Finite Group Databasebeta

← Group #7124413

Character table — Group #7124413

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83
size111111112222222244444444444444444444444444444444888888888888888888888888816161616161616161616
order12222222222244442244444444444444888888888888888822444444444444444888888882444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-11-111-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-111-11-1-1111
χ5111111111111111111-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111111111-1-11-1-111111-11111-1-1-1-111-1-1-1-1-1-111-11-1-1
χ6111111111111111111-1-111-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1111-1-1-1-11-1-1-1-1-1-1-1-1-111-1-11111-1-11-111
χ7111111111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-11-1-111111-1-1-1-1-11111-1-111-111-1-11-1-111
χ8111111111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-11-111111111-1-1111-1-111-111-1-1
χ91111111111111111-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-11111-1-1-1-1111111-1-1-1-1-1-1-1111-1-1-1-1-1-1
χ101111111111111111-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-11-1-1-1111111
χ111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-111-1-1111
χ121111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-111-1-11111-1-1111111111-1-111-1-1-1
χ131111111111111111-1-1-1-111-1-1-1-11111111111-1-1-1-11111-1-1-1-111-1-1-1-1-111-1-1-111111-1-111-1-1111-1-1-1-1-11-111
χ141111111111111111-1-1-1-111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-111-11-1-1-1-1-1-111-1-111-111111-11-1-1
χ151111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-111-1-1-11-1-1-1-111-1-111-1-1111-11-111-1-1
χ161111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-1-111-1-111-11111111-1-111-1-1-1-1-11-11-1-111
χ1711111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1111-11-1-1-1-1-1-1-1111-1-1-1-11111-1-1-11-11-11111-1
χ1811111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11-11111111-11-1-111-1-11111-1-11-11-11-1-1-1-11
χ1911111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111111-11-1-1-1-1-1-1-11-1-11111-1-1-1-111-1-111111-1-11
χ2011111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11-11111111-1111-1-111-1-1-1-11111-1-1-1-1-111-1
χ2111111111-1-1-1-1111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-11111-1-1-1-1-1-111-1-111-1-111111-11-1-11-11-11
χ2211111111-1-1-1-1111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-11111-11-111-11-11-1
χ2311111111-1-1-1-1111111-1-1-1-111-1-1-1-11111-1-1-1-111111111111111-11111-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-111-1-11-1
χ2411111111-1-1-1-1111111-1-1-1-111-1-1-1-11111-1-1-1-1111111111111-1-1-111-1-11111-1-111-1-1-1-111-1-1-1-1-1-111-1-111-11
χ2511111111-1-1-1-11111-1-111-1-1-1-111-1-1111111111111-1-1-1-11111111-1-1-1-1-1-1111-111-1-1-1-1-1-1-1-11111-111-1-1-1-11
χ2611111111-1-1-1-11111-1-111-1-1-1-111-1-1111111111111-1-1-1-11111-1-11-1-11111-1-11-1-1-111-1-1-1-1-1-111-1-11-1-11111-1
χ2711111111-1-1-1-11111-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111-1-1-1-1-1-1111-1-1-111111111-1-11-111-1-1-111-1
χ2811111111-1-1-1-11111-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11-1-11111-1-11-111-1-1111111-1-1-11-1-1111-1-11
χ2911111111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-11-111-1-1111111-1-11111-1-1-1-1-1-11-11-11-11-1
χ3011111111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-11-1-1-111-1-111-1-1111111-1-1-1-111-11-11-11-11
χ3111111111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-111-11-111-1-11111-1-111-1-1-1-11111-11-1-1-1-111-11
χ3211111111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-11-1-1-111-1-11111-1-1-1-1-1-111111-11111-1-11-1
χ33222222222222-2-2-2-22222-2-222222222-2-2000000000000000000-2-2-2000000-2-20000000000000000000000
χ34222222222222-2-2-2-222-2-2-2-2-2-222-2-2-2-22200000000000000000022-2000000-220000000000000000000000
χ35222222222222-2-2-2-2-2-222-2-222-2-2-2-2-2-222000000000000000000-2-22000000220000000000000000000000
χ36222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-20000000000000000002220000002-20000000000000000000000
χ3722222222-2-2-2-2-2-2-2-2222222-2-2-2-222-2-222000000000000000000-22-20000002-20000000000000000000000
χ3822222222-2-2-2-2-2-2-2-222-2-22222-2-2-2-222-2-20000000000000000002-2-2000000220000000000000000000000
χ3922222222-2-2-2-2-2-2-2-2-2-22222-2-222-2-222-2-2000000000000000000-222000000-220000000000000000000000
χ4022222222-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2220000000000000000002-22000000-2-20000000000000000000000
χ4122-2-22-22-222-2-200002-22-2002-22-22-22-200i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200000000000000000i2−i2i2−i2i2−i2i2−i20000000000
χ4222-2-22-22-222-2-200002-22-2002-22-22-22-200−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200000000000000000−i2i2−i2i2−i2i2−i2i20000000000
