Finite Group Databasebeta

← Group #280855

Character table — Group #280855

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size111122222222222244444444444888888888888888888816161616161616161616161616163232
order12222244444488884444444888822444488888888888884444444488888888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111-1-1-1-1111111111111111-1-111-1-1-1-111-1-1-1-1-1-1
χ4111111111111111111111111111-1-1-1-111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111-1-1-1-11111111111-1-11111-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-1
χ611111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-111-1-1-1-111
χ711111111111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-111111-1-1-1-11111-1-1-1-1-1-111
χ811111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1111111111111-1-1
χ9111111111111-1-1-1-11111111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-11-11111-1-1-1-111-1-11-1
χ10111111111111-1-1-1-11111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-111111-1-1-111-1-111-1-111-11
χ11111111111111-1-1-1-11111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111-1-111-1-1-1-111-11
χ12111111111111-1-1-1-11111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11111-11-1-1-1-1111111-1-11-1
χ13111111111111-1-1-1-11-1-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1-11-1-1-1-1-1111111-1-1-11
χ14111111111111-1-1-1-11-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-111111-111-1-111-1-1-1-1111-1
χ15111111111111-1-1-1-11-1-1-1-111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-11-1-111-1-111-1-1111-1
χ16111111111111-1-1-1-11-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-11111-11111-111111-1-1-1-111-1-1-11
χ172222222-2-22222222-20000-2-222-2-222220000000000-20000-2-200000000000000
χ182222222-2-22222222-20000-2-222-2-2-2-2-2-20000000000-200002200000000000000
χ192222222-2-2222-2-2-2-2-20000-2-2-2-22222-2-2000000000020000-2200000000000000
χ202222222-2-2222-2-2-2-2-20000-2-2-2-222-2-2220000000000200002-200000000000000
χ21222222-222-2-2-2000022222-2-200000000-2-20000000002i2i−2i−2i000000002i−2i000000
χ22222222-222-2-2-2000022222-2-200000000-2-2000000000−2i−2i2i2i00000000−2i2i000000
χ23222222-222-2-2-200002-2-2-2-2-2-200000000220000000002i2i−2i−2i00000000−2i2i000000
χ24222222-222-2-2-200002-2-2-2-2-2-20000000022000000000−2i−2i2i2i000000002i−2i000000
χ252222-2-2222-22-22222-200002-2-2-22200000000000000-2000000002i−2i2i−2i00000000
χ262222-2-2222-22-22222-200002-2-2-22200000000000000-200000000−2i2i−2i2i00000000
χ272222-2-2222-22-2-2-2-2-2-200002-222-2-2000000000000002000000002i−2i−2i2i00000000
χ282222-2-2222-22-2-2-2-2-2-200002-222-2-200000000000000200000000−2i2i2i−2i00000000
χ292222-2-22-2-2-22-2222222i2i−2i−2i-22-2-2-2-200002i−2i00002i2i−2i−2i200000000000000000000
χ302222-2-22-2-2-22-222222−2i−2i2i2i-22-2-2-2-20000−2i2i0000−2i−2i2i2i200000000000000000000
χ312222-2-22-2-2-22-2-2-2-2-222i2i−2i−2i-22222200002i−2i0000−2i−2i2i2i-200000000000000000000
χ322222-2-22-2-2-22-2-2-2-2-22−2i−2i2i2i-2222220000−2i2i00002i2i−2i−2i-200000000000000000000
χ332222-2-2-2-2-22-22000022i2i−2i−2i2-200000000−2i2i2i2i−2i−2i000000000002-2000000000000
χ342222-2-2-2-2-22-22000022i2i−2i−2i2-200000000−2i2i−2i−2i2i2i00000000000-22000000000000
χ352222-2-2-2-2-22-2200002−2i−2i2i2i2-2000000002i−2i2i2i−2i−2i00000000000-22000000000000
χ362222-2-2-2-2-22-2200002−2i−2i2i2i2-2000000002i−2i−2i−2i2i2i000000000002-2000000000000
χ3722-2-2-222002-2-222-2-200000002-2002-22-200i2−i2i2−i200000i2−i2i2−i20000000000i2−i2i2−i200
χ3822-2-2-222002-2-222-2-200000002-2002-22-200−i2i2−i2i200000−i2i2−i2i20000000000−i2i2−i2i200
χ3922-2-2-222002-2-222-2-200000002-200-22-2200i2−i2i2−i200000i2−i2i2−i20000000000−i2i2−i2i200
χ4022-2-2-222002-2-222-2-200000002-200-22-2200−i2i2−i2i200000−i2i2−i2i20000000000i2−i2i2−i200
χ4122-2-2-222002-2-2-2-2220000000-22002-2-2200i2−i2i2−i200000−i2i2−i2i20000000000i2−i2−i2i200
χ4222-2-2-222002-2-2-2-2220000000-22002-2-2200−i2i2−i2i200000i2−i2i2−i20000000000−i2i2i2−i200
χ4322-2-2-222002-2-2-2-2220000000-2200-222-200i2−i2i2−i200000−i2i2−i2i20000000000−i2i2i2−i200
χ4422-2-2-222002-2-2-2-2220000000-2200-222-200−i2i2−i2i200000i2−i2i2−i20000000000i2−i2−i2i200
χ45444444-4-4-4-4-4-40000-4000044000000000000000000000000000000000000000
χ464444-4-4-4444-440000-40000-44000000000000000000000000000000000000000
χ4744-4-44-4400-4-4444-4-40000000-440000000000000000000000000000000000000
χ4844-4-44-4400-4-44-4-44400000004-40000000000000000000000000000000000000
χ4944-4-44-4-40044-400000000000000000000022−22−22220000000000000000000000000
χ5044-4-44-4-40044-4000000000000000000000−222222−220000000000000000000000000
χ5144-4-4-44-400-44400000000000000000000000000000022−22−22220000000000000000
χ5244-4-4-44-400-444000000000000000000000000000000−222222−220000000000000000
χ534-44-40004i−4i0002i2−2i22i2−2i202+2i−2−2i2−2i−2+2i000022−2200000000002ζ3−2ζ32ζ−2ζ000000000000000000000
χ544-44-40004i−4i0002i2−2i22i2−2i20−2−2i2+2i−2+2i2−2i000022−220000000000−2ζ32ζ3−2ζ2ζ000000000000000000000
χ554-44-40004i−4i000−2i22i2−2i22i202+2i−2−2i2−2i−2+2i0000−22220000000000−2ζ32ζ3−2ζ2ζ000000000000000000000
χ564-44-40004i−4i000−2i22i2−2i22i20−2−2i2+2i−2+2i2−2i0000−222200000000002ζ3−2ζ32ζ−2ζ000000000000000000000
χ574-44-4000−4i4i0002i2−2i22i2−2i202−2i−2+2i2+2i−2−2i0000−222200000000002ζ−2ζ2ζ3−2ζ3000000000000000000000
χ584-44-4000−4i4i0002i2−2i22i2−2i20−2+2i2−2i−2−2i2+2i0000−22220000000000−2ζ2ζ−2ζ32ζ3000000000000000000000
χ594-44-4000−4i4i000−2i22i2−2i22i202−2i−2+2i2+2i−2−2i000022−220000000000−2ζ2ζ−2ζ32ζ3000000000000000000000
χ604-44-4000−4i4i000−2i22i2−2i22i20−2+2i2−2i−2−2i2+2i000022−2200000000002ζ−2ζ2ζ3−2ζ3000000000000000000000
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.