Finite Group Databasebeta

← Group #6575990

Character table — Group #6575990

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95
size11111111222222222222222222224444444444444444444444444444448888888888888888888888888888888161616161616
order12222222222244444444444444442222444444444444444444888888882224444444444444444888888888888244444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-111111111111111-1-1-1-1111111111-1-11-1-1-1-1-1-11-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-1-1-11-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111-1-1-1-1111111111-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-111-111-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-11-1
χ6111111111111111111111-1-1-1-1111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-111-111-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-111-1-111-11
χ7111111111111111111111-1-1-1-1111-1-1-1-111-1-111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111111111-1-1-1-111-1-1-1-111-11
χ8111111111111111111111-1-1-1-1111-1-1-1-111-1-111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-11111-1-1-1-1-1-11111-1-11111-1-11-1
χ9111111111111-1-1-1-11-1-1-1-111111111111-1-1-1-111-1-111-1-111111111111111-111-1-1-1-1-1-1-11-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111
χ10111111111111-1-1-1-11-1-1-1-111111111111-1-1-1-111-1-111-1-1111111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-11-1-1-1-111-1-111111111-1-1-1-11111-1-1
χ11111111111111-1-1-1-11-1-1-1-11111111-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ12111111111111-1-1-1-11-1-1-1-11111111-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-11111111111-1-1-1-1-1-1-1-111
χ13111111111111-1-1-1-11-1-1-1-1-1-1-1-11111111-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1111-1
χ14111111111111-1-1-1-11-1-1-1-1-1-1-1-11111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-11
χ15111111111111-1-1-1-11-1-1-1-1-1-1-1-1111-1-1-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-11-1-1111-1-1-1-1-111-1-11111-1-1-1-1111111-1-111-1-1-11
χ16111111111111-1-1-1-11-1-1-1-1-1-1-1-1111-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-111111-1-1111-1-1-1-1-1111111-1-11111-1-1-1-1-1-111-1-1111-1
χ1711111111-1-1-1-111111-1-1-1-1111111111111111-1-1-1-111-1-1-1-1111111111111-1-1-111111-1-1-1-1-111-1-11111-1-111-1-1-1-1-1-1-111-1-1-1
χ1811111111-1-1-1-111111-1-1-1-1111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111111-1-1111
χ1911111111-1-1-1-111111-1-1-1-11111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111111111-1111-1-1-1-111-111-1-111-1-111-1-111-1-1-1-1-1-11-1-1111
χ2011111111-1-1-1-111111-1-1-1-11111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-111-111111111-1-111-1-1111111-111-1-1-1
χ2111111111-1-1-1-111111-1-1-1-1-1-1-1-1111111111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-11-1-1-111-1-1111-1-11111-1-111-1-1-1-111-1-111-11-11-11
χ2211111111-1-1-1-111111-1-1-1-1-1-1-1-1111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111111-1-1-111-1-1111-1-1-1-11111-1-11111-1-111-1-11-11-11-1
χ2311111111-1-1-1-111111-1-1-1-1-1-1-1-1111-1-1-1-111-1-1-1-111-1-1-1-11111111111-1-1-1-1111-1-1-111-1-1111-1-1-1-11111-1-1-1-111-1-1111-11-11-1
