Finite Group Databasebeta

← Group #412339

Character table — Group #412339

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444488888888888888888888888888888888161616161616161616161616
order12222222222244444444444444444422222244444444444444444444444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-111111111-1-1-1-11111-1-1-1-1
χ6111111111111111111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ7111111111111111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111
χ8111111111111111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ9111111111111111111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111-1-111-1-1
χ10111111111111111111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-111-1-111
χ11111111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-111-1-11111-1-1-1-111-1-1-1-111-1-111
χ12111111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-111-1-1-1-1-1-11111-1-11111-1-111-1-1
χ13111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111
χ14111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1
χ15111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111111111-1-1-1-1-1-111-1-11111-1-1
χ16111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-1111111-1-111-1-1-1-111
χ17222222222222-2-2-2-2-2-22222-2-2-2-2-2-22222-2-200000000000022-2-2000000000000000000000000
χ18222222222222-2-2-2-2-2-22222-2-2-2-2-2-222-2-222000000000000-2-222000000000000000000000000
χ19222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-222-2-2000000000000-2-222000000000000000000000000
χ20222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-22200000000000022-2-2000000000000000000000000
χ2122222222-2-2-2-2222-2-2-222222-222-2-2-2-20000002222-2-20000000000-2-200000000000000000000
χ2222222222-2-2-2-2222-2-2-222222-222-2-2-2-2000000-2-2-2-22200000000002200000000000000000000
χ2322222222-2-2-2-2222-2-2-2-2-2-2-22-2-2-2222200000022-2-2220000000000-2-200000000000000000000
χ2422222222-2-2-2-2222-2-2-2-2-2-2-22-2-2-22222000000-2-222-2-200000000002200000000000000000000
χ2522222222-2-2-2-2-2-2-22222222-22-2-222-2-2000022000000-2-2-2-20000220000000000000000000000
χ2622222222-2-2-2-2-2-2-22222222-22-2-222-2-20000-2-200000022220000-2-20000000000000000000000
χ2722222222-2-2-2-2-2-2-2222-2-2-2-2-2222-2-222000022000000-2-2220000-2-20000000000000000000000
χ2822222222-2-2-2-2-2-2-2222-2-2-2-2-2222-2-2220000-2-200000022-2-20000220000000000000000000000
χ2922-2-22-2-2222-2-222-22-2-20000-2200000000002-2002i−2i2i−2i2-2002i−2i2i−2i000000000000000000000000
χ3022-2-22-2-2222-2-222-22-2-20000-2200000000002-200−2i2i−2i2i2-200−2i2i−2i2i000000000000000000000000
χ3122-2-22-2-2222-2-222-22-2-20000-220000000000-22002i−2i2i−2i-2200−2i2i−2i2i000000000000000000000000
χ3222-2-22-2-2222-2-222-22-2-20000-220000000000-2200−2i2i−2i2i-22002i−2i2i−2i000000000000000000000000
χ3322-2-22-2-2222-2-2-2-22-22200002-20000000000002-20000002i−2i2i−2i−2i2i2i−2i2-200000000000000000000
χ3422-2-22-2-2222-2-2-2-22-22200002-20000000000002-2000000−2i2i−2i2i2i−2i−2i2i2-200000000000000000000
χ3522-2-22-2-2222-2-2-2-22-22200002-2000000000000-220000002i−2i−2i2i2i−2i2i−2i-2200000000000000000000
χ3622-2-22-2-2222-2-2-2-22-22200002-2000000000000-22000000−2i2i2i−2i−2i2i−2i2i-2200000000000000000000
χ3722-2-22-2-22-2-22222-2-2220000-2-20000002-22-200002i−2i−2i2i002i−2i0000−2i2i0000000000000000000000
χ3822-2-22-2-22-2-22222-2-2220000-2-20000002-22-20000−2i2i2i−2i00−2i2i00002i−2i0000000000000000000000
