Finite Group Databasebeta

← Group #367166

Character table — Group #367166

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116
size1111111111111111222222222222222222222222222222224444444444444444444444444444444444444444444488888888888888881616161616161616
order12222222222222222222222244444444444444444444444444444444444488888888888888888888888888888888444444444444444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ7111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ8111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ91111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-1
χ101111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111
χ111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-111-1-111
χ121111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1111111-1-111-1-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111
χ171111-1-1111-1-1-1-1-1-111111-1-1-1-1iiii−i−i−i−i111-1-1-11111-1-1-1-11-1ii−i−iiiii−i−i−i−i1111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i11-1-111-1-1i−ii−i1-11-1
χ181111-1-1111-1-1-1-1-1-111111-1-1-1-1iiii−i−i−i−i111-1-1-11111-1-1-1-11-1ii−i−iiiii−i−i−i−i1111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii-1-111-1-111−ii−ii-11-11
χ191111-1-1111-1-1-1-1-1-111111-1-1-1-1iiii−i−i−i−i111-1-1-11111-1-1-1-11-1ii−i−iiiii−i−i−i−i-1-1-1-11111-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i11-1-111-1-1−ii−ii-11-11
χ201111-1-1111-1-1-1-1-1-111111-1-1-1-1iiii−i−i−i−i111-1-1-11111-1-1-1-11-1ii−i−iiiii−i−i−i−i-1-1-1-11111-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii-1-111-1-111i−ii−i1-11-1
χ211111-1-1111-1-1-1-1-1-111111-1-1-1-1−i−i−i−iiiii111-1-1-11111-1-1-1-11-1−i−iii−i−i−i−iiiii1111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i-1-111-1-111i−ii−i-11-11
χ221111-1-1111-1-1-1-1-1-111111-1-1-1-1−i−i−i−iiiii111-1-1-11111-1-1-1-11-1−i−iii−i−i−i−iiiii1111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii11-1-111-1-1−ii−ii1-11-1
χ231111-1-1111-1-1-1-1-1-111111-1-1-1-1−i−i−i−iiiii111-1-1-11111-1-1-1-11-1−i−iii−i−i−i−iiiii-1-1-1-11111-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i-1-111-1-111−ii−ii1-11-1
χ241111-1-1111-1-1-1-1-1-111111-1-1-1-1−i−i−i−iiiii111-1-1-11111-1-1-1-11-1−i−iii−i−i−i−iiiii-1-1-1-11111-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii11-1-111-1-1i−ii−i-11-11
χ251111-1-1111-1-1-1-1-1-11-1-1-1-11111iiii−i−i−i−i111-1-1-1-1-1-1-111111-1ii−i−i−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii11-1-1-1-111i−i−ii1-1-11
χ261111-1-1111-1-1-1-1-1-11-1-1-1-11111iiii−i−i−i−i111-1-1-1-1-1-1-111111-1ii−i−i−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i-1-11111-1-1−iii−i-111-1
χ271111-1-1111-1-1-1-1-1-11-1-1-1-11111iiii−i−i−i−i111-1-1-1-1-1-1-111111-1ii−i−i−i−i−i−iiiii-1-1-1-111111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii11-1-1-1-111−iii−i-111-1
χ281111-1-1111-1-1-1-1-1-11-1-1-1-11111iiii−i−i−i−i111-1-1-1-1-1-1-111111-1ii−i−i−i−i−i−iiiii-1-1-1-111111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i-1-11111-1-1i−i−ii1-1-11
χ291111-1-1111-1-1-1-1-1-11-1-1-1-11111−i−i−i−iiiii111-1-1-1-1-1-1-111111-1−i−iiiiiii−i−i−i−i1111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii-1-11111-1-1i−i−ii-111-1
χ301111-1-1111-1-1-1-1-1-11-1-1-1-11111−i−i−i−iiiii111-1-1-1-1-1-1-111111-1−i−iiiiiii−i−i−i−i1111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i11-1-1-1-111−iii−i1-1-11
χ311111-1-1111-1-1-1-1-1-11-1-1-1-11111−i−i−i−iiiii111-1-1-1-1-1-1-111111-1−i−iiiiiii−i−i−i−i-1-1-1-111111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii-1-11111-1-1−iii−i1-1-11
χ321111-1-1111-1-1-1-1-1-11-1-1-1-11111−i−i−i−iiiii111-1-1-1-1-1-1-111111-1−i−iiiiiii−i−i−i−i-1-1-1-111111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i11-1-1-1-111i−i−ii-111-1
