Finite Group Databasebeta

← Group #172117

Character table — Group #172117

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11111111222244444444444488888888888888888888161616161616161616161616161616161616
order12222222444444444444444444444444444488888888244444444488888888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-11-11-1-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-11111-1-1-1-11111
χ5111111111111111111111111-1-1-1-111-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ6111111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1
χ7111111111111111111111111-1-1-1-1-1-111-1-11111111111-1-1-11-111111-1-1-1-1-1-1-1-1
χ8111111111111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-111111111
χ911111111-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-11111-1-1-1-11-1-1-11111-1-111-1-111-1-1
χ1011111111-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-111111-1-1-111-1-111-1-111-1-111
χ1111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-11-111-1-1-11111-1-1-1-111
χ1211111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-11111-11-111-111-1-1-1-11111-1-1
χ1311111111-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1111111-1-1-1-11-111-1-1-1-111-1-11111-1-1
χ1411111111-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-111-1-1-1-111111-111-1-111-1-111-1-1-1-111
χ1511111111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-11111-1-11111-1-1-1-1-111-1-1111-1-1-1-111-1-111
χ1611111111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-11111-111-1-11-1-11111-1-111-1-1
χ1722222222222222-2-2-2-222-2-2-2-20000002200-2-20000000000020-2000000000000
χ1822222222222222-2-2-2-222-2-2-2-2000000-2-2002200000000000-202000000000000
χ19222222222222-2-222-2-2-2-222-2-200002200220000000000-2-20000000000000000
χ20222222222222-2-222-2-2-2-222-2-20000-2-200-2-20000000000220000000000000000
χ21222222222222-2-2-2-222-2-2-2-2222222000000000000000000-20-20000000000000
χ22222222222222-2-2-2-222-2-2-2-222-2-2-2-20000000000000000002020000000000000
χ2322222222-2-2-2-22222-2-2-2-2-2-22222-2-200000000000000000020-20000000000000
χ2422222222-2-2-2-22222-2-2-2-2-2-222-2-222000000000000000000-2020000000000000
χ2522222222-2-2-2-222-2-222-2-222-2-200002200-2-20000000000-220000000000000000
χ2622222222-2-2-2-222-2-222-2-222-2-20000-2-2002200000000002-20000000000000000
χ2722222222-2-2-2-2-2-2222222-2-2-2-200000022002200000000000-20-2000000000000
χ2822222222-2-2-2-2-2-2222222-2-2-2-2000000-2-200-2-200000000000202000000000000
χ2922-2-22-22-22i2i−2i−2i00002i−2i00002-22i−2i2-200000000i2i2−i2−i222−2−200000000002−2i2−i20000
χ3022-2-22-22-22i2i−2i−2i00002i−2i00002-22i−2i2-200000000−i2−i2i2i2−2−2220000000000−22−i2i20000
χ3122-2-22-22-22i2i−2i−2i00002i−2i00002-2−2i2i-2200000000i2i2−i2−i222−2−20000000000−22−i2i20000
χ3222-2-22-22-22i2i−2i−2i00002i−2i00002-2−2i2i-2200000000−i2−i2i2i2−2−22200000000002−2i2−i20000
χ3322-2-22-22-2−2i−2i2i2i0000−2i2i00002-22i−2i-2200000000i2i2−i2−i2−2−22200000000002−2−i2i20000
χ3422-2-22-22-2−2i−2i2i2i0000−2i2i00002-22i−2i-2200000000−i2−i2i2i222−2−20000000000−22i2−i20000
χ3522-2-22-22-2−2i−2i2i2i0000−2i2i00002-2−2i2i2-200000000i2i2−i2−i2−2−2220000000000−22i2−i20000
χ3622-2-22-22-2−2i−2i2i2i0000−2i2i00002-2−2i2i2-200000000−i2−i2i2i222−2−200000000002−2−i2i20000
χ3722-2-2-22-222i−2i2i−2i002i−2i00002-20000002i−2i002-200i2−i2i2−i22−22−2000000000000002−2i2−i2
χ3822-2-2-22-222i−2i2i−2i002i−2i00002-20000002i−2i002-200−i2i2−i2i2−22−2200000000000000−22−i2i2
χ3922-2-2-22-222i−2i2i−2i002i−2i00002-2000000−2i2i00-2200i2−i2i2−i22−22−200000000000000−22−i2i2
χ4022-2-2-22-222i−2i2i−2i002i−2i00002-2000000−2i2i00-2200−i2i2−i2i2−22−22000000000000002−2i2−i2
χ4122-2-2-22-22−2i2i−2i2i00−2i2i00002-20000002i−2i00-2200i2−i2i2−i2−22−22000000000000002−2−i2i2
χ4222-2-2-22-22−2i2i−2i2i00−2i2i00002-20000002i−2i00-2200−i2i2−i2i22−22−200000000000000−22i2−i2
χ4322-2-2-22-22−2i2i−2i2i00−2i2i00002-2000000−2i2i002-200i2−i2i2−i2−22−2200000000000000−22i2−i2
χ4422-2-2-22-22−2i2i−2i2i00−2i2i00002-2000000−2i2i002-200−i2i2−i2i22−22−2000000000000002−2−i2i2
χ454444-4-4-4-44-4-440000000000000000000000002-2-222-2-22000000000000000000
χ464444-4-4-4-44-4-44000000000000000000000000-222-2-222-2000000000000000000
χ474444-4-4-4-4-444-40000000000000000000000002-2-22-222-2000000000000000000
χ484444-4-4-4-4-444-4000000000000000000000000-222-22-2-22000000000000000000
χ4944-4-44-44-44i4i−4i−4i0000−4i4i0000-4400000000000000000000000000000000000000
χ5044-4-44-44-4−4i−4i4i4i00004i−4i0000-4400000000000000000000000000000000000000
χ5144-4-4-44-444i−4i4i−4i00−4i4i0000-440000000000000000000000000000000000000000
χ5244-4-4-44-44−4i4i−4i4i004i−4i0000-440000000000000000000000000000000000000000
χ534-44-44-4-4400000000004-4000000000000004i−4i00000000000000000000000000
χ544-44-44-4-4400000000004-400000000000000−4i4i00000000000000000000000000
χ554-44-44-4-440000000000-4400000000004i−4i000000000000000000000000000000
χ564-44-44-4-440000000000-440000000000−4i4i000000000000000000000000000000
χ574-44-4-444-400004i−4i0000000000000000000000000000000000002-22i−2i00000000
χ584-44-4-444-400004i−4i000000000000000000000000000000000000-22−2i2i00000000
χ594-44-4-444-40000−4i4i0000000000000000000000000000000000002-2−2i2i00000000
χ604-44-4-444-40000−4i4i000000000000000000000000000000000000-222i−2i00000000
χ618-8-8888-8-8000000000000000000000000000000000000000000000000000000
χ628-8-88-8-888000000000000000000000000000000000000000000000000000000

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