Finite Group Databasebeta

← Group #314708

Character table — Group #314708

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222222222222222244444444444444444444888888888888888816161616161616161616161616161616
order12222222222244444444888888884444444488888888888844444444888888884444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ811111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ911111111-1-1-1-11111111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-111-1-111-1-111-1-111-1-1
χ1011111111-1-1-1-11111111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-111-1-111-1-111-1-111
χ1111111111-1-1-1-11111111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-111-1-1-1-111-1-111
χ1211111111-1-1-1-11111111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-111-1-11111-1-111-1-1
χ1311111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-111
χ1411111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-1-1-11111-1-11111-1-1-1-11111-1-1
χ1511111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-11111-1-11111-1-1-1-111-1-1-1-111-1-11111-1-1
χ1611111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-11111-1-11111-1-1-1-1-1-11111-1-111-1-1-1-111
χ172222222222222-2-2222-2-22222222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-200000000000000000000000000000000
χ182222222222222-2-2222-2-2-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-2-2-22222222200000000000000000000000000000000
χ19222222222222-222-2-2-22200000000-2-2-2-222-2-20000000000002222-2-2-2-2000000000000000000000000
χ20222222222222-222-2-2-22200000000-2-2-2-222-2-2000000000000-2-2-2-22222000000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-200000000-2-222-2-222000000000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ22222222222222-2-2-2-2-2-2-2-200000000-2-222-2-22200000000000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ2322222222-2-2-2-22-2-2222-2-222222222-2-2-2-22222-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ2422222222-2-2-2-22-2-2222-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222222222-2-2-2-200000000000000000000000000000000
χ2522222222-2-2-2-2-222-2-2-2220000000022-2-2-2-22200000000000022-2-222-2-2000000000000000000000000
χ2622222222-2-2-2-2-222-2-2-2220000000022-2-2-2-222000000000000-2-222-2-222000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-200000000222222-2-2000000000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-200000000222222-2-200000000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ29222-22-2-2-222-2-2022000-2-22222−2−2−2−200002-20022−2−222−2−222−2−22-22-200002−22−22−22−20000000000000000
χ30222-22-2-2-222-2-2022000-2-22222−2−2−2−200002-20022−2−222−2−222−2−2-22-220000−22−22−22−220000000000000000
χ31222-22-2-2-222-2-2022000-2-2−2−2−2−2222200002-200−2−222−2−222−2−2222-22-20000−22−22−22−220000000000000000
χ32222-22-2-2-222-2-2022000-2-2−2−2−2−2222200002-200−2−222−2−222−2−222-22-2200002−22−22−22−20000000000000000
χ33222-22-2-2-222-2-20-2-2000222222−2−2−2−20000-220022−2−2−2−222−2−22200002i−2i2i−2ii2−i2−i2i2i2−i2−i2i20000000000000000
χ34222-22-2-2-222-2-20-2-2000222222−2−2−2−20000-220022−2−2−2−222−2−2220000−2i2i−2i2i−i2i2i2−i2−i2i2i2−i20000000000000000
χ35222-22-2-2-222-2-20-2-200022−2−2−2−222220000-2200−2−22222−2−222−2−200002i−2i2i−2i−i2i2i2−i2−i2i2i2−i20000000000000000
χ36222-22-2-2-222-2-20-2-200022−2−2−2−222220000-2200−2−22222−2−222−2−20000−2i2i−2i2ii2−i2−i2i2i2−i2−i2i20000000000000000
