Finite Group Databasebeta

← Group #172124

Character table — Group #172124

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11111111222244444444444488888888888888888888161616161616161616161616161616161616
order12222222444444444444444444444444444488888888444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-111-1-1-1-111111111-1-11-1111-111-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11-1-1-111111111
χ5111111111111111111111111-1-11111-1-1-1-1-1-111111111-1-1-11-1-1-11-1-11111-1-1-1-1
χ6111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1111-1-1-1-11111
χ7111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ8111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-1111111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-11111-1-1-1-11-1-11111-1-1-111-1-111-1-1
χ1011111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-111111-1-11-1-11-111-1-111-1-111
χ1111111111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1111111-1-1-1-1-11-1-11111-1-1-1-111-1-111
χ1211111111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111-1-1-1-11111-11-1-1-1-1111111-1-111-1-1
χ1311111111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-111-1-1111111-1-1-1-1-1111-1-1-1-11111-1-1-1-111
χ1411111111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-111-1-111-1-1-1-11111-111111-1-1-1-1-1-11111-1-1
χ1511111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-11111-1-1-1-11-11-1-1-1-1111-1-11111-1-1
χ1611111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-111111-11-111-11-1-111-1-1-1-111
χ1722222222222222-2-2-2-2-2-222-2-200222200000000000000000-2000-20000000000
χ1822222222222222-2-2-2-2-2-222-2-200-2-2-2-200000000000000000200020000000000
χ19222222222222-2-222-2-222-2-2-2-2220000-2-2000000000000002000-200000000000
χ20222222222222-2-222-2-222-2-2-2-2-2-200002200000000000000-2000200000000000
χ21222222222222-2-2-2-222-2-2-2-22200000000222200000000-2-20000000000000000
χ22222222222222-2-2-2-222-2-2-2-22200000000-2-2-2-200000000220000000000000000
χ2322222222-2-2-2-22222-2-2-2-2-2-2220000000022-2-200000000-220000000000000000
χ2422222222-2-2-2-22222-2-2-2-2-2-22200000000-2-222000000002-20000000000000000
χ2522222222-2-2-2-222-2-22222-2-2-2-22200002200000000000000-2000-200000000000
χ2622222222-2-2-2-222-2-22222-2-2-2-2-2-20000-2-2000000000000002000200000000000
χ2722222222-2-2-2-2-2-22222-2-222-2-20022-2-200000000000000000-200020000000000
χ2822222222-2-2-2-2-2-22222-2-222-2-200-2-222000000000000000002000-20000000000
χ292-222-2-2-222i2i−2i−2i00002i−2i00002-2000000002i−2i2-2i2i2−i2−i222−2−2000000000000002−2i2−i2
χ302-222-2-2-222i2i−2i−2i00002i−2i00002-2000000002i−2i2-2−i2−i2i2i2−2−22200000000000000−22−i2i2
χ312-222-2-2-222i2i−2i−2i00002i−2i00002-200000000−2i2i-22i2i2−i2−i222−2−200000000000000−22−i2i2
χ322-222-2-2-222i2i−2i−2i00002i−2i00002-200000000−2i2i-22−i2−i2i2i2−2−222000000000000002−2i2−i2
χ332-222-2-2-22−2i−2i2i2i0000−2i2i00002-2000000002i−2i-22i2i2−i2−i2−2−222000000000000002−2−i2i2
χ342-222-2-2-22−2i−2i2i2i0000−2i2i00002-2000000002i−2i-22−i2−i2i2i222−2−200000000000000−22i2−i2
χ352-222-2-2-22−2i−2i2i2i0000−2i2i00002-200000000−2i2i2-2i2i2−i2−i2−2−22200000000000000−22i2−i2
χ362-222-2-2-22−2i−2i2i2i0000−2i2i00002-200000000−2i2i2-2−i2−i2i2i222−2−2000000000000002−2−i2i2
χ372-2-22-222-22i−2i2i−2i2i−2i0000002-200002i−2i2-2000000i2−i2i2−i22−22−200000000002−2i2−i20000
χ382-2-22-222-22i−2i2i−2i2i−2i0000002-200002i−2i2-2000000−i2i2−i2i2−22−220000000000−22−i2i20000
χ392-2-22-222-22i−2i2i−2i2i−2i0000002-20000−2i2i-22000000i2−i2i2−i22−22−20000000000−22−i2i20000
χ402-2-22-222-22i−2i2i−2i2i−2i0000002-20000−2i2i-22000000−i2i2−i2i2−22−2200000000002−2i2−i20000
χ412-2-22-222-2−2i2i−2i2i−2i2i0000002-200002i−2i-22000000i2−i2i2−i2−22−2200000000002−2−i2i20000
χ422-2-22-222-2−2i2i−2i2i−2i2i0000002-200002i−2i-22000000−i2i2−i2i22−22−20000000000−22i2−i20000
χ432-2-22-222-2−2i2i−2i2i−2i2i0000002-20000−2i2i2-2000000i2−i2i2−i2−22−220000000000−22i2−i20000
χ442-2-22-222-2−2i2i−2i2i−2i2i0000002-20000−2i2i2-2000000−i2i2−i2i22−22−200000000002−2−i2i20000
χ45444-4-44-4-400000000004-400000000004-4000000000000000000000000000000
χ46444-4-44-4-400000000004-40000000000-44000000000000000000000000000000
χ47444-4-44-4-40000000000-4400004-4000000000000000000000000000000000000
χ48444-4-44-4-40000000000-440000-44000000000000000000000000000000000000
χ4944-444-4-4-44-4-440000000000000000000000002-2-222-2-22000000000000000000
χ5044-444-4-4-44-4-44000000000000000000000000-222-2-222-2000000000000000000
χ5144-444-4-4-4-444-40000000000000000000000002-2-22-222-2000000000000000000
χ5244-444-4-4-4-444-4000000000000000000000000-222-22-2-22000000000000000000
χ5344-4-4-4-4440000004i−4i000000000000000000000000000000002i−2i002-200000000
χ5444-4-4-4-4440000004i−4i00000000000000000000000000000000−2i2i00-2200000000
χ5544-4-4-4-444000000−4i4i000000000000000000000000000000002i−2i00-2200000000
χ5644-4-4-4-444000000−4i4i00000000000000000000000000000000−2i2i002-200000000
χ574-444-4-4-444i4i−4i−4i0000−4i4i0000-4400000000000000000000000000000000000000
χ584-444-4-4-44−4i−4i4i4i00004i−4i0000-4400000000000000000000000000000000000000
χ594-4-44-444-44i−4i4i−4i−4i4i000000-440000000000000000000000000000000000000000
χ604-4-44-444-4−4i4i−4i4i4i−4i000000-440000000000000000000000000000000000000000
χ618-88-88-88-8000000000000000000000000000000000000000000000000000000
χ628-8-8-888-88000000000000000000000000000000000000000000000000000000

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