Finite Group Databasebeta

← Group #396728

Character table — Group #396728

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444488888888888888888888888888888888161616161616161616161616
order12222222222222224444444422444444444444888888888888888888888888244444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-11-1-11111
χ5111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1111-1-11-1-1-1-1-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-111-1111111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ9111111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11-1-1111-1-111-1-1
χ10111111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-11111-1-1-1-1-111
χ11111111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-111-1-1-111-1-111
χ12111111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111-1-1-1-111111-1-1
χ13111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111111-1-1-1-1111-1-111
χ14111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1-1-11111-1-1
χ15111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-11111-1-1-111-1-1
χ16111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-11-1-1111-1-1-1-111
χ172222222222222222-2-2-2-2-2-2-2-222-2-2-2-200000000000000002i2i−2i−2i2i2i−2i−2i00000000000000000000
χ182222222222222222-2-2-2-2-2-2-2-222-2-2-2-20000000000000000−2i−2i2i2i−2i−2i2i2i00000000000000000000
χ19222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000002i2i−2i−2i−2i−2i2i2i00000000000000000000
χ20222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ2122222222-2-2-2-222222-222-2-22-2-2-222-2-20000000000000000000000000000000022-200-2000000
χ2222222222-2-2-2-222222-222-2-22-2-2-222-2-200000000000000000000000000000000-2-22002000000
χ2322222222-2-2-2-22222-22-2-222-22-2-2-2-2220000000022-2-222-2-20000000000000000000000000000
χ2422222222-2-2-2-22222-22-2-222-22-2-2-2-22200000000-2-222-2-2220000000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-22-222-2-22-222-2-222000000000000000000000000000000002-2200-2000000
χ2622222222-2-2-2-2-2-2-2-22-222-2-22-222-2-22200000000000000000000000000000000-22-2002000000
χ2722222222-2-2-2-2-2-2-2-2-22-2-222-222222-2-20000000022-2-2-2-2220000000000000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-22-2-222-222222-2-200000000-2-22222-2-20000000000000000000000000000
χ2922-2-2-222-222-2-200002-22-22-2-2200000000002i2i−2i−2i000000002-22-2000000002i2i−2i−2i000000000000
χ3022-2-2-222-222-2-200002-22-22-2-2200000000002i2i−2i−2i00000000-22-2200000000−2i−2i2i2i000000000000
χ3122-2-2-222-222-2-200002-22-22-2-220000000000−2i−2i2i2i000000002-22-200000000−2i−2i2i2i000000000000
χ3222-2-2-222-222-2-200002-22-22-2-220000000000−2i−2i2i2i00000000-22-22000000002i2i−2i−2i000000000000
χ3322-2-2-222-222-2-20000-22-22-222-20000002i2i−2i−2i0000000000002i−2i−2i2i000022-2-20000000000000000
χ3422-2-2-222-222-2-20000-22-22-222-20000002i2i−2i−2i000000000000−2i2i2i−2i0000-2-2220000000000000000
χ3522-2-2-222-222-2-20000-22-22-222-2000000−2i−2i2i2i0000000000002i−2i−2i2i0000-2-2220000000000000000
χ3622-2-2-222-222-2-20000-22-22-222-2000000−2i−2i2i2i000000000000−2i2i2i−2i000022-2-20000000000000000
χ372-22-2-2-2222-22-2000022-222-2-2-200000000002-22-20000000000002i−2i2i−2i2i−2i2i−2i0000000000000000
χ382-22-2-2-2222-22-2000022-222-2-2-200000000002-22-2000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000
χ392-22-2-2-2222-22-2000022-222-2-2-20000000000-22-220000000000002i−2i2i−2i−2i2i−2i2i0000000000000000
