Finite Group Databasebeta

← Group #317099

Character table — Group #317099

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11111111222244444444444488888888161616161616161616161616161616161616161616161616
order12224444224444448888888844448888244444448888888888888888
χ111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-111-1-11111-1-1-1-1
χ611111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-11111-1-1-1-1-1-11111
χ711111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-111-1-1-1-11111
χ811111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-111-1-111-1-1111111-1-1-1-1
χ91111111111111111-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-111-1-1
χ101111111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-111-1-111-1-111
χ111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1111111-1-1-1-111-1-1-1-111-1-111
χ121111111111111111-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-1111111-1-111-1-111-1-1
χ131111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-1-1-111-1-1-1-111
χ141111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-1
χ151111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-11111-1-1
χ161111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-111
χ17222222222222-2-2-2-22222222222-2-2-2-2-2-2000000000000000000000000
χ18222222222222-2-2-2-22222-2-2-2-2-2-222-2-222000000000000000000000000
χ19222222222222-2-2-2-2-2-2-2-22222-2-22222-2-2000000000000000000000000
χ20222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-22222000000000000000000000000
χ212222-2-2-2-222-2-22-22-22i2i−2i−2i000000002i−2i00002-200000000002i−2i00000000
χ222222-2-2-2-222-2-22-22-22i2i−2i−2i000000002i−2i0000-220000000000−2i2i00000000
χ232222-2-2-2-222-2-22-22-2−2i−2i2i2i00000000−2i2i00002-20000000000−2i2i00000000
χ242222-2-2-2-222-2-22-22-2−2i−2i2i2i00000000−2i2i0000-2200000000002i−2i00000000
χ252222-2-2-2-222-2-2-22-222i2i−2i−2i00000000−2i2i002-200000000002i−2i0000000000
χ262222-2-2-2-222-2-2-22-222i2i−2i−2i00000000−2i2i00-220000000000−2i2i0000000000
χ272222-2-2-2-222-2-2-22-22−2i−2i2i2i000000002i−2i002-20000000000−2i2i0000000000
χ282222-2-2-2-222-2-2-22-22−2i−2i2i2i000000002i−2i00-2200000000002i−2i0000000000
χ292222-2-2-2-2-2-22222-2-2000022-2-20000002-2000000002i−2i2i−2i000000000000
χ302222-2-2-2-2-2-22222-2-2000022-2-20000002-200000000−2i2i−2i2i000000000000
χ312222-2-2-2-2-2-22222-2-20000-2-222000000-22000000002i−2i−2i2i000000000000
χ322222-2-2-2-2-2-22222-2-20000-2-222000000-2200000000−2i2i2i−2i000000000000
χ332222-2-2-2-2-2-222-2-222000022-2-2000000-2200002-22-20000000000000000
χ342222-2-2-2-2-2-222-2-222000022-2-2000000-220000-22-220000000000000000
χ352222-2-2-2-2-2-222-2-2220000-2-2220000002-200002-2-220000000000000000
χ362222-2-2-2-2-2-222-2-2220000-2-2220000002-20000-222-20000000000000000
χ3722-2-2-2-2222-22-200002i−2i2i−2i2-22-22i−2i0000000000000000000000i2−i22−2i2−i22−2
χ3822-2-2-2-2222-22-200002i−2i2i−2i2-22-22i−2i0000000000000000000000−i2i2−22−i2i2−22
χ3922-2-2-2-2222-22-200002i−2i2i−2i-22-22−2i2i0000000000000000000000i2−i22−2−i2i2−22
χ4022-2-2-2-2222-22-200002i−2i2i−2i-22-22−2i2i0000000000000000000000−i2i2−22i2−i22−2
χ4122-2-2-2-2222-22-20000−2i2i−2i2i2-22-2−2i2i0000000000000000000000i2−i2−22i2−i2−22
χ4222-2-2-2-2222-22-20000−2i2i−2i2i2-22-2−2i2i0000000000000000000000−i2i22−2−i2i22−2
χ4322-2-2-2-2222-22-20000−2i2i−2i2i-22-222i−2i0000000000000000000000i2−i2−22−i2i22−2
χ4422-2-2-2-2222-22-20000−2i2i−2i2i-22-222i−2i0000000000000000000000−i2i22−2i2−i2−22
χ4544444444-4-4-4-44-4-440000000000000000000000000000000000000000
χ4644444444-4-4-4-4-444-40000000000000000000000000000000000000000
χ4744-4-444-4-44-4-4400004-4-44000000000000000000000000000000000000
χ4844-4-444-4-44-4-440000-444-4000000000000000000000000000000000000
χ4944-4-444-4-4-444-4000000004-4-4400000000000000000000000000000000
χ5044-4-444-4-4-444-400000000-444-400000000000000000000000000000000
χ5144-4-4-4-444-44-44000000000000004i−4i0000000000000000000000000000
χ5244-4-4-4-444-44-4400000000000000−4i4i0000000000000000000000000000
χ538-88-88i−8i8i−8i000000000000000000000000000000000000000000000000
χ548-88-8−8i8i−8i8i000000000000000000000000000000000000000000000000
χ558-8-888i−8i−8i8i000000000000000000000000000000000000000000000000
χ568-8-88−8i8i8i−8i000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).