Finite Group Databasebeta

← Group #72262227

Character table — Group #72262227

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97
size111122222244444444444444444444444444448888881616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616
order1222222222222222222222222244444444444422444422222444444444444444444444444444444444444444488888888
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-11-1-1-1-1-1111111111111-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-11111111111111111
χ511111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ611111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111
χ711111111111111111111111111111111111111-1-1-1-111-1-1111-1-1-1-11-1-1-1-111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ811111111111111111111111111111111111111-1-1-1-111-1-1111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1
χ91111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111111111-111-1-11-1-1-111-1-11111-1-1-1-111-1-11-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ101111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111111111-111-1-11-1-1-111-1-1-1-1-1-1111111-1-11-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1111-1-1-1-11-1-1-111-11-11-1-1111111-1-1-1-111-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ121111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1111-1-1-1-11-1-1-111-11-11-1-111-1-1-1-1111111-1-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ131111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-11-1-111-1-1-11-1-11-11-11111-1-11111-1-1-1-1-1-111-111-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ141111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-11-1-111-1-1-11-1-11-11-11111-1-1-1-1-1-11111-1-111-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ151111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-11-1-1-1-111-1111-11-111-1-1-1111111-1-1-1-1-1-1111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ161111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-11-1-1-1-111-1111-11-111-1-1-111-1-1-1-11111-1-1111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ171111-1-11-1-111111-1-1111111-1-1-1-111-111-1-1-1-1-1-1-1111111-111-11-1-11-1-11-11-1ii−i−iii−i−i1-11-1-11-1ii−i−iii−i−iii−i−iii−i−iii−i−iii−i−i
χ181111-1-11-1-111111-1-1111111-1-1-1-111-111-1-1-1-1-1-1-1111111-111-11-1-11-1-11-11-1−i−iii−i−iii1-11-1-11-1−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii
χ191111-1-11-1-111111-1-1111111-1-1-1-111-111-1-1-1-1-1-1-111-1-1-1-1-11-11-111-1-11-11-11ii−i−iii−i−i1-11-11-11ii−i−iii−i−i−i−iii−i−iii−i−iii−i−iii
χ201111-1-11-1-111111-1-1111111-1-1-1-111-111-1-1-1-1-1-1-111-1-1-1-1-11-11-111-1-11-11-11−i−iii−i−iii1-11-11-11−i−iii−i−iiiii−i−iii−i−iii−i−iii−i−i
χ211111-1-11-1-111111-1-1111111-1-1-1-111-111-1-1-1-1-1-1-1-1-111-1-11-1-11-1-1-11111-11-1ii−i−iii−i−i-11-111-11−i−iii−i−iiiii−i−iii−i−i−i−iii−i−iii
χ221111-1-11-1-111111-1-1111111-1-1-1-111-111-1-1-1-1-1-1-1-1-111-1-11-1-11-1-1-11111-11-1−i−iii−i−iii-11-111-11ii−i−iii−i−i−i−iii−i−iiiii−i−iii−i−i
χ231111-1-11-1-111111-1-1111111-1-1-1-111-111-1-1-1-1-1-1-1-1-1-1-1111-11-1111-11-1-11-11ii−i−iii−i−i-11-11-11-1−i−iii−i−iii−i−iii−i−iiiii−i−iii−i−i
