Finite Group Databasebeta

← Group #320233

Character table — Group #320233

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444444444444444444448888888888888888161616161616161632323232
order12222222444444444444444444444488888888888888888888888888888888444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ911111111-1-1-1-1111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-11-11-1
χ1011111111-1-1-1-1111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-11-11
χ1111111111-1-1-1-1111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-11-11
χ1211111111-1-1-1-1111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1111-11-1
χ1311111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1111-1-11
χ1411111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-111-1
χ1511111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-111-1-1-1-111-111-1
χ1611111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-11111-1-11-1-11
χ1722222222222222-2-2-2-2-2-222-2-222-2-2-2-200000000000000000000000022-2-222-2-2000000000000
χ1822222222222222-2-2-2-2-2-222-2-222-2-2-2-2000000000000000000000000-2-222-2-222000000000000
χ19222222222222-2-222-2-2-2-2-2-222-2-222-2-2000000000000000022-2-222-2-200000000000000000000
χ20222222222222-2-222-2-2-2-2-2-222-2-222-2-20000000000000000-2-222-2-22200000000000000000000
χ21222222222222-2-2-2-22222-2-2-2-2-2-2-2-2222222-2-2-2-22222-2-2-2-20000000000000000000000000000
χ22222222222222-2-2-2-22222-2-2-2-2-2-2-2-222-2-2-2-22222-2-2-2-222220000000000000000000000000000
χ2322222222-2-2-2-222-2-2-2-2-2-222-2-2-2-2222200000000000000000000000022-2-2-2-222000000000000
χ2422222222-2-2-2-222-2-2-2-2-2-222-2-2-2-22222000000000000000000000000-2-22222-2-2000000000000
χ2522222222-2-2-2-2-2-222-2-2-2-2-2-22222-2-222000000000000000022-2-2-2-22200000000000000000000
χ2622222222-2-2-2-2-2-222-2-2-2-2-2-22222-2-2220000000000000000-2-22222-2-200000000000000000000
χ2722222222-2-2-2-2-2-2-2-22222-2-2-2-22222-2-22222-2-2-2-2-2-2-2-222220000000000000000000000000000
χ2822222222-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-2-2-222222222-2-2-2-20000000000000000000000000000
χ2922-2-222-2-2000022-2-222-2-2-2-222000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000002i−2i2-2000000
χ3022-2-222-2-2000022-2-222-2-2-2-222000000000000002i2i−2i−2i2i2i−2i−2i000000000000000000−2i2i-22000000
χ3122-2-222-2-2000022-2-222-2-2-2-22200000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000002i−2i-22000000
χ3222-2-222-2-2000022-2-222-2-2-2-22200000000000000−2i−2i2i2i−2i−2i2i2i000000000000000000−2i2i2-2000000
χ3322-2-222-2-20000-2-22222-2-222-2-2000000000000002i2i−2i−2i−2i−2i2i2i00000000000000002-200002i−2i0000
χ3422-2-222-2-20000-2-22222-2-222-2-2000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000-220000−2i2i0000
χ3522-2-222-2-20000-2-22222-2-222-2-200000000000000−2i−2i2i2i2i2i−2i−2i00000000000000002-20000−2i2i0000
χ3622-2-222-2-20000-2-22222-2-222-2-200000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000-2200002i−2i0000
χ372-22-22-22-222-2-2002-20000002-2002-20022−2−222−2−22−22−22−22−2002i−2i002i−2ii2−i2i2−i2i2−i2i2−i2000000000000
χ382-22-22-22-222-2-2002-20000002-2002-20022−2−222−2−22−22−22−22−200−2i2i00−2i2i−i2i2−i2i2−i2i2−i2i2000000000000
χ392-22-22-22-222-2-2002-20000002-2002-200−2−222−2−222−22−22−22−22002i−2i002i−2i−i2i2−i2i2−i2i2−i2i2000000000000
χ402-22-22-22-222-2-2002-20000002-2002-200−2−222−2−222−22−22−22−2200−2i2i00−2i2ii2−i2i2−i2i2−i2i2−i2000000000000
