Finite Group Databasebeta

← Group #505668

Character table — Group #505668

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222222222222222244444444444444444444888888888888888816161616161616161616161616161616
order122222224444444444448888888822444444888888888888161616161616161616161616161616164444444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111
χ511111111111111-1-1-1-11111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1
χ611111111111111-1-1-1-11111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111
χ711111111111111-1-1-1-11111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-111
χ811111111111111-1-1-1-11111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111-1-1-1-111-1-1
χ911111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-1-111
χ1011111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1111111-1-1
χ1111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-111-1-1
χ1211111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-111-1-111
χ1311111111-1-1-1-111-1-1-1-11111111111-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1111111-1-1-1-1-1-1
χ1411111111-1-1-1-111-1-1-1-11111111111-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1111111
χ1511111111-1-1-1-111-1-1-1-11111111111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-111-1-1-1-1-1-11111
χ1611111111-1-1-1-111-1-1-1-11111111111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-1111111-1-1-1-1
χ1722222222222222222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000
χ1822222222222222-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-2-2-22222222200000000000000000000000000000000
χ19222222222222-2-22222-2-200000000-2-2-2-2-2-22200000000000022−2−222−2−222−2−222−2−20000000000000000
χ20222222222222-2-22222-2-200000000-2-2-2-2-2-222000000000000−2−222−2−222−2−222−2−2220000000000000000
χ21222222222222-2-2-2-2-2-2-2-2000000002222-2-2-2-200000000000022−2−222−2−2−2−222−2−2220000000000000000
χ22222222222222-2-2-2-2-2-2-2-2000000002222-2-2-2-2000000000000−2−222−2−22222−2−222−2−20000000000000000
χ2322222222-2-2-2-222222222-2-2-2-2-2-2-2-222-2-2-2-2-2-22222-2-2-2-2222200000000000000000000000000000000
χ2422222222-2-2-2-222-2-2-2-222-2-2-2-2-2-2-2-2-2-222-2-22222222222-2-2-2-200000000000000000000000000000000
χ2522222222-2-2-2-2-2-22222-2-200000000-2-22222-2-200000000000022−2−2−2−22222−2−2−2−2220000000000000000
χ2622222222-2-2-2-2-2-22222-2-200000000-2-22222-2-2000000000000−2−22222−2−2−2−22222−2−20000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-20000000022-2-2222200000000000022−2−2−2−222−2−22222−2−20000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-20000000022-2-22222000000000000−2−22222−2−222−2−2−2−2220000000000000000
χ2922-2-22-2-222i2i−2i−2i002i2i−2i−2i0022−2−222−2−20000002-2i2i2−i2−i2i2i2−i2−i222−2−2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ50000000000000000
χ3022-2-22-2-222i2i−2i−2i002i2i−2i−2i0022−2−222−2−20000002-2i2i2−i2−i2i2i2−i2−i222−2−2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ50000000000000000
χ3122-2-22-2-222i2i−2i−2i002i2i−2i−2i00−2−222−2−2220000002-2−i2−i2i2i2−i2−i2i2i2−2−222ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ70000000000000000
χ3222-2-22-2-222i2i−2i−2i002i2i−2i−2i00−2−222−2−2220000002-2−i2−i2i2i2−i2−i2i2i2−2−222−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ70000000000000000
χ3322-2-22-2-222i2i−2i−2i00−2i−2i2i2i0022−2−222−2−2000000-22i2i2−i2−i2−i2−i2i2i2−2−222ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ50000000000000000
χ3422-2-22-2-222i2i−2i−2i00−2i−2i2i2i0022−2−222−2−2000000-22i2i2−i2−i2−i2−i2i2i2−2−222−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ50000000000000000
χ3522-2-22-2-222i2i−2i−2i00−2i−2i2i2i00−2−222−2−222000000-22−i2−i2i2i2i2i2−i2−i222−2−2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ70000000000000000
χ3622-2-22-2-222i2i−2i−2i00−2i−2i2i2i00−2−222−2−222000000-22−i2−i2i2i2i2i2−i2−i222−2−2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ70000000000000000
χ3722-2-22-2-22−2i−2i2i2i002i2i−2i−2i0022−2−222−2−2000000-22−i2−i2i2i2i2i2−i2−i2−2−222ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ50000000000000000
χ3822-2-22-2-22−2i−2i2i2i002i2i−2i−2i0022−2−222−2−2000000-22−i2−i2i2i2i2i2−i2−i2−2−222−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ50000000000000000
χ3922-2-22-2-22−2i−2i2i2i002i2i−2i−2i00−2−222−2−222000000-22i2i2−i2−i2−i2−i2i2i222−2−2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ70000000000000000
χ4022-2-22-2-22−2i−2i2i2i002i2i−2i−2i00−2−222−2−222000000-22i2i2−i2−i2−i2−i2i2i222−2−2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ70000000000000000
