Finite Group Databasebeta

← Group #178065

Character table — Group #178065

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size1111111144444444448888881616161616161616161616161616161616161616161616161616
order12222222224444444422444422222244444444888888888888
χ111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1-1-11-1-11-1-1-1-1-1-1-1-1-1-11111
χ3111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111-1-1-1-1-1-1-1-11-1-11-1-111111111-1-1-1-1
χ5111111111111111111-1-1-1-11111111-11-1-11-1-11-11111-1-1-1-1-1-1-1-1
χ6111111111111111111-1-1-1-1111111-11-11-1-11-1-11-1-1-1-11111-1-1-1-1
χ7111111111111111111-1-1-1-111-1-1-1-11-11-1-11-1-11-1-1-1-1-111111111
χ8111111111111111111-1-1-1-111-1-1-1-1-11-11-1-11-1-111111-1-1-1-11111
χ911111111-1-11-1-11111111-1-1-1-111-1-11111-1-1-11-1-111-1-111-1-111-1-1
χ1011111111-1-11-1-11111111-1-1-1-111-1-1-1-1-1-1-111111-1-111-1-11111-1-1
χ1111111111-1-11-1-11111111-1-1-1-1-1-1111111-1-1-11-1-1-1-111-1-111-1-111
χ1211111111-1-11-1-11111111-1-1-1-1-1-111-1-1-1-1-11111111-1-111-1-1-1-111
χ1311111111-1-11-1-111111-1-111-1-111-1-11-11-11-11-1-1111-1-1-1-111-1-111
χ1411111111-1-11-1-111111-1-111-1-111-1-1-11-1111-1-11-1-1-11111-1-1-1-111
χ1511111111-1-11-1-111111-1-111-1-1-1-1111-11-11-11-1-11-1-11111-1-111-1-1
χ1611111111-1-11-1-111111-1-111-1-1-1-111-11-1111-1-11-111-1-1-1-11111-1-1
χ172222222222222-2-2-2-2222-2-2-2-200000000200-200000000000000
χ182222222222222-2-2-2-22-2-222-2-200000000-200200000000000000
χ192222222222-2-2-222-2-2-200002-20000020-200200-2000000000000
χ202222222222-2-2-222-2-2-200002-200000-20200-2002000000000000
χ212222222222-2-2-2-2-222-20000-22000020-200200-20000000000000
χ222222222222-2-2-2-2-222-20000-220000-20200-20020000000000000
χ2322222222-2-22-2-2-2-2-2-2222222200000000-200-200000000000000
χ2422222222-2-22-2-2-2-2-2-22-2-2-2-22200000000200200000000000000
χ2522222222-2-2-22222-2-2-20000-220000020-200-2002000000000000
χ2622222222-2-2-22222-2-2-20000-2200000-20200200-2000000000000
χ2722222222-2-2-222-2-222-200002-2000020-200-20020000000000000
χ2822222222-2-2-222-2-222-200002-20000-20200200-20000000000000
χ29444-44-4-4-4004000000-4004i−4i0000000000000000000000000000
χ30444-44-4-4-4004000000-400−4i4i0000000000000000000000000000
χ31444-44-4-4-400-400000044-4000000000000000000000000000000
χ32444-44-4-4-400-40000004-44000000000000000000000000000000
χ3344-4-4-44-4400000004-4000000000000000000000000022−22000000
χ3444-4-4-44-4400000004-40000000000000000000000000−2222000000
χ3544-4-4-44-440000000-4400000000000000000000000000022−220000
χ3644-4-4-44-440000000-44000000000000000000000000000−22220000
χ374-44-4-4-444000004-4000000000000000000000000022−2200000000
χ384-44-4-4-444000004-40000000000000000000000000−222200000000
χ394-44-4-4-44400000-440000000000000000000000022−220000000000
χ404-44-4-4-44400000-4400000000000000000000000−22220000000000
χ414-4-444-4-440004-40000000000000000000000000000000002-22-2
χ424-4-444-4-440004-4000000000000000000000000000000000-22-22
χ434-4-444-4-44000-440000000000000000000000000000000002-2-22
χ444-4-444-4-44000-44000000000000000000000000000000000-222-2
χ454-4-4-4444-44-4000000000000002-22-20000000000000000000000
χ464-4-4-4444-44-400000000000000-22-220000000000000000000000
χ474-4-4-4444-4-44000000000000002-2-220000000000000000000000
χ484-4-4-4444-4-4400000000000000-222-20000000000000000000000
χ4988-88-8-88-8000000000000000000000000000000000000000000
χ508-888-88-8-8000000000000000000000000000000000000000000

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