Finite Group Databasebeta

← Group #117151

Character table — Group #117151

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222222222222222244444444444444444444888888888888888816161616161616161616161616161616
order12222222222244444444444444444444888888888888888888888888888888884444444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ511111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ611111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111
χ91-111-1-1-1111-1-1111-1-1-1-1-1-11111-1-111-11-1iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1iiii−i−i−i−iii−i−iii−i−i11-1-111-1-1
χ101-111-1-1-1111-1-1111-1-1-1-1-1-11111-1-111-11-1iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1iiii−i−i−i−i−i−iii−i−iii-1-111-1-111
χ111-111-1-1-1111-1-1111-1-1-1-1-1-11111-1-111-11-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11111−i−i−i−iiiiiii−i−i−i−iii-1-11111-1-1
χ121-111-1-1-1111-1-1111-1-1-1-1-1-11111-1-111-11-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11111−i−i−i−iiiii−i−iiiii−i−i11-1-1-1-111
χ131-111-1-1-1111-1-1111-1-1-1-1-1-11111-1-111-11-1−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1−i−i−i−iiiiiii−i−iii−i−i-1-111-1-111
χ141-111-1-1-1111-1-1111-1-1-1-1-1-11111-1-111-11-1−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1−i−i−i−iiiii−i−iii−i−iii11-1-111-1-1
χ151-111-1-1-1111-1-1111-1-1-1-1-1-11111-1-111-11-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11111iiii−i−i−i−iii−i−i−i−iii11-1-1-1-111
χ161-111-1-1-1111-1-1111-1-1-1-1-1-11111-1-111-11-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11111iiii−i−i−i−i−i−iiiii−i−i-1-11111-1-1
χ1722222222222222-222-2-2-2-2-2-2-2-2-2-2-222-2-2000000000000000000000000000000000000000000002i−2i2i−2i
χ1822222222222222-222-2-2-2-2-2-2-2-2-2-2-222-2-200000000000000000000000000000000000000000000−2i2i−2i2i
χ19222222222222-2-22-2-22222-2-222-2-22-2-2-2-2000000000000000022-2-222-2-2000000000000000000000000
χ20222222222222-2-22-2-22222-2-222-2-22-2-2-2-20000000000000000-2-222-2-222000000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-2-222-2-222-2-2-22200000000000000000000000000000000000000002-22-20000
χ22222222222222-2-2-2-2-2-2-2-2-222-2-222-2-2-2220000000000000000000000000000000000000000-22-220000
χ2322222222-2-2-2-22222222-2-2-2-2-2-2-2-22-2-2222222-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ2422222222-2-2-2-22222222-2-2-2-2-2-2-2-22-2-222-2-2-2-22222-2-2-2-2222200000000000000000000000000000000
χ2522222222-2-2-2-222-222-2-222222222-2-2-2-2-2000000000000000000000000000000002-22-2000000000000
χ2622222222-2-2-2-222-222-2-222222222-2-2-2-2-200000000000000000000000000000000-22-22000000000000
χ2722222222-2-2-2-2-2-22-2-222-2-222-2-222222-2-200000000000000000000000022-2-222-2-20000000000000000
χ2822222222-2-2-2-2-2-22-2-222-2-222-2-222222-2-2000000000000000000000000-2-222-2-2220000000000000000
χ2922222222-2-2-2-2-2-2-2-2-2-2-222-2-222-2-2-222220000000000000000000000000000000000002-22-200000000
χ3022222222-2-2-2-2-2-2-2-2-2-2-222-2-222-2-2-22222000000000000000000000000000000000000-22-2200000000
χ31222-2-2-22-22-22-200-2002-22-2002-20020000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2002i−2i002i−2i2−22−22−22−20000000000000000
χ32222-2-2-22-22-22-200-2002-22-2002-20020000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200−2i2i00−2i2i−22−22−22−220000000000000000
χ33222-2-2-22-22-22-200-2002-22-2002-20020000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2002i−2i002i−2i−22−22−22−220000000000000000
χ34222-2-2-22-22-22-200-2002-22-2002-20020000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200−2i2i00−2i2i2−22−22−22−20000000000000000
χ35222-2-2-22-2-22-2200-2002-2-2200-220020000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i22i−2i002i−2i002−2−222−2−220000000000000000
χ36222-2-2-22-2-22-2200-2002-2-2200-220020000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2−2i2i00−2i2i00−222−2−222−20000000000000000
χ37222-2-2-22-2-22-2200-2002-2-2200-220020000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i22i−2i002i−2i00−222−2−222−20000000000000000
χ38222-2-2-22-2-22-2200-2002-2-2200-220020000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−2i2i00−2i2i002−2−222−2−220000000000000000
χ392-222-2-2-2222-2-222-2-2-22222-2-2-2-222-22-2-22000000000000000000000000000000000000000000002i−2i−2i2i
χ402-222-2-2-2222-2-222-2-2-22222-2-2-2-222-22-2-2200000000000000000000000000000000000000000000−2i2i2i−2i
