Finite Group Databasebeta

← Group #7125723

Character table — Group #7125723

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83
size111111112222222244444444444444444444444444444444888888888888888888888888816161616161616161616
order12222222222244444444444444444444888888888888888824444444444444444888888884444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-1-1-1-1-1-11-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-11-11-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-11-1-111111-1-1-1-1-1-1-1-11-1-11-11-1111
χ511111111111111111111-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1111111-1-1-111-1111111-1-1-1-1-1-11-1-1-1-111-1-1-1
χ611111111111111111111-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-11111-1-1111
χ711111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1111111-1-1-111-1-1-1-1-1-1-1111111-1-1-11-1-11111
χ811111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-1-1-111-1-1-1-11111-1-1111111111-111-1-1-1-1
χ91111111111111111-1-11111-1-111-1-1-1-1-1-11111-1-1-1-1111111111-1-1111111-1-1-111111-1-1-1-111-1-1-1-1-111-1-11-1-1
χ101111111111111111-1-11111-1-111-1-1-1-1-1-11111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-111-1-1111-1-111-111
χ111111111111111111-1-11111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-1-1111111-1-1-11-1-1-1-11111-1-1111-1-1-111-1-111
χ121111111111111111-1-11111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-111111111111-1-111-1111-1-111-1-1
χ131111111111111111-1-111-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-11111-1-11-1-1-11111-1-111-1-111-111-1-1-1-1-111
χ141111111111111111-1-111-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-111-1-1111-1-111111-1-1
χ151111111111111111-1-111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-11111-1-11-1-1-1-1-1-1-111-1-111-1-11111-11-11-1-1
χ161111111111111111-1-111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-111111-1111111-1-111-1-1-1-1-1-11-11-111
χ1711111111-1-1-1-1111111-1-111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111-111-1-111111-111-1-1-1-11111-1-1-11-11-11-1-11-1
χ1811111111-1-1-1-1111111-1-111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111-1-1-111-1-11-1-1-1-1-111-1-11111-1-11-11-11-111-11
χ1911111111-1-1-1-1111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111111-111-1-111111-1-1-11111-1-1-1-11111-1-1-1-1-11-11
χ2011111111-1-1-1-1111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-1-111-1-11-1-1-111-1-111-1-1-1-111-1-111111-11-1
χ2111111111-1-1-1-1111111-1-1-1-1-1-11111-1-11111111111-1-1-1-11111-11-111-1-1-1-1-111111-1-1-1-1-1-1-1-111-1-11-111-11-11
χ2211111111-1-1-1-1111111-1-1-1-1-1-11111-1-11111111111-1-1-1-11111-11-1-1-11111-1-1-11-1-111-1-1-1-1-1-11111-11-1-11-11-1
χ2311111111-1-1-1-1111111-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-11-111-1-1-1-1-1111-1-111111111-1-11-1111-1-1-11-1
χ2411111111-1-1-1-1111111-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-11-1-1-11111-1-1-1111-1-1111111-1-1-11-1-1-1111-11
χ2511111111-1-1-1-11111-1-1-1-11111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1111-1-111-1-1-1-111-1-111-1-111111-111-1-11-1-11
χ2611111111-1-1-1-11111-1-1-1-11111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-1-111-1-1-11111-1-11111-11-1-111-111-1
