Finite Group Databasebeta

← Group #401059

Character table — Group #401059

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size111111112222222222224444444444444444444488888888888888888816161616161616161616161616161616
order12222222222244444444224488888888888888882224444444888888884444444488888888
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
χ911111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-11111-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ1011111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-11111-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ1111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-11111
χ1211111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-11111-1-11111-1-1-1-111111111-1-1-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-1111111111111-111-1-1-1-1-111-1-111-1-1-1-111-1-1-1-11111-1-1-1-111
χ1411111111111111111111-1-1-1-1-1-1-1-1111111111111-111-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1
χ1511111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111111111-1-1-1-111-1-11111-1-1
χ1611111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1111111-1-11111-1-111-1-1-1-111
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
χ2122222222-2-2-2-222-22-2-2-2222222222222200000000-2000000-200-2-2-2-200000000000000000000
χ2222222222-2-2-2-222-22-2-2-222222-2-2-2-2-2-2-2-200000000-2000000-200222200000000000000000000
χ2322222222-2-2-2-222-22-2-2-22-2-2-2-22222-2-2-2-2000000002000000200-2-22200000000000000000000
χ2422222222-2-2-2-222-22-2-2-22-2-2-2-2-2-2-2-2222200000000200000020022-2-200000000000000000000
χ2522222222-2-2-2-2-2-22-2222-222-2-20000000000000000-22222-2-22-2-2000000000000000000000000
χ2622222222-2-2-2-2-2-22-2222-222-2-20000000000000000-2-2-2-2-222222000000000000000000000000
χ2722222222-2-2-2-2-2-22-2222-2-2-2220000000000000000222-2-222-2-2-2000000000000000000000000
χ2822222222-2-2-2-2-2-22-2222-2-2-22200000000000000002-2-222-2-2-222000000000000000000000000
χ2922-2-2-22-2222-2-22-2222-2-2-20000000000002i2i−2i−2i2i2i−2i−2i00000000000000000000002-20000002i−2i00
χ3022-2-2-22-2222-2-22-2222-2-2-20000000000002i2i−2i−2i2i2i−2i−2i0000000000000000000000-22000000−2i2i00
χ3122-2-2-22-2222-2-22-2222-2-2-2000000000000−2i−2i2i2i−2i−2i2i2i00000000000000000000002-2000000−2i2i00
χ3222-2-2-22-2222-2-22-2222-2-2-2000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000000000-220000002i−2i00
χ3322-2-2-22-2222-2-2-22-2-2-222200000000000022-2-2-2-2220000000000000000002-20000002-2000000
χ3422-2-2-22-2222-2-2-22-2-2-222200000000000022-2-2-2-222000000000000000000-22000000-22000000
χ3522-2-2-22-2222-2-2-22-2-2-2222000000000000-2-22222-2-20000000000000000002-2000000-22000000
χ3622-2-2-22-2222-2-2-22-2-2-2222000000000000-2-22222-2-2000000000000000000-220000002-2000000
χ372-22-2-2-2222-22-22-2-2-22-2220000000000002-22-22-22-2000000000000000000002-20000002-20000
χ382-22-2-2-2222-22-22-2-2-22-2220000000000002-22-22-22-200000000000000000000-22000000-220000
χ392-22-2-2-2222-22-22-2-2-22-222000000000000-22-22-22-22000000000000000000002-2000000-220000
χ402-22-2-2-2222-22-22-2-2-22-222000000000000-22-22-22-2200000000000000000000-220000002-20000
χ412-22-2-2-2222-22-2-2222-22-2-20000000000002i−2i2i−2i−2i2i−2i2i0000000000000000000000002-20000002i−2i
