Finite Group Databasebeta

← Group #121556

Character table — Group #121556

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444488888888888888888888888888888888161616161616161616161616
order12222222222244444444444444444444444444888888888888888888888888444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ5111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
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
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111
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
χ91-1111-1-1-111-1-11111-1-1-1-1-1-11111-1-11-1ii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−i1111-1-1-1-1i−ii−iii−i−i11-1-1
χ101-1111-1-1-111-1-11111-1-1-1-1-1-11111-1-11-1ii−i−iii−i−i1111-1-1-1-1−i−i−i−iiiii-1-1-1-11111−ii−iiii−i−i-1-111
χ111-1111-1-1-111-1-11111-1-1-1-1-1-11111-1-11-1ii−i−iii−i−i-1-1-1-11111iiii−i−i−i−i1111-1-1-1-1−ii−ii−i−iii-1-111
χ121-1111-1-1-111-1-11111-1-1-1-1-1-11111-1-11-1ii−i−iii−i−i-1-1-1-11111−i−i−i−iiiii-1-1-1-11111i−ii−i−i−iii11-1-1
χ131-1111-1-1-111-1-11111-1-1-1-1-1-11111-1-11-1−i−iii−i−iii1111-1-1-1-1iiii−i−i−i−i-1-1-1-11111i−ii−i−i−iii-1-111
χ141-1111-1-1-111-1-11111-1-1-1-1-1-11111-1-11-1−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii1111-1-1-1-1−ii−ii−i−iii11-1-1
χ151-1111-1-1-111-1-11111-1-1-1-1-1-11111-1-11-1−i−iii−i−iii-1-1-1-11111iiii−i−i−i−i-1-1-1-11111−ii−iiii−i−i11-1-1
χ161-1111-1-1-111-1-11111-1-1-1-1-1-11111-1-11-1−i−iii−i−iii-1-1-1-11111−i−i−i−iiiii1111-1-1-1-1i−ii−iii−i−i-1-111
χ1722222222222222-2-22222-2-222-2-2-2-2-2-22222-2-2-2-2000000000000000000000000000000000000
χ1822222222222222-2-22222-2-222-2-2-2-2-2-2-2-2-2-22222000000000000000000000000000000000000
χ19222222222222-2-222-2-2-2-222-2-22-22-2-2-200000000000000002i2i−2i−2i2i2i−2i−2i00000000000000000000
χ20222222222222-2-222-2-2-2-222-2-22-22-2-2-20000000000000000−2i−2i2i2i−2i−2i2i2i00000000000000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-2-2-2-22-222200000000000000000000000022-2-222-2-2000000000000
χ22222222222222-2-2-2-2-2-2-2-2-2-2-2-2-22-2222000000000000000000000000-2-222-2-222000000000000
χ2322222222-2-2-2-22-22222-2-2222-2-22-2-2-220000000022-2-222-2-20000000000000000000000000000
χ2422222222-2-2-2-22-22222-2-2222-2-22-2-2-2200000000-2-222-2-2220000000000000000000000000000
χ2522222222-2-2-2-22-2-2-222-2-2-2-22-22-2222-20000000000000000000000000000000000002-22-20000
χ2622222222-2-2-2-22-2-2-222-2-2-2-22-22-2222-2000000000000000000000000000000000000-22-220000
χ2722222222-2-2-2-2-2222-2-22222-22-2-2-222-20000000000000000000000000000000022-2-200000000
χ2822222222-2-2-2-2-2222-2-22222-22-2-2-222-200000000000000000000000000000000-2-22200000000
χ2922222222-2-2-2-2-22-2-2-2-222-2-2-22222-2-2200000000000000000000000000000000000000002-22-2
χ3022222222-2-2-2-2-22-2-2-2-222-2-2-22222-2-220000000000000000000000000000000000000000-22-22
χ31222-2-2-2-222-22-22-2002-22-200-220000002i−2i2i−2i0000000000002−22−22−22−2i2−i2i2−i2i2−i2i2−i2000000000000
χ32222-2-2-2-222-22-22-2002-22-200-220000002i−2i2i−2i000000000000−22−22−22−22−i2i2−i2i2−i2i2−i2i2000000000000
χ33222-2-2-2-222-22-22-2002-22-200-22000000−2i2i−2i2i0000000000002−22−22−22−2−i2i2−i2i2−i2i2−i2i2000000000000
χ34222-2-2-2-222-22-22-2002-22-200-22000000−2i2i−2i2i000000000000−22−22−22−22i2−i2i2−i2i2−i2i2−i2000000000000
χ35222-2-2-2-222-22-2-2200-22-22002-200000000002-22-200000000i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2000000000000
χ36222-2-2-2-222-22-2-2200-22-22002-200000000002-22-200000000−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2000000000000
χ37222-2-2-2-222-22-2-2200-22-22002-20000000000-22-2200000000i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2000000000000
