Finite Group Databasebeta

← Group #223165

Character table — Group #223165

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95
size11111111222222222222222222224444444444444444444444444444448888888888888888888888888888888161616161616
order12222222444444444444444444442244444444444488888888888888882444444888888888888888888888888444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-11ii−i−iiiii−i−i−i−iiiii−i−i−i−iii−i−i11-1-11-1
χ611111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii11-1-1111ii−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−iii-1-111-11
χ711111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i11-1-1111−i−iiiiiii−i−i−i−i−i−i−i−iiiiiii−i−i-1-111-11
χ811111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-11−i−iii−i−i−i−iiiii−i−i−i−iiiii−i−iii11-1-11-1
χ9111111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11111-1-11111111111111111-111111-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ10111111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-11-1-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1
χ11111111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-11-1-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1-1-11111-1-1
χ12111111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-111-1-111111111111111-1-1-1-111
χ13111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111iiii−i−i−i−iiiii−i−i−i−i-1111-1-1-1ii−i−iii−i−i−i−iii−i−i−i−iiiii−i−iii-1-1111-1
χ14111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii-11-1-111-1ii−i−i−i−iiiii−i−i−i−i−i−iiiiiii−i−i11-1-1-11
χ15111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i-11-1-111-1−i−iiiii−i−i−i−iiiiiii−i−i−i−i−i−iii11-1-1-11
χ16111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111−i−i−i−iiiii−i−i−i−iiiii-1111-1-1-1−i−iii−i−iiiii−i−iiiii−i−i−i−iii−i−i-1-1111-1
χ1711111111-1-1-1-11111-1-1-1-111111111111111-1-1-1-1-1-1-1-11111111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111111-11-1-1-1
χ1811111111-1-1-1-11111-1-1-1-111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111111111-1-111-1-1-1-1-1-1-11-1111
χ1911111111-1-1-1-11111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-111-1-1111111-11-1111
χ2011111111-1-1-1-11111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-111-1-111-1-1-1-11-11-1-1-1
χ2111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111iiii−i−i−i−iiiii−i−i−i−i-1-111-1-11−i−iii−i−i−i−iiiiiii−i−i−i−iiiii−i−i1-1-11-11
χ2211111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111iiii−i−i−i−i−i−i−i−iiiii-1-1-1-1111−i−iiiiiii−i−i−i−iii−i−i−i−iii−i−iii-111-11-1
χ2311111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-1111ii−i−i−i−i−i−iiiii−i−iiiii−i−iii−i−i-111-11-1
χ2411111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111−i−i−i−iiiii−i−i−i−iiiii-1-111-1-11ii−i−iiiii−i−i−i−i−i−iiiii−i−i−i−iii1-1-11-11
χ2511111111-1-1-1-1-1-1-1-1111111111111-1-111-1-111-1-1-1-11111111111111111111-11111-1-1-1-1-1-1-111-1-111-1-111-1-111-1-1-1-1-11-11-1-1
χ2611111111-1-1-1-1-1-1-1-1111111111111-1-111-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-11111111-11-111
