Finite Group Databasebeta

← Group #291024

Character table — Group #291024

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222222244444488888888888888888888888888888888888881616161616163232
order12222222444444444444224444444444444444488888888888888888888888844444444
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ3111111111111111111111111111111-1-1-1-1-1-11-1-111111111-1-1-1-1-1-1-1-1111111111-1-1-11-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1-11-111
χ511111111111111111111111111-1-1-1-11111-1-11-1-11111111111111111-1-1-1-1-1-1-1-1-111-1-1-1-1-1
χ611111111111111111111111111-1-1-1-11111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-111-1-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111
χ811111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-11111111111111111-1-1-11-11-1-1
χ911111111111-1-1-1-111111-1-1-1-11111-1-11111-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111-1
χ1011111111111-1-1-1-111111-1-1-1-11111-1-11111-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-11
χ1111111111111-1-1-1-111111-1-1-1-11111-1-1-1-1-1-111-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-11111-1-11
χ1211111111111-1-1-1-111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-11111-11-1
χ1311111111111-1-1-1-111111-1-1-1-111-1-111111111-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111-1-11-1-1-11
χ1411111111111-1-1-1-111111-1-1-1-111-1-111111111-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11-1-11-1-11-1
χ1511111111111-1-1-1-111111-1-1-1-111-1-111-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111111-1-111-1
χ1611111111111-1-1-1-111111-1-1-1-111-1-111-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-1111-1-11-11
χ17222222222222222-2-2-2-2222-2-2-2-22222000000-200000000000000000000000000-2000-2000
χ18222222222222222-2-2-2-2222-2-2-2-2-2-2-2-2000000-20000000000000000000000000020002000
χ1922222222222-2-2-2-2-2-2-2-22-2-222-2-222-2-20000002000000000000000000000000002000-2000
χ2022222222222-2-2-2-2-2-2-2-22-2-222-2-2-2-222000000200000000000000000000000000-20002000
χ2122222222-2-2-222222222-2-2-222-2-20000000022-222000000000000000000000000000-20-200
χ2222222222-2-2-222222222-2-2-222-2-200000000-2-2-2-2-200000000000000000000000000020200
χ2322222222-2-2-22222-2-2-2-2-2-2-2-2-222000022-2-20020000000000000000000000000002-200000
χ2422222222-2-2-22222-2-2-2-2-2-2-2-2-2220000-2-222002000000000000000000000000000-2200000
χ2522222222-2-2-2-2-2-2-22222-222-2-2-2-200000000222-2-2000000000000000000000000000-20200
χ2622222222-2-2-2-2-2-2-22222-222-2-2-2-200000000-2-222200000000000000000000000000020-200
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2222222000022-2-200-2000000000000000000000000000-2200000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-22222220000-2-22200-20000000000000000000000000002-200000
χ29222-22-2-2-22-2-222-2-2000022-200002i−2i2i−2i00000000022−2−222−2−200000000i2i2−i2−i2i2i2−i2−i200000000
χ30222-22-2-2-22-2-222-2-2000022-200002i−2i2i−2i000000000−2−222−2−22200000000−i2−i2i2i2−i2−i2i2i200000000
χ31222-22-2-2-22-2-222-2-2000022-20000−2i2i−2i2i00000000022−2−222−2−200000000−i2−i2i2i2−i2−i2i2i200000000
χ32222-22-2-2-22-2-222-2-2000022-20000−2i2i−2i2i000000000−2−222−2−22200000000i2i2−i2−i2i2i2−i2−i200000000
χ33222-22-2-2-22-2-2-2-22200002-2200002i−2i−2i2i00000000022−2−2−2−22200000000i2i2−i2−i2−i2−i2i2i200000000
χ34222-22-2-2-22-2-2-2-22200002-2200002i−2i−2i2i000000000−2−22222−2−200000000−i2−i2i2i2i2i2−i2−i200000000
χ35222-22-2-2-22-2-2-2-22200002-220000−2i2i2i−2i00000000022−2−2−2−22200000000−i2−i2i2i2i2i2−i2−i200000000
