Finite Group Databasebeta

← Group #393369

Character table — Group #393369

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size11111111222222222222222244444444444444444444444444444444444444444444444444444488888888161616161616161616161616
order12222222222244444444444422224444444444444444444444444444444444444444444444444444444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ5111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ6111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ9111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-111-1-1
χ10111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-111
χ11111111111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111
χ12111111111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1
χ13111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111111111-1-1-1-1-1-111-1-11111-1-1
χ14111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1111111-1-111-1-1-1-111
χ15111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111-1-111
χ16111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-111-1-1
χ171-1-111-1-1111-1-1111-1-1-111-1-11-111-1-1ii−i−iii−i−i11-1-111-1-111-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i1-111-1-1ii−i−iii−i−i1-11-1i−ii−i1-11-1
χ181-1-111-1-1111-1-1111-1-1-111-1-11-111-1-1ii−i−iii−i−i11-1-111-1-111-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i1-111-1-1−i−iii−i−iii-11-11−ii−ii-11-11
χ191-1-111-1-1111-1-1111-1-1-111-1-11-111-1-1−i−iii−i−iii11-1-111-1-111-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii1-111-1-1ii−i−iii−i−i-11-11i−ii−i-11-11
χ201-1-111-1-1111-1-1111-1-1-111-1-11-111-1-1−i−iii−i−iii11-1-111-1-111-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii1-111-1-1−i−iii−i−iii1-11-1−ii−ii1-11-1
χ211-1-111-1-1111-1-1111-1-1-111-1-11-1-1-111ii−i−iii−i−i11-1-1-1-111-1-111ii−i−iii−i−i−i−i−i−iiiii−i−i−i−iiiii1-1-1-111ii−i−iii−i−i-11-11−ii−ii1-11-1
χ221-1-111-1-1111-1-1111-1-1-111-1-11-1-1-111ii−i−iii−i−i11-1-1-1-111-1-111ii−i−iii−i−i−i−i−i−iiiii−i−i−i−iiiii1-1-1-111−i−iii−i−iii1-11-1i−ii−i-11-11
χ231-1-111-1-1111-1-1111-1-1-111-1-11-1-1-111−i−iii−i−iii11-1-1-1-111-1-111−i−iii−i−iiiiiii−i−i−i−iiiii−i−i−i−i1-1-1-111ii−i−iii−i−i1-11-1−ii−ii-11-11
χ241-1-111-1-1111-1-1111-1-1-111-1-11-1-1-111−i−iii−i−iii11-1-1-1-111-1-111−i−iii−i−iiiiiii−i−i−i−iiiii−i−i−i−i1-1-1-111−i−iii−i−iii-11-11i−ii−i1-11-1
χ251-1-111-1-1111-1-1111-1-1-1-1-1111-111-1-1ii−i−i−i−iii-1-11111-1-1-1-111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii-11-1-111ii−i−i−i−iii1-1-11i−i−ii1-1-11
χ261-1-111-1-1111-1-1111-1-1-1-1-1111-111-1-1ii−i−i−i−iii-1-11111-1-1-1-111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii-11-1-111−i−iiiii−i−i-111-1−iii−i-111-1
χ271-1-111-1-1111-1-1111-1-1-1-1-1111-111-1-1−i−iiiii−i−i-1-11111-1-1-1-111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i-11-1-111ii−i−i−i−iii-111-1i−i−ii-111-1
χ281-1-111-1-1111-1-1111-1-1-1-1-1111-111-1-1−i−iiiii−i−i-1-11111-1-1-1-111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i-11-1-111−i−iiiii−i−i1-1-11−iii−i1-1-11