χ2711111111-1-1-1-11111-1-1-1-11111-1-111-1-111-1-1-1-11111111111111-1111-1-111-1-1-1-1-1-111-1-111-1-1-1-1-1-11-1-11111-1
χ2811111111-1-1-1-11111-1-1-1-11111-1-111-1-111-1-1-1-11111111111111-11-1-111-1-1-111-111-1-1-1-111-1-1-1-111-111-1-1-1-11
χ2911111111-1-1-1-11111-1-1-1-1-1-11111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1111-1-1-1-11-1-1111-1-11111-1-1-1-111-1-11-1111-1
χ3011111111-1-1-1-11111-1-1-1-1-1-11111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-11-1-111111111-1-1111111-1-1-1-1-1-111-11-1-1-11
χ3111111111-1-1-1-11111-1-1-1-1-1-11111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1111-1-1-1-11-1-11-1-111-1-1-1-11111-11-11111-1-11
χ3211111111-1-1-1-11111-1-1-1-1-1-11111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-11-1-11111111111-1-1-1-1-1-111111-11-1-1-1-111-1
χ33222222222222-2-2-2-222-2-2222222-2-222220000000000000000-2-2-2000000-200-20000000000000000000000
χ34222222222222-2-2-2-222-2-2-2-222-2-222-2-2-2-200000000000000002-2-200000020020000000000000000000000
χ35222222222222-2-2-2-2-2-2-2-222-2-22222-2-2-2-20000000000000000-222000000200-20000000000000000000000
χ36222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000222000000-20020000000000000000000000
χ3722222222-2-2-2-2-2-2-2-2222222-2-2-2-22222-2-20000000000000000-2-22000000-20020000000000000000000000
χ3822222222-2-2-2-2-2-2-2-22222-2-2-2-222-2-2-2-22200000000000000002-22000000200-20000000000000000000000
χ3922222222-2-2-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2220000000000000000-22-200000020020000000000000000000000
χ4022222222-2-2-2-2-2-2-2-2-2-222-2-222222222-2-2000000000000000022-2000000-200-20000000000000000000000
χ412-222-2-2-2222-2-200002i−2i002i−2i2i−2i2i−2i002-22-222−2−2i2i2−i2−i222−2−2i2i2−i2−i200000000000000000i2−i22−2i2−i22−20000000000
χ422-222-2-2-2222-2-200002i−2i002i−2i2i−2i2i−2i002-22-2−2−222−i2−i2i2i2−2−222−i2−i2i2i200000000000000000−i2i2−22−i2i2−220000000000
χ432-222-2-2-2222-2-200002i−2i00−2i2i2i−2i−2i2i00-22-2222−2−2i2i2−i2−i222−2−2−i2−i2i2i200000000000000000i2−i2−22−i2i2−220000000000
χ442-222-2-2-2222-2-200002i−2i00−2i2i2i−2i−2i2i00-22-22−2−222−i2−i2i2i2−2−222i2i2−i2−i200000000000000000−i2i22−2i2−i22−20000000000
χ452-222-2-2-2222-2-20000−2i2i002i−2i−2i2i2i−2i00-22-2222−2−2−i2−i2i2i222−2−2i2i2−i2−i200000000000000000−i2i2−22i2−i2−220000000000
χ462-222-2-2-2222-2-20000−2i2i002i−2i−2i2i2i−2i00-22-22−2−222i2i2−i2−i2−2−222−i2−i2i2i200000000000000000i2−i22−2−i2i22−20000000000
χ472-222-2-2-2222-2-20000−2i2i00−2i2i−2i2i−2i2i002-22-222−2−2−i2−i2i2i222−2−2−i2−i2i2i200000000000000000−i2i22−2−i2i22−20000000000
χ482-222-2-2-2222-2-20000−2i2i00−2i2i−2i2i−2i2i002-22-2−2−222i2i2−i2−i2−2−222i2i2−i2−i200000000000000000i2−i2−22i2−i2−220000000000
χ492-222-2-2-22-2-22200002i−2i002i−2i−2i2i−2i2i002-2-2222−2−2i2i2−i2−i2−2−222−i2−i2i2i200000000000000000−i2i22−2i2−i2−220000000000
χ502-222-2-2-22-2-22200002i−2i002i−2i−2i2i−2i2i002-2-22−2−222−i2−i2i2i222−2−2i2i2−i2−i200000000000000000i2−i2−22−i2i22−20000000000
χ512-222-2-2-22-2-22200002i−2i00−2i2i−2i2i2i−2i00-222-222−2−2i2i2−i2−i2−2−222i2i2−i2−i200000000000000000−i2i2−22−i2i22−20000000000
χ522-222-2-2-22-2-22200002i−2i00−2i2i−2i2i2i−2i00-222-2−2−222−i2−i2i2i222−2−2−i2−i2i2i200000000000000000i2−i22−2i2−i2−220000000000
χ532-222-2-2-22-2-2220000−2i2i002i−2i2i−2i−2i2i00-222-222−2−2−i2−i2i2i2−2−222−i2−i2i2i200000000000000000i2−i2−22i2−i22−20000000000
