# Group 480.1192 downloaded from the LMFDB on 12 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(14327755925975818710343513820507289518147,480); a := GPC.1; b := GPC.2; c := GPC.5; d := GPC.6; GPerm := Group( (1,2)(3,4)(5,6)(8,9,10,11), (1,2)(3,4)(5,6), (1,3,5)(2,4,6), (8,10)(9,11), (3,4)(5,6), (1,2)(3,4), (7,8,9,11,10) ); GLZN := Group([[[ZmodnZObj(11,20), ZmodnZObj(10,20)], [ZmodnZObj(10,20), ZmodnZObj(1,20)]],[[ZmodnZObj(9,20), ZmodnZObj(0,20)], [ZmodnZObj(0,20), ZmodnZObj(1,20)]],[[ZmodnZObj(11,20), ZmodnZObj(0,20)], [ZmodnZObj(10,20), ZmodnZObj(11,20)]],[[ZmodnZObj(1,20), ZmodnZObj(4,20)], [ZmodnZObj(0,20), ZmodnZObj(1,20)]],[[ZmodnZObj(3,20), ZmodnZObj(0,20)], [ZmodnZObj(0,20), ZmodnZObj(1,20)]],[[ZmodnZObj(11,20), ZmodnZObj(15,20)], [ZmodnZObj(5,20), ZmodnZObj(16,20)]],[[ZmodnZObj(1,20), ZmodnZObj(10,20)], [ZmodnZObj(10,20), ZmodnZObj(1,20)]]]); # Booleans booleans_480_1192 := rec( Agroup := true, Zgroup := false, abelian := false, almost_simple := false, cyclic := false, metabelian := true, metacyclic := false, monomial := true, nilpotent := false, perfect := false, quasisimple := false, rational := false, solvable := true, supersolvable := false); # Character Table chartbl_480_1192:=rec(); chartbl_480_1192.IsFinite:= true; chartbl_480_1192.UnderlyingCharacteristic:= 0; chartbl_480_1192.UnderlyingGroup:= GPC; chartbl_480_1192.Size:= 480; chartbl_480_1192.InfoText:= "Character table for group 480.1192 downloaded from the LMFDB."; chartbl_480_1192.Identifier:= " C2*A4*F5 "; chartbl_480_1192.NrConjugacyClasses:= 40; chartbl_480_1192.ConjugacyClasses:= [ of ..., f1, f6*f7^2, f1*f6*f7^2, f3*f4*f7^4, f1*f3*f4, f3*f4*f6, f1*f3*f4*f6, f4, f4^2, f2*f3, f2*f4^2, f1*f2*f3, f1*f2*f4^2, f2*f3*f6, f2*f4^2*f6, f1*f2*f3*f6, f1*f2*f4^2*f6, f7, f1*f4^2, f1*f4, f1*f3, f1*f3*f4^2, f3, f3*f4^2, f1*f7^3, f6, f1*f6, f2, f2*f3*f4^2, f2*f4, f2*f3*f4, f1*f2, f1*f2*f3*f4^2, f1*f2*f4, f1*f2*f3*f4, f4^2*f7^2, f4*f7^3, f1*f4*f7, f1*f4^2*f7]; chartbl_480_1192.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, 36, 37, 38, 39, 40]; chartbl_480_1192.ComputedPowerMaps:= [ , [1, 1, 1, 1, 1, 1, 1, 1, 10, 9, 5, 5, 5, 5, 5, 5, 5, 5, 19, 9, 10, 9, 10, 9, 10, 19, 19, 19, 24, 25, 25, 24, 24, 25, 25, 24, 38, 37, 37, 38], [1, 2, 3, 4, 5, 6, 7, 8, 1, 1, 12, 11, 14, 13, 16, 15, 18, 17, 19, 2, 2, 6, 6, 5, 5, 26, 27, 28, 11, 12, 11, 12, 13, 14, 13, 14, 19, 19, 26, 26], [1, 2, 3, 4, 5, 6, 7, 8, 10, 9, 11, 12, 13, 14, 15, 16, 17, 18, 1, 21, 20, 23, 22, 25, 24, 2, 3, 4, 31, 32, 29, 30, 35, 36, 33, 34, 9, 10, 20, 21]]; chartbl_480_1192.SizesCentralizers:= [480, 480, 160, 160, 96, 96, 32, 32, 120, 120, 96, 96, 96, 96, 32, 32, 32, 32, 120, 120, 120, 24, 24, 24, 24, 120, 40, 40, 24, 24, 24, 24, 24, 24, 24, 24, 30, 30, 30, 