Finite Group Databasebeta

← Group #168851

Character table — Group #168851

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size111111112222444444444488888888888888888888816161616161616161616161616163232
order12222222444444444444442224444444444888888882444448888888844
χ111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111-1-1-1-1-1-1-1-11111111111-111-1-1-11111-1-1-1-1-1-1
χ41111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1111111
χ511111111111111111111111-1-111-1-111-1-1-1-1111111111-1-1-1-11-1-1-1-1-1-1-1-111
χ611111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1111111111-1-1
χ711111111111111111111111-1-1-1-111-1-111-1-111111111-1-1-111-1-1-1-1-11111-1-1
χ811111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-111-11111-1-1-1-111
χ911111111-1-1-1-1-1-1-1-1111111-1111111-1-1-1-1-1-11111-1-1-1-1-11-11-1111-1-111-1-11-1
χ1011111111-1-1-1-1-1-1-1-1111111-1111111-1-1-1-1-1-1-1-1-1-11111-11-11-11-1-111-1-111-11
χ1111111111-1-1-1-1-1-1-1-1111111-111-1-1-1-11111-1-11111-1-1-1-111-1-11-111-1-1-1-111-11
χ1211111111-1-1-1-1-1-1-1-1111111-111-1-1-1-11111-1-1-1-1-1-1111111-1-11-1-1-11111-1-11-1
χ1311111111-1-1-1-1-1-1-1-1111111-1-1-111-1-1-1-111111111-1-1-1-1-1-11-111-1-111-1-1111-1
χ1411111111-1-1-1-1-1-1-1-1111111-1-1-111-1-1-1-11111-1-1-1-11111-1-11-11111-1-111-1-1-11
χ1511111111-1-1-1-1-1-1-1-1111111-1-1-1-1-11111-1-1111111-1-1-1-11-111-1-1-1-11111-1-1-11
χ1611111111-1-1-1-1-1-1-1-1111111-1-1-1-1-11111-1-111-1-1-1-111111-111-1-111-1-1-1-1111-1
χ1722222222222222-2-222-2-2-2-2-200002200220000000000000-2-200000000000
χ1822222222222222-2-222-2-2-2-2-20000-2-200-2-200000000000002200000000000
χ19222222222222-2-222-2-222-2-2-2220000000022000000000-2-20000000000000
χ20222222222222-2-222-2-222-2-2-2-2-200000000-2-2000000000220000000000000
χ21222222222222-2-2-2-2-2-2-2-222200220022000000000000-20000-20000000000
χ22222222222222-2-2-2-2-2-2-2-222200-2-200-2-20000000000002000020000000000
χ2322222222-2-2-2-22222-2-2-2-222-2002200-2-200000000000020000-20000000000
χ2422222222-2-2-2-22222-2-2-2-222-200-2-20022000000000000-2000020000000000
χ2522222222-2-2-2-222-2-2-2-222-2-222200000000-2-2000000000-220000000000000
χ2622222222-2-2-2-222-2-2-2-222-2-22-2-200000000220000000002-20000000000000
χ2722222222-2-2-2-2-2-22222-2-2-2-2200002200-2-20000000000000-2200000000000
χ2822222222-2-2-2-2-2-22222-2-2-2-220000-2-2002200000000000002-200000000000
χ2922-22-2-22-22i2i−2i−2i002i−2i002-20002-2000000002i−2ii2i2−i2−i222−2−2000000i2−i22−2000000
χ3022-22-2-22-22i2i−2i−2i002i−2i002-20002-2000000002i−2i−i2−i2i2i2−2−222000000−i2i2−22000000
χ3122-22-2-22-22i2i−2i−2i002i−2i002-2000-2200000000−2i2ii2i2−i2−i222−2−2000000−i2i2−22000000
χ3222-22-2-22-22i2i−2i−2i002i−2i002-2000-2200000000−2i2i−i2−i2i2i2−2−222000000i2−i22−2000000
χ3322-22-2-22-2−2i−2i2i2i00−2i2i002-20002-200000000−2i2ii2i2−i2−i2−2−222000000i2−i2−22000000
χ3422-22-2-22-2−2i−2i2i2i00−2i2i002-20002-200000000−2i2i−i2−i2i2i222−2−2000000−i2i22−2000000
χ3522-22-2-22-2−2i−2i2i2i00−2i2i002-2000-22000000002i−2ii2i2−i2−i2−2−222000000−i2i22−2000000
χ3622-22-2-22-2−2i−2i2i2i00−2i2i002-2000-22000000002i−2i−i2−i2i2i222−2−2000000i2−i2−22000000
χ372-22-22-22-22i−2i2i−2i2i−2i002-20000000002i−2i002-200i2−i2i2−i22−22−200000000002−2i2−i200
χ382-22-22-22-22i−2i2i−2i2i−2i002-20000000002i−2i002-200−i2i2−i2i2−22−220000000000−22−i2i200
χ392-22-22-22-22i−2i2i−2i2i−2i002-2000000000−2i2i00-2200i2−i2i2−i22−22−20000000000−22−i2i200
χ402-22-22-22-22i−2i2i−2i2i−2i002-2000000000−2i2i00-2200−i2i2−i2i2−22−2200000000002−2i2−i200
χ412-22-22-22-2−2i2i−2i2i−2i2i002-20000000002i−2i00-2200i2−i2i2−i2−22−2200000000002−2−i2i200
χ422-22-22-22-2−2i2i−2i2i−2i2i002-20000000002i−2i00-2200−i2i2−i2i22−22−20000000000−22i2−i200
χ432-22-22-22-2−2i2i−2i2i−2i2i002-2000000000−2i2i002-200i2−i2i2−i2−22−220000000000−22i2−i200
χ442-22-22-22-2−2i2i−2i2i−2i2i002-2000000000−2i2i002-200−i2i2−i2i22−22−200000000002−2−i2i200
χ45444-4-4-4-440000000000004-400000004i−4i0000000000000000000000000000
χ46444-4-4-4-440000000000004-40000000−4i4i0000000000000000000000000000
χ47444-4-4-4-44000000000000-440004i−4i00000000000000000000000000000000
χ48444-4-4-4-44000000000000-44000−4i4i00000000000000000000000000000000
χ4944-44-4-44-44i4i−4i−4i00−4i4i00-44000000000000000000000000000000000000000
χ5044-44-4-44-4−4i−4i4i4i004i−4i00-44000000000000000000000000000000000000000
χ514-44-44-44-44i−4i4i−4i−4i4i00-4400000000000000000000000000000000000000000
χ524-44-44-44-4−4i4i−4i4i4i−4i00-4400000000000000000000000000000000000000000
χ534-4-4-4-44444-4-44000000000000000000000002-2-222-2-220000000000000000
χ544-4-4-4-44444-4-4400000000000000000000000-222-2-222-20000000000000000
χ554-4-4-4-4444-444-4000000000000000000000002-2-22-222-20000000000000000
χ564-4-4-4-4444-444-400000000000000000000000-222-22-2-220000000000000000
χ5788-8-888-8-8000000000000000000000000000000000000000000000000000
χ588-888-88-8-8000000000000000000000000000000000000000000000000000
χ598-8-888-8-88000000000000000000000000000000000000000000000000000

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