Finite Group Databasebeta

← Group #6816521

Character table — Group #6816521

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size11111111222222222222222244444444444444444444444444444488888888888888888888161616161616161616161616
order12222222444444448888888822224444444444444488888888888822444444444488888888444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ5111111111111111111111111-1-1-1-11111111111-1-1-1-111111111111111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-11111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ91111111111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1
χ101111111111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-111-1-111-1-111
χ111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1-11111-1-1-1-111
χ121111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-11111-1-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-11111111111-1-1-1-111-1-111
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-11111-1-111-1-1
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-111-1-1-1-11111-1-11111-1-1-1-1-1-111-1-11111-1-1
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-111-1-111-1-1-1-111
χ1711111111-1-1-1-111111111111111-1-11111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1111-1111-1-1-1-1-111-1-111-1-11-11-11-11-11-11-1
χ1811111111-1-1-1-111111111111111-1-11111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-11-1-1-11-1111111-1-111-1-1-11-11-11-11-11-11
χ1911111111-1-1-1-111111111111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1111-111-11-1-1-1-111-1-1-1-111-11-111-11-1-11-11
χ2011111111-1-1-1-111111111111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1-1-11-1-1-1-11111111-1-1-1-1111-11-1-11-111-11-1
χ2111111111-1-1-1-1111111111111-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1111-11-1-1-1-1-1-111-1-1111-11-1-11-11-11-11
χ2211111111-1-1-1-1111111111111-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-11-1-1-111111-1-111-1-111-11-111-11-11-11-1
χ2311111111-1-1-1-1111111111111-1-111-1-1-1-11111-1-111-1-1-1-1-1-11111-1-1-1-111-11111-1-1-1-1-1-1-11111-1-1-11-11-11-111-11-1
χ2411111111-1-1-1-1111111111111-1-111-1-1-1-11111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-11-1-11-11111-1-11111-1-11-11-11-11-1-11-11
χ2511111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-111-1-1-1-1-1-111111111111-1-1-11-1-1-111-1-111-1-1111-1-111-1-111-1-11
χ2611111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-111-1-1-1-1-1-111111111-1-11-1111-111-1-1-1-111-1-111-111-1-111-1-111-1
χ2711111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-11111111-1-1-1-11-1-111-1-11111-1-1-111-11-1-11-111-1
χ2811111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-11-111-1111-1-1-1-11111-1-11-1-11-111-11-1-11
χ2911111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-11111111111-11-1-1-11-1-11111-1-111-1-11-1-11-111-1-111-1
χ3011111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1111-1111-1-111-1-111-1-1-111-11-1-111-1-11
χ3111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-11111-1-1-1-1111111-11-1-11-1-1-11111-1-1-1-111-111-1-111-11-1-11
χ3211111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-11111-1-1-1-11111-1-1-11111-111-1-111-1-1-1-1111-1-111-1-11-111-1
χ33222222222222-2-2-2-200000000222222-2-222-2-2-2-2222200000000000000-2-200-2-2000000000000000000000000
χ34222222222222-2-2-2-2000000002222-2-222-2-222-2-2-2-2-2-200000000000000-2-20022000000000000000000000000
