Finite Group Databasebeta

← Group #396164

Character table — Group #396164

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222444444444444888888888888888888888888888888161616161616161616161616
order12222222222244444444224444444444244444444444444444444444444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-111-1-11-1-1-1-1-1-1-1-111-1-111111111-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111-1-1-1-111-1-11-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ51111111111111111111111-1-1-1-111-1-1-1-111111-1-1111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111
χ61111111111111111111111-1-1-1-111-1-1-1-111111-1-1111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ71111111111111111111111-1-1-1-111-1-1-1-11-1-1-1-1-1-1-1-1111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ81111111111111111111111-1-1-1-111-1-1-1-11-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ911111111111111111111-1-11111-1-11111-11111-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-111-1-1
χ1011111111111111111111-1-11111-1-11111-11111-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-111
χ1111111111111111111111-1-11111-1-11111-1-1-1-1-1-1-111-1-1-1-1-11111-1-1111111-1-1-1-1-1-11111-1-1-1-111
χ1211111111111111111111-1-11111-1-11111-1-1-1-1-1-1-111-1-1-1-1-11111-1-111-1-1-1-1111111-1-1-1-11111-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-111-1-11111-1-1
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-111-1-1-1-111
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11111-1-1-1-111111111-1-1-1-111-1-1-1-111-1-111
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11111-1-1-1-11111-1-1-1-11111-1-11111-1-111-1-1
χ17222222222222-2-2-2-2-2-2-2-2220000-2-20000200000000-222-2-222-2-2000000000000000000000000
χ18222222222222-2-2-2-2-2-2-2-2220000-2-20000200000000-2-2-222-2-222000000000000000000000000
χ19222222222222-2-2-2-2-2-2-2-2-2-20000220000-200000000222-2-2-2-222000000000000000000000000
χ20222222222222-2-2-2-2-2-2-2-2-2-20000220000-2000000002-2-22222-2-2000000000000000000000000
χ2122222222-2-2-2-222-2-222-2-2220000220000-222-2-20022-20000000000-2-200000000000000000000
χ2222222222-2-2-2-222-2-222-2-2220000220000-2-2-22200-2-2-200000000002200000000000000000000
χ2322222222-2-2-2-222-2-222-2-2-2-20000-2-20000222-2-200-2-2200000000002200000000000000000000
χ2422222222-2-2-2-222-2-222-2-2-2-20000-2-200002-2-222002220000000000-2-200000000000000000000
χ2522222222-2-2-2-2-2-222-2-222222222-2-2-2-2-2-2-200002200200000000-2-20000000000000000000000
χ2622222222-2-2-2-2-2-222-2-22222-2-2-2-2-2-22222-20000-2-200200000000220000000000000000000000
χ2722222222-2-2-2-2-2-222-2-222-2-2222222-2-2-2-220000-2-200-200000000220000000000000000000000
χ2822222222-2-2-2-2-2-222-2-222-2-2-2-2-2-2222222200002200-200000000-2-20000000000000000000000
χ2922-2-2-222-22-22-22-22-22-22-2000000000000000002i−2i2i−2i02-22-200002i−2i2i−2i00000000000000000000
χ3022-2-2-222-22-22-22-22-22-22-2000000000000000002i−2i−2i2i0-22-2200002i−2i−2i2i00000000000000000000
χ3122-2-2-222-22-22-22-22-22-22-200000000000000000−2i2i2i−2i0-22-220000−2i2i2i−2i00000000000000000000
χ3222-2-2-222-22-22-22-22-22-22-200000000000000000−2i2i−2i2i02-22-20000−2i2i−2i2i00000000000000000000
χ3322-2-2-222-22-22-2-22-22-22-22002i2i−2i−2i002i2i−2i−2i02i−2i2i−2i000002-2-220000000000000000000000000000
χ3422-2-2-222-22-22-2-22-22-22-22002i2i−2i−2i002i2i−2i−2i0−2i2i−2i2i00000-222-20000000000000000000000000000
χ3522-2-2-222-22-22-2-22-22-22-2200−2i−2i2i2i00−2i−2i2i2i02i−2i2i−2i00000-222-20000000000000000000000000000
χ3622-2-2-222-22-22-2-22-22-22-2200−2i−2i2i2i00−2i−2i2i2i0−2i2i−2i2i000002-2-220000000000000000000000000000
χ3722-2-2-222-2-22-222-2-222-2-22002i2i−2i−2i00−2i−2i2i2i00000002i−2i000002-22-200−2i2i00000000000000000000
