Finite Group Databasebeta

← Group #396911

Character table — Group #396911

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size111111112222222222224444444444444444444488888888888888888816161616161616161616161616161616
order12222222222244444444224488888888888888882444444444888888882244444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-11-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-11-1-1-1-1-1-1111111-1-111-1-111-1-111-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-11-1-1-1-1-1-11111-1-111-1-111-1-111-1-111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-111-1-1
χ911111111111111111111-1-1-1-11111-1-1-1-111111111-11111-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ1011111111111111111111-1-1-1-11111-1-1-1-111111111-11111-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ1111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11111-1-111111111-1-1-1-1-1-1-1-11111
χ1211111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11111-1-11111-1-1-1-111111111-1-1-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-111-111-1-111-1-1-1-111-1-1-1-11111-1-1-1-111
χ1411111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-111-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1
χ1511111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-111111111-1-1-1-111-1-11111-1-1
χ1611111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1111111-1-11111-1-111-1-1-1-111
χ17222222222222-2-2-2-2-2-2-2-222-2-2000000002i2i2i2i−2i−2i−2i−2i2000000-20000002i2i−2i−2i0000000000000000
χ18222222222222-2-2-2-2-2-2-2-222-2-200000000−2i−2i−2i−2i2i2i2i2i2000000-2000000−2i−2i2i2i0000000000000000
χ19222222222222-2-2-2-2-2-2-2-2-2-222000000002i2i2i2i−2i−2i−2i−2i-20000002000000−2i−2i2i2i0000000000000000
χ20222222222222-2-2-2-2-2-2-2-2-2-22200000000−2i−2i−2i−2i2i2i2i2i-200000020000002i2i−2i−2i0000000000000000
χ2122222222-2-2-2-22-222-2-22-222222222222200000000-2000000-200-2-2-2-200000000000000000000
χ2222222222-2-2-2-22-222-2-22-22222-2-2-2-2-2-2-2-200000000-2000000-200222200000000000000000000
χ2322222222-2-2-2-22-222-2-22-2-2-2-2-22222-2-2-2-2000000002000000200-2-22200000000000000000000
χ2422222222-2-2-2-22-222-2-22-2-2-2-2-2-2-2-2-2222200000000200000020022-2-200000000000000000000
χ2522222222-2-2-2-2-22-2-222-2222-2-20000000000000000-222-2-2222-2-2000000000000000000000000
χ2622222222-2-2-2-2-22-2-222-2222-2-20000000000000000-2-2-222-2-2222000000000000000000000000
χ2722222222-2-2-2-2-22-2-222-22-2-2220000000000000000222-2-2-2-2-222000000000000000000000000
χ2822222222-2-2-2-2-22-2-222-22-2-22200000000000000002-2-22222-2-2-2000000000000000000000000
χ2922-2-2-222-222-2-222-2-2-2-222000000002i2i−2i−2i0000000002i−2i2i−2i00000002i−2i2-22-20000000000000000
χ3022-2-2-222-222-2-222-2-2-2-222000000002i2i−2i−2i000000000−2i2i−2i2i00000002i−2i-22-220000000000000000
χ3122-2-2-222-222-2-222-2-2-2-22200000000−2i−2i2i2i0000000002i−2i2i−2i0000000−2i2i-22-220000000000000000
χ3222-2-2-222-222-2-222-2-2-2-22200000000−2i−2i2i2i000000000−2i2i−2i2i0000000−2i2i2-22-20000000000000000
χ3322-2-2-222-222-2-2-2-22222-2-2000022-2-2000000000000000002i−2i02i−2i2-2002i−2i−2i2i0000000000000000
χ3422-2-2-222-222-2-2-2-22222-2-2000022-2-200000000000000000−2i2i0−2i2i2-200−2i2i2i−2i0000000000000000
χ3522-2-2-222-222-2-2-2-22222-2-20000-2-222000000000000000002i−2i02i−2i-2200−2i2i2i−2i0000000000000000
χ3622-2-2-222-222-2-2-2-22222-2-20000-2-22200000000000000000−2i2i0−2i2i-22002i−2i−2i2i0000000000000000
χ3722-2-2-222-2-2-2222-2-2-2222-2000000002i2i−2i−2i22-2-222-2-2000002i−2i0−2i2i00−2i2i00000000000000000000
χ3822-2-2-222-2-2-2222-2-2-2222-2000000002i2i−2i−2i-2-222-2-22200000−2i2i02i−2i00−2i2i00000000000000000000
