Finite Group Databasebeta

← Group #7592189

Character table — Group #7592189

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111122222222222222222222444444444444444444444444444488888888888888888888888888881616161616161616
order12222222444444444444888888882222222244444444888888888888224444444444444444448888888844444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-11-1-1111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-111-1-1-1-111111111111111-111-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1
χ611111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-11-1-11-1-111
χ711111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1111111111111-111-1-1-111
χ811111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1111111-1-1-1-1111111111-1-1111-1-1
χ9111111111111-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-11111
χ10111111111111-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-1-11-1-111111111111111-1-1-1-111-1-111-1-1-1-1
χ11111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-111-111-1-1-1-111111111-1-11111-1-111-1-1-1-1-1-1
χ12111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111
χ13111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111111-1-11-1-1-1-111-1-1-1-11111-1-11111-1-1-11-1111-1-1
χ14111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-111-1-11111-1-1-1-1-1-11111-1-11-11-1-1-111
χ15111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-111-1-1111111-1-1-1-111-1-1-1-111-11-11-1-111
χ16111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-111-11111-1-1-1-1-1-1111111-1-1-1-1111-11-111-1-1
χ1711111111-1-1-1-11111111111111111-1-111-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-11111-1111111-1-111-1-1-1-111-1-111-1-1-1-11-11-1
χ1811111111-1-1-1-11111111111111111-1-111-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-111-1-111-1-111-1-1111111-11-11
χ1911111111-1-1-1-11111111111111111-1-111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-111111-1-111111-1-111-1-11111-1-111-1-1-1-1-1-1-11-11
χ2011111111-1-1-1-11111111111111111-1-111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-11-1-1-1-11-1-1-1-111-1-111-1-111-1-111-1-111111-11-1
χ2111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-11111-1-1-1-1111111-1-1-111-111-1-111-1-1-1-11111-1-111-1-11-1-111-1-11
χ2211111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-11111-1-1-1-11111-1-1-11111-1-1-111-1-11111-1-111-1-111-1-1-111-1-111-1
χ2311111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1111111-1-1-1-11111111-1-1-1-1111-1-1-1-11111-1-1-1-111-1-1111-1-11-111-1
χ2411111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1111111-1-1-1-11111-1-1111-1-11-1-11111-1-1-1-111-1-111-1-111-111-11-1-11
χ2511111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-1111111-1111-11-1-1-1-1-1-111-1-111-1-1-1-11111-1-1111-11-1
χ2611111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-11-11111111-1-111-1-1-1-1-1-1111111-1-1-11-11
χ2711111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1111111111-11-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-111-11-11
χ2811111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-11-1-1-11-11111-1-111-1-1111111-1-1-1-111-1-11-11-1
χ2911111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-11111111111-1-1-1-111-1-1-11-11-1-111-1-11111-1-11111-1-1-1-11-11-11-1-11
χ3011111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-11111111111-1-1-1-1-1-1-1111-1111-1-111-1-1-1-1111111-1-1-1-1-11-11-111-1
χ3111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-111111111-1-1-1-1111-1-1-11-1-1-11111-1-1-1-111-1-1-1-111111-11-1-111-1
χ3211111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-111111111-1-1-1-1-1-1111-11-111-1-1-1-11111-1-1-1-1-1-11111-11-111-1-11
χ332222222222222222-2-2-2-200000000-2-2-2-2222222-2-2222200000000000000-200-2-2-20000000000000000000000000000
