# Group 200.12 downloaded from the LMFDB on 13 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(132955018702568981058794511,200); a := GPC.1; b := GPC.3; GPerm := Group( (2,4,5,10)(3,8,9,20)(6,14,15,19)(7,17,18,11)(12,22,23,25)(13,16,21,24)(26,27), (26,27), (2,5)(3,9)(4,10)(6,15)(7,18)(8,20)(11,17)(12,23)(13,21)(14,19)(16,24)(22,25), (1,2,6,16,13,3,7,4,11,22,8,19,12,23,14,20,25,17,10,18,9,21,24,15,5), (1,3,8,20,9)(2,7,19,25,21)(4,12,17,24,6)(5,13,22,14,18)(10,15,16,11,23) ); GLZN := Group([[[ZmodnZObj(1,50), ZmodnZObj(2,50)], [ZmodnZObj(0,50), ZmodnZObj(1,50)]],[[ZmodnZObj(49,50), ZmodnZObj(0,50)], [ZmodnZObj(0,50), ZmodnZObj(1,50)]],[[ZmodnZObj(1,50), ZmodnZObj(10,50)], [ZmodnZObj(0,50), ZmodnZObj(1,50)]],[[ZmodnZObj(43,50), ZmodnZObj(0,50)], [ZmodnZObj(0,50), ZmodnZObj(1,50)]],[[ZmodnZObj(1,50), ZmodnZObj(25,50)], [ZmodnZObj(0,50), ZmodnZObj(1,50)]]]); GLZq := Group([[[ZmodnZObj(1,25), ZmodnZObj(1,25)], [ZmodnZObj(0,25), ZmodnZObj(1,25)]],[[ZmodnZObj(24,25), ZmodnZObj(0,25)], [ZmodnZObj(0,25), ZmodnZObj(1,25)]],[[ZmodnZObj(24,25), ZmodnZObj(0,25)], [ZmodnZObj(0,25), ZmodnZObj(7,25)]],[[ZmodnZObj(1,25), ZmodnZObj(5,25)], [ZmodnZObj(0,25), ZmodnZObj(1,25)]],[[ZmodnZObj(24,25), ZmodnZObj(0,25)], [ZmodnZObj(0,25), ZmodnZObj(24,25)]]]); # Booleans booleans_200_12 := rec( Agroup := true, Zgroup := false, 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_200_12:=rec(); chartbl_200_12.IsFinite:= true; chartbl_200_12.UnderlyingCharacteristic:= 0; chartbl_200_12.UnderlyingGroup:= GPC; chartbl_200_12.Size:= 200; chartbl_200_12.InfoText:= "Character table for group 200.12 downloaded from the LMFDB."; chartbl_200_12.Identifier:= " C50:C4 "; chartbl_200_12.NrConjugacyClasses:= 20; chartbl_200_12.ConjugacyClasses:= [ of ..., f3*f4^2*f5^2, f2*f5^2, f2*f3*f4^2*f5, f1*f5^3, f1*f2*f5^4, f1*f2*f3*f4^2*f5^4, f1*f3*f4^2*f5, f5, f3*f4^2, f4, f4^2, f4^3, f4*f5, f4^4*f5, f3, f3*f4, f3*f5^4, f3*f5, f3*f5^3]; chartbl_200_12.IdentificationOfConjugacyClasses:= [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]; chartbl_200_12.ComputedPowerMaps:= [ , [1, 1, 1, 1, 3, 3, 3, 3, 9, 9, 12, 13, 14, 15, 11, 11, 13, 15, 12, 14], [1, 2, 3, 4, 5, 6, 7, 8, 1, 2, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10]]; chartbl_200_12.SizesCentralizers:= [200, 200, 8, 8, 8, 8, 8, 8, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50]; chartbl_200_12.ClassNames:= ["1A", "2A", "2B", "2C", "4A1", "4A-1", "4B1", "4B-1", "5A", "10A", "25A1", "25A2", "25A3", "25A6", "25A9", "50A1", "50A3", "50A9", "50A11", "50A17"]; chartbl_200_12.OrderClassRepresentatives:= [1, 2, 2, 2, 4, 4, 4, 4, 5, 10, 25, 25, 25, 25, 25, 50, 50, 50, 50, 50]; chartbl_200_12.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*E(4), E(4), -1*E(4), E(4), 1, -1, 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, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1], [1, 1, -1, -1, -1*E(4), E(4), E(4), -1*E(4), 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, -1, -1, E(4), -1*E(4), -1*E(4), E(4), 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [4, 4, 0, 0, 0, 0, 0, 0, 4, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [4, -4, 0, 0, 0, 0, 0, 0, 4, -4, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1], [4, 4, 0, 0, 0, 0, 0, 0, -1, -1, E(25)^9+E(25)^12+E(25)^-12+E(25)^-9, E(25)^6+E(25)^8+E(25)^-8+E(25)^-6, -1*E(25)-E(25)^2+E(25)^3+E(25)^4-E(25)^6-E(25)^7-E(25)^11-E(25)^12-E(25)^-9-E(25)^-8, E(25)^2-E(25)^3-E(25)^8+E(25)^11-E(25)^-12+E(25)^-11-E(25)^-7, E(25)-E(25)^4+E(25)^7-E(25)^9-E(25)^-11+E(25)^-7-E(25)^-6, -1*E(25)-E(25)^2+E(25)^3+E(25)^4-E(25)^6-E(25)^7-E(25)^11-E(25)^12-E(25)^-9-E(25)^-8, E(25)-E(25)^4+E(25)^7-E(25)^9-E(25)^-11+E(25)^-7-E(25)^-6, E(25)^9+E(25)^12+E(25)^-12+E(25)^-9, E(25)^6+E(25)^8+E(25)^-8+E(25)^-6, E(25)^2-E(25)^3-E(25)^8+E(25)^11-E(25)^-12+E(25)^-11-E(25)^-7], [4, 4, 0, 0, 0, 0, 0, 0, -1, -1, E(25)^6+E(25)^8+E(25)^-8+E(25)^-6, -1*E(25)-E(25)^2+E(25)^3+E(25)^4-E(25)^6-E(25)^7-E(25)^11-E(25)^12-E(25)^-9-E(25)^-8, E(25)^2-E(25)^3-E(25)^8+E(25)^11-E(25)^-12+E(25)^-11-E(25)^-7, E(25)-E(25)^4+E(25)^7-E(25)^9-E(25)^-11+E(25)^-7-E(25)^-6, E(25)^9+E(25)^12+E(25)^-12+E(25)^-9, E(25)^2-E(25)^3-E(25)^8+E(25)^11-E(25)^-12+E(25)^-11-E(25)^-7, E(25)^9+E(25)^12+E(25)^-12+E(25)^-9, E(25)^6+E(25)^8+E(25)^-8+E(25)^-6, -1*E(25)-E(25)^2+E(25)^3+E(25)^4-E(25)^6-E(25)^7-E(25)^11-E(25)^12-E(25)^-9-E(25)^-8, E(25)-E(25)^4+E(25)^7-E(25)^9-E(25)^-11+E(25)^-7-E(25)^-6], [4, 4, 0, 0, 0, 0, 0, 