Finite Group Databasebeta

← Group #168694

Character table — Group #168694

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size111111112222444444444488888888888888888888816161616161616161616161616163232
order12222222444422444444444444444444444888888882244448888888844
χ111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-11-1-1-1-1-1-11111-1-1
χ4111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-11111-1-1-1-111
χ51111111111111111111111-1-1-1-1111-1-111-1-111111111-11-1-11-11111-1-1-1-1-1-1
χ61111111111111111111111-1-1-1-1111-1-111-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-1-1111111
χ71111111111111111111111-1-1-1-11-1-111-1-11111111111-1-11-1-11-1-1-1-1-1-1-1-111
χ81111111111111111111111-1-1-1-11-1-111-1-111-1-1-1-1-1-1-1-1-1-11-1-1111111111-1-1
χ911111111-1-1-1-1-1-111-1-1111111-1-1-11111-1-1-1-11111-1-1-1-11-1-1-11111-1-111-1-11-1
χ1011111111-1-1-1-1-1-111-1-1111111-1-1-11111-1-1-1-1-1-1-1-111111-1-1-111-1-111-1-111-11
χ1111111111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-111111111-1-1-1-1111-1-1-1-1-11111-1-1-11
χ1211111111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-11111-1-1-1-11111111-1-1-111-1-1-1-1111-1
χ1311111111-1-1-1-1-1-111-1-11111-1-111-111-1-1-1-1111111-1-1-1-1-1-1111-111-1-1-1-111-11
χ1411111111-1-1-1-1-1-111-1-11111-1-111-111-1-1-1-111-1-1-1-11111-1-1111-1-1-11111-1-11-1
χ1511111111-1-1-1-1-1-111-1-11111-1-111-1-1-11111-1-11111-1-1-1-1-11-11-11-1-111-1-1111-1
χ1611111111-1-1-1-1-1-111-1-11111-1-111-1-1-11111-1-1-1-1-1-11111-11-11-1111-1-111-1-1-11
χ17222222222222222-2-2-2-2-22-20000-222002200000000000-200-200000000000
χ18222222222222222-2-2-2-2-22-20000-2-2-200-2-200000000000200200000000000
χ19222222222222-2-2-22-2-2-2-2-2200002002200220000000000-200-20000000000
χ20222222222222-2-2-22-2-2-2-2-220000200-2-200-2-2000000000020020000000000
χ21222222222222-2-2-2-22222-2-22222-20000000000000000-200-2000000000000
χ22222222222222-2-2-2-22222-2-2-2-2-2-2-200000000000000002002000000000000
χ2322222222-2-2-2-222-2222-2-2-220000-2002200-2-20000000000200-20000000000
χ2422222222-2-2-2-222-2222-2-2-220000-200-2-200220000000000-20020000000000
χ2522222222-2-2-2-222-2-2-2-222-2-222-2-220000000000000000-2002000000000000
χ2622222222-2-2-2-222-2-2-2-222-2-2-2-22220000000000000000200-2000000000000
χ2722222222-2-2-2-2-2-22-222-2-22-2000022200-2-200000000000200-200000000000
χ2822222222-2-2-2-2-2-22-222-2-22-200002-2-2002200000000000-200200000000000
χ29222-2-22-2-222-2-22-2-20000020000002i−2i002i−2i0022−2−222−2−2000000i2−i2i2−i2000000
χ30222-2-22-2-222-2-22-2-20000020000002i−2i002i−2i00−2−222−2−222000000−i2i2−i2i2000000
χ31222-2-22-2-222-2-22-2-2000002000000−2i2i00−2i2i0022−2−222−2−2000000−i2i2−i2i2000000
χ32222-2-22-2-222-2-22-2-2000002000000−2i2i00−2i2i00−2−222−2−222000000i2−i2i2−i2000000
χ33222-2-22-2-2-2-222-22-20000020000002i−2i00−2i2i0022−2−2−2−222000000i2−i2−i2i2000000
χ34222-2-22-2-2-2-222-22-20000020000002i−2i00−2i2i00−2−22222−2−2000000−i2i2i2−i2000000
χ35222-2-22-2-2-2-222-22-2000002000000−2i2i002i−2i0022−2−2−2−222000000−i2i2i2−i2000000
χ36222-2-22-2-2-2-222-22-2000002000000−2i2i002i−2i00−2−22222−2−2000000i2−i2−i2i2000000
χ3722-22-2-22-22i−2i2i−2i00002i−2i2-2002i−2i2-2000000000i2−i2i2−i22−22−200000000002−2i2−i200
χ3822-22-2-22-22i−2i2i−2i00002i−2i2-2002i−2i2-2000000000−i2i2−i2i2−22−220000000000−22−i2i200
χ3922-22-2-22-22i−2i2i−2i00002i−2i2-200−2i2i-22000000000i2−i2i2−i22−22−20000000000−22−i2i200
χ4022-22-2-22-22i−2i2i−2i00002i−2i2-200−2i2i-22000000000−i2i2−i2i2−22−2200000000002−2i2−i200
χ4122-22-2-22-2−2i2i−2i2i0000−2i2i2-2002i−2i-22000000000i2−i2i2−i2−22−2200000000002−2−i2i200
χ4222-22-2-22-2−2i2i−2i2i0000−2i2i2-2002i−2i-22000000000−i2i2−i2i22−22−20000000000−22i2−i200
χ4322-22-2-22-2−2i2i−2i2i0000−2i2i2-200−2i2i2-2000000000i2−i2i2−i2−22−220000000000−22i2−i200
χ4422-22-2-22-2−2i2i−2i2i0000−2i2i2-200−2i2i2-2000000000−i2i2−i2i22−22−200000000002−2−i2i200
χ45444-4-44-4-444-4-4-44400000-400000000000000000000000000000000000000
χ46444-4-44-4-4-4-4444-4400000-400000000000000000000000000000000000000
χ4744-44-4-44-44i−4i4i−4i0000−4i4i-44000000000000000000000000000000000000000
χ4844-44-4-44-4−4i4i−4i4i00004i−4i-44000000000000000000000000000000000000000
χ4944-4-44-4-444i−4i−4i4i000000000000000000000002i−2i−2i2i2-2-220000000000000000
χ5044-4-44-4-444i−4i−4i4i00000000000000000000000−2i2i2i−2i-222-20000000000000000
χ5144-4-44-4-44−4i4i4i−4i000000000000000000000002i−2i−2i2i-222-20000000000000000
χ5244-4-44-4-44−4i4i4i−4i00000000000000000000000−2i2i2i−2i2-2-220000000000000000
χ534-44-4-4-4440000000400000-400000004i−4i0000000000000000000000000000
χ544-44-4-4-4440000000400000-40000000−4i4i0000000000000000000000000000
χ554-44-4-4-4440000000-4000004000000000004-4000000000000000000000000
χ564-44-4-4-4440000000-400000400000000000-44000000000000000000000000
χ578-8888-8-8-8000000000000000000000000000000000000000000000000000
χ588-8-88-88-88000000000000000000000000000000000000000000000000000
χ598-8-8-8888-8000000000000000000000000000000000000000000000000000

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