Finite Group Databasebeta

← Group #257051

Character table — Group #257051

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size111111112222222244444444888888888888888888888888816161616161616161616161616161616
order12222222222222222244444444444444444444444888888884444444444448888
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1111-1-111111111-1-1-1-1-1-1-1-11-1-1-11-1-1-11111-1-1-1-1
χ411111111111111111111111111-1-1111-1-1-1-1-1-1-1-1-1-1111111111-1-1-11-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1111-1-1111111111111111111-1-1-1-1-11-11-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111111111
χ7111111111111111111111111-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-1111-1-11-1-1-1-1-11111
χ8111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1111-1-11-11111-1-1-1-1
χ91111111111-1-1-1-111-1-11-1-11111111-1-1-1111111-1-1-1-11111-1-1-1-1-11-1-11-11-111-1-111-1-1
χ101111111111-1-1-1-111-1-11-1-11111111-1-1-111-1-1-1-11111-1-1-1-11111-11-1-11-11-1-1-111-1-111
χ111111111111-1-1-1-111-1-11-1-111111-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1111-1-1-1-111
χ121111111111-1-1-1-111-1-11-1-111111-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-11-1-11111-1-1
χ131111111111-1-1-1-111-1-11-1-1111-1-111-111111111-1-1-1-11111-1-1-1-11-111-1-1-1-1-1-111-1-111
χ141111111111-1-1-1-111-1-11-1-1111-1-111-11111-1-1-1-11111-1-1-1-111111-111-1-1-1-111-1-111-1-1
χ151111111111-1-1-1-111-1-11-1-1111-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1111-1-11111-1-1
χ161111111111-1-1-1-111-1-11-1-1111-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-111-1-1-111111-1-1-1-111
χ17222222222222222222-2-2-2-2-2-22200-222000000000000000000-2000-200000000000
χ18222222222222222222-2-2-2-2-2-2-2-200-2-2-20000000000000000002000200000000000
χ192222222222-2-2-2-222-2-2-222-2-2-222002-2-20000000000000000002000-200000000000
χ202222222222-2-2-2-222-2-2-222-2-2-2-2-200222000000000000000000-2000200000000000
χ2122222222-2-22222-2-2-2-2222-2-220022-200-2-200000000000000000000020-200000000
χ2222222222-2-22222-2-2-2-2222-2-2200-2-2-20022000000000000000000000-20200000000
χ2322222222-2-22222-2-2-2-2-2-2-222-20000200000000000000000000022-200-2000000000
χ2422222222-2-22222-2-2-2-2-2-2-222-200002000000000000000000000-2-22002000000000
χ2522222222-2-2-2-2-2-2-2-2222-2-2-2-220022200-2-2000000000000000000000-20200000000
χ2622222222-2-2-2-2-2-2-2-2222-2-2-2-2200-2-22002200000000000000000000020-200000000
χ2722222222-2-2-2-2-2-2-2-222-22222-20000-20000000000000000000002-2200-2000000000
χ2822222222-2-2-2-2-2-2-2-222-22222-20000-2000000000000000000000-22-2002000000000
χ29222-2-2-22-22-200002-200-2002-22002i−2i0002i−2i00002i2i−2i−2i000022-2-20000000000000000
χ30222-2-2-22-22-200002-200-2002-22002i−2i0002i−2i0000−2i−2i2i2i0000-2-2220000000000000000
χ31222-2-2-22-22-200002-200-2002-2200−2i2i000−2i2i00002i2i−2i−2i0000-2-2220000000000000000
χ32222-2-2-22-22-200002-200-2002-2200−2i2i000−2i2i0000−2i−2i2i2i000022-2-20000000000000000
χ33222-2-2-22-2-220000-2200-200-222002i−2i000−2i2i2i2i−2i−2i000022-2-200000000000000000000
χ34222-2-2-22-2-220000-2200-200-222002i−2i000−2i2i−2i−2i2i2i0000-2-22200000000000000000000
χ35222-2-2-22-2-220000-2200-200-22200−2i2i0002i−2i2i2i−2i−2i0000-2-22200000000000000000000
χ36222-2-2-22-2-220000-2200-200-22200−2i2i0002i−2i−2i−2i2i2i000022-2-200000000000000000000
χ3722-2-2-22-222222-2-2-2-22-20000002i−2i0002i−2i00000000002−22−22−22−2000000000000i2−i2i2−i2
χ3822-2-2-22-222222-2-2-2-22-20000002i−2i0002i−2i0000000000−22−22−22−22000000000000−i2i2−i2i2
χ3922-2-2-22-222222-2-2-2-22-2000000−2i2i000−2i2i00000000002−22−22−22−2000000000000−i2i2−i2i2
χ4022-2-2-22-222222-2-2-2-22-2000000−2i2i000−2i2i0000000000−22−22−22−22000000000000i2−i2i2−i2
χ4122-2-2-22-2222-2-222-2-2-220000002i−2i000−2i2i00000000002−22−2−22−22000000000000i2−i2−i2i2
χ4222-2-2-22-2222-2-222-2-2-220000002i−2i000−2i2i0000000000−22−222−22−2000000000000−i2i2i2−i2
χ4322-2-2-22-2222-2-222-2-2-22000000−2i2i0002i−2i00000000002−22−2−22−22000000000000−i2i2i2−i2
χ4422-2-2-22-2222-2-222-2-2-22000000−2i2i0002i−2i0000000000−22−222−22−2000000000000i2−i2−i2i2
χ45444-4-4-44-44-400004-400400-44-400000000000000000000000000000000000000000
χ46444-4-4-44-4-440000-44004004-4-400000000000000000000000000000000000000000
χ4744-444-4-4-44-40000-440000000000000000000000000000022−22−22220000000000000000
χ4844-444-4-4-44-40000-4400000000000000000000000000000−222222−220000000000000000
χ4944-444-4-4-4-4400004-4000000000000000000000000022−22−222200000000000000000000
χ5044-444-4-4-4-4400004-40000000000000000000000000−222222−2200000000000000000000
χ5144-4-4-44-44-4-444-4-444-4400000000000000000000000000000000000000000000000
χ5244-4-4-44-44-4-4-4-444444-400000000000000000000000000000000000000000000000
χ534-444-4-4-44004-44-400000000000000000000000000000000000000000002i−2i2i−2i0000
χ544-444-4-4-44004-44-40000000000000000000000000000000000000000000−2i2i−2i2i0000
χ554-444-4-4-4400-44-4400000000000000000000000000000000000000000002i−2i−2i2i0000
χ564-444-4-4-4400-44-440000000000000000000000000000000000000000000−2i2i2i−2i0000
χ574-4-44-444-4000000000004-40000000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ584-4-44-444-4000000000004-4000000000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ594-4-44-444-400000000000-440000000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ604-4-44-444-400000000000-44000000000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ614-4-4-44-444004-4-4400000000000000000002-2-222-2-22000000000000000000000000
χ624-4-4-44-444004-4-440000000000000000000-222-2-222-2000000000000000000000000
χ634-4-4-44-44400-444-400000000000000000002-2-22-222-2000000000000000000000000
χ644-4-4-44-44400-444-40000000000000000000-222-22-2-22000000000000000000000000
χ658-88-888-8-8000000000000000000000000000000000000000000000000000000000

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