Finite Group Databasebeta

← Group #190027

Character table — Group #190027

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size111122222222222222222244444444444444444444444444444444444444444444444444444416161616161616161616161616161616
order12222222224444444444444444444444444444444444444444444444444444444444444444448888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-111111111-1-1-1-1
χ911111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ1011111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1−i−iii−i−iii−i−iii−i−iii
χ1111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111ii−i−iii−i−i−i−iii−i−iii
χ1211111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111−i−iii−i−iiiii−i−iii−i−i
χ1311111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111ii−i−i−i−iiiii−i−i−i−iii
χ1411111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−i−iiiii−i−i−i−iiiii−i−i
χ1511111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1ii−i−i−i−iii−i−iiiii−i−i
χ1611111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1−i−iiiii−i−iii−i−i−i−iii
χ171111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11-11-11-11-11-11-11-11-1
χ181111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-11-11-11-11-11-11-11-11
χ191111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111111-11-11-11-1-11-11-11-11
χ201111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-11-11-11-111-11-11-11-1
χ211111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111-11-1-11-111-11-1-11-11
χ221111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-11-111-11-1-11-111-11-1
χ231111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-11-11-1-11-11-11-111-11-1
χ241111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-11-111-11-11-11-1-11-11
χ251111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111i−i−iii−i−iii−i−iii−i−ii
χ261111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111−iii−i−iii−i−iii−i−iii−i
χ271111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1i−i−iii−i−ii−iii−i−iii−i
χ281111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1−iii−i−iii−ii−i−iii−i−ii
χ291111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1i−i−ii−iii−ii−i−ii−iii−i
χ301111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1−iii−ii−i−ii−iii−ii−i−ii
χ311111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111i−i−ii−iii−i−iii−ii−i−ii
χ321111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111−iii−ii−i−iii−i−ii−iii−i
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χ34222222-2-2-2-222-2-22222-2-2-2-22-222-2-200000000000000000000000000000000−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i0000000000000000
χ35222222-2-2-2-222-2-2-2-2-2-222222-2-2-222000000000000000000000000000000002i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i0000000000000000
χ36222222-2-2-2-222-2-2-2-2-2-222222-2-2-22200000000000000000000000000000000−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i0000000000000000
χ37222222-2-2-2-2-2-2222222-2-2-2-2-22-2-222000000000000000000000000000000002i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i0000000000000000
χ38222222-2-2-2-2-2-2222222-2-2-2-2-22-2-22200000000000000000000000000000000−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i0000000000000000
χ39222222-2-2-2-2-2-222-2-2-2-22222-2222-2-2000000000000000000000000000000002i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i0000000000000000
