Finite Group Databasebeta

← Group #123773

Character table — Group #123773

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size11111111222222222222222222222222222288888888888888888888888888888888888888888888888888888888
order12222222222222222222444444444444444444444444444444444444444488888888888888888888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111
χ5111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ6111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1
χ9111-1-1-11-111111-1-1-1-1-11-1111111-1-1-1-1-1-111-1-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i1111-1-1-1-1
χ10111-1-1-11-111111-1-1-1-1-11-1111111-1-1-1-1-1-111-1-1iiii−i−i−i−i1111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii-1-1-1-11111
χ11111-1-1-11-111111-1-1-1-1-11-1111111-1-1-1-1-1-111-1-1iiii−i−i−i−i-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii-1-1-1-11111
χ12111-1-1-11-111111-1-1-1-1-11-1111111-1-1-1-1-1-111-1-1iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i1111-1-1-1-1
χ13111-1-1-11-111111-1-1-1-1-11-1111111-1-1-1-1-1-111-1-1−i−i−i−iiiii1111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i-1-1-1-11111
χ14111-1-1-11-111111-1-1-1-1-11-1111111-1-1-1-1-1-111-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii1111-1-1-1-1
χ15111-1-1-11-111111-1-1-1-1-11-1111111-1-1-1-1-1-111-1-1−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii1111-1-1-1-1
χ16111-1-1-11-111111-1-1-1-1-11-1111111-1-1-1-1-1-111-1-1−i−i−i−iiiii-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i-1-1-1-11111
χ171-1-111-11-1111-1-111-1-1-1-11111-1-1-1111-1-1-11-11-1ii−i−iii−i−iii−i−iii−i−i11-1-111-1-111-1-111-1-1ii−i−iii−i−iii−i−iii−i−i11-1-111-1-1
χ181-1-111-11-1111-1-111-1-1-1-11111-1-1-1111-1-1-11-11-1ii−i−iii−i−iii−i−iii−i−i-1-111-1-11111-1-111-1-1−i−iii−i−iii−i−iii−i−iii-1-111-1-111
χ191-1-111-11-1111-1-111-1-1-1-11111-1-1-1111-1-1-11-11-1ii−i−iii−i−i−i−iii−i−iii11-1-111-1-1-1-111-1-111ii−i−iii−i−i−i−iii−i−iii-1-111-1-111
χ201-1-111-11-1111-1-111-1-1-1-11111-1-1-1111-1-1-11-11-1ii−i−iii−i−i−i−iii−i−iii-1-111-1-111-1-111-1-111−i−iii−i−iiiii−i−iii−i−i11-1-111-1-1
χ211-1-111-11-1111-1-111-1-1-1-11111-1-1-1111-1-1-11-11-1−i−iii−i−iiiii−i−iii−i−i11-1-111-1-1-1-111-1-111−i−iii−i−iiiii−i−iii−i−i-1-111-1-111
χ221-1-111-11-1111-1-111-1-1-1-11111-1-1-1111-1-1-11-11-1−i−iii−i−iiiii−i−iii−i−i-1-111-1-111-1-111-1-111ii−i−iii−i−i−i−iii−i−iii11-1-111-1-1
χ231-1-111-11-1111-1-111-1-1-1-11111-1-1-1111-1-1-11-11-1−i−iii−i−iii−i−iii−i−iii11-1-111-1-111-1-111-1-1−i−iii−i−iii−i−iii−i−iii11-1-111-1-1
χ241-1-111-11-1111-1-111-1-1-1-11111-1-1-1111-1-1-11-11-1−i−iii−i−iii−i−iii−i−iii-1-111-1-11111-1-111-1-1ii−i−iii−i−iii−i−iii−i−i-1-111-1-111
χ251-1-1-1-1111111-1-1-1-1111-1-1111-1-1-1-1-1-11111-1-1111-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii−i−iiiii−i−i−i−iiiii−i−i-1-11111-1-1-1-11111-1-1
χ261-1-1-1-1111111-1-1-1-1111-1-1111-1-1-1-1-1-11111-1-1111-1-1-1-111ii−i−i−i−iii−i−iiiii−i−i−i−iiiii−i−iii−i−i−i−iii11-1-1-1-11111-1-1-1-111
χ271-1-1-1-1111111-1-1-1-1111-1-1111-1-1-1-1-1-11111-1-1111-1-1-1-111−i−iiiii−i−iii−i−i−i−iiiii−i−i−i−iii−i−iiiii−i−i11-1-1-1-11111-1-1-1-111
χ281-1-1-1-1111111-1-1-1-1111-1-1111-1-1-1-1-1-11111-1-1111-1-1-1-111−i−iiiii−i−i−i−iiiii−i−iii−i−i−i−iiiii−i−i−i−iii-1-11111-1-1-1-11111-1-1
χ291-1-1-1-1111111-1-1-1-1111-1-1111-1-1-1-1-1-11111-1-11-1-11111-1-1ii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iii-1-11111-1-111-1-1-1-111
χ301-1-1-1-1111111-1-1-1-1111-1-1111-1-1-1-1-1-11111-1-11-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−iii−i−i−i−iii−i−iiiii−i−i11-1-1-1-111-1-11111-1-1
χ311-1-1-1-1111111-1-1-1-1111-1-1111-1-1-1-1-1-11111-1-11-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii−i−iiiii−i−iii−i−i−i−iii11-1-1-1-111-1-11111-1-1
