Finite Group Databasebeta

← Group #500558

Character table — Group #500558

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222222222222222244444444444444444444888888888888888816161616161616161616161616161616
order122222224444444444448888888822444444888888888888161616161616161616161616161616162244444444444444
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
χ511111111111111-1-1-1-11111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-1
χ611111111111111-1-1-1-11111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-111
χ711111111111111-1-1-1-11111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-111
χ811111111111111-1-1-1-11111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-11111-1-1
χ911111111-1-1-1-11111111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-1
χ1011111111-1-1-1-11111111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-11111
χ1111111111-1-1-1-11111111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1111111
χ1211111111-1-1-1-11111111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111111111-1-1-1-1-1-1
χ1311111111-1-1-1-111-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-111
χ1411111111-1-1-1-111-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1111111-1-1
χ1511111111-1-1-1-111-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-111-1-111-1-111-1-1
χ1611111111-1-1-1-111-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-111-1-111-1-111
χ1722222222222222222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000
χ1822222222222222-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-22222222200000000000000000000000000000000
χ19222222222222-2-22222-2-200000000-2-2-2-222-2-200000000000022−2−222−2−222−2−222−2−20000000000000000
χ20222222222222-2-22222-2-200000000-2-2-2-222-2-2000000000000−2−222−2−222−2−222−2−2220000000000000000
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
χ2322222222-2-2-2-222222222-2-2-2-2-2-2-2-2-2-222-2-2-2-22222-2-2-2-2222200000000000000000000000000000000
χ2422222222-2-2-2-222-2-2-2-222-2-2-2-2-2-2-2-222-2-222-2-222222222-2-2-2-200000000000000000000000000000000
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
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-200000000-2-222222200000000000022−2−2−2−222−2−22222−2−20000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-200000000-2-2222222000000000000−2−22222−2−222−2−2−2−2220000000000000000
χ29222-2-2-2-222i2i−2i−2i0022-2-20022−2−222−2−200002i−2i00i2i2−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+ζ70000000000000000
χ30222-2-2-2-222i2i−2i−2i0022-2-20022−2−222−2−200002i−2i00i2i2−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−ζ70000000000000000
χ31222-2-2-2-222i2i−2i−2i0022-2-200−2−222−2−22200002i−2i00−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−ζ50000000000000000
χ32222-2-2-2-222i2i−2i−2i0022-2-200−2−222−2−22200002i−2i00−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+ζ50000000000000000
χ33222-2-2-2-222i2i−2i−2i00-2-2220022−2−222−2−20000−2i2i00i2i2−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−ζ70000000000000000
χ34222-2-2-2-222i2i−2i−2i00-2-2220022−2−222−2−20000−2i2i00i2i2−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+ζ70000000000000000
χ35222-2-2-2-222i2i−2i−2i00-2-22200−2−222−2−2220000−2i2i00−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+ζ50000000000000000
χ36222-2-2-2-222i2i−2i−2i00-2-22200−2−222−2−2220000−2i2i00−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−ζ50000000000000000
χ37222-2-2-2-22−2i−2i2i2i0022-2-20022−2−222−2−20000−2i2i00−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−ζ70000000000000000
χ38222-2-2-2-22−2i−2i2i2i0022-2-20022−2−222−2−20000−2i2i00−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+ζ70000000000000000
χ39222-2-2-2-22−2i−2i2i2i0022-2-200−2−222−2−2220000−2i2i00i2i2−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+ζ50000000000000000
χ40222-2-2-2-22−2i−2i2i2i0022-2-200−2−222−2−2220000−2i2i00i2i2−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−ζ50000000000000000
χ41222-2-2-2-22−2i−2i2i2i00-2-2220022−2−222−2−200002i−2i00−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+ζ70000000000000000
