Finite Group Databasebeta

← Group #508835

Character table — Group #508835

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444444444444444444448888888888888888161616161616161632323232
order122222224444444488888888224444444488888888888816161616161616161616161616161616224444444444
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
χ5111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1
χ6111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ7111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-111
χ8111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-111-1-1
χ91111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-11-1-11
χ101111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-111-1
χ111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-111-1
χ121111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1111-1-11
χ131111111111-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11-11-1
χ141111111111-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-11-11
χ151111111111-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-11-11
χ161111111111-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111-11-1
χ172222222222222222-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000
χ182222222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-2222222220000000000000000000000000000
χ192222222222-2-2-2-222-2-2-2-2-2-2-2-22222-2-2-2-2-2-22222-2-2-2-222220000000000000000000000000000
χ202222222222-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222222222-2-2-2-20000000000000000000000000000
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
χ2322222222-2-22222-2-200000000-2-222-2-222-2-200000000000022−2−222−2−2−2−222−2−222000000000000
χ2422222222-2-22222-2-200000000-2-222-2-222-2-2000000000000−2−222−2−22222−2−222−2−2000000000000
χ2522222222-2-2-2-2-2-2-2-20000000022-2-22222-2-200000000000022−2−2−2−22222−2−2−2−222000000000000
χ2622222222-2-2-2-2-2-2-2-20000000022-2-22222-2-2000000000000−2−22222−2−2−2−22222−2−2000000000000
χ2722222222-2-2-2-2-2-2-2-200000000-2-22222-2-22200000000000022−2−2−2−222−2−22222−2−2000000000000
χ2822222222-2-2-2-2-2-2-2-200000000-2-22222-2-222000000000000−2−22222−2−222−2−2−2−222000000000000
χ2922-2-2-222-2002i2i−2i−2i002222−2−2−2−22-20000002i−2ii2i2−i2−i222−2−2i2i2−i2−i2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7000000000000
χ3022-2-2-222-2002i2i−2i−2i002222−2−2−2−22-20000002i−2ii2i2−i2−i222−2−2i2i2−i2−i2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7000000000000
χ3122-2-2-222-2002i2i−2i−2i002222−2−2−2−2-22000000−2i2ii2i2−i2−i2−2−222−i2−i2i2i2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7000000000000
χ3222-2-2-222-2002i2i−2i−2i002222−2−2−2−2-22000000−2i2ii2i2−i2−i2−2−222−i2−i2i2i2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7000000000000
χ3322-2-2-222-2002i2i−2i−2i00−2−2−2−222222-20000002i−2i−i2−i2i2i2−2−222−i2−i2i2i2ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5000000000000
χ3422-2-2-222-2002i2i−2i−2i00−2−2−2−222222-20000002i−2i−i2−i2i2i2−2−222−i2−i2i2i2−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5000000000000
χ3522-2-2-222-2002i2i−2i−2i00−2−2−2−22222-22000000−2i2i−i2−i2i2i222−2−2i2i2−i2−i2ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5000000000000
χ3622-2-2-222-2002i2i−2i−2i00−2−2−2−22222-22000000−2i2i−i2−i2i2i222−2−2i2i2−i2−i2−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5000000000000
χ3722-2-2-222-200−2i−2i2i2i002222−2−2−2−22-2000000−2i2i−i2−i2i2i222−2−2−i2−i2i2i2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7000000000000
χ3822-2-2-222-200−2i−2i2i2i002222−2−2−2−22-2000000−2i2i−i2−i2i2i222−2−2−i2−i2i2i2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7000000000000
χ3922-2-2-222-200−2i−2i2i2i002222−2−2−2−2-220000002i−2i−i2−i2i2i2−2−222i2i2−i2−i2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7000000000000