χ342222222222222222-2-2-2-200000000-2-2-2-222-2-2-2-2-2-2-2-2-2-2000000000000002002220000000000000000000000000000
χ35222222222222-2-2-2-2-2-2-2-200000000-2-222-2-2222222-2-2-2-200000000000000-200-2220000000000000000000000000000
χ36222222222222-2-2-2-2-2-2-2-200000000-2-222-2-2-2-2-2-2222222000000000000002002-2-20000000000000000000000000000
χ3722222222-2-2-2-22222-2-2-2-20000000022-2-2-2-222-2-22222-2-200000000000000200-2-220000000000000000000000000000
χ3822222222-2-2-2-22222-2-2-2-20000000022-2-2-2-2-2-22222-2-22200000000000000-20022-20000000000000000000000000000
χ3922222222-2-2-2-2-2-2-2-2-2-2-2-20000000022222222-2-2-2-2-2-22200000000000000200-22-20000000000000000000000000000
χ4022222222-2-2-2-2-2-2-2-2-2-2-2-200000000222222-2-222-2-222-2-200000000000000-2002-220000000000000000000000000000
χ412222-2-2-2-222-2-200002-2-222222-2-2-2-22-20000000000000022-2-2000000000000000000002i−2i2i−2i2i−2i2i−2i0000000000000000
χ422222-2-2-2-222-2-200002-2-222222-2-2-2-22-20000000000000022-2-200000000000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000
χ432222-2-2-2-222-2-200002-2-22-2-2-2-222222-200000000000000-2-222000000000000000000002i−2i2i−2i−2i2i−2i2i0000000000000000
χ442222-2-2-2-222-2-200002-2-22-2-2-2-222222-200000000000000-2-22200000000000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000
χ452222-2-2-2-2-2-22200002-2-222222-2-2-2-2-2200000000000000-2-222000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ462222-2-2-2-2-2-22200002-2-222222-2-2-2-2-2200000000000000-2-22200000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ472222-2-2-2-2-2-22200002-2-22-2-2-2-22222-220000000000000022-2-2000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ482222-2-2-2-2-2-22200002-2-22-2-2-2-22222-220000000000000022-2-200000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ4922-2-222-2-22i−2i2i−2i2i2i−2i−2i0000i2i2−i2−i2i2i2−i2−i200002-22-22i−2i002i−2i2-22−22−222−2−2i2i2−i2−i2000000000000000000002−22−2i2−i2i2−i200000000
χ5022-2-222-2-22i−2i2i−2i2i2i−2i−2i0000i2i2−i2−i2i2i2−i2−i200002-2-22−2i2i00−2i2i-222−22−222−2−2i2i2−i2−i200000000000000000000−22−22−i2i2−i2i200000000
χ5122-2-222-2-22i−2i2i−2i2i2i−2i−2i0000−i2−i2i2i2−i2−i2i2i200002-22-22i−2i002i−2i2-2−22−22−2−222−i2−i2i2i200000000000000000000−22−22−i2i2−i2i200000000
χ5222-2-222-2-22i−2i2i−2i2i2i−2i−2i0000−i2−i2i2i2−i2−i2i2i200002-2-22−2i2i00−2i2i-22−22−22−2−222−i2−i2i2i2000000000000000000002−22−2i2−i2i2−i200000000
χ5322-2-222-2-22i−2i2i−2i−2i−2i2i2i0000i2i2−i2−i2i2i2−i2−i20000-222-22i−2i00−2i2i-222−22−2−2−222−i2−i2i2i2000000000000000000002−2−22−i2i2i2−i200000000
χ5422-2-222-2-22i−2i2i−2i−2i−2i2i2i0000i2i2−i2−i2i2i2−i2−i20000-22-22−2i2i002i−2i2-22−22−2−2−222−i2−i2i2i200000000000000000000−222−2i2−i2−i2i200000000
χ5522-2-222-2-22i−2i2i−2i−2i−2i2i2i0000−i2−i2i2i2−i2−i2i2i20000-222-22i−2i00−2i2i-22−22−2222−2−2i2i2−i2−i200000000000000000000−222−2i2−i2−i2i200000000
χ5622-2-222-2-22i−2i2i−2i−2i−2i2i2i0000−i2−i2i2i2−i2−i2i2i20000-22-22−2i2i002i−2i2-2−22−2222−2−2i2i2−i2−i2000000000000000000002−2−22−i2i2i2−i200000000
χ5722-2-222-2-2−2i2i−2i2i2i2i−2i−2i0000i2i2−i2−i2i2i2−i2−i20000-222-2−2i2i002i−2i-22−22−2222−2−2−i2−i2i2i200000000000000000000−222−2−i2i2i2−i200000000
χ5822-2-222-2-2−2i2i−2i2i2i2i−2i−2i0000i2i2−i2−i2i2i2−i2−i20000-22-222i−2i00−2i2i2-2−22−2222−2−2−i2−i2i2i2000000000000000000002−2−22i2−i2−i2i200000000
χ5922-2-222-2-2−2i2i−2i2i2i2i−2i−2i0000−i2−i2i2i2−i2−i2i2i20000-222-2−2i2i002i−2i-222−22−2−2−222i2i2−i2−i2000000000000000000002−2−22i2−i2−i2i200000000
χ6022-2-222-2-2−2i2i−2i2i2i2i−2i−2i0000−i2−i2i2i2−i2−i2i2i20000-22-222i−2i00−2i2i2-22−22−2−2−222i2i2−i2−i200000000000000000000−222−2−i2i2i2−i200000000
χ6122-2-222-2-2−2i2i−2i2i−2i−2i2i2i0000i2i2−i2−i2i2i2−i2−i200002-22-2−2i2i00−2i2i2-2−22−22−2−222i2i2−i2−i200000000000000000000−22−22i2−i2i2−i200000000
χ6222-2-222-2-2−2i2i−2i2i−2i−2i2i2i0000i2i2−i2−i2i2i2−i2−i200002-2-222i−2i002i−2i-22−22−22−2−222i2i2−i2−i2000000000000000000002−22−2−i2i2−i2i200000000
