Finite Group Databasebeta

← Group #136554

Character table — Group #136554

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
χ5111111111111111111-1-1-1-1111111111-1-11-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1
χ6111111111111111111-1-1-1-1111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111
χ7111111111111111111-1-1-1-111111-1-1-1-1-1-11-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111
χ8111111111111111111-1-1-1-111111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1
χ91111-1-1-1-1-111-111111-1ii−i−i1-1-1-1-1ii−i−ii−i1ii−i−iiiii−i−i−i−i11-1-1i−i11-1-111-1-1i−i
χ101111-1-1-1-1-111-111111-1ii−i−i1-1-1-1-1ii−i−ii−i1ii−i−i−i−i−i−iiiii11-1-1i−i-1-111-1-111−ii
χ111111-1-1-1-1-111-111111-1ii−i−i1-1-1-1-1−i−iiii−i1ii−i−iiiii−i−i−i−i-1-111−ii-1-11111-1-1−ii
χ121111-1-1-1-1-111-111111-1ii−i−i1-1-1-1-1−i−iiii−i1ii−i−i−i−i−i−iiiii-1-111−ii11-1-1-1-111i−i
χ131111-1-1-1-1-111-111111-1−i−iii1-1-1-1-1ii−i−i−ii1−i−iiiiiii−i−i−i−i-1-111i−i11-1-1-1-111−ii
χ141111-1-1-1-1-111-111111-1−i−iii1-1-1-1-1ii−i−i−ii1−i−iii−i−i−i−iiiii-1-111i−i-1-11111-1-1i−i
χ151111-1-1-1-1-111-111111-1−i−iii1-1-1-1-1−i−iii−ii1−i−iiiiiii−i−i−i−i11-1-1−ii-1-111-1-111i−i
χ161111-1-1-1-1-111-111111-1−i−iii1-1-1-1-1−i−iii−ii1−i−iii−i−i−i−iiiii11-1-1−ii11-1-111-1-1−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
χ192222222-2-22222222-2-20000-222-2-2222200-20000000000000000-2-20000000000
χ202222222-2-22222222-2-20000-222-2-2-2-2-2-200-20000000000000000220000000000
χ212222222-2-2222-2-2-2-2-2-20000-2-2-22200000020000000000002-22-2000000000000
χ222222222-2-2222-2-2-2-2-2-20000-2-2-2220000002000000000000-22-22000000000000
χ23222222-222-2-2-200002-22222-200000000-2-200000i2i2−i2−i2i2i2−i2−i20000000000i2−i2i2−i200
χ24222222-222-2-2-200002-22222-200000000-2-200000−i2−i2i2i2−i2−i2i2i20000000000−i2i2−i2i200
χ25222222-222-2-2-200002-2-2-2-2-2-2000000002200000i2i2−i2−i2i2i2−i2−i20000000000−i2i2−i2i200
χ26222222-222-2-2-200002-2-2-2-2-2-2000000002200000−i2−i2i2i2−i2−i2i2i20000000000i2−i2i2−i200
χ272222-2-22-2-2-2-220000222i2i−2i−2i-200000000−2i2i0000022−2−2−2−2220000000000−i2i2i2−i200
χ282222-2-22-2-2-2-220000222i2i−2i−2i-200000000−2i2i00000−2−22222−2−20000000000i2−i2−i2i200
χ292222-2-22-2-2-2-22000022−2i−2i2i2i-2000000002i−2i0000022−2−2−2−2220000000000i2−i2−i2i200
χ302222-2-22-2-2-2-22000022−2i−2i2i2i-2000000002i−2i00000−2−22222−2−20000000000−i2i2i2−i200
χ312222-2-2-22222-22222-220000-2-2-2222i2i−2i−2i00-20000000000000000−2i2i0000000000
χ322222-2-2-22222-22222-220000-2-2-222−2i−2i2i2i00-200000000000000002i−2i0000000000
χ332222-2-2-22222-2-2-2-2-2-220000-222-2-200000020000000000002-2-22000000000000
