Finite Group Databasebeta

← Group #507767

Character table — Group #507767

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11112222224444444444444444888888161616161616161616161616161616161616161616161616
order1244222444444488888888888844448824444444888888881616161616161616
χ111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-1-1-111-1-11111-1-1-1-1
χ611111111111111-1-1-1-111111111-1-1-1-1-1-11111-1-111-1-1-1-1-1-111-1-1-1-11111
χ711111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-11111
χ811111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1111111-1-1-1-1
χ91111111111-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-111-1-1-1-111-1-11111-1-111-1-1
χ101111111111-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-1-1-111-1-11111-1-1-1-111-1-111
χ111111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-11111-1-111-1-1-1-111-1-111-1-111
χ121111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-111-1-11111-1-111-1-111-1-111-1-1
χ131111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1111111-1-1-1-1-1-111-1-1-1-111
χ141111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-111-1-11111-1-11111-1-1
χ151111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1111111-1-111-1-1-1-1-1-11111-1-1
χ161111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-111-1-1-1-1-1-111111111-1-1-1-111
χ17222222222222222222-2-2-2-2-2-2-2-2-2-2-2-222000000000000000000000000
χ1822222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2000000000000000000000000
χ192222222222-2-2-2-222222222-2-2-2-2-2-222-2-2000000000000000000000000
χ202222222222-2-2-2-2-2-2-2-22222-2-2-2-222-2-222000000000000000000000000
χ212222-22-2-22-222-2-222-2-20000000000002-20000000000000000i2−i2i2−i2i2−i2i2−i2
χ222222-22-2-22-222-2-222-2-20000000000002-20000000000000000−i2i2−i2i2−i2i2−i2i2
χ232222-22-2-22-222-2-2-2-222000000000000-220000000000000000i2−i2i2−i2−i2i2−i2i2
χ242222-22-2-22-222-2-2-2-222000000000000-220000000000000000−i2i2−i2i2i2−i2i2−i2
χ252222-22-2-22-2-2-22222-2-2000000000000-220000000000000000i2−i2−i2i2i2−i2−i2i2
χ262222-22-2-22-2-2-22222-2-2000000000000-220000000000000000−i2i2i2−i2−i2i2i2−i2
χ272222-22-2-22-2-2-222-2-2220000000000002-20000000000000000i2−i2−i2i2−i2i2i2−i2
χ282222-22-2-22-2-2-222-2-2220000000000002-20000000000000000−i2i2i2−i2i2−i2−i2i2
χ2922-2-2-22-22-2200002i−2i2i−2i000022-2-22i−2i0000002-200002i−2i00000000000000
χ3022-2-2-22-22-2200002i−2i2i−2i000022-2-22i−2i000000-220000−2i2i00000000000000
χ3122-2-2-22-22-2200002i−2i2i−2i0000-2-222−2i2i00002-2000000002i−2i000000000000
χ3222-2-2-22-22-2200002i−2i2i−2i0000-2-222−2i2i0000-2200000000−2i2i000000000000
χ3322-2-2-22-22-220000−2i2i−2i2i000022-2-2−2i2i0000002-20000−2i2i00000000000000
χ3422-2-2-22-22-220000−2i2i−2i2i000022-2-2−2i2i000000-2200002i−2i00000000000000
χ3522-2-2-22-22-220000−2i2i−2i2i0000-2-2222i−2i00002-200000000−2i2i000000000000
χ3622-2-2-22-22-220000−2i2i−2i2i0000-2-2222i−2i0000-22000000002i−2i000000000000
χ3722-2-2-2-2222-22i−2i2i−2i00002i2i−2i−2i2-22-20000000000002-20000002i−2i00000000
χ3822-2-2-2-2222-22i−2i2i−2i00002i2i−2i−2i2-22-2000000000000-22000000−2i2i00000000
χ3922-2-2-2-2222-22i−2i2i−2i0000−2i−2i2i2i-22-2200000000002-20000002i−2i0000000000
χ4022-2-2-2-2222-22i−2i2i−2i0000−2i−2i2i2i-22-220000000000-22000000−2i2i0000000000
χ4122-2-2-2-2222-2−2i2i−2i2i00002i2i−2i−2i-22-2200000000002-2000000−2i2i0000000000
χ4222-2-2-2-2222-2−2i2i−2i2i00002i2i−2i−2i-22-220000000000-220000002i−2i0000000000
χ4322-2-2-2-2222-2−2i2i−2i2i0000−2i−2i2i2i2-22-20000000000002-2000000−2i2i00000000
χ4422-2-2-2-2222-2−2i2i−2i2i0000−2i−2i2i2i2-22-2000000000000-220000002i−2i00000000
χ4544444-4-44-4-40000000000004-4-44000000000000000000000000000000
χ4644444-4-44-4-4000000000000-444-4000000000000000000000000000000
χ474444-4-44-4-440000000000000000004-400000000000000000000000000
χ484444-4-44-4-44000000000000000000-4400000000000000000000000000
χ4944-4-4444-4-4-400004i−4i−4i4i00000000000000000000000000000000000000
χ5044-4-4444-4-4-40000−4i4i4i−4i00000000000000000000000000000000000000
χ5144-4-44-4-4-4444i−4i−4i4i000000000000000000000000000000000000000000
χ5244-4-44-4-4-444−4i4i4i−4i000000000000000000000000000000000000000000
χ538-88i−8i000000000000004ζ−4ζ4ζ3−4ζ30000000000000000000000000000000000
χ548-88i−8i00000000000000−4ζ4ζ−4ζ34ζ30000000000000000000000000000000000
χ558-8−8i8i000000000000004ζ3−4ζ34ζ−4ζ0000000000000000000000000000000000
χ568-8−8i8i00000000000000−4ζ34ζ3−4ζ4ζ0000000000000000000000000000000000

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