Finite Group Databasebeta

← Group #103809

Character table — Group #103809

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47
size1111111144444444444481616161616161616161616161616161616161616161616163232
order12222222444444444444422444444888888888888888844
χ111111111111111111111111111111111111111111111111
χ211111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
χ311111111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1
χ411111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ5111111111111111111111-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ7111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111
χ8111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1
χ922222222222-2-2-222-2-22-2-20000000000000000000000002-2
χ1022222222222-2-2-222-2-22-2-2000000000000000000000000-22
χ112222222222-22-2-2-2-222-22-2000000000000000022-2-2000000
χ122222222222-22-2-2-2-222-22-20000000000000000-2-222000000
χ132222222222-2-222-2-2-2-2-2-22000000002i2i−2i−2i00000000000000
χ142222222222-2-222-2-2-2-2-2-2200000000−2i−2i2i2i00000000000000
χ1522222222-2-22222-2-2-2-222-2002200-2-2000000000000000000
χ1622222222-2-22222-2-2-2-222-200-2-20022000000000000000000
χ1722222222-2-22-2-2-2-2-2222-220000000000000000000022-2-200
χ1822222222-2-22-2-2-2-2-2222-2200000000000000000000-2-22200
χ1922222222-2-2-22-2-222-2-2-2222200-2-200000000000000000000
χ2022222222-2-2-22-2-222-2-2-222-2-2002200000000000000000000
χ2122222222-2-2-2-2222222-2-2-200000000000022-2-20000000000
χ2222222222-2-2-2-2222222-2-2-2000000000000-2-2220000000000
χ2322-2-2-22-2200222-20000-2-20002i−2i0000i2−i2i2−i22−22−20000000000
χ2422-2-2-22-2200222-20000-2-20002i−2i0000−i2i2−i2i2−22−220000000000
χ2522-2-2-22-2200222-20000-2-2000−2i2i0000i2−i2i2−i2−22−220000000000
χ2622-2-2-22-2200222-20000-2-2000−2i2i0000−i2i2−i2i22−22−20000000000
χ2722-2-2-22-2200-2-22-200002200000002-22−2−222−2−220000000000
χ2822-2-2-22-2200-2-22-200002200000002-2−222−2−222−20000000000
χ2922-2-2-22-2200-2-22-20000220000000-222−2−22−222−20000000000
χ3022-2-2-22-2200-2-22-20000220000000-22−222−22−2−220000000000
χ314444-4-4-4-40000004-400000000000000000000000002-22-200
χ324444-4-4-4-40000004-40000000000000000000000000-22-2200
χ334444-4-4-4-4000000-4400000000000000000000000002-2-2200
χ344444-4-4-4-4000000-440000000000000000000000000-222-200
χ3544-4-4-44-44004-4-440000-44000000000000000000000000000
χ3644-4-4-44-4400-44-4400004-4000000000000000000000000000
χ374-44-4-444-4000000004i−4i0002-2002i−2i00000000000000000000
χ384-44-4-444-4000000004i−4i000-2200−2i2i00000000000000000000
χ394-44-4-444-400000000−4i4i0002-200−2i2i00000000000000000000
χ404-44-4-444-400000000−4i4i000-22002i−2i00000000000000000000
χ414-4-44-4-4444-40000000000000000000000000000022−22000000
χ424-4-44-4-4444-400000000000000000000000000000−2222000000
χ434-4-44-4-444-4400000000000000000000000000022−2200000000
χ444-4-44-4-444-44000000000000000000000000000−222200000000
χ4588-8-88-88-8000000000000000000000000000000000000000
χ468-88-88-8-88000000000000000000000000000000000000000
χ478-8-8888-8-8000000000000000000000000000000000000000

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