Finite Group Databasebeta

← Group #394939

Character table — Group #394939

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222444444444444888888888888888888888888888888161616161616161616161616
order12222222222222222222222244444444222244444444444444444444444444444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ7111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-11111
χ8111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1
χ911111111111111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111-1-111-1-111-1-1
χ1011111111111111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-111-1-111-1-111
χ1111111111111111111111-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111-1-111
χ1211111111111111111111-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-111-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111111111-1-1-1-1-1-111-1-11111-1-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1-1-11111111111-1-111-1-1-1-111
χ172222222222-2-2-2-222-2-2-2-222222222-2-2-2-2-2-200000000002200000000-2-2000000000000000000
χ182222222222-2-2-2-222-2-2-2-22222-2-2-2-22222-2-20000000000-2-20000000022000000000000000000
χ192222222222-2-2-2-222-2-2-2-2-2-2-2-22222-2-2-2-2220000000000-2-20000000022000000000000000000
χ202222222222-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-222222200000000002200000000-2-2000000000000000000
χ2122222222-2-222-2-2-2-222-2-222-2-2000000002-200000022-2-2000022000000-2-20000000000000000
χ2222222222-2-222-2-2-2-222-2-222-2-2000000002-2000000-2-2220000-2-2000000220000000000000000
χ2322222222-2-222-2-2-2-222-2-2-2-22200000000-2200000022-2-20000-2-2000000220000000000000000
χ2422222222-2-222-2-2-2-222-2-2-2-22200000000-22000000-2-222000022000000-2-20000000000000000
χ2522222222-2-2-2-222-2-2-2-22222-2-200000000-222222-2-2000000-2-200000000000000000000000000
χ2622222222-2-2-2-222-2-2-2-22222-2-200000000-22-2-2-2-2220000002200000000000000000000000000
χ2722222222-2-2-2-222-2-2-2-222-2-222000000002-222-2-222000000-2-200000000000000000000000000
χ2822222222-2-2-2-222-2-2-2-222-2-222000000002-2-2-222-2-20000002200000000000000000000000000
χ29222-2-22-2-22-222-2-22-2-2-22200002i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000002-2002i−2i00
χ30222-2-22-2-22-222-2-22-2-2-22200002i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000000-2200−2i2i00
χ31222-2-22-2-22-222-2-22-2-2-2220000−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000002-200−2i2i00
χ32222-2-22-2-22-222-2-22-2-2-2220000−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000000000-22002i−2i00
χ33222-2-22-2-22-2-2-2222-222-2-200002i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000002i−2i002-2
χ34222-2-22-2-22-2-2-2222-222-2-200002i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000−2i2i00-22
χ35222-2-22-2-22-2-2-2222-222-2-20000−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000000000002i−2i00-22
χ36222-2-22-2-22-2-2-2222-222-2-20000−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000−2i2i002-2
χ372-2-2222-2-22-22-22-2-222-22-200000000000000002-22-200002i−2i002i−2i00002i−2i2i−2i0000000000000000
χ382-2-2222-2-22-22-22-2-222-22-200000000000000002-22-20000−2i2i00−2i2i0000−2i2i−2i2i0000000000000000
χ392-2-2222-2-22-22-22-2-222-22-20000000000000000-22-2200002i−2i00−2i2i00002i−2i−2i2i0000000000000000
χ402-2-2222-2-22-22-22-2-222-22-20000000000000000-22-220000−2i2i002i−2i0000−2i2i2i−2i0000000000000000
