Finite Group Databasebeta

← Group #357490

Character table — Group #357490

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size11111111222222222222222222222222222288888888888888888888888888888888888888888888888888888888
order12222222222222222222444444444444444422222222444444444444444444444444444444448888888888888888
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
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ6111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111
χ911111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1-1-11111-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ1011111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ1111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ1211111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ1311111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ1411111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ1511111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-111-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ1611111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-111-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ171-1-1-111-1111-11111-1-1-1-1-11111-1-11111-1-1-1-1-1-11-11-11-11-111-1-111-1-1ii−i−iii−i−i1-11-11-11-1ii−i−iii−i−iii−i−iii−i−iii−i−iii−i−i
χ181-1-1-111-1111-11111-1-1-1-1-11111-1-11111-1-1-1-1-1-11-11-11-11-111-1-111-1-1−i−iii−i−iii1-11-11-11-1−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii
χ191-1-1-111-1111-11111-1-1-1-1-11111-1-11111-1-1-1-1-1-11-11-1-11-11-1-111-1-111ii−i−iii−i−i1-11-1-11-11−i−iii−i−iiiii−i−iii−i−i−i−iii−i−iii
χ201-1-1-111-1111-11111-1-1-1-1-11111-1-11111-1-1-1-1-1-11-11-1-11-11-1-111-1-111−i−iii−i−iii1-11-1-11-11ii−i−iii−i−i−i−iii−i−iiiii−i−iii−i−i
χ211-1-1-111-1111-11111-1-1-1-1-11111-1-11111-1-1-1-1-1-1-11-111-11-1-1-111-1-111ii−i−iii−i−i-11-111-11-1−i−iii−i−iii−i−iii−i−iiiii−i−iii−i−i
χ221-1-1-111-1111-11111-1-1-1-1-11111-1-11111-1-1-1-1-1-1-11-111-11-1-1-111-1-111−i−iii−i−iii-11-111-11-1ii−i−iii−i−iii−i−iii−i−i−i−iii−i−iii
χ231-1-1-111-1111-11111-1-1-1-1-11111-1-11111-1-1-1-1-1-1-11-11-11-1111-1-111-1-1ii−i−iii−i−i-11-11-11-11ii−i−iii−i−i−i−iii−i−iii−i−iii−i−iii
χ241-1-1-111-1111-11111-1-1-1-1-11111-1-11111-1-1-1-1-1-1-11-11-11-1111-1-111-1-1−i−iii−i−iii-11-11-11-11−i−iii−i−iiiii−i−iii−i−iii−i−iii−i−i
χ251-1-1-111-1111-1-1-1-1-11111-11111-1-1-1-1-1-11111-1-11-1-111-1-1111-1-1-1-111ii−i−i−i−iii1-1-111-1-11ii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iii
χ261-1-1-111-1111-1-1-1-1-11111-11111-1-1-1-1-1-11111-1-11-1-111-1-1111-1-1-1-111−i−iiiii−i−i1-1-111-1-11−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i
χ271-1-1-111-1111-1-1-1-1-11111-11111-1-1-1-1-1-11111-1-11-1-11-111-1-1-11111-1-1ii−i−i−i−iii1-1-11-111-1−i−iiiii−i−iii−i−i−i−iii−i−iiiii−i−i
χ281-1-1-111-1111-1-1-1-1-11111-11111-1-1-1-1-1-11111-1-11-1-11-111-1-1-11111-1-1−i−iiiii−i−i1-1-11-111-1ii−i−i−i−iii−i−iiiii−i−iii−i−i−i−iii
χ291-1-1-111-1111-1-1-1-1-11111-11111-1-1-1-1-1-11111-1-1-111-11-1-11-1-11111-1-1ii−i−i−i−iii-111-11-1-11−i−iiiii−i−i−i−iiiii−i−iii−i−i−i−iii
χ301-1-1-111-1111-1-1-1-1-11111-11111-1-1-1-1-1-11111-1-1-111-11-1-11-1-11111-1-1−i−iiiii−i−i-111-11-1-11ii−i−i−i−iiiii−i−i−i−iii−i−iiiii−i−i
χ311-1-1-111-1111-1-1-1-1-11111-11111-1-1-1-1-1-11111-1-1-111-1-111-111-1-1-1-111ii−i−i−i−iii-111-1-111-1ii−i−i−i−iii−i−iiiii−i−i−i−iiiii−i−i
χ321-1-1-111-1111-1-1-1-1-11111-11111-1-1-1-1-1-11111-1-1-111-1-111-111-1-1-1-111−i−iiiii−i−i-111-1-111-1−i−iiiii−i−iii−i−i−i−iiiii−i−i−i−iii