χ3322222222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-222-2-200000000000000000000000000000000000000000000000000000000
χ34222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-222-2-22200000000000000000000000000000000000000000000000000000000
χ352222222222222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-222222222-2-2-2-2-2-2-2-222-2-22200000000000000000000000000000000000000000000000000000000
χ362222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2222222-2-222-2-200000000000000000000000000000000000000000000000000000000
χ372222-2-2222-2-2-2-2-2-222222-2-2-2-22i2i2i2i−2i−2i−2i−2i-2-2-2222-2-2-2-22222-22−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000000000000000000000000000
χ382222-2-2222-2-2-2-2-2-222222-2-2-2-2−2i−2i−2i−2i2i2i2i2i-2-2-2222-2-2-2-22222-222i2i−2i−2i−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000000000000000000000000000
χ392222-2-2222-2-2-2-2-2-22-2-2-2-222222i2i2i2i−2i−2i−2i−2i-2-2-22222222-2-2-2-2-22−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000000000000000000000000000
χ402222-2-2222-2-2-2-2-2-22-2-2-2-22222−2i−2i−2i−2i2i2i2i2i-2-2-22222222-2-2-2-2-222i2i−2i−2i2i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000000000000000000000000000
χ4122-2-2222-2-222-2-2-2-22000000002i2i−2i−2i2i2i−2i−2i22-22-2-200000000-222i−2i2i−2i00000000000000002i2i−2i−2i2i2i−2i−2i0000000022-2-222-2-2000000000000000000000000
χ4222-2-2222-2-222-2-2-2-22000000002i2i−2i−2i2i2i−2i−2i22-22-2-200000000-222i−2i2i−2i0000000000000000−2i−2i2i2i−2i−2i2i2i00000000-2-222-2-222000000000000000000000000
χ4322-2-2222-2-222-2-2-2-22000000002i2i−2i−2i2i2i−2i−2i-2-22-222000000002-2−2i2i−2i2i0000000022-2-222-2-2000000002i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000
χ4422-2-2222-2-222-2-2-2-22000000002i2i−2i−2i2i2i−2i−2i-2-22-222000000002-2−2i2i−2i2i00000000-2-222-2-22200000000−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000
χ4522-2-2222-2-222-2-2-2-2200000000−2i−2i2i2i−2i−2i2i2i22-22-2-200000000-22−2i2i−2i2i00000000000000002i2i−2i−2i2i2i−2i−2i00000000-2-222-2-222000000000000000000000000
χ4622-2-2222-2-222-2-2-2-2200000000−2i−2i2i2i−2i−2i2i2i22-22-2-200000000-22−2i2i−2i2i0000000000000000−2i−2i2i2i−2i−2i2i2i0000000022-2-222-2-2000000000000000000000000
χ4722-2-2222-2-222-2-2-2-2200000000−2i−2i2i2i−2i−2i2i2i-2-22-222000000002-22i−2i2i−2i0000000022-2-222-2-200000000−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000
χ4822-2-2222-2-222-2-2-2-2200000000−2i−2i2i2i−2i−2i2i2i-2-22-222000000002-22i−2i2i−2i00000000-2-222-2-222000000002i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000
χ4922-2-2-2-22-2-2-2-2222220000000022-2-2-2-22222-2-22200000000-2-22-2-2200000000000000002i2i−2i−2i−2i−2i2i2i00000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ5022-2-2-2-22-2-2-2-2222220000000022-2-2-2-22222-2-22200000000-2-22-2-220000000000000000−2i−2i2i2i2i2i−2i−2i000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ5122-2-2-2-22-2-2-2-2222220000000022-2-2-2-222-2-222-2-20000000022-222-20000000022-2-2-2-2220000000022-2-2-2-22200000000000000000000000000000000
χ5222-2-2-2-22-2-2-2-2222220000000022-2-2-2-222-2-222-2-20000000022-222-200000000-2-22222-2-200000000-2-22222-2-200000000000000000000000000000000
χ5322-2-2-2-22-2-2-2-22222200000000-2-22222-2-222-2-22200000000-2-2-222-200000000000000002i2i−2i−2i−2i−2i2i2i000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ5422-2-2-2-22-2-2-2-22222200000000-2-22222-2-222-2-22200000000-2-2-222-20000000000000000−2i−2i2i2i2i2i−2i−2i00000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ5522-2-2-2-22-2-2-2-22222200000000-2-22222-2-2-2-222-2-200000000222-2-220000000022-2-2-2-22200000000-2-22222-2-200000000000000000000000000000000
χ5622-2-2-2-22-2-2-2-22222200000000-2-22222-2-2-2-222-2-200000000222-2-2200000000-2-22222-2-20000000022-2-2-2-22200000000000000000000000000000000