χ4322-2-22-22-222-2-200002-2-2200-222-2-22-2200i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i200000000000000000−i2i2−i2i2i2−i2−i2i20000000000
χ4422-2-22-22-222-2-200002-2-2200-222-2-22-2200−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i200000000000000000i2−i2i2−i2−i2i2i2−i20000000000
χ4522-2-22-22-222-2-20000-222-2002-2-22-22-2200i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i200000000000000000i2−i2−i2i2−i2i2−i2i20000000000
χ4622-2-22-22-222-2-20000-222-2002-2-22-22-2200−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i200000000000000000−i2i2i2−i2i2−i2i2−i20000000000
χ4722-2-22-22-222-2-20000-22-2200-22-222-22-200i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i200000000000000000−i2i2i2−i2−i2i2i2−i20000000000
χ4822-2-22-22-222-2-20000-22-2200-22-222-22-200−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i200000000000000000i2−i2−i2i2i2−i2−i2i20000000000
χ4922-2-22-22-2-2-22200002-22-200-22-222-2-2200i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i200000000000000000−i2i2i2−i2i2−i2−i2i20000000000
χ5022-2-22-22-2-2-22200002-22-200-22-222-2-2200−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i200000000000000000i2−i2−i2i2−i2i2i2−i20000000000
χ5122-2-22-22-2-2-22200002-2-22002-2-22-222-200i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200000000000000000i2−i2−i2i2i2−i2i2−i20000000000
χ5222-2-22-22-2-2-22200002-2-22002-2-22-222-200−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200000000000000000−i2i2i2−i2−i2i2−i2i20000000000
χ5322-2-22-22-2-2-2220000-222-200-222-2-222-200i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i200000000000000000−i2i2−i2i2−i2i2i2−i20000000000
χ5422-2-22-22-2-2-2220000-222-200-222-2-222-200−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i200000000000000000i2−i2i2−i2i2−i2−i2i20000000000
χ5522-2-22-22-2-2-2220000-22-22002-22-22-2-2200i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i200000000000000000i2−i2i2−i2−i2i2−i2i20000000000
χ5622-2-22-22-2-2-2220000-22-22002-22-22-2-2200−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i200000000000000000−i2i2−i2i2i2−i2i2−i20000000000
χ572-2-2-2-22222-22-2-22-2200002-200000000002-22-200002-22-200002-2000002-200002-22-2000000000000000000
χ582-2-2-2-22222-22-2-22-2200002-200000000002-22-200002-22-20000-2200000-220000-22-22000000000000000000
χ592-2-2-2-22222-22-2-22-2200002-20000000000-22-220000-22-2200002-2000002-20000-22-22000000000000000000
χ602-2-2-2-22222-22-2-22-2200002-20000000000-22-220000-22-220000-2200000-2200002-22-2000000000000000000
χ612-2-2-2-2222-22-22-22-220000-2200000000002-22-20000-22-2200002-200000-2200002-2-22000000000000000000
χ622-2-2-2-2222-22-22-22-220000-2200000000002-22-20000-22-220000-22000002-20000-222-2000000000000000000
χ632-2-2-2-2222-22-22-22-220000-220000000000-22-2200002-22-200002-200000-220000-222-2000000000000000000
χ642-2-2-2-2222-22-22-22-220000-220000000000-22-2200002-22-20000-22000002-200002-2-22000000000000000000
χ65444-4-44-4-400004-4-4400000000000000000000000000004-44-400000000000000000000000000000000000
χ66444-4-44-4-400004-4-440000000000000000000000000000-44-4400000000000000000000000000000000000
χ67444-4-44-4-40000-444-4000000000000000000004-44-40000000000000000000000000000000000000000000
χ68444-4-44-4-40000-444-400000000000000000000-44-440000000000000000000000000000000000000000000
χ6944-44-4-4-4400000000000000000000004-400002i2−2i2−2i22i200002i2−2i2−2i22i200000000000000000000000000000000000
χ7044-44-4-4-4400000000000000000000004-40000−2i22i22i2−2i20000−2i22i22i2−2i200000000000000000000000000000000000
χ7144-44-4-4-440000000000000000000000-4400002i2−2i2−2i22i20000−2i22i22i2−2i200000000000000000000000000000000000
χ7244-44-4-4-440000000000000000000000-440000−2i22i22i2−2i200002i2−2i2−2i22i200000000000000000000000000000000000
χ734-444-4-44-44-4-44000000000000000000002i2−2i2−2i22i200002i2−2i2−2i22i2000000000000000000000000000000000000000
χ744-444-4-44-44-4-4400000000000000000000−2i22i22i2−2i20000−2i22i22i2−2i2000000000000000000000000000000000000000
χ754-444-4-44-4-444-4000000000000000000002i2−2i2−2i22i20000−2i22i22i2−2i2000000000000000000000000000000000000000
χ764-444-4-44-4-444-400000000000000000000−2i22i22i2−2i200002i2−2i2−2i22i2000000000000000000000000000000000000000
χ774-4-4444-4-4000044-4-400000000000000000000000000000000000004-40000000000000000000000000000
χ784-4-4444-4-4000044-4-40000000000000000000000000000000000000-440000000000000000000000000000
χ794-4-4444-4-40000-4-444000000000000000000000000000000000000000004i−4i000000000000000000000000
χ804-4-4444-4-40000-4-44400000000000000000000000000000000000000000−4i4i000000000000000000000000
χ814-4-4-4-44444-44-44-44-40000-440000000000000000000000000000000000000000000000000000000000000
χ824-4-4-4-4444-44-444-44-400004-40000000000000000000000000000000000000000000000000000000000000
χ838-88-88-8-88000000000000000000000000000000000000000000000000000000000000000000000000000

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