Finite Group Databasebeta

← Group #172082

Character table — Group #172082

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11111111222244444444444488888888888888888888161616161616161616161616161616161616
order12222222444422444444444444444444444488888888244444444488888888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-111-1-1-1-1-1-111111111-1-11-1-1-11-1-1-11111-1-1-1-1
χ411111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-111-1-1-1-11111
χ5111111111111111111111111-1-111-1-1-1-111-1-111111111-1-1-1111-1111-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11-1-111111111
χ7111111111111111111111111-1-1-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ8111111111111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-111-1-111-1-1111111-1-1-1-1
χ911111111-1-1-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1111111-1-1-1-1-11-1-11111-1-111-1-111-1-1
χ1011111111-1-1-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-111-1-1-1-11111-11-1-1-1-11111-1-111-1-111
χ1111111111-1-1-1-1-1-11-1-1-1-11111111-1-1-1-11111-1-11111-1-1-1-11-1-11-1-11-11111-1-1-1-111
χ1211111111-1-1-1-1-1-11-1-1-1-11111111-1-1-1-11111-1-1-1-1-1-111111-1-11111-1-1-1-1-11111-1-1
χ1311111111-1-1-1-1-1-11-1-1-1-111111-1-1111111-1-1-1-11111-1-1-1-11-11-111-11-1-1-1-111-1-111
χ1411111111-1-1-1-1-1-11-1-1-1-111111-1-1111111-1-1-1-1-1-1-1-111111-11-1-1-1-111111-1-111-1-1
χ1511111111-1-1-1-1-1-11-1-1-1-111111-1-1-1-111-1-111111111-1-1-1-1-1111-1-1-1-111-1-11111-1-1
χ1611111111-1-1-1-1-1-11-1-1-1-111111-1-1-1-111-1-11111-1-1-1-11111-111111-1-1-1-111-1-1-1-111
χ17222222222222222-2-2-2-2-2-2-2-2200220000-2-200000000000002000-20000000000
χ18222222222222222-2-2-2-2-2-2-2-2200-2-20000220000000000000-200020000000000
χ19222222222222-2-2-222-2-2-2-222-200000022002200000000-2-20000000000000000
χ20222222222222-2-2-222-2-2-2-222-2000000-2-200-2-200000000220000000000000000
χ21222222222222-2-2-2-2-22222-2-2-22200220000000000000000-2000-200000000000
χ22222222222222-2-2-2-2-22222-2-2-2-2-200-2-200000000000000002000200000000000
χ2322222222-2-2-2-222-222-2-222-2-2-22200-2-200000000000000002000-200000000000
χ2422222222-2-2-2-222-222-2-222-2-2-2-2-200220000000000000000-2000200000000000
χ2522222222-2-2-2-222-2-2-222-2-222-20000002200-2-200000000-220000000000000000
χ2622222222-2-2-2-222-2-2-222-2-222-2000000-2-20022000000002-20000000000000000
χ2722222222-2-2-2-2-2-222222-2-2-2-2200220000220000000000000-2000-20000000000
χ2822222222-2-2-2-2-2-222222-2-2-2-2200-2-20000-2-20000000000000200020000000000
χ29222-2-2-2-222i2i−2i−2i0002i−2i00002-200000002i−2i002-2i2i2−i2−i222−2−200000000000000i2−i22−2
χ30222-2-2-2-222i2i−2i−2i0002i−2i00002-200000002i−2i002-2−i2−i2i2i2−2−22200000000000000−i2i2−22
χ31222-2-2-2-222i2i−2i−2i0002i−2i00002-20000000−2i2i00-22i2i2−i2−i222−2−200000000000000−i2i2−22
χ32222-2-2-2-222i2i−2i−2i0002i−2i00002-20000000−2i2i00-22−i2−i2i2i2−2−22200000000000000i2−i22−2
χ33222-2-2-2-22−2i−2i2i2i000−2i2i00002-200000002i−2i00-22i2i2−i2−i2−2−22200000000000000−i2i22−2
χ34222-2-2-2-22−2i−2i2i2i000−2i2i00002-200000002i−2i00-22−i2−i2i2i222−2−200000000000000i2−i2−22
χ35222-2-2-2-22−2i−2i2i2i000−2i2i00002-20000000−2i2i002-2i2i2−i2−i2−2−22200000000000000i2−i2−22
χ36222-2-2-2-22−2i−2i2i2i000−2i2i00002-20000000−2i2i002-2−i2−i2i2i222−2−200000000000000−i2i22−2
χ3722-2-2-222-22i−2i2i−2i000002i−2i2-20002-2002i−2i000000i2−i2i2−i22−22−20000000000i2−i22−20000
χ3822-2-2-222-22i−2i2i−2i000002i−2i2-20002-2002i−2i000000−i2i2−i2i2−22−220000000000−i2i2−220000
χ3922-2-2-222-22i−2i2i−2i000002i−2i2-2000-2200−2i2i000000i2−i2i2−i22−22−20000000000−i2i2−220000
χ4022-2-2-222-22i−2i2i−2i000002i−2i2-2000-2200−2i2i000000−i2i2−i2i2−22−220000000000i2−i22−20000
χ4122-2-2-222-2−2i2i−2i2i00000−2i2i2-20002-200−2i2i000000i2−i2i2−i2−22−220000000000i2−i2−220000
χ4222-2-2-222-2−2i2i−2i2i00000−2i2i2-20002-200−2i2i000000−i2i2−i2i22−22−20000000000−i2i22−20000
χ4322-2-2-222-2−2i2i−2i2i00000−2i2i2-2000-22002i−2i000000i2−i2i2−i2−22−220000000000−i2i22−20000
χ4422-2-2-222-2−2i2i−2i2i00000−2i2i2-2000-22002i−2i000000−i2i2−i2i22−22−20000000000i2−i2−220000
χ45444-4-4-4-444i4i−4i−4i000−4i4i0000-44000000000000000000000000000000000000000
χ46444-4-4-4-44−4i−4i4i4i0004i−4i0000-44000000000000000000000000000000000000000
χ4744-444-4-4-44-4-440000000000000000000000002-2-222-2-22000000000000000000
χ4844-444-4-4-44-4-44000000000000000000000000-222-2-222-2000000000000000000
χ4944-444-4-4-4-444-40000000000000000000000002-2-22-222-2000000000000000000
χ5044-444-4-4-4-444-4000000000000000000000000-222-22-2-22000000000000000000
χ5144-4-4-444-44i−4i4i−4i00000−4i4i-4400000000000000000000000000000000000000000
χ5244-4-4-444-4−4i4i−4i4i000004i−4i-4400000000000000000000000000000000000000000
χ534-44-444-4-4000000400000000-4004-40000000000000000000000000000000000
χ544-44-444-4-4000000400000000-400-440000000000000000000000000000000000
χ554-44-444-4-4000000-4000000004000000004i−4i0000000000000000000000000000
χ564-44-444-4-4000000-400000000400000000−4i4i0000000000000000000000000000
χ574-4-4-44-44400004-400000000000000000000000000000000002-2002-200000000
χ584-4-4-44-44400004-40000000000000000000000000000000000-2200-2200000000
χ594-4-4-44-4440000-4400000000000000000000000000000000002-200-2200000000
χ604-4-4-44-4440000-440000000000000000000000000000000000-22002-200000000
χ618-888-8-88-8000000000000000000000000000000000000000000000000000000
χ628-8-88-88-88000000000000000000000000000000000000000000000000000000

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