χ40222222-2-2-2-2-2-222-2-2-2-22222-2222-2-200000000000000000000000000000000−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i0000000000000000
χ412222-2-222-2-222-2-222-2-222-2-2-222-22-200000000000000002i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000
χ422222-2-222-2-222-2-222-2-222-2-2-222-22-20000000000000000−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000
χ432222-2-222-2-222-2-2-2-222-2-222-22-22-2200000000000000002i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000
χ442222-2-222-2-222-2-2-2-222-2-222-22-22-220000000000000000−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000
χ452222-2-222-2-2-2-22222-2-222-2-22-2-22-2200000000000000002i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ462222-2-222-2-2-2-22222-2-222-2-22-2-22-220000000000000000−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ472222-2-222-2-2-2-222-2-222-2-2222-22-22-200000000000000002i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ482222-2-222-2-2-2-222-2-222-2-2222-22-22-20000000000000000−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ492222-2-2-2-222222222-2-2-2-222-2-22-2-2222-2-222-2-222-2-222-2-2000000000000000000000000000000000000000000000000
χ502222-2-2-2-222222222-2-2-2-222-2-22-2-22-2-222-2-222-2-222-2-222000000000000000000000000000000000000000000000000
χ512222-2-2-2-2222222-2-22222-2-2-2-2-222-222-2-222-2-2-2-222-2-222000000000000000000000000000000000000000000000000
χ522222-2-2-2-2222222-2-22222-2-2-2-2-222-2-2-222-2-22222-2-222-2-2000000000000000000000000000000000000000000000000
χ532222-2-2-2-222-2-2-2-222-2-2-2-22222-222-222-2-2-2-22222-2-2-2-222000000000000000000000000000000000000000000000000
χ542222-2-2-2-222-2-2-2-222-2-2-2-22222-222-2-2-22222-2-2-2-22222-2-2000000000000000000000000000000000000000000000000
χ552222-2-2-2-222-2-2-2-2-2-22222-2-2222-2-2222-2-2-2-222-2-22222-2-2000000000000000000000000000000000000000000000000
χ562222-2-2-2-222-2-2-2-2-2-22222-2-2222-2-22-2-22222-2-222-2-2-2-222000000000000000000000000000000000000000000000000
χ572-22-22-22-22-200002i−2i2i−2i2i−2i2i−2i00000000002i−2i2i−2i00002-22-200002i−2i2i−2i00002-22-22-22-200002i−2i2i−2i00000000000000000000
χ582-22-22-22-22-200002i−2i2i−2i2i−2i2i−2i00000000002i−2i2i−2i00002-22-20000−2i2i−2i2i0000-22-22-22-220000−2i2i−2i2i00000000000000000000
χ592-22-22-22-22-200002i−2i2i−2i2i−2i2i−2i0000000000−2i2i−2i2i0000-22-2200002i−2i2i−2i00002-22-2-22-220000−2i2i−2i2i00000000000000000000
χ602-22-22-22-22-200002i−2i2i−2i2i−2i2i−2i0000000000−2i2i−2i2i0000-22-220000−2i2i−2i2i0000-22-222-22-200002i−2i2i−2i00000000000000000000
χ612-22-22-22-22-20000−2i2i−2i2i−2i2i−2i2i00000000002i−2i2i−2i0000-22-2200002i−2i2i−2i0000-22-222-22-20000−2i2i−2i2i00000000000000000000
χ622-22-22-22-22-20000−2i2i−2i2i−2i2i−2i2i00000000002i−2i2i−2i0000-22-220000−2i2i−2i2i00002-22-2-22-2200002i−2i2i−2i00000000000000000000
χ632-22-22-22-22-20000−2i2i−2i2i−2i2i−2i2i0000000000−2i2i−2i2i00002-22-200002i−2i2i−2i0000-22-22-22-2200002i−2i2i−2i00000000000000000000
χ642-22-22-22-22-20000−2i2i−2i2i−2i2i−2i2i0000000000−2i2i−2i2i00002-22-20000−2i2i−2i2i00002-22-22-22-20000−2i2i−2i2i00000000000000000000
χ652-22-22-2-22-2200002i−2i2i−2i−2i2i−2i2i0000002-22-200002i−2i2i−2i00002i−2i2i−2i00002-22-200002i−2i−2i2i0000-222-200000000000000000000
χ662-22-22-2-22-2200002i−2i2i−2i−2i2i−2i2i0000002-22-200002i−2i2i−2i0000−2i2i−2i2i0000-22-220000−2i2i2i−2i00002-2-2200000000000000000000
