Finite Group Databasebeta

← Group #508159

Character table — Group #508159

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444444444444444444448888888888888888161616161616161632323232
order122222224444444488888888224444444488888888888816161616161616161616161616161616222244442444
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
χ5111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11-1-11
χ6111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-111-1
χ7111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-111-1
χ8111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111-1-11
χ91111111111-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1
χ101111111111-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111
χ111111111111-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-111
χ121111111111-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-111-1-1
χ131111111111-1-1-1-11111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11-11-1
χ141111111111-1-1-1-11111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-11-11
χ151111111111-1-1-1-11111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-11-11
χ161111111111-1-1-1-11111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111-11-1
χ172222222222222222-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000
χ182222222222222222-2-2-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-2-2-2222222220000000000000000000000000000
χ192222222222-2-2-2-222-2-2-2-2-2-2-2-222-2-2-2-222-2-22222-2-2-2-222220000000000000000000000000000
χ202222222222-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-222-2-22222222222-2-2-2-20000000000000000000000000000
χ2122222222-2-22222-2-20000000022-2-2-2-2-2-22200000000000022−2−222−2−222−2−222−2−2000000000000
χ2222222222-2-22222-2-20000000022-2-2-2-2-2-222000000000000−2−222−2−222−2−222−2−222000000000000
χ2322222222-2-22222-2-200000000-2-2-2-22222-2-200000000000022−2−222−2−2−2−222−2−222000000000000
χ2422222222-2-22222-2-200000000-2-2-2-22222-2-2000000000000−2−222−2−22222−2−222−2−2000000000000
χ2522222222-2-2-2-2-2-2-2-200000000222222-2-2-2-200000000000022−2−2−2−22222−2−2−2−222000000000000
χ2622222222-2-2-2-2-2-2-2-200000000222222-2-2-2-2000000000000−2−22222−2−2−2−22222−2−2000000000000
χ2722222222-2-2-2-2-2-2-2-200000000-2-222-2-2222200000000000022−2−2−2−222−2−22222−2−2000000000000
χ2822222222-2-2-2-2-2-2-2-200000000-2-222-2-22222000000000000−2−22222−2−222−2−2−2−222000000000000
χ2922-222-2-2-2002i2i−2i−2i0022−2−222−2−200002-22i−2i00i2i2−i2−i2i2i2−i2−i222−2−2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7000000000000
χ3022-222-2-2-2002i2i−2i−2i0022−2−222−2−200002-22i−2i00i2i2−i2−i2i2i2−i2−i222−2−2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7000000000000
χ3122-222-2-2-2002i2i−2i−2i0022−2−222−2−20000-22−2i2i00i2i2−i2−i2−i2−i2i2i2−2−222ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7000000000000
χ3222-222-2-2-2002i2i−2i−2i0022−2−222−2−20000-22−2i2i00i2i2−i2−i2−i2−i2i2i2−2−222−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7000000000000
χ3322-222-2-2-2002i2i−2i−2i00−2−222−2−22200002-22i−2i00−i2−i2i2i2−i2−i2i2i2−2−222ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5000000000000
χ3422-222-2-2-2002i2i−2i−2i00−2−222−2−22200002-22i−2i00−i2−i2i2i2−i2−i2i2i2−2−222−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5000000000000
χ3522-222-2-2-2002i2i−2i−2i00−2−222−2−2220000-22−2i2i00−i2−i2i2i2i2i2−i2−i222−2−2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5000000000000
χ3622-222-2-2-2002i2i−2i−2i00−2−222−2−2220000-22−2i2i00−i2−i2i2i2i2i2−i2−i222−2−2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5000000000000
χ3722-222-2-2-200−2i−2i2i2i0022−2−222−2−200002-2−2i2i00−i2−i2i2i2−i2−i2i2i222−2−2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7000000000000
χ3822-222-2-2-200−2i−2i2i2i0022−2−222−2−200002-2−2i2i00−i2−i2i2i2−i2−i2i2i222−2−2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7000000000000
