Finite Group Databasebeta

← Group #242000

Character table — Group #242000

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444488888888888888888888888888888888161616161616161616161616
order12222222444444444444444444444444444444444444448888888888888888224444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111
χ5111111111111111111111111111111-1-1-1-1-1-11111-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1
χ6111111111111111111111111111111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-11111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ911111111-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1
χ1011111111-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111-1-111
χ1111111111-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111
χ1211111111-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-111-1-111-1-1
χ1311111111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-11111-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111
χ1411111111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1
χ1511111111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-111-1-11111-1-1111111-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1
χ1611111111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-111-1-11111-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111
χ1722222222222222-2-2222222-2-2-2-2-2-2-2-222-2-2-2-200002200000000000000000000000000000000
χ1822222222222222-2-2222222-2-2-2-2-2-2-2-2-2-222220000-2-200000000000000000000000000000000
χ19222222222222-2-222-2-2-2-2-2-222-2-222-2-2000000222200-2-2-2-20000000000000000000000000000
χ20222222222222-2-222-2-2-2-2-2-222-2-222-2-2000000-2-2-2-20022220000000000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-22200000000000000000000000000000000002-22-2000000
χ22222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-2220000000000000000000000000000000000-22-22000000
χ2322222222-2-2-2-222-2-2-2-2-2-222-2-22222-2-222-2-2220000-2-200000000000000000000000000000000
χ2422222222-2-2-2-222-2-2-2-2-2-222-2-22222-2-2-2-222-2-200002200000000000000000000000000000000
χ2522222222-2-2-2-2-2-2222222-2-22222-2-2-2-200000022-2-200-2-2220000000000000000000000000000
χ2622222222-2-2-2-2-2-2222222-2-22222-2-2-2-2000000-2-2220022-2-20000000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2222200000000000000000000000000000000002-2-22000000
χ2822222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-222220000000000000000000000000000000000-222-2000000
χ29222-2-22-2-222-2-2-2-20022-2-222000000002-2000000002-20000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2000000000000
χ30222-2-22-2-222-2-2-2-20022-2-222000000002-2000000002-20000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2000000000000
χ31222-2-22-2-222-2-2-2-20022-2-22200000000-2200000000-220000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2000000000000
χ32222-2-22-2-222-2-2-2-20022-2-22200000000-2200000000-220000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2000000000000
χ33222-2-22-2-2-2-222-2-200-2-22222000000002-200000000-220000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2000000000000
χ34222-2-22-2-2-2-222-2-200-2-22222000000002-200000000-220000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2000000000000
χ35222-2-22-2-2-2-222-2-200-2-2222200000000-22000000002-20000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2000000000000
χ36222-2-22-2-2-2-222-2-200-2-2222200000000-22000000002-20000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2000000000000
χ372-222-2-22-22i−2i2i−2i2-2002i−2i2i−2i2-200000000002i−2i2-200000000002−22−2i2−i2i2−i2i2−i2i2−i22−22−2000000000000
χ382-222-2-22-22i−2i2i−2i2-2002i−2i2i−2i2-200000000002i−2i2-20000000000−22−22−i2i2−i2i2−i2i2−i2i2−22−22000000000000