χ3822-2-2-222-2-22-222-2-222-2-22002i2i−2i−2i00−2i−2i2i2i0000000−2i2i00000-22-22002i−2i00000000000000000000
χ3922-2-2-222-2-22-222-2-222-2-2200−2i−2i2i2i002i2i−2i−2i00000002i−2i00000-22-2200−2i2i00000000000000000000
χ4022-2-2-222-2-22-222-2-222-2-2200−2i−2i2i2i002i2i−2i−2i0000000−2i2i000002-22-2002i−2i00000000000000000000
χ4122-2-2-222-2-22-22-222-2-222-200000000000002i−2i−2i2i2i−2i00000002-2-22−2i2i0000000000000000000000
χ4222-2-2-222-2-22-22-222-2-222-200000000000002i−2i−2i2i−2i2i0000000-222-22i−2i0000000000000000000000
χ4322-2-2-222-2-22-22-222-2-222-20000000000000−2i2i2i−2i2i−2i0000000-222-2−2i2i0000000000000000000000
χ4422-2-2-222-2-22-22-222-2-222-20000000000000−2i2i2i−2i−2i2i00000002-2-222i−2i0000000000000000000000
χ452-222-22-2-22-2-22-22-2-22-222002i−2i2i−2i002i−2i2i−2i000000000000000000000000000000002i−2i0000002-2
χ462-222-22-2-22-2-22-22-2-22-222002i−2i2i−2i002i−2i2i−2i00000000000000000000000000000000−2i2i000000-22
χ472-222-22-2-22-2-22-22-2-22-22200−2i2i−2i2i00−2i2i−2i2i000000000000000000000000000000002i−2i000000-22
χ482-222-22-2-22-2-22-22-2-22-22200−2i2i−2i2i00−2i2i−2i2i00000000000000000000000000000000−2i2i0000002-2
χ492-222-22-2-2-222-22-2-2-2-2222002i−2i2i−2i00−2i2i−2i2i0000000000000000000000000000002i−2i0000002-200
χ502-222-22-2-2-222-22-2-2-2-2222002i−2i2i−2i00−2i2i−2i2i000000000000000000000000000000−2i2i000000-2200
χ512-222-22-2-2-222-22-2-2-2-222200−2i2i−2i2i002i−2i2i−2i0000000000000000000000000000002i−2i000000-2200
χ522-222-22-2-2-222-22-2-2-2-222200−2i2i−2i2i002i−2i2i−2i000000000000000000000000000000−2i2i0000002-200
χ532-2-2-222-2222-2-2222-2-2-2-22002-2-22002-2-22000000000000000000000000002i2i−2i−2i0000002i−2i0000
χ542-2-2-222-2222-2-2222-2-2-2-22002-2-22002-2-2200000000000000000000000000−2i−2i2i2i000000−2i2i0000
χ552-2-2-222-2222-2-2222-2-2-2-2200-222-200-222-2000000000000000000000000002i2i−2i−2i000000−2i2i0000
χ562-2-2-222-2222-2-2222-2-2-2-2200-222-200-222-200000000000000000000000000−2i−2i2i2i0000002i−2i0000
χ572-2-2-222-22-2-222-2-22-222-22002-2-2200-222-2000000000000000000000022-2-2000000002-2000000
χ582-2-2-222-22-2-222-2-22-222-22002-2-2200-222-20000000000000000000000-2-22200000000-22000000
χ592-2-2-222-22-2-222-2-22-222-2200-222-2002-2-22000000000000000000000022-2-200000000-22000000
χ602-2-2-222-22-2-222-2-22-222-2200-222-2002-2-220000000000000000000000-2-222000000002-2000000
χ61444-44-4-4-40000000000004-4000000000000000000000000000000002-22-22-22-2000000000000
χ62444-44-4-4-40000000000004-400000000000000000000000000000000-22-22-22-22000000000000
χ63444-44-4-4-4000000000000-44000000000000000000000000000000002-22-2-22-22000000000000
χ64444-44-4-4-4000000000000-4400000000000000000000000000000000-22-222-22-2000000000000
χ654-444-44-4-44-4-444-444-44-4-4000000000000000000000000000000000000000000000000000000
χ664-444-44-4-4-444-4-44444-4-4-4000000000000000000000000000000000000000000000000000000
χ674-4-444-44-40000000000000000004i−4i000000000000000000000000002-2-222i−2i−2i2i000000000000
χ684-4-444-44-40000000000000000004i−4i00000000000000000000000000-222-2−2i2i2i−2i000000000000
χ694-4-444-44-4000000000000000000−4i4i000000000000000000000000002-2-22−2i2i2i−2i000000000000
χ704-4-444-44-4000000000000000000−4i4i00000000000000000000000000-222-22i−2i−2i2i000000000000
χ714-4-4-444-4444-4-4-4-4-44444-4000000000000000000000000000000000000000000000000000000
χ724-4-4-444-44-4-44444-44-4-44-4000000000000000000000000000000000000000000000000000000
χ7388-88-8-8-88000000000000000000000000000000000000000000000000000000000000000000
χ748-88-8-8-888000000000000000000000000000000000000000000000000000000000000000000

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