χ35222222222222-2-2-2-200000000-2-2-2-222-2-222-2-2-2-2-2-2-2-200000000000000220022000000000000000000000000
χ36222222222222-2-2-2-200000000-2-2-2-2-2-222-2-222-2-22222000000000000002200-2-2000000000000000000000000
χ3722222222-2-2-2-2-2-2-2-20000000022-2-222-2-2-2-2222222-2-200000000000000-2200-22000000000000000000000000
χ3822222222-2-2-2-2-2-2-2-20000000022-2-2-2-22222-2-222-2-22200000000000000-22002-2000000000000000000000000
χ3922222222-2-2-2-2-2-2-2-200000000-2-22222-2-2-2-22222-2-222000000000000002-2002-2000000000000000000000000
χ4022222222-2-2-2-2-2-2-2-200000000-2-222-2-22222-2-22222-2-2000000000000002-200-22000000000000000000000000
χ41222-2-2-22-222-2-20000i2i2i2i2−i2−i2−i2−i22-22-22-2002-200002-22-2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2000000000000i2−i2i2−i2i2−i2i2−i2000000000000
χ42222-2-2-22-222-2-20000i2i2i2i2−i2−i2−i2−i22-22-2-2200-220000-22-22−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2000000000000i2−i2i2−i2−i2i2−i2i2000000000000
χ43222-2-2-22-222-2-20000i2i2i2i2−i2−i2−i2−i2-22-222-2002-20000-22-22i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2000000000000−i2i2−i2i2−i2i2−i2i2000000000000
χ44222-2-2-22-222-2-20000i2i2i2i2−i2−i2−i2−i2-22-22-2200-2200002-22-2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2000000000000−i2i2−i2i2i2−i2i2−i2000000000000
χ45222-2-2-22-222-2-20000−i2−i2−i2−i2i2i2i2i22-22-22-2002-200002-22-2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2000000000000−i2i2−i2i2−i2i2−i2i2000000000000
χ46222-2-2-22-222-2-20000−i2−i2−i2−i2i2i2i2i22-22-2-2200-220000-22-22i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2000000000000−i2i2−i2i2i2−i2i2−i2000000000000
χ47222-2-2-22-222-2-20000−i2−i2−i2−i2i2i2i2i2-22-222-2002-20000-22-22−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2000000000000i2−i2i2−i2i2−i2i2−i2000000000000
χ48222-2-2-22-222-2-20000−i2−i2−i2−i2i2i2i2i2-22-22-2200-2200002-22-2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2000000000000i2−i2i2−i2−i2i2−i2i2000000000000
χ49222-2-2-22-2-2-2220000i2i2i2i2−i2−i2−i2−i22-2-222-200-2200002-2-22i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2000000000000i2−i2−i2i2i2−i2−i2i2000000000000
χ50222-2-2-22-2-2-2220000i2i2i2i2−i2−i2−i2−i22-2-22-22002-20000-222-2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2000000000000i2−i2−i2i2−i2i2i2−i2000000000000
χ51222-2-2-22-2-2-2220000i2i2i2i2−i2−i2−i2−i2-222-22-200-220000-222-2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2000000000000−i2i2i2−i2−i2i2i2−i2000000000000
χ52222-2-2-22-2-2-2220000i2i2i2i2−i2−i2−i2−i2-222-2-22002-200002-2-22−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2000000000000−i2i2i2−i2i2−i2−i2i2000000000000
χ53222-2-2-22-2-2-2220000−i2−i2−i2−i2i2i2i2i22-2-222-200-2200002-2-22−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2000000000000−i2i2i2−i2−i2i2i2−i2000000000000
χ54222-2-2-22-2-2-2220000−i2−i2−i2−i2i2i2i2i22-2-22-22002-20000-222-2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2000000000000−i2i2i2−i2i2−i2−i2i2000000000000
χ55222-2-2-22-2-2-2220000−i2−i2−i2−i2i2i2i2i2-222-22-200-220000-222-2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2000000000000i2−i2−i2i2i2−i2−i2i2000000000000
χ56222-2-2-22-2-2-2220000−i2−i2−i2−i2i2i2i2i2-222-2-22002-200002-2-22i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2000000000000i2−i2−i2i2−i2i2i2−i2000000000000
