Finite Group Databasebeta

← Group #136376

Character table — Group #136376

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size111122222222222244444444444888888888888888888816161616161616161616161616163232
order12222244444488884444444888844444488888161616161616161644444488881616161688
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1
χ4111111111111111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ5111111111111111111-1-1-1-1111111111-1-11-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1
χ6111111111111111111-1-1-1-1111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111
χ7111111111111111111-1-1-1-111111-1-1-1-1-1-11-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-111
χ8111111111111111111-1-1-1-111111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1
χ91111-1-1-1-111-1-1-1-1-1-11-1ii−i−i1111111-1-1i−i-1ii−i−i1111-1-1-1-11-1ii−i−i11-1-1ii−i−ii−i
χ101111-1-1-1-111-1-1-1-1-1-11-1ii−i−i1111111-1-1i−i-1ii−i−i-1-1-1-111111-1ii−i−i-1-111−i−iii−ii
χ111111-1-1-1-111-1-1-1-1-1-11-1ii−i−i11111-1-111i−i-1ii−i−i1111-1-1-1-1-11−i−iii-1-111ii−i−i−ii
χ121111-1-1-1-111-1-1-1-1-1-11-1ii−i−i11111-1-111i−i-1ii−i−i-1-1-1-11111-11−i−iii11-1-1−i−iiii−i
χ131111-1-1-1-111-1-1-1-1-1-11-1−i−iii1111111-1-1−ii-1−i−iii1111-1-1-1-11-1−i−iii11-1-1−i−iii−ii
χ141111-1-1-1-111-1-1-1-1-1-11-1−i−iii1111111-1-1−ii-1−i−iii-1-1-1-111111-1−i−iii-1-111ii−i−ii−i
χ151111-1-1-1-111-1-1-1-1-1-11-1−i−iii11111-1-111−ii-1−i−iii1111-1-1-1-1-11ii−i−i-1-111−i−iiii−i
χ161111-1-1-1-111-1-1-1-1-1-11-1−i−iii11111-1-111−ii-1−i−iii-1-1-1-11111-11ii−i−i11-1-1ii−i−i−ii
χ17222222222222-2-2-2-22222222-2-2-2-2000022-2-2-2-2-2000000000000000000000000
χ18222222222222-2-2-2-222-2-2-2-22-2-2-2-20000-2-2-22222000000000000000000000000
χ1922222222-2-2-2-200002-22222-200000000-2-200000i2i2−i2−i2i2i2−i2−i20000000000i2−i2i2−i200
χ2022222222-2-2-2-200002-22222-200000000-2-200000−i2−i2i2i2−i2−i2i2i20000000000−i2i2−i2i200
χ2122222222-2-2-2-200002-2-2-2-2-2-2000000002200000i2i2−i2−i2i2i2−i2−i20000000000−i2i2−i2i200
χ2222222222-2-2-2-200002-2-2-2-2-2-2000000002200000−i2−i2i2i2−i2−i2i2i20000000000i2−i2i2−i200
χ23222222-2-222222222-2-20000-222-2-2222200-2000000000000-2-200000000000000
χ24222222-2-222222222-2-20000-222-2-2-2-2-2-200-20000000000002200000000000000
χ25222222-2-22222-2-2-2-2-2-20000-2-2-2220000002000000000000002-22-20000000000
χ26222222-2-22222-2-2-2-2-2-20000-2-2-222000000200000000000000-22-220000000000
χ272222-2-22222-2-22222-220000-2-2-222000000-2000000000000002i−2i−2i2i0000000000
χ282222-2-22222-2-22222-220000-2-2-222000000-200000000000000−2i2i2i−2i0000000000
χ292222-2-22222-2-2-2-2-2-2-220000-222-2-222-2-2002000000000000-2200000000000000
χ302222-2-22222-2-2-2-2-2-2-220000-222-2-2-2-2220020000000000002-200000000000000
χ312222-2-2-2-222-2-222222-22i2i−2i−2i2-2-2-2-200002i−2i2−2i−2i2i2i000000000000000000000000
