Finite Group Databasebeta

← Group #172091

Character table — Group #172091

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11111111222244444444444488888888888888888888161616161616161616161616161616161616
order12222222444422444444444444444444444488888888222224444488888888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-1111-1-1111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-111-1-1-1-1111111111-1-1-1-11-1-1-1-11111-1-1-1-1
χ411111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-111-1-1-1-11111
χ5111111111111111111111111-1-111-1-1-1-111-1-111111111-11-1-1-1-11-1-1-1-1-1-1-11111
χ6111111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-11-111-11-1111111-1-1-1-1
χ7111111111111111111111111-1-1-1-111-1-1-1-11111111111-1-1111-1-1111-1-1-1-1-1-1-1-1
χ8111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-11-1-1-1-11-1-111111111
χ911111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1111111-1-1-1-111-111-1-11-1-111-1-111-1-1
χ1011111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1111-1-111-1-111
χ1111111111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-11111-1-1-1-11-11-1-1-11-11111-1-1-1-111
χ1211111111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-1-1-111111-1111-11-1-1-1-1-11111-1-1
χ1311111111-1-1-1-1-1-1-1-1-1-1111111-1-1111111-1-1-1-11111-1-1-1-1-111-1-11-1-111-1-11111-1-1
χ1411111111-1-1-1-1-1-1-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-11111-111111-1-1-1-111-1-1-1-111
χ1511111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-111111-1-1-1-111-1-111
χ1611111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-11111111-1-111-1-1
χ1722222222222222-2-2-2-22-2-2-2-220000220000-2-20000000000-2000020000000000
χ1822222222222222-2-2-2-22-2-2-2-220000-2-2000022000000000020000-20000000000
χ19222222222222-2-222-2-2-222-2-2-2002200002200000000000-20000-200000000000
χ20222222222222-2-222-2-2-222-2-2-200-2-20000-2-20000000000020000200000000000
χ21222222222222-2-2-2-222-2-2-222-222000022000000000000-20000-2000000000000
χ22222222222222-2-2-2-222-2-2-222-2-2-20000-2-2000000000000200002000000000000
χ2322222222-2-2-2-22222-2-2-2-2-222-2220000-2-2000000000000-200002000000000000
χ2422222222-2-2-2-22222-2-2-2-2-222-2-2-200002200000000000020000-2000000000000
χ2522222222-2-2-2-222-2-222-222-2-2-200220000-2-200000000000-20000200000000000
χ2622222222-2-2-2-222-2-222-222-2-2-200-2-20000220000000000020000-200000000000
χ2722222222-2-2-2-2-2-222222-2-2-2-220000220000220000000000-20000-20000000000
χ2822222222-2-2-2-2-2-222222-2-2-2-220000-2-20000-2-200000000002000020000000000
χ29222-22-2-2-22i2i−2i−2i00002i−2i0002-202i−2i00002-20000i2i2−i2−i222−2−200000000002−2i2−i20000
χ30222-22-2-2-22i2i−2i−2i00002i−2i0002-202i−2i00002-20000−i2−i2i2i2−2−2220000000000−22−i2i20000
χ31222-22-2-2-22i2i−2i−2i00002i−2i0002-20−2i2i0000-220000i2i2−i2−i222−2−20000000000−22−i2i20000
χ32222-22-2-2-22i2i−2i−2i00002i−2i0002-20−2i2i0000-220000−i2−i2i2i2−2−22200000000002−2i2−i20000
χ33222-22-2-2-2−2i−2i2i2i0000−2i2i0002-202i−2i0000-220000i2i2−i2−i2−2−22200000000002−2−i2i20000
χ34222-22-2-2-2−2i−2i2i2i0000−2i2i0002-202i−2i0000-220000−i2−i2i2i222−2−20000000000−22i2−i20000
χ35222-22-2-2-2−2i−2i2i2i0000−2i2i0002-20−2i2i00002-20000i2i2−i2−i2−2−2220000000000−22i2−i20000
χ36222-22-2-2-2−2i−2i2i2i0000−2i2i0002-20−2i2i00002-20000−i2−i2i2i222−2−200000000002−2−i2i20000
χ3722-22-22-2-22i−2i2i−2i002i−2i0002-2000002i−2i00002-200i2−i2i2−i22−22−2000000000000002−2i2−i2
χ3822-22-22-2-22i−2i2i−2i002i−2i0002-2000002i−2i00002-200−i2i2−i2i2−22−2200000000000000−22−i2i2
χ3922-22-22-2-22i−2i2i−2i002i−2i0002-200000−2i2i0000-2200i2−i2i2−i22−22−200000000000000−22−i2i2
χ4022-22-22-2-22i−2i2i−2i002i−2i0002-200000−2i2i0000-2200−i2i2−i2i2−22−22000000000000002−2i2−i2
χ4122-22-22-2-2−2i2i−2i2i00−2i2i0002-2000002i−2i0000-2200i2−i2i2−i2−22−22000000000000002−2−i2i2
χ4222-22-22-2-2−2i2i−2i2i00−2i2i0002-2000002i−2i0000-2200−i2i2−i2i22−22−200000000000000−22i2−i2
χ4322-22-22-2-2−2i2i−2i2i00−2i2i0002-200000−2i2i00002-200i2−i2i2−i2−22−2200000000000000−22i2−i2
χ4422-22-22-2-2−2i2i−2i2i00−2i2i0002-200000−2i2i00002-200−i2i2−i2i22−22−2000000000000002−2−i2i2
χ45444-44-4-4-44i4i−4i−4i0000−4i4i000-44000000000000000000000000000000000000000
χ46444-44-4-4-4−4i−4i4i4i00004i−4i000-44000000000000000000000000000000000000000
χ4744-44-44-4-44i−4i4i−4i00−4i4i000-4400000000000000000000000000000000000000000
χ4844-44-44-4-4−4i4i−4i4i004i−4i000-4400000000000000000000000000000000000000000
χ4944-4-4-4-4444-4-440000000000000000000000002-2-222-2-22000000000000000000
χ5044-4-4-4-4444-4-44000000000000000000000000-222-2-222-2000000000000000000
χ5144-4-4-4-444-444-40000000000000000000000002-2-22-222-2000000000000000000
χ5244-4-4-4-444-444-4000000000000000000000000-222-22-2-22000000000000000000
χ534-444-4-4-44000000000040000-400004i−4i00000000000000000000000000000000
χ544-444-4-4-44000000000040000-40000−4i4i00000000000000000000000000000000
χ554-444-4-4-440000000000-40000400000000004-400000000000000000000000000
χ564-444-4-4-440000000000-4000040000000000-4400000000000000000000000000
χ574-4-4-444-4400004-40000000000000000000000000000000002-20002-200000000
χ584-4-4-444-4400004-4000000000000000000000000000000000-22000-2200000000
χ594-4-4-444-440000-440000000000000000000000000000000002-2000-2200000000
χ604-4-4-444-440000-44000000000000000000000000000000000-220002-200000000
χ618-88-8-888-8000000000000000000000000000000000000000000000000000000
χ628-8-888-88-8000000000000000000000000000000000000000000000000000000

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