Finite Group Databasebeta

← Group #174995

Character table — Group #174995

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size11111111444444444444888888888161616161616161616161616161616161616161616161616
order12222222444444444444444444444444444444444888888888888
χ111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111-1-1-1-11-1-1-1-1111-1-1111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111-1-11-1-11111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1
χ611111111111111111111-1-11-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111
χ711111111111111111111-1-11-1-1-1-1-1-1-11111-111-1-111-1-1-1-1-1-1-1-11111
χ811111111111111111111-1-11-1-1-1-1-1-1-11111-1-1-1-1-1-1-111111111-1-1-1-1
χ911111111-1-1-1-11-1-11111111-1-1-111-1-1-111-1-11111-1-1-111-1-111-1-111-1-1
χ1011111111-1-1-1-11-1-11111111-1-1-111-1-1-111-1-11-1-11-111-1-111-1-111-1-111
χ1111111111-1-1-1-11-1-11111111-1-1-1-1-111-1-1-111111-11-1-111-1-1-1-111-1-111
χ1211111111-1-1-1-11-1-11111111-1-1-1-1-111-1-1-1111-1-1-1111-1-11111-1-111-1-1
χ1311111111-1-1-1-11-1-111111-1-1-11111-1-11-1-111-1111-1-1-1-1-11111-1-1-1-111
χ1411111111-1-1-1-11-1-111111-1-1-11111-1-11-1-111-1-1-11-11111-1-1-1-11111-1-1
χ1511111111-1-1-1-11-1-111111-1-1-111-1-111111-1-1-111-11-1-1-1-111-1-11111-1-1
χ1611111111-1-1-1-11-1-111111-1-1-111-1-111111-1-1-1-1-1-111111-1-111-1-1-1-111
χ17222222222222-2-2-222-2-2-200-20022-2-200000000-2200000000000000
χ18222222222222-2-2-222-2-2-200-200-2-222000000002-200000000000000
χ192222222222-2-2222-2-2-2-2200-200000002-22-20000000000000000000
χ202222222222-2-2222-2-2-2-2200-20000000-22-220000000000000000000
χ212222222222-2-2-2-2-2-2-222-2222-2-2000020000-2000000000000000000
χ222222222222-2-2-2-2-2-2-222-2-2-22220000-200002000000000000000000
χ2322222222-2-2222-2-2-2-2-2-2200200000002-2-220000000000000000000
χ2422222222-2-2222-2-2-2-2-2-220020000000-222-20000000000000000000
χ2522222222-2-222-222-2-222-222-2220000-20000-2000000000000000000
χ2622222222-2-222-222-2-222-2-2-2-2-2-20000200002000000000000000000
χ2722222222-2-2-2-2-22222-2-2-200200222200000000-2-200000000000000
χ2822222222-2-2-2-2-22222-2-2-200200-2-2-2-2000000002200000000000000
χ294444-4-4-4-44-4000000000000000000000000000000000002-22-20000
χ304444-4-4-4-44-400000000000000000000000000000000000-22-220000
χ314444-4-4-4-4-44000000000000000000000000000000000002-2-220000
χ324444-4-4-4-4-4400000000000000000000000000000000000-222-20000
χ3344-4-444-4-400004000000-40000000000000000000000022−2200000000
χ3444-4-444-4-400004000000-400000000000000000000000−222200000000
χ3544-4-444-4-40000-400000040000000000000000000002i2−2i20000000000
χ3644-4-444-4-40000-40000004000000000000000000000−2i22i20000000000
χ3744-4-4-4-4440000000004-400004i−4i0000000000000000000000000000
χ3844-4-4-4-4440000000004-40000−4i4i0000000000000000000000000000
χ3944-4-4-4-444000000000-4404i−4i0000000000000000000000000000000
χ4044-4-4-4-444000000000-440−4i4i0000000000000000000000000000000
χ414-44-4-44-44000004-400000000000000000000000000000000002i−2i2i−2i
χ424-44-4-44-44000004-40000000000000000000000000000000000−2i2i−2i2i
χ434-44-4-44-4400000-4400000000000000000000000000000000002i−2i−2i2i
χ444-44-4-44-4400000-440000000000000000000000000000000000−2i2i2i−2i
χ454-4-444-4-4400000004-400000000004i−4i000000000000000000000000
χ464-4-444-4-4400000004-40000000000−4i4i000000000000000000000000
χ474-4-444-4-440000000-44000000004i−4i00000000000000000000000000
χ484-4-444-4-440000000-4400000000−4i4i00000000000000000000000000
χ494-4-44-444-4004i−4i000000000000000000000002-2002i−2i000000000000
χ504-4-44-444-4004i−4i00000000000000000000000-2200−2i2i000000000000
χ514-4-44-444-400−4i4i000000000000000000000002-200−2i2i000000000000
χ524-4-44-444-400−4i4i00000000000000000000000-22002i−2i000000000000
χ538-88-88-88-8000000000000000000000000000000000000000000000

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