Finite Group Databasebeta

← Group #358185

Character table — Group #358185

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size11111111222222222222222222222222222288888888888888888888888888888888888888888888888888888888
order12222222222244444444444444444444444422444444444444444444444488888888888888888888888888888888
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
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111
χ5111111111111111111111111111111111111-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ6111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111
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
χ9111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ10111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ11111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ12111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ13111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ14111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ15111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-11111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ16111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-11111-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ171-1-11-1-11111-1-11111-1-1-1-1111111-1-1-1-111-1-1-1-11-11-1ii−i−iii−i−i1-11-111-1-111-1-1ii−i−iii−i−i11-1-111-1-1ii−i−iii−i−iii−i−iii−i−i
χ181-1-11-1-11111-1-11111-1-1-1-1111111-1-1-1-111-1-1-1-11-11-1ii−i−iii−i−i1-11-1-1-111-1-111ii−i−iii−i−i-1-111-1-111−i−iii−i−iii−i−iii−i−iii
χ191-1-11-1-11111-1-11111-1-1-1-1111111-1-1-1-111-1-1-1-11-11-1−i−iii−i−iii1-11-111-1-111-1-1−i−iii−i−iii11-1-111-1-1−i−iii−i−iii−i−iii−i−iii
χ201-1-11-1-11111-1-11111-1-1-1-1111111-1-1-1-111-1-1-1-11-11-1−i−iii−i−iii1-11-1-1-111-1-111−i−iii−i−iii-1-111-1-111ii−i−iii−i−iii−i−iii−i−i
χ211-1-11-1-11111-1-11111-1-1-1-1111111-1-1-1-111-1-1-1-1-11-11ii−i−iii−i−i-11-1111-1-111-1-1−i−iii−i−iii-1-111-1-111ii−i−iii−i−i−i−iii−i−iii
χ221-1-11-1-11111-1-11111-1-1-1-1111111-1-1-1-111-1-1-1-1-11-11ii−i−iii−i−i-11-11-1-111-1-111−i−iii−i−iii11-1-111-1-1−i−iii−i−iiiii−i−iii−i−i
χ231-1-11-1-11111-1-11111-1-1-1-1111111-1-1-1-111-1-1-1-1-11-11−i−iii−i−iii-11-1111-1-111-1-1ii−i−iii−i−i-1-111-1-111−i−iii−i−iiiii−i−iii−i−i
χ241-1-11-1-11111-1-11111-1-1-1-1111111-1-1-1-111-1-1-1-1-11-11−i−iii−i−iii-11-11-1-111-1-111ii−i−iii−i−i11-1-111-1-1ii−i−iii−i−i−i−iii−i−iii
χ251-1-11-1-11111-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-11-1-11ii−i−i−i−iii1-1-1111-1-1-1-111ii−i−i−i−iii11-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii
χ261-1-11-1-11111-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-11-1-11ii−i−i−i−iii1-1-11-1-11111-1-1ii−i−i−i−iii-1-11111-1-1−i−iiiii−i−i−i−iiiii−i−i
χ271-1-11-1-11111-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-11-1-11−i−iiiii−i−i1-1-1111-1-1-1-111−i−iiiii−i−i11-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i
χ281-1-11-1-11111-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-11-1-11−i−iiiii−i−i1-1-11-1-11111-1-1−i−iiiii−i−i-1-11111-1-1ii−i−i−i−iiiii−i−i−i−iii
χ291-1-11-1-11111-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-111-1ii−i−i−i−iii-111-111-1-1-1-111−i−iiiii−i−i-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ301-1-11-1-11111-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-111-1ii−i−i−i−iii-111-1-1-11111-1-1−i−iiiii−i−i11-1-1-1-111−i−iiiii−i−iii−i−i−i−iii
χ311-1-11-1-11111-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-111-1−i−iiiii−i−i-111-111-1-1-1-111ii−i−i−i−iii-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii
χ321-1-11-1-11111-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-111-1−i−iiiii−i−i-111-1-1-11111-1-1ii−i−i−i−iii11-1-1-1-111ii−i−i−i−iii−i−iiiii−i−i