χ6322-2-222-2-2−2i2i−2i2i−2i−2i2i2i0000−i2−i2i2i2−i2−i2i2i200002-22-2−2i2i00−2i2i2-22−22−222−2−2−i2−i2i2i2000000000000000000002−22−2−i2i2−i2i200000000
χ6422-2-222-2-2−2i2i−2i2i−2i−2i2i2i0000−i2−i2i2i2−i2−i2i2i200002-2-222i−2i002i−2i-222−22−222−2−2−i2−i2i2i200000000000000000000−22−22i2−i2i2−i200000000
χ652-2-222-22-200002-22-222-2-22i−2i2i−2i2i−2i2i−2i002-200000000000000002i−2i2i−2i00002-202i−2i0002-22i−2i000000000000000000000000
χ662-2-222-22-200002-22-222-2-22i−2i2i−2i2i−2i2i−2i002-200000000000000002i−2i2i−2i0000-220−2i2i000-22−2i2i000000000000000000000000
χ672-2-222-22-200002-22-222-2-2−2i2i−2i2i−2i2i−2i2i002-20000000000000000−2i2i−2i2i00002-20−2i2i0002-2−2i2i000000000000000000000000
χ682-2-222-22-200002-22-222-2-2−2i2i−2i2i−2i2i−2i2i002-20000000000000000−2i2i−2i2i0000-2202i−2i000-222i−2i000000000000000000000000
χ692-2-222-22-20000-22-2222-2-22i−2i2i−2i2i−2i2i−2i00-220000000000000000−2i2i−2i2i00002-202i−2i000-22−2i2i000000000000000000000000
χ702-2-222-22-20000-22-2222-2-22i−2i2i−2i2i−2i2i−2i00-220000000000000000−2i2i−2i2i0000-220−2i2i0002-22i−2i000000000000000000000000
χ712-2-222-22-20000-22-2222-2-2−2i2i−2i2i−2i2i−2i2i00-2200000000000000002i−2i2i−2i00002-20−2i2i000-222i−2i000000000000000000000000
χ722-2-222-22-20000-22-2222-2-2−2i2i−2i2i−2i2i−2i2i00-2200000000000000002i−2i2i−2i0000-2202i−2i0002-2−2i2i000000000000000000000000
χ734444-4-4-4-444-4-40000-444-400000000-4400000000000000000000000000000000000000000000000000000000000000
χ744444-4-4-4-4-4-4440000-444-4000000004-400000000000000000000000000000000000000000000000000000000000000
χ7544-4-4-4-4444i−4i−4i4i000000002i22i2−2i2−2i2−2i2−2i22i22i2000000000000000022−22−222200000000000000000000000000000000000000000000
χ7644-4-4-4-4444i−4i−4i4i00000000−2i2−2i22i22i22i22i2−2i2−2i20000000000000000−222222−2200000000000000000000000000000000000000000000
χ7744-4-4-4-444−4i4i4i−4i000000002i22i2−2i2−2i2−2i2−2i22i22i20000000000000000−222222−2200000000000000000000000000000000000000000000
χ7844-4-4-4-444−4i4i4i−4i00000000−2i2−2i22i22i22i22i2−2i2−2i2000000000000000022−22−222200000000000000000000000000000000000000000000
χ794-44-44-4-4400004i−4i−4i4i000022−22−222222−22−222200000000000000000000−2i22i22i2−2i20000000000000000000000000000000000000000
χ804-44-44-4-4400004i−4i−4i4i0000−222222−22−222222−22000000000000000000002i2−2i2−2i22i20000000000000000000000000000000000000000
χ814-44-44-4-440000−4i4i4i−4i000022−22−222222−22−2222000000000000000000002i2−2i2−2i22i20000000000000000000000000000000000000000
χ824-44-44-4-440000−4i4i4i−4i0000−222222−22−222222−2200000000000000000000−2i22i22i2−2i20000000000000000000000000000000000000000
χ834-44-4-444-400000000000022−22−2222−222222−2200000000004i−4i0000000000002i2−2i22i2−2i2000000000000000000000000000000000000
χ844-44-4-444-400000000000022−22−2222−222222−220000000000−4i4i000000000000−2i22i2−2i22i2000000000000000000000000000000000000
χ854-44-4-444-4000000000000−222222−2222−22−222200000000004i−4i000000000000−2i22i2−2i22i2000000000000000000000000000000000000
χ864-44-4-444-4000000000000−222222−2222−22−22220000000000−4i4i0000000000002i2−2i22i2−2i2000000000000000000000000000000000000
χ874-4-444-44-400004-44-4-4-4440000000000-44000000000000000000000000000000000000000000000000000000000000
χ884-4-444-44-40000-44-44-4-44400000000004-4000000000000000000000000000000000000000000000000000000000000
χ894-4-44-44-44000000004-44-44i−4i4i−4i−4i4i−4i4i0000000000000000000000000000000000000000000000000000000000000000
χ904-4-44-44-44000000004-44-4−4i4i−4i4i4i−4i4i−4i0000000000000000000000000000000000000000000000000000000000000000
χ914-4-44-44-4400000000-44-44000000000000000000000000000000004-4-44000000000000000000000000000000000000
χ924-4-44-44-4400000000-44-4400000000000000000000000000000000-444-4000000000000000000000000000000000000

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