χ322222-2-2-2-222-2-222222-2−2i−2i2i2i2-2-2-2-20000−2i2i22i2i−2i−2i000000000000000000000000
χ332222-2-2-2-2-2-2220000222i2i−2i−2i-200000000−2i2i00000i2i2−i2−i2−i2−i2i2i20000000000−222−200
χ342222-2-2-2-2-2-2220000222i2i−2i−2i-200000000−2i2i00000−i2−i2i2i2i2i2−i2−i200000000002−2−2200
χ352222-2-2-2-2-2-222000022−2i−2i2i2i-2000000002i−2i00000i2i2−i2−i2−i2−i2i2i200000000002−2−2200
χ362222-2-2-2-2-2-222000022−2i−2i2i2i-2000000002i−2i00000−i2−i2i2i2i2i2−i2−i20000000000−222−200
χ372-22-22-2002-2-22-2-22200000002-2002-22-20000000i2−i2i2−i2i2−i2i2−i2000000i2−i2i2−i2000000
χ382-22-22-2002-2-22-2-22200000002-2002-22-20000000−i2i2−i2i2−i2i2−i2i2000000−i2i2−i2i2000000
χ392-22-22-2002-2-22-2-22200000002-200-22-220000000i2−i2i2−i2i2−i2i2−i2000000−i2i2−i2i2000000
χ402-22-22-2002-2-22-2-22200000002-200-22-220000000−i2i2−i2i2−i2i2−i2i2000000i2−i2i2−i2000000
χ412-22-2-22002-22-222-2-200000002-2002-2-220000000i2−i2i2−i2−i2i2−i2i2000000i2−i2−i2i2000000
χ422-22-2-22002-22-222-2-200000002-2002-2-220000000−i2i2−i2i2i2−i2i2−i2000000−i2i2i2−i2000000
χ432-22-2-22002-22-222-2-200000002-200-222-20000000i2−i2i2−i2−i2i2−i2i2000000−i2i2i2−i2000000
χ442-22-2-22002-22-222-2-200000002-200-222-20000000−i2i2−i2i2i2−i2i2−i2000000i2−i2−i2i2000000
χ45444444-4-4-4-4-4-40000-4400004000000000000000000000000000000000000000
χ464444-4-444-4-4440000-4-400004000000000000000000000000000000000000000
χ474-44-44-4004-4-4444-4-40000000-440000000000000000000000000000000000000
χ484-44-44-400-444-4000000000000000000000000002-2-222-2-220000000000000000
χ494-44-44-400-444-400000000000000000000000000-222-2-222-20000000000000000
χ504-44-4-44004-44-4-4-4440000000-440000000000000000000000000000000000000
χ514-44-4-4400-44-44000000000000000000000000002-2-22-222-20000000000000000
χ524-44-4-4400-44-4400000000000000000000000000-222-22-2-220000000000000000
χ534-4-44004i−4i000022−2222−22002+2i−2−2i2−2i−2+2i0002i2−2i200000002ζ3−2ζ32ζ−2ζ000000000000000000000000
χ544-4-44004i−4i000022−2222−2200−2−2i2+2i−2+2i2−2i0002i2−2i20000000−2ζ32ζ3−2ζ2ζ000000000000000000000000
χ554-4-44004i−4i0000−2222−2222002+2i−2−2i2−2i−2+2i000−2i22i20000000−2ζ32ζ3−2ζ2ζ000000000000000000000000
χ564-4-44004i−4i0000−2222−222200−2−2i2+2i−2+2i2−2i000−2i22i200000002ζ3−2ζ32ζ−2ζ000000000000000000000000
χ574-4-4400−4i4i000022−2222−22002−2i−2+2i2+2i−2−2i000−2i22i20000000−2ζ2ζ−2ζ32ζ3000000000000000000000000
χ584-4-4400−4i4i000022−2222−2200−2+2i2−2i−2−2i2+2i000−2i22i200000002ζ−2ζ2ζ3−2ζ3000000000000000000000000
χ594-4-4400−4i4i0000−2222−2222002−2i−2+2i2+2i−2−2i0002i2−2i200000002ζ−2ζ2ζ3−2ζ3000000000000000000000000
χ604-4-4400−4i4i0000−2222−222200−2+2i2−2i−2−2i2+2i0002i2−2i20000000−2ζ2ζ−2ζ32ζ3000000000000000000000000
χ6188-8-80000000042−42−42420000000000000000000000000000000000000000000000
χ6288-8-800000000−424242−420000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.