Finite Group Databasebeta

← Group #7516004

Character table — Group #7516004

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89
size1111111122222222222244444444444444444444444444444444448888888888888888888888888881616161616161616
order12222222222222224444224444444444444444888888888888888822244444444444444448888888824444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-111-11-11-1
χ31111111111111111111111111111-1-1-1-111111111111111111111111-1-111-1-1-1-11-1-1-1-1-1-11-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1111-1-1-1-1-1-1-1-11-1-11-11-11
χ51111111111111111111111-1-1-1-1-1-111111111-1-11111-1-1-1-11111-1-1-1-1-111-1-111-1-1-11111111-1-111-1-111-1-11-1-11-1-1-1-1
χ61111111111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-111-1111111111-1-111-1-111-1-1-1-1-11-11
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-111111-1-111-1-1-111-11111
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-111-1-111-1-1-1-1-1-1-1-1-11-1-1-1-111-1-11111111-11-1
χ9111111111111-1-1-1-11111-1-11111-1-1111111-1-1-1-111111111-1-1-1-11111-1-1-1111111-111-1-1-1-1-11111-1-1-1-1-1-1-1111-1-1-1-1
χ10111111111111-1-1-1-11111-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11111-1-1-1-1-111-1-1-1-1-1-1-1-1-1111111111-1-11-11
χ11111111111111-1-1-1-11111-1-11111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-11111-11111-1-1-1-1-1-1-11111-1-1-111-1-1-1-1-1-11-1-1-11111
χ12111111111111-1-1-1-11111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1111111-1-1-11111-111-1-1111111-1-1-111-11-1
χ13111111111111-1-1-1-11111-1-1-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111-1-1111-1-1-1-1-1-1-11111-1-111-1-1-111111
χ14111111111111-1-1-1-11111-1-1-1-1-1-111111111-1-111-1-1-1-1111111111111111-1-1-1-111111-1-1-1-1-111-1-1-1-111-1-11-1-1-11-11-1
χ15111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1111-1-11111-1111111-1-111111-1-1-1-1-1
χ16111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-111-1-111-1-1-1-11111111111111-1-1-1-111-1-11-1-11111-1-1-1-1-1-1-111-1-1-1111-11-11
χ1711111111-1-1-1-111111111-1-111-1-1111111-1-111-1-1111111111111-1-1-1-1-1111-111111-1-111-1-1-1-1-1-1-111-1-1-1-1-11-1-1-111-1
χ1811111111-1-1-1-111111111-1-111-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-11-1-1-1-1-11-1-111-1-1-11111-1-1111111-11-1-111
χ1911111111-1-1-1-111111111-1-111-1-111-1-1-1-1-1-111-1-1111111111111-1-1-1-1-1-1-11-1-1-1-1-1111-1-111-111-1-111-1-1-1-11-1111-1-11
χ2011111111-1-1-1-111111111-1-111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1111-11111111-1-111-1-1-111-1-11111-1-11-111-1-1
χ2111111111-1-1-1-111111111-1-1-1-111-1-11111-1-111111111-1-1-1-111111111111-1111-1-1-1-1-111-1-1-111-1-1-1-1-1-111-1-11-11-1-11
χ2211111111-1-1-1-111111111-1-1-1-111-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-11-1-111-1-1-111-1-1-1-1-1111111-1-11-11111-1-1
χ2311111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1111111111-1-1-11-1-111-111-1-111-1-1-1-1-1-1-1-1-11111-11-111-1
χ2411111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111-1111-1-1-111-1-111-111111111-1-1-11-1-1-1-111
χ2511111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-11-1-11-11111-1-1-1-1-1111-1-1-1-1-1-1111111-1-11-1-11
χ2611111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-11-1111-1-1
χ2711111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1111-1-1-1-11111-1-111-111-1
χ2811111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111-1-11-11111-11111-1-11-1-11111-1-1-1-11-11-1-1-111
χ2911111111-1-1-1-1-1-1-1-1111111-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111-1-11-1-1-1-111111-1-11111-1-11-11-1-111-1
