Finite Group Databasebeta

← Group #6811331

Character table — Group #6811331

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size11111111222222222222222244444444444444444444444444444488888888888888888888161616161616161616161616
order12222222444444448888888822224444444444444488888888888822244444444488888888222444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-1-111-1-1-1-11-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1-1-111111111-1-1111111111111-111-1-11111-111-1-1-1-1-1-1-1-11-1-1-1-1-1-1111-1-1
χ411111111111111111111111111-1-1-1-1-1-111111111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-111
χ5111111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111-1-11111111-1-1-1-11111-111-1-1-1-1-1-1-111
χ6111111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11-1-1-1-1-1-111111-1-11111111-1-1
χ7111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111111111-1111111-1-1-1-1-1-1-11111-1-1-1-1-1
χ8111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-11111-1-1-1-1111-1-1-1-111111
χ91111111111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-11-1-1-1-1-1-1-1-1-1-111-111-1-11-1-11-1
χ101111111111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-111111-1-1-1-1-1-1-1-1-1-11-1-111-111-11
χ111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1111111111-11-1-1111-1-1-11
χ121111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11111111111-11-111-1-1-1111-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-111-1-1-1-111111111111-1-111-1-11-1-11111-1-1-1-1-11-1-1-111-1111-1
χ141111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-111-1-1-1-1111111111-1-1-1-1-1-1111111111-1-1-1-11-1111-1-11-1-1-11
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1111111-1-1-1-1-1-1-1-1-11111-1-1111-1-1-111-11
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-111-1-111-111-1-1-1-1111111-1-1-1111-1-11-1
χ1711111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1111-1-1-1-1-111111-1-111-1-1-11-11-11-111-1-11
χ1811111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-11-111111-1-111-1-111-1-11-11-11-11-1-111-1
χ1911111111-1-1-1-111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111-11-1-1-1-1-111-1-111-1-111-1-11-11-1111-11-1
χ2011111111-1-1-1-111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111-1-1-111111-1-1-1-1-111-1-11111-11-11-1-1-11-11
χ2111111111-1-1-1-1111111111111-1-111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-111-11-1-1-1-1111-1-11111-1-111-1-11-11-1-11-11
χ2211111111-1-1-1-1111111111111-1-111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111-11-111-11-1
χ2311111111-1-1-1-1111111111111-1-1-1-111-1-1-1-11111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1111-111-11-1-1-111-1
χ2411111111-1-1-1-1111111111111-1-1-1-111-1-1-1-11111-1-111-1-1-1-11111-1-1-1-11-1-11-11111-1-1-111-1-1-1-111-11-1-11-1111-1-11
χ2511111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1111-1-1-1111-1-1-1-111-1-111-1111-1-111-11-1-1
χ2611111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-11-111-1-1111-1-111-1-1111-1-1-111-1-11-111
χ2711111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1111111111111-1-1-1-1111-11-1-111-1-1-111-1-111-1-1-1-1-1-111-11-1111
χ2811111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1111111111111-1-1-1-11-1-1-1111-1-1-11111-1-111-1-11111-1-11-11-1-1-1
χ2911111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-111-11-1-1111-1-111-1-1-1-111111-111-1-11-1-1-1