χ291-1-111-1-1111-1-1111-1-1-1-1-1111-1-1-111ii−i−i−i−iii-1-111-1-11111-1-1ii−i−i−i−iii−i−i−i−iiiiiiiii−i−i−i−i-1111-1-1ii−i−i−i−iii-111-1−iii−i1-1-11
χ301-1-111-1-1111-1-1111-1-1-1-1-1111-1-1-111ii−i−i−i−iii-1-111-1-11111-1-1ii−i−i−i−iii−i−i−i−iiiiiiiii−i−i−i−i-1111-1-1−i−iiiii−i−i1-1-11i−i−ii-111-1
χ311-1-111-1-1111-1-1111-1-1-1-1-1111-1-1-111−i−iiiii−i−i-1-111-1-11111-1-1−i−iiiii−i−iiiii−i−i−i−i−i−i−i−iiiii-1111-1-1ii−i−i−i−iii1-1-11−iii−i-111-1
χ321-1-111-1-1111-1-1111-1-1-1-1-1111-1-1-111−i−iiiii−i−i-1-111-1-11111-1-1−i−iiiii−i−iiiii−i−i−i−i−i−i−i−iiiii-1111-1-1−i−iiiii−i−i-111-1i−i−ii1-1-11
χ33222222222222-2-2-2-2-2-22222-2-2000000000000-2-2-2-2000000000000000022-2-222-2-222-2-222-2-222000000000000000000000000
χ34222222222222-2-2-2-2-2-22222-2-2000000000000-2-2-2-20000000000000000-2-222-2-222-2-222-2-22222000000000000000000000000
χ35222222222222-2-2-2-2-2-2-2-2-2-2-2-20000000000002222000000000000000022-2-222-2-2-2-222-2-222-2-2000000000000000000000000
χ36222222222222-2-2-2-2-2-2-2-2-2-2-2-200000000000022220000000000000000-2-222-2-22222-2-222-2-2-2-2000000000000000000000000
χ3722222222-2-2-2-222-22-2-22222-220000222222222-22-200000000-2-2-2-2-2-2-2-20000000000000000-2-2000000000000000000000000
χ3822222222-2-2-2-222-22-2-22222-220000-2-2-2-2-2-2-2-22-22-200000000222222220000000000000000-2-2000000000000000000000000
χ3922222222-2-2-2-222-22-2-2-2-2-2-2-2200002222-2-2-2-2-22-2200000000-2-2-2-22222000000000000000022000000000000000000000000
χ4022222222-2-2-2-222-22-2-2-2-2-2-2-220000-2-2-2-22222-22-22000000002222-2-2-2-2000000000000000022000000000000000000000000
χ4122222222-2-2-2-2-2-22-22222222-2222200000000-22-22-2-2-2-2-2-2-2-2000000000000000000000000-2-2222200000000000000000000
χ4222222222-2-2-2-2-2-22-22222222-2-2-2-2-200000000-22-2222222222000000000000000000000000-2-2-2-2-2-200000000000000000000
χ4322222222-2-2-2-2-2-22-222-2-2-2-22-22222000000002-22-2-2-2-2-2222200000000000000000000000022-2-2-2-200000000000000000000
χ4422222222-2-2-2-2-2-22-222-2-2-2-22-2-2-2-2-2000000002-22-22222-2-2-2-200000000000000000000000022222200000000000000000000
χ4522-22-22-2-22-22-22-2222-20000-2-22-22-200002-22-200002-22-2000000002-22-2000000002-22-22-22-200000000000000000000000000
χ4622-22-22-2-22-22-22-2222-20000-2-22-22-20000-22-2200002-22-200000000-22-2200000000-22-22-22-2200000000000000000000000000
χ4722-22-22-2-22-22-22-2222-20000-2-2-22-2200002-22-20000-22-22000000002-22-200000000-22-22-22-2200000000000000000000000000
χ4822-22-22-2-22-22-22-2222-20000-2-2-22-220000-22-220000-22-2200000000-22-22000000002-22-22-22-200000000000000000000000000
χ4922-22-22-2-22-22-2-22-2-2-2200002200002i−2i2i−2i0000000000002i−2i2i−2i2i−2i2i−2i0000000000002-2-222-2-22002i−2i2i−2i00000000000000000000
χ5022-22-22-2-22-22-2-22-2-2-2200002200002i−2i2i−2i000000000000−2i2i−2i2i2i−2i2i−2i000000000000-222-2-222-200−2i2i−2i2i00000000000000000000
χ5122-22-22-2-22-22-2-22-2-2-220000220000−2i2i−2i2i0000000000002i−2i2i−2i−2i2i−2i2i000000000000-222-2-222-2002i−2i2i−2i00000000000000000000
χ5222-22-22-2-22-22-2-22-2-2-220000220000−2i2i−2i2i000000000000−2i2i−2i2i−2i2i−2i2i0000000000002-2-222-2-2200−2i2i−2i2i00000000000000000000
