Finite Group Databasebeta

← Group #6576549

Character table — Group #6576549

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size1111111122222222222222222222222244444444444444444444444444444444448888888888888888888888881616161616161616
order12222222222222222222444488888888224444444444444444444488888888888844444444444444448888888844444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1111111111111111-1-1-1-1-1-11-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111111111-1-1-1111111-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11-11-1
χ6111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-111-11-11
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-111111111-1-111-11-11
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-11-11-1
χ9111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-11-1-111-1-1-1-1111-1-1-1-111-1-1-1-1111-11-11-1-11
χ10111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-1-111111-1-1111111-1-1-1-111-11-11-111-1
χ11111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-11111-1-1-1-1-111-1-1-1-1-1-11111-1-1-11-11-111-1
χ12111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-11111-1-1-11111-1-11111-1-11-11-11-1-11
χ13111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-111-1-1-1-11-1-11111-1-11111-1-11-1-1111-1-1
χ14111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111111111-1-1-1-11111111-1-1-1-1-1-11111-1-1-111-1-1-111
χ15111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-11111-1-1-1-1-1-1-1111111-1-1-1-111-111-1-1-111
χ16111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-111111111-111-1-11111-111-1-1-1-111-1-1-1-1111-1-1111-1-1
χ1711111111-1-1-1-11111-1-1-1-111111111111111-1-111-1-11111-1-111-1-11111-1-1-1-11111-1-1-1-1-11-1-1-111-1-11-1-111-1-1-1-111-1-111-11-111-1-11
χ1811111111-1-1-1-11111-1-1-1-111111111111111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11-111-1-111111-1-111-1-111-1-1111-11-1-111-1
χ1911111111-1-1-1-11111-1-1-1-1111111111111-1-111-1-1111111-1-111-1-11111-1-1-1-11111-1-1-1-11-11-1-111-1-1-1-1-111-1-111-1-111-1-11-11-1-111-1
χ2011111111-1-1-1-11111-1-1-1-1111111111111-1-111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-1111-1-111-111-1-11111-1-111-1-1-11-111-1-11
χ2111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-11111-1-111-1-1-1-1-1-11111-1-1-1-11111-11-1-1-111-1-1111-1-11111-1-111-1-1-111-111-1-1
χ2211111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-11111-11-111-1-1111-1-111-1-111-1-111-1-11-1-11-1-111
χ2311111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-111111-11-1-111-1-1-111-1-111-1-111-1-1111-1-11-1-111
χ2411111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-111-1-111111111-1-1-1-111111-1111-1-111-1-1-111-1-1-1-111-1-111-111-111-1-1
χ2511111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-11-1-1-1-1111-1-1-1-111-1-1-1-11111-1-1-1-11111
χ2611111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111-1-111111-1-1-1-1-1-111111111-1-1-1-1
χ2711111111-1-1-1-1-1-1-1-11111111111111111-1-11111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-111-1-1-1-1-1111111-1-1-1-11111-1-1-1-1