χ3011111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1111-1-111111-1-1-1-111-1-1-11-1-111-1111
χ3111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1111111-1-1-1-111111111-1-1-111-1-1-1-1-11111-1-11-1-11-1-11-11-111
χ3211111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1111111-1-1-1-111111-1-11-111-1-1-111-1-11111-1-1-111-111-11-11-1-1
χ33222222222222-2-2-2-2000000002222-2-2-2-2-2-222-2-2-2-222000000000000-200220000-20000000000000000000000
χ34222222222222-2-2-2-20000000022-2-22222-2-222-2-2-2-2-2-2000000000000200-2-2000020000000000000000000000
χ35222222222222-2-2-2-200000000-2-2222222-2-2-2-2222222000000000000-200-2-20000-20000000000000000000000
χ36222222222222-2-2-2-200000000-2-2-2-2-2-2-2-2-2-2-2-22222-2-200000000000020022000020000000000000000000000
χ3722222222-2-2-2-2-2-2-2-2000000002222-2-22222-2-222-2-2-2-20000000000002002-20000-20000000000000000000000
χ3822222222-2-2-2-2-2-2-2-20000000022-2-222-2-222-2-222-2-222000000000000-200-22000020000000000000000000000
χ3922222222-2-2-2-2-2-2-2-200000000-2-22222-2-22222-2-222-2-2000000000000200-220000-20000000000000000000000
χ4022222222-2-2-2-2-2-2-2-200000000-2-2-2-2-2-2222222-2-22222000000000000-2002-2000020000000000000000000000
χ4122-22-22-2-22i2i−2i−2i0000i2i2i2i2−i2−i2−i2−i2002-22i−2i2-200002-22i−2i2i−2i22−2−2i2i2−i2−i222−2−20000000000002−2i2−i2i2−i22−2000000000000
χ4222-22-22-2-22i2i−2i−2i0000i2i2i2i2−i2−i2−i2−i2002-2−2i2i-220000-22−2i2i2i−2i22−2−2−i2−i2i2i2−2−222000000000000−22−i2i2i2−i22−2000000000000
χ4322-22-22-2-22i2i−2i−2i0000i2i2i2i2−i2−i2−i2−i200-222i−2i2-20000-22−2i2i−2i2i22−2−2−i2−i2i2i2−2−2220000000000002−2i2−i2−i2i2−22000000000000
χ4422-22-22-2-22i2i−2i−2i0000i2i2i2i2−i2−i2−i2−i200-22−2i2i-2200002-22i−2i−2i2i22−2−2i2i2−i2−i222−2−2000000000000−22−i2i2−i2i2−22000000000000
χ4522-22-22-2-22i2i−2i−2i0000−i2−i2−i2−i2i2i2i2i2002-22i−2i2-200002-22i−2i2i−2i−2−222−i2−i2i2i2−2−222000000000000−22−i2i2−i2i2−22000000000000
χ4622-22-22-2-22i2i−2i−2i0000−i2−i2−i2−i2i2i2i2i2002-2−2i2i-220000-22−2i2i2i−2i−2−222i2i2−i2−i222−2−20000000000002−2i2−i2−i2i2−22000000000000
χ4722-22-22-2-22i2i−2i−2i0000−i2−i2−i2−i2i2i2i2i200-222i−2i2-20000-22−2i2i−2i2i−2−222i2i2−i2−i222−2−2000000000000−22−i2i2i2−i22−2000000000000
χ4822-22-22-2-22i2i−2i−2i0000−i2−i2−i2−i2i2i2i2i200-22−2i2i-2200002-22i−2i−2i2i−2−222−i2−i2i2i2−2−2220000000000002−2i2−i2i2−i22−2000000000000
χ4922-22-22-2-2−2i−2i2i2i0000i2i2i2i2−i2−i2−i2−i2002-22i−2i-220000-222i−2i−2i2i−2−222−i2−i2i2i222−2−20000000000002−2−i2i2i2−i2−22000000000000
χ5022-22-22-2-2−2i−2i2i2i0000i2i2i2i2−i2−i2−i2−i2002-2−2i2i2-200002-2−2i2i−2i2i−2−222i2i2−i2−i2−2−222000000000000−22i2−i2i2−i2−22000000000000
χ5122-22-22-2-2−2i−2i2i2i0000i2i2i2i2−i2−i2−i2−i200-222i−2i-2200002-2−2i2i2i−2i−2−222i2i2−i2−i2−2−2220000000000002−2−i2i2−i2i22−2000000000000
χ5222-22-22-2-2−2i−2i2i2i0000i2i2i2i2−i2−i2−i2−i200-22−2i2i2-20000-222i−2i2i−2i−2−222−i2−i2i2i222−2−2000000000000−22i2−i2−i2i22−2000000000000
χ5322-22-22-2-2−2i−2i2i2i0000−i2−i2−i2−i2i2i2i2i2002-22i−2i-220000-222i−2i−2i2i22−2−2i2i2−i2−i2−2−222000000000000−22i2−i2−i2i22−2000000000000
χ5422-22-22-2-2−2i−2i2i2i0000−i2−i2−i2−i2i2i2i2i2002-2−2i2i2-200002-2−2i2i−2i2i22−2−2−i2−i2i2i222−2−20000000000002−2−i2i2−i2i22−2000000000000
χ5522-22-22-2-2−2i−2i2i2i0000−i2−i2−i2−i2i2i2i2i200-222i−2i-2200002-2−2i2i2i−2i22−2−2−i2−i2i2i222−2−2000000000000−22i2−i2i2−i2−22000000000000
χ5622-22-22-2-2−2i−2i2i2i0000−i2−i2−i2−i2i2i2i2i200-22−2i2i2-20000-222i−2i2i−2i22−2−2i2i2−i2−i2−2−2220000000000002−2−i2i2i2−i2−22000000000000
