Finite Group Databasebeta

← Group #119596

Character table — Group #119596

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444488888888888888888888888888888888161616161616161616161616
order12222222222244444444444444444444444444888888888888888888888888444488888888
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
χ5111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111
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
χ91-1-1-1-111111-1-11111-1-1-1-1-111-11-111-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iii−i−i11-1-111-1-1
χ101-1-1-1-111111-1-11111-1-1-1-1-111-11-111-1-11111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−iii-1-111-1-111
χ111-1-1-1-111111-1-11111-1-1-1-1-111-11-111-1-11111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiii−i−i-1-111-1-111
χ121-1-1-1-111111-1-11111-1-1-1-1-111-11-111-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−iii11-1-111-1-1
χ131-1-1-1-111111-1-11111-1-1-1-1-111-11-111-1-1-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−iii11-1-1-1-111
χ141-1-1-1-111111-1-11111-1-1-1-1-111-11-111-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiii−i−i-1-11111-1-1
χ151-1-1-1-111111-1-11111-1-1-1-1-111-11-111-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−iii-1-11111-1-1
χ161-1-1-1-111111-1-11111-1-1-1-1-111-11-111-1-1-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iii−i−i11-1-1-1-111
χ1722222222222222-2-2-2-2-222-2-2-222-2-2-2-20000000000000000000000000000000000002i−2i2i−2i0000
χ1822222222222222-2-2-2-2-222-2-2-222-2-2-2-2000000000000000000000000000000000000−2i2i−2i2i0000
χ19222222222222-2-222222-2-2222-2-2-2-2-2-222-2-222-2-2000000000000000000000000000000000000
χ20222222222222-2-222222-2-2222-2-2-2-2-2-2-2-222-2-222000000000000000000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000000000000000002i−2i2i−2i
χ22222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000000000000000000000000000−2i2i−2i2i
χ2322222222-2-2-2-2222-222-2222-2-2-2-22-22-2000000000000000000000000000000002i−2i2i−2i00000000
χ2422222222-2-2-2-2222-222-2222-2-2-2-22-22-200000000000000000000000000000000−2i2i−2i2i00000000
χ2522222222-2-2-2-222-22-2-2222-222-2-2-22-2200000000000000000000000022-2-222-2-2000000000000
χ2622222222-2-2-2-222-22-2-2222-222-2-2-22-22000000000000000000000000-2-222-2-222000000000000
χ2722222222-2-2-2-2-2-22-222-2-2-22-2-222-22-2200000000000000002i2i−2i−2i2i2i−2i−2i00000000000000000000
χ2822222222-2-2-2-2-2-22-222-2-2-22-2-222-22-220000000000000000−2i−2i2i2i−2i−2i2i2i00000000000000000000
χ2922222222-2-2-2-2-2-2-22-2-22-2-2-222222-22-2000000002i2i−2i−2i2i2i−2i−2i0000000000000000000000000000
χ3022222222-2-2-2-2-2-2-22-2-22-2-2-222222-22-200000000−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000
χ31222-2-2-22-22-22-200222-2200-2-2-2000000002-2002-22−22−22−22−2000000002−22−22−22−2000000000000
χ32222-2-2-22-22-22-200222-2200-2-2-2000000002-2002-2−22−22−22−2200000000−22−22−22−22000000000000
χ33222-2-2-22-22-22-200222-2200-2-2-200000000-2200-222−22−22−22−200000000−22−22−22−22000000000000
χ34222-2-2-22-22-22-200222-2200-2-2-200000000-2200-22−22−22−22−22000000002−22−22−22−2000000000000
χ35222-2-2-22-2-22-2200-22-222002-2-20000002i−2i002i−2i00i2−i2−i2i2i2−i2−i2i2000000002−2−222−2−22000000000000
χ36222-2-2-22-2-22-2200-22-222002-2-20000002i−2i002i−2i00−i2i2i2−i2−i2i2i2−i200000000−222−2−222−2000000000000
χ37222-2-2-22-2-22-2200-22-222002-2-2000000−2i2i00−2i2i00i2−i2−i2i2i2−i2−i2i200000000−222−2−222−2000000000000
χ38222-2-2-22-2-22-2200-22-222002-2-2000000−2i2i00−2i2i00−i2i2i2−i2−i2i2i2−i2000000002−2−222−2−22000000000000