30]; chartbl_480_1192.ClassNames:= ["1A", "2A", "2B", "2C", "2D", "2E", "2F", "2G", "3A1", "3A-1", "4A1", "4A-1", "4B1", "4B-1", "4C1", "4C-1", "4D1", "4D-1", "5A", "6A1", "6A-1", "6B1", "6B-1", "6C1", "6C-1", "10A", "10B", "10C", "12A1", "12A-1", "12A5", "12A-5", "12B1", "12B-1", "12B5", "12B-5", "15A1", "15A-1", "30A1", "30A-1"]; chartbl_480_1192.OrderClassRepresentatives:= [1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 5, 6, 6, 6, 6, 6, 6, 10, 10, 10, 12, 12, 12, 12, 12, 12, 12, 12, 15, 15, 30, 30]; chartbl_480_1192.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, 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), 1, 1, 1, 1, 1, 1, 1, 1, 1, E(3), E(3)^-1, E(3)^-1, E(3), E(3), E(3)^-1, 1, 1, 1, E(3)^-1, E(3)^-1, E(3)^-1, E(3), E(3)^-1, E(3), E(3), E(3), E(3), E(3)^-1, E(3)^-1, E(3)], [1, 1, 1, 1, 1, 1, 1, 1, E(3), E(3)^-1, 1, 1, 1, 1, 1, 1, 1, 1, 1, E(3)^-1, E(3), E(3), E(3)^-1, E(3)^-1, E(3), 1, 1, 1, E(3), E(3), E(3), E(3)^-1, E(3), E(3)^-1, E(3)^-1, E(3)^-1, E(3)^-1, E(3), E(3), E(3)^-1], [1, -1, 1, -1, -1, 1, -1, 1, 1, 1, -1*E(4), E(4), E(4), -1*E(4), -1*E(4), E(4), -1*E(4), E(4), 1, -1, -1, -1, 1, -1, 1, -1, 1, -1, E(4), -1*E(4), -1*E(4), -1*E(4), E(4), E(4), E(4), -1*E(4), 1, 1, -1, -1], [1, -1, 1, -1, -1, 1, -1, 1, 1, 1, E(4), -1*E(4), -1*E(4), E(4), E(4), -1*E(4), E(4), -1*E(4), 1, -1, -1, -1, 1, -1, 1, -1, 1, -1, -1*E(4), E(4), E(4), E(4), -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*E(4), E(4), -1*E(4), E(4), E(4), E(4), -1*E(4), -1*E(4), 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, E(4), -1*E(4), E(4), E(4), -1*E(4), E(4), -1*E(4), -1*E(4), 1, 1, 1, 1], [1, 1, 1, 1, -1, -1, -1, -1, 1, 1, E(4), -1*E(4), E(4), -1*E(4), -1*E(4), -1*E(4), E(4), E(4), 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, -1*E(4), E(4), -1*E(4), -1*E(4), E(4), -1*E(4), E(4), E(4), 1, 1, 1, 1], [1, -1, 1, -1, 1, -1, 1, -1, E(3)^-1, E(3), -1, -1, 1, 1, 1, -1, -1, 1, 1, -1*E(3), -1*E(3)^-1, E(3)^-1, -1*E(3), E(3), -1*E(3)^-1, -1, 1, -1, -1*E(3)^-1, -1*E(3)^-1, E(3)^-1, E(3), E(3)^-1, -1*E(3), E(3), -1*E(3), E(3), E(3)^-1, -1*E(3)^-1, -1*E(3)], [1, -1, 1, -1, 1, -1, 1, -1, E(3), E(3)^-1, -1, -1, 1, 1, 1, -1, -1, 1, 1, -1*E(3)^-1, -1*E(3), E(3), -1*E(3)^-1, E(3)^-1, -1*E(3), -1, 1, -1, -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, E(3), -1*E(3), -1*E(3)^-1], [1, -1, 1, -1, 1, -1, 1, -1, E(3)^-1, E(3), 1, 1, -1, -1, -1, 1, 1, -1, 1, -1*E(3), -1*E(3)^-1, E(3)^-1, -1*E(3), E(3), -1*E(3)^-1, -1, 1, -1, E(3)^-1, E(3)^-1, -1*E(3)^-1, -1*E(3), -1*E(3)^-1, E(3), -1*E(3), E(3), E(3), E(3)^-1, -1*E(3)^-1, -1*E(3)], [1, -1, 1, -1, 1, -1, 1, -1, E(3), E(3)^-1, 1, 1, -1, -1, -1, 1, 1, -1, 1, -1*E(3)^-1, -1*E(3), E(3), -1*E(3)^-1, E(3)^-1, -1*E(3), -1, 1, -1, E(3), E(3), -1*E(3), -1*E(3)^-1, -1*E(3), E(3)^-1, -1*E(3)^-1, E(3)^-1, E(3)^-1, E(3), -1*E(3), -1*E(3)^-1], [1, 1, 1, 1, 1, 1, 1, 1, E(3)^-1, E(3), -1, -1, -1, -1, -1, -1, -1, -1, 