χ412-2-2222-2-22-2-22-22-22-22-22000000000000002-200002i−2i2i−2i2i−2i2-2000000−2i2i000000000000000000
χ422-2-2222-2-22-2-22-22-22-22-22000000000000002-20000−2i2i−2i2i−2i2i2-20000002i−2i000000000000000000
χ432-2-2222-2-22-2-22-22-22-22-2200000000000000-2200002i−2i2i−2i−2i2i-220000002i−2i000000000000000000
χ442-2-2222-2-22-2-22-22-22-22-2200000000000000-220000−2i2i−2i2i2i−2i-22000000−2i2i000000000000000000
χ452-2-2222-2-2-222-2-222-22-2-2200002i−2i2i−2i2i−2i2i−2i002-20000000000-222i−2i000000−2i2i0000000000000000
χ462-2-2222-2-2-222-2-222-22-2-2200002i−2i2i−2i2i−2i2i−2i00-2200000000002-2−2i2i0000002i−2i0000000000000000
χ472-2-2222-2-2-222-2-222-22-2-220000−2i2i−2i2i−2i2i−2i2i002-20000000000-22−2i2i0000002i−2i0000000000000000
χ482-2-2222-2-2-222-2-222-22-2-220000−2i2i−2i2i−2i2i−2i2i00-2200000000002-22i−2i000000−2i2i0000000000000000
χ492-2-2222-2-2-22-222-22-2-222-200002i−2i2i−2i−2i2i−2i2i00002-2-222i−2i−2i2i000000000000000000000000000000
χ502-2-2222-2-2-22-222-22-2-222-200002i−2i2i−2i−2i2i−2i2i0000-222-2−2i2i2i−2i000000000000000000000000000000
χ512-2-2222-2-2-22-222-22-2-222-20000−2i2i−2i2i2i−2i2i−2i00002-2-22−2i2i2i−2i000000000000000000000000000000
χ522-2-2222-2-2-22-222-22-2-222-20000−2i2i−2i2i2i−2i2i−2i0000-222-22i−2i−2i2i000000000000000000000000000000
χ532-2-2-2-2222-2-22-22-222-22-2200002-2-222-2-2200000000000000000022-2-2000000002-20000000000
χ542-2-2-2-2222-2-22-22-222-22-2200002-2-222-2-22000000000000000000-2-22200000000-220000000000
χ552-2-2-2-2222-2-22-22-222-22-220000-222-2-222-200000000000000000022-2-200000000-220000000000
χ562-2-2-2-2222-2-22-22-222-22-220000-222-2-222-2000000000000000000-2-222000000002-20000000000
χ572-2-2-2-2222-2-2-22-22222-22-200002-2-22-222-20000000000000000000000000022-2-2002-200000000
χ582-2-2-2-2222-2-2-22-22222-22-200002-2-22-222-200000000000000000000000000-2-22200-2200000000
χ592-2-2-2-2222-2-2-22-22222-22-20000-222-22-2-220000000000000000000000000022-2-200-2200000000
χ602-2-2-2-2222-2-2-22-22222-22-20000-222-22-2-2200000000000000000000000000-2-222002-200000000
χ61444-4-44-4-4-444444-44-4-4-4-4000000000000000000000000000000000000000000000000000000
χ62444-4-44-4-4-44-4-4-4-4-444444000000000000000000000000000000000000000000000000000000
χ6344-44-4-44-4000000000000004-4000000000000000000000000002i−2i2i−2i00002i−2i2i−2i000000000000
χ6444-44-4-44-4000000000000004-400000000000000000000000000−2i2i−2i2i0000−2i2i−2i2i000000000000
χ6544-44-4-44-400000000000000-44000000000000000000000000002i−2i2i−2i0000−2i2i−2i2i000000000000
χ6644-44-4-44-400000000000000-4400000000000000000000000000−2i2i−2i2i00002i−2i2i−2i000000000000
χ674-44-44-44-40000000000004-400000000000000000000000000002i−2i−2i2i00002i−2i−2i2i000000000000
χ684-44-44-44-40000000000004-40000000000000000000000000000−2i2i2i−2i0000−2i2i2i−2i000000000000
χ694-44-44-44-4000000000000-4400000000000000000000000000002i−2i−2i2i0000−2i2i2i−2i000000000000
χ704-44-44-44-4000000000000-440000000000000000000000000000−2i2i2i−2i00002i−2i−2i2i000000000000
χ714-4-4-4-4444444-4-44-4-4-444-4000000000000000000000000000000000000000000000000000000
χ724-4-4-4-444444-444-4-4-44-4-44000000000000000000000000000000000000000000000000000000
χ7388-8-88-8-88000000000000000000000000000000000000000000000000000000000000000000
χ748-888-8-8-88000000000000000000000000000000000000000000000000000000000000000000

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