χ42222-2-2-2-22−2i−2i2i2i00-2-2220022−2−222−2−200002i−2i00−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−ζ70000000000000000
χ43222-2-2-2-22−2i−2i2i2i00-2-22200−2−222−2−22200002i−2i00i2i2−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−ζ50000000000000000
χ44222-2-2-2-22−2i−2i2i2i00-2-22200−2−222−2−22200002i−2i00i2i2−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+ζ50000000000000000
χ4522-2-22-22-22i−2i2i−2i2-200002-22-22-22-22-20000002i−2i2i−2i2i−2i0000000000000000000000002-22i−2i000000000000
χ4622-2-22-22-22i−2i2i−2i2-200002-22-22-22-22-20000002i−2i2i−2i2i−2i000000000000000000000000-22−2i2i000000000000
χ4722-2-22-22-22i−2i2i−2i2-200002-2-22-22-22-220000002i−2i−2i2i−2i2i00000000000000000000000000002-200002i−2i0000
χ4822-2-22-22-22i−2i2i−2i2-200002-2-22-22-22-220000002i−2i−2i2i−2i2i0000000000000000000000000000-220000−2i2i0000
χ4922-2-22-22-2−2i2i−2i2i2-200002-22-22-22-22-2000000−2i2i−2i2i−2i2i0000000000000000000000002-2−2i2i000000000000
χ5022-2-22-22-2−2i2i−2i2i2-200002-22-22-22-22-2000000−2i2i−2i2i−2i2i000000000000000000000000-222i−2i000000000000
χ5122-2-22-22-2−2i2i−2i2i2-200002-2-22-22-22-22000000−2i2i2i−2i2i−2i00000000000000000000000000002-20000−2i2i0000
χ5222-2-22-22-2−2i2i−2i2i2-200002-2-22-22-22-22000000−2i2i2i−2i2i−2i0000000000000000000000000000-2200002i−2i0000
χ532-2-22-2-2220000-2-22-22-2222-22-2-22-22002-2000000002-22-2000000000000000000000000000000002-22-2
χ542-2-22-2-2220000-2-22-22-2222-22-2-22-22002-2000000002-22-200000000000000000000000000000000-22-22
χ552-2-22-2-2220000-2-22-22-222-22-222-22-2002-200000000-22-22000000000000000000000000002-22-2000000
χ562-2-22-2-2220000-2-22-22-222-22-222-22-2002-200000000-22-2200000000000000000000000000-22-22000000
χ572-2-22-2-2220000-2-2-22-22222-22-2-22-2200-2200000000-22-22000000000000000000000000000000002-2-22
χ582-2-22-2-2220000-2-2-22-22222-22-2-22-2200-2200000000-22-2200000000000000000000000000000000-222-2
χ592-2-22-2-2220000-2-2-22-2222-22-222-22-200-22000000002-22-2000000000000000000000000002-2-22000000
χ602-2-22-2-2220000-2-2-22-2222-22-222-22-200-22000000002-22-200000000000000000000000000-222-2000000
χ6144-44-44-4-44-4-440000000022−22−222222−22−22220000000022−22−22220000000000000000000000000000000000000000
χ6244-44-44-4-44-4-4400000000−222222−22−222222−2200000000−222222−220000000000000000000000000000000000000000
χ6344-44-44-4-4-444-40000000022−22−222222−22−222200000000−222222−220000000000000000000000000000000000000000
χ6444-44-44-4-4-444-400000000−222222−22−222222−220000000022−22−22220000000000000000000000000000000000000000
χ6544-4-44-44-44i−4i4i−4i-440000-4400000000000000−4i4i00000000000000000000000000000000000000000000
χ6644-4-44-44-4−4i4i−4i4i-440000-44000000000000004i−4i00000000000000000000000000000000000000000000
χ674-4444-4-4-40000000000002222−22−22−22−2222224-40000000000000022−2222−2200000000000000000000000000000000
χ684-4444-4-4-40000000000002222−22−22−22−222222-4400000000000000−2222−222200000000000000000000000000000000
χ694-4444-4-4-4000000000000−22−2222222222−22−224-400000000000000−2222−222200000000000000000000000000000000
χ704-4444-4-4-4000000000000−22−2222222222−22−22-440000000000000022−2222−2200000000000000000000000000000000
χ714-44-4-444-400004-40000-440000000000000000000000004i−4i−4i4i00000000000000000000000000000000
χ724-44-4-444-400004-40000-44000000000000000000000000−4i4i4i−4i00000000000000000000000000000000
χ734-44-4-444-40000-4400004-44444-4-4-4-40000000000000000000000000000000000000000000000000000
χ744-44-4-444-40000-4400004-4-4-4-4-444440000000000000000000000000000000000000000000000000000
χ754-4-44-4-4440000444-44-4-4-40000000000-44000000000000000000000000000000000000000000000000
χ764-4-44-4-444000044-44-44-4-400000000004-4000000000000000000000000000000000000000000000000
χ774-4-4-444-440000004-4-440022−22−2222−222222−2200000000000022−22−2222000000000000000000000000000000000000
χ784-4-4-444-440000004-4-4400−222222−2222−22−2222000000000000−222222−22000000000000000000000000000000000000
χ794-4-4-444-44000000-444-40022−22−2222−222222−22000000000000−222222−22000000000000000000000000000000000000
χ804-4-4-444-44000000-444-400−222222−2222−22−222200000000000022−22−2222000000000000000000000000000000000000

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