# Group 1440.5848 downloaded from the LMFDB on 29 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 GPerm := Group( (1,3)(2,4)(7,9,8), (1,4,5,3,2)(6,9,8,7) ); # Booleans booleans_1440_5848 := rec( Agroup := false, Zgroup := false, abelian := false, almost_simple := false, cyclic := false, metabelian := false, metacyclic := false, monomial := false, nilpotent := false, perfect := false, quasisimple := false, rational := false, solvable := false, supersolvable := false); # Character Table chartbl_1440_5848:=rec(); chartbl_1440_5848.IsFinite:= true; chartbl_1440_5848.UnderlyingCharacteristic:= 0; chartbl_1440_5848.UnderlyingGroup:= GPerm; chartbl_1440_5848.Size:= 1440; chartbl_1440_5848.InfoText:= "Character table for group 1440.5848 downloaded from the LMFDB."; chartbl_1440_5848.Identifier:= " S4*A5 "; chartbl_1440_5848.NrConjugacyClasses:= 25; chartbl_1440_5848.ConjugacyClasses:= [(), (6,9)(7,8), (6,8), (1,2)(3,4), (1,3)(4,5)(6,7)(8,9), (2,5)(3,4)(6,7), (6,9,8), (2,5,3), (1,5,3)(6,9,7), (6,7,9,8), (1,5)(3,4)(6,7,9,8), (1,2,3,5,4), (1,3,4,2,5), (2,3,5)(6,9)(7,8), (1,2,3)(6,8), (1,2)(3,4)(6,9,8), (1,2,4,3,5)(6,8)(7,9), (1,3,2,5,4)(6,8)(7,9), (1,5,4,3,2)(8,9), (1,3,5,2,4)(8,9), (2,5,3)(6,8,9,7), (1,3,4,2,5)(6,8,9), (1,4,5,3,2)(6,9,8), (1,3,2,5,4)(6,9,8,7), (1,5,3,4,2)(6,7,8,9)]; chartbl_1440_5848.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]; chartbl_1440_5848.ComputedPowerMaps:= [ , [1, 1, 1, 1, 1, 1, 7, 8, 9, 2, 2, 13, 12, 8, 8, 7, 13, 12, 12, 13, 14, 23, 22, 17, 18], [1, 2, 3, 4, 5, 6, 1, 1, 1, 10, 11, 13, 12, 2, 3, 4, 18, 17, 20, 19, 10, 12, 13, 25, 24], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 1, 1, 14, 15, 16, 2, 2, 3, 3, 21, 7, 7, 10, 10]]; chartbl_1440_5848.SizesCentralizers:= [1440, 480, 240, 96, 32, 16, 180, 72, 9, 240, 16, 120, 120, 24, 12, 12, 40, 40, 20, 20, 12, 15, 15, 20, 20]; chartbl_1440_5848.ClassNames:= ["1A", "2A", "2B", "2C", "2D", "2E", "3A", "3B", "3C", "4A", "4B", "5A1", "5A2", "6A", "6B", "6C", "10A1", "10A3", "10B1", "10B3", "12A", "15A1", "15A2", "20A1", "20A3"]; chartbl_1440_5848.OrderClassRepresentatives:= [1, 2, 2, 2, 2, 2, 3, 3, 3, 4, 4, 5, 5, 6, 6, 6, 10, 10, 10, 10, 12, 15, 15, 20, 20]; chartbl_1440_5848.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], [2, 2, 0, 2, 2, 0, -1, 2, -1, 0, 0, 2, 2, 2, 0, -1, 2, 2, 0, 0, 0, -1, -1, 0, 0], [3, -1, 1, 3, -1, 1, 0, 3, 0, -1, -1, 3, 3, -1, 1, 0, -1, -1, 1, 1, -1, 0, 0, -1, -1], [3, -1, -1, 3, -1, -1, 0, 3, 0, 1, 1, 3, 3, -1, -1, 0, -1, -1, -1, -1, 1, 0, 0, 1, 1], [3, 3, 3, -1, -1, -1, 3, 0, 0, 3, -1, -1*E(5)-E(5)^-1, -1*E(5)^2-E(5)^-2, 0, 0, -1, -1*E(5)-E(5)^-1, -1*E(5)^2-E(5)^-2, -1*E(5)^2-E(5)^-2, -1*E(5)-E(5)^-1, 0, -1*E(5)^2-E(5)^-2, -1*E(5)-E(5)^-1, -1*E(5)^2-E(5)^-2, -1*E(5)-E(5)^-1], [3, 3, 3, -1, -1, -1, 