χ2711111111-1-1-1-1-1-1-1-1111111111111-1-111-1-111-1-1-1-111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-11111-1-111-1-11111-1-111-1-1-1-1-1-11-11-111
χ2811111111-1-1-1-1-1-1-1-1111111111111-1-111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11111-1111111-1-111-1-111-1-111-1-11111-11-11-1-1
χ2911111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-11111-1-1iiii−i−i−i−iiiii−i−i−i−i1-111-1-1-1−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−iii-111-1-11
χ3011111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiii1-1-1-111-1−i−iiiii−i−i−i−iii−i−iiiii−i−iii−i−i1-1-111-1
χ3111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-11111-1-1−i−i−i−iiiiiiiii−i−i−i−i1-1-1-111-1ii−i−i−i−iiiii−i−iii−i−i−i−iii−i−iii1-1-111-1
χ3211111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-11111-1-1−i−i−i−iiiii−i−i−i−iiiii1-111-1-1-1ii−i−iii−i−i−i−iiiii−i−i−i−iiiii−i−i-111-1-11
χ33222222222222222222222-222-2-22-222-2-2-2-2-2-222-2-2220000000000000000-2-20000-2000000000000000000000000000000
χ3422222222222222222222-22-2-222-22-2-2-2-22222-2-222-2-20000000000000000-2-20000-2000000000000000000000000000000
χ35222222222222-2-2-2-2-2-2-2-22-222-2-22-2-2-2-2-2222222-2-2-2-200000000000000002-200002000000000000000000000000000000
χ36222222222222-2-2-2-2-2-2-2-2-22-2-222-2222-2-2-2-2-2-2-2-2222200000000000000002-200002000000000000000000000000000000
χ3722222222-2-2-2-22222-2-2-2-22-222-2-22-222-2-2-2-222-2-222-2-20000000000000000220000-2000000000000000000000000000000
χ3822222222-2-2-2-22222-2-2-2-2-22-2-222-22-2-2-2-222-2-222-2-2220000000000000000220000-2000000000000000000000000000000
χ3922222222-2-2-2-2-2-2-2-222222-222-2-22-2-2-2-2-222-2-2-2-222220000000000000000-2200002000000000000000000000000000000
χ4022222222-2-2-2-2-2-2-2-22222-22-2-222-2222-2-2-2-22222-2-2-2-20000000000000000-2200002000000000000000000000000000000
χ4122-2-22-2-2222-2-22i2i−2i−2i2i2i−2i−2i0200-2-20200002i−2i2i−2i002-20000000000i2i2−i2−i2i2i2−i2−i200000000000i2−i22−2i2−i22−2000000002−22−2000000
χ4222-2-22-2-2222-2-22i2i−2i−2i2i2i−2i−2i0200-2-20200002i−2i2i−2i002-20000000000−i2−i2i2i2−i2−i2i2i200000000000−i2i2−22−i2i2−2200000000−22−22000000
χ4322-2-22-2-2222-2-22i2i−2i−2i2i2i−2i−2i0-200220-20000−2i2i−2i2i00-22000000000022−2−2−2−222000000000002−2−i2i2−22i2−i200000000−i2i2i2−i2000000
χ4422-2-22-2-2222-2-22i2i−2i−2i2i2i−2i−2i0-200220-20000−2i2i−2i2i00-220000000000−2−22222−2−200000000000−22i2−i22−2−i2i200000000i2−i2−i2i2000000
χ4522-2-22-2-2222-2-2−2i−2i2i2i−2i−2i2i2i0200-2-2020000−2i2i−2i2i002-20000000000i2i2−i2−i2i2i2−i2−i200000000000i2−i2−22i2−i2−2200000000−22−22000000
χ4622-2-22-2-2222-2-2−2i−2i2i2i−2i−2i2i2i0200-2-2020000−2i2i−2i2i002-20000000000−i2−i2i2i2−i2−i2i2i200000000000−i2i22−2−i2i22−2000000002−22−2000000
χ4722-2-22-2-2222-2-2−2i−2i2i2i−2i−2i2i2i0-200220-200002i−2i2i−2i00-22000000000022−2−2−2−222000000000002−2i2−i2−22−i2i200000000i2−i2−i2i2000000
χ4822-2-22-2-2222-2-2−2i−2i2i2i−2i−2i2i2i0-200220-200002i−2i2i−2i00-220000000000−2−22222−2−200000000000−22−i2i22−2i2−i200000000−i2i2i2−i2000000
χ4922-2-22-2-22-2-2222i2i−2i−2i−2i−2i2i2i0200-2-20200002i−2i−2i2i00-220000000000i2i2−i2−i2i2i2−i2−i200000000000−i2i2−22−i2i2−22000000002−22−2000000
