Finite Group Databasebeta

← Group #175354

Character table — Group #175354

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size11111111444444444444888888888161616161616161616161616161616161616161616161616
order12222222444444444444224444444224444444444888888888888
χ111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111-1-1-1-11-1-1-11-1-111-111-1-1-1-1-1-1-1-11111
χ41111111111111111111111111-1-1-1-11-1-1-11-1-1-1-1-1-1-111111111-1-1-1-1
χ511111111111111111111-1-11-1-11111-111-1-1-1-111-1111111-1-1-1-1-1-1-1-1
χ611111111111111111111-1-11-1-11111-111-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ711111111111111111111-1-11-1-1-1-1-1-1-1-1-11-11111111-1-1-1-11111-1-1-1-1
χ811111111111111111111-1-11-1-1-1-1-1-1-1-1-11-111-1-11-1-11111-1-1-1-11111
χ911111111-1-1-1-1-1-111111111-1-1-111-1-1-11-1-111-1111-1-111-1-111-1-111-1-1
χ1011111111-1-1-1-1-1-111111111-1-1-111-1-1-11-1-111-1-1-1111-1-111-1-111-1-111
χ1111111111-1-1-1-1-1-111111111-1-1-1-1-111-1-1111-1111-1-1-1-1-111-1-11111-1-1
χ1211111111-1-1-1-1-1-111111111-1-1-1-1-111-1-1111-11-1-1-11111-1-111-1-1-1-111
χ1311111111-1-1-1-1-1-1111111-1-1-11111-1-111-11-1-1111-1-1-111-1-1-1-111-1-111
χ1411111111-1-1-1-1-1-1111111-1-1-11111-1-111-11-1-11-1-1-111-1-11111-1-111-1-1
χ1511111111-1-1-1-1-1-1111111-1-1-111-1-1111-11-1-11-1111-1-1-1-11111-1-1-1-111
χ1611111111-1-1-1-1-1-1111111-1-1-111-1-1111-11-1-11-1-1-111111-1-1-1-11111-1-1
χ17222222222222-2-22-2-2-2-2222-2220000-2000-20000000000000000000
χ18222222222222-2-22-2-2-2-22-2-2-2-2-20000200020000000000000000000
χ192222222222-2-222-222-2-2-200-200000000020-2-200200000000000000
χ202222222222-2-222-222-2-2-200-2000000000-202200-200000000000000
χ212222222222-2-2-2-2-2-2-222-20020022220-2-2000000000000000000000
χ222222222222-2-2-2-2-2-2-222-200200-2-2-2-2022000000000000000000000
χ2322222222-2-22222-2-2-222-200-20022-2-20-22000000000000000000000
χ2422222222-2-22222-2-2-222-200-200-2-22202-2000000000000000000000
χ2522222222-2-222-2-2-222-2-2-2002000000000202-200-200000000000000
χ2622222222-2-222-2-2-222-2-2-2002000000000-20-2200200000000000000
χ2722222222-2-2-2-2222-2-2-2-22222-2-200002000-20000000000000000000
χ2822222222-2-2-2-2222-2-2-2-22-2-22220000-200020000000000000000000
χ29444-4-4-4-44004i−4i0000000000000000000000002i−2i02-2000000000000
χ30444-4-4-4-44004i−4i000000000000000000000000−2i2i0-22000000000000
χ31444-4-4-4-4400−4i4i0000000000000000000000002i−2i0-22000000000000
χ32444-4-4-4-4400−4i4i000000000000000000000000−2i2i02-2000000000000
χ3344-444-4-4-400000004-400000000000000000000000000000000002i2−2i2
χ3444-444-4-4-400000004-40000000000000000000000000000000000−2i22i2
χ3544-444-4-4-40000000-44000000000000000000000000000000002i2−2i200
χ3644-444-4-4-40000000-4400000000000000000000000000000000−2i22i200
χ3744-4-4-444-44i−4i000000000000000000000000000000000002i−2i2-20000
χ3844-4-4-444-44i−4i00000000000000000000000000000000000−2i2i-220000
χ3944-4-4-444-4−4i4i000000000000000000000000000000000002i−2i-220000
χ4044-4-4-444-4−4i4i00000000000000000000000000000000000−2i2i2-20000
χ414-444-44-4-40000000004-4000000004i−4i000000000000000000000000
χ424-444-44-4-40000000004-400000000−4i4i000000000000000000000000
χ434-444-44-4-4000000000-440000004i−4i00000000000000000000000000
χ444-444-44-4-4000000000-44000000−4i4i00000000000000000000000000
χ454-44-44-44-400004-40000000000000000000000000002i−2i2i−2i00000000
χ464-44-44-44-400004-4000000000000000000000000000−2i2i−2i2i00000000
χ474-44-44-44-40000-440000000000000000000000000002i−2i−2i2i00000000
χ484-44-44-44-40000-44000000000000000000000000000−2i2i2i−2i00000000
χ494-4-4-444-4400000040000-40004i−4i0000000000000000000000000000
χ504-4-4-444-4400000040000-4000−4i4i0000000000000000000000000000
χ514-4-4-444-44000000-4000044-40000000000000000000000000000000
χ524-4-4-444-44000000-400004-440000000000000000000000000000000
χ538-8-88-8-888000000000000000000000000000000000000000000000

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