χ3922-2-2-222-2-2-2222-2-2-2222-200000000−2i−2i2i2i22-2-222-2-200000−2i2i02i−2i002i−2i00000000000000000000
χ4022-2-2-222-2-2-2222-2-2-2222-200000000−2i−2i2i2i-2-222-2-222000002i−2i0−2i2i002i−2i00000000000000000000
χ4122-2-2-222-2-2-222-2222-2-2-22000022-2-200002i2i−2i−2i−2i−2i2i2i02i−2i−2i2i00000-220000000000000000000000
χ4222-2-2-222-2-2-222-2222-2-2-22000022-2-20000−2i−2i2i2i2i2i−2i−2i0−2i2i2i−2i00000-220000000000000000000000
χ4322-2-2-222-2-2-222-2222-2-2-220000-2-22200002i2i−2i−2i−2i−2i2i2i0−2i2i2i−2i000002-20000000000000000000000
χ4422-2-2-222-2-2-222-2222-2-2-220000-2-2220000−2i−2i2i2i2i2i−2i−2i02i−2i−2i2i000002-20000000000000000000000
χ452-222-22-2-22-22-22-22-22-2-220000000000002i−2i2i−2i2i−2i2i−2i000000000000000000002i−2i0000002-20000
χ462-222-22-2-22-22-22-22-22-2-220000000000002i−2i2i−2i2i−2i2i−2i00000000000000000000−2i2i000000-220000
χ472-222-22-2-22-22-22-22-22-2-22000000000000−2i2i−2i2i−2i2i−2i2i000000000000000000002i−2i000000-220000
χ482-222-22-2-22-22-22-22-22-2-22000000000000−2i2i−2i2i−2i2i−2i2i00000000000000000000−2i2i0000002-20000
χ492-222-22-2-22-22-2-22-22-222-20000000000002-22-2-22-220000000000000000000000002i−2i0000002i−2i
χ502-222-22-2-22-22-2-22-22-222-20000000000002-22-2-22-22000000000000000000000000−2i2i000000−2i2i
χ512-222-22-2-22-22-2-22-22-222-2000000000000-22-222-22-20000000000000000000000002i−2i000000−2i2i
χ522-222-22-2-22-22-2-22-22-222-2000000000000-22-222-22-2000000000000000000000000−2i2i0000002i−2i
χ532-2-2-222-22-222-222-222-2-2-20000000000002i−2i−2i2i2i−2i−2i2i00000000000000000000002-20000002i−2i00
χ542-2-2-222-22-222-222-222-2-2-20000000000002i−2i−2i2i2i−2i−2i2i0000000000000000000000-22000000−2i2i00
χ552-2-2-222-22-222-222-222-2-2-2000000000000−2i2i2i−2i−2i2i2i−2i00000000000000000000002-2000000−2i2i00
χ562-2-2-222-22-222-222-222-2-2-2000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000000000-220000002i−2i00
χ572-2-2-222-22-222-2-2-22-2-22220000000000002-2-22-222-20000000000000000002-20000002-2000000
χ582-2-2-222-22-222-2-2-22-2-22220000000000002-2-22-222-2000000000000000000-22000000-22000000
χ592-2-2-222-22-222-2-2-22-2-2222000000000000-222-22-2-220000000000000000002-2000000-22000000
χ602-2-2-222-22-222-2-2-22-2-2222000000000000-222-22-2-22000000000000000000-220000002-2000000
χ614-444-44-4-4-44-44444-4-44-4-4000000000000000000000000000000000000000000000000000000
χ624-444-44-4-4-44-44-4-4-444-444000000000000000000000000000000000000000000000000000000
χ634-44-44-44-4000000000000004i−4i22−2222−222i2−2i22i2−2i2000000000000000000000000000000000000000000
χ644-44-44-44-4000000000000004i−4i−2222−2222−2i22i2−2i22i2000000000000000000000000000000000000000000
χ654-44-44-44-400000000000000−4i4i22−2222−22−2i22i2−2i22i2000000000000000000000000000000000000000000
χ664-44-44-44-400000000000000−4i4i−2222−22222i2−2i22i2−2i2000000000000000000000000000000000000000000
χ674-4-44-4-4440000000000004-40022−22−222222−22−2222000000000000000000000000000000000000000000
χ684-4-44-4-4440000000000004-400−222222−22−222222−22000000000000000000000000000000000000000000
χ694-4-44-4-444000000000000-440022−22−2222−222222−22000000000000000000000000000000000000000000
χ704-4-44-4-444000000000000-4400−222222−2222−22−2222000000000000000000000000000000000000000000
χ714-4-4-444-444-4-444-4-44-44-44000000000000000000000000000000000000000000000000000000
χ724-4-4-444-444-4-44-444-44-44-4000000000000000000000000000000000000000000000000000000
χ73888-8-8-8-88000000000000000000000000000000000000000000000000000000000000000000
χ7488-888-8-8-8000000000000000000000000000000000000000000000000000000000000000000

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