χ402-22-2-2-2222-22-2000022-222-2-2-20000000000-22-22000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000
χ412-22-2-2-2222-22-20000-2-22-2-22220000002-22-200000000000000002-2-2200002-22-2000000000000
χ422-22-2-2-2222-22-20000-2-22-2-22220000002-22-20000000000000000-222-20000-22-22000000000000
χ432-22-2-2-2222-22-20000-2-22-2-2222000000-22-2200000000000000002-2-220000-22-22000000000000
χ442-22-2-2-2222-22-20000-2-22-2-2222000000-22-220000000000000000-222-200002-22-2000000000000
χ452-2-222-22-22-2-2222-2-22-2-2-2222-22-22-22-22i−2i−2i2i2i−2i−2i2i000000000000000000000000000000000000
χ462-2-222-22-22-2-2222-2-22-2-2-2222-22-22-22-2−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000000000
χ472-2-222-22-22-2-2222-2-2-2222-2-2-222-2-22-220000000000000000000000002i−2i−2i2i−2i2i2i−2i000000000000
χ482-2-222-22-22-2-2222-2-2-2222-2-2-222-2-22-22000000000000000000000000−2i2i2i−2i2i−2i−2i2i000000000000
χ492-2-222-22-22-2-22-2-2222-2-2-2222-2-22-22-222i−2i−2i2i−2i2i2i−2i000000000000000000000000000000000000
χ502-2-222-22-22-2-22-2-2222-2-2-2222-2-22-22-22−2i2i2i−2i2i−2i−2i2i000000000000000000000000000000000000
χ512-2-222-22-22-2-22-2-222-2222-2-2-22-222-22-20000000000000000000000002i−2i−2i2i2i−2i−2i2i000000000000
χ522-2-222-22-22-2-22-2-222-2222-2-2-22-222-22-2000000000000000000000000−2i2i2i−2i−2i2i2i−2i000000000000
χ532-2-222-22-2-222-222-2-222-2-2-2-222-222-2-2200000000000000000000000000000000000000002i−2i2i−2i
χ542-2-222-22-2-222-222-2-222-2-2-2-222-222-2-220000000000000000000000000000000000000000−2i2i−2i2i
χ552-2-222-22-2-222-222-2-2-2-22222-2-2-22-222-2000000000000000000000000000000000002i−2i02i−2i0000
χ562-2-222-22-2-222-222-2-2-2-22222-2-2-22-222-200000000000000000000000000000000000−2i2i0−2i2i0000
χ572-2-222-22-2-222-2-2-22222-2-2-2-2222-2-222-200000000000000000000000000000000000000002i−2i−2i2i
χ582-2-222-22-2-222-2-2-22222-2-2-2-2222-2-222-20000000000000000000000000000000000000000−2i2i2i−2i
χ592-2-222-22-2-222-2-2-222-2-22222-2-22-22-2-22000000000000000000000000000000000002i−2i0−2i2i0000
χ602-2-222-22-2-222-2-2-222-2-22222-2-22-22-2-2200000000000000000000000000000000000−2i2i02i−2i0000
χ614444-4-4-4-400004-44-400000000000000000000000022−220022−220000000000000000000000000000
χ624444-4-4-4-400004-44-4000000000000000000000000−222200−22220000000000000000000000000000
χ634444-4-4-4-40000-44-4400000000000000000000000022−2200−22220000000000000000000000000000
χ644444-4-4-4-40000-44-44000000000000000000000000−22220022−220000000000000000000000000000
χ6544-4-4-444-4-4-4440000444-4-44-4-400000000000000000000000000000000000000000000000000
χ6644-4-4-444-4-4-4440000-4-4-444-44400000000000000000000000000000000000000000000000000
χ674-44-4-4-444-44-4400004-4-44-44-4400000000000000000000000000000000000000000000000000
χ684-44-4-4-444-44-440000-444-44-44-400000000000000000000000000000000000000000000000000
χ694-4-44-44-4400004-4-44000000000000000000000022−220022−22000000000000000000000000000000
χ704-4-44-44-4400004-4-440000000000000000000000−222200−2222000000000000000000000000000000
χ714-4-44-44-440000-444-4000000000000000000000022−2200−2222000000000000000000000000000000
χ724-4-44-44-440000-444-40000000000000000000000−22220022−22000000000000000000000000000000
χ7388-8-88-8-88000000000000000000000000000000000000000000000000000000000000000000
χ748-88-888-8-8000000000000000000000000000000000000000000000000000000000000000000

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