# Group 88.7 downloaded from the LMFDB on 27 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(371267080009,88); a := GPC.1; b := GPC.2; c := GPC.3; GPerm := Group( (2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15), (13,15), (12,14)(13,15), (1,2,4,6,8,10,11,9,7,5,3) ); GLFp := Group([[[ 0*Z(23), Z(23)^0 ], [ Z(23)^0, 0*Z(23) ]], [[ Z(23), 0*Z(23) ], [ 0*Z(23), Z(23)^21 ]], [[ Z(23)^0, 0*Z(23) ], [ 0*Z(23), Z(23)^11 ]]]); # Booleans booleans_88_7 := rec( Agroup := false, 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 := true); # Character Table chartbl_88_7:=rec(); chartbl_88_7.IsFinite:= true; chartbl_88_7.UnderlyingCharacteristic:= 0; chartbl_88_7.UnderlyingGroup:= GLFp; chartbl_88_7.Size:= 88; chartbl_88_7.InfoText:= "Character table for group 88.7 downloaded from the LMFDB."; chartbl_88_7.Identifier:= " C11:D4 "; chartbl_88_7.NrConjugacyClasses:= 25; chartbl_88_7.ConjugacyClasses:= [[1, 0, 0, 1], [22, 0, 0, 22], [1, 0, 0, 22], [0, 22, 22, 0], [0, 5, 9, 0], [2, 0, 0, 12], [4, 0, 0, 6], [8, 0, 0, 3], [16, 0, 0, 13], [9, 0, 0, 18], [5, 0, 0, 14], [7, 0, 0, 10], [15, 0, 0, 20], [17, 0, 0, 19], [11, 0, 0, 21], [2, 0, 0, 11], [12, 0, 0, 21], [8, 0, 0, 20], [3, 0, 0, 15], [5, 0, 0, 9], [14, 0, 0, 18], [7, 0, 0, 13], [10, 0, 0, 16], [6, 0, 0, 19], [4, 0, 0, 17]]; chartbl_88_7.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_88_7.ComputedPowerMaps:= [ , [1, 1, 1, 1, 2, 7, 9, 10, 8, 6, 6, 8, 10, 9, 7, 7, 7, 10, 10, 6, 6, 8, 8, 9, 9], [1, 2, 3, 4, 5, 10, 6, 9, 7, 8, 13, 14, 12, 15, 11, 20, 21, 23, 22, 18, 19, 25, 24, 16, 17]]; chartbl_88_7.SizesCentralizers:= [88, 88, 44, 4, 4, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44]; chartbl_88_7.ClassNames:= ["1A", "2A", "2B", "2C", "4A", "11A1", "11A2", "11A3", "11A4", "11A5", "22A1", "22A3", "22A5", "22A7", "22A9", "22B1", "22B-1", "22B3", "22B-3", "22B5", "22B-5", "22B7", "22B-7", "22B9", "22B-9"]; chartbl_88_7.OrderClassRepresentatives:= [1, 2, 2, 2, 4, 11, 11, 11, 11, 11, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22]; chartbl_88_7.