χ572-22-222-22-2-2-222-2-2222-2-222-2-2000000002-22-22-222-2-222-2-2-2200000000000000000000000000000000000000000000000000002i−2i2i−2i2i−2i2i−2i00000000
χ582-22-222-22-2-2-222-2-2222-2-222-2-2000000002-22-22-222-2-222-2-2-220000000000000000000000000000000000000000000000000000−2i2i−2i2i−2i2i−2i2i00000000
χ592-22-222-22-2-2-222-2-2222-2-222-2-200000000-22-22-22-2-222-2-2222-2000000000000000000000000000000000000000000002i−2i2i−2i2i−2i2i−2i0000000000000000
χ602-22-222-22-2-2-222-2-2222-2-222-2-200000000-22-22-22-2-222-2-2222-200000000000000000000000000000000000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000
χ612-22-222-22-2-2-222-2-22-2-222-2-222000000002-22-22-2-2-222-2-222-2200000000000000000000000000000000000000000000000000002i−2i2i−2i−2i2i−2i2i00000000
χ622-22-222-22-2-2-222-2-22-2-222-2-222000000002-22-22-2-2-222-2-222-220000000000000000000000000000000000000000000000000000−2i2i−2i2i2i−2i2i−2i00000000
χ632-22-222-22-2-2-222-2-22-2-222-2-22200000000-22-22-2222-2-222-2-22-2000000000000000000000000000000000000000000002i−2i2i−2i−2i2i−2i2i0000000000000000
χ642-22-222-22-2-2-222-2-22-2-222-2-22200000000-22-22-2222-2-222-2-22-200000000000000000000000000000000000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000
χ652-22-22-22-222-22-22-2-22-22-22-22-22-22-22-22-2000000000000000000002-2002-200i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000000000000000000000
χ662-22-22-22-222-22-22-2-22-22-22-22-22-22-22-22-2000000000000000000002-2002-200−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000000000000000000000
χ672-22-22-22-222-22-22-2-22-22-22-22-2-22-22-22-2200000000000000000000-2200-2200i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000000000000000000000
χ682-22-22-22-222-22-22-2-22-22-22-22-2-22-22-22-2200000000000000000000-2200-2200−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000000000000000000000
χ692-22-22-22-222-22-22-2-2-22-22-22-222-22-22-22-200000000000000000000-2200-2200i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2000000000000000000000000
χ702-22-22-22-222-22-22-2-2-22-22-22-222-22-22-22-200000000000000000000-2200-2200−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2000000000000000000000000
χ712-22-22-22-222-22-22-2-2-22-22-22-22-22-22-22-22000000000000000000002-2002-200i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2000000000000000000000000
χ722-22-22-22-222-22-22-2-2-22-22-22-22-22-22-22-22000000000000000000002-2002-200−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2000000000000000000000000
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χ10544444-4-4-4-4-444-4-44-44-4-444-4-4400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10644444-4-4-4-4-444-4-44-4-444-4-444-400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
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χ11144-4-4-44-4444-44-4-44-400000000000000000000004i−4i−4i4i−4i4i4i−4i0000000000000000000000000000000000000000000000000000000000000000000000
χ11244-4-4-44-4444-44-4-44-40000000000000000000000−4i4i4i−4i4i−4i−4i4i0000000000000000000000000000000000000000000000000000000000000000000000
χ1134-4-4444-4-44-4-4-4-444400000000000000004-4-4-4-44000000004400000000000000000000000000000000000000000000000000000000000000000000
χ1144-4-4444-4-44-4-4-4-44440000000000000000-44444-400000000-4-400000000000000000000000000000000000000000000000000000000000000000000
χ1154-4-44-4-4-4-444444-4-4400000000000000004-4-444-4000000004-400000000000000000000000000000000000000000000000000000000000000000000
χ1164-4-44-4-4-4-444444-4-440000000000000000-444-4-4400000000-4400000000000000000000000000000000000000000000000000000000000000000000

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