Finite Group Databasebeta

← Group #114149

Character table — Group #114149

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444488888888888888888888888888888888161616161616161616161616
order12222222222244444444444444444488888888888888888888888888888888222222448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
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
χ6111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111
χ91-1-1-1-111111-1-111-111-1-111-1-1-1111-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i11-1-11-11-1ii−i−i
χ101-1-1-1-111111-1-111-111-1-111-1-1-1111-1-1-11111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-111-11-11−i−iii
χ111-1-1-1-111111-1-111-111-1-111-1-1-1111-1-1-11111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii-1-111-11-11ii−i−i
χ121-1-1-1-111111-1-111-111-1-111-1-1-1111-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii11-1-11-11-1−i−iii
χ131-1-1-1-111111-1-111-111-1-111-1-1-1111-1-1-1-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii11-1-1-11-11−i−iii
χ141-1-1-1-111111-1-111-111-1-111-1-1-1111-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-1-1111-11-1ii−i−i
χ151-1-1-1-111111-1-111-111-1-111-1-1-1111-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i-1-1111-11-1−i−iii
χ161-1-1-1-111111-1-111-111-1-111-1-1-1111-1-1-1-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i11-1-1-11-11ii−i−i
χ17222222222222222-2-2-2-2-2-22-2-22-2-22-2-20000000000000000000000002i2i−2i−2i2i2i−2i−2i000000000000
χ18222222222222222-2-2-2-2-2-22-2-22-2-22-2-2000000000000000000000000−2i−2i2i2i−2i−2i2i2i000000000000
χ19222222222222-2-2-2222222-222-2-2-2-2-2-222-2-222-2-2000000000000000000000000000000000000
χ20222222222222-2-2-2222222-222-2-2-2-2-2-2-2-222-2-222000000000000000000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-2-2-2-222-222000000002i2i−2i−2i2i2i−2i−2i0000000000000000000000000000
χ22222222222222-2-2-2-2-2-2-2-2-2-2-2-2-222-22200000000−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000
χ2322222222-2-2-2-2222222-2-2-222-2-22-2-2-22000000000000000022-2-222-2-200000000000000000000
χ2422222222-2-2-2-2222222-2-2-222-2-22-2-2-220000000000000000-2-222-2-22200000000000000000000
χ2522222222-2-2-2-2222-2-2-22222-22-2-22-22-200000000000000000000000000000000000022-2-20000
χ2622222222-2-2-2-2222-2-2-22222-22-2-22-22-2000000000000000000000000000000000000-2-2220000
χ2722222222-2-2-2-2-2-2-2222-2-2-2-22-22-2222-200000000000000000000000000000000000000002i−2i2i−2i
χ2822222222-2-2-2-2-2-2-2222-2-2-2-22-22-2222-20000000000000000000000000000000000000000−2i2i−2i2i
χ2922222222-2-2-2-2-2-2-2-2-2-2222-2-2222-22-22000000000000000000000000000000002-22-200000000
χ3022222222-2-2-2-2-2-2-2-2-2-2222-2-2222-22-2200000000000000000000000000000000-22-2200000000
χ31222-2-2-2-222-22-20002-2222-20-2-2000000002-2002-2i2−i2i2−i2i2−i2i2−i200000000i2−i2i2−i2i2−i2i2−i2000000000000
χ32222-2-2-2-222-22-20002-2222-20-2-2000000002-2002-2−i2i2−i2i2−i2i2−i2i200000000−i2i2−i2i2−i2i2−i2i2000000000000
χ33222-2-2-2-222-22-20002-2222-20-2-200000000-2200-22i2−i2i2−i2i2−i2i2−i200000000−i2i2−i2i2−i2i2−i2i2000000000000
χ34222-2-2-2-222-22-20002-2222-20-2-200000000-2200-22−i2i2−i2i2−i2i2−i2i200000000i2−i2i2−i2i2−i2i2−i2000000000000
χ35222-2-2-2-222-22-2000-22-2-2-220220000002-2002-2002−2−222−2−22000000002−2−222−2−22000000000000
χ36222-2-2-2-222-22-2000-22-2-2-220220000002-2002-200−222−2−222−200000000−222−2−222−2000000000000
χ37222-2-2-2-222-22-2000-22-2-2-22022000000-2200-22002−2−222−2−2200000000−222−2−222−2000000000000
χ38222-2-2-2-222-22-2000-22-2-2-22022000000-2200-2200−222−2−222−2000000002−2−222−2−22000000000000
