Finite Group Databasebeta

← Group #505654

Character table — Group #505654

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11112222222222222222224444444444444444444444161616161616161616161616161616161616161616161616
order1244222444444488888888224444444488888888888824448888888888881616161616161616
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-11111-1-111-1-11111-1-1-1-111-1-11111-1-1-1-1
χ611111111111111-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-11111-1-111-1-111-1-111-1-1-1-111-1-1-1-11111
χ711111111111111-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-111-1-111-1-11111-1-1-1-1-1-11111
χ811111111111111-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1111111-1-1-1-1
χ91111111-1-1-1-111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-111-1-1
χ101111111-1-1-1-111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-111
χ111111111-1-1-1-111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111-1-111
χ121111111-1-1-1-111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1111111-1-111-1-1
χ131111111-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-111-1-1-1-1-1-11111-1-1-1-111
χ141111111-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-111-1-111-1-1-1-11111-1-1
χ151111111-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-11111-1-1
χ161111111-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-111-1-1-1-111
χ17222222222222222222-2-2-2-2-2-2-2-222-2-2-2-2-2-22222-2-2-2-222000000000000000000000000
χ1822222222222222-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000
χ192222222-2-2-2-22222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-2222222000000000000000000000000
χ202222222-2-2-2-2222-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-222222222-2-2000000000000000000000000
χ2122-2-22-2-22i2i−2i−2i-22222-2-2000000002i−2i0000002i2i−2i−2i00002-20000000000000000i2−i22−2i2−i22−2
χ2222-2-22-2-22i2i−2i−2i-22222-2-2000000002i−2i0000002i2i−2i−2i00002-20000000000000000−i2i2−22−i2i2−22
χ2322-2-22-2-22i2i−2i−2i-222-2-222000000002i−2i000000−2i−2i2i2i0000-220000000000000000i2−i22−2−i2i2−22
χ2422-2-22-2-22i2i−2i−2i-222-2-222000000002i−2i000000−2i−2i2i2i0000-220000000000000000−i2i2−22i2−i22−2
χ2522-2-22-2-2−2i−2i2i2i-22222-2-200000000−2i2i000000−2i−2i2i2i00002-20000000000000000i2−i2−22i2−i2−22
χ2622-2-22-2-2−2i−2i2i2i-22222-2-200000000−2i2i000000−2i−2i2i2i00002-20000000000000000−i2i22−2−i2i22−2
χ2722-2-22-2-2−2i−2i2i2i-222-2-22200000000−2i2i0000002i2i−2i−2i0000-220000000000000000i2−i2−22−i2i22−2
χ2822-2-22-2-2−2i−2i2i2i-222-2-22200000000−2i2i0000002i2i−2i−2i0000-220000000000000000−i2i22−2i2−i2−22
χ2922-2-2-22-2000022-222-2-222-2-200000022-2-22-200000000-220000000000002i−2i2i−2i00000000
χ3022-2-2-22-2000022-222-2-222-2-200000022-2-22-200000000-22000000000000−2i2i−2i2i00000000
χ3122-2-2-22-2000022-222-2-2-2-222000000-2-222-2200000000-220000002i−2i2i−2i00000000000000
χ3222-2-2-22-2000022-222-2-2-2-222000000-2-222-2200000000-22000000−2i2i−2i2i00000000000000
χ3322-2-2-22-2000022-2-2-22222-2-2000000-2-2222-2000000002-20000000000002i−2i−2i2i00000000
χ3422-2-2-22-2000022-2-2-22222-2-2000000-2-2222-2000000002-2000000000000−2i2i2i−2i00000000
χ3522-2-2-22-2000022-2-2-222-2-22200000022-2-2-22000000002-20000002i−2i−2i2i00000000000000
χ3622-2-2-22-2000022-2-2-222-2-22200000022-2-2-22000000002-2000000−2i2i2i−2i00000000000000
χ3722-2-2-2-222i2i−2i−2i2-22000022-2-20000−2i2i0000-2200002i2i−2i−2i00002-20000002i−2i000000000000
