Finite Group Databasebeta

← Group #168803

Character table — Group #168803

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size111111112222444444444488888888888888888888816161616161616161616161616163232
order12222222444444444444444444444444444888888882244448888888824
χ111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111-1-1-1-1-1-1-1-1111111111-11-1-1-11111-1-1-1-1-1-1
χ4111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-1-1-1-1111111
χ511111111111111111111111-1-1-1-111-1-1-1-11111111111-11-11-1-1-1-1-1-1-1-1-1-111
χ611111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-11-11-1-111111111-1-1
χ711111111111111111111111-1-1-1-1-1-11111-1-111111111-1-1-1-111-1-1-1-11111-1-1
χ811111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111
χ911111111-1-1-1-1-1-1-1-1111111-111-1-11111-1-1-1-11111-1-1-1-111-1-11-111-1-111-1-11-1
χ1011111111-1-1-1-1-1-1-1-1111111-111-1-11111-1-1-1-1-1-1-1-1111111-1-11-1-1-111-1-111-11
χ1111111111-1-1-1-1-1-1-1-1111111-111-1-1-1-1-1-111111111-1-1-1-11-1-11-1111-1-1-1-111-11
χ1211111111-1-1-1-1-1-1-1-1111111-111-1-1-1-1-1-11111-1-1-1-111111-1-11-11-1-11111-1-11-1
χ1311111111-1-1-1-1-1-1-1-1111111-1-1-11111-1-111-1-11111-1-1-1-1-111-1-11-1-111-1-1111-1
χ1411111111-1-1-1-1-1-1-1-1111111-1-1-11111-1-111-1-1-1-1-1-11111-111-1-1111-1-111-1-1-11
χ1511111111-1-1-1-1-1-1-1-1111111-1-1-111-1-111-1-1111111-1-1-1-1-1-1111-1-1-11111-1-1-11
χ1611111111-1-1-1-1-1-1-1-1111111-1-1-111-1-111-1-111-1-1-1-11111-1-1111-111-1-1-1-1111-1
χ1722222222222222-2-22-2-2-2-22-222220000000000000000-20-20000000000000
χ1822222222222222-2-22-2-2-2-22-2-2-2-2-200000000000000002020000000000000
χ19222222222222-2-222-2-2-222-2-2000000222200000000000000-2-20000000000
χ20222222222222-2-222-2-2-222-2-2000000-2-2-2-200000000000000220000000000
χ21222222222222-2-2-2-2-222-2-2-22000022000022000000000-20-2000000000000
χ22222222222222-2-2-2-2-222-2-2-220000-2-20000-2-2000000000202000000000000
χ2322222222-2-2-2-22222-222-2-2-2-20000220000-2-2000000000-202000000000000
χ2422222222-2-2-2-22222-222-2-2-2-20000-2-200002200000000020-2000000000000
χ2522222222-2-2-2-222-2-2-2-2-222-2200000022-2-200000000000000-220000000000
χ2622222222-2-2-2-222-2-2-2-2-222-22000000-2-222000000000000002-20000000000
χ2722222222-2-2-2-2-2-2222-2-2-2-22222-2-20000000000000000-2020000000000000
χ2822222222-2-2-2-2-2-2222-2-2-2-222-2-222000000000000000020-20000000000000
χ29222-22-2-2-22i2i−2i−2i002i−2i0002-2000000002-22i−2i0022−2−2i2i2−i2−i200000000002−2i2−i200
χ30222-22-2-2-22i2i−2i−2i002i−2i0002-2000000002-22i−2i00−2−222−i2−i2i2i20000000000−22−i2i200
χ31222-22-2-2-22i2i−2i−2i002i−2i0002-200000000-22−2i2i0022−2−2i2i2−i2−i20000000000−22−i2i200
χ32222-22-2-2-22i2i−2i−2i002i−2i0002-200000000-22−2i2i00−2−222−i2−i2i2i200000000002−2i2−i200
χ33222-22-2-2-2−2i−2i2i2i00−2i2i0002-2000000002-2−2i2i0022−2−2−i2−i2i2i200000000002−2−i2i200
χ34222-22-2-2-2−2i−2i2i2i00−2i2i0002-2000000002-2−2i2i00−2−222i2i2−i2−i20000000000−22i2−i200
χ35222-22-2-2-2−2i−2i2i2i00−2i2i0002-200000000-222i−2i0022−2−2−i2−i2i2i20000000000−22i2−i200
χ36222-22-2-2-2−2i−2i2i2i00−2i2i0002-200000000-222i−2i00−2−222i2i2−i2−i200000000002−2−i2i200
χ3722-2-2-22-222-22-22-20020000-202i−2i2i−2i000000002−22−22−22−2000000i2−i2i2−i2000000
χ3822-2-2-22-222-22-22-20020000-202i−2i2i−2i00000000−22−22−22−22000000−i2i2−i2i2000000
χ3922-2-2-22-222-22-22-20020000-20−2i2i−2i2i000000002−22−22−22−2000000−i2i2−i2i2000000
χ4022-2-2-22-222-22-22-20020000-20−2i2i−2i2i00000000−22−22−22−22000000i2−i2i2−i2000000
χ4122-2-2-22-22-22-22-220020000-202i−2i−2i2i000000002−22−2−22−22000000i2−i2−i2i2000000
χ4222-2-2-22-22-22-22-220020000-202i−2i−2i2i00000000−22−222−22−2000000−i2i2i2−i2000000
χ4322-2-2-22-22-22-22-220020000-20−2i2i2i−2i000000002−22−2−22−22000000−i2i2i2−i2000000
χ4422-2-2-22-22-22-22-220020000-20−2i2i2i−2i00000000−22−222−22−2000000i2−i2−i2i2000000
χ45444-44-4-4-44i4i−4i−4i00−4i4i000-4400000000000000000000000000000000000000
χ46444-44-4-4-4−4i−4i4i4i004i−4i000-4400000000000000000000000000000000000000
χ4744-44-4-44-44i−4i−4i4i000000000000000000000002-2-222i−2i−2i2i0000000000000000
χ4844-44-4-44-44i−4i−4i4i00000000000000000000000-222-2−2i2i2i−2i0000000000000000
χ4944-44-4-44-4−4i4i4i−4i000000000000000000000002-2-22−2i2i2i−2i0000000000000000
χ5044-44-4-44-4−4i4i4i−4i00000000000000000000000-222-22i−2i−2i2i0000000000000000
χ5144-4-4-44-444-44-4-4400-4000040000000000000000000000000000000000000
χ5244-4-4-44-44-44-444-400-4000040000000000000000000000000000000000000
χ534-444-44-4-40000000004-4000000000000004i−4i000000000000000000000000
χ544-444-44-4-40000000004-400000000000000−4i4i000000000000000000000000
χ554-444-44-4-4000000000-44000000004i−4i000000000000000000000000000000
χ564-444-44-4-4000000000-4400000000−4i4i000000000000000000000000000000
χ578-88-8-8-888000000000000000000000000000000000000000000000000000
χ588-8-888-8-88000000000000000000000000000000000000000000000000000
χ598-8-8-8888-8000000000000000000000000000000000000000000000000000

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