Finite Group Databasebeta

← Group #174921

Character table — Group #174921

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size11111111444444444444888888888161616161616161616161616161616161616161616161616
order12222222444444444444224444444224444444444888888888888
χ111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111-1-1-1-1-1-111-1-11111-1-11111-1-1-1-1-1-1-1-1
χ41111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111-1-11-1-1111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1
χ611111111111111111111-1-11-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111-1-11-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ811111111111111111111-1-11-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1
χ911111111-1-11-1-1-1-11111111-1-1-111-1-11-11-11-111-1-11-111-1-111-1-111-1-1
χ1011111111-1-11-1-1-1-11111111-1-1-111-1-11-11-11-1-1-1111-1-1-111-1-111-1-111
χ1111111111-1-11-1-1-1-11111111-1-1-1-1-111-111-1-1111-1-1-1111-1-1-1-111-1-111
χ1211111111-1-11-1-1-1-11111111-1-1-1-1-111-111-1-11-1-111-11-1-11111-1-111-1-1
χ1311111111-1-11-1-1-1-111111-1-1-11111-1-11-1-11-1111-1-1-11-1-11111-1-1-1-111
χ1411111111-1-11-1-1-1-111111-1-1-11111-1-11-1-11-11-1-111-1111-1-1-1-11111-1-1
χ1511111111-1-11-1-1-1-111111-1-1-111-1-111-11-111-111-1-11-1-1-111-1-11111-1-1
χ1611111111-1-11-1-1-1-111111-1-1-111-1-111-11-111-1-1-1111-111-1-111-1-1-1-111
χ172222222222222-2-2-2-2-2-2200-20000000000220000-2-2000000000000
χ182222222222222-2-2-2-2-2-2200-20000000000-2-2000022000000000000
χ192222222222-2-2-22222-2-2-200-20022-2-2-220000000000000000000000
χ202222222222-2-2-22222-2-2-200-200-2-2222-20000000000000000000000
χ212222222222-2-2-2-2-2-2-222-2222-2-2000000-2200000000000000000000
χ222222222222-2-2-2-2-2-2-222-2-2-22220000002-200000000000000000000
χ2322222222-2-22-2-222-2-2-2-2200200000000002-20000-22000000000000
χ2422222222-2-22-2-222-2-2-2-220020000000000-2200002-2000000000000
χ2522222222-2-2-22222-2-222-222-222000000-2-200000000000000000000
χ2622222222-2-2-22222-2-222-2-2-2-2-2-20000002200000000000000000000
χ2722222222-2-2-222-2-222-2-2-2002002222-2-20000000000000000000000
χ2822222222-2-2-222-2-222-2-2-200200-2-2-2-2220000000000000000000000
χ29444-4-4-4-444-4000000000000000000000000000000000002i−2i2i−2i0000
χ30444-4-4-4-444-400000000000000000000000000000000000−2i2i−2i2i0000
χ31444-4-4-4-44-44000000000000000000000000000000000002i−2i−2i2i0000
χ32444-4-4-4-44-4400000000000000000000000000000000000−2i2i2i−2i0000
χ3344-4-44-44-40004-40000000000000000000000000000000000002i−2i2i−2i
χ3444-4-44-44-40004-4000000000000000000000000000000000000−2i2i−2i2i
χ3544-4-44-44-4000-440000000000000000000000000000000000002i−2i−2i2i
χ3644-4-44-44-4000-44000000000000000000000000000000000000−2i2i2i−2i
χ374-444-4-44-400000004-400000000004i−4i000000000000000000000000
χ384-444-4-44-400000004-40000000000−4i4i000000000000000000000000
χ394-444-4-44-40000000-44000000004i−4i00000000000000000000000000
χ404-444-4-44-40000000-4400000000−4i4i00000000000000000000000000
χ414-44-444-4-4000004i−4i000000000000000000002-22i−2i00000000000000
χ424-44-444-4-4000004i−4i00000000000000000000-22−2i2i00000000000000
χ434-44-444-4-400000−4i4i000000000000000000002-2−2i2i00000000000000
χ444-44-444-4-400000−4i4i00000000000000000000-222i−2i00000000000000
χ454-4-444-4-4400400000000-4000000000000000000000002i2−2i200000000
χ464-4-444-4-4400400000000-400000000000000000000000−2i22i200000000
χ474-4-444-4-4400-400000000400000000000000000000022−220000000000
χ484-4-444-4-4400-4000000004000000000000000000000−22220000000000
χ494-4-4-4-44440000000004-400004-40000000000000000000000000000
χ504-4-4-4-44440000000004-40000-440000000000000000000000000000
χ514-4-4-4-4444000000000-4404-40000000000000000000000000000000
χ524-4-4-4-4444000000000-440-440000000000000000000000000000000
χ5388-88-88-8-8000000000000000000000000000000000000000000000

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