Finite Group Databasebeta

← Group #500280

Character table — Group #500280

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222222222222222244444444444444444444888888888888888816161616161616161616161616161616
order122222222222444444448888888844444444888888888888161616161616161616161616161616162244444444444444
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
χ511111111111111-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1
χ611111111111111-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111
χ711111111111111-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111
χ811111111111111-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111111111-1-1-1-1-1-1
χ911111111-1-1-1-11111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-111-1-1
χ1011111111-1-1-1-11111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-111
χ1111111111-1-1-1-11111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-111
χ1211111111-1-1-1-11111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-11111-1-1
χ1311111111-1-1-1-111-1-1-1-11111111111-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-111
χ1411111111-1-1-1-111-1-1-1-11111111111-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1111111-1-1
χ1511111111-1-1-1-111-1-1-1-11111111111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-111-1-111-1-111-1-1
χ1611111111-1-1-1-111-1-1-1-11111111111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-111-1-111-1-111
χ1722222222222222222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000
χ1822222222222222-2-2-2-222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-2-2-22222222200000000000000000000000000000000
χ19222222222222-2-22222-2-200000000-2-222-2-2-2-200000000000022−2−222−2−222−2−222−2−20000000000000000
χ20222222222222-2-22222-2-200000000-2-222-2-2-2-2000000000000−2−222−2−222−2−222−2−2220000000000000000
χ21222222222222-2-2-2-2-2-2-2-200000000-2-2-2-2222200000000000022−2−222−2−2−2−222−2−2220000000000000000
χ22222222222222-2-2-2-2-2-2-2-200000000-2-2-2-22222000000000000−2−222−2−22222−2−222−2−20000000000000000
χ2322222222-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-22222-2-2-2-2222200000000000000000000000000000000
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
χ2522222222-2-2-2-2-2-22222-2-20000000022-2-2-2-22200000000000022−2−2−2−22222−2−2−2−2220000000000000000
χ2622222222-2-2-2-2-2-22222-2-20000000022-2-2-2-222000000000000−2−22222−2−2−2−22222−2−20000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-200000000222222-2-200000000000022−2−2−2−222−2−22222−2−20000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-200000000222222-2-2000000000000−2−22222−2−222−2−2−2−2220000000000000000
χ29222-2-2-2-2222-2-2002i2i−2i−2i002222−2−2−2−2002i−2i000022−2−2i2i2−i2−i2i2i2−i2−i2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ70000000000000000
χ30222-2-2-2-2222-2-2002i2i−2i−2i002222−2−2−2−2002i−2i000022−2−2i2i2−i2−i2i2i2−i2−i2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ70000000000000000
χ31222-2-2-2-2222-2-2002i2i−2i−2i00−2−2−2−22222002i−2i0000−2−222−i2−i2i2i2−i2−i2i2i2ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ50000000000000000
χ32222-2-2-2-2222-2-2002i2i−2i−2i00−2−2−2−22222002i−2i0000−2−222−i2−i2i2i2−i2−i2i2i2−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ50000000000000000
χ33222-2-2-2-2222-2-200−2i−2i2i2i002222−2−2−2−200−2i2i000022−2−2−i2−i2i2i2−i2−i2i2i2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ70000000000000000
χ34222-2-2-2-2222-2-200−2i−2i2i2i002222−2−2−2−200−2i2i000022−2−2−i2−i2i2i2−i2−i2i2i2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ70000000000000000
χ35222-2-2-2-2222-2-200−2i−2i2i2i00−2−2−2−2222200−2i2i0000−2−222i2i2−i2−i2i2i2−i2−i2ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ50000000000000000
χ36222-2-2-2-2222-2-200−2i−2i2i2i00−2−2−2−2222200−2i2i0000−2−222i2i2−i2−i2i2i2−i2−i2−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ50000000000000000
χ37222-2-2-2-22-2-222002i2i−2i−2i002222−2−2−2−200−2i2i0000−2−222i2i2−i2−i2−i2−i2i2i2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ70000000000000000
χ38222-2-2-2-22-2-222002i2i−2i−2i002222−2−2−2−200−2i2i0000−2−222i2i2−i2−i2−i2−i2i2i2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ70000000000000000
χ39222-2-2-2-22-2-222002i2i−2i−2i00−2−2−2−2222200−2i2i000022−2−2−i2−i2i2i2i2i2−i2−i2ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ50000000000000000
χ40222-2-2-2-22-2-222002i2i−2i−2i00−2−2−2−2222200−2i2i000022−2−2−i2−i2i2i2i2i2−i2−i2−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ50000000000000000