χ672-22-22-2-22-2200002i−2i2i−2i−2i2i−2i2i000000-22-220000−2i2i−2i2i00002i−2i2i−2i00002-22-20000−2i2i2i−2i00002-2-2200000000000000000000
χ682-22-22-2-22-2200002i−2i2i−2i−2i2i−2i2i000000-22-220000−2i2i−2i2i0000−2i2i−2i2i0000-22-2200002i−2i−2i2i0000-222-200000000000000000000
χ692-22-22-2-22-220000−2i2i−2i2i2i−2i2i−2i0000002-22-20000−2i2i−2i2i00002i−2i2i−2i0000-22-2200002i−2i−2i2i00002-2-2200000000000000000000
χ702-22-22-2-22-220000−2i2i−2i2i2i−2i2i−2i0000002-22-20000−2i2i−2i2i0000−2i2i−2i2i00002-22-20000−2i2i2i−2i0000-222-200000000000000000000
χ712-22-22-2-22-220000−2i2i−2i2i2i−2i2i−2i000000-22-2200002i−2i2i−2i00002i−2i2i−2i0000-22-220000−2i2i2i−2i0000-222-200000000000000000000
χ722-22-22-2-22-220000−2i2i−2i2i2i−2i2i−2i000000-22-2200002i−2i2i−2i0000−2i2i−2i2i00002-22-200002i−2i−2i2i00002-2-2200000000000000000000
χ732-22-2-222-2-2200002i−2i−2i2i2i−2i−2i2i0000002-2-2200002i−2i−2i2i000000002-2-220000−2i2i2i−2i00002-22-200002i−2i2i−2i0000000000000000
χ742-22-2-222-2-2200002i−2i−2i2i2i−2i−2i2i0000002-2-2200002i−2i−2i2i00000000-222-200002i−2i−2i2i0000-22-220000−2i2i−2i2i0000000000000000
χ752-22-2-222-2-2200002i−2i−2i2i2i−2i−2i2i000000-222-20000−2i2i2i−2i000000002-2-220000−2i2i2i−2i0000-22-220000−2i2i−2i2i0000000000000000
χ762-22-2-222-2-2200002i−2i−2i2i2i−2i−2i2i000000-222-20000−2i2i2i−2i00000000-222-200002i−2i−2i2i00002-22-200002i−2i2i−2i0000000000000000
χ772-22-2-222-2-220000−2i2i2i−2i−2i2i2i−2i0000002-2-220000−2i2i2i−2i000000002-2-2200002i−2i−2i2i00002-22-20000−2i2i−2i2i0000000000000000
χ782-22-2-222-2-220000−2i2i2i−2i−2i2i2i−2i0000002-2-220000−2i2i2i−2i00000000-222-20000−2i2i2i−2i0000-22-2200002i−2i2i−2i0000000000000000
χ792-22-2-222-2-220000−2i2i2i−2i−2i2i2i−2i000000-222-200002i−2i−2i2i000000002-2-2200002i−2i−2i2i0000-22-2200002i−2i2i−2i0000000000000000
χ802-22-2-222-2-220000−2i2i2i−2i−2i2i2i−2i000000-222-200002i−2i−2i2i00000000-222-20000−2i2i2i−2i00002-22-20000−2i2i−2i2i0000000000000000
χ812-22-2-22-222-200002i−2i−2i2i−2i2i2i−2i00000000002i−2i−2i2i00002-2-222-2-220000−2i2i2i−2i000000002i−2i−2i2i0000-222-20000000000000000
χ822-22-2-22-222-200002i−2i−2i2i−2i2i2i−2i00000000002i−2i−2i2i00002-2-22-222-200002i−2i−2i2i00000000−2i2i2i−2i00002-2-220000000000000000
χ832-22-2-22-222-200002i−2i−2i2i−2i2i2i−2i0000000000−2i2i2i−2i0000-222-22-2-220000−2i2i2i−2i00000000−2i2i2i−2i00002-2-220000000000000000
χ842-22-2-22-222-200002i−2i−2i2i−2i2i2i−2i0000000000−2i2i2i−2i0000-222-2-222-200002i−2i−2i2i000000002i−2i−2i2i0000-222-20000000000000000
χ852-22-2-22-222-20000−2i2i2i−2i2i−2i−2i2i00000000002i−2i−2i2i0000-222-22-2-2200002i−2i−2i2i000000002i−2i−2i2i00002-2-220000000000000000
χ862-22-2-22-222-20000−2i2i2i−2i2i−2i−2i2i00000000002i−2i−2i2i0000-222-2-222-20000−2i2i2i−2i00000000−2i2i2i−2i0000-222-20000000000000000
χ872-22-2-22-222-20000−2i2i2i−2i2i−2i−2i2i0000000000−2i2i2i−2i00002-2-222-2-2200002i−2i−2i2i00000000−2i2i2i−2i0000-222-20000000000000000
χ882-22-2-22-222-20000−2i2i2i−2i2i−2i−2i2i0000000000−2i2i2i−2i00002-2-22-222-20000−2i2i2i−2i000000002i−2i−2i2i00002-2-220000000000000000
χ8988-8-8000000008-8000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9088-8-800000000-88000000000000000000000000000000000000000000000000000000000000000000000000000000
χ918-8-880000008i−8i00000000000000000000000000000000000000000000000000000000000000000000000000000000
χ928-8-88000000−8i8i00000000000000000000000000000000000000000000000000000000000000000000000000000000

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