χ412-222-2-2-2222-2-2-2-2222-2-2-2-2-2-222222-22-22000000000000000022-2-2-2-222000000000000000000000000
χ422-222-2-2-2222-2-2-2-2222-2-2-2-2-2-222222-22-220000000000000000-2-22222-2-2000000000000000000000000
χ432-222-2-2-2222-2-2-2-2-222222222-2-2-2-2-2-222-200000000000000000000000000000000000000002-2-220000
χ442-222-2-2-2222-2-2-2-2-222222222-2-2-2-2-2-222-20000000000000000000000000000000000000000-222-20000
χ452-222-2-2-22-2-222222-2-2-2-222-2-2-2-2222-222-22i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i00000000000000000000000000000000
χ462-222-2-2-22-2-222222-2-2-2-222-2-2-2-2222-222-2−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i00000000000000000000000000000000
χ472-222-2-2-22-2-22222-2-2-222-2-22222-2-2-2-22-22000000000000000000000000000000002i−2i−2i2i000000000000
χ482-222-2-2-22-2-22222-2-2-222-2-22222-2-2-2-22-2200000000000000000000000000000000−2i2i2i−2i000000000000
χ492-222-2-2-22-2-222-2-2222-2-22222-2-2-2-222-2-220000000000000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ502-222-2-2-22-2-222-2-2222-2-22222-2-2-2-222-2-22000000000000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ512-222-2-2-22-2-222-2-2-22222-2-2-2-22222-22-22-20000000000000000000000000000000000002i−2i−2i2i00000000
χ522-222-2-2-22-2-222-2-2-22222-2-2-2-22222-22-22-2000000000000000000000000000000000000−2i2i2i−2i00000000
χ532-22-222-2-22-2-2200-200-22-22002-2002000022−2−222−2−2−2−222−2−222002i−2i00−2i2i−i2i2−i2i2i2−i2i2−i20000000000000000
χ542-22-222-2-22-2-2200-200-22-22002-2002000022−2−222−2−2−2−222−2−22200−2i2i002i−2ii2−i2i2−i2−i2i2−i2i20000000000000000
χ552-22-222-2-22-2-2200-200-22-22002-20020000−2−222−2−22222−2−222−2−2002i−2i00−2i2ii2−i2i2−i2−i2i2−i2i20000000000000000
χ562-22-222-2-22-2-2200-200-22-22002-20020000−2−222−2−22222−2−222−2−200−2i2i002i−2i−i2i2−i2i2i2−i2i2−i20000000000000000
χ572-22-222-2-2-222-200-200-222-200-22002000022−2−2−2−222−2−22222−2−22i−2i00−2i2i00−i2i2i2−i2i2−i2−i2i20000000000000000
χ582-22-222-2-2-222-200-200-222-200-22002000022−2−2−2−222−2−22222−2−2−2i2i002i−2i00i2−i2−i2i2−i2i2i2−i20000000000000000
χ592-22-222-2-2-222-200-200-222-200-220020000−2−22222−2−222−2−2−2−2222i−2i00−2i2i00i2−i2−i2i2−i2i2i2−i20000000000000000
χ602-22-222-2-2-222-200-200-222-200-220020000−2−22222−2−222−2−2−2−222−2i2i002i−2i00−i2i2i2−i2i2−i2−i2i20000000000000000
χ61444-4-4-44-44-44-400400-44-4400-4400-40000000000000000000000000000000000000000000000000000
χ62444-4-4-44-4-44-4400400-444-4004-400-40000000000000000000000000000000000000000000000000000
χ6344-444-4-4-400004-404-4000000000000000000022−2222−22000022−2222−2200000000000000000000000000000000
χ6444-444-4-4-400004-404-40000000000000000000−2222−22220000−2222−222200000000000000000000000000000000
χ6544-444-4-4-40000-440-4400000000000000022−2222−22000022−2222−22000000000000000000000000000000000000
χ6644-444-4-4-40000-440-44000000000000000−2222−22220000−2222−2222000000000000000000000000000000000000
χ6744-4-4-44-4400000000000004-4004-4000002i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i00000000000000000000000000000000
χ6844-4-4-44-4400000000000004-4004-400000−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i00000000000000000000000000000000
χ6944-4-4-44-440000000000000-4400-44000002i−2i−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i00000000000000000000000000000000
χ7044-4-4-44-440000000000000-4400-4400000−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i00000000000000000000000000000000
χ714-44-444-4-44-4-44004004-44-400-4400-40000000000000000000000000000000000000000000000000000
χ724-44-444-4-4-444-4004004-4-44004-400-40000000000000000000000000000000000000000000000000000
χ734-4-44-444-400004-40-4400000000000000000002i2−2i22i2−2i20000−2i22i2−2i22i200000000000000000000000000000000
χ744-4-44-444-400004-40-440000000000000000000−2i22i2−2i22i200002i2−2i22i2−2i200000000000000000000000000000000
χ754-4-44-444-40000-4404-40000000000000002i2−2i22i2−2i20000−2i22i2−2i22i2000000000000000000000000000000000000
χ764-4-44-444-40000-4404-4000000000000000−2i22i2−2i22i200002i2−2i22i2−2i2000000000000000000000000000000000000
χ774-4-4-44-44400000000000004-400-44000002-2-222-2-22-222-2-222-200000000000000000000000000000000
χ784-4-4-44-44400000000000004-400-4400000-222-2-222-22-2-222-2-2200000000000000000000000000000000
χ794-4-4-44-4440000000000000-44004-4000002-2-22-222-2-222-22-2-2200000000000000000000000000000000
χ804-4-4-44-4440000000000000-44004-400000-222-22-2-222-2-22-222-200000000000000000000000000000000

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