χ2811111111-1-1-1-1-1-1-1-11111111111111111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-11111-1-1-11111-1-11111-1-1-1-1-1-1-1-11111
χ2911111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-11-1-1-1-11111111-1-11111-1-1-1-1-1-1111-11-1
χ3011111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-111111-1-11-1-1-1-1111111-1-1-1-111-1-1-11-11
χ3111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-111-1-1-1-1-111-11111-1-1-1-1-1-1111111-1-1-11-11
χ3211111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-111-11111-1-1-1-1-1-1-111-1-1-1-11111-1-1111-11-1
χ3322222222222222222222-2-2-2-200000000222222220000-2-2-2-2-2-20000000000000000-2-2-2000000-20000000000000000000000
χ3422222222222222222222-2-2-2-200000000-2-2-2-2-2-2-2-20000-2-2-2-2-2-2000000000000000022200000020000000000000000000000
χ35222222222222-2-2-2-2-2-2-2-2-2-2-2-2000000002222-2-2-2-20000-2-222220000000000000000-222000000-20000000000000000000000
χ36222222222222-2-2-2-2-2-2-2-2-2-2-2-200000000-2-2-2-222220000-2-2222200000000000000002-2-200000020000000000000000000000
χ3722222222-2-2-2-22222-2-2-2-2-2-2-2-20000000022-2-222-2-2000022-2-22200000000000000002-22000000-20000000000000000000000
χ3822222222-2-2-2-22222-2-2-2-2-2-2-2-200000000-2-222-2-222000022-2-2220000000000000000-22-200000020000000000000000000000
χ3922222222-2-2-2-2-2-2-2-22222-2-2-2-20000000022-2-2-2-22200002222-2-2000000000000000022-2000000-20000000000000000000000
χ4022222222-2-2-2-2-2-2-2-22222-2-2-2-200000000-2-22222-2-200002222-2-20000000000000000-2-2200000020000000000000000000000
χ412222-2-2-2-222-2-222-2-222-2-200002222−2−2−2−22-22-22-22-20000000000000022−2−222−2−222−2−200000000000000002−22−22−22−200000000
χ422222-2-2-2-222-2-222-2-222-2-200002222−2−2−2−2-22-22-22-220000000000000022−2−222−2−222−2−20000000000000000−22−22−22−2200000000
χ432222-2-2-2-222-2-222-2-222-2-20000−2−2−2−222222-22-22-22-200000000000000−2−222−2−222−2−2220000000000000000−22−22−22−2200000000
χ442222-2-2-2-222-2-222-2-222-2-20000−2−2−2−22222-22-22-22-2200000000000000−2−222−2−222−2−22200000000000000002−22−22−22−200000000
χ452222-2-2-2-222-2-2-2-222-2-22200002222−2−2−2−22-22-2-22-220000000000000022−2−2−2−222−2−22200000000000000002−2−22−222−200000000
χ462222-2-2-2-222-2-2-2-222-2-22200002222−2−2−2−2-22-222-22-20000000000000022−2−2−2−222−2−2220000000000000000−222−22−2−2200000000
χ472222-2-2-2-222-2-2-2-222-2-2220000−2−2−2−222222-22-2-22-2200000000000000−2−22222−2−222−2−20000000000000000−222−22−2−2200000000
χ482222-2-2-2-222-2-2-2-222-2-2220000−2−2−2−22222-22-222-22-200000000000000−2−22222−2−222−2−200000000000000002−2−22−222−200000000
χ492222-2-2-2-2-2-22222-2-2-2-22200002222−2−2−2−22-2-222-2-2200000000000000−2−22222−2−2−2−2220000000000000000−222−2−222−200000000
χ502222-2-2-2-2-2-22222-2-2-2-22200002222−2−2−2−2-222-2-222-200000000000000−2−22222−2−2−2−22200000000000000002−2−222−2−2200000000
χ512222-2-2-2-2-2-22222-2-2-2-2220000−2−2−2−222222-2-222-2-220000000000000022−2−2−2−22222−2−200000000000000002−2−222−2−2200000000
χ522222-2-2-2-2-2-22222-2-2-2-2220000−2−2−2−22222-222-2-222-20000000000000022−2−2−2−22222−2−20000000000000000−222−2−222−200000000
