Finite Group Databasebeta

← Group #178056

Character table — Group #178056

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size1111111144444444448888881616161616161616161616161616161616161616161616161616
order12222222444444444444444444444444444444888888888888
χ111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111-1-1-1-11111-1-111-1-111-1-1-1-1-1-11111-1-1-1-1
χ611111111111111111111-1-1-1-11111-1-1-1-111-1-111-1-1-1-1-1-1-1-11111
χ711111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111
χ811111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-1
χ911111111-1-1-1-1111111-1-111-1-111-1-11-11-11-11-11-111-1-111-1-111-1-1
χ1011111111-1-1-1-1111111-1-111-1-111-1-11-1-11-11-11-1111-1-1-1-111-1-111
χ1111111111-1-1-1-1111111-1-111-1-1-1-1111-11-11-11-11-1-1-111-1-111-1-111
χ1211111111-1-1-1-1111111-1-111-1-1-1-1111-1-11-11-11-11-1-11111-1-111-1-1
χ1311111111-1-1-1-1111111-1-1-1-11111-1-1-111-1-111-1-11-1-11111-1-1-1-111
χ1411111111-1-1-1-1111111-1-1-1-11111-1-1-11-111-1-111-1-1-111-1-11111-1-1
χ1511111111-1-1-1-1111111-1-1-1-111-1-111-111-1-111-1-1111-1-1-1-11111-1-1
χ1611111111-1-1-1-1111111-1-1-1-111-1-111-11-111-1-111-111-1-111-1-1-1-111
χ1722222222222222-2-2-2-2-2-222-2-20000-2200000000000000000000
χ1822222222222222-2-2-2-2-2-2-2-22200002-200000000000000000000
χ192222222222-2-2-2-222-2-22-20000000000002200-2-2000000000000
χ202222222222-2-2-2-222-2-22-2000000000000-2-20022000000000000
χ212222222222-2-2-2-2-2-222-2200000000002200-2-200000000000000
χ222222222222-2-2-2-2-2-222-220000000000-2-2002200000000000000
χ2322222222-2-222-2-222-2-2-220000000000002-200-22000000000000
χ2422222222-2-222-2-222-2-2-22000000000000-22002-2000000000000
χ2522222222-2-222-2-2-2-2222-200000000002-200-2200000000000000
χ2622222222-2-222-2-2-2-2222-20000000000-22002-200000000000000
χ2722222222-2-2-2-222-2-2-2-22222220000-2-200000000000000000000
χ2822222222-2-2-2-222-2-2-2-222-2-2-2-200002200000000000000000000
χ294444-4-4-4-400004-4000000004-400000000000000000000000000
χ304444-4-4-4-400004-400000000-4400000000000000000000000000
χ314444-4-4-4-40000-440000004-40000000000000000000000000000
χ324444-4-4-4-40000-44000000-440000000000000000000000000000
χ3344-4-4-44-44000000004-40000000000000000000000000000002i2−2i2
χ3444-4-4-44-44000000004-4000000000000000000000000000000−2i22i2
χ3544-4-4-44-4400000000-4400000000000000000000000000002i2−2i200
χ3644-4-4-44-4400000000-440000000000000000000000000000−2i22i200
χ374-44-4-4-4440000004-400000000000000000000000000002i2−2i20000
χ384-44-4-4-4440000004-40000000000000000000000000000−2i22i20000
χ394-44-4-4-444000000-44000000000000000000000000002i2−2i2000000
χ404-44-4-4-444000000-4400000000000000000000000000−2i22i2000000
χ414-4-444-4-444-400000000000000000000000000002i−2i2i−2i00000000
χ424-4-444-4-444-40000000000000000000000000000−2i2i−2i2i00000000
χ434-4-444-4-44-4400000000000000000000000000002i−2i−2i2i00000000
χ444-4-444-4-44-440000000000000000000000000000−2i2i2i−2i00000000
χ454-4-44-444-4004i−4i0000000000002-22i−2i0000000000000000000000
χ464-4-44-444-4004i−4i000000000000-22−2i2i0000000000000000000000
χ474-4-44-444-400−4i4i0000000000002-2−2i2i0000000000000000000000
χ484-4-44-444-400−4i4i000000000000-222i−2i0000000000000000000000
χ4988-8-88-88-8000000000000000000000000000000000000000000
χ508-88-888-8-8000000000000000000000000000000000000000000

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