χ4022-2-2-222-200−2i−2i2i2i002222−2−2−2−2-220000002i−2i−i2−i2i2i2−2−222i2i2−i2−i2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7000000000000
χ4122-2-2-222-200−2i−2i2i2i00−2−2−2−222222-2000000−2i2ii2i2−i2−i2−2−222i2i2−i2−i2ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5000000000000
χ4222-2-2-222-200−2i−2i2i2i00−2−2−2−222222-2000000−2i2ii2i2−i2−i2−2−222i2i2−i2−i2−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5000000000000
χ4322-2-2-222-200−2i−2i2i2i00−2−2−2−22222-220000002i−2ii2i2−i2−i222−2−2−i2−i2i2i2ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5000000000000
χ4422-2-2-222-200−2i−2i2i2i00−2−2−2−22222-220000002i−2ii2i2−i2−i222−2−2−i2−i2i2i2−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5000000000000
χ452-222-2-22-22-22i−2i2i−2i2-222-2-222-2-200002i−2i00002i−2i2i−2i0000000000000000000000002-200002i−2i0000
χ462-222-2-22-22-22i−2i2i−2i2-222-2-222-2-200002i−2i00002i−2i2i−2i000000000000000000000000-220000−2i2i0000
χ472-222-2-22-22-22i−2i2i−2i2-2-2-222-2-22200002i−2i0000−2i2i−2i2i000000000000000000000000002i−2i2-2000000
χ482-222-2-22-22-22i−2i2i−2i2-2-2-222-2-22200002i−2i0000−2i2i−2i2i00000000000000000000000000−2i2i-22000000
χ492-222-2-22-22-2−2i2i−2i2i2-222-2-222-2-20000−2i2i0000−2i2i−2i2i0000000000000000000000002-20000−2i2i0000
χ502-222-2-22-22-2−2i2i−2i2i2-222-2-222-2-20000−2i2i0000−2i2i−2i2i000000000000000000000000-2200002i−2i0000
χ512-222-2-22-22-2−2i2i−2i2i2-2-2-222-2-2220000−2i2i00002i−2i2i−2i000000000000000000000000002i−2i-22000000
χ522-222-2-22-22-2−2i2i−2i2i2-2-2-222-2-2220000−2i2i00002i−2i2i−2i00000000000000000000000000−2i2i2-2000000
χ53444-44-4-4-44-40000-44000000000000000000000000004-44-40000000000000000000000000000
χ54444-44-4-4-44-40000-4400000000000000000000000000-44-440000000000000000000000000000
χ55444-44-4-4-4-4400004-44-44-44-44-400000000000000000000000000000000000000000000000000
χ56444-44-4-4-4-4400004-4-44-44-44-4400000000000000000000000000000000000000000000000000
χ5744-44-4-4-440000000022−2222−22−2222−22220000004i−4i00000000002i2−2i2−2i22i20000000000000000000000000000
χ5844-44-4-4-440000000022−2222−22−2222−2222000000−4i4i0000000000−2i22i22i2−2i20000000000000000000000000000
χ5944-44-4-4-4400000000−2222−222222−2222−220000004i−4i0000000000−2i22i22i2−2i20000000000000000000000000000
χ6044-44-4-4-4400000000−2222−222222−2222−22000000−4i4i00000000002i2−2i2−2i22i20000000000000000000000000000
χ614-444-4-44-4-444i−4i4i−4i-44000000000000−4i4i00000000000000000000000000000000000000000000
χ624-444-4-44-4-44−4i4i−4i4i-440000000000004i−4i00000000000000000000000000000000000000000000
χ634-44-4-44-44440000-4-400000000000000000000004i−4i4i−4i00000000000000000000000000000000
χ644-44-4-44-44440000-4-40000000000000000000000−4i4i−4i4i00000000000000000000000000000000
χ654-44-4-44-44-4-40000444-4-444-4-4400000000000000000000000000000000000000000000000000
χ664-44-4-44-44-4-4000044-444-4-444-400000000000000000000000000000000000000000000000000
χ674-4-4444-4-40000000022−22−2222−222222−22004i−4i00000000002i2−2i2−2i22i200000000000000000000000000000000
χ684-4-4444-4-40000000022−22−2222−222222−2200−4i4i0000000000−2i22i22i2−2i200000000000000000000000000000000
χ694-4-4444-4-400000000−222222−2222−22−2222004i−4i0000000000−2i22i22i2−2i200000000000000000000000000000000
χ704-4-4444-4-400000000−222222−2222−22−222200−4i4i00000000002i2−2i2−2i22i200000000000000000000000000000000
χ714-4-4-44-444004-4-44002222−22−22−22−222222000000000022−22−2222000000000000000000000000000000000000
χ724-4-4-44-444004-4-4400−22−2222222222−22−220000000000−222222−22000000000000000000000000000000000000
χ734-4-4-44-44400-444-4002222−22−22−22−2222220000000000−222222−22000000000000000000000000000000000000
χ744-4-4-44-44400-444-400−22−2222222222−22−22000000000022−22−2222000000000000000000000000000000000000

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