Finite Group Databasebeta

← Group #6996325

Character table — Group #6996325

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1111111122222222444444444444444444444488888888888888888888888888888888881616161616161616
order12222222222244442222224444444488888888222244444444444444444488888888888822444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-1111-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-111-1-111-1-111-111-1-1-1-1-1-11111-1-1-1-11-11-11-11-1
χ611111111111111111111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-111-1-11111-1-1-111-1-1-1-11111-1-1-1-1-11-11-11-11
χ711111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-111-1-1-1-11111-1-1-1111111-1-1-1-111111-11-1-11-11
χ811111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-11111-1-111-111-1-11111-1-1-1-11111-11-111-11-1
χ91111111111111111-1-1-1-111-1-111-1-111111111111111-11-111-1-111-1-1-1-111111-1-1-1-1-1-1-1-11111-11-1-1-1-1-11
χ101111111111111111-1-1-1-111-1-111-1-11111111111-1-1-1-1-11-1-1-111-1-111-1-11-1-1-1-1-1-1-1-1-1-1-1-111111-111111-1
χ111111111111111111-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1-11111-11-111-1-1-1-111-1-11-1-1-1-111111111-1-1-1-1-11-1-1111-1
χ121111111111111111-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11111-1-1-1-11111111111111-1-1-1-11-111-1-1-11
χ131111111111111111-1-1-1-1-1-111-1-111111111111111-1-11-1111111111-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-11-11-1-1
χ141111111111111111-1-1-1-1-1-111-1-1111111111111-1-1111-11-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111-11-111
χ151111111111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-111-1-11-111111-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-111-111
χ161111111111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1111-11-1-1-1-11111-1-1-111-1-1-1-1-1-111111111111-1-11-1-1
χ1711111111-1-1-1-1111111-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-11-1-1-1-111-1-11-11-1-1-1-111-1-111-1-111-1-1-1-11111-11
χ1811111111-1-1-1-1111111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111-1-1111-11111111-1-111-1-111-1-111-1-1-1-11-1
χ1911111111-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-11-1-1-1-1-1-1111-111111-1-111-1-111-1-111-1-111-1-11-1
χ2011111111-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111-1-11-11-1-1-1-1-1-111-1-111-1-11111-1-111-11
χ2111111111-1-1-1-1111111-1-1-1-1-1-11111-1-11111-1-1-1-111-1-111-1-1-11111111-1-1-1-111-1-11111-1-1-1-111-111-11-1-1-1
χ2211111111-1-1-1-1111111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-11111-111-1-1-1-1-1-11-1-111-1-1-1-11111-1-1-1-1111-1-11-1111
χ2311111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-111-1-1-111-1-1-1-11-1-111-1-111-1-1-1-11111-1-1-111-1-1111
χ2411111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-11111-111-1-111111-1-1-1-11111-1-1-1-11111-1-11-1-111-1-1-1
χ2511111111-1-1-1-11111-1-11111-1-1-1-111-1-11111-1-1-1-111111-1-1-1-1111111-111-1-1-1-1-1-111-1-11111-1-11-1-1-1-1-111
χ2611111111-1-1-1-11111-1-11111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11-1-111-1-1-1-1-1-1-1111111-1-111-1-11111-1-1-111111-1-1
χ2711111111-1-1-1-11111-1-11111-1-1-1-111-1-1-1-1-1-1111111111-1-1-1-111-1-1-1-1-111111111-1-111-1-1-1-1111-1-1-111-1-1
χ2811111111-1-1-1-11111-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11-1-111-1-11111-111-1-1-1-111-1-111-1-1-1-111-1111-1-111
χ2911111111-1-1-1-11111-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1-111-1-1-1-111-1-1-11-1-1-11111-1-1-1-111-1-11111-11-111-1
χ3011111111-1-1-1-11111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-111-1111111-1-111-11-111-1-111-1-1-1-111-1-111-1-11-11-1-11
χ3111111111-1-1-1-11111-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-1-111-1-1-1-1-1-111-11-111-1-1-1-11111-1-111-1-111-111-1-11
χ3211111111-1-1-1-11111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111-111111111-1-1-11-1-1-111-1-11111-1-111-1-1-1-11-1-111-1
χ33222222222222-2-2-2-2222222222222-2-2000000000000-2-2-200000000-2-2-2000000000000000000000000
χ34222222222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-200000000000022200000000-2-22000000000000000000000000
χ35222222222222-2-2-2-2-2-2-2-222-2-222-2-2-2-20000000000002-220000000022-2000000000000000000000000
χ36222222222222-2-2-2-2-2-2-2-2-2-222-2-222-2-2000000000000-22-200000000222000000000000000000000000
χ3722222222-2-2-2-2-2-2-2-222-2-22222-2-2-2-22200000000000022-200000000-22-2000000000000000000000000
χ3822222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2222222000000000000-2-2200000000-222000000000000000000000000
χ3922222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-22222000000000000-222000000002-2-2000000000000000000000000
