Finite Group Databasebeta

← Group #7576663

Character table — Group #7576663

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89
size1111111122222222222244444444444444444444444444444444448888888888888888888888888881616161616161616
order12222222444444444444224444444444444444888888888888888844444444444444444448888888822244444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-11-1-111-11-1
χ3111111111111111111111111111111-1-1-1-111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-1-111-1-11-11
χ511111111111111111111-1-11111-1-1-1-1111111-1-111111111-1-1-1-1-1-1-1-11-1-11111-1-11111-1-1-1-1111111-1-1-1-1-11-1-1-11-1-1
χ611111111111111111111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111111-1-111-1-1-1-111-1-1111111-1-1-1-11111-1-11-1-1-1-11
χ711111111111111111111-1-11111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11-1111-111
χ811111111111111111111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111-11111-1
χ9111111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111-11111-1-11
χ10111111111111-1-1-1-111111111-1-1-1-1-1-11111-1-111-1-1-1-1111111111111-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-1-1111-1-1
χ11111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111111111-1-11111111-1-1-1-111-1
χ12111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111-1-1-111
χ13111111111111-1-1-1-11111-1-111-1-111111111-1-1-1-11111-1-1-1-111111111-111-1-111-1-111-1-11111-1-1-1-111-1-1-1-111-1-1-1-11-1
χ14111111111111-1-1-1-11111-1-111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-111-1-111111-11-1-1111
χ15111111111111-1-1-1-11111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-11111-1-1-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-11111-11
χ16111111111111-1-1-1-11111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111111-1-11111-11-111-1-1-1
χ1711111111-1-1-1-11111111111-1-1-1-111-1-1111111-1-1111111111111-1-1-1-1-11-111111-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111-1-11-1
χ1811111111-1-1-1-11111111111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11-111-1-11-1-1-1-1-1-1-111-1-11111-1-111-11-11-1111
χ1911111111-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-111-1-1111111111111-1-1-1-1-11-1-1-1-1-11-111-1-1-1-11111-1-1-1-111-1-111-1-111-11
χ2011111111-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11-1-1-1111-1111111-1-1111111-1-1111-11-11-1-1-1
χ2111111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-11111-1-111111-11-1-111-1-111-1-1-1-1-1-1-1-1111-1-1-11-1-11
χ2211111111-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111-1-1-11-1-1-1-111-1-1-1-1111111-1-1111-111-1-1
χ2311111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-11111-1-11-1-1-1-1-1111-1-111-1-111-1-1-1-1-1-111-1111-111-1
χ2411111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11-1-111-111111-1-11111111111-1-1-1-1-11-1-111
χ2511111111-1-1-1-1-1-1-1-1111111-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-111111-11-1-1111-1-1-1-1-1-1-1111111-1-111-1-11-111-11-1-1
χ2611111111-1-1-1-1-1-1-1-1111111-1-111-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-11-11-1-1-1-11-1-1-11111-1-111-1-111-1-11111-11-1-1-11
χ2711111111-1-1-1-1-1-1-1-1111111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111-1111-1-11-1111111-1-1-1-111-1-111-1-1-11-1-11-111
χ2811111111-1-1-1-1-1-1-1-1111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11-1111111-111-1-1-1-111-1-1-1-111-1-111-1-11-1111-1
χ2911111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1111111-1-1-1-11111-1-1-1-111-1-1-111-11-1-1-1-111-1-11111-1-1-1-111-1-1-1-11111
χ3011111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-11-1-111-1-11111-1-11111-1-1-111-11-11-1