χ3822-2-2-2-222i2i−2i−2i2-22000022-2-20000−2i2i0000-2200002i2i−2i−2i0000-22000000−2i2i000000000000
χ3922-2-2-2-222i2i−2i−2i2-220000-2-2220000−2i2i00002-20000−2i−2i2i2i002-2002i−2i000000000000000000
χ4022-2-2-2-222i2i−2i−2i2-220000-2-2220000−2i2i00002-20000−2i−2i2i2i00-2200−2i2i000000000000000000
χ4122-2-2-2-22−2i−2i2i2i2-22000022-2-200002i−2i0000-220000−2i−2i2i2i00002-2000000−2i2i000000000000
χ4222-2-2-2-22−2i−2i2i2i2-22000022-2-200002i−2i0000-220000−2i−2i2i2i0000-220000002i−2i000000000000
χ4322-2-2-2-22−2i−2i2i2i2-220000-2-22200002i−2i00002-200002i2i−2i−2i002-200−2i2i000000000000000000
χ4422-2-2-2-22−2i−2i2i2i2-220000-2-22200002i−2i00002-200002i2i−2i−2i00-22002i−2i000000000000000000
χ4544444-4-400004-4-4000044440000000000-4-40000000000000000000000000000000000
χ4644444-4-400004-4-40000-4-4-4-40000000000440000000000000000000000000000000000
χ474444-44-44444-4-44000000000000-4-40000000000000000000000000000000000000000
χ484444-44-4-4-4-4-4-4-44000000000000440000000000000000000000000000000000000000
χ494444-4-440000-44-44444000000000000000000000000-4-4000000000000000000000000
χ504444-4-440000-44-4-4-4-4-400000000000000000000000044000000000000000000000000
χ5144-4-44440000-4-4-40000000044-4-4000000000000000000000000000000000000000000
χ5244-4-44440000-4-4-400000000-4-444000000000000000000000000000000000000000000
χ534-44i−4i0002+2i−2−2i2−2i−2+2i0002i2−2i222−222i2−2i222−222-22i−2i002-22i−2i002ζ3−2ζ32ζ−2ζ2ζ3−2ζ32ζ−2ζ00000000000000000000000000
χ544-44i−4i0002+2i−2−2i2−2i−2+2i0002i2−2i222−22−2i22i2−2222-22−2i2i00-22−2i2i002ζ3−2ζ32ζ−2ζ−2ζ32ζ3−2ζ2ζ00000000000000000000000000
χ554-44i−4i0002+2i−2−2i2−2i−2+2i000−2i22i2−22222i2−2i222−22-22−2i2i00-22−2i2i00−2ζ32ζ3−2ζ2ζ2ζ3−2ζ32ζ−2ζ00000000000000000000000000
χ564-44i−4i0002+2i−2−2i2−2i−2+2i000−2i22i2−2222−2i22i2−22222-22i−2i002-22i−2i00−2ζ32ζ3−2ζ2ζ−2ζ32ζ3−2ζ2ζ00000000000000000000000000
χ574-44i−4i000−2−2i2+2i−2+2i2−2i0002i2−2i222−222i2−2i222−22-22−2i2i002-22i−2i00−2ζ32ζ3−2ζ2ζ−2ζ32ζ3−2ζ2ζ00000000000000000000000000
χ584-44i−4i000−2−2i2+2i−2+2i2−2i0002i2−2i222−22−2i22i2−22222-22i−2i00-22−2i2i00−2ζ32ζ3−2ζ2ζ2ζ3−2ζ32ζ−2ζ00000000000000000000000000
χ594-44i−4i000−2−2i2+2i−2+2i2−2i000−2i22i2−22222i2−2i222−222-22i−2i00-22−2i2i002ζ3−2ζ32ζ−2ζ−2ζ32ζ3−2ζ2ζ00000000000000000000000000
χ604-44i−4i000−2−2i2+2i−2+2i2−2i000−2i22i2−2222−2i22i2−2222-22−2i2i002-22i−2i002ζ3−2ζ32ζ−2ζ2ζ3−2ζ32ζ−2ζ00000000000000000000000000
χ614-4−4i4i0002−2i−2+2i2+2i−2−2i0002i2−2i2−22222i2−2i2−22222-2−2i2i002-2−2i2i002ζ−2ζ2ζ3−2ζ32ζ−2ζ2ζ3−2ζ300000000000000000000000000
χ624-4−4i4i0002−2i−2+2i2+2i−2−2i0002i2−2i2−2222−2i22i222−22-222i−2i00-222i−2i002ζ−2ζ2ζ3−2ζ3−2ζ2ζ−2ζ32ζ300000000000000000000000000
χ634-4−4i4i0002−2i−2+2i2+2i−2−2i000−2i22i222−222i2−2i2−2222-222i−2i00-222i−2i00−2ζ2ζ−2ζ32ζ32ζ−2ζ2ζ3−2ζ300000000000000000000000000
χ644-4−4i4i0002−2i−2+2i2+2i−2−2i000−2i22i222−22−2i22i222−222-2−2i2i002-2−2i2i00−2ζ2ζ−2ζ32ζ3−2ζ2ζ−2ζ32ζ300000000000000000000000000
χ654-4−4i4i000−2+2i2−2i−2−2i2+2i0002i2−2i2−22222i2−2i2−2222-222i−2i002-2−2i2i00−2ζ2ζ−2ζ32ζ3−2ζ2ζ−2ζ32ζ300000000000000000000000000
χ664-4−4i4i000−2+2i2−2i−2−2i2+2i0002i2−2i2−2222−2i22i222−222-2−2i2i00-222i−2i00−2ζ2ζ−2ζ32ζ32ζ−2ζ2ζ3−2ζ300000000000000000000000000
χ674-4−4i4i000−2+2i2−2i−2−2i2+2i000−2i22i222−222i2−2i2−22222-2−2i2i00-222i−2i002ζ−2ζ2ζ3−2ζ3−2ζ2ζ−2ζ32ζ300000000000000000000000000
χ684-4−4i4i000−2+2i2−2i−2−2i2+2i000−2i22i222−22−2i22i222−22-222i−2i002-2−2i2i002ζ−2ζ2ζ3−2ζ32ζ−2ζ2ζ3−2ζ300000000000000000000000000

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