χ342222-2-2-22222-2-2-2-2-2-220000-222-2-20000002000000000000-222-2000000000000
χ352222-2-2-2-2-222-2-2-2-2-22-22i2i−2i−2i2222200002i−2i-2−2i−2i2i2i000000000000000000000000
χ362222-2-2-2-2-222-2-2-2-2-22-2−2i−2i2i2i222220000−2i2i-22i2i−2i−2i000000000000000000000000
χ3722-2-22-22002-2-222-2-200000002-2002-22-200000002−22−22−22−20000002−22−2000000
χ3822-2-22-22002-2-222-2-200000002-2002-22-20000000−22−22−22−22000000−22−22000000
χ3922-2-22-22002-2-222-2-200000002-200-22-2200000002−22−22−22−2000000−22−22000000
χ4022-2-22-22002-2-222-2-200000002-200-22-220000000−22−22−22−220000002−22−2000000
χ4122-2-2-22-2002-2222-2-20000000-22002i−2i−2i2i0000000i2−i2i2−i2−i2i2−i2i20000002−2−22000000
χ4222-2-2-22-2002-2222-2-20000000-22002i−2i−2i2i0000000−i2i2−i2i2i2−i2i2−i2000000−222−2000000
χ4322-2-2-22-2002-2222-2-20000000-2200−2i2i2i−2i0000000i2−i2i2−i2−i2i2−i2i2000000−222−2000000
χ4422-2-2-22-2002-2222-2-20000000-2200−2i2i2i−2i0000000−i2i2−i2i2i2−i2i2−i20000002−2−22000000
χ45444444-4-4-4-4-4-40000-4400004000000000000000000000000000000000000000
χ464444-4-4444-4-440000-4-400004000000000000000000000000000000000000000
χ4744-4-44-44004-4-4-4-4440000000-440000000000000000000000000000000000000
χ4844-4-44-4-400-444000000000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ4944-4-44-4-400-44400000000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ5044-4-4-44400-44-4000000000000000000000000002-2-22-222-20000000000000000
χ5144-4-4-44400-44-400000000000000000000000000-222-22-2-220000000000000000
χ5244-4-4-44-4004-44-4-44400000004-40000000000000000000000000000000000000
χ534-44-40004i−4i0002i2−2i22i2−2i2002+2i−2−2i2−2i−2+2i00022−2200000002ζ3−2ζ32ζ−2ζ000000000000000000000000
χ544-44-40004i−4i0002i2−2i22i2−2i200−2−2i2+2i−2+2i2−2i00022−220000000−2ζ32ζ3−2ζ2ζ000000000000000000000000
χ554-44-40004i−4i000−2i22i2−2i22i2002+2i−2−2i2−2i−2+2i000−22220000000−2ζ32ζ3−2ζ2ζ000000000000000000000000
χ564-44-40004i−4i000−2i22i2−2i22i200−2−2i2+2i−2+2i2−2i000−222200000002ζ3−2ζ32ζ−2ζ000000000000000000000000
χ574-44-4000−4i4i0002i2−2i22i2−2i2002−2i−2+2i2+2i−2−2i000−222200000002ζ−2ζ2ζ3−2ζ3000000000000000000000000
χ584-44-4000−4i4i0002i2−2i22i2−2i200−2+2i2−2i−2−2i2+2i000−22220000000−2ζ2ζ−2ζ32ζ3000000000000000000000000
χ594-44-4000−4i4i000−2i22i2−2i22i2002−2i−2+2i2+2i−2−2i00022−220000000−2ζ2ζ−2ζ32ζ3000000000000000000000000
χ604-44-4000−4i4i000−2i22i2−2i22i200−2+2i2−2i−2−2i2+2i00022−2200000002ζ−2ζ2ζ3−2ζ3000000000000000000000000
χ618-8-88000000004i2−4i2−4i24i20000000000000000000000000000000000000000000000
χ628-8-8800000000−4i24i24i2−4i20000000000000000000000000000000000000000000000

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