χ3922-2-22-2-22-2-22222-2-2220000-2-2000000-22-2200002i−2i−2i2i00−2i2i00002i−2i0000000000000000000000
χ4022-2-22-2-22-2-22222-2-2220000-2-2000000-22-220000−2i2i2i−2i002i−2i0000−2i2i0000000000000000000000
χ4122-2-22-2-22-2-222-2-222-2-20000220000002-2-222-2-220000-22000000002-200000000000000000000
χ4222-2-22-2-22-2-222-2-222-2-20000220000002-2-22-222-200002-200000000-2200000000000000000000
χ4322-2-22-2-22-2-222-2-222-2-2000022000000-222-22-22-20000-2200000000-2200000000000000000000
χ4422-2-22-2-22-2-222-2-222-2-2000022000000-222-2-22-2200002-2000000002-200000000000000000000
χ452-2-2-2222-22-22-22-22-22-222-2-2-222-22-22-20000000000000000000000002i2i−2i−2i2i2i−2i−2i000000000000
χ462-2-2-2222-22-22-22-22-22-222-2-2-222-22-22-2000000000000000000000000−2i−2i2i2i−2i−2i2i2i000000000000
χ472-2-2-2222-22-22-22-22-22-2-2-222-22-22-22-220000000000000000000000002i2i−2i−2i−2i−2i2i2i000000000000
χ482-2-2-2222-22-22-22-22-22-2-2-222-22-22-22-22000000000000000000000000−2i−2i2i2i2i2i−2i−2i000000000000
χ492-2-2-2222-22-22-2-22-22-2222-2-22-2-22-222-2000000000000000000000000000000002i−2i2i−2i00000000
χ502-2-2-2222-22-22-2-22-22-2222-2-22-2-22-222-200000000000000000000000000000000−2i2i−2i2i00000000
χ512-2-2-2222-22-22-2-22-22-22-2-2222-22-22-2-22000000000000000000000000000000002i−2i−2i2i00000000
χ522-2-2-2222-22-22-2-22-22-22-2-2222-22-22-2-2200000000000000000000000000000000−2i2i2i−2i00000000
χ532-2-2-2222-2-22-222-222-2222-2-2-2-22-2-22-2200000000000000000000000000000000000000002i−2i2i−2i
χ542-2-2-2222-2-22-222-222-2222-2-2-2-22-2-22-220000000000000000000000000000000000000000−2i2i−2i2i
χ552-2-2-2222-2-22-222-222-22-2-222-2-2-222-22-200000000000000000000000000000000000000002i−2i−2i2i
χ562-2-2-2222-2-22-222-222-22-2-222-2-2-222-22-20000000000000000000000000000000000000000−2i2i2i−2i
χ572-2-2-2222-2-22-22-22-2-22-222-2-222-222-2-220000000000000000000000000000000000002-22-20000
χ582-2-2-2222-2-22-22-22-2-22-222-2-222-222-2-22000000000000000000000000000000000000-22-220000
χ592-2-2-2222-2-22-22-22-2-22-2-2-222222-2-222-20000000000000000000000000000000000002-2-220000
χ602-2-2-2222-2-22-22-22-2-22-2-2-222222-2-222-2000000000000000000000000000000000000-222-20000
χ61444-4-4-44-400000000004-44-4000000000000000000000000000000002i−2i2i−2i2i−2i2i−2i000000000000
χ62444-4-4-44-400000000004-44-400000000000000000000000000000000−2i2i−2i2i−2i2i−2i2i000000000000
χ63444-4-4-44-40000000000-44-44000000000000000000000000000000002i−2i2i−2i−2i2i−2i2i000000000000
χ64444-4-4-44-40000000000-44-4400000000000000000000000000000000−2i2i−2i2i2i−2i2i−2i000000000000
χ654-4444-4-4-44-4-444-4-4-4-4400004400000000000000000000000000000000000000000000000000
χ664-4444-4-4-44-4-44-44444-40000-4-400000000000000000000000000000000000000000000000000
χ674-4444-4-4-4-444-44-4-444-400004-400000000000000000000000000000000000000000000000000
χ684-4444-4-4-4-444-4-444-4-440000-4400000000000000000000000000000000000000000000000000
χ694-4-44-4-44400000000004-4-44000000000000000000000000000000002-2-222-2-22000000000000
χ704-4-44-4-44400000000004-4-4400000000000000000000000000000000-222-2-222-2000000000000
χ714-4-44-4-4440000000000-444-4000000000000000000000000000000002-2-22-222-2000000000000
χ724-4-44-4-4440000000000-444-400000000000000000000000000000000-222-22-2-22000000000000
χ7388-88-88-8-8000000000000000000000000000000000000000000000000000000000000000000
χ748-88-8-88-88000000000000000000000000000000000000000000000000000000000000000000

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