Finite Group Databasebeta

← Group #6803878

Character table — Group #6803878

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size11111111222222222222222244444444444444444444444444444488888888888888888888161616161616161616161616
order12222222222244444444444444444444444444888888888888888844444444444488888888224444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-11-1-11-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ5111111111111111111111111-1-111-1-1-1-11111-1-11111111111111111-1-11111-111-111-1-1-1-1-1-1-1-1-1-11-1-111-1-11-1-1
χ6111111111111111111111111-1-111-1-1-1-11111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-111-111
χ7111111111111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111111-111-11-1-11-1-1
χ8111111111111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11111111111-1-11-1-11-111-111
χ9111111111111-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-11111111-111-1-1-1-111111-1-11-1-1-11-1-11-1
χ10111111111111-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1-1-1-11-1-1-1-1-1-1-1-1-11111-111-1111-111-11
χ11111111111111-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-111111-1-1-1-1-11111-1-1-1-1-111-111-11-1-11-1
χ12111111111111-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1111-1111111-1-1-1-11-1-11-1-11-111-11
χ13111111111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-111111-1111111111-1-1-1-1-11-1-11-1-1-11-1-11
χ14111111111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-11-1-11111-1-1-1-11-111-1111-111-1
χ15111111111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-111111-1-1-11-1-1-1-1-1-111111-111-11-1-11-1-11
χ16111111111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-11-1-1-1-1-111111-1-1-1-11111-11-1-11-111-111-1
χ1711111111-1-1-1-111111-1-1-1-111111-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-11111-1-111-1-111-1-1-1111-1-11-11-11-1
χ1811111111-1-1-1-111111-1-1-1-111111-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111-1-111111-1-111-1-11-1-1-111-11-11-11
χ1911111111-1-1-1-111111-1-1-1-111111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-11-1-1111-1-111-1-1111-1-1-1111-11-11-1
χ2011111111-1-1-1-111111-1-1-1-111111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-111-1111-1-1-11-11-11
χ2111111111-1-1-1-111111-1-1-1-1111-1-1-1-1-1-11111-1-1111111-1-1-1-11111-1-1-1-11111-1-1-111-1-1-1-1-111-1-1111-11-11-111-1-1-11
χ2211111111-1-1-1-111111-1-1-1-1111-1-1-1-1-1-11111-1-1111111-1-1-1-11111-1-1-1-111-1-111-1-1-1-111-1-111-1-111-11-11-11-1-1111-1
χ2311111111-1-1-1-111111-1-1-1-1111-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-11111-1-111-1-1-11-11-1111-1-1-11
χ2411111111-1-1-1-111111-1-1-1-1111-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-1111111-1-111-111-1-1-111-1-111-1-11-11-11-1-1-1111-1
χ2511111111-1-1-1-1-1-1-1-11-1-1-1-11111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1111-1-1111-1-1-1-1-11111-1-1-1-1-1111-1-1-1111
χ2611111111-1-1-1-1-1-1-1-11-1-1-1-11111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-11-1-1111-1-1-111-1-11111-1-1111-1-1-1111-1-1-1
χ2711111111-1-1-1-1-1-1-1-11-1-1-1-11111111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1111-1-11-1-1-11111-1-1-1-111111-1-1-1-1-1-1111
χ2811111111-1-1-1-1-1-1-1-11-1-1-1-11111111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-11-1-111111-1-1-111-1-1-1-111-1-1-1111111-1-1-1
χ2911111111-1-1-1-1-1-1-1-11-1-1-1-1111-1-1111111-1-111-1-11111-1-1-1-1-1-1-1-111111-111-1-1-1111-1-111-1-1-1-11111-1-1-11-1111-1-1