χ5022-2-22-2-22-2-2222i2i−2i−2i−2i−2i2i2i0200-2-20200002i−2i−2i2i00-220000000000−i2−i2i2i2−i2−i2i2i200000000000i2−i22−2i2−i22−200000000−22−22000000
χ5122-2-22-2-22-2-2222i2i−2i−2i−2i−2i2i2i0-200220-20000−2i2i2i−2i002-2000000000022−2−2−2−22200000000000−22i2−i22−2−i2i200000000−i2i2i2−i2000000
χ5222-2-22-2-22-2-2222i2i−2i−2i−2i−2i2i2i0-200220-20000−2i2i2i−2i002-20000000000−2−22222−2−2000000000002−2−i2i2−22i2−i200000000i2−i2−i2i2000000
χ5322-2-22-2-22-2-222−2i−2i2i2i2i2i−2i−2i0200-2-2020000−2i2i2i−2i00-220000000000i2i2−i2−i2i2i2−i2−i200000000000−i2i22−2−i2i22−200000000−22−22000000
χ5422-2-22-2-22-2-222−2i−2i2i2i2i2i−2i−2i0200-2-2020000−2i2i2i−2i00-220000000000−i2−i2i2i2−i2−i2i2i200000000000i2−i2−22i2−i2−22000000002−22−2000000
χ5522-2-22-2-22-2-222−2i−2i2i2i2i2i−2i−2i0-200220-200002i−2i−2i2i002-2000000000022−2−2−2−22200000000000−22−i2i22−2i2−i200000000i2−i2−i2i2000000
χ5622-2-22-2-22-2-222−2i−2i2i2i2i2i−2i−2i0-200220-200002i−2i−2i2i002-20000000000−2−22222−2−2000000000002−2i2−i2−22−i2i200000000−i2i2i2−i2000000
χ572-222-2-2-220000000000002-22-22-2-22002-2000000000022-2-222-2-22i−2i2i−2i2i−2i2i−2i002i−2i2i−2i0000000000000000000000000000000
χ582-222-2-2-220000000000002-22-22-2-22002-2000000000022-2-222-2-2−2i2i−2i2i−2i2i−2i2i00−2i2i−2i2i0000000000000000000000000000000
χ592-222-2-2-220000000000002-22-22-2-22002-20000000000-2-222-2-2222i−2i2i−2i2i−2i2i−2i00−2i2i−2i2i0000000000000000000000000000000
χ602-222-2-2-220000000000002-22-22-2-22002-20000000000-2-222-2-222−2i2i−2i2i−2i2i−2i2i002i−2i2i−2i0000000000000000000000000000000
χ612-222-2-2-22000000000000-22-22-222-2002-200000000002i2i−2i−2i−2i−2i2i2i2-22-2-22-2200−2i2i2i−2i0000000000000000000000000000000
χ622-222-2-2-22000000000000-22-22-222-2002-200000000002i2i−2i−2i−2i−2i2i2i-22-222-22-2002i−2i−2i2i0000000000000000000000000000000
χ632-222-2-2-22000000000000-22-22-222-2002-20000000000−2i−2i2i2i2i2i−2i−2i2-22-2-22-22002i−2i−2i2i0000000000000000000000000000000
χ642-222-2-2-22000000000000-22-22-222-2002-20000000000−2i−2i2i2i2i2i−2i−2i-22-222-22-200−2i2i2i−2i0000000000000000000000000000000
χ652-22-222-2-22i−2i2i−2i2-22-22i−2i2i−2i20-2-200202-20000002i−2i002i−2i2−22−22−22−2000000000000000i2−i2i2−i2000000002−2i2−i22−2i2−i20000000000
χ662-22-222-2-22i−2i2i−2i2-22-22i−2i2i−2i20-2-200202-20000002i−2i002i−2i−22−22−22−22000000000000000−i2i2−i2i200000000−22−i2i2−22−i2i20000000000
χ672-22-222-2-22i−2i2i−2i2-22-22i−2i2i−2i-202200-20-22000000−2i2i00−2i2ii2−i2i2−i2−i2i2−i2i2000000000000000−222−200000000i2−i2−22−i2i22−20000000000
χ682-22-222-2-22i−2i2i−2i2-22-22i−2i2i−2i-202200-20-22000000−2i2i00−2i2i−i2i2−i2i2i2−i2i2−i20000000000000002−2−2200000000−i2i22−2i2−i2−220000000000
χ692-22-222-2-22i−2i2i−2i-22-22−2i2i−2i2i20-2-20020-220000002i−2i00−2i2i2−22−22−22−2000000000000000i2−i2i2−i200000000−22−i2i2−22−i2i20000000000
χ702-22-222-2-22i−2i2i−2i-22-22−2i2i−2i2i20-2-20020-220000002i−2i00−2i2i−22−22−22−22000000000000000−i2i2−i2i2000000002−2i2−i22−2i2−i20000000000
χ712-22-222-2-22i−2i2i−2i-22-22−2i2i−2i2i-202200-202-2000000−2i2i002i−2ii2−i2i2−i2−i2i2−i2i2000000000000000−222−200000000−i2i22−2i2−i2−220000000000