1, E(3), E(3)^-1, E(3)^-1, E(3), E(3), E(3)^-1, 1, 1, 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), E(3), E(3)^-1, E(3)^-1, E(3)], [1, 1, 1, 1, 1, 1, 1, 1, E(3), E(3)^-1, -1, -1, -1, -1, -1, -1, -1, -1, 1, E(3)^-1, E(3), E(3), E(3)^-1, E(3)^-1, E(3), 1, 1, 1, -1*E(3), -1*E(3), -1*E(3), -1*E(3)^-1, -1*E(3), -1*E(3)^-1, -1*E(3)^-1, -1*E(3)^-1, E(3)^-1, E(3), E(3), E(3)^-1], [1, -1, 1, -1, -1, 1, -1, 1, -1*E(12)^2, E(12)^4, -1*E(12)^3, E(12)^3, E(12)^3, -1*E(12)^3, -1*E(12)^3, E(12)^3, -1*E(12)^3, E(12)^3, 1, -1*E(12)^4, E(12)^2, E(12)^2, E(12)^4, -1*E(12)^4, -1*E(12)^2, -1, 1, -1, -1*E(12)^5, E(12)^5, E(12)^5, E(12), -1*E(12)^5, -1*E(12), -1*E(12), E(12), E(12)^4, -1*E(12)^2, E(12)^2, -1*E(12)^4], [1, -1, 1, -1, -1, 1, -1, 1, E(12)^4, -1*E(12)^2, E(12)^3, -1*E(12)^3, -1*E(12)^3, E(12)^3, E(12)^3, -1*E(12)^3, E(12)^3, -1*E(12)^3, 1, E(12)^2, -1*E(12)^4, -1*E(12)^4, -1*E(12)^2, E(12)^2, E(12)^4, -1, 1, -1, E(12), -1*E(12), -1*E(12), -1*E(12)^5, E(12), E(12)^5, E(12)^5, -1*E(12)^5, -1*E(12)^2, E(12)^4, -1*E(12)^4, E(12)^2], [1, -1, 1, -1, -1, 1, -1, 1, -1*E(12)^2, E(12)^4, E(12)^3, -1*E(12)^3, -1*E(12)^3, E(12)^3, E(12)^3, -1*E(12)^3, E(12)^3, -1*E(12)^3, 1, -1*E(12)^4, E(12)^2, E(12)^2, E(12)^4, -1*E(12)^4, -1*E(12)^2, -1, 1, -1, E(12)^5, -1*E(12)^5, -1*E(12)^5, -1*E(12), E(12)^5, E(12), E(12), -1*E(12), E(12)^4, -1*E(12)^2, E(12)^2, -1*E(12)^4], [1, -1, 1, -1, -1, 1, -1, 1, E(12)^4, -1*E(12)^2, -1*E(12)^3, E(12)^3, E(12)^3, -1*E(12)^3, -1*E(12)^3, E(12)^3, -1*E(12)^3, E(12)^3, 1, E(12)^2, -1*E(12)^4, -1*E(12)^4, -1*E(12)^2, E(12)^2, E(12)^4, -1, 1, -1, -1*E(12), E(12), E(12), E(12)^5, -1*E(12), -1*E(12)^5, -1*E(12)^5, E(12)^5, -1*E(12)^2, E(12)^4, -1*E(12)^4, E(12)^2], [1, 1, 1, 1, -1, -1, -1, -1, -1*E(12)^2, E(12)^4, -1*E(12)^3, E(12)^3, -1*E(12)^3, E(12)^3, E(12)^3, E(12)^3, -1*E(12)^3, -1*E(12)^3, 1, E(12)^4, -1*E(12)^2, E(12)^2, -1*E(12)^4, -1*E(12)^4, E(12)^2, 1, 1, 1, -1*E(12)^5, E(12)^5, -1*E(12)^5, -1*E(12), E(12)^5, -1*E(12), E(12), E(12), E(12)^4, -1*E(12)^2, -1*E(12)^2, E(12)^4], [1, 1, 1, 1, -1, -1, -1, -1, E(12)^4, -1*E(12)^2, E(12)^3, -1*E(12)^3, E(12)^3, -1*E(12)^3, -1*E(12)^3, -1*E(12)^3, E(12)^3, E(12)^3, 1, -1*E(12)^2, E(12)^4, -1*E(12)^4, E(12)^2, E(12)^2, -1*E(12)^4, 1, 1, 1, E(12), -1*E(12), E(12), E(12)^5, -1*E(12), E(12)^5, -1*E(12)^5, -1*E(12)^5, -1*E(12)^2, E(12)^4, E(12)^4, -1*E(12)^2], [1, 1, 1, 1, -1, -1, -1, -1, -1*E(12)^2, E(12)^4, E(12)^3, -1*E(12)^3, E(12)^3, -1*E(12)^3, -1*E(12)^3, -1*E(12)^3, E(12)^3, E(12)^3, 1, E(12)^4, -1*E(12)^2, E(12)^2, -1*E(12)^4, -1*E(12)^4, E(12)^2, 1, 1, 1, E(12)^5, -1*E(12)^5, E(12)^5, E(12), -1*E(12)^5, E(12), -1*E(12), -1*E(12), E(12)^4, -1*E(12)^2, -1*E(12)^2, E(12)^4], [1, 1, 1, 1, -1, -1, -1, -1, E(12)^4, -1*E(12)^2, -1*E(12)^3, E(12)^3, -1*E(12)^3, E(12)^3, E(12)^3, E(12)^3, -1*E(12)^3, -1*E(12)^3, 