χ3322222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000002-22-22-22-20000000000000000000000000000000000000000
χ3422222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000-22-22-22-220000000000000000000000000000000000000000
χ3522222222222-2-2-2-2-2-2-2-22-2-2-2-2-2-222222222-2-2000000002-22-2-22-220000000000000000000000000000000000000000
χ3622222222222-2-2-2-2-2-2-2-22-2-2-2-2-2-222222222-2-200000000-22-222-22-20000000000000000000000000000000000000000
χ3722222222-2-2-222-2-222-2-2-222-2-22-222-2-222-2-22-20000222200000000000000000000-2-2-2-2000000000000000000000000
χ3822222222-2-2-222-2-222-2-2-222-2-22-222-2-222-2-22-20000-2-2-2-2000000000000000000002222000000000000000000000000
χ3922222222-2-2-222-2-222-2-2-2-2-222-22-2-222-2-222-2222-2-200000000000000000000-2-2220000000000000000000000000000
χ4022222222-2-2-222-2-222-2-2-2-2-222-22-2-222-2-222-22-2-2220000000000000000000022-2-20000000000000000000000000000
χ4122222222-2-2-2-2-222-2-222-222-2-22-2-2-222-2-2222-2000022-2-200000000000000000000-2-222000000000000000000000000
χ4222222222-2-2-2-2-222-2-222-222-2-22-2-2-222-2-2222-20000-2-2220000000000000000000022-2-2000000000000000000000000
χ4322222222-2-2-2-2-222-2-222-2-2-222-2222-2-222-2-2-22222200000000000000000000-2-2-2-20000000000000000000000000000
χ4422222222-2-2-2-2-222-2-222-2-2-222-2222-2-222-2-2-22-2-2-2-20000000000000000000022220000000000000000000000000000
χ45222-2-2-2-222-222-22-22-22-2-22-22-22-22-22-22-22-2-220000000000000000000000000000000000000000000000002i−2i2i−2i2i−2i2i−2i
χ46222-2-2-2-222-222-22-22-22-2-22-22-22-22-22-22-22-2-22000000000000000000000000000000000000000000000000−2i2i−2i2i−2i2i−2i2i
χ47222-2-2-2-222-222-22-22-22-2-2-22-22-22-22-22-22-222-200000000000000000000000000000000000000002i−2i2i−2i2i−2i2i−2i00000000
χ48222-2-2-2-222-222-22-22-22-2-2-22-22-22-22-22-22-222-20000000000000000000000000000000000000000−2i2i−2i2i−2i2i−2i2i00000000
χ49222-2-2-2-222-22-22-22-22-22-22-22-22-2-22-22-22-22-220000000000000000000000000000000000000000000000002i−2i2i−2i−2i2i−2i2i
χ50222-2-2-2-222-22-22-22-22-22-22-22-22-2-22-22-22-22-22000000000000000000000000000000000000000000000000−2i2i−2i2i2i−2i2i−2i
χ51222-2-2-2-222-22-22-22-22-22-2-22-22-222-22-22-22-22-200000000000000000000000000000000000000002i−2i2i−2i−2i2i−2i2i00000000
χ52222-2-2-2-222-22-22-22-22-22-2-22-22-222-22-22-22-22-20000000000000000000000000000000000000000−2i2i−2i2i2i−2i2i−2i00000000
χ53222-2-2-2-22-22-22-2-222-2-2222-2-22222-2-222-2-22-2-200000000000000002i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000
χ54222-2-2-2-22-22-22-2-222-2-2222-2-22222-2-222-2-22-2-20000000000000000−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000
χ55222-2-2-2-22-22-22-2-222-2-222-222-2-2-2-222-2-222-222000000000000000000000000000000002-22-22-22-20000000000000000
χ56222-2-2-2-22-22-22-2-222-2-222-222-2-2-2-222-2-222-22200000000000000000000000000000000-22-22-22-220000000000000000
χ57222-2-2-2-22-22-2-222-2-222-222-2-2222-222-2-222-2-2-200000000000000002i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000
χ58222-2-2-2-22-22-2-222-2-222-222-2-2222-222-2-222-2-2-20000000000000000−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000
χ59222-2-2-2-22-22-2-222-2-222-22-222-2-2-22-2-222-2-2222000000000000000000000000000000002-22-2-22-220000000000000000
χ60222-2-2-2-22-22-2-222-2-222-22-222-2-2-22-2-222-2-222200000000000000000000000000000000-22-222-22-20000000000000000
χ612-2-22-2-2222-2-22-22-2-22-2222-22-2-222-22-2-22-222-20000000000000000000000000000000000000000000000002-2-222-2-22