χ422-22-2-2-2222-22-2-2222-22-2-20000000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000-22000000−2i2i
χ432-22-2-2-2222-22-2-2222-22-2-2000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000000000002-2000000−2i2i
χ442-22-2-2-2222-22-2-2222-22-2-2000000000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000-220000002i−2i
χ452-2-222-2-222-2-2222-2-222-2-2000000002i2i−2i−2i2i−2i−2i2i2i−2i−2i2i02-2000002-2002i−2i00000000000000000000
χ462-2-222-2-222-2-2222-2-222-2-2000000002i2i−2i−2i−2i2i2i−2i−2i2i2i−2i0-2200000-22002i−2i00000000000000000000
χ472-2-222-2-222-2-2222-2-222-2-200000000−2i−2i2i2i2i−2i−2i2i2i−2i−2i2i0-2200000-2200−2i2i00000000000000000000
χ482-2-222-2-222-2-2222-2-222-2-200000000−2i−2i2i2i−2i2i2i−2i−2i2i2i−2i02-2000002-200−2i2i00000000000000000000
χ492-2-222-2-222-2-22-2-222-2-222000022-2-200002-2-22-222-20002-22-20002-20000000000000000000000
χ502-2-222-2-222-2-22-2-222-2-222000022-2-20000-222-22-2-22000-22-220002-20000000000000000000000
χ512-2-222-2-222-2-22-2-222-2-2220000-2-22200002-2-22-222-2000-22-22000-220000000000000000000000
χ522-2-222-2-222-2-22-2-222-2-2220000-2-2220000-222-22-2-220002-22-2000-220000000000000000000000
χ532-2-222-2-22-222-2222-2-2-22-2000000002i2i−2i−2i000000000002-2-2200000−2i2i2i−2i2i−2i0000000000000000
χ542-2-222-2-22-222-2222-2-2-22-2000000002i2i−2i−2i00000000000-222-200000−2i2i−2i2i−2i2i0000000000000000
χ552-2-222-2-22-222-2222-2-2-22-200000000−2i−2i2i2i000000000002-2-22000002i−2i−2i2i−2i2i0000000000000000
χ562-2-222-2-22-222-2222-2-2-22-200000000−2i−2i2i2i00000000000-222-2000002i−2i2i−2i2i−2i0000000000000000
χ572-2-222-2-22-222-2-2-2-2222-22000022-2-200000000000002-200000-22-22002-2-220000000000000000
χ582-2-222-2-22-222-2-2-2-2222-22000022-2-20000000000000-22000002-2-2200-222-20000000000000000
χ592-2-222-2-22-222-2-2-2-2222-220000-2-22200000000000002-200000-222-200-222-20000000000000000
χ602-2-222-2-22-222-2-2-2-2222-220000-2-2220000000000000-22000002-22-2002-2-220000000000000000
χ614444-4-4-4-40000000000004-40022−2222−2222−2222−22000000000000000000000000000000000000000000
χ624444-4-4-4-40000000000004-400−2222−2222−2222−2222000000000000000000000000000000000000000000
χ634444-4-4-4-4000000000000-440022−2222−22−2222−2222000000000000000000000000000000000000000000
χ644444-4-4-4-4000000000000-4400−2222−222222−2222−22000000000000000000000000000000000000000000
χ6544-4-4-44-44-4-4444-4-44-444-4000000000000000000000000000000000000000000000000000000
χ6644-4-4-44-44-4-444-444-44-4-44000000000000000000000000000000000000000000000000000000
χ674-44-4-4-444-44-444-44-4-44-44000000000000000000000000000000000000000000000000000000
χ684-44-4-4-444-44-44-44-444-44-4000000000000000000000000000000000000000000000000000000
χ694-4-44-444-4000000000000004i−4i22−22−22222i2−2i2−2i22i2000000000000000000000000000000000000000000
χ704-4-44-444-4000000000000004i−4i−222222−22−2i22i22i2−2i2000000000000000000000000000000000000000000
χ714-4-44-444-400000000000000−4i4i22−22−2222−2i22i22i2−2i2000000000000000000000000000000000000000000
χ724-4-44-444-400000000000000−4i4i−222222−222i2−2i2−2i22i2000000000000000000000000000000000000000000
χ7388-8-88-88-8000000000000000000000000000000000000000000000000000000000000000000
χ748-88-888-8-8000000000000000000000000000000000000000000000000000000000000000000

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