χ241111-1-11-1-111111-1-1111111-1-1-1-111-111-1-1-1-1-1-1-1-1-1-1-1111-11-1111-11-1-11-11−i−iii−i−iii-11-11-11-1ii−i−iii−i−iii−i−iii−i−i−i−iii−i−iii
χ251111-1-11-1-111111-1-1-1-1-1-1-1-111-1-111-1-1-1111111-1111111-1-11-1-11-1-1111-1-11ii−i−i−i−iii1-1-11-1-11ii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iii
χ261111-1-11-1-111111-1-1-1-1-1-1-1-111-1-111-1-1-1111111-1111111-1-11-1-11-1-1111-1-11−i−iiiii−i−i1-1-11-1-11−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i
χ271111-1-11-1-111111-1-1-1-1-1-1-1-111-1-111-1-1-1111111-111-1-1-1-1-1-1-111-1111-1-111-1ii−i−i−i−iii1-1-1111-1ii−i−i−i−iii−i−iiiii−i−i−i−iiiii−i−i
χ281111-1-11-1-111111-1-1-1-1-1-1-1-111-1-111-1-1-1111111-111-1-1-1-1-1-1-111-1111-1-111-1−i−iiiii−i−i1-1-1111-1−i−iiiii−i−iii−i−i−i−iiiii−i−i−i−iii
χ291111-1-11-1-111111-1-1-1-1-1-1-1-111-1-111-1-1-1111111-1-1-111-1-111-1111-1-1-1-11-1-11ii−i−i−i−iii-111-111-1−i−iiiii−i−iii−i−i−i−iii−i−iiiii−i−i
χ301111-1-11-1-111111-1-1-1-1-1-1-1-111-1-111-1-1-1111111-1-1-111-1-111-1111-1-1-1-11-1-11−i−iiiii−i−i-111-111-1ii−i−i−i−iii−i−iiiii−i−iii−i−i−i−iii
χ311111-1-11-1-111111-1-1-1-1-1-1-1-111-1-111-1-1-1111111-1-1-1-1-111111-1-1-111-11-111-1ii−i−i−i−iii-111-1-1-11−i−iiiii−i−i−i−iiiii−i−iii−i−i−i−iii
χ321111-1-11-1-111111-1-1-1-1-1-1-1-111-1-111-1-1-1111111-1-1-1-1-111111-1-1-111-11-111-1−i−iiiii−i−i-111-1-1-11ii−i−i−i−iiiii−i−i−i−iii−i−iiiii−i−i
χ33222222222222-2-22-22222-2-2-2-22-2-2-2-2-2-22222-2-2-20022000000022200-2-2-2-2000000000000000000000000000000000000000
χ34222222222222-2-22-22222-2-2-2-22-2-2-2-2-2-22222-2-2-200-2-20000000-2-2-2002222000000000000000000000000000000000000000
χ35222222222222-2-22-2-2-2-2-222222-2-2-2-222-2-2-2-222-200220000000-22-200-2-222000000000000000000000000000000000000000
χ36222222222222-2-22-2-2-2-2-222222-2-2-2-222-2-2-2-222-200-2-200000002-220022-2-2000000000000000000000000000000000000000
χ372222222222-2-222-2222-2-222-2-2-22-2-2-2-2-222-2-222-22200002200000020000000000000-2-2-2-2000000000000000000000000000
χ382222222222-2-222-2222-2-222-2-2-22-2-2-2-2-222-2-222-2-2-20000-2-2000000-200000000000002222000000000000000000000000000
χ392222222222-2-222-22-2-222-2-222-22-2-2-222-2-222-2-2-22200002-2000000-20000000000000-2-222000000000000000000000000000
χ402222222222-2-222-22-2-222-2-222-22-2-2-222-2-222-2-2-2-2-20000-220000002000000000000022-2-2000000000000000000000000000
χ412222222222-2-2-2-2-2-222-2-2-2-222-2-22222222-2-2-2-2200002200-2-2-20000-20000000000000000222000000000000000000000000
χ422222222222-2-2-2-2-2-222-2-2-2-222-2-22222222-2-2-2-220000-2-200222000020000000000000000-2-2-2000000000000000000000000
χ432222222222-2-2-2-2-2-2-2-22222-2-2-2-2222-2-2-2-22222200002200-2-220000200000000000000002-2-2000000000000000000000000
χ442222222222-2-2-2-2-2-2-2-22222-2-2-2-2222-2-2-2-2222220000-2-20022-20000-20000000000000000-222000000000000000000000000
χ452222-2-22-2-2222-2-2-222222-2-222-22-2-22-2-2-2-2-2-222200220000000-2-2200-22-22000000000000000000000000000000000000000
χ462222-2-22-2-2222-2-2-222222-2-222-22-2-22-2-2-2-2-2-222200-2-2000000022-2002-22-2000000000000000000000000000000000000000