χ3011111111-1-1-1-1-1-1-1-11-1-1-1-1111-1-1111111-1-111-1-11111-1-1-1-1-1-1-1-111111-1-1-111-1-1-111111-1-1-1-111-1-1111-11-1-1-111
χ3111111111-1-1-1-1-1-1-1-11-1-1-1-1111-1-1111111-1-111-1-1-1-1-1-111111111-1-1-1-11-111-1-1-1-1-1111-1-11111-1-1-1-1111-1-1111-1-1
χ3211111111-1-1-1-1-1-1-1-11-1-1-1-1111-1-1111111-1-111-1-1-1-1-1-111111111-1-1-1-11-1-1-111-1111-1-1-1-11111-1-111-1-1-111-1-1-111
χ332222222222222222-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2-2-20000000000000000220000-200-20000000000000000000000
χ342222222222222222-2-2-2-2-2-2-2-2-2-222-2-222-2-2-2-2220000000000000000-2-2000020020000000000000000000000
χ35222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-2-2-222222200000000000000002-20000-20020000000000000000000000
χ36222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222-2-20000000000000000-220000200-20000000000000000000000
χ3722222222-2-2-2-22222-22222-2-2-222-2-22222-2-222220000000000000000-2-20000-200-20000000000000000000000
χ3822222222-2-2-2-22222-22222-2-2-2-2-2-2-2-2-2-2-2-2-222-2-2000000000000000022000020020000000000000000000000
χ3922222222-2-2-2-2-2-2-2-2-22222-2-2-22222-2-22222-2-2-2-20000000000000000-220000-20020000000000000000000000
χ4022222222-2-2-2-2-2-2-2-2-22222-2-2-2-2-22222-2-222-2-22200000000000000002-20000200-20000000000000000000000
χ41222-2-2-2-2200002i2i−2i−2i02i2i−2i−2i0002-2002i−2i2i−2i002-22-2i2i2−i2−i222−2−222−2−2i2i2−i2−i20000000000002−2i2−i2i2−i22−2000000000000
χ42222-2-2-2-2200002i2i−2i−2i02i2i−2i−2i0002-2002i−2i2i−2i002-22-2−i2−i2i2i2−2−222−2−222−i2−i2i2i2000000000000−22−i2i2−i2i2−22000000000000
χ43222-2-2-2-2200002i2i−2i−2i02i2i−2i−2i000-2200−2i2i−2i2i002-2-22i2i2−i2−i222−2−222−2−2i2i2−i2−i2000000000000−22−i2i2−i2i2−22000000000000
χ44222-2-2-2-2200002i2i−2i−2i02i2i−2i−2i000-2200−2i2i−2i2i002-2-22−i2−i2i2i2−2−222−2−222−i2−i2i2i20000000000002−2i2−i2i2−i22−2000000000000
χ45222-2-2-2-2200002i2i−2i−2i0−2i−2i2i2i0002-2002i−2i−2i2i00-22-22i2i2−i2−i2−2−22222−2−2−i2−i2i2i20000000000002−2−i2i2i2−i2−22000000000000
χ46222-2-2-2-2200002i2i−2i−2i0−2i−2i2i2i0002-2002i−2i−2i2i00-22-22−i2−i2i2i222−2−2−2−222i2i2−i2−i2000000000000−22i2−i2−i2i22−2000000000000
χ47222-2-2-2-2200002i2i−2i−2i0−2i−2i2i2i000-2200−2i2i2i−2i00-222-2i2i2−i2−i2−2−22222−2−2−i2−i2i2i2000000000000−22i2−i2−i2i22−2000000000000
χ48222-2-2-2-2200002i2i−2i−2i0−2i−2i2i2i000-2200−2i2i2i−2i00-222-2−i2−i2i2i222−2−2−2−222i2i2−i2−i20000000000002−2−i2i2i2−i2−22000000000000
χ49222-2-2-2-220000−2i−2i2i2i02i2i−2i−2i0002-200−2i2i2i−2i00-22-22i2i2−i2−i222−2−2−2−222−i2−i2i2i2000000000000−22−i2i2i2−i22−2000000000000
χ50222-2-2-2-220000−2i−2i2i2i02i2i−2i−2i0002-200−2i2i2i−2i00-22-22−i2−i2i2i2−2−22222−2−2i2i2−i2−i20000000000002−2i2−i2−i2i2−22000000000000
χ51222-2-2-2-220000−2i−2i2i2i02i2i−2i−2i000-22002i−2i−2i2i00-222-2i2i2−i2−i222−2−2−2−222−i2−i2i2i20000000000002−2i2−i2−i2i2−22000000000000
χ52222-2-2-2-220000−2i−2i2i2i02i2i−2i−2i000-22002i−2i−2i2i00-222-2−i2−i2i2i2−2−22222−2−2i2i2−i2−i2000000000000−22−i2i2i2−i22−2000000000000
χ53222-2-2-2-220000−2i−2i2i2i0−2i−2i2i2i0002-200−2i2i−2i2i002-22-2i2i2−i2−i2−2−222−2−222i2i2−i2−i2000000000000−22i2−i2i2−i2−22000000000000
χ54222-2-2-2-220000−2i−2i2i2i0−2i−2i2i2i0002-200−2i2i−2i2i002-22-2−i2−i2i2i222−2−222−2−2−i2−i2i2i20000000000002−2−i2i2−i2i22−2000000000000
χ55222-2-2-2-220000−2i−2i2i2i0−2i−2i2i2i000-22002i−2i2i−2i002-2-22i2i2−i2−i2−2−222−2−222i2i2−i2−i20000000000002−2−i2i2−i2i22−2000000000000