χ722-22-222-2-22i−2i2i−2i-22-22−2i2i−2i2i-202200-202-2000000−2i2i002i−2i−i2i2−i2i2i2−i2i2−i20000000000000002−2−2200000000i2−i2−22−i2i22−20000000000
χ732-22-222-2-2−2i2i−2i2i2-22-2−2i2i−2i2i20-2-200202-2000000−2i2i00−2i2i2−22−22−22−2000000000000000−i2i2−i2i2000000002−2−i2i22−2−i2i20000000000
χ742-22-222-2-2−2i2i−2i2i2-22-2−2i2i−2i2i20-2-200202-2000000−2i2i00−2i2i−22−22−22−22000000000000000i2−i2i2−i200000000−22i2−i2−22i2−i20000000000
χ752-22-222-2-2−2i2i−2i2i2-22-2−2i2i−2i2i-202200-20-220000002i−2i002i−2ii2−i2i2−i2−i2i2−i2i20000000000000002−2−2200000000i2−i22−2−i2i2−220000000000
χ762-22-222-2-2−2i2i−2i2i2-22-2−2i2i−2i2i-202200-20-220000002i−2i002i−2i−i2i2−i2i2i2−i2i2−i2000000000000000−222−200000000−i2i2−22i2−i22−20000000000
χ772-22-222-2-2−2i2i−2i2i-22-222i−2i2i−2i20-2-20020-22000000−2i2i002i−2i2−22−22−22−2000000000000000−i2i2−i2i200000000−22i2−i2−22i2−i20000000000
χ782-22-222-2-2−2i2i−2i2i-22-222i−2i2i−2i20-2-20020-22000000−2i2i002i−2i−22−22−22−22000000000000000i2−i2i2−i2000000002−2−i2i22−2−i2i20000000000
χ792-22-222-2-2−2i2i−2i2i-22-222i−2i2i−2i-202200-202-20000002i−2i00−2i2ii2−i2i2−i2−i2i2−i2i20000000000000002−2−2200000000−i2i2−22i2−i22−20000000000
χ802-22-222-2-2−2i2i−2i2i-22-222i−2i2i−2i-202200-202-20000002i−2i00−2i2i−i2i2−i2i2i2−i2i2−i2000000000000000−222−200000000i2−i22−2−i2i2−220000000000
χ81444-4-4-44-400000000000040-4400-400000000000000022−22−222222−22−2222000000000000000000000000000000000000000000000
χ82444-4-4-44-400000000000040-4400-4000000000000000−222222−22−222222−22000000000000000000000000000000000000000000000
χ83444-4-4-44-4000000000000-404-40040000000000000002i2−2i2−2i22i2−2i22i22i2−2i2000000000000000000000000000000000000000000000
χ84444-4-4-44-4000000000000-404-4004000000000000000−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000000000000000000000000000000
χ854-444-4-4-44000000000000444-4-44-4-400-44000000000000000000000000000000000000000000000000000000000000000
χ864-444-4-4-44000000000000-4-4-444-44400-44000000000000000000000000000000000000000000000000000000000000000
χ874-4-444-44-44i−4i−4i4i4i−4i−4i4i-444-4000000000000000000000000000000000000000000000000000000000000000000000000000
χ884-4-444-44-44i−4i−4i4i−4i4i4i−4i4-4-44000000000000000000000000000000000000000000000000000000000000000000000000000
χ894-4-444-44-4−4i4i4i−4i4i−4i−4i4i4-4-44000000000000000000000000000000000000000000000000000000000000000000000000000
χ904-4-444-44-4−4i4i4i−4i−4i4i4i−4i-444-4000000000000000000000000000000000000000000000000000000000000000000000000000
χ914-4-4-4-444400000000000004004-40-400000000000000000000002i2−2i2−2i22i2−2i22i22i2−2i20000000000000000000000000000000000000
χ924-4-4-4-444400000000000004004-40-40000000000000000000000−2i22i22i2−2i22i2−2i2−2i22i20000000000000000000000000000000000000
χ934-4-4-4-44440000000000000-400-4404000000000000000000000022−22−222222−22−22220000000000000000000000000000000000000
χ944-4-4-4-44440000000000000-400-44040000000000000000000000−222222−22−222222−220000000000000000000000000000000000000
χ9588-88-88-8-8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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