χ392-2-222-2-222-2-220002-2-2-22-2022000000002-200-222−22−2−22−22000000002−22−2−22−22000000000000
χ402-2-222-2-222-2-220002-2-2-22-2022000000002-200-22−22−222−22−200000000−22−222−22−2000000000000
χ412-2-222-2-222-2-220002-2-2-22-202200000000-22002-22−22−2−22−2200000000−22−222−22−2000000000000
χ422-2-222-2-222-2-220002-2-2-22-202200000000-22002-2−22−222−22−2000000002−22−2−22−22000000000000
χ432-2-222-2-222-2-22000-2222-220-2-20000002-200-2200i2−i2−i2i2−i2i2i2−i200000000i2−i2−i2i2−i2i2i2−i2000000000000
χ442-2-222-2-222-2-22000-2222-220-2-20000002-200-2200−i2i2i2−i2i2−i2−i2i200000000−i2i2i2−i2i2−i2−i2i2000000000000
χ452-2-222-2-222-2-22000-2222-220-2-2000000-22002-200i2−i2−i2i2−i2i2i2−i200000000−i2i2i2−i2i2−i2−i2i2000000000000
χ462-2-222-2-222-2-22000-2222-220-2-2000000-22002-200−i2i2i2−i2i2−i2−i2i200000000i2−i2−i2i2−i2i2i2−i2000000000000
χ472-2-2-2-222222-2-222-2-2-222-2-2-2222-2-2-22200000000000000000000000022-2-2-2-222000000000000
χ482-2-2-2-222222-2-222-2-2-222-2-2-2222-2-2-222000000000000000000000000-2-22222-2-2000000000000
χ492-2-2-2-222222-2-2-2-2222-2-2222-2-2-2-2-222222-2-2-2-222000000000000000000000000000000000000
χ502-2-2-2-222222-2-2-2-2222-2-2222-2-2-2-2-2222-2-22222-2-2000000000000000000000000000000000000
χ512-2-2-2-222222-2-2-2-22-2-222-2-2222-2222-2-20000000022-2-2-2-2220000000000000000000000000000
χ522-2-2-2-222222-2-2-2-22-2-222-2-2222-2222-2-200000000-2-22222-2-20000000000000000000000000000
χ532-2-2-2-2222-2-22222-222-22-2-2-2-22-22-222-200000000000000002i2i−2i−2i−2i−2i2i2i00000000000000000000
χ542-2-2-2-2222-2-22222-222-22-2-2-2-22-22-222-20000000000000000−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ552-2-2-2-2222-2-22222-2-2-22-222-22-2-2-222-220000000000000000000000000000000000002-2-220000
χ562-2-2-2-2222-2-22222-2-2-22-222-22-2-2-222-22000000000000000000000000000000000000-222-20000
χ572-2-2-2-2222-2-222-2-2222-22-2-22-222-22-2-2200000000000000000000000000000000000000002-2-22
χ582-2-2-2-2222-2-222-2-2222-22-2-22-222-22-2-220000000000000000000000000000000000000000-222-2
χ592-2-2-2-2222-2-222-2-22-2-22-22222-222-2-22-2000000000000000000000000000000002-2-2200000000
χ602-2-2-2-2222-2-222-2-22-2-22-22222-222-2-22-200000000000000000000000000000000-222-200000000
χ61444-4-4-4-44-44-440004-44-4-440-4400000000000000000000000000000000000000000000000000
χ62444-4-4-4-44-44-44000-44-444-404-400000000000000000000000000000000000000000000000000
χ6344-44-44-4-400004-44000000-4000000000000000000000000002i2−2i2002i2−2i200000000000000000000
χ6444-44-44-4-400004-44000000-400000000000000000000000000−2i22i200−2i22i200000000000000000000
χ6544-44-44-4-40000-44-4000000400000000000000000000000022−220022−220000000000000000000000
χ6644-44-44-4-40000-44-40000004000000000000000000000000−222200−22220000000000000000000000
χ674-44-444-4-400004-4-400000040000000000000000000000000022−2200−222200000000000000000000
χ684-44-444-4-400004-4-4000000400000000000000000000000000−22220022−2200000000000000000000
χ694-44-444-4-40000-444000000-40000000000000000000000002i2−2i200−2i22i20000000000000000000000
χ704-44-444-4-40000-444000000-4000000000000000000000000−2i22i2002i2−2i20000000000000000000000
χ714-4-444-4-44-444-40004-4-44-4404-400000000000000000000000000000000000000000000000000
χ724-4-444-4-44-444-4000-444-44-40-4400000000000000000000000000000000000000000000000000
χ7388-8-88-88-8000000000000000000000000000000000000000000000000000000000000000000
χ748-888-8-88-8000000000000000000000000000000000000000000000000000000000000000000

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