Finite Group Databasebeta

← Group #506167

Character table — Group #506167

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222444444444444444444444444444488888888888888161616161616161632323232
order12222222444488888888224444448888161616161616161616161616161616164488881616161616161616444444442444
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-11-11-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-111-11-11
χ51111111111111111111111-1-111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1
χ61111111111111111111111-1-111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11-1-11
χ81111111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-111-1
χ911111111111111111111-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1
χ1011111111111111111111-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ1111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1111111-1-111-1-1-11-11
χ1211111111111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-11111-1-111-1-1111-11-1
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1111111-1-1-1-111-1-111
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-11111-1-111-1-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1111111-1-1-1-11111-1-1-1-1-111-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1111111-1-1-1-1-1-1-1-111111-1-11
χ17222222222222-2-2-2-2-2-2-2-222222222-2-2-2-2000000000000000022-2-2-2-200000000000000000000
χ18222222222222-2-2-2-2-2-2-2-222-2-222-2-2-2-2-2-20000000000000000-2-2222200000000000000000000
χ19222222222222-2-2-2-2-2-2-2-2-2-222-2-22222220000000000000000-2-2-2-22200000000000000000000
χ20222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000002222-2-200000000000000000000
χ2122222222-2-2-2-2000000002222-2-2-2-200002222−2−2−2−22222−2−2−2−22-2000022−2−222−2−2000000000000
χ2222222222-2-2-2-2000000002222-2-2-2-20000−2−2−2−22222−2−2−2−222222-20000−2−222−2−222000000000000
χ2322222222-2-2-2-20000000022-2-2-2-22200002222−2−2−2−22222−2−2−2−2-220000−2−222−2−222000000000000
χ2422222222-2-2-2-20000000022-2-2-2-2220000−2−2−2−22222−2−2−2−22222-22000022−2−222−2−2000000000000
χ2522222222-2-2-2-200000000-2-22222-2-200002222−2−2−2−2−2−2−2−22222-22000022−2−2−2−222000000000000
χ2622222222-2-2-2-200000000-2-22222-2-20000−2−2−2−222222222−2−2−2−2-220000−2−22222−2−2000000000000
χ2722222222-2-2-2-200000000-2-2-2-2222200002222−2−2−2−2−2−2−2−222222-20000−2−22222−2−2000000000000
χ2822222222-2-2-2-200000000-2-2-2-222220000−2−2−2−222222222−2−2−2−22-2000022−2−2−2−222000000000000
χ2922-22-2-2-222-2-2222-2-2-2-222002i−2i002i−2i00000000000022-2-222-2-2002i−2i0000002i−2i2i−2i000000000000
χ3022-22-2-2-222-2-2222-2-2-2-222002i−2i002i−2i000000000000-2-222-2-222002i−2i000000−2i2i−2i2i000000000000
χ3122-22-2-2-222-2-2222-2-2-2-22200−2i2i00−2i2i00000000000022-2-222-2-200−2i2i000000−2i2i−2i2i000000000000
χ3222-22-2-2-222-2-2222-2-2-2-22200−2i2i00−2i2i000000000000-2-222-2-22200−2i2i0000002i−2i2i−2i000000000000
χ3322-22-2-2-222-2-22-2-22222-2-2002i−2i002i−2i00002i2i−2i−2i2i2i−2i−2i0000000000−2i2i002-22-20000000000000000
χ3422-22-2-2-222-2-22-2-22222-2-2002i−2i002i−2i0000−2i−2i2i2i−2i−2i2i2i0000000000−2i2i00-22-220000000000000000
χ3522-22-2-2-222-2-22-2-22222-2-200−2i2i00−2i2i00002i2i−2i−2i2i2i−2i−2i00000000002i−2i00-22-220000000000000000
χ3622-22-2-2-222-2-22-2-22222-2-200−2i2i00−2i2i0000−2i−2i2i2i−2i−2i2i2i00000000002i−2i002-22-20000000000000000
χ3722-22-2-2-22-222-200000000002i−2i00−2i2i2i2i−2i−2ii2i2−i2−i2−i2−i2i2i222−2−2−2−22200002-22−2−22i2−i2−i2i2000000000000
χ3822-22-2-2-22-222-200000000002i−2i00−2i2i2i2i−2i−2i−i2−i2i2i2i2i2−i2−i2−2−22222−2−200002-2−222−2−i2i2i2−i2000000000000
χ3922-22-2-2-22-222-200000000002i−2i00−2i2i−2i−2i2i2ii2i2−i2−i2−i2−i2i2i2−2−22222−2−20000-222−2−22−i2i2i2−i2000000000000
χ4022-22-2-2-22-222-200000000002i−2i00−2i2i−2i−2i2i2i−i2−i2i2i2i2i2−i2−i222−2−2−2−2220000-22−222−2i2−i2−i2i2000000000000
χ4122-22-2-2-22-222-20000000000−2i2i002i−2i2i2i−2i−2ii2i2−i2−i2−i2−i2i2i222−2−2−2−2220000-22−222−2−i2i2i2−i2000000000000