χ36222-22-2-2-22-2-2-2-22200002-220000−2i2i2i−2i000000000−2−22222−2−200000000i2i2−i2−i2−i2−i2i2i200000000
χ3722-2-2-22-2222-20000-2-222-200002-200002i−2i2i−2i0000000002-22-200002i2i−2i−2i0000000000000000
χ3822-2-2-22-2222-20000-2-222-200002-200002i−2i2i−2i000000000-22-220000−2i−2i2i2i0000000000000000
χ3922-2-2-22-2222-20000-2-222-200002-20000−2i2i−2i2i0000000002-22-20000−2i−2i2i2i0000000000000000
χ4022-2-2-22-2222-20000-2-222-200002-20000−2i2i−2i2i000000000-22-2200002i2i−2i−2i0000000000000000
χ4122-2-2-22-22-2-22000022-2-2200002-200002i−2i−2i2i000002i−2i2i−2i000022-2-200000000000000000000
χ4222-2-2-22-22-2-22000022-2-2200002-200002i−2i−2i2i00000−2i2i−2i2i0000-2-22200000000000000000000
χ4322-2-2-22-22-2-22000022-2-2200002-20000−2i2i2i−2i000002i−2i2i−2i0000-2-22200000000000000000000
χ4422-2-2-22-22-2-22000022-2-2200002-20000−2i2i2i−2i00000−2i2i−2i2i000022-2-200000000000000000000
χ452-2-222-2-220002i−2i2i−2i2-22-20002i−2i00000000002i−2i02-200000000i2−i2i2−i22−22−2i2−i2i2−i22−22−200000000
χ462-2-222-2-220002i−2i2i−2i2-22-20002i−2i00000000002i−2i02-200000000−i2i2−i2i2−22−22−i2i2−i2i2−22−2200000000
χ472-2-222-2-220002i−2i2i−2i2-22-20002i−2i0000000000−2i2i0-2200000000i2−i2i2−i22−22−2−i2i2−i2i2−22−2200000000
χ482-2-222-2-220002i−2i2i−2i2-22-20002i−2i0000000000−2i2i0-2200000000−i2i2−i2i2−22−22i2−i2i2−i22−22−200000000
χ492-2-222-2-22000−2i2i−2i2i2-22-2000−2i2i00000000002i−2i0-2200000000i2−i2i2−i2−22−22−i2i2−i2i22−22−200000000
χ502-2-222-2-22000−2i2i−2i2i2-22-2000−2i2i00000000002i−2i0-2200000000−i2i2−i2i22−22−2i2−i2i2−i2−22−2200000000
χ512-2-222-2-22000−2i2i−2i2i2-22-2000−2i2i0000000000−2i2i02-200000000i2−i2i2−i2−22−22i2−i2i2−i2−22−2200000000
χ522-2-222-2-22000−2i2i−2i2i2-22-2000−2i2i0000000000−2i2i02-200000000−i2i2−i2i22−22−2−i2i2−i2i22−22−200000000
χ53444-44-4-4-4-44444-4-40000-4-440000000000000000000000000000000000000000000000000
χ54444-44-4-4-4-444-4-4440000-44-40000000000000000000000000000000000000000000000000
χ5544-44-4-44-44-4400000000-40000000000000000000000022−22−2222000000000000000000000000
χ5644-44-4-44-44-4400000000-400000000000000000000000−222222−22000000000000000000000000
χ5744-44-4-44-4-44-400000000400000000000000000002i2−2i2−2i22i20000000000000000000000000000
χ5844-44-4-44-4-44-40000000040000000000000000000−2i22i22i2−2i20000000000000000000000000000
χ5944-4-4-44-4444-4000044-4-4-40000-44000000000000000000000000000000000000000000000
χ6044-4-4-44-44-4-440000-4-44440000-44000000000000000000000000000000000000000000000
χ614-44-4-4-44400000004-4-4400000000000000000000000000002i2−2i2−2i22i200000000000000000000
χ624-44-4-4-44400000004-4-440000000000000000000000000000−2i22i22i2−2i200000000000000000000
χ634-44-4-4-4440000000-444-4000000000000000000000000000000002i2−2i2−2i22i20000000000000000
χ644-44-4-4-4440000000-444-400000000000000000000000000000000−2i22i22i2−2i20000000000000000
χ654-4-444-4-440004i−4i4i−4i-44-44000−4i4i00000000000000000000000000000000000000000000000
χ664-4-444-4-44000−4i4i−4i4i-44-440004i−4i00000000000000000000000000000000000000000000000
χ674-4-4-4444-40004i−4i−4i4i00000000000000000000000000000000000000002-2-22−2i2i2i−2i00000000
χ684-4-4-4444-40004i−4i−4i4i0000000000000000000000000000000000000000-222-22i−2i−2i2i00000000
χ694-4-4-4444-4000−4i4i4i−4i00000000000000000000000000000000000000002-2-222i−2i−2i2i00000000
χ704-4-4-4444-4000−4i4i4i−4i0000000000000000000000000000000000000000-222-2−2i2i2i−2i00000000
χ718-888-88-8-8000000000000000000000000000000000000000000000000000000000000000

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