χ542-222-2-2-22-2-2220000−2i2i002i−2i2i−2i−2i2i00-222-2−2−222i2i2−i2−i222−2−2i2i2−i2−i200000000000000000−i2i22−2−i2i2−220000000000
χ552-222-2-2-22-2-2220000−2i2i00−2i2i2i−2i2i−2i002-2-2222−2−2−i2−i2i2i2−2−222i2i2−i2−i200000000000000000i2−i22−2−i2i2−220000000000
χ562-222-2-2-22-2-2220000−2i2i00−2i2i2i−2i2i−2i002-2-22−2−222i2i2−i2−i222−2−2−i2−i2i2i200000000000000000−i2i2−22i2−i22−20000000000
χ572-2-2-22-2222-22-222-2-2002-20000000000002i−2i2i−2i00002i−2i2i−2i00000002i−2i2i−2i0000002-22-2000000000000000000
χ582-2-2-22-2222-22-222-2-2002-20000000000002i−2i2i−2i00002i−2i2i−2i0000000−2i2i−2i2i000000-22-22000000000000000000
χ592-2-2-22-2222-22-222-2-2002-2000000000000−2i2i−2i2i0000−2i2i−2i2i00000002i−2i2i−2i000000-22-22000000000000000000
χ602-2-2-22-2222-22-222-2-2002-2000000000000−2i2i−2i2i0000−2i2i−2i2i0000000−2i2i−2i2i0000002-22-2000000000000000000
χ612-2-2-22-222-22-2222-2-200-220000000000002i−2i2i−2i0000−2i2i−2i2i00000002i−2i−2i2i0000002-2-22000000000000000000
χ622-2-2-22-222-22-2222-2-200-220000000000002i−2i2i−2i0000−2i2i−2i2i0000000−2i2i2i−2i000000-222-2000000000000000000
χ632-2-2-22-222-22-2222-2-200-22000000000000−2i2i−2i2i00002i−2i2i−2i00000002i−2i−2i2i000000-222-2000000000000000000
χ642-2-2-22-222-22-2222-2-200-22000000000000−2i2i−2i2i00002i−2i2i−2i0000000−2i2i2i−2i0000002-2-22000000000000000000
χ65444-44-4-4-400004-4-4400000000000000000000000000004-44-400000000000000000000000000000000000
χ66444-44-4-4-400004-4-440000000000000000000000000000-44-4400000000000000000000000000000000000
χ67444-44-4-4-40000-444-4000000000000000000004-44-40000000000000000000000000000000000000000000
χ68444-44-4-4-40000-444-400000000000000000000-44-440000000000000000000000000000000000000000000
χ6944-4-4-44-444-4-44000000000000000000002i2−2i2−2i22i200002i2−2i2−2i22i2000000000000000000000000000000000000000
χ7044-4-4-44-444-4-4400000000000000000000−2i22i22i2−2i20000−2i22i22i2−2i2000000000000000000000000000000000000000
χ7144-4-4-44-44-444-4000000000000000000002i2−2i2−2i22i20000−2i22i22i2−2i2000000000000000000000000000000000000000
χ7244-4-4-44-44-444-400000000000000000000−2i22i22i2−2i200002i2−2i2−2i22i2000000000000000000000000000000000000000
χ734-44-4-444-40000000000000000004-4000000002i2−2i2−2i22i200002i2−2i2−2i22i200000000000000000000000000000000000
χ744-44-4-444-40000000000000000004-400000000−2i22i22i2−2i20000−2i22i22i2−2i200000000000000000000000000000000000
χ754-44-4-444-4000000000000000000-44000000002i2−2i2−2i22i20000−2i22i22i2−2i200000000000000000000000000000000000
χ764-44-4-444-4000000000000000000-4400000000−2i22i22i2−2i200002i2−2i2−2i22i200000000000000000000000000000000000
χ774-4-4444-4-400004-44-40000000000000000000000000000000000000004-400000000000000000000000000
χ784-4-4444-4-400004-44-4000000000000000000000000000000000000000-4400000000000000000000000000
χ794-4-4444-4-40000-44-440000000000000000000000000000000000000000004i−4i00000000000000000000000
χ804-4-4444-4-40000-44-44000000000000000000000000000000000000000000−4i4i00000000000000000000000
χ814-4-4-44-4444-44-4-4-44400-44000000000000000000000000000000000000000000000000000000000000000
χ824-4-4-44-444-44-44-4-444004-4000000000000000000000000000000000000000000000000000000000000000
χ8388-88-8-88-8000000000000000000000000000000000000000000000000000000000000000000000000000

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