Finite Group Databasebeta

← Group #175208

Character table — Group #175208

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size11111111444444444444888888888161616161616161616161616161616161616161616161616
order12222222444444444444444444444444444444444888888888888
χ111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111-1-1-1-111111-1-1-1-11-1-1111111-1-1-1-1-1-1-1-1
χ411111111111111111111111-1-1-1-111-1-11-1-1-1-11-1-1-1-1-1-1-1-111111111
χ511111111111111111111-1-111111-1-111-111-1-1-1-1-111-1-1-1-11111-1-1-1-1
χ611111111111111111111-1-111111-1-1-1-1-111-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111-1-11-1-1-1-1-1-111-1-1-111-11111-1-1-1-1-1-1-1-11111
χ811111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-111-111-1-111111111-1-1-1-1
χ911111111-1-1-1-11-1-11111111-111-1-1-1-11111-11-1-11-1-1-111-1-111-1-111-1-1
χ1011111111-1-1-1-11-1-11111111-111-1-1-1-1-1-111-11-1-11-111-1-111-1-111-1-111
χ1111111111-1-1-1-11-1-11111111-1-1-111-1-1111-11-11-1-11-1-111-1-1-1-111-1-111
χ1211111111-1-1-1-11-1-11111111-1-1-111-1-1-1-11-11-11-1-1111-1-11111-1-111-1-1
χ1311111111-1-1-1-11-1-111111-1-1-111-1-11111-11-1-111-11-1-1-1-11111-1-1-1-111
χ1411111111-1-1-1-11-1-111111-1-1-111-1-111-1-1-11-1-111-111111-1-1-1-11111-1-1
χ1511111111-1-1-1-11-1-111111-1-1-1-1-1111111-1-111-111-1-1-1-1-111-1-11111-1-1
χ1611111111-1-1-1-11-1-111111-1-1-1-1-11111-1-1-1-111-111-11111-1-111-1-1-1-111
χ172222222222222-2-2-2-2-2-2200-200000000000220-2-200000000000000
χ182222222222222-2-2-2-2-2-2200-200000000000-2-202200000000000000
χ192222222222-2-2-222-2-222-222-200002200-20000-20000000000000000
χ202222222222-2-2-222-2-222-2-2-2-20000-2-2002000020000000000000000
χ212222222222-2-2-2-2-222-2-2-2002222200000-2-20000000000000000000
χ222222222222-2-2-2-2-222-2-2-2002-2-2-2-200000220000000000000000000
χ2322222222-2-222-22222-2-2-200-222-2-200000-220000000000000000000
χ2422222222-2-222-22222-2-2-200-2-2-222000002-20000000000000000000
χ2522222222-2-222-2-2-2-2-222-22220000-2-200-2000020000000000000000
χ2622222222-2-222-2-2-2-2-222-2-2-220000220020000-20000000000000000
χ2722222222-2-2-2-2222-2-2-2-22002000000000002-20-2200000000000000
χ2822222222-2-2-2-2222-2-2-2-2200200000000000-2202-200000000000000
χ29444-4-44-4-44-40000000000000000000000000000000000000002-22-2
χ30444-4-44-4-44-4000000000000000000000000000000000000000-22-22
χ31444-4-44-4-4-440000000000000000000000000000000000000002-2-22
χ32444-4-44-4-4-44000000000000000000000000000000000000000-222-2
χ3344-444-4-4-400000004-4000000004-400000000000000000000000000
χ3444-444-4-4-400000004-400000000-4400000000000000000000000000
χ3544-444-4-4-40000000-440000004-40000000000000000000000000000
χ3644-444-4-4-40000000-44000000-440000000000000000000000000000
χ3744-4-4-4-4440000000004-4000000004i−4i000000000000000000000000
χ3844-4-4-4-4440000000004-400000000−4i4i000000000000000000000000
χ3944-4-4-4-444000000000-4404i−4i0000000000000000000000000000000
χ4044-4-4-4-444000000000-440−4i4i0000000000000000000000000000000
χ414-444-4-4-44004-40000000000000000000000000000000002i−2i2i−2i0000
χ424-444-4-4-44004-4000000000000000000000000000000000−2i2i−2i2i0000
χ434-444-4-4-4400-440000000000000000000000000000000002i−2i−2i2i0000
χ444-444-4-4-4400-44000000000000000000000000000000000−2i2i2i−2i0000
χ454-4-44-444-4000004i−4i000000000000002-2000000002i−2i000000000000
χ464-4-44-444-4000004i−4i00000000000000-2200000000−2i2i000000000000
χ474-4-44-444-400000−4i4i000000000000002-200000000−2i2i000000000000
χ484-4-44-444-400000−4i4i00000000000000-22000000002i−2i000000000000
χ494-4-4-444-4400004000000-4000000000000000000000002i2−2i200000000
χ504-4-4-444-4400004000000-400000000000000000000000−2i22i200000000
χ514-4-4-444-440000-4000000400000000000000000000022−220000000000
χ524-4-4-444-440000-40000004000000000000000000000−22220000000000
χ538-88-88-88-8000000000000000000000000000000000000000000000

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