χ38222-2-2-2-222-22-2-2200-22-22002-20000000000-22-2200000000−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2000000000000
χ392-2222-2-2-222-2-222-2-2-2-2-2-22222-2-222-222i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000
χ402-2222-2-2-222-2-222-2-2-2-2-2-22222-2-222-22−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000
χ412-2222-2-2-222-2-2-2-2222222-2-2-2-22-2-22-22000000000000000022-2-2-2-22200000000000000000000
χ422-2222-2-2-222-2-2-2-2222222-2-2-2-22-2-22-220000000000000000-2-22222-2-200000000000000000000
χ432-2222-2-2-222-2-2-2-2-2-2222222-2-2-222-22-200000000000000000000000022-2-2-2-222000000000000
χ442-2222-2-2-222-2-2-2-2-2-2222222-2-2-222-22-2000000000000000000000000-2-22222-2-2000000000000
χ452-2222-2-2-2-2-2222-222-2-222-2-22-2-2222-2-20000000022-2-2-2-2220000000000000000000000000000
χ462-2222-2-2-2-2-2222-222-2-222-2-22-2-2222-2-200000000-2-22222-2-20000000000000000000000000000
χ472-2222-2-2-2-2-2222-2-2-2-2-222222-22-2-2-2220000000000000000000000000000000000002i−2i−2i2i0000
χ482-2222-2-2-2-2-2222-2-2-2-2-222222-22-2-2-222000000000000000000000000000000000000−2i2i2i−2i0000
χ492-2222-2-2-2-2-222-222222-2-2-2-2-22-2-22-222000000000000000000000000000000002i−2i−2i2i00000000
χ502-2222-2-2-2-2-222-222222-2-2-2-2-22-2-22-22200000000000000000000000000000000−2i2i2i−2i00000000
χ512-2222-2-2-2-2-222-22-2-222-2-222-2222-22-2-200000000000000000000000000000000000000002-2-22
χ522-2222-2-2-2-2-222-22-2-222-2-222-2222-22-2-20000000000000000000000000000000000000000-222-2
χ532-22-2-222-22-2-222-200-22-2200-220000002-2-22000000000000i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2000000000000
χ542-22-2-222-22-2-222-200-22-2200-220000002-2-22000000000000−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2000000000000
χ552-22-2-222-22-2-222-200-22-2200-22000000-222-2000000000000i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2000000000000
χ562-22-2-222-22-2-222-200-22-2200-22000000-222-2000000000000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2000000000000
χ572-22-2-222-22-2-22-22002-22-2002-200000000002i−2i−2i2i000000002−2−22−222−2−i2i2i2−i2i2−i2−i2i2000000000000
χ582-22-2-222-22-2-22-22002-22-2002-200000000002i−2i−2i2i00000000−222−22−2−22i2−i2−i2i2−i2i2i2−i2000000000000
χ592-22-2-222-22-2-22-22002-22-2002-20000000000−2i2i2i−2i000000002−2−22−222−2i2−i2−i2i2−i2i2i2−i2000000000000
χ602-22-2-222-22-2-22-22002-22-2002-20000000000−2i2i2i−2i00000000−222−22−2−22−i2i2i2−i2i2−i2−i2i2000000000000
χ61444-4-4-4-44-44-4444004-4-4400-4-400000000000000000000000000000000000000000000000000
χ62444-4-4-4-44-44-44-4-400-444-4004400000000000000000000000000000000000000000000000000
χ6344-44-44-4-40000004-400004-400000000000000000022−220022−220000000000000000000000000000
χ6444-44-44-4-40000004-400004-4000000000000000000−222200−22220000000000000000000000000000
χ6544-44-44-4-4000000-440000-44000000000000000022−220022−22000000000000000000000000000000
χ6644-44-44-4-4000000-440000-440000000000000000−222200−2222000000000000000000000000000000
χ674-44-4-444-4-444-44400-444-400-4-400000000000000000000000000000000000000000000000000
χ684-44-4-444-4-444-4-4-4004-4-44004400000000000000000000000000000000000000000000000000
χ694-4-44-4-4440000004-40000-4400000000000000000022−2200−22220000000000000000000000000000
χ704-4-44-4-4440000004-40000-44000000000000000000−22220022−220000000000000000000000000000
χ714-4-44-4-444000000-4400004-4000000000000000022−2200−2222000000000000000000000000000000
χ724-4-44-4-444000000-4400004-40000000000000000−22220022−22000000000000000000000000000000
χ7388-8-88-88-8000000000000000000000000000000000000000000000000000000000000000000
χ748-8-8-888-88000000000000000000000000000000000000000000000000000000000000000000

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