χ321-1-1-1-1111111-1-1-1-1111-1-1111-1-1-1-1-1-11111-1-11-1-11111-1-1−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i-1-11111-1-111-1-1-1-111
χ3322222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000000000000000000000002i−2i2i−2i2i−2i2i−2i
χ3422222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000000000−2i2i−2i2i−2i2i−2i2i
χ35222222222-2-22-22-22-2-2-2-222-222-22-2-22-2-2-2-22200000000000000002i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000
χ36222222222-2-22-22-22-2-2-2-222-222-22-2-22-2-2-2-2220000000000000000−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000
χ37222222222-2-22-22-22-2-2-2-2-2-22-2-22-222-22222-2-20000000000000000000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ38222222222-2-22-22-22-2-2-2-2-2-22-2-22-222-22222-2-2000000000000000000000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ3922222222-22-2-22-2-2-22-2-222-222-2-2-22-2-22-2-2222000000000000000000000000000000002-22-22-22-20000000000000000
χ4022222222-22-2-22-2-2-22-2-222-222-2-2-22-2-22-2-222200000000000000000000000000000000-22-22-22-220000000000000000
χ4122222222-22-2-22-2-2-22-2-22-22-2-2222-222-222-2-2-2000000002i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000000000
χ4222222222-22-2-22-2-2-22-2-22-22-2-2222-222-222-2-2-200000000−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000000000000
χ4322222222-2-22-2-2-22-2-222-22-2-22-22-2-22-2-222-2222-22-22-22-2000000000000000000000000000000000000000000000000
χ4422222222-2-22-2-2-22-2-222-22-2-22-22-2-22-2-222-222-22-22-22-22000000000000000000000000000000000000000000000000
χ4522222222-2-22-2-2-22-2-222-2-222-22-222-222-2-22-2-200000000000000000000000000000000000000002i−2i2i−2i2i−2i2i−2i00000000
χ4622222222-2-22-2-2-22-2-222-2-222-22-222-222-2-22-2-20000000000000000000000000000000000000000−2i2i−2i2i−2i2i−2i2i00000000
χ47222-2-2-22-222222-2-2-2-2-22-2-2-2-2-2-2-2222222-2-2220000000000000000000000000000000000000000000000002i−2i2i−2i−2i2i−2i2i
χ48222-2-2-22-222222-2-2-2-2-22-2-2-2-2-2-2-2222222-2-222000000000000000000000000000000000000000000000000−2i2i−2i2i2i−2i2i−2i
χ49222-2-2-22-22-2-22-2-22-222-2222-222-2-222-222-2-2-2-200000000000000002-22-2-22-2200000000000000000000000000000000
χ50222-2-2-22-22-2-22-2-22-222-2222-222-2-222-222-2-2-2-20000000000000000-22-222-22-200000000000000000000000000000000
χ51222-2-2-22-22-2-22-2-22-222-22-2-22-2-222-2-22-2-222220000000000000000000000002-22-2-22-22000000000000000000000000
χ52222-2-2-22-22-2-22-2-22-222-22-2-22-2-222-2-22-2-22222000000000000000000000000-22-222-22-2000000000000000000000000
χ53222-2-2-22-2-22-2-22222-22-2-22-222-2-22-222-22-22-2-2000000000000000000000000000000002-22-2-22-220000000000000000
χ54222-2-2-22-2-22-2-22222-22-2-22-222-2-22-222-22-22-2-200000000000000000000000000000000-22-222-22-20000000000000000
χ55222-2-2-22-2-22-2-22222-22-2-2-22-2-222-22-2-22-22-222000000002i−2i2i−2i−2i2i−2i2i0000000000000000000000000000000000000000
χ56222-2-2-22-2-22-2-22222-22-2-2-22-2-222-22-2-22-22-22200000000−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000000000000000
χ57222-2-2-22-2-2-22-2-22-222-2222-2-22-2222-222-22-2-2-22i−2i2i−2i−2i2i−2i2i000000000000000000000000000000000000000000000000
χ58222-2-2-22-2-2-22-2-22-222-2222-2-22-2222-222-22-2-2-2−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000000000000000000000
χ59222-2-2-22-2-2-22-2-22-222-222-222-22-2-2-22-2-22-222200000000000000000000000000000000000000002-22-2-22-2200000000
χ60222-2-2-22-2-2-22-2-22-222-222-222-22-2-2-22-2-22-22220000000000000000000000000000000000000000-22-222-22-200000000
χ612-2-222-22-2222-2-222-2-2-2-22-2-2-2222-2-2-2222-22-220000000000000000000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i