χ41222-2-2-2-22-2-22200−2i−2i2i2i002222−2−2−2−2002i−2i0000−2−222−i2−i2i2i2i2i2−i2−i2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ70000000000000000
χ42222-2-2-2-22-2-22200−2i−2i2i2i002222−2−2−2−2002i−2i0000−2−222−i2−i2i2i2i2i2−i2−i2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ70000000000000000
χ43222-2-2-2-22-2-22200−2i−2i2i2i00−2−2−2−22222002i−2i000022−2−2i2i2−i2−i2−i2−i2i2i2ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ50000000000000000
χ44222-2-2-2-22-2-22200−2i−2i2i2i00−2−2−2−22222002i−2i000022−2−2i2i2−i2−i2−i2−i2i2i2−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ50000000000000000
χ4522-2-22-22-200002-22i−2i2i−2i2-222-2-222-2-200002i−2i0000002i−2i2i−2i000000000000000000000000002-200002i−2i00
χ4622-2-22-22-200002-22i−2i2i−2i2-222-2-222-2-200002i−2i0000002i−2i2i−2i00000000000000000000000000-220000−2i2i00
χ4722-2-22-22-200002-22i−2i2i−2i2-2-2-222-2-22200002i−2i000000−2i2i−2i2i00000000000000000000000000002-200002i−2i
χ4822-2-22-22-200002-22i−2i2i−2i2-2-2-222-2-22200002i−2i000000−2i2i−2i2i0000000000000000000000000000-220000−2i2i
χ4922-2-22-22-200002-2−2i2i−2i2i2-222-2-222-2-20000−2i2i000000−2i2i−2i2i000000000000000000000000002-20000−2i2i00
χ5022-2-22-22-200002-2−2i2i−2i2i2-222-2-222-2-20000−2i2i000000−2i2i−2i2i00000000000000000000000000-2200002i−2i00
χ5122-2-22-22-200002-2−2i2i−2i2i2-2-2-222-2-2220000−2i2i0000002i−2i2i−2i00000000000000000000000000002-20000−2i2i
χ5222-2-22-22-200002-2−2i2i−2i2i2-2-2-222-2-2220000−2i2i0000002i−2i2i−2i0000000000000000000000000000-2200002i−2i
χ532-2-2-222-222-22-2-2-20000222-22-22-22-22-20000002-22-2000000000000000000000000002-22-20000000000
χ542-2-2-222-222-22-2-2-20000222-22-22-22-22-20000002-22-200000000000000000000000000-22-220000000000
χ552-2-2-222-222-22-2-2-2000022-22-22-22-222-2000000-22-220000000000000000000000002-2000000002-20000
χ562-2-2-222-222-22-2-2-2000022-22-22-22-222-2000000-22-22000000000000000000000000-2200000000-220000
χ572-2-2-222-22-22-22-2-20000222-22-22-22-2-22000000-22-22000000000000000000000000002-2-220000000000
χ582-2-2-222-22-22-22-2-20000222-22-22-22-2-22000000-22-2200000000000000000000000000-222-20000000000
χ592-2-2-222-22-22-22-2-2000022-22-22-22-22-220000002-22-20000000000000000000000002-200000000-220000
χ602-2-2-222-22-22-22-2-2000022-22-22-22-22-220000002-22-2000000000000000000000000-22000000002-20000
χ6144-44-44-4-40000004-4-44002222−22−22−22−22222200000000000022−22−2222000000000000000000000000000000000000
χ6244-44-44-4-40000004-4-4400−22−2222222222−22−22000000000000−222222−22000000000000000000000000000000000000
χ6344-44-44-4-4000000-444-4002222−22−22−22−222222000000000000−222222−22000000000000000000000000000000000000
χ6444-44-44-4-4000000-444-400−22−2222222222−22−2200000000000022−22−2222000000000000000000000000000000000000
χ6544-4-44-44-40000-444i−4i4i−4i-44000000000000−4i4i0000000000000000000000000000000000000000000000
χ6644-4-44-44-40000-44−4i4i−4i4i-440000000000004i−4i0000000000000000000000000000000000000000000000
χ674-4444-4-4-400004-40000-440000000000000000000000004-44-400000000000000000000000000000000
χ684-4444-4-4-400004-40000-44000000000000000000000000-44-4400000000000000000000000000000000
χ694-4444-4-4-40000-4400004-44-4-444-4-440000000000000000000000000000000000000000000000000000
χ704-4444-4-4-40000-4400004-4-444-4-444-40000000000000000000000000000000000000000000000000000
χ714-44-4-444-400000000000022−22−2222−222222−220000004i−4i000000002i2−2i2−2i22i200000000000000000000000000000000
χ724-44-4-444-400000000000022−22−2222−222222−22000000−4i4i00000000−2i22i22i2−2i200000000000000000000000000000000
χ734-44-4-444-4000000000000−222222−2222−22−22220000004i−4i00000000−2i22i22i2−2i200000000000000000000000000000000
χ744-44-4-444-4000000000000−222222−2222−22−2222000000−4i4i000000002i2−2i2−2i22i200000000000000000000000000000000
χ754-4-44-4-4444-4-440000000022−2222−22−2222−22220000000022−22−22220000000000000000000000000000000000000000
χ764-4-44-4-4444-4-4400000000−2222−222222−2222−2200000000−222222−220000000000000000000000000000000000000000
χ774-4-44-4-444-444-40000000022−2222−22−2222−222200000000−222222−220000000000000000000000000000000000000000
χ784-4-44-4-444-444-400000000−2222−222222−2222−220000000022−22−22220000000000000000000000000000000000000000
χ794-4-4-444-444-44-4440000-4-400000000-4400000000000000000000000000000000000000000000000000
χ804-4-4-444-44-44-44440000-4-4000000004-400000000000000000000000000000000000000000000000000

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