1, -1*E(12)^2, E(12)^4, -1*E(12)^4, E(12)^2, E(12)^2, -1*E(12)^4, 1, 1, 1, -1*E(12), E(12), -1*E(12), -1*E(12)^5, E(12), -1*E(12)^5, E(12)^5, E(12)^5, -1*E(12)^2, E(12)^4, E(12)^4, -1*E(12)^2], [3, 3, -1, -1, 3, 3, -1, -1, 0, 0, 3, 3, 3, 3, -1, -1, -1, -1, 3, 0, 0, 0, 0, 0, 0, 3, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, -3, -1, 1, 3, -3, -1, 1, 0, 0, -3, -3, 3, 3, -1, 1, 1, -1, 3, 0, 0, 0, 0, 0, 0, -3, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, -3, -1, 1, 3, -3, -1, 1, 0, 0, 3, 3, -3, -3, 1, -1, -1, 1, 3, 0, 0, 0, 0, 0, 0, -3, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, 3, -1, -1, 3, 3, -1, -1, 0, 0, -3, -3, -3, -3, 1, 1, 1, 1, 3, 0, 0, 0, 0, 0, 0, 3, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, -3, -1, 1, -3, 3, 1, -1, 0, 0, -3*E(4), 3*E(4), 3*E(4), -3*E(4), E(4), -1*E(4), E(4), -1*E(4), 3, 0, 0, 0, 0, 0, 0, -3, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, -3, -1, 1, -3, 3, 1, -1, 0, 0, 3*E(4), -3*E(4), -3*E(4), 3*E(4), -1*E(4), E(4), -1*E(4), E(4), 3, 0, 0, 0, 0, 0, 0, -3, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, 3, -1, -1, -3, -3, 1, 1, 0, 0, -3*E(4), 3*E(4), -3*E(4), 3*E(4), -1*E(4), -1*E(4), E(4), E(4), 3, 0, 0, 0, 0, 0, 0, 3, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, 3, -1, -1, -3, -3, 1, 1, 0, 0, 3*E(4), -3*E(4), 3*E(4), -3*E(4), E(4), E(4), -1*E(4), -1*E(4), 3, 0, 0, 0, 0, 0, 0, 3, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, 4, 4, 4, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, -1, 4, 4, 0, 0, 0, 0, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1], [4, -4, 4, -4, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, -1, -4, -4, 0, 0, 0, 0, 1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 1, 1], [4, 4, 4, 4, 0, 0, 0, 0, 4*E(3)^-1, 4*E(3), 0, 0, 0, 0, 0, 0, 0, 0, -1, 4*E(3), 4*E(3)^-1, 0, 0, 0, 0, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1*E(3), -1*E(3)^-1, -1*E(3)^-1, -1*E(3)], [4, 4, 4, 4, 0, 0, 0, 0, 4*E(3), 4*E(3)^-1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 4*E(3)^-1, 4*E(3), 0, 0, 0, 0, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1*E(3)^-1, -1*E(3), -1*E(3), -1*E(3)^-1], [4, -4, 4, -4, 0, 0, 0, 0, 4*E(3)^-1, 4*E(3), 0, 0, 0, 0, 0, 0, 0, 0, -1, -4*E(3), -4*E(3)^-1, 0, 0, 0, 0, 1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1*E(3), -1*E(3)^-1, E(3)^-1, E(3)], [4, -4, 4, -4, 0, 0, 0, 0, 4*E(3), 4*E(3)^-1, 0, 0, 0, 0, 0, 0, 0, 0, -1, -4*E(3)^-1, -4*E(3), 0, 0, 0, 0, 1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1*E(3)^-1, -1*E(3), E(3), E(3)^-1], [12, 12, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, -3, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [12, -12, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 3, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]; ConvertToLibraryCharacterTableNC(chartbl_480_1192);