χ56222-2-2-2-220000−2i−2i2i2i0−2i−2i2i2i000-22002i−2i2i−2i002-2-22−i2−i2i2i222−2−222−2−2−i2−i2i2i2000000000000−22i2−i2i2−i2−22000000000000
χ572-222-22-2-222-2-20000-22-22-22-22000000000000002i−2i2i−2i2i−2i2i−2i00000000002-22-202i−2i02i−2i00000000000000000000
χ582-222-22-2-222-2-20000-22-22-22-22000000000000002i−2i2i−2i2i−2i2i−2i0000000000-22-220−2i2i0−2i2i00000000000000000000
χ592-222-22-2-222-2-20000-22-22-22-2200000000000000−2i2i−2i2i−2i2i−2i2i00000000002-22-20−2i2i0−2i2i00000000000000000000
χ602-222-22-2-222-2-20000-22-22-22-2200000000000000−2i2i−2i2i−2i2i−2i2i0000000000-22-2202i−2i02i−2i00000000000000000000
χ612-222-22-2-2-2-2220000-2-22-222-22000000000000002i−2i2i−2i−2i2i−2i2i00000000002-2-2202i−2i0−2i2i00000000000000000000
χ622-222-22-2-2-2-2220000-2-22-222-22000000000000002i−2i2i−2i−2i2i−2i2i0000000000-222-20−2i2i02i−2i00000000000000000000
χ632-222-22-2-2-2-2220000-2-22-222-2200000000000000−2i2i−2i2i2i−2i2i−2i00000000002-2-220−2i2i02i−2i00000000000000000000
χ642-222-22-2-2-2-2220000-2-22-222-2200000000000000−2i2i−2i2i2i−2i2i−2i0000000000-222-202i−2i0−2i2i00000000000000000000
χ6544-444-4-4-44-44-44-44-400000000004-40000000000000000000000000000000000000000000000000000000000
χ6644-444-4-4-44-44-4-44-440000000000-440000000000000000000000000000000000000000000000000000000000
χ6744-444-4-4-4-44-444-44-40000000000-440000000000000000000000000000000000000000000000000000000000
χ6844-444-4-4-4-44-44-44-4400000000004-40000000000000000000000000000000000000000000000000000000000
χ6944-4-4-444-400004i−4i−4i4i40000-4-44000000004i−4i0000000000000000000000000000000000000000000000000000
χ7044-4-4-444-400004i−4i−4i4i-4000044-400000000−4i4i0000000000000000000000000000000000000000000000000000
χ7144-4-4-444-40000−4i4i4i−4i40000-4-4400000000−4i4i0000000000000000000000000000000000000000000000000000
χ7244-4-4-444-40000−4i4i4i−4i-4000044-4000000004i−4i0000000000000000000000000000000000000000000000000000
χ734-444-44-4-444-4-400004-44-44-44-400000000000000000000000000000000000000000000000000000000000000
χ744-444-44-4-4-4-444000044-44-4-44-400000000000000000000000000000000000000000000000000000000000000
χ754-44-44-44-40000000004i−4i−4i4i0000000000000000022−22−2222−2i22i22i2−2i20000000000000000000000000000000000000000
χ764-44-44-44-40000000004i−4i−4i4i00000000000000000−222222−222i2−2i2−2i22i20000000000000000000000000000000000000000
χ774-44-44-44-4000000000−4i4i4i−4i0000000000000000022−22−22222i2−2i2−2i22i20000000000000000000000000000000000000000
χ784-44-44-44-4000000000−4i4i4i−4i00000000000000000−222222−22−2i22i22i2−2i20000000000000000000000000000000000000000
χ794-4-44-4-4444-4-44000000000000000000000000000000000022−2222−2222−2222−2200000000000000000000000000000000
χ804-4-44-4-4444-4-440000000000000000000000000000000000−2222−2222−2222−222200000000000000000000000000000000
χ814-4-44-4-444-444-4000000000000000000000000000000000022−2222−22−2222−222200000000000000000000000000000000
χ824-4-44-4-444-444-40000000000000000000000000000000000−2222−222222−2222−2200000000000000000000000000000000
χ834-4-4-444-4400000000400004-4-4000000000000000000000000004i−4i−4i4i00000000000000000000000000000000
χ844-4-4-444-4400000000400004-4-400000000000000000000000000−4i4i4i−4i00000000000000000000000000000000
χ854-4-4-444-4400000000-40000-44400000000000000000000004-4-44000000000000000000000000000000000000
χ864-4-4-444-4400000000-40000-4440000000000000000000000-444-4000000000000000000000000000000000000

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