χ392-2-222-22-22-2-220022-22-200-2-22000000002-200-22i2−i2i2−i2−i2i2−i2i200000000i2−i2i2−i2−i2i2−i2i2000000000000
χ402-2-222-22-22-2-220022-22-200-2-22000000002-200-22−i2i2−i2i2i2−i2i2−i200000000−i2i2−i2i2i2−i2i2−i2000000000000
χ412-2-222-22-22-2-220022-22-200-2-2200000000-22002-2i2−i2i2−i2−i2i2−i2i200000000−i2i2−i2i2i2−i2i2−i2000000000000
χ422-2-222-22-22-2-220022-22-200-2-2200000000-22002-2−i2i2−i2i2i2−i2i2−i200000000i2−i2i2−i2−i2i2−i2i2000000000000
χ432-2-222-22-2-222-200-222-2-2002-220000002i−2i00−2i2i002−2−22−222−200000000−i2i2i2−i2i2−i2−i2i2000000000000
χ442-2-222-22-2-222-200-222-2-2002-220000002i−2i00−2i2i00−222−22−2−2200000000i2−i2−i2i2−i2i2i2−i2000000000000
χ452-2-222-22-2-222-200-222-2-2002-22000000−2i2i002i−2i002−2−22−222−200000000i2−i2−i2i2−i2i2i2−i2000000000000
χ462-2-222-22-2-222-200-222-2-2002-22000000−2i2i002i−2i00−222−22−2−2200000000−i2i2i2−i2i2−i2−i2i2000000000000
χ472-2-2-2-222222-2-222-2-2222-2-2-2-222-2-2-2220000000000000000000000000000000000002i−2i−2i2i0000
χ482-2-2-2-222222-2-222-2-2222-2-2-2-222-2-2-222000000000000000000000000000000000000−2i2i2i−2i0000
χ492-2-2-2-222222-2-2-2-222-2-2-22222-2-22-2-22222-2-2-2-222000000000000000000000000000000000000
χ502-2-2-2-222222-2-2-2-222-2-2-22222-2-22-2-222-2-22222-2-2000000000000000000000000000000000000
χ512-2-2-2-222222-2-2-2-2-2-222222-2-22-2222-2-200000000000000000000000000000000000000002i−2i−2i2i
χ522-2-2-2-222222-2-2-2-2-2-222222-2-22-2222-2-20000000000000000000000000000000000000000−2i2i2i−2i
χ532-2-2-2-2222-2-222222-2-2-22-2-22-22-222-2-22000000000000000000000000000000002-2-2200000000
χ542-2-2-2-2222-2-222222-2-2-22-2-22-22-222-2-2200000000000000000000000000000000-222-200000000
χ552-2-2-2-2222-2-22222-2222-2-2-2-22-2-22-222-20000000000000000000000002i2i−2i−2i−2i−2i2i2i000000000000
χ562-2-2-2-2222-2-22222-2222-2-2-2-22-2-22-222-2000000000000000000000000−2i−2i2i2i2i2i−2i−2i000000000000
χ572-2-2-2-2222-2-222-2-22-2-2-22222-222-2-222-2000000000000000022-2-2-2-22200000000000000000000
χ582-2-2-2-2222-2-222-2-22-2-2-22222-222-2-222-20000000000000000-2-22222-2-200000000000000000000
χ592-2-2-2-2222-2-222-2-2-2222-222-22-22-22-2-220000000022-2-2-2-2220000000000000000000000000000
χ602-2-2-2-2222-2-222-2-2-2222-222-22-22-22-2-2200000000-2-22222-2-20000000000000000000000000000
χ61444-4-4-44-44-44-400-4-4-44-40044400000000000000000000000000000000000000000000000000
χ62444-4-4-44-4-44-44004-44-4-400-44400000000000000000000000000000000000000000000000000
χ6344-44-4-4-4400004i−4i000004i−4i00000000000000000000000002ζ−2ζ2ζ3−2ζ32ζ−2ζ2ζ3−2ζ300000000000000000000
χ6444-44-4-4-4400004i−4i000004i−4i0000000000000000000000000−2ζ2ζ−2ζ32ζ3−2ζ2ζ−2ζ32ζ300000000000000000000
χ6544-44-4-4-440000−4i4i00000−4i4i00000000000000000000000002ζ3−2ζ32ζ−2ζ2ζ3−2ζ32ζ−2ζ00000000000000000000
χ6644-44-4-4-440000−4i4i00000−4i4i0000000000000000000000000−2ζ32ζ3−2ζ2ζ−2ζ32ζ3−2ζ2ζ00000000000000000000
χ674-44-44-4-4400004i−4i00000−4i4i00000000000000000000000002ζ3−2ζ3−2ζ2ζ−2ζ32ζ32ζ−2ζ00000000000000000000
χ684-44-44-4-4400004i−4i00000−4i4i0000000000000000000000000−2ζ32ζ32ζ−2ζ2ζ3−2ζ3−2ζ2ζ00000000000000000000
χ694-44-44-4-440000−4i4i000004i−4i00000000000000000000000002ζ−2ζ−2ζ32ζ3−2ζ2ζ2ζ3−2ζ300000000000000000000
χ704-44-44-4-440000−4i4i000004i−4i0000000000000000000000000−2ζ2ζ2ζ3−2ζ32ζ−2ζ−2ζ32ζ300000000000000000000
χ714-4-444-44-44-4-4400-4-44-440044-400000000000000000000000000000000000000000000000000
χ724-4-444-44-4-444-4004-4-44400-44-400000000000000000000000000000000000000000000000000
χ7388-8-888-8-8000000000000000000000000000000000000000000000000000000000000000000
χ748-888-88-8-8000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.