Finite Group Databasebeta

← Group #120800

Character table — Group #120800

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
χ91-1-1111-1-111-1-11111-1-1-1-1-111-111-1-1-11ii−i−iii−i−iiiii−i−i−i−i1111-1-1-1-11111-1-1-1-1ii−i−iii−i−i11-1-1
χ101-1-1111-1-111-1-11111-1-1-1-1-111-111-1-1-11ii−i−iii−i−iiiii−i−i−i−i-1-1-1-111111111-1-1-1-1−i−iii−i−iii-1-111
χ111-1-1111-1-111-1-11111-1-1-1-1-111-111-1-1-11ii−i−iii−i−i−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111ii−i−i−i−iii-1-111
χ121-1-1111-1-111-1-11111-1-1-1-1-111-111-1-1-11ii−i−iii−i−i−i−i−i−iiiii-1-1-1-11111-1-1-1-11111−i−iiiii−i−i11-1-1
χ131-1-1111-1-111-1-11111-1-1-1-1-111-111-1-1-11−i−iii−i−iiiiiii−i−i−i−i1111-1-1-1-1-1-1-1-11111−i−iiiii−i−i-1-111
χ141-1-1111-1-111-1-11111-1-1-1-1-111-111-1-1-11−i−iii−i−iiiiiii−i−i−i−i-1-1-1-11111-1-1-1-11111ii−i−i−i−iii11-1-1
χ151-1-1111-1-111-1-11111-1-1-1-1-111-111-1-1-11−i−iii−i−iii−i−i−i−iiiii1111-1-1-1-11111-1-1-1-1−i−iii−i−iii11-1-1
χ161-1-1111-1-111-1-11111-1-1-1-1-111-111-1-1-11−i−iii−i−iii−i−i−i−iiiii-1-1-1-111111111-1-1-1-1ii−i−iii−i−i-1-111
χ1722222222222222-2-2222-2-2222-2-2-2-2-2-22222-2-2-2-2000000000000000000000000000000000000
χ1822222222222222-2-2222-2-2222-2-2-2-2-2-2-2-2-2-22222000000000000000000000000000000000000
χ19222222222222-2-222-2-2-222-2-2-22-22-2-2-20000000000000000000000000000000000002i−2i2i−2i0000
χ20222222222222-2-222-2-2-222-2-2-22-22-2-2-2000000000000000000000000000000000000−2i2i−2i2i0000
χ21222222222222-2-2-2-2-2-2-2-2-2-2-2-2-22-222200000000000000000000000000000000000000002i−2i2i−2i
χ22222222222222-2-2-2-2-2-2-2-2-2-2-2-2-22-22220000000000000000000000000000000000000000−2i2i−2i2i
χ2322222222-2-2-2-22-22222-2222-2-2-2-2-22-220000000022-2-222-2-20000000000000000000000000000
χ2422222222-2-2-2-22-22222-2222-2-2-2-2-22-2200000000-2-222-2-2220000000000000000000000000000
χ2522222222-2-2-2-22-2-2-222-2-2-22-2-2222-22-20000000000000000000000002i2i−2i−2i2i2i−2i−2i000000000000
χ2622222222-2-2-2-22-2-2-222-2-2-22-2-2222-22-2000000000000000000000000−2i−2i2i2i−2i−2i2i2i000000000000
χ2722222222-2-2-2-2-2222-2-2222-222-22-2-22-2000000000000000022-2-222-2-200000000000000000000
χ2822222222-2-2-2-2-2222-2-2222-222-22-2-22-20000000000000000-2-222-2-22200000000000000000000
χ2922222222-2-2-2-2-22-2-2-2-22-2-2-2222-222-22000000000000000000000000000000002-22-200000000
χ3022222222-2-2-2-2-22-2-2-2-22-2-2-2222-222-2200000000000000000000000000000000-22-2200000000
χ3122-22-2-22-22-22-222002-2200-2-2-20000002-22-200002−22−22−22−2000000002−22−22−22−2000000000000
χ3222-22-2-22-22-22-222002-2200-2-2-20000002-22-20000−22−22−22−2200000000−22−22−22−22000000000000
χ3322-22-2-22-22-22-222002-2200-2-2-2000000-22-2200002−22−22−22−200000000−22−22−22−22000000000000
χ3422-22-2-22-22-22-222002-2200-2-2-2000000-22-220000−22−22−22−22000000002−22−22−22−2000000000000
χ3522-22-2-22-2-22-222-2002-2-200-22200000000002i−2i2i−2i2−2−222−2−2200000000i2−i2−i2i2i2−i2−i2i2000000000000
χ3622-22-2-22-2-22-222-2002-2-200-22200000000002i−2i2i−2i−222−2−222−200000000−i2i2i2−i2−i2i2i2−i2000000000000
χ3722-22-2-22-2-22-222-2002-2-200-2220000000000−2i2i−2i2i2−2−222−2−2200000000−i2i2i2−i2−i2i2i2−i2000000000000
χ3822-22-2-22-2-22-222-2002-2-200-2220000000000−2i2i−2i2i−222−2−222−200000000i2−i2−i2i2i2−i2−i2i2000000000000
χ392-222-2-2-222-2-222200-22-200-2-220000002i−2i−2i2i0000i2−i2i2−i2−i2i2−i2i2000000002−22−2−22−22000000000000
χ402-222-2-2-222-2-222200-22-200-2-220000002i−2i−2i2i0000−i2i2−i2i2i2−i2i2−i200000000−22−222−22−2000000000000