χ472222-2-22-2-2222-2-2-22-2-2-2-222-2-2-22-2-22222222-2-22002200000002-2-200-222-2000000000000000000000000000000000000000
χ482222-2-22-2-2222-2-2-22-2-2-2-222-2-2-22-2-22222222-2-2200-2-20000000-222002-2-22000000000000000000000000000000000000000
χ492222-2-22-2-22-2-2222-222-2-222222-2-2-22-2-2-2-222-2-22220000-22000000-20000000000000-22-22000000000000000000000000000
χ502222-2-22-2-22-2-2222-222-2-222222-2-2-22-2-2-2-222-2-22-2-200002-2000000200000000000002-22-2000000000000000000000000000
χ512222-2-22-2-22-2-2222-2-2-222-2-2-2-22-2-2-222222-2-2222220000-2-200000020000000000000-222-2000000000000000000000000000
χ522222-2-22-2-22-2-2222-2-2-222-2-2-2-22-2-2-222222-2-2222-2-2000022000000-200000000000002-2-22000000000000000000000000000
χ532222-2-22-2-22-2-2-2-22222-2-2-2-2-2-22222-222-2-22222-200002200-22-2000020000000000000000-22-2000000000000000000000000
χ542222-2-22-2-22-2-2-2-22222-2-2-2-2-2-22222-222-2-22222-20000-2-2002-220000-200000000000000002-22000000000000000000000000
χ552222-2-22-2-22-2-2-2-222-2-22222222222-2-2-222-2-2-2-2-200002200-2220000-20000000000000000-2-22000000000000000000000000
χ562222-2-22-2-22-2-2-2-222-2-22222222222-2-2-222-2-2-2-2-20000-2-2002-2-200002000000000000000022-2000000000000000000000000
χ572-2-2222-2-2-222-22-2222-22-22-22-2-2-22-2-22-22-22-22-22000000000000000000000000000000000002i−2i2i−2i2i−2i2i−2i0000000000000000
χ582-2-2222-2-2-222-22-2222-22-22-22-2-2-22-2-22-22-22-22-2200000000000000000000000000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000
χ592-2-2222-2-2-222-22-222-22-22-22-22-2-22-2-2-22-22-22-222000000000000000000000000000000000002i−2i2i−2i−2i2i−2i2i0000000000000000
χ602-2-2222-2-2-222-22-222-22-22-22-22-2-22-2-2-22-22-22-22200000000000000000000000000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000
χ612-2-2222-2-2-222-2-222-22-22-2-22-22-22-222-222-22-2-22-20000000000000000000000000000000000000000000000000002i−2i2i−2i2i−2i2i−2i
χ622-2-2222-2-2-222-2-222-22-22-2-22-22-22-222-222-22-2-22-2000000000000000000000000000000000000000000000000000−2i2i−2i2i−2i2i−2i2i
χ632-2-2222-2-2-222-2-222-2-22-222-22-2-22-2222-2-22-222-2-20000000000000000000000000000000000000000000000000002i−2i2i−2i−2i2i−2i2i
χ642-2-2222-2-2-222-2-222-2-22-222-22-2-22-2222-2-22-222-2-2000000000000000000000000000000000000000000000000000−2i2i−2i2i2i−2i2i−2i
χ652-2-2222-2-2-22-222-2-222-2-222-2-222-2-222-222-2-222-2-2000000000000000000002i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000
χ662-2-2222-2-2-22-222-2-222-2-222-2-222-2-222-222-2-222-2-200000000000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000
χ672-2-2222-2-2-22-222-2-22-222-2-222-22-2-2222-2-222-2-22-2000000000000000000002i−2i2i−2i−2i2i−2i2i0000000000000000000000000000000
χ682-2-2222-2-2-22-222-2-22-222-2-222-22-2-2222-2-222-2-22-200000000000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000000
χ692-2-2222-2-2-22-22-22-2-22-2-22-222-2222-2-22-22-2-22-22200000000000000000000000000000000000000000002-22-22-22-200000000
χ702-2-2222-2-2-22-22-22-2-22-2-22-222-2222-2-22-22-2-22-2220000000000000000000000000000000000000000000-22-22-22-2200000000
