Finite Group Databasebeta

← Group #103821

Character table — Group #103821

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47
size1111111144444444444481616161616161616161616161616161616161616161616163232
order12222222444444444444422444444888888888888888844
χ111111111111111111111111111111111111111111111111
χ211111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
χ31111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1
χ41111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ5111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111
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
χ9222222222222-2-2-2-2-2-222-2000022-2-2000000000000000000
χ10222222222222-2-2-2-2-2-222-20000-2-222000000000000000000
χ11222222222-2-2-22222-2-22-2-20000000000000000000000002-2
χ12222222222-2-2-22222-2-22-2-2000000000000000000000000-22
χ13222222222-2-2-2-2-2-2-2222-220000000000000000000022-2-200
χ14222222222-2-2-2-2-2-2-2222-2200000000000000000000-2-22200
χ1522222222-222-222-2-2-2-2-2-22000000002i2i−2i−2i00000000000000
χ1622222222-222-222-2-2-2-2-2-2200000000−2i−2i2i2i00000000000000
χ1722222222-222-2-2-22222-2-2-200000000000022-2-20000000000
χ1822222222-222-2-2-22222-2-2-2000000000000-2-2220000000000
χ1922222222-2-2-2222-2-222-22-2000000000000000022-2-2000000
χ2022222222-2-2-2222-2-222-22-20000000000000000-2-222000000
χ2122222222-2-2-22-2-222-2-2-22222-2-20000000000000000000000
χ2222222222-2-2-22-2-222-2-2-222-2-2220000000000000000000000
χ2322-222-2-2-222-2-2000000-2200000002-2i2−i2i2−i2i2−i2i2−i20000000000
χ2422-222-2-2-222-2-2000000-2200000002-2−i2i2−i2i2−i2i2−i2i20000000000
χ2522-222-2-2-222-2-2000000-220000000-22i2−i2i2−i2−i2i2−i2i20000000000
χ2622-222-2-2-222-2-2000000-220000000-22−i2i2−i2i2i2−i2i2−i20000000000
χ2722-222-2-2-2-22-220000002-2000002i−2i002−2−22i2−i2−i2i20000000000
χ2822-222-2-2-2-22-220000002-2000002i−2i00−222−2−i2i2i2−i20000000000
χ2922-222-2-2-2-22-220000002-200000−2i2i002−2−22−i2i2i2−i20000000000
χ3022-222-2-2-2-22-220000002-200000−2i2i00−222−2i2−i2−i2i20000000000
χ3144-444-4-4-44-444000000-4-4000000000000000000000000000
χ3244-444-4-4-4-4-44-400000044000000000000000000000000000
χ3344-4-4-444-40000004-400000000000000000000000002i−2i2i−2i00
χ3444-4-4-444-40000004-40000000000000000000000000−2i2i−2i2i00
χ3544-4-4-444-4000000-4400000000000000000000000002i−2i−2i2i00
χ3644-4-4-444-4000000-440000000000000000000000000−2i2i2i−2i00
χ374-444-44-4-400004-400000000000000000000000002i2−2i2000000
χ384-444-44-4-400004-40000000000000000000000000−2i22i2000000
χ394-444-44-4-40000-44000000000000000000000002i2−2i200000000
χ404-444-44-4-40000-4400000000000000000000000−2i22i200000000
χ414-44-44-44-4000000004i−4i0002-22i−2i0000000000000000000000
χ424-44-44-44-4000000004i−4i000-22−2i2i0000000000000000000000
χ434-44-44-44-400000000−4i4i0002-2−2i2i0000000000000000000000
χ444-44-44-44-400000000−4i4i000-222i−2i0000000000000000000000
χ45888-8-8-8-88000000000000000000000000000000000000000
χ468-8-88-8-888000000000000000000000000000000000000000
χ478-8-8-888-88000000000000000000000000000000000000000

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