χ3922-222-2-2-200−2i−2i2i2i0022−2−222−2−20000-222i−2i00−i2−i2i2i2i2i2−i2−i2−2−222ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7000000000000
χ4022-222-2-2-200−2i−2i2i2i0022−2−222−2−20000-222i−2i00−i2−i2i2i2i2i2−i2−i2−2−222−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7000000000000
χ4122-222-2-2-200−2i−2i2i2i00−2−222−2−22200002-2−2i2i00i2i2−i2−i2i2i2−i2−i2−2−222ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5000000000000
χ4222-222-2-2-200−2i−2i2i2i00−2−222−2−22200002-2−2i2i00i2i2−i2−i2i2i2−i2−i2−2−222−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5000000000000
χ4322-222-2-2-200−2i−2i2i2i00−2−222−2−2220000-222i−2i00i2i2−i2−i2−i2−i2i2i222−2−2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5000000000000
χ4422-222-2-2-200−2i−2i2i2i00−2−222−2−2220000-222i−2i00i2i2−i2−i2−i2−i2i2i222−2−2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5000000000000
χ452-2-22-2-222-2-22-22-2222-22-22-22-2002-20000002-22-20000000000000000000000002-2002-2000000
χ462-2-22-2-222-2-22-22-2222-22-22-22-2002-20000002-22-2000000000000000000000000-2200-22000000
χ472-2-22-2-222-2-22-22-222-22-22-22-22002-2000000-22-22000000000000000000000000002-2002-20000
χ482-2-22-2-222-2-22-22-222-22-22-22-22002-2000000-22-2200000000000000000000000000-2200-220000
χ492-2-22-2-222-2-2-22-22222-22-22-22-200-22000000-22-220000000000000000000000002-200-22000000
χ502-2-22-2-222-2-2-22-22222-22-22-22-200-22000000-22-22000000000000000000000000-22002-2000000
χ512-2-22-2-222-2-2-22-2222-22-22-22-2200-220000002-22-2000000000000000000000000002-200-220000
χ522-2-22-2-222-2-2-22-2222-22-22-22-2200-220000002-22-200000000000000000000000000-22002-20000
χ53444-4-4-44-44-400004-400000000000000000000004i−4i4i−4i00000000000000000000000000000000
χ54444-4-4-44-44-400004-40000000000000000000000−4i4i−4i4i00000000000000000000000000000000
χ55444-4-4-44-4-440000-444444-4-4-4-400000000000000000000000000000000000000000000000000
χ56444-4-4-44-4-440000-44-4-4-4-4444400000000000000000000000000000000000000000000000000
χ5744-4-4-44-44000000002222−22−22−22−2222224-400000000000022−22−222200000000000000000000000000000000
χ5844-4-4-44-44000000002222−22−22−22−222222-44000000000000−222222−2200000000000000000000000000000000
χ5944-4-4-44-4400000000−22−2222222222−22−224-4000000000000−222222−2200000000000000000000000000000000
χ6044-4-4-44-4400000000−22−2222222222−22−22-4400000000000022−22−222200000000000000000000000000000000
χ614-444-44-4-4004i−4i−4i4i0022−22−222222−22−222200000000002i2−2i2−2i22i2000000000000000000000000000000000000
χ624-444-44-4-4004i−4i−4i4i00−222222−22−222222−220000000000−2i22i22i2−2i2000000000000000000000000000000000000
χ634-444-44-4-400−4i4i4i−4i0022−22−222222−22−22220000000000−2i22i22i2−2i2000000000000000000000000000000000000
χ644-444-44-4-400−4i4i4i−4i00−222222−22−222222−2200000000002i2−2i2−2i22i2000000000000000000000000000000000000
χ654-44-44-4-440000000022−22−2222−222222−22000000004-40000000022−2222−220000000000000000000000000000
χ664-44-44-4-440000000022−22−2222−222222−2200000000-4400000000−2222−22220000000000000000000000000000
χ674-44-44-4-4400000000−222222−2222−22−2222000000004-400000000−2222−22220000000000000000000000000000
χ684-44-44-4-4400000000−222222−2222−22−222200000000-440000000022−2222−220000000000000000000000000000
χ694-4-44-4-444444-44-4-4-40000000000-440000000000000000000000000000000000000000000000
χ704-4-44-4-44444-44-44-4-400000000004-40000000000000000000000000000000000000000000000
χ714-4-4-4444-44-40000-444-44-4-44-4400000000000000000000000000000000000000000000000000
χ724-4-4-4444-44-40000-44-44-444-44-400000000000000000000000000000000000000000000000000
χ734-4-4-4444-4-4400004-4000000000000000000000000004-4-440000000000000000000000000000
χ744-4-4-4444-4-4400004-400000000000000000000000000-444-40000000000000000000000000000

Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.