Finite Group Databasebeta

← Group #396449

Character table — Group #396449

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222444444444444888888888888888888888888888888161616161616161616161616
order12222222222244444444444444444444222244444444444444444444444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-11-1-1-1-111-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ41111111111111111111111111111111111-1-1-1-11-1-1-1-111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ5111111111111111111111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-111-1-1-111111111-1-1-1-111-1-111-1-111-1-1
χ6111111111111111111111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-111-1-1-11111-1-1-1-11111-1-111-1-111-1-111
χ7111111111111111111111111-1-11111-1-1-1-1-1-111-11111-1-1-1-111-1-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1
χ8111111111111111111111111-1-11111-1-1-1-1-1-111-11111-1-1-1-111-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111
χ911111111111111111111-1-1-1-111-1-1-1-111-1-111111-1-1-1-1-1-111111-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ1011111111111111111111-1-1-1-111-1-1-1-111-1-111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ1111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-111111-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1
χ1211111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111111111-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-111-1-111-111111111-1-1-1-111-1-1-1-111-1-111
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-111-1-111-11111-1-1-1-11111-1-11111-1-111-1-1
χ17222222222222-2-2-2-2-2-2-2-20000220000-2-2000000222-2-2000000-222-2-200000000000000000000
χ18222222222222-2-2-2-2-2-2-2-20000220000-2-20000002-2-222000000-2-2-22200000000000000000000
χ19222222222222-2-2-2-2-2-2-2-20000-2-2000022000000-222-2-20000002-2-22200000000000000000000
χ20222222222222-2-2-2-2-2-2-2-20000-2-2000022000000-2-2-222000000222-2-200000000000000000000
χ2122222222-2-2-2-2222-2-2-2-22000022000022002222-2000000-2-2-2-2-2000000000000000000000000
χ2222222222-2-2-2-2222-2-2-2-2200002200002200-2-2-2-2-20000002222-2000000000000000000000000
χ2322222222-2-2-2-2222-2-2-2-220000-2-20000-2-20022-2-22000000-2-2222000000000000000000000000
χ2422222222-2-2-2-2222-2-2-2-220000-2-20000-2-200-2-222200000022-2-22000000000000000000000000
χ2522222222-2-2-2-2-2-2-22222-2222222-2-2-2-2-2-2220000-20000-2-200002000000000000000000000000
χ2622222222-2-2-2-2-2-2-22222-22222-2-2-2-2-2-222-2-2000020000220000-2000000000000000000000000
χ2722222222-2-2-2-2-2-2-22222-2-2-2-2-2222222-2-2-2-20000-200002200002000000000000000000000000
χ2822222222-2-2-2-2-2-2-22222-2-2-2-2-2-2-222222222000020000-2-20000-2000000000000000000000000
χ2922-22-22-2-222-2-222-222-2-2-20000000000002-22-20002-22-22-22-2000000000000000000000000000
χ3022-22-22-2-222-2-222-222-2-2-20000000000002-2-22000-22-222-2-22000000000000000000000000000
χ3122-22-22-2-222-2-222-222-2-2-2000000000000-222-2000-22-22-222-2000000000000000000000000000
χ3222-22-22-2-222-2-222-222-2-2-2000000000000-22-220002-22-2-22-22000000000000000000000000000
χ3322-22-22-2-222-2-2-2-22-2-22222i2i−2i−2i002i2i−2i−2i0000002i−2i02-2-2200002i−2i0000000000000000000000000
χ3422-22-22-2-222-2-2-2-22-2-22222i2i−2i−2i002i2i−2i−2i000000−2i2i0-222-20000−2i2i0000000000000000000000000
χ3522-22-22-2-222-2-2-2-22-2-2222−2i−2i2i2i00−2i−2i2i2i0000002i−2i0-222-200002i−2i0000000000000000000000000
χ3622-22-22-2-222-2-2-2-22-2-2222−2i−2i2i2i00−2i−2i2i2i000000−2i2i02-2-220000−2i2i0000000000000000000000000
χ3722-22-22-2-2-2-22222-2-2-222-22i2i−2i−2i00−2i−2i2i2i00002-2000000000-220002i−2i2i−2i00000000000000000000