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
χ35222222222222-2-2-2-2-2-2-2-2-2-222222222-2-2-2-2-2-20000000000000000000000000000000000000000000000002i−2i2i−2i−2i2i−2i2i
χ36222222222222-2-2-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2000000000000000000000000000000000000000000000000−2i2i−2i2i2i−2i2i−2i
χ3722222222-2-2-2-222-2-222-2-22222-2-222-2-2-2-2-2-22200000000000000000000000000000000000000002-22-22-22-200000000
χ3822222222-2-2-2-222-2-222-2-22222-2-222-2-2-2-2-2-2220000000000000000000000000000000000000000-22-22-22-2200000000
χ3922222222-2-2-2-222-2-222-2-2-2-2-2-222-2-2222222-2-2222200000000-2-2-2-20000000000000000000000000000000000000000
χ4022222222-2-2-2-222-2-222-2-2-2-2-2-222-2-2222222-2-2-2-2-2-20000000022220000000000000000000000000000000000000000
χ4122222222-2-2-2-2-2-222-2-22222-2-222-2-222-2-2-2-22200000000000000000000000000000000000000002-22-2-22-2200000000
χ4222222222-2-2-2-2-2-222-2-22222-2-222-2-222-2-2-2-2220000000000000000000000000000000000000000-22-222-22-200000000
χ4322222222-2-2-2-2-2-222-2-222-2-222-2-222-2-22222-2-222-2-200000000-2-2220000000000000000000000000000000000000000
χ4422222222-2-2-2-2-2-222-2-222-2-222-2-222-2-22222-2-2-2-2220000000022-2-20000000000000000000000000000000000000000
χ4522-2-22-22-22-22-22i−2i2i−2i2i−2i2i−2i2-22i−2i2i−2i2i−2i2i−2i2-22-22-2000000000000000000000000000000002-22-22i−2i2i−2i0000000000000000
χ4622-2-22-22-22-22-22i−2i2i−2i2i−2i2i−2i2-22i−2i2i−2i2i−2i2i−2i2-22-22-200000000000000000000000000000000-22-22−2i2i−2i2i0000000000000000
χ4722-2-22-22-22-22-22i−2i2i−2i2i−2i2i−2i-22−2i2i−2i2i−2i2i−2i2i-22-22-2200002-22-22i−2i2i−2i00000000000000000000000000000000000000000000
χ4822-2-22-22-22-22-22i−2i2i−2i2i−2i2i−2i-22−2i2i−2i2i−2i2i−2i2i-22-22-220000-22-22−2i2i−2i2i00000000000000000000000000000000000000000000
χ4922-2-22-22-22-22-2−2i2i−2i2i−2i2i−2i2i2-2−2i2i−2i2i−2i2i−2i2i2-22-22-2000000000000000000000000000000002-22-2−2i2i−2i2i0000000000000000
χ5022-2-22-22-22-22-2−2i2i−2i2i−2i2i−2i2i2-2−2i2i−2i2i−2i2i−2i2i2-22-22-200000000000000000000000000000000-22-222i−2i2i−2i0000000000000000
χ5122-2-22-22-22-22-2−2i2i−2i2i−2i2i−2i2i-222i−2i2i−2i2i−2i2i−2i-22-22-2200002-22-2−2i2i−2i2i00000000000000000000000000000000000000000000
χ5222-2-22-22-22-22-2−2i2i−2i2i−2i2i−2i2i-222i−2i2i−2i2i−2i2i−2i-22-22-220000-22-222i−2i2i−2i00000000000000000000000000000000000000000000
χ5322-2-22-22-2-22-222i−2i−2i2i2i−2i−2i2i2-22i−2i−2i2i2i−2i−2i2i-22-222-20000000000000000000000002-22-22i−2i2i−2i000000000000000000000000
χ5422-2-22-22-2-22-222i−2i−2i2i2i−2i−2i2i2-22i−2i−2i2i2i−2i−2i2i-22-222-2000000000000000000000000-22-22−2i2i−2i2i000000000000000000000000
χ5522-2-22-22-2-22-222i−2i−2i2i2i−2i−2i2i-22−2i2i2i−2i−2i2i2i−2i2-22-2-2200000000000000002-22-22i−2i2i−2i00000000000000000000000000000000
χ5622-2-22-22-2-22-222i−2i−2i2i2i−2i−2i2i-22−2i2i2i−2i−2i2i2i−2i2-22-2-220000000000000000-22-22−2i2i−2i2i00000000000000000000000000000000
χ5722-2-22-22-2-22-22−2i2i2i−2i−2i2i2i−2i2-2−2i2i2i−2i−2i2i2i−2i-22-222-20000000000000000000000002-22-2−2i2i−2i2i000000000000000000000000
χ5822-2-22-22-2-22-22−2i2i2i−2i−2i2i2i−2i2-2−2i2i2i−2i−2i2i2i−2i-22-222-2000000000000000000000000-22-222i−2i2i−2i000000000000000000000000
χ5922-2-22-22-2-22-22−2i2i2i−2i−2i2i2i−2i-222i−2i−2i2i2i−2i−2i2i2-22-2-2200000000000000002-22-2−2i2i−2i2i00000000000000000000000000000000
χ6022-2-22-22-2-22-22−2i2i2i−2i−2i2i2i−2i-222i−2i−2i2i2i−2i−2i2i2-22-2-220000000000000000-22-222i−2i2i−2i00000000000000000000000000000000
χ612-22-2-222-22-2-222i−2i2i−2i−2i2i−2i2i2-22i−2i2i−2i−2i2i−2i2i2-2-22-22000000000000000000000000000000002-2-222i−2i−2i2i0000000000000000
χ622-22-2-222-22-2-222i−2i2i−2i−2i2i−2i2i2-22i−2i2i−2i−2i2i−2i2i2-2-22-2200000000000000000000000000000000-222-2−2i2i2i−2i0000000000000000