χ4122-2-22-2-22−2i−2i2i2i00−2i−2i2i2i0022−2−222−2−20000002-2−i2−i2i2i2−i2−i2i2i222−2−2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ50000000000000000
χ4222-2-22-2-22−2i−2i2i2i00−2i−2i2i2i0022−2−222−2−20000002-2−i2−i2i2i2−i2−i2i2i222−2−2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ50000000000000000
χ4322-2-22-2-22−2i−2i2i2i00−2i−2i2i2i00−2−222−2−2220000002-2i2i2−i2−i2i2i2−i2−i2−2−222ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ70000000000000000
χ4422-2-22-2-22−2i−2i2i2i00−2i−2i2i2i00−2−222−2−2220000002-2i2i2−i2−i2i2i2−i2−i2−2−222−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ70000000000000000
χ452-22-222-2-22-22-2-2-20000222-22-22-22-200002-2002-22-20000000000000000000000000000002i−2i00002i−2i00
χ462-22-222-2-22-22-2-2-20000222-22-22-22-200002-2002-22-2000000000000000000000000000000−2i2i0000−2i2i00
χ472-22-222-2-22-22-2-2-2000022-22-22-22-2200002-200-22-22000000000000000000000000000000002i−2i00002i−2i
χ482-22-222-2-22-22-2-2-2000022-22-22-22-2200002-200-22-2200000000000000000000000000000000−2i2i0000−2i2i
χ492-22-222-2-2-22-22-2-20000222-22-22-22-20000-2200-22-220000000000000000000000000000002i−2i0000−2i2i00
χ502-22-222-2-2-22-22-2-20000222-22-22-22-20000-2200-22-22000000000000000000000000000000−2i2i00002i−2i00
χ512-22-222-2-2-22-22-2-2000022-22-22-22-220000-22002-22-2000000000000000000000000000000002i−2i0000−2i2i
χ522-22-222-2-2-22-22-2-2000022-22-22-22-220000-22002-22-200000000000000000000000000000000−2i2i00002i−2i
χ532-2-2-2-222200002-22-22-22-22222-2-2-2-22-200000000002-22-2000000000000000000002i−2i2i−2i000000000000
χ542-2-2-2-222200002-22-22-22-22222-2-2-2-22-200000000002-22-200000000000000000000−2i2i−2i2i000000000000
χ552-2-2-2-222200002-22-22-22-2-2-2-2-222222-20000000000-22-220000000000000000000000002-200002-20000
χ562-2-2-2-222200002-22-22-22-2-2-2-2-222222-20000000000-22-22000000000000000000000000-220000-220000
χ572-2-2-2-222200002-2-22-222-22222-2-2-2-2-220000000000-22-22000000000000000000002i−2i−2i2i000000000000
χ582-2-2-2-222200002-2-22-222-22222-2-2-2-2-220000000000-22-2200000000000000000000−2i2i2i−2i000000000000
χ592-2-2-2-222200002-2-22-222-2-2-2-2-22222-2200000000002-22-20000000000000000000000002-20000-220000
χ602-2-2-2-222200002-2-22-222-2-2-2-2-22222-2200000000002-22-2000000000000000000000000-2200002-20000
χ61444-4-4-44-400000000000022−22−2222−222222−22004-400000000000022−2222−2200000000000000000000000000000000
χ62444-4-4-44-400000000000022−22−2222−222222−2200-44000000000000−2222−222200000000000000000000000000000000
χ63444-4-4-44-4000000000000−222222−2222−22−2222004-4000000000000−2222−222200000000000000000000000000000000
χ64444-4-4-44-4000000000000−222222−2222−22−222200-4400000000000022−2222−2200000000000000000000000000000000
χ6544-44-44-4-400004-40000-440000000000000000000000004-4-4400000000000000000000000000000000
χ6644-44-44-4-400004-40000-44000000000000000000000000-444-400000000000000000000000000000000
χ6744-44-44-4-40000-4400004-44-44-4-44-440000000000000000000000000000000000000000000000000000
χ6844-44-44-4-40000-4400004-4-44-444-44-40000000000000000000000000000000000000000000000000000
χ694-444-4-4-440000004i−4i−4i4i002222−22−22−22−2222220000000000002i2−2i2−2i22i2000000000000000000000000000000000000
χ704-444-4-4-440000004i−4i−4i4i00−22−2222222222−22−22000000000000−2i22i22i2−2i2000000000000000000000000000000000000
χ714-444-4-4-44000000−4i4i4i−4i002222−22−22−22−222222000000000000−2i22i22i2−2i2000000000000000000000000000000000000
χ724-444-4-4-44000000−4i4i4i−4i00−22−2222222222−22−220000000000002i2−2i2−2i22i2000000000000000000000000000000000000
χ734-44-444-4-44-44-4440000-4-4000000000000-440000000000000000000000000000000000000000000000
χ744-44-444-4-4-44-44440000-4-40000000000004-40000000000000000000000000000000000000000000000
χ754-4-444-44-44i−4i−4i4i0000000022−22−222222−22−2222000000002i2−2i2−2i22i20000000000000000000000000000000000000000
χ764-4-444-44-44i−4i−4i4i00000000−222222−22−222222−2200000000−2i22i22i2−2i20000000000000000000000000000000000000000
χ774-4-444-44-4−4i4i4i−4i0000000022−22−222222−22−222200000000−2i22i22i2−2i20000000000000000000000000000000000000000
χ784-4-444-44-4−4i4i4i−4i00000000−222222−22−222222−22000000002i2−2i2−2i22i20000000000000000000000000000000000000000
χ794-4-4-4-44440000-444-44-4-4400000000-4400000000000000000000000000000000000000000000000000
χ804-4-4-4-44440000-44-44-44-44000000004-400000000000000000000000000000000000000000000000000

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