χ392-222-2-22-22i−2i2i−2i2-2002i−2i2i−2i2-20000000000−2i2i-2200000000002−22−2i2−i2i2−i2−i2i2−i2i2−22−22000000000000
χ402-222-2-22-22i−2i2i−2i2-2002i−2i2i−2i2-20000000000−2i2i-220000000000−22−22−i2i2−i2i2i2−i2i2−i22−22−2000000000000
χ412-222-2-22-2−2i2i−2i2i2-200−2i2i−2i2i2-200000000002i−2i-2200000000002−22−2−i2i2−i2i2i2−i2i2−i2−22−22000000000000
χ422-222-2-22-2−2i2i−2i2i2-200−2i2i−2i2i2-200000000002i−2i-220000000000−22−22i2−i2i2−i2−i2i2−i2i22−22−2000000000000
χ432-222-2-22-2−2i2i−2i2i2-200−2i2i−2i2i2-20000000000−2i2i2-200000000002−22−2−i2i2−i2i2−i2i2−i2i22−22−2000000000000
χ442-222-2-22-2−2i2i−2i2i2-200−2i2i−2i2i2-20000000000−2i2i2-20000000000−22−22i2−i2i2−i2i2−i2i2−i2−22−22000000000000
χ452-22-22-2-222i−2i−2i2i2-22-2−2i2i2i−2i-222-22i−2i2i−2i2-200000000000000000000000000000000000000002-22i−2i
χ462-22-22-2-222i−2i−2i2i2-22-2−2i2i2i−2i-222-22i−2i2i−2i2-20000000000000000000000000000000000000000-22−2i2i
χ472-22-22-2-222i−2i−2i2i2-2-22−2i2i2i−2i-22-22−2i2i−2i2i-22000000000000000000000000000000002-200002i−2i0000
χ482-22-22-2-222i−2i−2i2i2-2-22−2i2i2i−2i-22-22−2i2i−2i2i-2200000000000000000000000000000000-220000−2i2i0000
χ492-22-22-2-222i−2i−2i2i-222-22i−2i−2i2i2-22-2−2i2i2i−2i-220000000000000000000000002-2-22−2i2i2i−2i000000000000
χ502-22-22-2-222i−2i−2i2i-222-22i−2i−2i2i2-22-2−2i2i2i−2i-22000000000000000000000000-222-22i−2i−2i2i000000000000
χ512-22-22-2-222i−2i−2i2i-22-222i−2i−2i2i2-2-222i−2i−2i2i2-200000000000000002i−2i−2i2i-222-200000000000000000000
χ522-22-22-2-222i−2i−2i2i-22-222i−2i−2i2i2-2-222i−2i−2i2i2-20000000000000000−2i2i2i−2i2-2-2200000000000000000000
χ532-22-22-2-22−2i2i2i−2i2-22-22i−2i−2i2i-222-2−2i2i−2i2i2-200000000000000000000000000000000000000002-2−2i2i
χ542-22-22-2-22−2i2i2i−2i2-22-22i−2i−2i2i-222-2−2i2i−2i2i2-20000000000000000000000000000000000000000-222i−2i
χ552-22-22-2-22−2i2i2i−2i2-2-222i−2i−2i2i-22-222i−2i2i−2i-22000000000000000000000000000000002-20000−2i2i0000
χ562-22-22-2-22−2i2i2i−2i2-2-222i−2i−2i2i-22-222i−2i2i−2i-2200000000000000000000000000000000-2200002i−2i0000
χ572-22-22-2-22−2i2i2i−2i-222-2−2i2i2i−2i2-22-22i−2i−2i2i-220000000000000000000000002-2-222i−2i−2i2i000000000000
χ582-22-22-2-22−2i2i2i−2i-222-2−2i2i2i−2i2-22-22i−2i−2i2i-22000000000000000000000000-222-2−2i2i2i−2i000000000000
χ592-22-22-2-22−2i2i2i−2i-22-22−2i2i2i−2i2-2-22−2i2i2i−2i2-200000000000000002i−2i−2i2i2-2-2200000000000000000000
χ602-22-22-2-22−2i2i2i−2i-22-22−2i2i2i−2i2-2-22−2i2i2i−2i2-20000000000000000−2i2i2i−2i-222-200000000000000000000
χ61444-4-44-4-444-4-44400-4-444-4-40000000000000000000000000000000000000000000000000000
χ62444-4-44-4-4-4-444440044-4-4-4-40000000000000000000000000000000000000000000000000000
χ6344-4-4-4-4440000004-4000000-440000000000004i−4i000000000000000000000000000000000000
χ6444-4-4-4-4440000004-4000000-44000000000000−4i4i000000000000000000000000000000000000
χ6544-4-4-4-444000000-440000004-4000000000000004i−4i0000000000000000000000000000000000
χ6644-4-4-4-444000000-440000004-400000000000000−4i4i0000000000000000000000000000000000
χ674-444-4-44-44i−4i4i−4i-4400−4i4i−4i4i-440000000000000000000000000000000000000000000000000000
χ684-444-4-44-4−4i4i−4i4i-44004i−4i4i−4i-440000000000000000000000000000000000000000000000000000
χ694-4-44-44-4400000044000000-4-40000000000000000004i−4i000000000000000000000000000000
χ704-4-44-44-4400000044000000-4-4000000000000000000−4i4i000000000000000000000000000000
χ714-4-44-44-44000000-4-400000044000000000000000000004-40000000000000000000000000000
χ724-4-44-44-44000000-4-40000004400000000000000000000-440000000000000000000000000000
χ7388-888-8-8-8000000000000000000000000000000000000000000000000000000000000000000
χ748-8-8-8888-8000000000000000000000000000000000000000000000000000000000000000000

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