χ3111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111-111-1-1-111111-1-111-1-111-1-1-1-1111111-1-1-1-1
χ3211111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111111-11111-1111-1-111-1-1-1-1-1-11111-1-11-1-11-11-11
χ332222222222222222-2-2-2-222-2-22222220000-2-2220000000000000000-2-2-20000-2-200000000000000000000000000
χ342222222222222222-2-2-2-2-2-2-2-222-2-2-2-20000-2-2-2-20000000000000000-22200002200000000000000000000000000
χ35222222222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-20000222200000000000000002220000-2-200000000000000000000000000
χ36222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-22222000022-2-200000000000000002-2-200002200000000000000000000000000
χ3722222222-2-2-2-22222-2-2-2-22222-2-222-2-20000-2-2-2-200000000000000002-220000-2200000000000000000000000000
χ3822222222-2-2-2-22222-2-2-2-2-2-222-2-2-2-2220000-2-222000000000000000022-200002-200000000000000000000000000
χ3922222222-2-2-2-2-2-2-2-2-2-2-2-2222222-2-222000022-2-20000000000000000-22-20000-2200000000000000000000000000
χ4022222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222-2-2000022220000000000000000-2-2200002-200000000000000000000000000
χ41222-2-2-2-2222-2-22i2i−2i−2i00002-2002i−2i2i−2i2i−2i0000002-2i2i2−i2−i222−2−222−2−222−2−200000000000000000002−2i2−i2i2−i2i2−i200000000
χ42222-2-2-2-2222-2-22i2i−2i−2i00002-2002i−2i2i−2i2i−2i0000002-2−i2−i2i2i2−2−222−2−222−2−2220000000000000000000−22−i2i2−i2i2−i2i200000000
χ43222-2-2-2-2222-2-22i2i−2i−2i0000-22002i−2i−2i2i−2i2i000000-22i2i2−i2−i222−2−2−2−222−2−22200000000000000000002−2i2−i2−i2i2−i2i200000000
χ44222-2-2-2-2222-2-22i2i−2i−2i0000-22002i−2i−2i2i−2i2i000000-22−i2−i2i2i2−2−22222−2−222−2−20000000000000000000−22−i2i2i2−i2i2−i200000000
χ45222-2-2-2-2222-2-2−2i−2i2i2i00002-200−2i2i−2i2i−2i2i0000002-2i2i2−i2−i2−2−222−2−222−2−2220000000000000000000−22i2−i2i2−i2i2−i200000000
χ46222-2-2-2-2222-2-2−2i−2i2i2i00002-200−2i2i−2i2i−2i2i0000002-2−i2−i2i2i222−2−222−2−222−2−200000000000000000002−2−i2i2−i2i2−i2i200000000
χ47222-2-2-2-2222-2-2−2i−2i2i2i0000-2200−2i2i2i−2i2i−2i000000-22i2i2−i2−i2−2−22222−2−222−2−20000000000000000000−22i2−i2−i2i2−i2i200000000
χ48222-2-2-2-2222-2-2−2i−2i2i2i0000-2200−2i2i2i−2i2i−2i000000-22−i2−i2i2i222−2−2−2−222−2−22200000000000000000002−2−i2i2i2−i2i2−i200000000
χ49222-2-2-2-22-2-2222i2i−2i−2i00002-200−2i2i2i−2i−2i2i000000-22i2i2−i2−i222−2−222−2−2−2−2220000000000000000000−22−i2i2i2−i2−i2i200000000
χ50222-2-2-2-22-2-2222i2i−2i−2i00002-200−2i2i2i−2i−2i2i000000-22−i2−i2i2i2−2−222−2−22222−2−200000000000000000002−2i2−i2−i2i2i2−i200000000
χ51222-2-2-2-22-2-2222i2i−2i−2i0000-2200−2i2i−2i2i2i−2i0000002-2i2i2−i2−i222−2−2−2−22222−2−20000000000000000000−22−i2i2−i2i2i2−i200000000
χ52222-2-2-2-22-2-2222i2i−2i−2i0000-2200−2i2i−2i2i2i−2i0000002-2−i2−i2i2i2−2−22222−2−2−2−22200000000000000000002−2i2−i2i2−i2−i2i200000000
χ53222-2-2-2-22-2-222−2i−2i2i2i00002-2002i−2i−2i2i2i−2i000000-22i2i2−i2−i2−2−222−2−22222−2−200000000000000000002−2−i2i2i2−i2−i2i200000000
χ54222-2-2-2-22-2-222−2i−2i2i2i00002-2002i−2i−2i2i2i−2i000000-22−i2−i2i2i222−2−222−2−2−2−2220000000000000000000−22i2−i2−i2i2i2−i200000000
χ55222-2-2-2-22-2-222−2i−2i2i2i0000-22002i−2i2i−2i−2i2i0000002-2i2i2−i2−i2−2−22222−2−2−2−22200000000000000000002−2−i2i2−i2i2i2−i200000000
χ56222-2-2-2-22-2-222−2i−2i2i2i0000-22002i−2i2i−2i−2i2i0000002-2−i2−i2i2i222−2−2−2−22222−2−20000000000000000000−22i2−i2i2−i2−i2i200000000
χ5722-222-2-2-200002i−2i2i−2i2-22-2000000000022-2-22i−2i002-22-22i−2i2i−2i000000000002i−2i2-200002i−2i0000000000000000000000
χ5822-222-2-2-200002i−2i2i−2i2-22-2000000000022-2-22i−2i00-22-22−2i2i−2i2i000000000002i−2i-220000−2i2i0000000000000000000000
