Finite Group Databasebeta

← Group #171984

Character table — Group #171984

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11111111222244444444444488888888888888888888161616161616161616161616161616161616
order12222222444422444444444444444444444488888888444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-1111-1-1111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-111-1-1-1-1-1-1111111111-1-1-1-11-1-1-1-11111-1-1-1-1
χ411111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-111-1-1-1-11111
χ5111111111111111111111111-1-111-1-111-1-1-1-111111111-11-111-11-111-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11-1-1-111111111
χ7111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-11-1-1-1-11-1-1-1-1-1-11111
χ8111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111-1-11111111-1-1-1-1
χ911111111-1-1-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1111111-1-1-1-1-1-111111-1-1-111-1-111-1-1
χ1011111111-1-1-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-111-1-1-1-11111-1-11-1-111-111-1-111-1-111
χ1111111111-1-1-1-1-1-11-1-1-1-11111111-1-1-1-11111-1-11111-1-1-1-1-11-1-1-11-111111-1-1-1-111
χ1211111111-1-1-1-1-1-11-1-1-1-11111111-1-1-1-11111-1-1-1-1-1-11111-11-1111-11-1-1-1-11111-1-1
χ1311111111-1-1-1-1-1-11-1-1-1-111111-1-11111-1-111-1-11111-1-1-1-11-1-111-111-1-1-1-111-1-111
χ1411111111-1-1-1-1-1-11-1-1-1-111111-1-11111-1-111-1-1-1-1-1-111111-1-1-1-1-1111111-1-111-1-1
χ1511111111-1-1-1-1-1-11-1-1-1-111111-1-1-1-11111-1-1111111-1-1-1-1111-1-1-1-1-111-1-11111-1-1
χ1611111111-1-1-1-1-1-11-1-1-1-111111-1-1-1-11111-1-111-1-1-1-1111111111-1-1-1-1-111-1-1-1-111
χ17222222222222222-2-2-2-2-2-2-2-2222002200000000000000-20000-2000000000000
χ18222222222222222-2-2-2-2-2-2-2-22-2-200-2-200000000000000200002000000000000
χ19222222222222-2-2-222-2-2-2-222-20000000022220000000000-20000-20000000000
χ20222222222222-2-2-222-2-2-2-222-200000000-2-2-2-200000000002000020000000000
χ21222222222222-2-2-2-2-22222-2-2-2002200-2-2000000000000020000-200000000000
χ22222222222222-2-2-2-2-22222-2-2-200-2-200220000000000000-20000200000000000
χ2322222222-2-2-2-222-222-2-222-2-2-2002200220000000000000-20000-200000000000
χ2422222222-2-2-2-222-222-2-222-2-2-200-2-200-2-2000000000000020000200000000000
χ2522222222-2-2-2-222-2-2-222-2-222-20000000022-2-2000000000020000-20000000000
χ2622222222-2-2-2-222-2-2-222-2-222-200000000-2-2220000000000-2000020000000000
χ2722222222-2-2-2-2-2-222222-2-2-2-222200-2-20000000000000020000-2000000000000
χ2822222222-2-2-2-2-2-222222-2-2-2-22-2-2002200000000000000-200002000000000000
χ29222-22-2-2-222-2-22-2200000000-22-2002-200000022−2−222−2−200000000002−22−20000
χ30222-22-2-2-222-2-22-2200000000-22-2002-2000000−2−222−2−2220000000000−22−220000
χ31222-22-2-2-222-2-22-2200000000-2-2200-2200000022−2−222−2−20000000000−22−220000
χ32222-22-2-2-222-2-22-2200000000-2-2200-22000000−2−222−2−22200000000002−22−20000
χ33222-22-2-2-2-2-222-22200000000-22-200-2200000022−2−2−2−22200000000002−2−220000
χ34222-22-2-2-2-2-222-22200000000-22-200-22000000−2−22222−2−20000000000−222−20000
χ35222-22-2-2-2-2-222-22200000000-2-22002-200000022−2−2−2−2220000000000−222−20000
χ36222-22-2-2-2-2-222-22200000000-2-22002-2000000−2−22222−2−200000000002−2−220000
χ372-222-2-2-222i−2i2i−2i0002i−2i00002-20000000002i−2i2-2i2−i2i2−i22−22−200000000000000i2−i22−2
χ382-222-2-2-222i−2i2i−2i0002i−2i00002-20000000002i−2i2-2−i2i2−i2i2−22−2200000000000000−i2i2−22
χ392-222-2-2-222i−2i2i−2i0002i−2i00002-2000000000−2i2i-22i2−i2i2−i22−22−200000000000000−i2i2−22
χ402-222-2-2-222i−2i2i−2i0002i−2i00002-2000000000−2i2i-22−i2i2−i2i2−22−2200000000000000i2−i22−2
χ412-222-2-2-22−2i2i−2i2i000−2i2i00002-20000000002i−2i-22i2−i2i2−i2−22−2200000000000000−i2i22−2
χ422-222-2-2-22−2i2i−2i2i000−2i2i00002-20000000002i−2i-22−i2i2−i2i22−22−200000000000000i2−i2−22
χ432-222-2-2-22−2i2i−2i2i000−2i2i00002-2000000000−2i2i2-2i2−i2i2−i2−22−2200000000000000i2−i2−22
χ442-222-2-2-22−2i2i−2i2i000−2i2i00002-2000000000−2i2i2-2−i2i2−i2i22−22−200000000000000−i2i22−2
χ45444-44-4-4-444-4-4-44-400000000400000000000000000000000000000000000000
χ46444-44-4-4-4-4-4444-4-400000000400000000000000000000000000000000000000
χ4744-44-44-4-4000000000004-40000000004-4000000000000000000000000000000
χ4844-44-44-4-4000000000004-4000000000-44000000000000000000000000000000
χ4944-44-44-4-400000000000-44000004-40000000000000000000000000000000000
χ5044-44-44-4-400000000000-4400000-440000000000000000000000000000000000
χ514-444-4-4-444i−4i4i−4i000−4i4i0000-44000000000000000000000000000000000000000
χ524-444-4-4-44−4i4i−4i4i0004i−4i0000-44000000000000000000000000000000000000000
χ534-44-4-444-44i−4i−4i4i0000000000000000000000002i−2i−2i2i2-2-22000000000000000000
χ544-44-4-444-44i−4i−4i4i000000000000000000000000−2i2i2i−2i-222-2000000000000000000
χ554-44-4-444-4−4i4i4i−4i0000000000000000000000002i−2i−2i2i-222-2000000000000000000
χ564-44-4-444-4−4i4i4i−4i000000000000000000000000−2i2i2i−2i2-2-22000000000000000000
χ574-4-4-444-440000000004-400000000000000000000000000002-20002-200000000
χ584-4-4-444-440000000004-40000000000000000000000000000-22000-2200000000
χ594-4-4-444-44000000000-4400000000000000000000000000002-2000-2200000000
χ604-4-4-444-44000000000-440000000000000000000000000000-220002-200000000
χ6188-8-8-8-888000000000000000000000000000000000000000000000000000000
χ628-8-888-88-8000000000000000000000000000000000000000000000000000000

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