χ572-2-2-2-22222-22-2-22-2222-2-222-2-2000000002-2000000002-22-20000000002-2002-22-202-200000000000000000000
χ582-2-2-2-22222-22-2-22-2222-2-222-2-2000000002-2000000002-22-2000000000-2200-22-220-2200000000000000000000
χ592-2-2-2-22222-22-2-22-22-2-222-2-222000000002-200000000-22-220000000002-2002-2-220-2200000000000000000000
χ602-2-2-2-22222-22-2-22-22-2-222-2-222000000002-200000000-22-22000000000-2200-222-202-200000000000000000000
χ612-2-2-2-2222-22-22-22-2222-2-222-2-200000000-2200000000-22-220000000002-200-22-2202-200000000000000000000
χ622-2-2-2-2222-22-22-22-2222-2-222-2-200000000-2200000000-22-22000000000-22002-22-20-2200000000000000000000
χ632-2-2-2-2222-22-22-22-22-2-222-2-22200000000-22000000002-22-20000000002-200-222-20-2200000000000000000000
χ642-2-2-2-2222-22-22-22-22-2-222-2-22200000000-22000000002-22-2000000000-22002-2-2202-200000000000000000000
χ65444-4-4-4-44000044-4-400000000000000000000000000000000004i−4i4i−4i00000000000000000000000000000000
χ66444-4-4-4-44000044-4-40000000000000000000000000000000000−4i4i−4i4i00000000000000000000000000000000
χ67444-4-4-4-440000-4-4444-44-44-44-400000000000000000000000000000000000000000000000000000000000000
χ68444-4-4-4-440000-4-444-44-44-44-4400000000000000000000000000000000000000000000000000000000000000
χ6944-4-44-44-4000000002i2−2i22i2−2i2−2i22i2−2i22i24-40000000000000000000000002i2−2i2−2i22i200000000000000000000000000000000
χ7044-4-44-44-4000000002i2−2i22i2−2i2−2i22i2−2i22i2-44000000000000000000000000−2i22i22i2−2i200000000000000000000000000000000
χ7144-4-44-44-400000000−2i22i2−2i22i22i2−2i22i2−2i24-4000000000000000000000000−2i22i22i2−2i200000000000000000000000000000000
χ7244-4-44-44-400000000−2i22i2−2i22i22i2−2i22i2−2i2-440000000000000000000000002i2−2i2−2i22i200000000000000000000000000000000
χ734-444-4-44-4000000002i2−2i2−2i22i2−2i22i22i2−2i200000000004-400000000002i2−2i22i2−2i2000000000000000000000000000000000000
χ744-444-4-44-4000000002i2−2i2−2i22i2−2i22i22i2−2i20000000000-440000000000−2i22i2−2i22i2000000000000000000000000000000000000
χ754-444-4-44-400000000−2i22i22i2−2i22i2−2i2−2i22i200000000004-40000000000−2i22i2−2i22i2000000000000000000000000000000000000
χ764-444-4-44-400000000−2i22i22i2−2i22i2−2i2−2i22i20000000000-4400000000002i2−2i22i2−2i2000000000000000000000000000000000000
χ774-44-444-4-44i−4i−4i4i00002i22i2−2i2−2i2−2i2−2i22i22i200000000000000000022−22−22220000000000000000000000000000000000000000
χ784-44-444-4-44i−4i−4i4i0000−2i2−2i22i22i22i22i2−2i2−2i2000000000000000000−222222−220000000000000000000000000000000000000000
χ794-44-444-4-4−4i4i4i−4i00002i22i2−2i2−2i2−2i2−2i22i22i2000000000000000000−222222−220000000000000000000000000000000000000000
χ804-44-444-4-4−4i4i4i−4i0000−2i2−2i22i22i22i22i2−2i2−2i200000000000000000022−22−22220000000000000000000000000000000000000000
χ814-4-444-4-4400004-4-444-4-444-4-4400000000000000000000000000000000000000000000000000000000000000
χ824-4-444-4-4400004-4-44-444-4-444-400000000000000000000000000000000000000000000000000000000000000
χ834-4-444-4-440000-444-40000000000000000000000000000004-4-44000000000000000000000000000000000000
χ844-4-444-4-440000-444-4000000000000000000000000000000-444-4000000000000000000000000000000000000
χ854-4-4-4-44444-44-44-44-40000000000000000-440000000000000000000000000000000000000000000000000000
χ864-4-4-4-4444-44-444-44-400000000000000004-40000000000000000000000000000000000000000000000000000

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