χ412-22-22-22-222-2-200-22000000-2200-220022−2−2−2−2222−22−2−22−222i−2i002i−2i00i2−i2−i2i2i2−i2−i2i2000000000000
χ422-22-22-22-222-2-200-22000000-2200-220022−2−2−2−2222−22−2−22−22−2i2i00−2i2i00−i2i2i2−i2−i2i2i2−i2000000000000
χ432-22-22-22-222-2-200-22000000-2200-2200−2−22222−2−2−22−222−22−22i−2i002i−2i00−i2i2i2−i2−i2i2i2−i2000000000000
χ442-22-22-22-222-2-200-22000000-2200-2200−2−22222−2−2−22−222−22−2−2i2i00−2i2i00i2−i2−i2i2i2−i2−i2i2000000000000
χ452-22-22-22-2-2-222002-20000002-200-220022−2−222−2−2−22−22−22−22002i−2i00−2i2ii2−i2i2−i2−i2i2−i2i2000000000000
χ462-22-22-22-2-2-222002-20000002-200-220022−2−222−2−2−22−22−22−2200−2i2i002i−2i−i2i2−i2i2i2−i2i2−i2000000000000
χ472-22-22-22-2-2-222002-20000002-200-2200−2−222−2−2222−22−22−22−2002i−2i00−2i2i−i2i2−i2i2i2−i2i2−i2000000000000
χ482-22-22-22-2-2-222002-20000002-200-2200−2−222−2−2222−22−22−22−200−2i2i002i−2ii2−i2i2−i2−i2i2−i2i2000000000000
χ492-22-22-22-2-2-22200-22000000-22002-20022−2−2−2−222−22−222−22−22i−2i00−2i2i00i2−i2−i2i2−i2i2i2−i2000000000000
χ502-22-22-22-2-2-22200-22000000-22002-20022−2−2−2−222−22−222−22−2−2i2i002i−2i00−i2i2i2−i2i2−i2−i2i2000000000000
χ512-22-22-22-2-2-22200-22000000-22002-200−2−22222−2−22−22−2−22−222i−2i00−2i2i00−i2i2i2−i2i2−i2−i2i2000000000000
χ522-22-22-22-2-2-22200-22000000-22002-200−2−22222−2−22−22−2−22−22−2i2i002i−2i00i2−i2−i2i2−i2i2i2−i2000000000000
χ53444-4-4-4-444-44-400004-44-4000000004-400000000000000000000000000000000000000000000
χ54444-4-4-4-444-44-40000-44-4400000000-4400000000000000000000000000000000000000000000
χ55444-4-4-4-44-44-4400004-44-400000000-4400000000000000000000000000000000000000000000
χ56444-4-4-4-44-44-440000-44-44000000004-400000000000000000000000000000000000000000000
χ5744-44-4-44-4000000004-4-4400000000004-44-40000000000000000000000000000000000000000
χ5844-44-4-44-4000000004-4-440000000000-44-440000000000000000000000000000000000000000
χ5944-44-4-44-400000000-444-4000000000000004-44-4000000000000000000000000000000000000
χ6044-44-4-44-400000000-444-400000000000000-44-44000000000000000000000000000000000000
χ6144-4-444-4-400004444-4-444-4-4-4-400000000000000000000000000000000000000000000000000
χ6244-4-444-4-40000-4-4-4-4-4-444444400000000000000000000000000000000000000000000000000
χ634-444-44-4-44-4-444-40000004-4004-4000000000000000000000000000000000000000000000000
χ644-444-44-4-44-4-44-44000000-4400-44000000000000000000000000000000000000000000000000
χ654-444-44-4-4-444-44-40000004-400-44000000000000000000000000000000000000000000000000
χ664-444-44-4-4-444-4-44000000-44004-4000000000000000000000000000000000000000000000000
χ674-4-444-4-440000004-4000000-44000000000000002i2−2i2−2i22i2−2i22i22i2−2i20000000000000000000000000000
χ684-4-444-4-440000004-4000000-4400000000000000−2i22i22i2−2i22i2−2i2−2i22i20000000000000000000000000000
χ694-4-444-4-44000000-440000004-4000000000000002i2−2i2−2i22i22i2−2i2−2i22i20000000000000000000000000000
χ704-4-444-4-44000000-440000004-400000000000000−2i22i22i2−2i2−2i22i22i2−2i20000000000000000000000000000
χ714-4-4-4-444400004-4000000-440000000022−22−222222−22−2222000000000000000000000000000000000000
χ724-4-4-4-444400004-4000000-4400000000−222222−22−222222−22000000000000000000000000000000000000
χ734-4-4-4-44440000-440000004-40000000022−22−2222−222222−22000000000000000000000000000000000000
χ744-4-4-4-44440000-440000004-400000000−222222−2222−22−2222000000000000000000000000000000000000

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