χ622-2-222-22-2222-2-222-2-2-2-22-2-2-2222-2-2-2222-22-22000000000000000000000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i
χ632-2-222-22-22-2-2-222-2-2222-222-2-2-222-2-2-222-222-200000000000000002i−2i−2i2i2i−2i−2i2i00000000000000000000000000000000
χ642-2-222-22-22-2-2-222-2-2222-222-2-2-222-2-2-222-222-20000000000000000−2i2i2i−2i−2i2i2i−2i00000000000000000000000000000000
χ652-2-222-22-22-2-2-222-2-2222-2-2-2222-2-2222-2-22-2-220000000000000000000000002i−2i−2i2i2i−2i−2i2i000000000000000000000000
χ662-2-222-22-22-2-2-222-2-2222-2-2-2222-2-2222-2-22-2-22000000000000000000000000−2i2i2i−2i−2i2i2i−2i000000000000000000000000
χ672-2-222-22-2-22-22-2-2-22-22222-22-222-22-22-22-2-22-2000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ682-2-222-22-2-22-22-2-2-22-22222-22-222-22-22-22-2-22-200000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ692-2-222-22-2-22-22-2-2-22-2222-22-22-2-22-22-22-222-22000000002-2-222-2-220000000000000000000000000000000000000000
χ702-2-222-22-2-22-22-2-2-22-2222-22-22-2-22-22-22-222-2200000000-222-2-222-20000000000000000000000000000000000000000
χ712-2-222-22-2-2-2222-2222-2-2-22-2-2-22-2-2-2222-2222-22i−2i−2i2i2i−2i−2i2i000000000000000000000000000000000000000000000000
χ722-2-222-22-2-2-2222-2222-2-2-22-2-2-22-2-2-2222-2222-2−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000000000000000000000
χ732-2-222-22-2-2-2222-2222-2-2-2-2222-2222-2-2-22-2-2-2200000000000000000000000000000000000000002-2-222-2-2200000000
χ742-2-222-22-2-2-2222-2222-2-2-2-2222-2222-2-2-22-2-2-220000000000000000000000000000000000000000-222-2-222-200000000
χ752-2-2-2-2222222-2-2-2-2222-2-2-2-2-2222222-2-2-2-222-20000000000000000000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i
χ762-2-2-2-2222222-2-2-2-2222-2-2-2-2-2222222-2-2-2-222-2000000000000000000000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i
χ772-2-2-2-22222-2-2-22-222-2-22222-2-2-22-2222-2-2-22-2200000000000000002-2-22-222-200000000000000000000000000000000
χ782-2-2-2-22222-2-2-22-222-2-22222-2-2-22-2222-2-2-22-220000000000000000-222-22-2-2200000000000000000000000000000000
χ792-2-2-2-22222-2-2-22-222-2-222-2-2222-22-2-2-2222-22-20000000000000000000000002-2-22-222-2000000000000000000000000
χ802-2-2-2-22222-2-2-22-222-2-222-2-2222-22-2-2-2222-22-2000000000000000000000000-222-22-2-22000000000000000000000000
χ812-2-2-2-2222-22-22-222-22-22-22-22-2222-22-22-2-2-2-22000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ822-2-2-2-2222-22-22-222-22-22-22-22-2222-22-22-2-2-2-2200000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ832-2-2-2-2222-22-22-222-22-22-2-22-22-2-2-22-22-22222-2000000002-2-22-222-20000000000000000000000000000000000000000
χ842-2-2-2-2222-22-22-222-22-22-2-22-22-2-2-22-22-22222-200000000-222-22-2-220000000000000000000000000000000000000000
χ852-2-2-2-2222-2-22222-2-2-22-222-2-2-22-222-2-2-2222-222-2-22-222-2000000000000000000000000000000000000000000000000
χ862-2-2-2-2222-2-22222-2-2-22-222-2-2-22-222-2-2-2222-22-222-22-2-22000000000000000000000000000000000000000000000000
χ872-2-2-2-2222-2-22222-2-2-22-22-2222-22-2-2222-2-2-22-200000000000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i00000000
χ882-2-2-2-2222-2-22222-2-2-22-22-2222-22-2-2222-2-2-22-20000000000000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i00000000
χ8988-88-88-8-8000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9088-8-88-8-88000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ918-888-8-8-88000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ928-88-888-8-8000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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