χ3822-22-22-2-2-2-22222-2-2-222-22i2i−2i−2i00−2i−2i2i2i0000-220000000002-2000−2i2i−2i2i00000000000000000000
χ3922-22-22-2-2-2-22222-2-2-222-2−2i−2i2i2i002i2i−2i−2i00002-2000000000-22000−2i2i−2i2i00000000000000000000
χ4022-22-22-2-2-2-22222-2-2-222-2−2i−2i2i2i002i2i−2i−2i0000-220000000002-20002i−2i2i−2i00000000000000000000
χ4122-22-22-2-2-2-222-2-2222-2-220000000000002-2002i−2i00000-2200−2i2i02i−2i−2i2i00000000000000000000
χ4222-22-22-2-2-2-222-2-2222-2-220000000000002-200−2i2i00000-22002i−2i0−2i2i2i−2i00000000000000000000
χ4322-22-22-2-2-2-222-2-2222-2-22000000000000-22002i−2i000002-200−2i2i0−2i2i2i−2i00000000000000000000
χ4422-22-22-2-2-2-222-2-2222-2-22000000000000-2200−2i2i000002-2002i−2i02i−2i−2i2i00000000000000000000
χ452-22-2-222-22-22-22-2-22-22-222i−2i2i−2i002i−2i2i−2i000000000000000000000000000000002-2002i−2i000000
χ462-22-2-222-22-22-22-2-22-22-222i−2i2i−2i002i−2i2i−2i00000000000000000000000000000000-2200−2i2i000000
χ472-22-2-222-22-22-22-2-22-22-22−2i2i−2i2i00−2i2i−2i2i000000000000000000000000000000002-200−2i2i000000
χ482-22-2-222-22-22-22-2-22-22-22−2i2i−2i2i00−2i2i−2i2i00000000000000000000000000000000-22002i−2i000000
χ492-22-2-222-2-22-22-2222-22-2-22i−2i2i−2i00−2i2i−2i2i00000000000000000000000000000000002i−2i002-20000
χ502-22-2-222-2-22-22-2222-22-2-22i−2i2i−2i00−2i2i−2i2i0000000000000000000000000000000000−2i2i00-220000
χ512-22-2-222-2-22-22-2222-22-2-2−2i2i−2i2i002i−2i2i−2i00000000000000000000000000000000002i−2i00-220000
χ522-22-2-222-2-22-22-2222-22-2-2−2i2i−2i2i002i−2i2i−2i0000000000000000000000000000000000−2i2i002-20000
χ532-2-2-222-222-2-22-22-2-222-222-2-22002-2-22000000000000000000000000000022-2-200000000002-2
χ542-2-2-222-222-2-22-22-2-222-222-2-22002-2-220000000000000000000000000000-2-2220000000000-22
χ552-2-2-222-222-2-22-22-2-222-22-222-200-222-2000000000000000000000000000022-2-20000000000-22
χ562-2-2-222-222-2-22-22-2-222-22-222-200-222-20000000000000000000000000000-2-22200000000002-2
χ572-2-2-222-22-222-22-22-222-2-22-2-2200-222-20000000000000000000000002i2i−2i−2i0000000000002i−2i00
χ582-2-2-222-22-222-22-22-222-2-22-2-2200-222-2000000000000000000000000−2i−2i2i2i000000000000−2i2i00
χ592-2-2-222-22-222-22-22-222-2-2-222-2002-2-220000000000000000000000002i2i−2i−2i000000000000−2i2i00
χ602-2-2-222-22-222-22-22-222-2-2-222-2002-2-22000000000000000000000000−2i−2i2i2i0000000000002i−2i00
χ61444-44-4-4-400000000000000004-400000000000000000000000000002-22-22-22-2000000000000
χ62444-44-4-4-400000000000000004-40000000000000000000000000000-22-22-22-22000000000000
χ63444-44-4-4-40000000000000000-4400000000000000000000000000002-22-2-22-22000000000000
χ64444-44-4-4-40000000000000000-440000000000000000000000000000-22-222-22-2000000000000
χ654-44-4-444-44-44-4-444-44-44-4000000000000000000000000000000000000000000000000000000
χ664-44-4-444-4-44-444-4-4-44-444000000000000000000000000000000000000000000000000000000
χ674-4-444-44-400000000000000000000004i−4i00000000000000000000002i−2i−2i2i2-2-22000000000000
χ684-4-444-44-400000000000000000000004i−4i0000000000000000000000−2i2i2i−2i-222-2000000000000
χ694-4-444-44-40000000000000000000000−4i4i00000000000000000000002i−2i−2i2i-222-2000000000000
χ704-4-444-44-40000000000000000000000−4i4i0000000000000000000000−2i2i2i−2i2-2-22000000000000
χ714-4-4-444-444-4-444-444-4-44-4000000000000000000000000000000000000000000000000000000
χ724-4-4-444-44-444-4-44-44-4-444000000000000000000000000000000000000000000000000000000
χ7388-8-8-8-888000000000000000000000000000000000000000000000000000000000000000000
χ748-888-8-8-88000000000000000000000000000000000000000000000000000000000000000000

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