χ5322-22-22-2-2-22-222-2-22-2200002-2000000002-22-2000000002i−2i2i−2i0000-22-222i−2i2i−2i2i−2i2i−2i0000000000−2i2i−2i2i00000000000000000000
χ5422-22-22-2-2-22-222-2-22-2200002-2000000002-22-200000000−2i2i−2i2i0000-22-22−2i2i−2i2i−2i2i−2i2i00000000002i−2i2i−2i00000000000000000000
χ5522-22-22-2-2-22-222-2-22-2200002-200000000-22-22000000002i−2i2i−2i00002-22-2−2i2i−2i2i−2i2i−2i2i0000000000−2i2i−2i2i00000000000000000000
χ5622-22-22-2-2-22-222-2-22-2200002-200000000-22-2200000000−2i2i−2i2i00002-22-22i−2i2i−2i2i−2i2i−2i00000000002i−2i2i−2i00000000000000000000
χ5722-22-22-2-2-22-22-222-22-20000-222-22-22i−2i2i−2i00000000-22-220000−2i2i−2i2i0000−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000000000
χ5822-22-22-2-2-22-22-222-22-20000-222-22-2−2i2i−2i2i00000000-22-2200002i−2i2i−2i00002i−2i−2i2i2i−2i−2i2i0000000000000000000000000000000000
χ5922-22-22-2-2-22-22-222-22-20000-22-22-222i−2i2i−2i000000002-22-20000−2i2i−2i2i00002i−2i−2i2i2i−2i−2i2i0000000000000000000000000000000000
χ6022-22-22-2-2-22-22-222-22-20000-22-22-22−2i2i−2i2i000000002-22-200002i−2i2i−2i0000−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000000000
χ612-222-2-22-22-2-222-22-2-220000-222-2-2200002i−2i−2i2i00002-2-22000000002i−2i−2i2i000000002i−2i2i−2i−2i2i−2i2i00000000000000000000000000
χ622-222-2-22-22-2-222-22-2-220000-222-2-220000−2i2i2i−2i00002-2-2200000000−2i2i2i−2i00000000−2i2i−2i2i2i−2i2i−2i00000000000000000000000000
χ632-222-2-22-22-2-222-22-2-220000-22-222-200002i−2i−2i2i0000-222-2000000002i−2i−2i2i00000000−2i2i−2i2i2i−2i2i−2i00000000000000000000000000
χ642-222-2-22-22-2-222-22-2-220000-22-222-20000−2i2i2i−2i0000-222-200000000−2i2i2i−2i000000002i−2i2i−2i−2i2i−2i2i00000000000000000000000000
χ652-222-2-22-22-2-22-22-222-200002-200002-2-220000000000002i−2i−2i2i2-2-22000000000000−2i2i2i−2i2i−2i−2i2i002i−2i−2i2i00000000000000000000
χ662-222-2-22-22-2-22-22-222-200002-200002-2-22000000000000−2i2i2i−2i2-2-220000000000002i−2i−2i2i−2i2i2i−2i00−2i2i2i−2i00000000000000000000
χ672-222-2-22-22-2-22-22-222-200002-20000-222-20000000000002i−2i−2i2i-222-20000000000002i−2i−2i2i−2i2i2i−2i002i−2i−2i2i00000000000000000000
χ682-222-2-22-22-2-22-22-222-200002-20000-222-2000000000000−2i2i2i−2i-222-2000000000000−2i2i2i−2i2i−2i−2i2i00−2i2i2i−2i00000000000000000000
χ692-222-2-22-2-222-22-2-2-22-2000022000000002i−2i−2i2i000000002i−2i−2i2i0000−2i2i2i−2i-22-222-22-20000000000−2i2i2i−2i00000000000000000000
χ702-222-2-22-2-222-22-2-2-22-2000022000000002i−2i−2i2i00000000−2i2i2i−2i0000−2i2i2i−2i2-22-2-22-2200000000002i−2i−2i2i00000000000000000000
χ712-222-2-22-2-222-22-2-2-22-200002200000000−2i2i2i−2i000000002i−2i−2i2i00002i−2i−2i2i2-22-2-22-220000000000−2i2i2i−2i00000000000000000000
χ722-222-2-22-2-222-22-2-2-22-200002200000000−2i2i2i−2i00000000−2i2i2i−2i00002i−2i−2i2i-22-222-22-200000000002i−2i−2i2i00000000000000000000
χ732-222-2-22-2-222-2-2222-220000-2-22-2-222-2-2200000000-222-20000-222-20000-222-22-2-220000000000000000000000000000000000
χ742-222-2-22-2-222-2-2222-220000-2-22-2-22-222-200000000-222-200002-2-2200002-2-22-222-20000000000000000000000000000000000
