Finite Group Databasebeta

← Group #256304

Character table — Group #256304

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222222224444444488888888888888888888888816161616161616161616161616161616
order12222222222222222222444444444444444444444444444444444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111-1-1-1-11111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1
χ611111111111111111111-1-1-1-11111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111
χ711111111111111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-11111
χ811111111111111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-1
χ911111111111-1-1-1-1-1-1-1-1111111111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11-11-11-11-111-1-111-1-1
χ1011111111111-1-1-1-1-1-1-1-1111111111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-11-11-11-11-1-111-1-111
χ1111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111111-11-11-11-1-1-111-1-111
χ1211111111111-1-1-1-1-1-1-1-1111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-11-11-11-1111-1-111-1-1
χ1311111111111-1-1-1-1-1-1-1-11-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-111111-1-111-1-1111-1-1-1-111
χ1411111111111-1-1-1-1-1-1-1-11-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-111-1-111-1-1-11111-1-1
χ1511111111111-1-1-1-1-1-1-1-11-1-1-1-1111111-1-1-1-111-1-1-1-111111111-1-1-1-11-1-111-1-11-1-11111-1-1
χ1611111111111-1-1-1-1-1-1-1-11-1-1-1-1111111-1-1-1-111-1-1-1-111111111-1-1-1-1-111-1-111-111-1-1-1-111
χ17222222222222222222222222-2-2-2-222-2-2-2-2-2-200000000000000000000000000000000
χ1822222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ1922222222222-2-2-2-2-2-2-2-222222-2-2-2-2-2-222-2-22200000000000000000000000000000000
χ2022222222222-2-2-2-2-2-2-2-22-2-2-2-2-2-2-2-2222222-2-200000000000000000000000000000000
χ2122222222-2-2-22222-2-2-2-2-2000022-2-2002-200000000000000000000002200-2-200000000
χ2222222222-2-2-22222-2-2-2-2-2000022-2-2002-20000000000000000000000-2-2002200000000
χ2322222222-2-2-22222-2-2-2-2-20000-2-22200-22000000000000000000002200-2-20000000000
χ2422222222-2-2-22222-2-2-2-2-20000-2-22200-2200000000000000000000-2-200220000000000
χ2522222222-2-2-2-2-2-2-22222-2000022-2-200-2200000000000000000000002-200-2200000000
χ2622222222-2-2-2-2-2-2-22222-2000022-2-200-220000000000000000000000-22002-200000000
χ2722222222-2-2-2-2-2-2-22222-20000-2-222002-2000000000000000000002-200-220000000000
χ2822222222-2-2-2-2-2-2-22222-20000-2-222002-200000000000000000000-22002-20000000000
χ29222-2-22-2-22-2-20000000022i2i−2i−2i2-22-200002i−2i0000002i2i−2i−2i000022-2-20000000000000000
χ30222-2-22-2-22-2-20000000022i2i−2i−2i2-22-200002i−2i000000−2i−2i2i2i0000-2-2220000000000000000
χ31222-2-22-2-22-2-20000000022i2i−2i−2i-22-220000−2i2i002i2i−2i−2i000022-2-200000000000000000000
χ32222-2-22-2-22-2-20000000022i2i−2i−2i-22-220000−2i2i00−2i−2i2i2i0000-2-22200000000000000000000
χ33222-2-22-2-22-2-2000000002−2i−2i2i2i2-22-20000−2i2i0000002i2i−2i−2i0000-2-2220000000000000000
χ34222-2-22-2-22-2-2000000002−2i−2i2i2i2-22-20000−2i2i000000−2i−2i2i2i000022-2-20000000000000000
χ35222-2-22-2-22-2-2000000002−2i−2i2i2i-22-2200002i−2i002i2i−2i−2i0000-2-22200000000000000000000
χ36222-2-22-2-22-2-2000000002−2i−2i2i2i-22-2200002i−2i00−2i−2i2i2i000022-2-200000000000000000000
χ3722-22-2-22-2-22-222-2-222-2-222-22-200002-2000000000000000000000000000000i2−i2i2−i2i2−i2i2−i2
χ3822-22-2-22-2-22-222-2-222-2-222-22-200002-2000000000000000000000000000000−i2i2−i2i2−i2i2−i2i2
χ3922-22-2-22-2-22-222-2-222-2-22-22-220000-22000000000000000000000000000000i2−i2i2−i2−i2i2−i2i2
χ4022-22-2-22-2-22-222-2-222-2-22-22-220000-22000000000000000000000000000000−i2i2−i2i2i2−i2i2−i2
χ4122-22-2-22-2-22-2-2-222-2-22222-22-20000-22000000000000000000000000000000i2−i2−i2i2i2−i2−i2i2
χ4222-22-2-22-2-22-2-2-222-2-22222-22-20000-22000000000000000000000000000000−i2i2i2−i2−i2i2i2−i2
χ4322-22-2-22-2-22-2-2-222-2-2222-22-2200002-2000000000000000000000000000000i2−i2−i2i2−i2i2i2−i2
χ4422-22-2-22-2-22-2-2-222-2-2222-22-2200002-2000000000000000000000000000000−i2i2i2−i2i2−i2−i2i2
χ45444-4-44-4-4-44400000000-400004-4-440000000000000000000000000000000000000000
χ46444-4-44-4-4-44400000000-40000-444-40000000000000000000000000000000000000000
χ4744-44-4-44-44-4444-4-4-4-444-4000000000000000000000000000000000000000000000000
χ4844-44-4-44-44-44-4-44444-4-4-4000000000000000000000000000000000000000000000000
χ4944-4-44-4-4444-400000000-4000000000000004-400000000000000000000000000000000
χ5044-4-44-4-4444-400000000-400000000000000-4400000000000000000000000000000000
χ5144-4-44-4-44-4-440000000044i−4i−4i4i00000000000000000000000000000000000000000000
χ5244-4-44-4-44-4-44000000004−4i4i4i−4i00000000000000000000000000000000000000000000
χ534-444-4-4-4400000004-44-400000000000000000000000002i−2i2i−2i2i−2i2i−2i0000000000000000
χ544-444-4-4-4400000004-44-40000000000000000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000
χ554-444-4-4-440000000-44-4400000000000000000000000002i−2i2i−2i−2i2i−2i2i0000000000000000
χ564-444-4-4-440000000-44-440000000000000000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000
χ574-44-44-44-40004-44-4000000000000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ584-44-44-44-40004-44-400000000000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ594-44-44-44-4000-44-44000000000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ604-44-44-44-4000-44-4400000000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ614-4-4444-4-400000004-4-44000000000000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ624-4-4444-4-400000004-4-4400000000000000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ634-4-4444-4-40000000-444-4000000000000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ644-4-4444-4-40000000-444-400000000000000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ654-4-4-4-44440004-4-440000000000000000000002-2-222-2-22000000000000000000000000
χ664-4-4-4-44440004-4-44000000000000000000000-222-2-222-2000000000000000000000000
χ674-4-4-4-4444000-444-40000000000000000000002-2-22-222-2000000000000000000000000
χ684-4-4-4-4444000-444-4000000000000000000000-222-22-2-22000000000000000000000000

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