Finite Group Databasebeta

← Group #175919

Character table — Group #175919

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size1111111144444444448888881616161616161616161616161616161616161616161616161616
order12222222224444444444444422444444444444888888888888
χ111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-111-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ4111111111111111111111111-1-1-111-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ51111111111111111111-1-11-1-11-11-1-11-11-1-111111111-1-1-1-1-1-1-1-1
χ61111111111111111111-1-11-1-11-11-1-11-11-1-1-1-1-1-1-1-1-1-111111111
χ71111111111111111111-1-11-1-1-11-1-1-1-11-1111111-1-1-1-11111-1-1-1-1
χ81111111111111111111-1-11-1-1-11-1-1-1-11-111-1-1-1-11111-1-1-1-11111
χ911111111-1-1-1-1111111-111-1-1-111-11-11-1-1-1111-1-111-1-111-1-111-1-1
χ1011111111-1-1-1-1111111-111-1-1-111-11-11-1-1-11-1-111-1-111-1-111-1-111
χ1111111111-1-1-1-1111111-111-1-1-1-1-111-1-1111-111-1-1-1-111-1-11111-1-1
χ1211111111-1-1-1-1111111-111-1-1-1-1-111-1-1111-1-1-11111-1-111-1-1-1-111
χ1311111111-1-1-1-1111111-1-1-1-1111-1-1-1111-11-111-1-111-1-1-1-111-1-111
χ1411111111-1-1-1-1111111-1-1-1-1111-1-1-1111-11-1-1-111-1-11111-1-111-1-1
χ1511111111-1-1-1-1111111-1-1-1-111-111-11-1-11-1111-1-1-1-11111-1-1-1-111
χ1611111111-1-1-1-1111111-1-1-1-111-111-11-1-11-11-1-11111-1-1-1-11111-1-1
χ17222222222222-222-2-2-2-200-20020-200-202000000000000000000
χ18222222222222-222-2-2-2-200-200-2020020-2000000000000000000
χ192222222222-2-22-2-2-2-22222-2-2-2000-22000000000000000000000
χ202222222222-2-22-2-2-2-222-2-2-2220002-2000000000000000000000
χ212222222222-2-2-2-2-222-2-20020002000020-2-20000000000000000
χ222222222222-2-2-2-2-222-2-2002000-20000-20220000000000000000
χ2322222222-2-2222-2-2-2-22-222222000-2-2000000000000000000000
χ2422222222-2-2222-2-2-2-22-2-2-22-2-200022000000000000000000000
χ2522222222-2-222-2-2-222-2200-200020000-202-20000000000000000
χ2622222222-2-222-2-2-222-2200-2000-2000020-220000000000000000
χ2722222222-2-2-2-2-222-2-2-220020020200-20-2000000000000000000
χ2822222222-2-2-2-2-222-2-2-2200200-20-200202000000000000000000
χ29444-4-4-4-44000004-40000000000000000000000000000000002i2−2i2
χ30444-4-4-4-44000004-4000000000000000000000000000000000−2i22i2
χ31444-4-4-4-4400000-4400000000000000000000000000000002i2−2i200
χ32444-4-4-4-4400000-440000000000000000000000000000000−2i22i200
χ3344-44-4-44-400000004-4000000000000000000000002i2−2i200000000
χ3444-44-4-44-400000004-400000000000000000000000−2i22i200000000
χ3544-44-4-44-40000000-440000000000000000000002i2−2i20000000000
χ3644-44-4-44-40000000-44000000000000000000000−2i22i20000000000
χ374-44-44-44-4004-400000000000000000000002i−2i2i−2i000000000000
χ384-44-44-44-4004-40000000000000000000000−2i2i−2i2i000000000000
χ394-44-44-44-400-4400000000000000000000002i−2i−2i2i000000000000
χ404-44-44-44-400-440000000000000000000000−2i2i2i−2i000000000000
χ414-4-444-4-44000040000-400004i−4i00000000000000000000000000
χ424-4-444-4-44000040000-40000−4i4i00000000000000000000000000
χ434-4-444-4-440000-40000404-400000000000000000000000000000
χ444-4-444-4-440000-4000040-4400000000000000000000000000000
χ454-4-4-4-44444-4000000000000000000000000000000002-22-20000
χ464-4-4-4-44444-400000000000000000000000000000000-22-220000
χ474-4-4-4-4444-44000000000000000000000000000000002-2-220000
χ484-4-4-4-4444-4400000000000000000000000000000000-222-20000
χ4988-8-888-8-8000000000000000000000000000000000000000000
χ508-888-88-8-8000000000000000000000000000000000000000000

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