2, E(35)^11+E(35)^-11, E(35)^17+E(35)^-17, E(35)^8+E(35)^-8, E(35)^16+E(35)^-16], [2, 0, E(35)^14+E(35)^-14, E(35)^7+E(35)^-7, E(35)^5+E(35)^-5, E(35)^10+E(35)^-10, E(35)^15+E(35)^-15, E(35)^6+E(35)^-6, E(35)^3+E(35)^-3, E(35)^11+E(35)^-11, E(35)^8+E(35)^-8, E(35)^2+E(35)^-2, E(35)^4+E(35)^-4, E(35)^9+E(35)^-9, E(35)^13+E(35)^-13, E(35)^16+E(35)^-16, E(35)^12+E(35)^-12, E(35)^17+E(35)^-17, E(35)+E(35)^-1], [2, 0, E(35)^14+E(35)^-14, E(35)^7+E(35)^-7, E(35)^5+E(35)^-5, E(35)^10+E(35)^-10, E(35)^15+E(35)^-15, E(35)+E(35)^-1, E(35)^17+E(35)^-17, E(35)^4+E(35)^-4, E(35)^13+E(35)^-13, E(35)^12+E(35)^-12, E(35)^11+E(35)^-11, E(35)^16+E(35)^-16, E(35)^8+E(35)^-8, E(35)^9+E(35)^-9, E(35)^2+E(35)^-2, E(35)^3+E(35)^-3, E(35)^6+E(35)^-6], [2, 0, E(35)^7+E(35)^-7, E(35)^14+E(35)^-14, E(35)^15+E(35)^-15, E(35)^5+E(35)^-5, E(35)^10+E(35)^-10, E(35)^17+E(35)^-17, E(35)^9+E(35)^-9, E(35)^2+E(35)^-2, E(35)^11+E(35)^-11, E(35)^6+E(35)^-6, E(35)^12+E(35)^-12, E(35)^8+E(35)^-8, E(35)^4+E(35)^-4, E(35)^13+E(35)^-13, E(35)+E(35)^-1, E(35)^16+E(35)^-16, E(35)^3+E(35)^-3], [2, 0, E(35)^7+E(35)^-7, E(35)^14+E(35)^-14, E(35)^15+E(35)^-15, E(35)^5+E(35)^-5, E(35)^10+E(35)^-10, E(35)^3+E(35)^-3, E(35)^16+E(35)^-16, E(35)^12+E(35)^-12, E(35)^4+E(35)^-4, E(35)+E(35)^-1, E(35)^2+E(35)^-2, E(35)^13+E(35)^-13, E(35)^11+E(35)^-11, E(35)^8+E(35)^-8, E(35)^6+E(35)^-6, E(35)^9+E(35)^-9, E(35)^17+E(35)^-17], [2, 0, E(35)^7+E(35)^-7, E(35)^14+E(35)^-14, E(35)^10+E(35)^-10, E(35)^15+E(35)^-15, E(35)^5+E(35)^-5, E(35)^12+E(35)^-12, E(35)^6+E(35)^-6, E(35)^13+E(35)^-13, E(35)^16+E(35)^-16, E(35)^4+E(35)^-4, E(35)^8+E(35)^-8, E(35)^17+E(35)^-17, E(35)^9+E(35)^-9, E(35)^3+E(35)^-3, E(35)^11+E(35)^-11, E(35)+E(35)^-1, E(35)^2+E(35)^-2], [2, 0, E(35)^7+E(35)^-7, E(35)^14+E(35)^-14, E(35)^10+E(35)^-10, E(35)^15+E(35)^-15, E(35)^5+E(35)^-5, E(35)^2+E(35)^-2, E(35)+E(35)^-1, E(35)^8+E(35)^-8, E(35)^9+E(35)^-9, E(35)^11+E(35)^-11, E(35)^13+E(35)^-13, E(35)^3+E(35)^-3, E(35)^16+E(35)^-16, E(35)^17+E(35)^-17, E(35)^4+E(35)^-4, E(35)^6+E(35)^-6, E(35)^12+E(35)^-12], [2, 0, E(35)^7+E(35)^-7, E(35)^14+E(35)^-14, E(35)^5+E(35)^-5, E(35)^10+E(35)^-10, E(35)^15+E(35)^-15, E(35)^13+E(35)^-13, E(35)^11+E(35)^-11, E(35)^17+E(35)^-17, E(35)^6+E(35)^-6, E(35)^16+E(35)^-16, E(35)^3+E(35)^-3, E(35)^2+E(35)^-2, E(35)+E(35)^-1, E(35)^12+E(35)^-12, E(35)^9+E(35)^-9, E(35)^4+E(35)^-4, E(35)^8+E(35)^-8], [2, 0, E(35)^7+E(35)^-7, E(35)^14+E(35)^-14, E(35)^5+E(35)^-5, E(35)^10+E(35)^-10, E(35)^15+E(35)^-15, E(35)^8+E(35)^-8, E(35)^4+E(35)^-4, E(35)^3+E(35)^-3, E(35)+E(35)^-1, E(35)^9+E(35)^-9, E(35)^17+E(35)^-17, E(35)^12+E(35)^-12, E(35)^6+E(35)^-6, E(35)^2+E(35)^-2, E(35)^16+E(35)^-16, E(35)^11+E(35)^-11, E(35)^13+E(35)^-13]]; ConvertToLibraryCharacterTableNC(chartbl_70_3);