Finite Group Databasebeta

← Group #314995

Character table — Group #314995

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122224444444444444444888888888888881616161616161616161616161616161616161616
order12224444224444444444888888882444448888888844888888888888888888
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-1
χ611111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-1-1-11111
χ711111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111-1-1-1-11111
χ811111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1
χ911111111111111-1-1-1-11111111111-1-111111111-1-1-1-1-1-111-1-1-1-111-1-111-1-111-1-1
χ1011111111111111-1-1-1-11111111111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111
χ1111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111
χ1211111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-11111-1-111-1-1
χ1311111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-111
χ1411111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1111111-1-11111-1-1
χ1511111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-11111-1-1
χ1611111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-111-1-1-1-111
χ17222222222222-2-22222-2-22222-2-2-2-2-2-200000000-2-22200000000000000000000
χ18222222222222-2-22222-2-2-2-2-2-22222-2-20000000022-2-200000000000000000000
χ19222222222222-2-2-2-2-2-2-2-22222-2-2-2-2220000000022-2-200000000000000000000
χ20222222222222-2-2-2-2-2-2-2-2-2-2-2-222222200000000-2-22200000000000000000000
χ212222-2-2-2-222-2-22222-2-2-2-2000000002-222-2-2000000002-2000000000000000000
χ222222-2-2-2-222-2-22222-2-2-2-2000000002-2-2-22200000000-22000000000000000000
χ232222-2-2-2-222-2-222-2-222-2-200000000-2222-2-200000000-22000000000000000000
χ242222-2-2-2-222-2-222-2-222-2-200000000-22-2-222000000002-2000000000000000000
χ252222-2-2-2-222-2-2-2-222-2-22200000000-2200002i2i−2i−2i000000000000002i−2i00000000
χ262222-2-2-2-222-2-2-2-222-2-22200000000-220000−2i−2i2i2i00000000000000−2i2i00000000
χ272222-2-2-2-222-2-2-2-2-2-22222000000002-200002i2i−2i−2i00000000000000−2i2i00000000
χ282222-2-2-2-222-2-2-2-2-2-22222000000002-20000−2i−2i2i2i000000000000002i−2i00000000
χ292222-2-2-2-2-2-2222-200002-222-2-222-2-20000000000000000002i−2i2i−2i000000000000
χ302222-2-2-2-2-2-2222-200002-222-2-222-2-2000000000000000000−2i2i−2i2i000000000000
χ312222-2-2-2-2-2-2222-200002-2-2-222-2-2220000000000000000002i−2i−2i2i000000000000
χ322222-2-2-2-2-2-2222-200002-2-2-222-2-222000000000000000000−2i2i2i−2i000000000000
χ332222-2-2-2-2-2-222-220000-2222-2-2-2-22200000000000000002i−2i00002i−2i0000000000
χ342222-2-2-2-2-2-222-220000-2222-2-2-2-2220000000000000000−2i2i0000−2i2i0000000000
χ352222-2-2-2-2-2-222-220000-22-2-22222-2-200000000000000002i−2i0000−2i2i0000000000
χ362222-2-2-2-2-2-222-220000-22-2-22222-2-20000000000000000−2i2i00002i−2i0000000000
χ3722-2-222-2-2-22-22002i−2i2i−2i002i−2i2i−2i00000000000000002-20000000000002−2i2−i2i2−i22−2
χ3822-2-222-2-2-22-22002i−2i2i−2i002i−2i2i−2i00000000000000002-2000000000000−22−i2i2−i2i2−22
χ3922-2-222-2-2-22-22002i−2i2i−2i00−2i2i−2i2i0000000000000000-220000000000002−2i2−i2−i2i2−22
χ4022-2-222-2-2-22-22002i−2i2i−2i00−2i2i−2i2i0000000000000000-22000000000000−22−i2i2i2−i22−2
χ4122-2-222-2-2-22-2200−2i2i−2i2i002i−2i2i−2i0000000000000000-220000000000002−2−i2i2i2−i2−22
χ4222-2-222-2-2-22-2200−2i2i−2i2i002i−2i2i−2i0000000000000000-22000000000000−22i2−i2−i2i22−2
χ4322-2-222-2-2-22-2200−2i2i−2i2i00−2i2i−2i2i00000000000000002-20000000000002−2−i2i2−i2i22−2
χ4422-2-222-2-2-22-2200−2i2i−2i2i00−2i2i−2i2i00000000000000002-2000000000000−22i2−i2i2−i2−22
χ4544444444-4-4-4-44-40000-44000000000000000000000000000000000000000000
χ4644444444-4-4-4-4-4400004-4000000000000000000000000000000000000000000
χ4744-4-444-4-44-44-4000000000000000000000000004-40000000000000000000000
χ4844-4-444-4-44-44-400000000000000000000000000-440000000000000000000000
χ4944-4-4-4-4444-4-44000000004i−4i−4i4i00000000000000000000000000000000000000
χ5044-4-4-4-4444-4-4400000000−4i4i4i−4i00000000000000000000000000000000000000
χ5144-4-4-4-444-444-4004i−4i−4i4i00000000000000000000000000000000000000000000
χ5244-4-4-4-444-444-400−4i4i4i−4i00000000000000000000000000000000000000000000
χ534-44-44i−4i4i−4i00000000000000002i2−2i222−22002-22i−2i2ζ−2ζ2ζ3−2ζ3000000000000000000000000
χ544-44-44i−4i4i−4i00000000000000002i2−2i222−2200-22−2i2i−2ζ2ζ−2ζ32ζ3000000000000000000000000
χ554-44-44i−4i4i−4i0000000000000000−2i22i2−2222002-22i−2i−2ζ2ζ−2ζ32ζ3000000000000000000000000
χ564-44-44i−4i4i−4i0000000000000000−2i22i2−222200-22−2i2i2ζ−2ζ2ζ3−2ζ3000000000000000000000000
χ574-44-4−4i4i−4i4i00000000000000002i2−2i2−2222002-2−2i2i2ζ3−2ζ32ζ−2ζ000000000000000000000000
χ584-44-4−4i4i−4i4i00000000000000002i2−2i2−222200-222i−2i−2ζ32ζ3−2ζ2ζ000000000000000000000000
χ594-44-4−4i4i−4i4i0000000000000000−2i22i222−22002-2−2i2i−2ζ32ζ3−2ζ2ζ000000000000000000000000
χ604-44-4−4i4i−4i4i0000000000000000−2i22i222−2200-222i−2i2ζ3−2ζ32ζ−2ζ000000000000000000000000
χ618-8-888i−8i−8i8i000000000000000000000000000000000000000000000000000000
χ628-8-88−8i8i8i−8i000000000000000000000000000000000000000000000000000000

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