0, -1, -1, E(25)^2-E(25)^3-E(25)^8+E(25)^11-E(25)^-12+E(25)^-11-E(25)^-7, E(25)-E(25)^4+E(25)^7-E(25)^9-E(25)^-11+E(25)^-7-E(25)^-6, E(25)^9+E(25)^12+E(25)^-12+E(25)^-9, E(25)^6+E(25)^8+E(25)^-8+E(25)^-6, -1*E(25)-E(25)^2+E(25)^3+E(25)^4-E(25)^6-E(25)^7-E(25)^11-E(25)^12-E(25)^-9-E(25)^-8, E(25)^9+E(25)^12+E(25)^-12+E(25)^-9, -1*E(25)-E(25)^2+E(25)^3+E(25)^4-E(25)^6-E(25)^7-E(25)^11-E(25)^12-E(25)^-9-E(25)^-8, E(25)^2-E(25)^3-E(25)^8+E(25)^11-E(25)^-12+E(25)^-11-E(25)^-7, E(25)-E(25)^4+E(25)^7-E(25)^9-E(25)^-11+E(25)^-7-E(25)^-6, E(25)^6+E(25)^8+E(25)^-8+E(25)^-6], [4, 4, 0, 0, 0, 0, 0, 0, -1, -1, E(25)-E(25)^4+E(25)^7-E(25)^9-E(25)^-11+E(25)^-7-E(25)^-6, E(25)^9+E(25)^12+E(25)^-12+E(25)^-9, E(25)^6+E(25)^8+E(25)^-8+E(25)^-6, -1*E(25)-E(25)^2+E(25)^3+E(25)^4-E(25)^6-E(25)^7-E(25)^11-E(25)^12-E(25)^-9-E(25)^-8, E(25)^2-E(25)^3-E(25)^8+E(25)^11-E(25)^-12+E(25)^-11-E(25)^-7, E(25)^6+E(25)^8+E(25)^-8+E(25)^-6, E(25)^2-E(25)^3-E(25)^8+E(25)^11-E(25)^-12+E(25)^-11-E(25)^-7, E(25)-E(25)^4+E(25)^7-E(25)^9-E(25)^-11+E(25)^-7-E(25)^-6, E(25)^9+E(25)^12+E(25)^-12+E(25)^-9, -1*E(25)-E(25)^2+E(25)^3+E(25)^4-E(25)^6-E(25)^7-E(25)^11-E(25)^12-E(25)^-9-E(25)^-8], [4, 4, 0, 0, 0, 0, 0, 0, -1, -1, -1*E(25)-E(25)^2+E(25)^3+E(25)^4-E(25)^6-E(25)^7-E(25)^11-E(25)^12-E(25)^-9-E(25)^-8, E(25)^2-E(25)^3-E(25)^8+E(25)^11-E(25)^-12+E(25)^-11-E(25)^-7, E(25)-E(25)^4+E(25)^7-E(25)^9-E(25)^-11+E(25)^-7-E(25)^-6, E(25)^9+E(25)^12+E(25)^-12+E(25)^-9, E(25)^6+E(25)^8+E(25)^-8+E(25)^-6, E(25)-E(25)^4+E(25)^7-E(25)^9-E(25)^-11+E(25)^-7-E(25)^-6, E(25)^6+E(25)^8+E(25)^-8+E(25)^-6, -1*E(25)-E(25)^2+E(25)^3+E(25)^4-E(25)^6-E(25)^7-E(25)^11-E(25)^12-E(25)^-9-E(25)^-8, E(25)^2-E(25)^3-E(25)^8+E(25)^11-E(25)^-12+E(25)^-11-E(25)^-7, E(25)^9+E(25)^12+E(25)^-12+E(25)^-9], [4, -4, 0, 0, 0, 0, 0, 0, -1, 1, E(25)^9+E(25)^12+E(25)^-12+E(25)^-9, E(25)^6+E(25)^8+E(25)^-8+E(25)^-6, -1*E(25)-E(25)^2+E(25)^3+E(25)^4-E(25)^6-E(25)^7-E(25)^11-E(25)^12-E(25)^-9-E(25)^-8, E(25)^2-E(25)^3-E(25)^8+E(25)^11-E(25)^-12+E(25)^-11-E(25)^-7, E(25)-E(25)^4+E(25)^7-E(25)^9-E(25)^-11+E(25)^-7-E(25)^-6, E(25)+E(25)^2-E(25)^3-E(25)^4+E(25)^6+E(25)^7+E(25)^11+E(25)^12+E(25)^-9+E(25)^-8, -1*E(25)+E(25)^4-E(25)^7+E(25)^9+E(25)^-11-E(25)^-7+E(25)^-6, -1*E(25)^9-E(25)^12-E(25)^-12-E(25)^-9, -1*E(25)^6-E(25)^8-E(25)^-8-E(25)^-6, -1*E(25)^2+E(25)^3+E(25)^8-E(25)^11+E(25)^-12-E(25)^-11+E(25)^-7], [4, -4, 0, 0, 0, 0, 0, 0, -1, 