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], [2, -2, 0, 0, 0, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, 0, 0, E(11)^5+E(11)^-5, E(11)^2+E(11)^-2, E(11)^4+E(11)^-4, E(11)^3+E(11)^-3, E(11)+E(11)^-1, E(11)^2+E(11)^-2, E(11)^4+E(11)^-4, E(11)+E(11)^-1, E(11)^5+E(11)^-5, E(11)^3+E(11)^-3, E(11)^5+E(11)^-5, E(11)^4+E(11)^-4, E(11)^4+E(11)^-4, E(11)^3+E(11)^-3, E(11)^3+E(11)^-3, E(11)^2+E(11)^-2, E(11)^2+E(11)^-2, E(11)+E(11)^-1, E(11)+E(11)^-1, E(11)^5+E(11)^-5], [2, 2, 2, 0, 0, E(11)^4+E(11)^-4, E(11)^5+E(11)^-5, E(11)+E(11)^-1, E(11)^2+E(11)^-2, E(11)^3+E(11)^-3, E(11)^5+E(11)^-5, E(11)+E(11)^-1, E(11)^3+E(11)^-3, E(11)^4+E(11)^-4, E(11)^2+E(11)^-2, E(11)^4+E(11)^-4, E(11)+E(11)^-1, E(11)+E(11)^-1, E(11)^2+E(11)^-2, E(11)^2+E(11)^-2, E(11)^5+E(11)^-5, E(11)^5+E(11)^-5, E(11)^3+E(11)^-3, E(11)^3+E(11)^-3, E(11)^4+E(11)^-4], [2, 2, 2, 0, 0, E(11)^3+E(11)^-3, E(11)+E(11)^-1, E(11)^2+E(11)^-2, E(11)^4+E(11)^-4, E(11)^5+E(11)^-5, E(11)+E(11)^-1, E(11)^2+E(11)^-2, E(11)^5+E(11)^-5, E(11)^3+E(11)^-3, E(11)^4+E(11)^-4, E(11)^3+E(11)^-3, E(11)^2+E(11)^-2, E(11)^2+E(11)^-2, E(11)^4+E(11)^-4, E(11)^4+E(11)^-4, E(11)+E(11)^-1, E(11)+E(11)^-1, E(11)^5+E(11)^-5, E(11)^5+E(11)^-5, E(11)^3+E(11)^-3], [2, 2, 2, 0, 0, E(11)^2+E(11)^-2, E(11)^3+E(11)^-3, E(11)^5+E(11)^-5, E(11)+E(11)^-1, E(11)^4+E(11)^-4, E(11)^3+E(11)^-3, E(11)^5+E(11)^-5, E(11)^4+E(11)^-4, E(11)^2+E(11)^-2, E(11)+E(11)^-1, E(11)^2+E(11)^-2, E(11)^5+E(11)^-5, E(11)^5+E(11)^-5, E(11)+E(11)^-1, E(11)+E(11)^-1, E(11)^3+E(11)^-3, E(11)^3+E(11)^-3, E(11)^4+E(11)^-4, E(11)^4+E(11)^-4, E(11)^2+E(11)^-2], [2, 2, 2, 0, 0, E(11)+E(11)^-1, E(11)^4+E(11)^-4, E(11)^3+E(11)^-3, E(11)^5+E(11)^-5, E(11)^2+E(11)^-2, E(11)^4+E(11)^-4, E(11)^3+E(11)^-3, E(11)^2+E(11)^-2, E(11)+E(11)^-1, E(11)^5+E(11)^-5, E(11)+E(11)^-1, E(11)^3+E(11)^-3, E(11)^3+E(11)^-3, E(11)^5+E(11)^-5, E(11)^5+E(11)^-5, E(11)^4+E(11)^-4, E(11)^4+E(11)^-4, E(11)^2+E(11)^-2, E(11)^2+E(11)^-2, E(11)+E(11)^-1], [2, 2, -2, 0, 