Finite Group Databasebeta

← Group #508791

Character table — Group #508791

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444444444444444444448888888888888888161616161616161632323232
order122222224444444488888888444444444488888888888816161616161616161616161616161616224444444444
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
χ5111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11-11-1
χ6111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-11-11
χ7111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-11-11
χ8111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111-11-1
χ911111111-1-1-1-111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11-1-11
χ1011111111-1-1-1-111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-111-1
χ1111111111-1-1-1-111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-111-1
χ1211111111-1-1-1-111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111-1-11
χ1311111111-1-1-1-1111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1
χ1411111111-1-1-1-1111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111
χ1511111111-1-1-1-1111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-111-1-111
χ1611111111-1-1-1-1111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-11111-1-111-1-1
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
χ19222222222222-2-2-2-20000000022-2-2-2-2-2-22200000000000022−2−222−2−222−2−222−2−2000000000000
χ20222222222222-2-2-2-20000000022-2-2-2-2-2-222000000000000−2−222−2−222−2−222−2−222000000000000
χ21222222222222-2-2-2-200000000-2-222-2-222-2-200000000000022−2−222−2−2−2−222−2−222000000000000
χ22222222222222-2-2-2-200000000-2-222-2-222-2-2000000000000−2−222−2−22222−2−222−2−2000000000000
χ2322222222-2-2-2-22222-2-2-2-2-2-2-2-222-2-2-2-222-2-22222-2-2-2-222220000000000000000000000000000
χ2422222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-222-2-2-2-22222222222-2-2-2-20000000000000000000000000000
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
χ2722222222-2-2-2-2-2-2-2-200000000-2-2-2-222222200000000000022−2−2−2−222−2−22222−2−2000000000000
χ2822222222-2-2-2-2-2-2-2-200000000-2-2-2-2222222000000000000−2−22222−2−222−2−2−2−222000000000000
χ2922-22-2-22-222-2-2000022−2−222−2−2002i−2i002i−2i0022−2−2i2i2−i2−i2i2i2−i2−i2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5000000000000
χ3022-22-2-22-222-2-2000022−2−222−2−2002i−2i002i−2i0022−2−2i2i2−i2−i2i2i2−i2−i2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5000000000000
χ3122-22-2-22-222-2-2000022−2−222−2−200−2i2i00−2i2i0022−2−2−i2−i2i2i2−i2−i2i2i2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5000000000000
χ3222-22-2-22-222-2-2000022−2−222−2−200−2i2i00−2i2i0022−2−2−i2−i2i2i2−i2−i2i2i2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5000000000000
χ3322-22-2-22-222-2-20000−2−222−2−222002i−2i002i−2i00−2−222−i2−i2i2i2−i2−i2i2i2ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7000000000000
χ3422-22-2-22-222-2-20000−2−222−2−222002i−2i002i−2i00−2−222−i2−i2i2i2−i2−i2i2i2−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7000000000000
χ3522-22-2-22-222-2-20000−2−222−2−22200−2i2i00−2i2i00−2−222i2i2−i2−i2i2i2−i2−i2ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7000000000000
χ3622-22-2-22-222-2-20000−2−222−2−22200−2i2i00−2i2i00−2−222i2i2−i2−i2i2i2−i2−i2−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7000000000000
χ3722-22-2-22-2-2-222000022−2−222−2−2002i−2i00−2i2i00−2−222−i2−i2i2i2i2i2−i2−i2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5000000000000
χ3822-22-2-22-2-2-222000022−2−222−2−2002i−2i00−2i2i00−2−222−i2−i2i2i2i2i2−i2−i2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5000000000000
χ3922-22-2-22-2-2-222000022−2−222−2−200−2i2i002i−2i00−2−222i2i2−i2−i2−i2−i2i2i2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5000000000000