χ532222-2-2-2-2-2-222-2-22222-2-200002222−2−2−2−22-2-22-222-200000000000000−2−222−2−22222−2−20000000000000000−22−222−22−200000000
χ542222-2-2-2-2-2-222-2-22222-2-200002222−2−2−2−2-222-22-2-2200000000000000−2−222−2−22222−2−200000000000000002−22−2−22−2200000000
χ552222-2-2-2-2-2-222-2-22222-2-20000−2−2−2−222222-2-22-222-20000000000000022−2−222−2−2−2−22200000000000000002−22−2−22−2200000000
χ562222-2-2-2-2-2-222-2-22222-2-20000−2−2−2−22222-222-22-2-220000000000000022−2−222−2−2−2−2220000000000000000−22−222−22−200000000
χ5722-2-22-2-2200002-22-2000022-2-22i2i−2i−2i2i2i−2i−2i000000002i2i−2i−2i002-20022-2-200002i−2i2i−2i0000000002i−2i000002-2000000000000000000
χ5822-2-22-2-2200002-22-2000022-2-22i2i−2i−2i2i2i−2i−2i00000000−2i−2i2i2i002-200-2-22200002i−2i2i−2i000000000−2i2i00000-22000000000000000000
χ5922-2-22-2-2200002-22-2000022-2-2−2i−2i2i2i−2i−2i2i2i000000002i2i−2i−2i002-200-2-2220000−2i2i−2i2i0000000002i−2i00000-22000000000000000000
χ6022-2-22-2-2200002-22-2000022-2-2−2i−2i2i2i−2i−2i2i2i00000000−2i−2i2i2i002-20022-2-20000−2i2i−2i2i000000000−2i2i000002-2000000000000000000
χ6122-2-22-2-220000-22-22000022-2-22i2i−2i−2i2i2i−2i−2i000000002i2i−2i−2i00-220022-2-20000−2i2i−2i2i000000000−2i2i00000-22000000000000000000
χ6222-2-22-2-220000-22-22000022-2-22i2i−2i−2i2i2i−2i−2i00000000−2i−2i2i2i00-2200-2-2220000−2i2i−2i2i0000000002i−2i000002-2000000000000000000
χ6322-2-22-2-220000-22-22000022-2-2−2i−2i2i2i−2i−2i2i2i000000002i2i−2i−2i00-2200-2-22200002i−2i2i−2i000000000−2i2i000002-2000000000000000000
χ6422-2-22-2-220000-22-22000022-2-2−2i−2i2i2i−2i−2i2i2i00000000−2i−2i2i2i00-220022-2-200002i−2i2i−2i0000000002i−2i00000-22000000000000000000
χ652-22-2-22-222-22-2000000002-22-22i−2i2i−2i2i−2i2i−2i000000002i−2i2i−2i2-200002-22-22i−2i2i−2i000000000002i−2i000002-200000000000000000000
χ662-22-2-22-222-22-2000000002-22-22i−2i2i−2i2i−2i2i−2i00000000−2i2i−2i2i2-20000-22-222i−2i2i−2i00000000000−2i2i00000-2200000000000000000000
χ672-22-2-22-222-22-2000000002-22-2−2i2i−2i2i−2i2i−2i2i000000002i−2i2i−2i2-20000-22-22−2i2i−2i2i000000000002i−2i00000-2200000000000000000000
χ682-22-2-22-222-22-2000000002-22-2−2i2i−2i2i−2i2i−2i2i00000000−2i2i−2i2i2-200002-22-2−2i2i−2i2i00000000000−2i2i000002-200000000000000000000
χ692-22-2-22-22-22-22000000002-22-22i−2i2i−2i2i−2i2i−2i000000002i−2i2i−2i-2200002-22-2−2i2i−2i2i00000000000−2i2i00000-2200000000000000000000
χ702-22-2-22-22-22-22000000002-22-22i−2i2i−2i2i−2i2i−2i00000000−2i2i−2i2i-220000-22-22−2i2i−2i2i000000000002i−2i000002-200000000000000000000
χ712-22-2-22-22-22-22000000002-22-2−2i2i−2i2i−2i2i−2i2i000000002i−2i2i−2i-220000-22-222i−2i2i−2i00000000000−2i2i000002-200000000000000000000
χ722-22-2-22-22-22-22000000002-22-2−2i2i−2i2i−2i2i−2i2i00000000−2i2i−2i2i-2200002-22-22i−2i2i−2i000000000002i−2i00000-2200000000000000000000
χ732-2-22-2-222000000002-22-22-2-222-2-222-2-22000000002-2-2200002-22-2-22000000002-22-200000002-2000002-20000000000000000
χ742-2-22-2-222000000002-22-22-2-222-2-222-2-2200000000-222-200002-2-222-2000000002-22-20000000-2200000-220000000000000000