0, E(11)^5+E(11)^-5, E(11)^2+E(11)^-2, E(11)^4+E(11)^-4, E(11)^3+E(11)^-3, E(11)+E(11)^-1, E(11)^2+E(11)^-2, E(11)^4+E(11)^-4, E(11)+E(11)^-1, E(11)^5+E(11)^-5, E(11)^3+E(11)^-3, -1*E(11)^5-E(11)^-5, -1*E(11)^4-E(11)^-4, -1*E(11)^4-E(11)^-4, -1*E(11)^3-E(11)^-3, -1*E(11)^3-E(11)^-3, -1*E(11)^2-E(11)^-2, -1*E(11)^2-E(11)^-2, -1*E(11)-E(11)^-1, -1*E(11)-E(11)^-1, -1*E(11)^5-E(11)^-5], [2, 2, -2, 0, 0, E(11)^4+E(11)^-4, E(11)^5+E(11)^-5, E(11)+E(11)^-1, E(11)^2+E(11)^-2, E(11)^3+E(11)^-3, E(11)^5+E(11)^-5, E(11)+E(11)^-1, E(11)^3+E(11)^-3, E(11)^4+E(11)^-4, E(11)^2+E(11)^-2, -1*E(11)^4-E(11)^-4, -1*E(11)-E(11)^-1, -1*E(11)-E(11)^-1, -1*E(11)^2-E(11)^-2, -1*E(11)^2-E(11)^-2, -1*E(11)^5-E(11)^-5, -1*E(11)^5-E(11)^-5, -1*E(11)^3-E(11)^-3, -1*E(11)^3-E(11)^-3, -1*E(11)^4-E(11)^-4], [2, 2, -2, 0, 0, E(11)^3+E(11)^-3, E(11)+E(11)^-1, E(11)^2+E(11)^-2, E(11)^4+E(11)^-4, E(11)^5+E(11)^-5, E(11)+E(11)^-1, E(11)^2+E(11)^-2, E(11)^5+E(11)^-5, E(11)^3+E(11)^-3, E(11)^4+E(11)^-4, -1*E(11)^3-E(11)^-3, -1*E(11)^2-E(11)^-2, -1*E(11)^2-E(11)^-2, -1*E(11)^4-E(11)^-4, -1*E(11)^4-E(11)^-4, -1*E(11)-E(11)^-1, -1*E(11)-E(11)^-1, -1*E(11)^5-E(11)^-5, -1*E(11)^5-E(11)^-5, -1*E(11)^3-E(11)^-3], [2, 2, -2, 0, 0, E(11)^2+E(11)^-2, E(11)^3+E(11)^-3, E(11)^5+E(11)^-5, E(11)+E(11)^-1, E(11)^4+E(11)^-4, E(11)^3+E(11)^-3, E(11)^5+E(11)^-5, E(11)^4+E(11)^-4, E(11)^2+E(11)^-2, E(11)+E(11)^-1, -1*E(11)^2-E(11)^-2, -1*E(11)^5-E(11)^-5, -1*E(11)^5-E(11)^-5, -1*E(11)-E(11)^-1, -1*E(11)-E(11)^-1, -1*E(11)^3-E(11)^-3, -1*E(11)^3-E(11)^-3, -1*E(11)^4-E(11)^-4, -1*E(11)^4-E(11)^-4, -1*E(11)^2-E(11)^-2], [2, 2, -2, 0, 0, E(11)+E(11)^-1, E(11)^4+E(11)^-4, E(11)^3+E(11)^-3, E(11)^5+E(11)^-5, E(11)^2+E(11)^-2, E(11)^4+E(11)^-4, E(11)^3+E(11)^-3, E(11)^2+E(11)^-2, E(11)+E(11)^-1, E(11)^5+E(11)^-5, -1*E(11)-E(11)^-1, -1*E(11)^3-E(11)^-3, -1*E(11)^3-E(11)^-3, -1*E(11)^5-E(11)^-5, -1*E(11)^5-E(11)^-5, -1*E(11)^4-E(11)^-4, -1*E(11)^4-E(11)^-4, -1*E(11)^2-E(11)^-2, -1*E(11)^2-E(11)^-2, -1*E(11)-E(11)^-1], [2, -2, 0, 0, 