Finite Group Databasebeta

← Group #178221

Character table — Group #178221

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size1111111144444444448888881616161616161616161616161616161616161616161616161616
order12222222444444444444444444444444444444888888888888
χ111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-1-111-1-1-11111-1-1-1-11111-1-1-1-1
χ4111111111111111111111111-1-1-1-1-111-1-1-1-1-1-1-11111-1-1-1-11111
χ51111111111111111111-1-1-1-11111-1-1-1-11-1-11111-1-1-1-1-1-1-1-11111
χ61111111111111111111-1-1-1-11111-1-1-1-11-1-1-1-1-1-111111111-1-1-1-1
χ71111111111111111111-1-1-1-11-1-1-111-1-1-11111111111-1-1-1-1-1-1-1-1
χ81111111111111111111-1-1-1-11-1-1-111-1-1-111-1-1-1-1-1-1-1-111111111
χ911111111-1-11-1-111111-111-1-1-11-1-11-11-111-111-1-111-1-111-1-111-1-1
χ1011111111-1-11-1-111111-111-1-1-11-1-11-11-111-1-1-111-1-111-1-111-1-111
χ1111111111-1-11-1-111111-111-1-1-1-111-111-1-1-1111-1-1-1-11111-1-1-1-111
χ1211111111-1-11-1-111111-111-1-1-1-111-111-1-1-11-1-11111-1-1-1-11111-1-1
χ1311111111-1-11-1-111111-1-1-111-11-1-1-11-111-1111-1-1-1-111-1-11111-1-1
χ1411111111-1-11-1-111111-1-1-111-11-1-1-11-111-11-1-11111-1-111-1-1-1-111
χ1511111111-1-11-1-111111-1-1-111-1-1111-1-11-11-111-1-111-1-1-1-111-1-111
χ1611111111-1-11-1-111111-1-1-111-1-1111-1-11-11-1-1-111-1-11111-1-111-1-1
χ1722222222222-2-2-2-2-22-2-20000222-20000-2000000000000000000
χ1822222222222-2-2-2-2-22-2-200002-2-2200002000000000000000000
χ192222222222-2222-2-2-22-222-2-2-200000-220000000000000000000
χ202222222222-2222-2-2-22-2-2-222-2000002-20000000000000000000
χ212222222222-2-2-2-222-2-220000-20002-2000-220000000000000000
χ222222222222-2-2-2-222-2-220000-2000-220002-20000000000000000
χ2322222222-2-2222-2-2-22-220000-22-220000-2000000000000000000
χ2422222222-2-2222-2-2-22-220000-2-22-200002000000000000000000
χ2522222222-2-2-222-222-2-2-20000200022000-2-20000000000000000
χ2622222222-2-2-222-222-2-2-200002000-2-2000220000000000000000
χ2722222222-2-2-2-2-22-2-2-2222222200000-2-20000000000000000000
χ2822222222-2-2-2-2-22-2-2-222-2-2-2-2200000220000000000000000000
χ29444-4-44-4-4000004000-40004-4000000000000000000000000000
χ30444-4-44-4-4000004000-4000-44000000000000000000000000000
χ31444-4-44-4-400000-4000404i−4i00000000000000000000000000000
χ32444-4-44-4-400000-400040−4i4i00000000000000000000000000000
χ3344-44-4-44-400400000-400000000000000000000022−220000000000
χ3444-44-4-44-400400000-4000000000000000000000−22220000000000
χ3544-44-4-44-400-4000004000000000000000000000002i2−2i200000000
χ3644-44-4-44-400-400000400000000000000000000000−2i22i200000000
χ374-44-4-4-4440000004-40000000000000000000000000000002i2−2i200
χ384-44-4-4-4440000004-4000000000000000000000000000000−2i22i200
χ394-44-4-4-444000000-44000000000000000000000000000000002i2−2i2
χ404-44-4-4-444000000-4400000000000000000000000000000000−2i22i2
χ414-4-44-44-440004i−4i0000000000000000000002i−2i2-2000000000000
χ424-4-44-44-440004i−4i000000000000000000000−2i2i-22000000000000
χ434-4-44-44-44000−4i4i0000000000000000000002i−2i-22000000000000
χ444-4-44-44-44000−4i4i000000000000000000000−2i2i2-2000000000000
χ454-4-4-4444-44i−4i000000000000000000000000000000002-22i−2i0000
χ464-4-4-4444-44i−4i00000000000000000000000000000000-22−2i2i0000
χ474-4-4-4444-4−4i4i000000000000000000000000000000002-2−2i2i0000
χ484-4-4-4444-4−4i4i00000000000000000000000000000000-222i−2i0000
χ4988-8-88-8-88000000000000000000000000000000000000000000
χ508-8888-8-8-8000000000000000000000000000000000000000000

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