χ752-222-2-22-2-222-2-2222-220000-2-2-222-22-2-22000000002-2-220000-222-200002-2-22-222-20000000000000000000000000000000000
χ762-222-2-22-2-222-2-2222-220000-2-2-222-2-222-2000000002-2-2200002-2-220000-222-22-2-220000000000000000000000000000000000
χ772-2-222-2-2222-2-2-2-2-222222-2-2-22000000000000-2-22200000000000000002i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2-2000000000000000000000000
χ782-2-222-2-2222-2-2-2-2-222222-2-2-22000000000000-2-2220000000000000000−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i2-2000000000000000000000000
χ792-2-222-2-2222-2-2-2-2-2222-2-222-2200000000000022-2-200000000000000002i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i-22000000000000000000000000
χ802-2-222-2-2222-2-2-2-2-2222-2-222-2200000000000022-2-20000000000000000−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i-22000000000000000000000000
χ812-2-222-2-22-2-22222-2-22222-2-2-2-200002i2i−2i−2i2i2i−2i−2i2-2-2200000000−2i−2i2i2i−2i−2i2i2i0000000000000000-22000000000000000000000000
χ822-2-222-2-22-2-22222-2-22222-2-2-2-20000−2i−2i2i2i−2i−2i2i2i2-2-22000000002i2i−2i−2i2i2i−2i−2i0000000000000000-22000000000000000000000000
χ832-2-222-2-22-2-22222-2-222-2-222-2-200002i2i−2i−2i−2i−2i2i2i-222-200000000−2i−2i2i2i2i2i−2i−2i00000000000000002-2000000000000000000000000
χ842-2-222-2-22-2-22222-2-222-2-222-2-20000−2i−2i2i2i2i2i−2i−2i-222-2000000002i2i−2i−2i−2i−2i2i2i00000000000000002-2000000000000000000000000
χ852-2-222-2-22-2-222-2-222-2-222-2-22222-2-200000000-222-2-2-222-2-222000000000000000000000000-2222-2-200000000000000000000
χ862-2-222-2-22-2-222-2-222-2-222-2-222-2-22200000000-222-222-2-222-2-2000000000000000000000000-22-2-22200000000000000000000
χ872-2-222-2-22-2-222-2-222-2-2-2-2222222-2-2000000002-2-22-2-22222-2-20000000000000000000000002-2-2-22200000000000000000000
χ882-2-222-2-22-2-222-2-222-2-2-2-22222-2-222000000002-2-2222-2-2-2-2220000000000000000000000002-222-2-200000000000000000000
χ89444-4-4-4-4400000000004-44-4000000000000000000000000000000000000000000000000000000002i−2i2i−2i2i−2i2i−2i000000000000
χ90444-4-4-4-4400000000004-44-400000000000000000000000000000000000000000000000000000000−2i2i−2i2i−2i2i−2i2i000000000000
χ91444-4-4-4-440000000000-44-44000000000000000000000000000000000000000000000000000000002i−2i2i−2i−2i2i−2i2i000000000000
χ92444-4-4-4-440000000000-44-4400000000000000000000000000000000000000000000000000000000−2i2i−2i2i2i−2i2i−2i000000000000
χ934-4-4-4-444400000000004-4-44000000000000000000000000000000000000000000000000000000002-2-222-2-22000000000000
χ944-4-4-4-444400000000004-4-4400000000000000000000000000000000000000000000000000000000-222-2-222-2000000000000
χ954-4-4-4-44440000000000-444-4000000000000000000000000000000000000000000000000000000002-2-22-222-2000000000000
χ964-4-4-4-44440000000000-444-400000000000000000000000000000000000000000000000000000000-222-22-2-22000000000000
χ9788-8-88-88-8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ988-88-888-8-8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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