Finite Group Databasebeta

← Group #239889

Character table — Group #239889

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444488888888888888888888888888888888161616161616161616161616
order12222222222244444444444444444444444444888888888888888888888888224444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ5111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111
χ911111111-1-1-1-111111-1-1-1-11111-1-1-1-111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111-1-1
χ1011111111-1-1-1-111111-1-1-1-11111-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-111-1-111
χ1111111111-1-1-1-111111-1-1-1-11111-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1
χ1211111111-1-1-1-111111-1-1-1-11111-1-1-1-111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-111
χ1311111111-1-1-1-111111-1-1-1-11111-1-1-1-11-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111
χ1411111111-1-1-1-111111-1-1-1-11111-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-111-1-1
χ1511111111-1-1-1-111111-1-1-1-11111-1-1-1-11-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111
χ1611111111-1-1-1-111111-1-1-1-11111-1-1-1-11-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-11111-1-1
χ17222222222222222-2-22222-2-22-2-2-2-2-2-222-2-222-2-2000000000000000000000000000000000000
χ18222222222222222-2-22222-2-22-2-2-2-2-2-2-2-222-2-222000000000000000000000000000000000000
χ19222222222222-2-2-222-2-2-2-222-2-222-2-2-20000000000000000000000000000000000002-22-20000
χ20222222222222-2-2-222-2-2-2-222-2-222-2-2-2000000000000000000000000000000000000-22-220000
χ21222222222222-2-2-2-2-2-2-2-2-2-2-2-22-2-2222000000000000000000000000000000002-22-200000000
χ22222222222222-2-2-2-2-2-2-2-2-2-2-2-22-2-222200000000000000000000000000000000-22-2200000000
χ2322222222-2-2-2-2222-2-2-2-2-2-2-2-22-22222-222-2-2-2-222000000000000000000000000000000000000
χ2422222222-2-2-2-2222-2-2-2-2-2-2-2-22-22222-2-2-22222-2-2000000000000000000000000000000000000
χ2522222222-2-2-2-2-2-2-222222222-2-2-2-222-20000000000000000000000000000000000002-2-220000
χ2622222222-2-2-2-2-2-2-222222222-2-2-2-222-2000000000000000000000000000000000000-222-20000
χ2722222222-2-2-2-2-2-2-2-2-22222-2-2-2222-2-22000000000000000000000000000000002-2-2200000000
χ2822222222-2-2-2-2-2-2-2-2-22222-2-2-2222-2-2200000000000000000000000000000000-222-200000000
χ29222-22-2-2-222-2-22-2-20022-2-2002000000002i−2i002i−2i22−2−222−2−200000000i2i2−i2−i2i2i2−i2−i2000000000000
χ30222-22-2-2-222-2-22-2-20022-2-2002000000002i−2i002i−2i−2−222−2−22200000000−i2−i2i2i2−i2−i2i2i2000000000000
χ31222-22-2-2-222-2-22-2-20022-2-200200000000−2i2i00−2i2i22−2−222−2−200000000−i2−i2i2i2−i2−i2i2i2000000000000
χ32222-22-2-2-222-2-22-2-20022-2-200200000000−2i2i00−2i2i−2−222−2−22200000000i2i2−i2−i2i2i2−i2−i2000000000000
χ33222-22-2-2-2-2-2222-2-200-2-222002000000002i−2i00−2i2i22−2−2−2−22200000000i2i2−i2−i2−i2−i2i2i2000000000000
χ34222-22-2-2-2-2-2222-2-200-2-222002000000002i−2i00−2i2i−2−22222−2−200000000−i2−i2i2i2i2i2−i2−i2000000000000
χ35222-22-2-2-2-2-2222-2-200-2-22200200000000−2i2i002i−2i22−2−2−2−22200000000−i2−i2i2i2i2i2−i2−i2000000000000
χ36222-22-2-2-2-2-2222-2-200-2-22200200000000−2i2i002i−2i−2−22222−2−200000000i2i2−i2−i2−i2−i2i2i2000000000000
χ372-2-222-2-222-22-222-2002-22-200-20000002i−2i002i−2i00i2−i2i2−i2i2−i2i2−i2000000002−22−22−22−2000000000000
χ382-2-222-2-222-22-222-2002-22-200-20000002i−2i002i−2i00−i2i2−i2i2−i2i2−i2i200000000−22−22−22−22000000000000
χ392-2-222-2-222-22-222-2002-22-200-2000000−2i2i00−2i2i00i2−i2i2−i2i2−i2i2−i200000000−22−22−22−22000000000000