χ412-222-2-2-222-2-222200-22-200-2-22000000−2i2i2i−2i0000i2−i2i2−i2−i2i2−i2i200000000−22−222−22−2000000000000
χ422-222-2-2-222-2-222200-22-200-2-22000000−2i2i2i−2i0000−i2i2−i2i2i2−i2i2−i2000000002−22−2−22−22000000000000
χ432-222-2-2-22-222-22-200-22200-22-200000000002-2-22i2−i2−i2i2−i2i2i2−i200000000−i2i2i2−i2i2−i2−i2i2000000000000
χ442-222-2-2-22-222-22-200-22200-22-200000000002-2-22−i2i2i2−i2i2−i2−i2i200000000i2−i2−i2i2−i2i2i2−i2000000000000
χ452-222-2-2-22-222-22-200-22200-22-20000000000-222-2i2−i2−i2i2−i2i2i2−i200000000i2−i2−i2i2−i2i2i2−i2000000000000
χ462-222-2-2-22-222-22-200-22200-22-20000000000-222-2−i2i2i2−i2i2−i2−i2i200000000−i2i2i2−i2i2−i2−i2i2000000000000
χ472-2-2222-2-222-2-222-2-2-2-2-22222-2-2-2222-22i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000
χ482-2-2222-2-222-2-222-2-2-2-2-22222-2-2-2222-2−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000
χ492-2-2222-2-222-2-2-2-222222-2-2-2-222-2-222-20000000000000000000000000000000000002-2-220000
χ502-2-2222-2-222-2-2-2-222222-2-2-2-222-2-222-2000000000000000000000000000000000000-222-20000
χ512-2-2222-2-222-2-2-2-2-2-222222-2-22-222-2-2200000000000000000000000000000000000000002i−2i−2i2i
χ522-2-2222-2-222-2-2-2-2-2-222222-2-22-222-2-220000000000000000000000000000000000000000−2i2i2i−2i
χ532-2-2222-2-2-2-2222-222-2-22-2-22-22-2-22-222000000002i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ542-2-2222-2-2-2-2222-222-2-22-2-22-22-2-22-22200000000−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ552-2-2222-2-2-2-2222-2-2-2-2-22222-2222-22-2-20000000000000000000000002i2i−2i−2i−2i−2i2i2i000000000000
χ562-2-2222-2-2-2-2222-2-2-2-2-22222-2222-22-2-2000000000000000000000000−2i−2i2i2i2i2i−2i−2i000000000000
χ572-2-2222-2-2-2-222-222222-2-2-2-22-2-2222-2-2000000000000000022-2-2-2-22200000000000000000000
χ582-2-2222-2-2-2-222-222222-2-2-2-22-2-2222-2-20000000000000000-2-22222-2-200000000000000000000
χ592-2-2222-2-2-2-222-22-2-222-222-22-22-2-2-222000000000000000000000000000000002i−2i−2i2i00000000
χ602-2-2222-2-2-2-222-22-2-222-222-22-22-2-2-22200000000000000000000000000000000−2i2i2i−2i00000000
χ61444-44-4-4-40000004-40004-400000000000000000000000000022−220022−2200000000000000000000
χ62444-44-4-4-40000004-40004-4000000000000000000000000000−222200−222200000000000000000000
χ63444-44-4-4-4000000-44000-44000000000000000000000000022−220022−220000000000000000000000
χ64444-44-4-4-4000000-44000-440000000000000000000000000−222200−22220000000000000000000000
χ6544-44-4-44-44-44-4-4-400-44-40044400000000000000000000000000000000000000000000000000
χ6644-44-4-44-4-44-44-4400-444004-4-400000000000000000000000000000000000000000000000000
χ674-444-4-4-444-4-44-4-4004-440044-400000000000000000000000000000000000000000000000000
χ684-444-4-4-44-444-4-44004-4-4004-4400000000000000000000000000000000000000000000000000
χ694-4-4-44-4440000004-4000-4400000000000000000000000000022−2200−222200000000000000000000
χ704-4-4-44-4440000004-4000-44000000000000000000000000000−22220022−2200000000000000000000
χ714-4-4-44-444000000-440004-4000000000000000000000000022−2200−22220000000000000000000000
χ724-4-4-44-444000000-440004-40000000000000000000000000−22220022−220000000000000000000000
χ7388-8-8-88-88000000000000000000000000000000000000000000000000000000000000000000
χ748-88-8-888-8000000000000000000000000000000000000000000000000000000000000000000

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