χ5922-222-2-2-200002i−2i2i−2i2-22-20000000000-2-2222i−2i002-22-22i−2i2i−2i00000000000−2i2i-220000−2i2i0000000000000000000000
χ6022-222-2-2-200002i−2i2i−2i2-22-20000000000-2-2222i−2i00-22-22−2i2i−2i2i00000000000−2i2i2-200002i−2i0000000000000000000000
χ6122-222-2-2-20000−2i2i−2i2i2-22-2000000000022-2-2−2i2i002-22-2−2i2i−2i2i00000000000−2i2i2-20000−2i2i0000000000000000000000
χ6222-222-2-2-20000−2i2i−2i2i2-22-2000000000022-2-2−2i2i00-22-222i−2i2i−2i00000000000−2i2i-2200002i−2i0000000000000000000000
χ6322-222-2-2-20000−2i2i−2i2i2-22-20000000000-2-222−2i2i002-22-2−2i2i−2i2i000000000002i−2i-2200002i−2i0000000000000000000000
χ6422-222-2-2-20000−2i2i−2i2i2-22-20000000000-2-222−2i2i00-22-222i−2i2i−2i000000000002i−2i2-20000−2i2i0000000000000000000000
χ652-222-22-2-22i−2i2i−2i00002-2-22002i−2i0000002i−2i2i−2i0000000000002-22-22i−2i2i−2i0000000002-2002i−2i2-2000000000000000000
χ662-222-22-2-22i−2i2i−2i00002-2-22002i−2i0000002i−2i2i−2i000000000000-22-22−2i2i−2i2i0000000002-200−2i2i-22000000000000000000
χ672-222-22-2-22i−2i2i−2i00002-2-22002i−2i000000−2i2i−2i2i0000000000002-22-22i−2i2i−2i000000000-2200−2i2i-22000000000000000000
χ682-222-22-2-22i−2i2i−2i00002-2-22002i−2i000000−2i2i−2i2i000000000000-22-22−2i2i−2i2i000000000-22002i−2i2-2000000000000000000
χ692-222-22-2-2−2i2i−2i2i00002-2-2200−2i2i0000002i−2i2i−2i0000000000002-22-2−2i2i−2i2i000000000-22002i−2i-22000000000000000000
χ702-222-22-2-2−2i2i−2i2i00002-2-2200−2i2i0000002i−2i2i−2i000000000000-22-222i−2i2i−2i000000000-2200−2i2i2-2000000000000000000
χ712-222-22-2-2−2i2i−2i2i00002-2-2200−2i2i000000−2i2i−2i2i0000000000002-22-2−2i2i−2i2i0000000002-200−2i2i2-2000000000000000000
χ722-222-22-2-2−2i2i−2i2i00002-2-2200−2i2i000000−2i2i−2i2i000000000000-22-222i−2i2i−2i0000000002-2002i−2i-22000000000000000000
χ7344-444-4-4-400004i−4i4i−4i-44-4400000000000000−4i4i00000000000000000000000000000000000000000000000000000
χ7444-444-4-4-40000−4i4i−4i4i-44-44000000000000004i−4i00000000000000000000000000000000000000000000000000000
χ7544-4-4-444-400004-4-4400000000000000000000002i2−2i2−2i22i2−2i22i22i2−2i20000000000000000000000000000000000000000000
χ7644-4-4-444-400004-4-440000000000000000000000−2i22i22i2−2i22i2−2i2−2i22i20000000000000000000000000000000000000000000
χ7744-4-4-444-40000-444-400000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i20000000000000000000000000000000000000000000
χ7844-4-4-444-40000-444-40000000000000000000000−2i22i22i2−2i2−2i22i22i2−2i20000000000000000000000000000000000000000000
χ794-444-44-4-44i−4i4i−4i0000-444-400−4i4i00000000000000000000000000000000000000000000000000000000000000000
χ804-444-44-4-4−4i4i−4i4i0000-444-4004i−4i00000000000000000000000000000000000000000000000000000000000000000
χ814-44-44-44-44i−4i−4i4i000000000000000000000000000000000022−22−22222i2−2i2−2i22i200000000000000000000000000000000000
χ824-44-44-44-44i−4i−4i4i0000000000000000000000000000000000−222222−22−2i22i22i2−2i200000000000000000000000000000000000
χ834-44-44-44-4−4i4i4i−4i000000000000000000000000000000000022−22−2222−2i22i22i2−2i200000000000000000000000000000000000
χ844-44-44-44-4−4i4i4i−4i0000000000000000000000000000000000−222222−222i2−2i2−2i22i200000000000000000000000000000000000
χ854-4-44-4-4440000000044-4-400000000004i−4i−4i4i0000000000000000000000000000000000000000000000000000000
χ864-4-44-4-4440000000044-4-40000000000−4i4i4i−4i0000000000000000000000000000000000000000000000000000000
χ874-4-44-4-44400000000-4-4440000000000000000000000000000000000000000000000000004-40000000000000000
χ884-4-44-4-44400000000-4-444000000000000000000000000000000000000000000000000000-440000000000000000
χ898-8-8-888-88000000000000000000000000000000000000000000000000000000000000000000000000000000000

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