χ712-2-2222-2-2-22-22-22-2-2-222-22-2-22222-2-2-22-222-22-2200000000000000000000000000000000000000000002-22-2-22-2200000000
χ722-2-2222-2-2-22-22-22-2-2-222-22-2-22222-2-2-22-222-22-220000000000000000000000000000000000000000000-22-222-22-200000000
χ732-2-22-2-2-22222-22-2-2-22-22-22-2-22222-222-2-22-22-22-2000000000000000000000000000000000002-2-222-2-220000000000000000
χ742-2-22-2-2-22222-22-2-2-22-22-22-2-22222-222-2-22-22-22-200000000000000000000000000000000000-222-2-222-20000000000000000
χ752-2-22-2-2-22222-22-2-2-2-22-22-222-2222-22-222-22-22-2-2000000000000000000000000000000000002-2-22-222-20000000000000000
χ762-2-22-2-2-22222-22-2-2-2-22-22-222-2222-22-222-22-22-2-200000000000000000000000000000000000-222-22-2-220000000000000000
χ772-2-22-2-2-22222-2-22-222-22-2-222-22-2-22-2-22-22-222-220000000000000000000000000000000000000000000000000002-2-222-2-22
χ782-2-22-2-2-22222-2-22-222-22-2-222-22-2-22-2-22-22-222-22000000000000000000000000000000000000000000000000000-222-2-222-2
χ792-2-22-2-2-22222-2-22-22-22-222-2-222-2-22-22-22-22-2-2220000000000000000000000000000000000000000000000000002-2-22-222-2
χ802-2-22-2-2-22222-2-22-22-22-222-2-222-2-22-22-22-22-2-222000000000000000000000000000000000000000000000000000-222-22-2-22
χ812-2-22-2-2-2222-222-22-22-2-222-22-2-22-22-2-22-222-2-222000000000000000000002-2-222-2-220000000000000000000000000000000
χ822-2-22-2-2-2222-222-22-22-2-222-22-2-22-22-2-22-222-2-22200000000000000000000-222-2-222-20000000000000000000000000000000
χ832-2-22-2-2-2222-222-22-2-222-2-22-22-22-22-22-22-2-222-22000000000000000000002-2-22-222-20000000000000000000000000000000
χ842-2-22-2-2-2222-222-22-2-222-2-22-22-22-22-22-22-2-222-2200000000000000000000-222-22-2-220000000000000000000000000000000
χ852-2-22-2-2-2222-22-22222-2-22-22-22-2-22-222-2-222-22-2-200000000000000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i00000000
χ862-2-22-2-2-2222-22-22222-2-22-22-22-2-22-222-2-222-22-2-20000000000000000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i00000000
χ872-2-22-2-2-2222-22-2222-222-22-22-2-2-22-22-222-2-22-22-200000000000000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i00000000
χ882-2-22-2-2-2222-22-2222-222-22-22-2-2-22-22-222-2-22-22-20000000000000000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i00000000
χ8988888-8-88-8-8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ908888-88-8-88-8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ918-88-800000000000000000000000000000000004-44-44-400000000000000000000000000000000000000000000000000000
χ928-88-800000000000000000000000000000000004-4-44-4400000000000000000000000000000000000000000000000000000
χ938-88-80000000000000000000000000000000000-444-4-4400000000000000000000000000000000000000000000000000000
χ948-88-80000000000000000000000000000000000-44-444-400000000000000000000000000000000000000000000000000000
χ958-8-888-88-88-8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ968-8-88-8888-8-8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ971616-16-16000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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