χ572-2-2-2-22222-22-2-2-22222-2-222-2-20000000000002-20000000000002-22-22-2002-2002-22-200000000000000000000
χ582-2-2-2-22222-22-2-2-22222-2-222-2-20000000000002-20000000000002-22-2-2200-2200-22-2200000000000000000000
χ592-2-2-2-22222-22-2-2-222-2-222-2-2220000000000002-2000000000000-22-222-200-22002-2-2200000000000000000000
χ602-2-2-2-22222-22-2-2-222-2-222-2-2220000000000002-2000000000000-22-22-22002-200-222-200000000000000000000
χ612-2-2-2-2222-22-22-2-22222-2-222-2-2000000000000-22000000000000-22-222-2002-200-22-2200000000000000000000
χ622-2-2-2-2222-22-22-2-22222-2-222-2-2000000000000-22000000000000-22-22-2200-22002-22-200000000000000000000
χ632-2-2-2-2222-22-22-2-222-2-222-2-222000000000000-220000000000002-22-22-200-2200-222-200000000000000000000
χ642-2-2-2-2222-22-22-2-222-2-222-2-222000000000000-220000000000002-22-2-22002-2002-2-2200000000000000000000
χ6544-44-44-4-400004-44-40000000000000000000000000000004-44-4000000000000000000000000000000000000
χ6644-44-44-4-400004-44-4000000000000000000000000000000-44-44000000000000000000000000000000000000
χ6744-44-44-4-40000-44-444-44-44-44-400000000000000000000000000000000000000000000000000000000000000
χ6844-44-44-4-40000-44-44-44-44-44-4400000000000000000000000000000000000000000000000000000000000000
χ6944-4-44-4-44000000002i2−2i22i2−2i2−2i22i2−2i22i200000000004-400000000002i2−2i2−2i22i2000000000000000000000000000000000000
χ7044-4-44-4-44000000002i2−2i22i2−2i2−2i22i2−2i22i20000000000-440000000000−2i22i22i2−2i2000000000000000000000000000000000000
χ7144-4-44-4-4400000000−2i22i2−2i22i22i2−2i22i2−2i200000000004-40000000000−2i22i22i2−2i2000000000000000000000000000000000000
χ7244-4-44-4-4400000000−2i22i2−2i22i22i2−2i22i2−2i20000000000-4400000000002i2−2i2−2i22i2000000000000000000000000000000000000
χ734-444-4-4-44000000002i2−2i2−2i22i2−2i22i22i2−2i20000004-400000000002i2−2i22i2−2i20000000000000000000000000000000000000000
χ744-444-4-4-44000000002i2−2i2−2i22i2−2i22i22i2−2i2000000-440000000000−2i22i2−2i22i20000000000000000000000000000000000000000
χ754-444-4-4-4400000000−2i22i22i2−2i22i2−2i2−2i22i20000004-40000000000−2i22i2−2i22i20000000000000000000000000000000000000000
χ764-444-4-4-4400000000−2i22i22i2−2i22i2−2i2−2i22i2000000-4400000000002i2−2i22i2−2i20000000000000000000000000000000000000000
χ774-44-444-4-400004-4-444-4-444-4-4400000000000000000000000000000000000000000000000000000000000000
χ784-44-444-4-400004-4-44-444-4-444-400000000000000000000000000000000000000000000000000000000000000
χ794-44-444-4-40000-444-4000000000000000000000000004-4-440000000000000000000000000000000000000000
χ804-44-444-4-40000-444-400000000000000000000000000-444-40000000000000000000000000000000000000000
χ814-4-444-44-44-4-4400002i22i2−2i2−2i2−2i2−2i22i22i2000000000000000000000000002i2−2i2−2i22i200000000000000000000000000000000
χ824-4-444-44-44-4-440000−2i2−2i22i22i22i22i2−2i2−2i200000000000000000000000000−2i22i22i2−2i200000000000000000000000000000000
χ834-4-444-44-4-444-400002i22i2−2i2−2i2−2i2−2i22i22i200000000000000000000000000−2i22i22i2−2i200000000000000000000000000000000
χ844-4-444-44-4-444-40000−2i2−2i22i22i22i22i2−2i2−2i2000000000000000000000000002i2−2i2−2i22i200000000000000000000000000000000
χ854-4-4-4-44444-44-444-4-400000000000000000000-44000000000000000000000000000000000000000000000000
χ864-4-4-4-4444-44-4444-4-4000000000000000000004-4000000000000000000000000000000000000000000000000

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