χ3011111111-1-1-1-1-1-1-1-1111111-1-111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-111-11-1-1111-1-1-1-1111-1-111-1-1-1-111-1-111-1-111
χ3111111111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-111-11-1-11111111-1-11-1-1-1-11111-1-1-11-111-1-11
χ3211111111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111-1-111111-1-111111-1-1-1-11111-1-111-1-1
χ332222222222222222-2-2-2-2222222220000-2-2-2-2220000000000000000-200-2-20000-2000000-2000000000000000000
χ342222222222222222-2-2-2-222-2-2-2-2-2-20000-2-2-2-2-2-200000000000000002002200002000000-2000000000000000000
χ35222222222222-2-2-2-2-2-2-2-2-2-22222-2-20000-2-222-2-20000000000000000200-2-2000020000002000000000000000000
χ36222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2220000-2-222220000000000000000-200220000-20000002000000000000000000
χ3722222222-2-2-2-22222-2-2-2-2-2-222-2-222000022-2-2-2-20000000000000000200-220000-20000002000000000000000000
χ3822222222-2-2-2-22222-2-2-2-2-2-2-2-222-2-2000022-2-2220000000000000000-2002-2000020000002000000000000000000
χ3922222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-200002222220000000000000000-200-2200002000000-2000000000000000000
χ4022222222-2-2-2-2-2-2-2-2-2-2-2-222-2-2222200002222-2-200000000000000002002-20000-2000000-2000000000000000000
χ4122-2-22-22-222-2-222-2-200002-22i−2i2i−2i2i−2i000000002i−2i22−2−2i2i2−i2−i222−2−2i2i2−i2−i200000000000000000002−2i2−i22−2i2−i200000000
χ4222-2-22-22-222-2-222-2-200002-22i−2i2i−2i2i−2i000000002i−2i−2−222−i2−i2i2i2−2−222−i2−i2i2i20000000000000000000−22−i2i2−22−i2i200000000
χ4322-2-22-22-222-2-222-2-200002-2−2i2i−2i2i−2i2i00000000−2i2i22−2−2−i2−i2i2i222−2−2−i2−i2i2i200000000000000000002−2−i2i22−2−i2i200000000
χ4422-2-22-22-222-2-222-2-200002-2−2i2i−2i2i−2i2i00000000−2i2i−2−222i2i2−i2−i2−2−222i2i2−i2−i20000000000000000000−22i2−i2−22i2−i200000000
χ4522-2-22-22-222-2-2-2-2220000-222i−2i2i−2i−2i2i00000000−2i2i22−2−2i2i2−i2−i2−2−222i2i2−i2−i200000000000000000002−2−i2i2−22−i2i200000000
χ4622-2-22-22-222-2-2-2-2220000-222i−2i2i−2i−2i2i00000000−2i2i−2−222−i2−i2i2i222−2−2−i2−i2i2i20000000000000000000−22i2−i22−2i2−i200000000
χ4722-2-22-22-222-2-2-2-2220000-22−2i2i−2i2i2i−2i000000002i−2i22−2−2−i2−i2i2i2−2−222−i2−i2i2i200000000000000000002−2i2−i2−22i2−i200000000
χ4822-2-22-22-222-2-2-2-2220000-22−2i2i−2i2i2i−2i000000002i−2i−2−222i2i2−i2−i222−2−2i2i2−i2−i20000000000000000000−22−i2i22−2−i2i200000000
χ4922-2-22-22-2-2-22222-2-20000-222i−2i−2i2i2i−2i00000000−2i2i22−2−2i2i2−i2−i222−2−2−i2−i2i2i20000000000000000000−22i2−i2−22−i2i200000000
χ5022-2-22-22-2-2-22222-2-20000-222i−2i−2i2i2i−2i00000000−2i2i−2−222−i2−i2i2i2−2−222i2i2−i2−i200000000000000000002−2−i2i22−2i2−i200000000
χ5122-2-22-22-2-2-22222-2-20000-22−2i2i2i−2i−2i2i000000002i−2i22−2−2−i2−i2i2i222−2−2i2i2−i2−i20000000000000000000−22−i2i2−22i2−i200000000
χ5222-2-22-22-2-2-22222-2-20000-22−2i2i2i−2i−2i2i000000002i−2i−2−222i2i2−i2−i2−2−222−i2−i2i2i200000000000000000002−2i2−i22−2−i2i200000000
χ5322-2-22-22-2-2-222-2-22200002-22i−2i−2i2i−2i2i000000002i−2i22−2−2i2i2−i2−i2−2−222−i2−i2i2i20000000000000000000−22−i2i22−2i2−i200000000
χ5422-2-22-22-2-2-222-2-22200002-22i−2i−2i2i−2i2i000000002i−2i−2−222−i2−i2i2i222−2−2i2i2−i2−i200000000000000000002−2i2−i2−22−i2i200000000
χ5522-2-22-22-2-2-222-2-22200002-2−2i2i2i−2i2i−2i00000000−2i2i22−2−2−i2−i2i2i2−2−222i2i2−i2−i20000000000000000000−22i2−i22−2−i2i200000000
χ5622-2-22-22-2-2-222-2-22200002-2−2i2i2i−2i2i−2i00000000−2i2i−2−222i2i2−i2−i222−2−2−i2−i2i2i200000000000000000002−2−i2i2−22i2−i200000000
χ572-22-22-2-2200002-22-222-2-2000000002i2i−2i−2i002-2002i−2i2i−2i00002i−2i2i−2i000002-2002-2000002i−2i000000000000000000000
