Finite Group Databasebeta

← Group #406772

Character table — Group #406772

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444488888888888888888888888888888888161616161616161616161616
order12222222222244444444444422224444444444444444448888888888888888444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-111-1-1-1-111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-11111-1-1
χ91111111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1
χ101111111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-11111
χ111111111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111
χ121111111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1111111-1-1-1-1
χ131111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111-1-111
χ141111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-111-1-1
χ151111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-11111-1-111-1-1
χ161111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-111111111-1-1-1-111-1-1-1-111-1-111
χ17222222222222-2-2-2-22222-2-2-2-2-2-2-2-222000000000000000000000000000000000000002i−2i2i−2i00
χ18222222222222-2-2-2-22222-2-2-2-2-2-2-2-22200000000000000000000000000000000000000−2i2i−2i2i00
χ19222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2000000000000000000000000000000000000002i−2i−2i2i00
χ20222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-200000000000000000000000000000000000000−2i2i2i−2i00
χ2122222222-2-2-2-222-2-222222-2-2222-2-2-2-20000000022-2-2-2-2220000000000000000000000000000
χ2222222222-2-2-2-222-2-222222-2-2222-2-2-2-200000000-2-22222-2-20000000000000000000000000000
χ2322222222-2-2-2-222-2-2-2-2-2-22-2-22-2-22222000000002222-2-2-2-20000000000000000000000000000
χ2422222222-2-2-2-222-2-2-2-2-2-22-2-22-2-2222200000000-2-2-2-222220000000000000000000000000000
χ2522222222-2-2-2-2-2-2222222-222-2-2-222-2-2000000000000000022-2-222-2-200000000000000000000
χ2622222222-2-2-2-2-2-2222222-222-2-2-222-2-20000000000000000-2-222-2-22200000000000000000000
χ2722222222-2-2-2-2-2-222-2-2-2-2-222-222-2-222000000000000000022-2-2-2-22200000000000000000000
χ2822222222-2-2-2-2-2-222-2-2-2-2-222-222-2-2220000000000000000-2-22222-2-200000000000000000000
χ292222-2-2-2-222-2-22-22-20000-22-2200000000002i2i−2i−2i2i−2i002i−2i0000000000000022-2-2000000000000
χ302222-2-2-2-222-2-22-22-20000-22-2200000000002i2i−2i−2i−2i2i00−2i2i00000000000000-2-222000000000000
χ312222-2-2-2-222-2-22-22-20000-22-220000000000−2i−2i2i2i2i−2i002i−2i00000000000000-2-222000000000000
χ322222-2-2-2-222-2-22-22-20000-22-220000000000−2i−2i2i2i−2i2i00−2i2i0000000000000022-2-2000000000000
χ332222-2-2-2-2-2-2222-2-220000-2-2220000002i2i−2i−2i00002i−2i00−2i2i000000000022-2-20000000000000000
χ342222-2-2-2-2-2-2222-2-220000-2-2220000002i2i−2i−2i0000−2i2i002i−2i0000000000-2-2220000000000000000
χ352222-2-2-2-2-2-2222-2-220000-2-222000000−2i−2i2i2i00002i−2i00−2i2i0000000000-2-2220000000000000000
χ362222-2-2-2-2-2-2222-2-220000-2-222000000−2i−2i2i2i0000−2i2i002i−2i000000000022-2-20000000000000000
χ372-22-222-2-22-22-2222222-2-2-2-2-2-22-22-22-22-22-22-22-2000000000000000000000000000000000000
χ382-22-222-2-22-22-2222222-2-2-2-2-2-22-22-22-2-22-22-22-22000000000000000000000000000000000000
χ392-22-222-2-22-22-22222-2-222-2-2-2-2-22-22-222-22-2-22-22000000000000000000000000000000000000
χ402-22-222-2-22-22-22222-2-222-2-2-2-2-22-22-22-22-222-22-2000000000000000000000000000000000000