1, E(25)^6+E(25)^8+E(25)^-8+E(25)^-6, -1*E(25)-E(25)^2+E(25)^3+E(25)^4-E(25)^6-E(25)^7-E(25)^11-E(25)^12-E(25)^-9-E(25)^-8, E(25)^2-E(25)^3-E(25)^8+E(25)^11-E(25)^-12+E(25)^-11-E(25)^-7, E(25)-E(25)^4+E(25)^7-E(25)^9-E(25)^-11+E(25)^-7-E(25)^-6, E(25)^9+E(25)^12+E(25)^-12+E(25)^-9, -1*E(25)^2+E(25)^3+E(25)^8-E(25)^11+E(25)^-12-E(25)^-11+E(25)^-7, -1*E(25)^9-E(25)^12-E(25)^-12-E(25)^-9, -1*E(25)^6-E(25)^8-E(25)^-8-E(25)^-6, E(25)+E(25)^2-E(25)^3-E(25)^4+E(25)^6+E(25)^7+E(25)^11+E(25)^12+E(25)^-9+E(25)^-8, -1*E(25)+E(25)^4-E(25)^7+E(25)^9+E(25)^-11-E(25)^-7+E(25)^-6], [4, -4, 0, 0, 0, 0, 0, 0, -1, 1, E(25)^2-E(25)^3-E(25)^8+E(25)^11-E(25)^-12+E(25)^-11-E(25)^-7, E(25)-E(25)^4+E(25)^7-E(25)^9-E(25)^-11+E(25)^-7-E(25)^-6, E(25)^9+E(25)^12+E(25)^-12+E(25)^-9, E(25)^6+E(25)^8+E(25)^-8+E(25)^-6, -1*E(25)-E(25)^2+E(25)^3+E(25)^4-E(25)^6-E(25)^7-E(25)^11-E(25)^12-E(25)^-9-E(25)^-8, -1*E(25)^9-E(25)^12-E(25)^-12-E(25)^-9, E(25)+E(25)^2-E(25)^3-E(25)^4+E(25)^6+E(25)^7+E(25)^11+E(25)^12+E(25)^-9+E(25)^-8, -1*E(25)^2+E(25)^3+E(25)^8-E(25)^11+E(25)^-12-E(25)^-11+E(25)^-7, -1*E(25)+E(25)^4-E(25)^7+E(25)^9+E(25)^-11-E(25)^-7+E(25)^-6, -1*E(25)^6-E(25)^8-E(25)^-8-E(25)^-6], [4, -4, 0, 0, 0, 0, 0, 0, -1, 1, E(25)-E(25)^4+E(25)^7-E(25)^9-E(25)^-11+E(25)^-7-E(25)^-6, E(25)^9+E(25)^12+E(25)^-12+E(25)^-9, E(25)^6+E(25)^8+E(25)^-8+E(25)^-6, -1*E(25)-E(25)^2+E(25)^3+E(25)^4-E(25)^6-E(25)^7-E(25)^11-E(25)^12-E(25)^-9-E(25)^-8, E(25)^2-E(25)^3-E(25)^8+E(25)^11-E(25)^-12+E(25)^-11-E(25)^-7, -1*E(25)^6-E(25)^8-E(25)^-8-E(25)^-6, -1*E(25)^2+E(25)^3+E(25)^8-E(25)^11+E(25)^-12-E(25)^-11+E(25)^-7, -1*E(25)+E(25)^4-E(25)^7+E(25)^9+E(25)^-11-E(25)^-7+E(25)^-6, -1*E(25)^9-E(25)^12-E(25)^-12-E(25)^-9, E(25)+E(25)^2-E(25)^3-E(25)^4+E(25)^6+E(25)^7+E(25)^11+E(25)^12+E(25)^-9+E(25)^-8], [4, -4, 0, 0, 0, 0, 0, 0, -1, 1, -1*E(25)-E(25)^2+E(25)^3+E(25)^4-E(25)^6-E(25)^7-E(25)^11-E(25)^12-E(25)^-9-E(25)^-8, E(25)^2-E(25)^3-E(25)^8+E(25)^11-E(25)^-12+E(25)^-11-E(25)^-7, E(25)-E(25)^4+E(25)^7-E(25)^9-E(25)^-11+E(25)^-7-E(25)^-6, E(25)^9+E(25)^12+E(25)^-12+E(25)^-9, E(25)^6+E(25)^8+E(25)^-8+E(25)^-6, -1*E(25)+E(25)^4-E(25)^7+E(25)^9+E(25)^-11-E(25)^-7+E(25)^-6, -1*E(25)^6-E(25)^8-E(25)^-8-E(25)^-6, E(25)+E(25)^2-E(25)^3-E(25)^4+E(25)^6+E(25)^7+E(25)^11+E(25)^12+E(25)^-9+E(25)^-8, -1*E(25)^2+E(25)^3+E(25)^8-E(25)^11+E(25)^-12-E(25)^-11+E(25)^-7, -1*E(25)^9-E(25)^12-E(25)^-12-E(25)^-9]]; ConvertToLibraryCharacterTableNC(chartbl_200_12);