Finite Group Databasebeta

← Group #168638

Character table — Group #168638

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size111111112222444444444488888888888888888888816161616161616161616161616163232
order12222222444422444444444444444444444888888882444448888888824
χ111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-11-1-1-1-1-1-111111111-1-1-111-1-1-1-1-1-1-1-1-111
χ411111111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111111111-1-1
χ51111111111111111111111-1-1-1-1111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1
χ61111111111111111111111-1-1-1-1111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111
χ71111111111111111111111-1-1-1-1-1-111111-1-111111111-1-11-1-111111-1-1-1-1-1-1
χ81111111111111111111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-1111111
χ911111111-1-1-1-1-1-111-1-1111111-1-111-111-1-1-1-11111-1-1-1-1-1111-1-111-1-111-1-11-1
χ1011111111-1-1-1-1-1-111-1-1111111-1-111-111-1-1-1-1-1-1-1-11111-1111-1-1-1-111-1-111-11
χ1111111111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-111111111-1-1-1-11-1-11-11-1-111-1-1111-1
χ1211111111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-11111-1-1-1-111111-1-11-1111-1-111-1-1-11
χ1311111111-1-1-1-1-1-111-1-11111-1-11111-1-1-111-1-11111-1-1-1-1-11-1-111-1-11111-1-1-11
χ1411111111-1-1-1-1-1-111-1-11111-1-11111-1-1-111-1-1-1-1-1-11111-11-1-11111-1-1-1-1111-1
χ1511111111-1-1-1-1-1-111-1-11111-1-111-1-1-111-1-1111111-1-1-1-11-11-11-111-1-1-1-111-11
χ1611111111-1-1-1-1-1-111-1-11111-1-111-1-1-111-1-111-1-1-1-111111-11-11-1-1-11111-1-11-1
χ17222222222222222-2-2-2-2-22-2000000-22222000000000000-200-20000000000
χ18222222222222222-2-2-2-2-22-2000000-2-2-2-2-200000000000020020000000000
χ19222222222222-2-2-22-2-2-2-2-22222200200000000000000000-2-200000000000
χ20222222222222-2-2-22-2-2-2-2-22-2-2-2-2002000000000000000002200000000000
χ21222222222222-2-2-2-22222-2-2000022-200002200000000-2-200000000000000
χ22222222222222-2-2-2-22222-2-20000-2-2-20000-2-2000000002200000000000000
χ2322222222-2-2-2-222-2222-2-2-2222-2-200-200000000000000000-2200000000000
χ2422222222-2-2-2-222-2222-2-2-22-2-22200-2000000000000000002-200000000000
χ2522222222-2-2-2-222-2-2-2-222-2-200002220000-2-2000000002-200000000000000
χ2622222222-2-2-2-222-2-2-2-222-2-20000-2-2200002200000000-2200000000000000
χ2722222222-2-2-2-2-2-22-222-2-22-2000000222-2-2000000000000-20020000000000
χ2822222222-2-2-2-2-2-22-222-2-22-20000002-2-222000000000000200-20000000000
χ2922-22-22-2-22i2i−2i−2i00002i−2i2-20000002-2000002i−2i22−2−2i2i2−i2−i200000000002−2i2−i200
χ3022-22-22-2-22i2i−2i−2i00002i−2i2-20000002-2000002i−2i−2−222−i2−i2i2i20000000000−22−i2i200
χ3122-22-22-2-22i2i−2i−2i00002i−2i2-2000000-2200000−2i2i22−2−2i2i2−i2−i20000000000−22−i2i200
χ3222-22-22-2-22i2i−2i−2i00002i−2i2-2000000-2200000−2i2i−2−222−i2−i2i2i200000000002−2i2−i200
χ3322-22-22-2-2−2i−2i2i2i0000−2i2i2-20000002-200000−2i2i22−2−2−i2−i2i2i200000000002−2−i2i200
χ3422-22-22-2-2−2i−2i2i2i0000−2i2i2-20000002-200000−2i2i−2−222i2i2−i2−i20000000000−22i2−i200
χ3522-22-22-2-2−2i−2i2i2i0000−2i2i2-2000000-22000002i−2i22−2−2−i2−i2i2i20000000000−22i2−i200
χ3622-22-22-2-2−2i−2i2i2i0000−2i2i2-2000000-22000002i−2i−2−222i2i2−i2−i200000000002−2−i2i200
χ372-2-222-2-222-22-22-2200000-2000000002i−2i2i−2i00i2−i2i2−i2i2−i2i2−i20000002−22−2000000
χ382-2-222-2-222-22-22-2200000-2000000002i−2i2i−2i00−i2i2−i2i2−i2i2−i2i2000000−22−22000000
χ392-2-222-2-222-22-22-2200000-200000000−2i2i−2i2i00i2−i2i2−i2i2−i2i2−i2000000−22−22000000
χ402-2-222-2-222-22-22-2200000-200000000−2i2i−2i2i00−i2i2−i2i2−i2i2−i2i20000002−22−2000000
χ412-2-222-2-22-22-22-22200000-2000000002i−2i−2i2i00i2−i2i2−i2−i2i2−i2i20000002−2−22000000
χ422-2-222-2-22-22-22-22200000-2000000002i−2i−2i2i00−i2i2−i2i2i2−i2i2−i2000000−222−2000000
χ432-2-222-2-22-22-22-22200000-200000000−2i2i2i−2i00i2−i2i2−i2−i2i2−i2i2000000−222−2000000
χ442-2-222-2-22-22-22-22200000-200000000−2i2i2i−2i00−i2i2−i2i2i2−i2i2−i20000002−2−22000000
χ4544-44-44-4-44i4i−4i−4i0000−4i4i-44000000000000000000000000000000000000000
χ4644-44-44-4-4−4i−4i4i4i00004i−4i-44000000000000000000000000000000000000000
χ4744-4-4-4-4440000000400000-4004i−4i000000000000000000000000000000000
χ4844-4-4-4-4440000000400000-400−4i4i000000000000000000000000000000000
χ4944-4-4-4-4440000000-40000044-400000000000000000000000000000000000
χ5044-4-4-4-4440000000-4000004-4400000000000000000000000000000000000
χ514-444-4-44-44i−4i−4i4i000000000000000000000002i−2i−2i2i-222-20000000000000000
χ524-444-4-44-44i−4i−4i4i00000000000000000000000−2i2i2i−2i2-2-220000000000000000
χ534-444-4-44-4−4i4i4i−4i000000000000000000000002i−2i−2i2i2-2-220000000000000000
χ544-444-4-44-4−4i4i4i−4i00000000000000000000000−2i2i2i−2i-222-20000000000000000
χ554-4-444-4-444-44-4-44-400000400000000000000000000000000000000000000
χ564-4-444-4-44-44-444-4-400000400000000000000000000000000000000000000
χ57888-88-8-8-8000000000000000000000000000000000000000000000000000
χ588-88-8-88-88000000000000000000000000000000000000000000000000000
χ598-8-8-8888-8000000000000000000000000000000000000000000000000000

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