χ752-2-22-2-222000000002-22-22-2-22-222-2-222-2000000002-2-2200002-2-222-200000000-22-2200000002-200000-220000000000000000
χ762-2-22-2-222000000002-22-22-2-22-222-2-222-200000000-222-200002-22-2-2200000000-22-220000000-22000002-20000000000000000
χ772-2-22-2-22200000000-22-222-2-222-2-222-2-22000000002-2-220000-222-2-2200000000-22-220000000-2200000-220000000000000000
χ782-2-22-2-22200000000-22-222-2-222-2-222-2-2200000000-222-20000-22-222-200000000-22-2200000002-2000002-20000000000000000
χ792-2-22-2-22200000000-22-222-2-22-222-2-222-2000000002-2-220000-22-222-2000000002-22-20000000-22000002-20000000000000000
χ802-2-22-2-22200000000-22-222-2-22-222-2-222-200000000-222-20000-222-2-22000000002-22-200000002-200000-220000000000000000
χ8144-4-44-4-4400004-44-40000-4-4440000000000000000000000-4400000000000000000000000000000000000000000000000000
χ8244-4-44-4-440000-44-440000-4-44400000000000000000000004-400000000000000000000000000000000000000000000000000
χ8344-4-4-444-400004-4-44000000002i22i2−2i2−2i2−2i2−2i22i22i2000000000000000000000000002i2−2i2−2i22i2000000000000000000000000000000000000
χ8444-4-4-444-400004-4-4400000000−2i2−2i22i22i22i22i2−2i2−2i200000000000000000000000000−2i22i22i2−2i2000000000000000000000000000000000000
χ8544-4-4-444-40000-444-4000000002i22i2−2i2−2i2−2i2−2i22i22i200000000000000000000000000−2i22i22i2−2i2000000000000000000000000000000000000
χ8644-4-4-444-40000-444-400000000−2i2−2i22i22i22i22i2−2i2−2i2000000000000000000000000002i2−2i2−2i22i2000000000000000000000000000000000000
χ874-44-44-44-44-4-440000000000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000002i2−2i2−2i22i20000000000000000000000000000000000000000
χ884-44-44-44-44-4-44000000000000−2i22i2−2i22i22i2−2i22i2−2i20000000000000000000000−2i22i22i2−2i20000000000000000000000000000000000000000
χ894-44-44-44-4-444-40000000000002i2−2i22i2−2i2−2i22i2−2i22i20000000000000000000000−2i22i22i2−2i20000000000000000000000000000000000000000
χ904-44-44-44-4-444-4000000000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000002i2−2i2−2i22i20000000000000000000000000000000000000000
χ914-44-4-44-444-44-400000000-44-4400000000000000000000-440000000000000000000000000000000000000000000000000000
χ924-44-4-44-44-44-4400000000-44-44000000000000000000004-40000000000000000000000000000000000000000000000000000
χ934-4-4444-4-4000000004-4-44000022−22−2222−222222−2200000000000000000000000000000022−22−222200000000000000000000000000000000
χ944-4-4444-4-4000000004-4-440000−222222−2222−22−2222000000000000000000000000000000−222222−2200000000000000000000000000000000
χ954-4-4444-4-400000000-444-4000022−22−2222−222222−22000000000000000000000000000000−222222−2200000000000000000000000000000000
χ964-4-4444-4-400000000-444-40000−222222−2222−22−222200000000000000000000000000000022−22−222200000000000000000000000000000000
χ974-4-44-4-444000000004-44-4-444-4000000000000000000000000-44000000000000000000000000000000000000000000000000
χ984-4-44-4-44400000000-44-44-444-40000000000000000000000004-4000000000000000000000000000000000000000000000000

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