χ2411111111-1-1-1-111111-1-1-1-1-1-1-1-1111-1-1-1-111-1-1-1-111-1-1-1-1111111-1-1-1-11111111-1-1-111-1-111111-1-1-1-1-1-11111-1-111-1-1-11-11-11
χ2511111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1111111-1-11111111111111-1-1-1-1-1-1-111-11111-1-111-1-111-1-111-1-1-1-11-1-11-1-1
χ2611111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-111-111-1-1-1-1-1-111-1-111-1-11111-111-111
χ2711111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111111111-11111-1-1-1-1-1-1-111-1-1-1-111-1-111-1-1-1-1-111-111
χ2811111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-11111-1-1-1-1-111111111-1-111-1-111111-1-11-1-1
χ2911111111-1-1-1-1-1-1-1-111111-1-1-1-11111111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-11-1-111-1-11111111-1-1-1-11111-1-1-1-1111-11-1-11
χ3011111111-1-1-1-1-1-1-1-111111-1-1-1-11111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-11-1-111-1-1111-1-1111111-1-1-1-11111-1-1-11-111-1
χ3111111111-1-1-1-1-1-1-1-111111-1-1-1-1111-1-1-1-1-1-111-1-1-1-1-1-1111111111111-1-1-1-1-111111-1-1111-1-1-1-1-1-111-1-11111-1-1-1-111-11-111-1
χ3211111111-1-1-1-1-1-1-1-111111-1-1-1-1111-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-11111-111111-1-1111-1-111-1-1-1-111-1-1-1-11111-1-11-11-1-11
χ332222222222222222-222222222-2-2-20000-2-222-2-222-2-2-2-222000000000000-200-2000000-200000000000000000000000000
χ342222222222222222-22222-2-2-2-2-2-2-20000-2-2-2-2-2-2-2-222-2-2-2-20000000000002002000000200000000000000000000000000
χ35222222222222-2-2-2-2-2-2-2-2-22222-2-2-2000022-2-2-2-2-2-2-2-222220000000000002002000000-200000000000000000000000000
χ36222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200002222-2-2222222-2-2000000000000-200-2000000200000000000000000000000000
χ3722222222-2-2-2-22222-2-2-2-2-22222-2-2-20000-2-22222-2-2-2-222-2-2000000000000200-2000000200000000000000000000000000
χ3822222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-20000-2-2-2-22222222222000000000000-2002000000-200000000000000000000000000
χ3922222222-2-2-2-2-2-2-2-2-222222222-2-2-2000022-2-22222-2-2-2-2-2-2000000000000-2002000000200000000000000000000000000
χ4022222222-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-20000222222-2-222-2-222000000000000200-2000000-200000000000000000000000000
χ412-222-2-22-222-2-222-2-2022-2-22i2i−2i−2i0000000002i−2i002i−2i00002i−2i000022−2−2i2i2−i2−i200000000000000000002−22−2i2−i2i2−i22−2i2−i2000000
χ422-222-2-22-222-2-222-2-2022-2-22i2i−2i−2i0000000002i−2i002i−2i00002i−2i0000−2−222−i2−i2i2i20000000000000000000−22−22−i2i2−i2i2−22−i2i2000000
χ432-222-2-22-222-2-222-2-2022-2-2−2i−2i2i2i000000000−2i2i00−2i2i0000−2i2i000022−2−2−i2−i2i2i200000000000000000002−22−2−i2i2−i2i22−2−i2i2000000
χ442-222-2-22-222-2-222-2-2022-2-2−2i−2i2i2i000000000−2i2i00−2i2i0000−2i2i0000−2−222i2i2−i2−i20000000000000000000−22−22i2−i2i2−i2−22i2−i2000000
χ452-222-2-22-222-2-2-2-2220-2-2222i2i−2i−2i000000000−2i2i00−2i2i00002i−2i000022−2−2i2i2−i2−i20000000000000000000−22−22−i2i2−i2i22−2i2−i2000000
χ462-222-2-22-222-2-2-2-2220-2-2222i2i−2i−2i000000000−2i2i00−2i2i00002i−2i0000−2−222−i2−i2i2i200000000000000000002−22−2i2−i2i2−i2−22−i2i2000000
