Finite Group Databasebeta

← Group #178054

Character table — Group #178054

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size1111111144444444448888881616161616161616161616161616161616161616161616161616
order12222222444444444444444444444444444444888888888888
χ111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111-1-1-1-111-1-111-1-11111-1-1-1-1-1-11111-1-1-1-1
χ611111111111111111111-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111
χ711111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-11111
χ811111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1
χ911111111-1-1-1-1111111-1-111-1-1111-11-11-1-1-11-11-111-1-111-1-111-1-1
χ1011111111-1-1-1-1111111-1-111-1-1111-1-11-11-1-1-11-1111-1-1-1-111-1-111
χ1111111111-1-1-1-1111111-1-111-1-1-1-11-11-11-1111-11-1-1-111-1-111-1-111
χ1211111111-1-1-1-1111111-1-111-1-1-1-11-1-11-1111-11-11-1-11111-1-111-1-1
χ1311111111-1-1-1-1111111-1-1-1-11111-111-1-11-1-11-1-11-1-11111-1-1-1-111
χ1411111111-1-1-1-1111111-1-1-1-11111-11-111-1-1-1-111-1-1-111-1-11111-1-1
χ1511111111-1-1-1-1111111-1-1-1-111-1-1-111-1-11111-1-1111-1-1-1-11111-1-1
χ1611111111-1-1-1-1111111-1-1-1-111-1-1-11-111-111-111-111-1-111-1-1-1-111
χ1722222222222222-2-2-2-2-2-222-2-200-220000000000000000000000
χ1822222222222222-2-2-2-2-2-2-2-222002-20000000000000000000000
χ192222222222-2-2-2-222-2-22-200000000002-20000-22000000000000
χ202222222222-2-2-2-222-2-22-20000000000-2200002-2000000000000
χ212222222222-2-2-2-2-2-222-22000000002-20000-2200000000000000
χ222222222222-2-2-2-2-2-222-2200000000-2200002-200000000000000
χ2322222222-2-222-2-222-2-2-220000000000220000-2-2000000000000
χ2422222222-2-222-2-222-2-2-220000000000-2-2000022000000000000
χ2522222222-2-222-2-2-2-2222-200000000220000-2-200000000000000
χ2622222222-2-222-2-2-2-2222-200000000-2-200002200000000000000
χ2722222222-2-2-2-222-2-2-2-222222200-2-20000000000000000000000
χ2822222222-2-2-2-222-2-2-2-222-2-2-2-200220000000000000000000000
χ29444-4-44-4-4000000004-4000000000000000000000000000022−2200
χ30444-4-44-4-4000000004-40000000000000000000000000000−222200
χ31444-4-44-4-400000000-4400000000000000000000000000000022−22
χ32444-4-44-4-400000000-44000000000000000000000000000000−2222
χ3344-44-4-44-40000004-4000000000000000000000000000022−220000
χ3444-44-4-44-40000004-40000000000000000000000000000−22220000
χ3544-44-4-44-4000000-440000000000000000000000000022−22000000
χ3644-44-4-44-4000000-4400000000000000000000000000−2222000000
χ3744-4-44-4-44004-4000000000000000000000000002i−2i2i−2i00000000
χ3844-4-44-4-44004-400000000000000000000000000−2i2i−2i2i00000000
χ3944-4-44-4-4400-44000000000000000000000000002i−2i−2i2i00000000
χ4044-4-44-4-4400-4400000000000000000000000000−2i2i2i−2i00000000
χ414-4444-4-4-400004-4000000004-400000000000000000000000000
χ424-4444-4-4-400004-400000000-4400000000000000000000000000
χ434-4444-4-4-40000-440000004-40000000000000000000000000000
χ444-4444-4-4-40000-44000000-440000000000000000000000000000
χ454-4-4-4444-44i−4i000000000000002-20000002i−2i0000000000000000
χ464-4-4-4444-44i−4i00000000000000-22000000−2i2i0000000000000000
χ474-4-4-4444-4−4i4i000000000000002-2000000−2i2i0000000000000000
χ484-4-4-4444-4−4i4i00000000000000-220000002i−2i0000000000000000
χ498-88-8-8-888000000000000000000000000000000000000000000
χ508-8-88-88-88000000000000000000000000000000000000000000

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