0, E(11)^5+E(11)^-5, E(11)^2+E(11)^-2, E(11)^4+E(11)^-4, E(11)^3+E(11)^-3, E(11)+E(11)^-1, -1*E(11)^2-E(11)^-2, -1*E(11)^4-E(11)^-4, -1*E(11)-E(11)^-1, -1*E(11)^5-E(11)^-5, -1*E(11)^3-E(11)^-3, -1*E(11)^5+E(11)^-5, E(11)^4-E(11)^-4, -1*E(11)^4+E(11)^-4, E(11)^3-E(11)^-3, -1*E(11)^3+E(11)^-3, E(11)^2-E(11)^-2, -1*E(11)^2+E(11)^-2, E(11)-E(11)^-1, -1*E(11)+E(11)^-1, E(11)^5-E(11)^-5], [2, -2, 0, 0, 0, E(11)^5+E(11)^-5, E(11)^2+E(11)^-2, E(11)^4+E(11)^-4, E(11)^3+E(11)^-3, E(11)+E(11)^-1, -1*E(11)^2-E(11)^-2, -1*E(11)^4-E(11)^-4, -1*E(11)-E(11)^-1, -1*E(11)^5-E(11)^-5, -1*E(11)^3-E(11)^-3, E(11)^5-E(11)^-5, -1*E(11)^4+E(11)^-4, E(11)^4-E(11)^-4, -1*E(11)^3+E(11)^-3, E(11)^3-E(11)^-3, -1*E(11)^2+E(11)^-2, E(11)^2-E(11)^-2, -1*E(11)+E(11)^-1, E(11)-E(11)^-1, -1*E(11)^5+E(11)^-5], [2, -2, 0, 0, 0, E(11)^4+E(11)^-4, E(11)^5+E(11)^-5, E(11)+E(11)^-1, E(11)^2+E(11)^-2, E(11)^3+E(11)^-3, -1*E(11)^5-E(11)^-5, -1*E(11)-E(11)^-1, -1*E(11)^3-E(11)^-3, -1*E(11)^4-E(11)^-4, -1*E(11)^2-E(11)^-2, -1*E(11)^4+E(11)^-4, E(11)-E(11)^-1, -1*E(11)+E(11)^-1, -1*E(11)^2+E(11)^-2, E(11)^2-E(11)^-2, -1*E(11)^5+E(11)^-5, E(11)^5-E(11)^-5, E(11)^3-E(11)^-3, -1*E(11)^3+E(11)^-3, E(11)^4-E(11)^-4], [2, -2, 0, 0, 0, E(11)^4+E(11)^-4, E(11)^5+E(11)^-5, E(11)+E(11)^-1, E(11)^2+E(11)^-2, E(11)^3+E(11)^-3, -1*E(11)^5-E(11)^-5, -1*E(11)-E(11)^-1, -1*E(11)^3-E(11)^-3, -1*E(11)^4-E(11)^-4, -1*E(11)^2-E(11)^-2, E(11)^4-E(11)^-4, -1*E(11)+E(11)^-1, E(11)-E(11)^-1, E(11)^2-E(11)^-2, -1*E(11)^2+E(11)^-2, E(11)^5-E(11)^-5, -1*E(11)^5+E(11)^-5, -1*E(11)^3+E(11)^-3, E(11)^3-E(11)^-3, -1*E(11)^4+E(11)^-4], [2, -2, 0, 0, 0, E(11)^3+E(11)^-3, E(11)+E(11)^-1, E(11)^2+E(11)^-2, E(11)^4+E(11)^-4, E(11)^5+E(11)^-5, -1*E(11)-E(11)^-1, -1*E(11)^2-E(11)^-2, -1*E(11)^5-E(11)^-5, -1*E(11)^3-E(11)^-3, -1*E(11)^4-E(11)^-4, -1*E(11)^3+E(11)^-3, -1*E(11)^2+E(11)^-2, E(11)^2-E(11)^-2, E(11)^4-E(11)^-4, -1*E(11)^4+E(11)^-4, -1*E(11)+E(11)^-1, E(11)-E(11)^-1, E(11)^5-E(11)^-5, -1*E(11)^5+E(11)^-5, E(11)^3-E(11)^-3], [2, -2, 0, 0, 