χ4022-22-2-22-2-2-222000022−2−222−2−200−2i2i002i−2i00−2−222i2i2−i2−i2−i2−i2i2i2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5000000000000
χ4122-22-2-22-2-2-2220000−2−222−2−222002i−2i00−2i2i0022−2−2i2i2−i2−i2−i2−i2i2i2ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7000000000000
χ4222-22-2-22-2-2-2220000−2−222−2−222002i−2i00−2i2i0022−2−2i2i2−i2−i2−i2−i2i2i2−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7000000000000
χ4322-22-2-22-2-2-2220000−2−222−2−22200−2i2i002i−2i0022−2−2−i2−i2i2i2i2i2−i2−i2ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7000000000000
χ4422-22-2-22-2-2-2220000−2−222−2−22200−2i2i002i−2i0022−2−2−i2−i2i2i2i2i2−i2−i2−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7000000000000
χ452-222-2-2-222i−2i2i−2i22-2-22-22-22-22-200002i−2i00002i−2i2i−2i000000000000000000000000002i−2i002-20000
χ462-222-2-2-222i−2i2i−2i22-2-22-22-22-22-200002i−2i00002i−2i2i−2i00000000000000000000000000−2i2i00-220000
χ472-222-2-2-222i−2i2i−2i22-2-2-22-22-22-2200002i−2i0000−2i2i−2i2i0000000000000000000000002-2002i−2i000000
χ482-222-2-2-222i−2i2i−2i22-2-2-22-22-22-2200002i−2i0000−2i2i−2i2i000000000000000000000000-2200−2i2i000000
χ492-222-2-2-22−2i2i−2i2i22-2-22-22-22-22-20000−2i2i0000−2i2i−2i2i000000000000000000000000002i−2i00-220000
χ502-222-2-2-22−2i2i−2i2i22-2-22-22-22-22-20000−2i2i0000−2i2i−2i2i00000000000000000000000000−2i2i002-20000
χ512-222-2-2-22−2i2i−2i2i22-2-2-22-22-22-220000−2i2i00002i−2i2i−2i0000000000000000000000002-200−2i2i000000
χ522-222-2-2-22−2i2i−2i2i22-2-2-22-22-22-220000−2i2i00002i−2i2i−2i000000000000000000000000-22002i−2i000000
χ53444-44-4-4-4000000002222−22−22−22−2222224-400000000000022−2222−2200000000000000000000000000000000
χ54444-44-4-4-4000000002222−22−22−22−222222-44000000000000−2222−222200000000000000000000000000000000
χ55444-44-4-4-400000000−22−2222222222−22−224-4000000000000−2222−222200000000000000000000000000000000
χ56444-44-4-4-400000000−22−2222222222−22−22-4400000000000022−2222−2200000000000000000000000000000000
χ5744-4-4-44-4400004-44-400000000000000000000004i−4i−4i4i00000000000000000000000000000000
χ5844-4-4-44-4400004-44-40000000000000000000000−4i4i4i−4i00000000000000000000000000000000
χ5944-4-4-44-440000-44-444444-4-4-4-400000000000000000000000000000000000000000000000000
χ6044-4-4-44-440000-44-44-4-4-4-4444400000000000000000000000000000000000000000000000000
χ614-444-4-4-444i−4i4i−4i-4-444000000000000−4i4i00000000000000000000000000000000000000000000
χ624-444-4-4-44−4i4i−4i4i-4-4440000000000004i−4i00000000000000000000000000000000000000000000
χ634-44-4-444-40000000022−22−2222−222222−22000000004i−4i000000002i2−2i22i2−2i20000000000000000000000000000
χ644-44-4-444-40000000022−22−2222−222222−2200000000−4i4i00000000−2i22i2−2i22i20000000000000000000000000000
χ654-44-4-444-400000000−222222−2222−22−2222000000004i−4i00000000−2i22i2−2i22i20000000000000000000000000000
χ664-44-4-444-400000000−222222−2222−22−222200000000−4i4i000000002i2−2i22i2−2i20000000000000000000000000000
χ674-4-4444-4-44i−4i−4i4i000022−22−222222−22−222200000000002i2−2i2−2i22i2000000000000000000000000000000000000
χ684-4-4444-4-44i−4i−4i4i0000−222222−22−222222−220000000000−2i22i22i2−2i2000000000000000000000000000000000000
χ694-4-4444-4-4−4i4i4i−4i000022−22−222222−22−22220000000000−2i22i22i2−2i2000000000000000000000000000000000000
χ704-4-4444-4-4−4i4i4i−4i0000−222222−22−222222−2200000000002i2−2i2−2i22i2000000000000000000000000000000000000
χ714-4-4-44-44400004-4-44000000000000000000000000004-4-440000000000000000000000000000
χ724-4-4-44-44400004-4-4400000000000000000000000000-444-40000000000000000000000000000
χ734-4-4-44-4440000-444-44-44-4-44-4400000000000000000000000000000000000000000000000000
χ744-4-4-44-4440000-444-4-44-444-44-400000000000000000000000000000000000000000000000000

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