χ472-222-2-22-222-2-2-2-2220-2-222−2i−2i2i2i0000000002i−2i002i−2i0000−2i2i000022−2−2−i2−i2i2i20000000000000000000−22−22i2−i2i2−i22−2−i2i2000000
χ482-222-2-22-222-2-2-2-2220-2-222−2i−2i2i2i0000000002i−2i002i−2i0000−2i2i0000−2−222i2i2−i2−i200000000000000000002−22−2−i2i2−i2i2−22i2−i2000000
χ492-222-2-22-2-2-22222-2-20-2-2222i2i−2i−2i0000000002i−2i00−2i2i0000−2i2i000022−2−2i2i2−i2−i200000000000000000002−2−22i2−i2−i2i2−22−i2i2000000
χ502-222-2-22-2-2-22222-2-20-2-2222i2i−2i−2i0000000002i−2i00−2i2i0000−2i2i0000−2−222−i2−i2i2i20000000000000000000−222−2−i2i2i2−i22−2i2−i2000000
χ512-222-2-22-2-2-22222-2-20-2-222−2i−2i2i2i000000000−2i2i002i−2i00002i−2i000022−2−2−i2−i2i2i200000000000000000002−2−22−i2i2i2−i2−22i2−i2000000
χ522-222-2-22-2-2-22222-2-20-2-222−2i−2i2i2i000000000−2i2i002i−2i00002i−2i0000−2−222i2i2−i2−i20000000000000000000−222−2i2−i2−i2i22−2−i2i2000000
χ532-222-2-22-2-2-222-2-222022-2-22i2i−2i−2i000000000−2i2i002i−2i0000−2i2i000022−2−2i2i2−i2−i20000000000000000000−222−2−i2i2i2−i2−22−i2i2000000
χ542-222-2-22-2-2-222-2-222022-2-22i2i−2i−2i000000000−2i2i002i−2i0000−2i2i0000−2−222−i2−i2i2i200000000000000000002−2−22i2−i2−i2i22−2i2−i2000000
χ552-222-2-22-2-2-222-2-222022-2-2−2i−2i2i2i0000000002i−2i00−2i2i00002i−2i000022−2−2−i2−i2i2i20000000000000000000−222−2i2−i2−i2i2−22i2−i2000000
χ562-222-2-22-2-2-222-2-222022-2-2−2i−2i2i2i0000000002i−2i00−2i2i00002i−2i0000−2−222i2i2−i2−i200000000000000000002−2−22−i2i2i2−i22−2−i2i2000000
χ572-22-222-2-22-22-22i−2i2i−2i22i−2i2i−2i0000-2-2200002i−2i002-200002i−2i002i2i−2i−2i000000000000002-22-2000002i−2i00000000000000000000
χ582-22-222-2-22-22-22i−2i2i−2i22i−2i2i−2i0000-2-2200002i−2i002-200002i−2i00−2i−2i2i2i00000000000000-22-2200000−2i2i00000000000000000000
χ592-22-222-2-22-22-22i−2i2i−2i-22i−2i2i−2i000022-222-2-2−2i2i00-220000−2i2i0000000000000002-202i−2i000002i−2i000000000000000000000000
χ602-22-222-2-22-22-22i−2i2i−2i-22i−2i2i−2i000022-2-2-222−2i2i00-220000−2i2i000000000000000-220−2i2i00000−2i2i000000000000000000000000
χ612-22-222-2-22-22-2−2i2i−2i2i2−2i2i−2i2i0000-2-220000−2i2i002-20000−2i2i002i2i−2i−2i00000000000000-22-22000002i−2i00000000000000000000
χ622-22-222-2-22-22-2−2i2i−2i2i2−2i2i−2i2i0000-2-220000−2i2i002-20000−2i2i00−2i−2i2i2i000000000000002-22-200000−2i2i00000000000000000000
χ632-22-222-2-22-22-2−2i2i−2i2i-2−2i2i−2i2i000022-222-2-22i−2i00-2200002i−2i0000000000000002-20−2i2i00000−2i2i000000000000000000000000
χ642-22-222-2-22-22-2−2i2i−2i2i-2−2i2i−2i2i000022-2-2-2222i−2i00-2200002i−2i000000000000000-2202i−2i000002i−2i000000000000000000000000
χ652-22-222-2-2-22-222i−2i2i−2i2−2i2i−2i2i0000-2-2200002i−2i00-220000−2i2i002i2i−2i−2i000000000000002-2-2200000−2i2i00000000000000000000
χ662-22-222-2-2-22-222i−2i2i−2i2−2i2i−2i2i0000-2-2200002i−2i00-220000−2i2i00−2i−2i2i2i00000000000000-222-2000002i−2i00000000000000000000
χ672-22-222-2-2-22-222i−2i2i−2i-2−2i2i−2i2i000022-222-2-2−2i2i002-200002i−2i000000000000000-2202i−2i00000−2i2i000000000000000000000000
χ682-22-222-2-2-22-222i−2i2i−2i-2−2i2i−2i2i000022-2-2-222−2i2i002-200002i−2i0000000000000002-20−2i2i000002i−2i000000000000000000000000
χ692-22-222-2-2-22-22−2i2i−2i2i22i−2i2i−2i0000-2-220000−2i2i00-2200002i−2i002i2i−2i−2i00000000000000-222-200000−2i2i00000000000000000000