χ4222-22-2-2-22-222-20000000000−2i2i002i−2i2i2i−2i−2i−i2−i2i2i2i2i2−i2−i2−2−22222−2−20000-222−2−22i2−i2−i2i2000000000000
χ4322-22-2-2-22-222-20000000000−2i2i002i−2i−2i−2i2i2ii2i2−i2−i2−i2−i2i2i2−2−22222−2−200002-2−222−2i2−i2−i2i2000000000000
χ4422-22-2-2-22-222-20000000000−2i2i002i−2i−2i−2i2i2i−i2−i2i2i2i2i2−i2−i222−2−2−2−22200002-22−2−22−i2i2i2−i2000000000000
χ452-2222-2-2-2-22-22-2-222-2-2220000000000002-22-22-22-20000000000000000000000002i−2i2i−2i000000
χ462-2222-2-2-2-22-22-2-222-2-2220000000000002-22-22-22-2000000000000000000000000−2i2i−2i2i000000
χ472-2222-2-2-2-22-22-2-222-2-222000000000000-22-22-22-220000000000000000000000002i−2i−2i2i000000
χ482-2222-2-2-2-22-22-2-222-2-222000000000000-22-22-22-22000000000000000000000000−2i2i2i−2i000000
χ492-2-22-222-2-2-2222222-2-2-2-20000000000002i−2i−2i2i2i−2i−2i2i00000000000000000000002-200002i−2i0000
χ502-2-22-222-2-2-2222222-2-2-2-20000000000002i−2i−2i2i2i−2i−2i2i0000000000000000000000-220000−2i2i0000
χ512-2-22-222-2-2-2222222-2-2-2-2000000000000−2i2i2i−2i−2i2i2i−2i00000000000000000000002-20000−2i2i0000
χ522-2-22-222-2-2-2222222-2-2-2-2000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000000000-2200002i−2i0000
χ53444-4-44-4-4000022−2222−2222−2222−224-400000022−2222−22000000000000000000000000000000000000000000
χ54444-4-44-4-4000022−2222−2222−2222−22-44000000−2222−2222000000000000000000000000000000000000000000
χ55444-4-44-4-40000−2222−2222−2222−22224-4000000−2222−2222000000000000000000000000000000000000000000
χ56444-4-44-4-40000−2222−2222−2222−2222-4400000022−2222−22000000000000000000000000000000000000000000
χ5744-4-44-44-4000022−22−2222−222222−2200004i−4i002i2−2i2−2i22i2000000000000000000000000000000000000000000
χ5844-4-44-44-4000022−22−2222−222222−220000−4i4i00−2i22i22i2−2i2000000000000000000000000000000000000000000
χ5944-4-44-44-40000−222222−2222−22−222200004i−4i00−2i22i22i2−2i2000000000000000000000000000000000000000000
χ6044-4-44-44-40000−222222−2222−22−22220000−4i4i002i2−2i2−2i22i2000000000000000000000000000000000000000000
χ614-4444-4-4-44-44-40000000000000000000022−2222−22−2222−22220000000000000000000000000000000000
χ624-4444-4-4-44-44-400000000000000000000−2222−222222−2222−220000000000000000000000000000000000
χ634-4444-4-4-4-44-4444-4-444-4-4000000000000000000000000000000000000000000000000000000
χ644-44-4-4-444000022−22−222222−22−2222000000000000000000002ζ3−2ζ5−2ζ3+2ζ52ζ3−2ζ5−2ζ3+2ζ52ζ−2ζ7−2ζ+2ζ72ζ−2ζ7−2ζ+2ζ700000000000000000000000000
χ654-44-4-4-444000022−22−222222−22−222200000000000000000000−2ζ3+2ζ52ζ3−2ζ5−2ζ3+2ζ52ζ3−2ζ5−2ζ+2ζ72ζ−2ζ7−2ζ+2ζ72ζ−2ζ700000000000000000000000000
χ664-44-4-4-4440000−222222−22−222222−22000000000000000000002ζ−2ζ7−2ζ+2ζ72ζ−2ζ7−2ζ+2ζ7−2ζ3+2ζ52ζ3−2ζ5−2ζ3+2ζ52ζ3−2ζ500000000000000000000000000
χ674-44-4-4-4440000−222222−22−222222−2200000000000000000000−2ζ+2ζ72ζ−2ζ7−2ζ+2ζ72ζ−2ζ72ζ3−2ζ5−2ζ3+2ζ52ζ3−2ζ5−2ζ3+2ζ500000000000000000000000000
χ684-4-44-444-444-4-4000000000000000000002i2−2i2−2i22i2−2i22i22i2−2i20000000000000000000000000000000000
χ694-4-44-444-444-4-400000000000000000000−2i22i22i2−2i22i2−2i2−2i22i20000000000000000000000000000000000
χ704-4-44-444-4-4-444-4-4-4-44444000000000000000000000000000000000000000000000000000000
χ714-4-4-444-44000022−2222−22−2222−2222000000000000000000002ζ3−2ζ5−2ζ3+2ζ5−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ7−2ζ+2ζ72ζ−2ζ700000000000000000000000000
χ724-4-4-444-44000022−2222−22−2222−222200000000000000000000−2ζ3+2ζ52ζ3−2ζ52ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ72ζ−2ζ7−2ζ+2ζ700000000000000000000000000
χ734-4-4-444-440000−2222−222222−2222−22000000000000000000002ζ−2ζ7−2ζ+2ζ7−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ52ζ3−2ζ5−2ζ3+2ζ500000000000000000000000000
χ744-4-4-444-440000−2222−222222−2222−2200000000000000000000−2ζ+2ζ72ζ−2ζ72ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ5−2ζ3+2ζ52ζ3−2ζ500000000000000000000000000

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