Finite Group Databasebeta

← Group #178164

Character table — Group #178164

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size1111111144444444448888881616161616161616161616161616161616161616161616161616
order12222222224444444422444444444444444444888888888888
χ111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-1-1-11-1-111111-1-1-1-1-1-1-1-11111
χ4111111111111111111111111-1-1-1-1-1-11-1-11-1-1-1-111111111-1-1-1-1
χ5111111111111111111-1-111-1-11-11-11-1-11-1-111111111-1-1-1-1-1-1-1-1
χ6111111111111111111-1-111-1-11-11-11-1-11-1-1-1-1-1-1-1-1-1-111111111
χ7111111111111111111-1-111-1-1-11-11-11-1-11-11111-1-1-1-11111-1-1-1-1
χ8111111111111111111-1-111-1-1-11-11-11-1-11-1-1-1-1-11111-1-1-1-11111
χ911111111-1-11-1-11111111-1-1-1-111-1-1-1-1-111111-1-111-1-111-1-111-1-1
χ1011111111-1-11-1-11111111-1-1-1-111-1-1-1-1-1111-1-111-1-111-1-111-1-111
χ1111111111-1-11-1-11111111-1-1-1-1-1-11111-1-1-1111-1-1-1-111-1-11111-1-1
χ1211111111-1-11-1-11111111-1-1-1-1-1-11111-1-1-11-1-11111-1-111-1-1-1-111
χ1311111111-1-11-1-111111-1-1-1-1111-1-11-1111-1-111-1-111-1-1-1-111-1-111
χ1411111111-1-11-1-111111-1-1-1-1111-1-11-1111-1-1-1-111-1-11111-1-111-1-1
χ1511111111-1-11-1-111111-1-1-1-111-111-11-11-11-111-1-1-1-11111-1-1-1-111
χ1611111111-1-11-1-111111-1-1-1-111-111-11-11-11-1-1-11111-1-1-1-11111-1-1
χ172222222222222-2-2-2-2222-2-2-2-2000000200-20000000000000000
χ182222222222222-2-2-2-22-2-2-2-222000000-20020000000000000000
χ192222222222-2-2-222-2-2-2002-200020-20200-200000000000000000
χ202222222222-2-2-222-2-2-2002-2000-2020-200200000000000000000
χ212222222222-2-2-2-2-222-200-220020-20200-2000000000000000000
χ222222222222-2-2-2-2-222-200-2200-2020-2002000000000000000000
χ2322222222-2-22-2-2-2-2-2-22222222000000-200-20000000000000000
χ2422222222-2-22-2-2-2-2-2-22-2-222-2-200000020020000000000000000
χ2522222222-2-2-22222-2-2-200-220002020-200-200000000000000000
χ2622222222-2-2-22222-2-2-200-22000-20-20200200000000000000000
χ2722222222-2-2-222-2-222-2002-2002020-200-2000000000000000000
χ2822222222-2-2-222-2-222-2002-200-20-202002000000000000000000
χ29444-4-4-44-4004000000-44-4000000000000000000000000000000
χ30444-4-4-44-4004000000-4-44000000000000000000000000000000
χ31444-4-4-44-400-4000000400004i−4i00000000000000000000000000
χ32444-4-4-44-400-400000040000−4i4i00000000000000000000000000
χ3344-44-4-4-4400000004-40000000000000000000000000002i2−2i20000
χ3444-44-4-4-4400000004-4000000000000000000000000000−2i22i20000
χ3544-44-4-4-440000000-4400000000000000000000000002i2−2i2000000
χ3644-44-4-4-440000000-440000000000000000000000000−2i22i2000000
χ374-44-44-4-44000004-400000000000000000000000002i2−2i200000000
χ384-44-44-4-44000004-40000000000000000000000000−2i22i200000000
χ394-44-44-4-4400000-44000000000000000000000002i2−2i20000000000
χ404-44-44-4-4400000-4400000000000000000000000−2i22i20000000000
χ414-4-444-44-44-40000000000000000000000002i−2i2i−2i000000000000
χ424-4-444-44-44-4000000000000000000000000−2i2i−2i2i000000000000
χ434-4-444-44-4-440000000000000000000000002i−2i−2i2i000000000000
χ444-4-444-44-4-44000000000000000000000000−2i2i2i−2i000000000000
χ454-4-4-4-44440004-40000000000000000000000000000000002-22-2
χ464-4-4-4-44440004-4000000000000000000000000000000000-22-22
χ474-4-4-4-4444000-440000000000000000000000000000000002-2-22
χ484-4-4-4-4444000-44000000000000000000000000000000000-222-2
χ4988-8-888-8-8000000000000000000000000000000000000000000
χ508-888-88-8-8000000000000000000000000000000000000000000

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