3, 0, 0, 3, -1, -1*E(5)^2-E(5)^-2, -1*E(5)-E(5)^-1, 0, 0, -1, -1*E(5)^2-E(5)^-2, -1*E(5)-E(5)^-1, -1*E(5)-E(5)^-1, -1*E(5)^2-E(5)^-2, 0, -1*E(5)-E(5)^-1, -1*E(5)^2-E(5)^-2, -1*E(5)-E(5)^-1, -1*E(5)^2-E(5)^-2], [3, 3, -3, -1, -1, 1, 3, 0, 0, -3, 1, -1*E(5)-E(5)^-1, -1*E(5)^2-E(5)^-2, 0, 0, -1, -1*E(5)-E(5)^-1, -1*E(5)^2-E(5)^-2, E(5)^2+E(5)^-2, E(5)+E(5)^-1, 0, -1*E(5)^2-E(5)^-2, -1*E(5)-E(5)^-1, E(5)^2+E(5)^-2, E(5)+E(5)^-1], [3, 3, -3, -1, -1, 1, 3, 0, 0, -3, 1, -1*E(5)^2-E(5)^-2, -1*E(5)-E(5)^-1, 0, 0, -1, -1*E(5)^2-E(5)^-2, -1*E(5)-E(5)^-1, E(5)+E(5)^-1, E(5)^2+E(5)^-2, 0, -1*E(5)-E(5)^-1, -1*E(5)^2-E(5)^-2, E(5)+E(5)^-1, E(5)^2+E(5)^-2], [4, 4, 4, 0, 0, 0, 4, 1, 1, 4, 0, -1, -1, 1, 1, 0, -1, -1, -1, -1, 1, -1, -1, -1, -1], [4, 4, -4, 0, 0, 0, 4, 1, 1, -4, 0, -1, -1, 1, -1, 0, -1, -1, 1, 1, -1, -1, -1, 1, 1], [5, 5, 5, 1, 1, 1, 5, -1, -1, 5, 1, 0, 0, -1, -1, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0], [5, 5, -5, 1, 1, -1, 5, -1, -1, -5, -1, 0, 0, -1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0], [6, 6, 0, -2, -2, 0, -3, 0, 0, 0, 0, -2*E(5)-2*E(5)^-1, -2*E(5)^2-2*E(5)^-2, 0, 0, 1, -2*E(5)-2*E(5)^-1, -2*E(5)^2-2*E(5)^-2, 0, 0, 0, E(5)^2+E(5)^-2, E(5)+E(5)^-1, 0, 0], [6, 6, 0, -2, -2, 0, -3, 0, 0, 0, 0, -2*E(5)^2-2*E(5)^-2, -2*E(5)-2*E(5)^-1, 0, 0, 1, -2*E(5)^2-2*E(5)^-2, -2*E(5)-2*E(5)^-1, 0, 0, 0, E(5)+E(5)^-1, E(5)^2+E(5)^-2, 0, 0], [8, 8, 0, 0, 0, 0, -4, 2, -1, 0, 0, -2, -2, 2, 0, 0, -2, -2, 0, 0, 0, 1, 1, 0, 0], [9, -3, -3, -3, 1, 1, 0, 0, 0, 3, -1, -3*E(5)-3*E(5)^-1, -3*E(5)^2-3*E(5)^-2, 0, 0, 0, E(5)+E(5)^-1, E(5)^2+E(5)^-2, E(5)^2+E(5)^-2, E(5)+E(5)^-1, 0, 0, 0, -1*E(5)^2-E(5)^-2, -1*E(5)-E(5)^-1], [9, -3, -3, -3, 1, 1, 0, 0, 0, 3, -1, -3*E(5)^2-3*E(5)^-2, -3*E(5)-3*E(5)^-1, 0, 0, 0, E(5)^2+E(5)^-2, E(5)+E(5)^-1, E(5)+E(5)^-1, E(5)^2+E(5)^-2, 0, 0, 0, -1*E(5)-E(5)^-1, -1*E(5)^2-E(5)^-2], [9, -3, 3, -3, 1, -1, 0, 0, 0, -3, 1, -3*E(5)-3*E(5)^-1, -3*E(5)^2-3*E(5)^-2, 0, 0, 0, E(5)+E(5)^-1, E(5)^2+E(5)^-2, -1*E(5)^2-E(5)^-2, -1*E(5)-E(5)^-1, 0, 0, 0, E(5)^2+E(5)^-2, E(5)+E(5)^-1], [9, -3, 3, -3, 1, -1, 0, 0, 0, -3, 1, -3*E(5)^2-3*E(5)^-2, -3*E(5)-3*E(5)^-1, 0, 0, 0, E(5)^2+E(5)^-2, E(5)+E(5)^-1, -1*E(5)-E(5)^-1, -1*E(5)^2-E(5)^-2, 0, 0, 0, E(5)+E(5)^-1, E(5)^2+E(5)^-2], [10, 10, 0, 2, 2, 0, -5, -2, 1, 0, 0, 0, 0, -2, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [12, -4, 4, 0, 0, 0, 0, 3, 0, -4, 0, -3, -3, -1, 1, 0, 1, 1, -1, -1, -1, 0, 0, 1, 1], [12, -4, -4, 0, 0, 0, 0, 3, 0, 4, 0, -3, -3, -1, -1, 0, 1, 1, 1, 1, 1, 0, 0, -1, -1], [15, -5, 5, 3, -1, 1, 0, -3, 0, -5, -1, 0, 0, 1, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [15, -5, -5, 3, -1, -1, 0, -3, 0, 5, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0]]; ConvertToLibraryCharacterTableNC(chartbl_1440_5848);