χ412-22-222-2-22-22-2-2-2-2-222-2-22222-22-222-20000000000000000000000000000000000002-200002-2
χ422-22-222-2-22-22-2-2-2-2-222-2-22222-22-222-2000000000000000000000000000000000000-220000-22
χ432-22-222-2-22-22-2-2-2-2-2-2-22222222-22-2-220000000000000000000000000000000000002-20000-22
χ442-22-222-2-22-22-2-2-2-2-2-2-22222222-22-2-22000000000000000000000000000000000000-2200002-2
χ452-22-222-2-2-22-2222-2-222-2-2-222-22-2-22-220000000000000000000000002i−2i2i−2i2i−2i2i−2i000000000000
χ462-22-222-2-2-22-2222-2-222-2-2-222-22-2-22-22000000000000000000000000−2i2i−2i2i−2i2i−2i2i000000000000
χ472-22-222-2-2-22-2222-2-2-2-222-222-2-222-22-20000000000000000000000002i−2i2i−2i−2i2i−2i2i000000000000
χ482-22-222-2-2-22-2222-2-2-2-222-222-2-222-22-2000000000000000000000000−2i2i−2i2i2i−2i2i−2i000000000000
χ492-22-222-2-2-22-22-2-22222-2-22-2-22-222-2-22000000000000000000000000000000002i−2i2i−2i00000000
χ502-22-222-2-2-22-22-2-22222-2-22-2-22-222-2-2200000000000000000000000000000000−2i2i−2i2i00000000
χ512-22-222-2-2-22-22-2-222-2-2222-2-222-2-222-2000000000000000000000000000000002i−2i−2i2i00000000
χ522-22-222-2-2-22-22-2-222-2-2222-2-222-2-222-200000000000000000000000000000000−2i2i2i−2i00000000
χ532-22-2-2-2222-2-222-22-200002-22-200000000002i−2i−2i2i002-2002-2000000002i−2i−2i2i0000000000000000
χ542-22-2-2-2222-2-222-22-200002-22-200000000002i−2i−2i2i00-2200-2200000000−2i2i2i−2i0000000000000000
χ552-22-2-2-2222-2-222-22-200002-22-20000000000−2i2i2i−2i002-2002-200000000−2i2i2i−2i0000000000000000
χ562-22-2-2-2222-2-222-22-200002-22-20000000000−2i2i2i−2i00-2200-22000000002i−2i−2i2i0000000000000000
χ572-22-2-2-222-222-22-2-22000022-2-20000002i−2i−2i2i0000002-200-22000000000000−2i2i2i−2i000000000000
χ582-22-2-2-222-222-22-2-22000022-2-20000002i−2i−2i2i000000-22002-20000000000002i−2i−2i2i000000000000
χ592-22-2-2-222-222-22-2-22000022-2-2000000−2i2i2i−2i0000002-200-220000000000002i−2i−2i2i000000000000
χ602-22-2-2-222-222-22-2-22000022-2-2000000−2i2i2i−2i000000-22002-2000000000000−2i2i2i−2i000000000000
χ614444-4-4-4-444-4-4-44-4400004-44-400000000000000000000000000000000000000000000000000
χ624444-4-4-4-4-4-444-444-4000044-4-400000000000000000000000000000000000000000000000000
χ6344-4-44-4-44000000004i−4i4i−4i00000000000000000000000000002i2−2i20022−2200000000000000000000
χ6444-4-44-4-44000000004i−4i4i−4i0000000000000000000000000000−2i22i200−222200000000000000000000
χ6544-4-44-4-4400000000−4i4i−4i4i00000000000000000000000000002i2−2i200−222200000000000000000000
χ6644-4-44-4-4400000000−4i4i−4i4i0000000000000000000000000000−2i22i20022−2200000000000000000000
χ674-44-4-4-4444-4-44-44-440000-44-4400000000000000000000000000000000000000000000000000
χ684-44-4-4-444-444-4-444-40000-4-44400000000000000000000000000000000000000000000000000
χ694-4-444-44-4000000004i−4i−4i4i0000000000000000000000000022−22002i2−2i20000000000000000000000
χ704-4-444-44-4000000004i−4i−4i4i00000000000000000000000000−222200−2i22i20000000000000000000000
χ714-4-444-44-400000000−4i4i4i−4i0000000000000000000000000022−2200−2i22i20000000000000000000000
χ724-4-444-44-400000000−4i4i4i−4i00000000000000000000000000−2222002i2−2i20000000000000000000000
χ7388-8-8-888-8000000000000000000000000000000000000000000000000000000000000000000
χ748-8-88-88-88000000000000000000000000000000000000000000000000000000000000000000

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