χ622-2-22-2-2222-2-22-22-2-22-2222-22-2-222-22-2-22-222-2000000000000000000000000000000000000000000000000-222-2-222-2
χ632-2-22-2-2222-2-22-22-2-22-222-22-222-2-22-222-22-2-2200000000000000000000000000000000000000002-2-222-2-2200000000
χ642-2-22-2-2222-2-22-22-2-22-222-22-222-2-22-222-22-2-220000000000000000000000000000000000000000-222-2-222-200000000
χ652-2-22-2-2222-2-2-22-222-22-222-22-2-22-22-222-22-22-20000000000000000000000000000000000000000000000002-2-22-222-2
χ662-2-22-2-2222-2-2-22-222-22-222-22-2-22-22-222-22-22-2000000000000000000000000000000000000000000000000-222-22-2-22
χ672-2-22-2-2222-2-2-22-222-22-22-22-222-22-22-2-22-22-2200000000000000000000000000000000000000002-2-22-222-200000000
χ682-2-22-2-2222-2-2-22-222-22-22-22-222-22-22-2-22-22-220000000000000000000000000000000000000000-222-22-2-2200000000
χ692-2-22-2-222-2222-2-22-222-2-22-2-22-2-22-2-22-222-22200000000000000002-2-222-2-2200000000000000000000000000000000
χ702-2-22-2-222-2222-2-22-222-2-22-2-22-2-22-2-22-222-2220000000000000000-222-2-222-200000000000000000000000000000000
χ712-2-22-2-222-2222-2-22-222-2-2-222-222-222-22-2-22-2-2000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ722-2-22-2-222-2222-2-22-222-2-2-222-222-222-22-2-22-2-200000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ732-2-22-2-222-222-222-22-2-22-22-2-22-2-2-222-22-2-222200000000000000002-2-22-222-200000000000000000000000000000000
χ742-2-22-2-222-222-222-22-2-22-22-2-22-2-2-222-22-2-22220000000000000000-222-22-2-2200000000000000000000000000000000
χ752-2-22-2-222-222-222-22-2-22-2-222-2222-2-22-222-2-2-2000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ762-2-22-2-222-222-222-22-2-22-2-222-2222-2-22-222-2-2-200000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ772-2-2-222-2222-22222-2-2-2-2-2-2-2-2-222-2-2-2-2222222000000002-2-222-2-220000000000000000000000000000000000000000
χ782-2-2-222-2222-22222-2-2-2-2-2-2-2-2-222-2-2-2-222222200000000-222-2-222-20000000000000000000000000000000000000000
χ792-2-2-222-2222-2-2-2-2-22222-2-2-2-2-2222222-2-2-2-222000000002-2-22-222-20000000000000000000000000000000000000000
χ802-2-2-222-2222-2-2-2-2-22222-2-2-2-2-2222222-2-2-2-22200000000-222-22-2-220000000000000000000000000000000000000000
χ812-2-2-222-22-2-2222-2-2-2-222222-2-2-2222-2-2-2-222-2200002-22-200000000000000000000-22-22000000000000000000000000
χ822-2-2-222-22-2-2222-2-2-2-222222-2-2-2222-2-2-2-222-220000-22-22000000000000000000002-22-2000000000000000000000000
χ832-2-2-222-22-2-2222-2-2-2-2222-2-2222-2-2-22222-2-22-22-2-2200000000000000000000-222-20000000000000000000000000000
χ842-2-2-222-22-2-2222-2-2-2-2222-2-2222-2-2-22222-2-22-2-222-2000000000000000000002-2-220000000000000000000000000000
χ852-2-2-222-22-2-22-2-22222-2-2222-2-2-22-2-22222-2-2-2200002-2-2200000000000000000000-222-2000000000000000000000000
χ862-2-2-222-22-2-22-2-22222-2-2222-2-2-22-2-22222-2-2-220000-222-2000000000000000000002-2-22000000000000000000000000
χ872-2-2-222-22-2-22-2-22222-2-22-2-2222-222-2-2-2-2222-22-22-200000000000000000000-22-220000000000000000000000000000
χ882-2-2-222-22-2-22-2-22222-2-22-2-2222-222-2-2-2-2222-2-22-22000000000000000000002-22-20000000000000000000000000000
χ8988-888-8-8-8000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9088-8-8-888-8000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ918-888-88-8-8000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ928-88-88-88-8000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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