Finite Group Databasebeta

← Group #168849

Character table — Group #168849

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size111111112222444444444488888888888888888888816161616161616161616161616163232
order12222222444444444444442444444444444888888882244448888888824
χ111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-11-1-11111-1-1-1-1-1-1
χ4111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-1-1-1111111
χ511111111111111111111111-1-1-1-11111-1-1-1-111111111-1-11-1-11-1-1-1-11111-1-1
χ611111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111111-1-1-1-111
χ711111111111111111111111-1-1-1-1-1-1-1-1111111111111-11-1-11-1-1-1-1-1-1-1-1-111
χ811111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-1-11-111111111-1-1
χ911111111-1-1-1-1-1-1-1-1111111-111-1-111-1-111-1-11111-1-1-1-111-1-1-1111-1-111-1-11-1
χ1011111111-1-1-1-1-1-1-1-1111111-111-1-111-1-111-1-1-1-1-1-1111111-1-1-11-1-111-1-111-11
χ1111111111-1-1-1-1-1-1-1-1111111-111-1-1-1-111-1-1111111-1-1-1-11-11-11-111-1-1-1-111-11
χ1211111111-1-1-1-1-1-1-1-1111111-111-1-1-1-111-1-111-1-1-1-111111-11-11-1-1-11111-1-11-1
χ1311111111-1-1-1-1-1-1-1-1111111-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1111-1-11111-1-1-11
χ1411111111-1-1-1-1-1-1-1-1111111-1-1-11111-1-1-1-111-1-1-1-11111-1-1-111111-1-1-1-1111-1
χ1511111111-1-1-1-1-1-1-1-1111111-1-1-111-1-11111-1-11111-1-1-1-1-1111-1-1-1-111-1-1111-1
χ1611111111-1-1-1-1-1-1-1-1111111-1-1-111-1-11111-1-1-1-1-1-11111-1111-1-111-1-111-1-1-11
χ1722222222222222-2-222-2-2-2-2-20000222200000000000000-200-20000000000
χ1822222222222222-2-222-2-2-2-2-20000-2-2-2-20000000000000020020000000000
χ19222222222222-2-222-2-222-2-2-222220000000000000000-200-2000000000000
χ20222222222222-2-222-2-222-2-2-2-2-2-2-200000000000000002002000000000000
χ21222222222222-2-2-2-2-2-2-2-2222000000002222000000000-200-200000000000
χ22222222222222-2-2-2-2-2-2-2-222200000000-2-2-2-2000000000200200000000000
χ2322222222-2-2-2-22222-2-2-2-222-20000000022-2-2000000000-200200000000000
χ2422222222-2-2-2-22222-2-2-2-222-200000000-2-222000000000200-200000000000
χ2522222222-2-2-2-222-2-2-2-222-2-2222-2-20000000000000000-2002000000000000
χ2622222222-2-2-2-222-2-2-2-222-2-22-2-2220000000000000000200-2000000000000
χ2722222222-2-2-2-2-2-22222-2-2-2-22000022-2-200000000000000200-20000000000
χ2822222222-2-2-2-2-2-22222-2-2-2-220000-2-22200000000000000-20020000000000
χ2922-222-2-2-22i2i−2i−2i002i−2i002-20002i−2i2-20000000022−2−2i2i2−i2−i2000000i2−i22−2000000
χ3022-222-2-2-22i2i−2i−2i002i−2i002-20002i−2i2-200000000−2−222−i2−i2i2i2000000−i2i2−22000000
χ3122-222-2-2-22i2i−2i−2i002i−2i002-2000−2i2i-220000000022−2−2i2i2−i2−i2000000−i2i2−22000000
χ3222-222-2-2-22i2i−2i−2i002i−2i002-2000−2i2i-2200000000−2−222−i2−i2i2i2000000i2−i22−2000000
χ3322-222-2-2-2−2i−2i2i2i00−2i2i002-20002i−2i-220000000022−2−2−i2−i2i2i2000000i2−i2−22000000
χ3422-222-2-2-2−2i−2i2i2i00−2i2i002-20002i−2i-2200000000−2−222i2i2−i2−i2000000−i2i22−2000000
χ3522-222-2-2-2−2i−2i2i2i00−2i2i002-2000−2i2i2-20000000022−2−2−i2−i2i2i2000000−i2i22−2000000
χ3622-222-2-2-2−2i−2i2i2i00−2i2i002-2000−2i2i2-200000000−2−222i2i2−i2−i2000000i2−i2−22000000
χ372-222-22-2-22i−2i2i−2i2i−2i002-20000000002-22i−2i00002−22−2i2−i2i2−i200000000002−2i2−i200
χ382-222-22-2-22i−2i2i−2i2i−2i002-20000000002-22i−2i0000−22−22−i2i2−i2i20000000000−22−i2i200
χ392-222-22-2-22i−2i2i−2i2i−2i002-2000000000-22−2i2i00002−22−2i2−i2i2−i20000000000−22−i2i200
χ402-222-22-2-22i−2i2i−2i2i−2i002-2000000000-22−2i2i0000−22−22−i2i2−i2i200000000002−2i2−i200
χ412-222-22-2-2−2i2i−2i2i−2i2i002-20000000002-2−2i2i00002−22−2−i2i2−i2i200000000002−2−i2i200
χ422-222-22-2-2−2i2i−2i2i−2i2i002-20000000002-2−2i2i0000−22−22i2−i2i2−i20000000000−22i2−i200
χ432-222-22-2-2−2i2i−2i2i−2i2i002-2000000000-222i−2i00002−22−2−i2i2−i2i20000000000−22i2−i200
χ442-222-22-2-2−2i2i−2i2i−2i2i002-2000000000-222i−2i0000−22−22i2−i2i2−i200000000002−2−i2i200
χ45444-4-4-44-40000000000004-4000000000004i−4i000000000000000000000000
χ46444-4-4-44-40000000000004-400000000000−4i4i000000000000000000000000
χ47444-4-4-44-4000000000000-440000000004i−4i00000000000000000000000000
χ48444-4-4-44-4000000000000-44000000000−4i4i00000000000000000000000000
χ4944-444-4-4-44i4i−4i−4i00−4i4i00-44000000000000000000000000000000000000000
χ5044-444-4-4-4−4i−4i4i4i004i−4i00-44000000000000000000000000000000000000000
χ514-444-44-4-44i−4i4i−4i−4i4i00-4400000000000000000000000000000000000000000
χ524-444-44-4-4−4i4i−4i4i4i−4i00-4400000000000000000000000000000000000000000
χ534-4-44-4-4444-4-44000000000000000000000002-2-222-2-220000000000000000
χ544-4-44-4-4444-4-4400000000000000000000000-222-2-222-20000000000000000
χ554-4-44-4-444-444-4000000000000000000000002-2-22-222-20000000000000000
χ564-4-44-4-444-444-400000000000000000000000-222-22-2-220000000000000000
χ5788-8-8-88-88000000000000000000000000000000000000000000000000000
χ588-88-88-8-88000000000000000000000000000000000000000000000000000
χ598-8-8-8888-8000000000000000000000000000000000000000000000000000

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