χ582-22-22-2-2200002-22-222-2-2000000002i2i−2i−2i002-200−2i2i−2i2i0000−2i2i−2i2i00000-2200-22000002i−2i000000000000000000000
χ592-22-22-2-2200002-22-222-2-200000000−2i−2i2i2i002-2002i−2i2i−2i00002i−2i2i−2i00000-2200-2200000−2i2i000000000000000000000
χ602-22-22-2-2200002-22-222-2-200000000−2i−2i2i2i002-200−2i2i−2i2i0000−2i2i−2i2i000002-2002-200000−2i2i000000000000000000000
χ612-22-22-2-220000-22-2222-2-2000000002i2i−2i−2i00-22002i−2i2i−2i0000−2i2i−2i2i00000-22002-200000−2i2i000000000000000000000
χ622-22-22-2-220000-22-2222-2-2000000002i2i−2i−2i00-2200−2i2i−2i2i00002i−2i2i−2i000002-200-2200000−2i2i000000000000000000000
χ632-22-22-2-220000-22-2222-2-200000000−2i−2i2i2i00-22002i−2i2i−2i0000−2i2i−2i2i000002-200-22000002i−2i000000000000000000000
χ642-22-22-2-220000-22-2222-2-200000000−2i−2i2i2i00-2200−2i2i−2i2i00002i−2i2i−2i00000-22002-2000002i−2i000000000000000000000
χ652-2-2-2-22222-22-20000-22-22000000002-22-22-2000000002-22-200002-22-200000002-202-2000002-20000000000000000
χ662-2-2-2-22222-22-20000-22-22000000002-22-22-200000000-22-220000-22-220000000-2202-200000-220000000000000000
χ672-2-2-2-22222-22-20000-22-2200000000-22-222-2000000002-22-200002-22-20000000-220-2200000-220000000000000000
χ682-2-2-2-22222-22-20000-22-2200000000-22-222-200000000-22-220000-22-2200000002-20-22000002-20000000000000000
χ692-2-2-2-2222-22-220000-22-22000000002-22-2-22000000002-22-20000-22-2200000002-20-2200000-220000000000000000
χ702-2-2-2-2222-22-220000-22-22000000002-22-2-2200000000-22-2200002-22-20000000-220-22000002-20000000000000000
χ712-2-2-2-2222-22-220000-22-2200000000-22-22-22000000002-22-20000-22-220000000-2202-2000002-20000000000000000
χ722-2-2-2-2222-22-220000-22-2200000000-22-22-2200000000-22-2200002-22-200000002-202-200000-220000000000000000
χ7344-44-4-4-44000000004-4-440000000000000000000000000000000000000000000000004i−4i0000000000000000000
χ7444-44-4-4-44000000004-4-44000000000000000000000000000000000000000000000000−4i4i0000000000000000000
χ7544-44-4-4-4400000000-444-4000000004i−4i−4i4i000000000000000000000000000000000000000000000000000000000
χ7644-44-4-4-4400000000-444-400000000−4i4i4i−4i000000000000000000000000000000000000000000000000000000000
χ774-444-4-44-44-4-440000000000000000000000000000002i2−2i2−2i22i200002i2−2i2−2i22i200000000000000000000000000000000000
χ784-444-4-44-44-4-44000000000000000000000000000000−2i22i22i2−2i20000−2i22i22i2−2i200000000000000000000000000000000000
χ794-444-4-44-4-444-40000000000000000000000000000002i2−2i2−2i22i20000−2i22i22i2−2i200000000000000000000000000000000000
χ804-444-4-44-4-444-4000000000000000000000000000000−2i22i22i2−2i200002i2−2i2−2i22i200000000000000000000000000000000000
χ814-44-44-4-4400004-44-4-4-44400000000000000-4400000000000000000000000000000000000000000000000000000
χ824-44-44-4-440000-44-44-4-444000000000000004-400000000000000000000000000000000000000000000000000000
χ834-4-4444-4-400004-4-4400000000000000000000002i2−2i2−2i22i200002i2−2i2−2i22i2000000000000000000000000000000000000000
χ844-4-4444-4-400004-4-440000000000000000000000−2i22i22i2−2i20000−2i22i22i2−2i2000000000000000000000000000000000000000
χ854-4-4444-4-40000-444-400000000000000000000002i2−2i2−2i22i20000−2i22i22i2−2i2000000000000000000000000000000000000000
χ864-4-4444-4-40000-444-40000000000000000000000−2i22i22i2−2i200002i2−2i2−2i22i2000000000000000000000000000000000000000
χ874-4-4-4-44444-44-400004-44-4000000000000-440000000000000000000000000000000000000000000000000000000
χ884-4-4-4-4444-44-4400004-44-40000000000004-40000000000000000000000000000000000000000000000000000000
χ89888-8-88-8-8000000000000000000000000000000000000000000000000000000000000000000000000000000000

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