χ702-22-222-2-2-22-22−2i2i−2i2i22i−2i2i−2i0000-2-220000−2i2i00-2200002i−2i00−2i−2i2i2i000000000000002-2-22000002i−2i00000000000000000000
χ712-22-222-2-2-22-22−2i2i−2i2i-22i−2i2i−2i000022-222-2-22i−2i002-20000−2i2i000000000000000-220−2i2i000002i−2i000000000000000000000000
χ722-22-222-2-2-22-22−2i2i−2i2i-22i−2i2i−2i000022-2-2-2222i−2i002-20000−2i2i0000000000000002-202i−2i00000−2i2i000000000000000000000000
χ732-2-2-2-222200000000-200002-22-22-222-22-2000000002-200002-22-22-22-22-22-200000000000002-2002-2000000000000000000
χ742-2-2-2-222200000000-200002-22-22-222-22-2000000002-200002-22-2-22-22-22-220000000000000-2200-22000000000000000000
χ752-2-2-2-222200000000-200002-22-22-22-22-22000000002-20000-22-222-22-22-22-20000000000000-2200-22000000000000000000
χ762-2-2-2-222200000000-200002-22-22-22-22-22000000002-20000-22-22-22-22-22-2200000000000002-2002-2000000000000000000
χ772-2-2-2-222200000000-20000-22-222-222-22-200000000-220000-22-222-22-2-22-2200000000000002-200-22000000000000000000
χ782-2-2-2-222200000000-20000-22-222-222-22-200000000-220000-22-22-22-222-22-20000000000000-22002-2000000000000000000
χ792-2-2-2-222200000000-20000-22-222-22-22-2200000000-2200002-22-22-22-2-22-220000000000000-22002-2000000000000000000
χ802-2-2-2-222200000000-20000-22-222-22-22-2200000000-2200002-22-2-22-222-22-200000000000002-200-22000000000000000000
χ81444-4-4-4-444-4-444i−4i−4i4i04i−4i−4i4i00000000000000000000000000000000000000000000000000000000000000000000000000
χ82444-4-4-4-444-4-44−4i4i4i−4i0−4i4i4i−4i00000000000000000000000000000000000000000000000000000000000000000000000000
χ83444-4-4-4-44-444-44i−4i−4i4i0−4i4i4i−4i00000000000000000000000000000000000000000000000000000000000000000000000000
χ84444-4-4-4-44-444-4−4i4i4i−4i04i−4i−4i4i00000000000000000000000000000000000000000000000000000000000000000000000000
χ8544-44-44-4-4000000004000000004-4-44-4-44000000000000000000000000000000000000000000000000000000000000000
χ8644-44-44-4-4000000004000000004-4-4-444-4000000000000000000000000000000000000000000000000000000000000000
χ8744-44-44-4-400000000-400000000-4440000000000000000004i−4i−4i4i000000000000000000000000000000000000000000000
χ8844-44-44-4-400000000-400000000-444000000000000000000−4i4i4i−4i000000000000000000000000000000000000000000000
χ8944-4-44-44-400000000000004i−4i−4i4i000000000000000000000000022−22−22222i2−2i2−2i22i20000000000000000000000000000000000000
χ9044-4-44-44-400000000000004i−4i−4i4i0000000000000000000000000−222222−22−2i22i22i2−2i20000000000000000000000000000000000000
χ9144-4-44-44-40000000000000−4i4i4i−4i000000000000000000000000022−22−2222−2i22i22i2−2i20000000000000000000000000000000000000
χ9244-4-44-44-40000000000000−4i4i4i−4i0000000000000000000000000−222222−222i2−2i2−2i22i20000000000000000000000000000000000000
χ934-4-4-4-444400000000400004-44-4-44-4000000000000-4400000000000000000000000000000000000000000000000000000
χ944-4-4-4-44440000000040000-44-44-44-40000000000004-400000000000000000000000000000000000000000000000000000
χ958-8-888-8-88000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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