χ402-2-222-2-222-22-222-2002-22-200-2000000−2i2i00−2i2i00−i2i2−i2i2−i2i2−i2i2000000002−22−22−22−2000000000000
χ412-2-222-2-22-22-2222-200-22-2200-20000002i−2i00−2i2i00i2−i2i2−i2−i2i2−i2i2000000002−22−2−22−22000000000000
χ422-2-222-2-22-22-2222-200-22-2200-20000002i−2i00−2i2i00−i2i2−i2i2i2−i2i2−i200000000−22−222−22−2000000000000
χ432-2-222-2-22-22-2222-200-22-2200-2000000−2i2i002i−2i00i2−i2i2−i2−i2i2−i2i200000000−22−222−22−2000000000000
χ442-2-222-2-22-22-2222-200-22-2200-2000000−2i2i002i−2i00−i2i2−i2i2i2−i2i2−i2000000002−22−2−22−22000000000000
χ452-2-2-2222-22-2-222-22222-2-22-2-2-2-22-22-22000000002i−2i−2i2i2i−2i−2i2i0000000000000000000000000000
χ462-2-2-2222-22-2-222-22222-2-22-2-2-2-22-22-2200000000−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000
χ472-2-2-2222-22-2-222-22-2-22-2-2222-22-22-22-20000000000000000000000002i−2i−2i2i2i−2i−2i2i000000000000
χ482-2-2-2222-22-2-222-22-2-22-2-2222-22-22-22-2000000000000000000000000−2i2i2i−2i−2i2i2i−2i000000000000
χ492-2-2-2222-22-2-22-22-222-222-2-2-2222-2-22-200000000000000000000000000000000000000002i−2i2i−2i
χ502-2-2-2222-22-2-22-22-222-222-2-2-2222-2-22-20000000000000000000000000000000000000000−2i2i−2i2i
χ512-2-2-2222-22-2-22-22-2-2-2-222-2222-2-222-22000000000000000022-2-222-2-200000000000000000000
χ522-2-2-2222-22-2-22-22-2-2-2-222-2222-2-222-220000000000000000-2-222-2-22200000000000000000000
χ532-2-2-2222-2-222-22-2222-222-2-2-2-2-2-22-222000000002i−2i−2i2i−2i2i2i−2i0000000000000000000000000000
χ542-2-2-2222-2-222-22-2222-222-2-2-2-2-2-22-22200000000−2i2i2i−2i2i−2i−2i2i0000000000000000000000000000
χ552-2-2-2222-2-222-22-22-2-2-222-222-222-22-2-20000000000000000000000002i−2i−2i2i−2i2i2i−2i000000000000
χ562-2-2-2222-2-222-22-22-2-2-222-222-222-22-2-2000000000000000000000000−2i2i2i−2i2i−2i−2i2i000000000000
χ572-2-2-2222-2-222-2-22-2222-2-22-2-222-222-2-200000000000000000000000000000000000000002i−2i−2i2i
χ582-2-2-2222-2-222-2-22-2222-2-22-2-222-222-2-20000000000000000000000000000000000000000−2i2i2i−2i
χ592-2-2-2222-2-222-2-22-2-2-22-2-22222-22-2-222000000000000000022-2-2-2-22200000000000000000000
χ602-2-2-2222-2-222-2-22-2-2-22-2-22222-22-2-2220000000000000000-2-22222-2-200000000000000000000
χ61444-44-4-4-444-4-4-44400-4-44400-400000000000000000000000000000000000000000000000000
χ62444-44-4-4-4-4-444-4440044-4-400-400000000000000000000000000000000000000000000000000
χ6344-4-4-44-4400000004-400004-40000000000000000000000000002i2−2i22i2−2i200000000000000000000
χ6444-4-4-44-4400000004-400004-4000000000000000000000000000−2i22i2−2i22i200000000000000000000
χ6544-4-4-44-440000000-440000-44000000000000000000000002i2−2i22i2−2i2000000000000000000000000
χ6644-4-4-44-440000000-440000-4400000000000000000000000−2i22i2−2i22i2000000000000000000000000
χ674-444-44-4-400000004-40000-44000000000000000000000002i2−2i2−2i22i2000000000000000000000000
χ684-444-44-4-400000004-40000-4400000000000000000000000−2i22i22i2−2i2000000000000000000000000
χ694-444-44-4-40000000-4400004-40000000000000000000000000002i2−2i2−2i22i200000000000000000000
χ704-444-44-4-40000000-4400004-4000000000000000000000000000−2i22i22i2−2i200000000000000000000
χ714-4-444-4-444-44-4-4-4400-44-4400400000000000000000000000000000000000000000000000000
χ724-4-444-4-44-44-44-4-44004-44-400400000000000000000000000000000000000000000000000000
χ7388-88-8-88-8000000000000000000000000000000000000000000000000000000000000000000
χ748-88-8-8-888000000000000000000000000000000000000000000000000000000000000000000

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