0, E(11)^3+E(11)^-3, E(11)+E(11)^-1, E(11)^2+E(11)^-2, E(11)^4+E(11)^-4, E(11)^5+E(11)^-5, -1*E(11)-E(11)^-1, -1*E(11)^2-E(11)^-2, -1*E(11)^5-E(11)^-5, -1*E(11)^3-E(11)^-3, -1*E(11)^4-E(11)^-4, E(11)^3-E(11)^-3, E(11)^2-E(11)^-2, -1*E(11)^2+E(11)^-2, -1*E(11)^4+E(11)^-4, E(11)^4-E(11)^-4, E(11)-E(11)^-1, -1*E(11)+E(11)^-1, -1*E(11)^5+E(11)^-5, E(11)^5-E(11)^-5, -1*E(11)^3+E(11)^-3], [2, -2, 0, 0, 0, E(11)^2+E(11)^-2, E(11)^3+E(11)^-3, E(11)^5+E(11)^-5, E(11)+E(11)^-1, E(11)^4+E(11)^-4, -1*E(11)^3-E(11)^-3, -1*E(11)^5-E(11)^-5, -1*E(11)^4-E(11)^-4, -1*E(11)^2-E(11)^-2, -1*E(11)-E(11)^-1, -1*E(11)^2+E(11)^-2, -1*E(11)^5+E(11)^-5, E(11)^5-E(11)^-5, -1*E(11)+E(11)^-1, E(11)-E(11)^-1, E(11)^3-E(11)^-3, -1*E(11)^3+E(11)^-3, -1*E(11)^4+E(11)^-4, E(11)^4-E(11)^-4, E(11)^2-E(11)^-2], [2, -2, 0, 0, 0, E(11)^2+E(11)^-2, E(11)^3+E(11)^-3, E(11)^5+E(11)^-5, E(11)+E(11)^-1, E(11)^4+E(11)^-4, -1*E(11)^3-E(11)^-3, -1*E(11)^5-E(11)^-5, -1*E(11)^4-E(11)^-4, -1*E(11)^2-E(11)^-2, -1*E(11)-E(11)^-1, E(11)^2-E(11)^-2, E(11)^5-E(11)^-5, -1*E(11)^5+E(11)^-5, E(11)-E(11)^-1, -1*E(11)+E(11)^-1, -1*E(11)^3+E(11)^-3, E(11)^3-E(11)^-3, E(11)^4-E(11)^-4, -1*E(11)^4+E(11)^-4, -1*E(11)^2+E(11)^-2], [2, -2, 0, 0, 0, E(11)+E(11)^-1, E(11)^4+E(11)^-4, E(11)^3+E(11)^-3, E(11)^5+E(11)^-5, E(11)^2+E(11)^-2, -1*E(11)^4-E(11)^-4, -1*E(11)^3-E(11)^-3, -1*E(11)^2-E(11)^-2, -1*E(11)-E(11)^-1, -1*E(11)^5-E(11)^-5, -1*E(11)+E(11)^-1, E(11)^3-E(11)^-3, -1*E(11)^3+E(11)^-3, E(11)^5-E(11)^-5, -1*E(11)^5+E(11)^-5, -1*E(11)^4+E(11)^-4, E(11)^4-E(11)^-4, -1*E(11)^2+E(11)^-2, E(11)^2-E(11)^-2, E(11)-E(11)^-1], [2, -2, 0, 0, 0, E(11)+E(11)^-1, E(11)^4+E(11)^-4, E(11)^3+E(11)^-3, E(11)^5+E(11)^-5, E(11)^2+E(11)^-2, -1*E(11)^4-E(11)^-4, -1*E(11)^3-E(11)^-3, -1*E(11)^2-E(11)^-2, -1*E(11)-E(11)^-1, -1*E(11)^5-E(11)^-5, E(11)-E(11)^-1, -1*E(11)^3+E(11)^-3, E(11)^3-E(11)^-3, -1*E(11)^5+E(11)^-5, E(11)^5-E(11)^-5, E(11)^4-E(11)^-4, -1*E(11)^4+E(11)^-4, E(11)^2-E(11)^-2, -1*E(11)^2+E(11)^-2, -1*E(11)+E(11)^-1]]; ConvertToLibraryCharacterTableNC(chartbl_88_7);