χ632-22-2-222-22-2-222i−2i2i−2i−2i2i−2i2i-22−2i2i−2i2i2i−2i2i−2i-222-22-200002i−2i−2i2i-222-200000000000000000000000000000000000000000000
χ642-22-2-222-22-2-222i−2i2i−2i−2i2i−2i2i-22−2i2i−2i2i2i−2i2i−2i-222-22-20000−2i2i2i−2i2-2-2200000000000000000000000000000000000000000000
χ652-22-2-222-22-2-22−2i2i−2i2i2i−2i2i−2i2-2−2i2i−2i2i2i−2i2i−2i2-2-22-22000000000000000000000000000000002-2-22−2i2i2i−2i0000000000000000
χ662-22-2-222-22-2-22−2i2i−2i2i2i−2i2i−2i2-2−2i2i−2i2i2i−2i2i−2i2-2-22-2200000000000000000000000000000000-222-22i−2i−2i2i0000000000000000
χ672-22-2-222-22-2-22−2i2i−2i2i2i−2i2i−2i-222i−2i2i−2i−2i2i−2i2i-222-22-200002i−2i−2i2i2-2-2200000000000000000000000000000000000000000000
χ682-22-2-222-22-2-22−2i2i−2i2i2i−2i2i−2i-222i−2i2i−2i−2i2i−2i2i-222-22-20000−2i2i2i−2i-222-200000000000000000000000000000000000000000000
χ692-22-2-222-2-222-22i−2i−2i2i−2i2i2i−2i2-22i−2i−2i2i−2i2i2i−2i-222-2-220000000000000000000000002i−2i−2i2i-222-2000000000000000000000000
χ702-22-2-222-2-222-22i−2i−2i2i−2i2i2i−2i2-22i−2i−2i2i−2i2i2i−2i-222-2-22000000000000000000000000−2i2i2i−2i2-2-22000000000000000000000000
χ712-22-2-222-2-222-22i−2i−2i2i−2i2i2i−2i-22−2i2i2i−2i2i−2i−2i2i2-2-222-200000000000000002-2-222i−2i−2i2i00000000000000000000000000000000
χ722-22-2-222-2-222-22i−2i−2i2i−2i2i2i−2i-22−2i2i2i−2i2i−2i−2i2i2-2-222-20000000000000000-222-2−2i2i2i−2i00000000000000000000000000000000
χ732-22-2-222-2-222-2−2i2i2i−2i2i−2i−2i2i2-2−2i2i2i−2i2i−2i−2i2i-222-2-220000000000000000000000002i−2i−2i2i2-2-22000000000000000000000000
χ742-22-2-222-2-222-2−2i2i2i−2i2i−2i−2i2i2-2−2i2i2i−2i2i−2i−2i2i-222-2-22000000000000000000000000−2i2i2i−2i-222-2000000000000000000000000
χ752-22-2-222-2-222-2−2i2i2i−2i2i−2i−2i2i-222i−2i−2i2i−2i2i2i−2i2-2-222-200000000000000002-2-22−2i2i2i−2i00000000000000000000000000000000
χ762-22-2-222-2-222-2−2i2i2i−2i2i−2i−2i2i-222i−2i−2i2i−2i2i2i−2i2-2-222-20000000000000000-222-22i−2i−2i2i00000000000000000000000000000000
χ772-2-22-2-22222-2-22222-2-2-2-2-2-2-2-2-2-22222-2-222220000000000000000000000000000000000000000000000002-2-222-2-22
χ782-2-22-2-22222-2-22222-2-2-2-2-2-2-2-2-2-22222-2-22222000000000000000000000000000000000000000000000000-222-2-222-2
χ792-2-22-2-22222-2-2-2-2-2-22222-2-22222-2-2-2-2-2-222220000000000000000000000000000000000000000000000002-2-22-222-2
χ802-2-22-2-22222-2-2-2-2-2-22222-2-22222-2-2-2-2-2-22222000000000000000000000000000000000000000000000000-222-22-2-22
χ812-2-22-2-222-2-22222-2-2-2-2222222-2-2-2-222-2-222-2-200000000000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i00000000
χ822-2-22-2-222-2-22222-2-2-2-2222222-2-2-2-222-2-222-2-20000000000000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i00000000
χ832-2-22-2-222-2-22222-2-2-2-222-2-2-2-22222-2-222-2-2222-22-200000000-22-220000000000000000000000000000000000000000
χ842-2-22-2-222-2-22222-2-2-2-222-2-2-2-22222-2-222-2-222-22-22000000002-22-20000000000000000000000000000000000000000
χ852-2-22-2-222-2-222-2-22222-2-222-2-22222-2-2-2-222-2-200000000000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i00000000
χ862-2-22-2-222-2-222-2-22222-2-222-2-22222-2-2-2-222-2-20000000000000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i00000000
χ872-2-22-2-222-2-222-2-22222-2-2-2-222-2-2-2-22222-2-2222-2-2200000000-222-20000000000000000000000000000000000000000
χ882-2-22-2-222-2-222-2-22222-2-2-2-222-2-2-2-22222-2-222-222-2000000002-2-220000000000000000000000000000000000000000
χ89888-8-8-8-88000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9088-88-88-8-8000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ918-8888-8-8-8000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ928-8-8-888-88000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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