Finite Group Databasebeta

← Group #171964

Character table — Group #171964

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11111111222244444444444488888888888888888888161616161616161616161616161616161616
order12222222444444444444444444444444444488888888444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-111-1-1-1-11111-1-1-1-1
χ411111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111
χ5111111111111111111111111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-11111
χ6111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1
χ7111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-111-1-1-1-1-1-1-1-1
χ8111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111
χ911111111-1-1-1-11-1-1-1-11-1-111111111-1-1-1-111-1-11111-1-1-1-11-1111-11-1-1-111-1-111-1-1
χ1011111111-1-1-1-11-1-1-1-11-1-111111111-1-1-1-111-1-1-1-1-1-111111-1-1-11-11-111-1-111-1-111
χ1111111111-1-1-1-11-1-1-1-11-1-1111111-1-111-1-1-1-1111111-1-1-1-1-11-1-11-1-111111-1-1-1-111
χ1211111111-1-1-1-11-1-1-1-11-1-1111111-1-111-1-1-1-111-1-1-1-11111-11111-1-11-1-1-1-11111-1-1
χ1311111111-1-1-1-11-1-1-1-11-1-11111-1-111-1-111-1-1111111-1-1-1-1-11-1-1-111-111-1-11111-1-1
χ1411111111-1-1-1-11-1-1-1-11-1-11111-1-111-1-111-1-111-1-1-1-11111-1111-111-1-1-111-1-1-1-111
χ1511111111-1-1-1-11-1-1-1-11-1-11111-1-1-1-1111111-1-11111-1-1-1-11-111-11-11-1-1-1-111-1-111
χ1611111111-1-1-1-11-1-1-1-11-1-11111-1-1-1-1111111-1-1-1-1-1-111111-1-1-1-11-111111-1-111-1-1
χ172222222222222-2-2-2-2-222-2-22-2220000220000000000000000-2-2000000000000
χ182222222222222-2-2-2-2-222-2-22-2-2-20000-2-2000000000000000022000000000000
χ19222222222222-222-2-22-2-2-2-2-220000000022-2-200000000-220000000000000000
χ20222222222222-222-2-22-2-2-2-2-2200000000-2-222000000002-20000000000000000
χ21222222222222-2-2-222-2-2-222-2-200222200000000000000000000-2-20000000000
χ22222222222222-2-2-222-2-2-222-2-200-2-2-2-200000000000000000000220000000000
χ2322222222-2-2-2-222222-2-2-2-2-22-2220000-2-20000000000000000-22000000000000
χ2422222222-2-2-2-222222-2-2-2-2-22-2-2-200002200000000000000002-2000000000000
χ2522222222-2-2-2-2-222-2-2-22222-2-20022-2-200000000000000000000-220000000000
χ2622222222-2-2-2-2-222-2-2-22222-2-200-2-222000000000000000000002-20000000000
χ2722222222-2-2-2-2-2-2-222222-2-2-2200000000222200000000-2-20000000000000000
χ2822222222-2-2-2-2-2-2-222222-2-2-2200000000-2-2-2-200000000220000000000000000
χ29222-2-22-2-222-2-2-2000002-200202-200002-20000i2i2−i2−i2i2i2−i2−i20000000000i2−i2i2−i20000
χ30222-2-22-2-222-2-2-2000002-200202-200002-20000−i2−i2i2i2−i2−i2i2i20000000000−i2i2−i2i20000
χ31222-2-22-2-222-2-2-2000002-20020-220000-220000i2i2−i2−i2i2i2−i2−i20000000000−i2i2−i2i20000
χ32222-2-22-2-222-2-2-2000002-20020-220000-220000−i2−i2i2i2−i2−i2i2i20000000000i2−i2i2−i20000
χ33222-2-22-2-2-2-222-200000-2200202-20000-220000i2i2−i2−i2−i2−i2i2i20000000000i2−i2−i2i20000
χ34222-2-22-2-2-2-222-200000-2200202-20000-220000−i2−i2i2i2i2i2−i2−i20000000000−i2i2i2−i20000
χ35222-2-22-2-2-2-222-200000-220020-2200002-20000i2i2−i2−i2−i2−i2i2i20000000000−i2i2i2−i20000
χ36222-2-22-2-2-2-222-200000-220020-2200002-20000−i2−i2i2i2i2i2−i2−i20000000000i2−i2−i2i20000
χ372-2-22-222-22i−2i2i−2i0002i−2i0002-200002-22i−2i0000002−22−2i2−i2i2−i2000000000000002−2i2−i2
χ382-2-22-222-22i−2i2i−2i0002i−2i0002-200002-22i−2i000000−22−22−i2i2−i2i200000000000000−22−i2i2
χ392-2-22-222-22i−2i2i−2i0002i−2i0002-20000-22−2i2i0000002−22−2i2−i2i2−i200000000000000−22−i2i2
χ402-2-22-222-22i−2i2i−2i0002i−2i0002-20000-22−2i2i000000−22−22−i2i2−i2i2000000000000002−2i2−i2
χ412-2-22-222-2−2i2i−2i2i000−2i2i0002-200002-2−2i2i0000002−22−2−i2i2−i2i2000000000000002−2−i2i2
χ422-2-22-222-2−2i2i−2i2i000−2i2i0002-200002-2−2i2i000000−22−22i2−i2i2−i200000000000000−22i2−i2
χ432-2-22-222-2−2i2i−2i2i000−2i2i0002-20000-222i−2i0000002−22−2−i2i2−i2i200000000000000−22i2−i2
χ442-2-22-222-2−2i2i−2i2i000−2i2i0002-20000-222i−2i000000−22−22i2−i2i2−i2000000000000002−2−i2i2
χ45444-4-44-4-444-4-4400000-4400-4000000000000000000000000000000000000000
χ46444-4-44-4-4-4-4444000004-400-4000000000000000000000000000000000000000
χ4744-44-4-4-44000000000400000-4000000004-40000000000000000000000000000
χ4844-44-4-4-44000000000400000-400000000-440000000000000000000000000000
χ4944-44-4-4-44000000000-400000400000000004i−4i00000000000000000000000000
χ5044-44-4-4-44000000000-40000040000000000−4i4i00000000000000000000000000
χ514-44-4-4-444000004i−4i00000000000000000000000000000002-200002i−2i00000000
χ524-44-4-4-444000004i−4i0000000000000000000000000000000-220000−2i2i00000000
χ534-44-4-4-44400000−4i4i00000000000000000000000000000002-20000−2i2i00000000
χ544-44-4-4-44400000−4i4i0000000000000000000000000000000-2200002i−2i00000000
χ554-4-44-444-44i−4i4i−4i000−4i4i000-440000000000000000000000000000000000000000
χ564-4-44-444-4−4i4i−4i4i0004i−4i000-440000000000000000000000000000000000000000
χ574-4-4-444-444i−4i−4i4i0000000000000000000000002i−2i−2i2i-222-2000000000000000000
χ584-4-4-444-444i−4i−4i4i000000000000000000000000−2i2i2i−2i2-2-22000000000000000000
χ594-4-4-444-44−4i4i4i−4i0000000000000000000000002i−2i−2i2i2-2-22000000000000000000
χ604-4-4-444-44−4i4i4i−4i000000000000000000000000−2i2i2i−2i-222-2000000000000000000
χ6188-8-88-88-8000000000000000000000000000000000000000000000000000000
χ628-8888-8-8-8000000000000000000000000000000000000000000000000000000

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