χ4022222222-2-2-2-2-2-2-2-2-2-222-2-22222-2-2220000000000002-2-2000000002-22000000000000000000000000
χ4122-222-2-2-222-2-200002-22-22-22-22-22-200i2i2−i2−i2i2i2−i2−i20000000000000000000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i200000000
χ4222-222-2-2-222-2-200002-22-22-22-22-22-200−i2−i2i2i2−i2−i2i2i20000000000000000000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i200000000
χ4322-222-2-2-222-2-200002-22-2-22-22-22-2200i2i2−i2−i2i2i2−i2−i20000000000000000000000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i200000000
χ4422-222-2-2-222-2-200002-22-2-22-22-22-2200−i2−i2i2i2−i2−i2i2i20000000000000000000000i2−i2i2−i2−i2i2−i2i2i2−i2i2−i200000000
χ4522-222-2-2-222-2-20000-22-222-2-222-2-2200i2i2−i2−i2i2i2−i2−i20000000000000000000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i200000000
χ4622-222-2-2-222-2-20000-22-222-2-222-2-2200−i2−i2i2i2−i2−i2i2i20000000000000000000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i200000000
χ4722-222-2-2-222-2-20000-22-22-222-2-222-200i2i2−i2−i2i2i2−i2−i20000000000000000000000i2−i2i2−i2−i2i2−i2i2−i2i2−i2i200000000
χ4822-222-2-2-222-2-20000-22-22-222-2-222-200−i2−i2i2i2−i2−i2i2i20000000000000000000000−i2i2−i2i2i2−i2i2−i2i2−i2i2−i200000000
χ4922-222-2-2-2-2-22200002-2-222-22-2-22-2200i2i2−i2−i2−i2−i2i2i20000000000000000000000i2−i2−i2i2i2−i2−i2i2i2−i2−i2i200000000
χ5022-222-2-2-2-2-22200002-2-222-22-2-22-2200−i2−i2i2i2i2i2−i2−i20000000000000000000000−i2i2i2−i2−i2i2i2−i2−i2i2i2−i200000000
χ5122-222-2-2-2-2-22200002-2-22-22-222-22-200i2i2−i2−i2−i2−i2i2i20000000000000000000000−i2i2i2−i2i2−i2−i2i2−i2i2i2−i200000000
χ5222-222-2-2-2-2-22200002-2-22-22-222-22-200−i2−i2i2i2i2i2−i2−i20000000000000000000000i2−i2−i2i2−i2i2i2−i2i2−i2−i2i200000000
χ5322-222-2-2-2-2-2220000-222-22-2-22-222-200i2i2−i2−i2−i2−i2i2i20000000000000000000000−i2i2i2−i2−i2i2i2−i2i2−i2−i2i200000000
χ5422-222-2-2-2-2-2220000-222-22-2-22-222-200−i2−i2i2i2i2i2−i2−i20000000000000000000000i2−i2−i2i2i2−i2−i2i2−i2i2i2−i200000000
χ5522-222-2-2-2-2-2220000-222-2-222-22-2-2200i2i2−i2−i2−i2−i2i2i20000000000000000000000i2−i2−i2i2−i2i2i2−i2−i2i2i2−i200000000
χ5622-222-2-2-2-2-2220000-222-2-222-22-2-2200−i2−i2i2i2i2i2−i2−i20000000000000000000000−i2i2i2−i2i2−i2−i2i2i2−i2−i2i200000000
χ572-2-22-22-222-22-2-2-2220000000000002-22-22-22-22-22-2000002-2002-2000002-20000000000000000000000
χ582-2-22-22-222-22-2-2-2220000000000002-22-22-22-22-2-2200000-2200-2200000-220000000000000000000000
χ592-2-22-22-222-22-2-2-2220000000000002-2-22-22-22-222-2000002-200-2200000-220000000000000000000000
χ602-2-22-22-222-22-2-2-2220000000000002-2-22-22-22-22-2200000-22002-2000002-20000000000000000000000
χ612-2-22-22-22-22-22-2-222000000000000-222-22-2-22-222-200000-22002-200000-220000000000000000000000
χ622-2-22-22-22-22-22-2-222000000000000-222-22-2-22-22-22000002-200-22000002-20000000000000000000000
χ632-2-22-22-22-22-22-2-222000000000000-22-22-222-22-22-200000-2200-22000002-20000000000000000000000
χ642-2-22-22-22-22-22-2-222000000000000-22-22-222-22-2-22000002-2002-200000-220000000000000000000000
χ6544-4-4-4-44400004-44-40000000000000000000000000000000000000000004-400000000000000000000
χ6644-4-4-4-44400004-44-4000000000000000000000000000000000000000000-4400000000000000000000
χ6744-4-4-4-4440000-44-44000000000000000000000000000000000004-4000000000000000000000000000
χ6844-4-4-4-4440000-44-4400000000000000000000000000000000000-44000000000000000000000000000
χ694-444-4-44-44-4-440000000000000000002i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000000000000000000000000000
χ704-444-4-44-44-4-44000000000000000000−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000000000000000000000000000
χ714-444-4-44-4-444-40000000000000000002i2−2i2−2i22i2−2i22i22i2−2i2000000000000000000000000000000000000000000
χ724-444-4-44-4-444-4000000000000000000−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000000000000000000000000000
χ734-44-44-4-4400004-4-4400000000000000000000000000000004-40000000000000000000000000000000
χ744-44-44-4-4400004-4-440000000000000000000000000000000-440000000000000000000000000000000
χ754-44-44-4-440000-444-40000000000000000000000004-400000000000000000000000000000000000000
χ764-44-44-4-440000-444-4000000000000000000000000-4400000000000000000000000000000000000000
χ774-4-44-44-444-44-444-4-4000000000000-4400000000000000000000000000000000000000000000000000
χ784-4-44-44-44-44-4444-4-40000000000004-400000000000000000000000000000000000000000000000000
χ79888-8-88-8-8000000000000000000000000000000000000000000000000000000000000000000000000
χ808-8-8-8888-8000000000000000000000000000000000000000000000000000000000000000000000000

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