Finite Group Databasebeta

← Group #168848

Character table — Group #168848

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size111111112222444444444488888888888888888888816161616161616161616161616163232
order12222222444444444444442444444444444888888884444448888888844
χ111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111-1-1-1-111-1-1-1-111111111-1-11-11-1-1-1-1-1-1-1-1-111
χ41111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-111111111-1-1
χ511111111111111111111111-1-11111-1-1-1-1-1-111111111-1-1-11-111111-1-1-1-1-1-1
χ611111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-1111111
χ711111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-11111-1-1
χ811111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111
χ911111111-1-1-1-1-1-1-1-1111111-11111-1-1-1-111-1-11111-1-1-1-11-1-1-11111-1-111-1-11-1
χ1011111111-1-1-1-1-1-1-1-1111111-11111-1-1-1-111-1-1-1-1-1-111111-1-1-111-1-111-1-111-11
χ1111111111-1-1-1-1-1-1-1-1111111-111-1-111-1-1-1-1111111-1-1-1-1-11-111-1-1-111-1-1111-1
χ1211111111-1-1-1-1-1-1-1-1111111-111-1-111-1-1-1-111-1-1-1-11111-11-111-111-1-111-1-1-11
χ1311111111-1-1-1-1-1-1-1-1111111-1-1-111-1-111-1-1111111-1-1-1-1-111-1-1111-1-1-1-111-11
χ1411111111-1-1-1-1-1-1-1-1111111-1-1-111-1-111-1-111-1-1-1-11111-111-1-11-1-11111-1-11-1
χ1511111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1111111-1-11111-1-1-1-11-111-1-1-1-11111-1-1-11
χ1611111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1111111-1-1-1-1-1-111111-111-1-111-1-1-1-1111-1
χ1722222222222222-2-2-2-2-2-222-200222200000000000000000-20-20000000000
χ1822222222222222-2-2-2-2-2-222-200-2-2-2-2000000000000000002020000000000
χ19222222222222-2-222-2-222-2-2-200000000222200000000-2-200000000000000
χ20222222222222-2-222-2-222-2-2-200000000-2-2-2-2000000002200000000000000
χ21222222222222-2-2-2-222-2-2-2-222200002200000000000000-20-200000000000
χ22222222222222-2-2-2-222-2-2-2-22-2-20000-2-20000000000000020200000000000
χ2322222222-2-2-2-2222222-2-2-2-2-2220000-2-20000000000000020-200000000000
χ2422222222-2-2-2-2222222-2-2-2-2-2-2-200002200000000000000-20200000000000
χ2522222222-2-2-2-222-2-2-2-222-2-220000000022-2-200000000-2200000000000000
χ2622222222-2-2-2-222-2-2-2-222-2-2200000000-2-222000000002-200000000000000
χ2722222222-2-2-2-2-2-222-2-2-2-22220022-2-20000000000000000020-20000000000
χ2822222222-2-2-2-2-2-222-2-2-2-222200-2-22200000000000000000-2020000000000
χ2922-22-2-2-222i2i−2i−2i2i−2i0000002-20002i−2i2-2000000i2i2−i2−i222−2−20000002−2i2−i2000000
χ3022-22-2-2-222i2i−2i−2i2i−2i0000002-20002i−2i2-2000000−i2−i2i2i2−2−222000000−22−i2i2000000
χ3122-22-2-2-222i2i−2i−2i2i−2i0000002-2000−2i2i-22000000i2i2−i2−i222−2−2000000−22−i2i2000000
χ3222-22-2-2-222i2i−2i−2i2i−2i0000002-2000−2i2i-22000000−i2−i2i2i2−2−2220000002−2i2−i2000000
χ3322-22-2-2-22−2i−2i2i2i−2i2i0000002-20002i−2i-22000000i2i2−i2−i2−2−2220000002−2−i2i2000000
χ3422-22-2-2-22−2i−2i2i2i−2i2i0000002-20002i−2i-22000000−i2−i2i2i222−2−2000000−22i2−i2000000
χ3522-22-2-2-22−2i−2i2i2i−2i2i0000002-2000−2i2i2-2000000i2i2−i2−i2−2−222000000−22i2−i2000000
χ3622-22-2-2-22−2i−2i2i2i−2i2i0000002-2000−2i2i2-2000000−i2−i2i2i222−2−20000002−2−i2i2000000
χ372-2-22-222-22i−2i2i−2i002i−2i002-2000000000002-22i−2ii2−i2i2−i22−22−20000000000i2−i22−200
χ382-2-22-222-22i−2i2i−2i002i−2i002-2000000000002-22i−2i−i2i2−i2i2−22−220000000000−i2i2−2200
χ392-2-22-222-22i−2i2i−2i002i−2i002-200000000000-22−2i2ii2−i2i2−i22−22−20000000000−i2i2−2200
χ402-2-22-222-22i−2i2i−2i002i−2i002-200000000000-22−2i2i−i2i2−i2i2−22−220000000000i2−i22−200
χ412-2-22-222-2−2i2i−2i2i00−2i2i002-2000000000002-2−2i2ii2−i2i2−i2−22−220000000000i2−i2−2200
χ422-2-22-222-2−2i2i−2i2i00−2i2i002-2000000000002-2−2i2i−i2i2−i2i22−22−20000000000−i2i22−200
χ432-2-22-222-2−2i2i−2i2i00−2i2i002-200000000000-222i−2ii2−i2i2−i2−22−220000000000−i2i22−200
χ442-2-22-222-2−2i2i−2i2i00−2i2i002-200000000000-222i−2i−i2i2−i2i22−22−20000000000i2−i2−2200
χ45444-4-44-4-4000000004-4000000000004-40000000000000000000000000000
χ46444-4-44-4-4000000004-400000000000-440000000000000000000000000000
χ47444-4-44-4-400000000-44000004-40000000000000000000000000000000000
χ48444-4-44-4-400000000-4400000-440000000000000000000000000000000000
χ4944-44-4-4-444i4i−4i−4i−4i4i000000-440000000000000000000000000000000000000
χ5044-44-4-4-44−4i−4i4i4i4i−4i000000-440000000000000000000000000000000000000
χ514-4444-4-4-44-4-44000000000000000000000002-2-222-2-220000000000000000
χ524-4444-4-4-44-4-4400000000000000000000000-222-2-222-20000000000000000
χ534-4444-4-4-4-444-4000000000000000000000002-2-22-222-20000000000000000
χ544-4444-4-4-4-444-400000000000000000000000-222-22-2-220000000000000000
χ554-4-44-444-44i−4i4i−4i00−4i4i00-44000000000000000000000000000000000000000
χ564-4-44-444-4−4i4i−4i4i004i−4i00-44000000000000000000000000000000000000000
χ5788-8-88-88-8000000000000000000000000000000000000000000000000000
χ588-88-8-8-888000000000000000000000000000000000000000000000000000
χ598-8-8-888-88000000000000000000000000000000000000000000000000000

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