χ37222-22-2-2-2-2-222022000-2-22222−2−2−2−20000-2200−2−22222−2−2−2−2222-2-2200002−22−2−22−220000000000000000
χ38222-22-2-2-2-2-222022000-2-22222−2−2−2−20000-2200−2−22222−2−2−2−222-222-20000−22−222−22−20000000000000000
χ39222-22-2-2-2-2-222022000-2-2−2−2−2−222220000-220022−2−2−2−22222−2−22-2-220000−22−222−22−20000000000000000
χ40222-22-2-2-2-2-222022000-2-2−2−2−2−222220000-220022−2−2−2−22222−2−2-222-200002−22−2−22−220000000000000000
χ41222-22-2-2-2-2-2220-2-2000222222−2−2−2−200002-200−2−222−2−22222−2−200002i−2i−2i2i−i2i2i2−i2i2−i2−i2i20000000000000000
χ42222-22-2-2-2-2-2220-2-2000222222−2−2−2−200002-200−2−222−2−22222−2−20000−2i2i2i−2ii2−i2−i2i2−i2i2i2−i20000000000000000
χ43222-22-2-2-2-2-2220-2-200022−2−2−2−2222200002-20022−2−222−2−2−2−22200002i−2i−2i2ii2−i2−i2i2−i2i2i2−i20000000000000000
χ44222-22-2-2-2-2-2220-2-200022−2−2−2−2222200002-20022−2−222−2−2−2−2220000−2i2i2i−2i−i2i2i2−i2i2−i2−i2i20000000000000000
χ4522-22-2-22-22-22-2-2002-22002i2i−2i−2i2i2i−2i−2i2-20000002i−2i2i−2i00000000000000000000000000000000i2−i2i2−i22−22−2
χ4622-22-2-22-22-22-2-2002-22002i2i−2i−2i2i2i−2i−2i2-20000002i−2i2i−2i00000000000000000000000000000000−i2i2−i2i2−22−22
χ4722-22-2-22-22-22-2-2002-2200−2i−2i2i2i−2i−2i2i2i2-2000000−2i2i−2i2i00000000000000000000000000000000i2−i2i2−i2−22−22
χ4822-22-2-22-22-22-2-2002-2200−2i−2i2i2i−2i−2i2i2i2-2000000−2i2i−2i2i00000000000000000000000000000000−i2i2−i2i22−22−2
χ4922-22-2-22-2-22-22-2002-22002i2i−2i−2i2i2i−2i−2i-22000000−2i2i−2i2i00000000000000000000000000000000i2−i2−i2i22−2−22
χ5022-22-2-22-2-22-22-2002-22002i2i−2i−2i2i2i−2i−2i-22000000−2i2i−2i2i00000000000000000000000000000000−i2i2i2−i2−222−2
χ5122-22-2-22-2-22-22-2002-2200−2i−2i2i2i−2i−2i2i2i-220000002i−2i2i−2i00000000000000000000000000000000i2−i2−i2i2−222−2
χ5222-22-2-22-2-22-22-2002-2200−2i−2i2i2i−2i−2i2i2i-220000002i−2i2i−2i00000000000000000000000000000000−i2i2i2−i22−2−22
χ532-2-2222-2-20000-22-2-2222-22-22-22-22-2002-2000000002-22-200000000000000000000002i−2i002i−2i00000000
χ542-2-2222-2-20000-22-2-2222-22-22-22-22-2002-2000000002-22-20000000000000000000000−2i2i00−2i2i00000000
χ552-2-2222-2-20000-22-2-2222-2-22-22-22-22002-200000000-22-2200000000000000000000002i−2i00−2i2i00000000
χ562-2-2222-2-20000-22-2-2222-2-22-22-22-22002-200000000-22-220000000000000000000000−2i2i002i−2i00000000
χ572-2-2222-2-20000-2-22-222-222-22-22-22-200-2200000000-22-22000000000000000000002i−2i002i−2i0000000000
χ582-2-2222-2-20000-2-22-222-222-22-22-22-200-2200000000-22-2200000000000000000000−2i2i00−2i2i0000000000
χ592-2-2222-2-20000-2-22-222-22-22-22-22-2200-22000000002-22-2000000000000000000002i−2i00−2i2i0000000000
χ602-2-2222-2-20000-2-22-222-22-22-22-22-2200-22000000002-22-200000000000000000000−2i2i002i−2i0000000000
χ6144-44-4-44-44-44-4400-44-40000000000-4400000000000000000000000000000000000000000000000000
χ6244-44-4-44-4-44-44400-44-400000000004-400000000000000000000000000000000000000000000000000
χ6344-4-4-44-444-4-44000000002i22i2−2i2−2i2−2i2−2i22i22i2000000002i2−2i2−2i22i20000000000000000000000000000000000000000
χ6444-4-4-44-444-4-4400000000−2i2−2i22i22i22i22i2−2i2−2i200000000−2i22i22i2−2i20000000000000000000000000000000000000000
χ6544-4-4-44-44-444-4000000002i22i2−2i2−2i2−2i2−2i22i22i200000000−2i22i22i2−2i20000000000000000000000000000000000000000
χ6644-4-4-44-44-444-400000000−2i2−2i22i22i22i22i2−2i2−2i2000000002i2−2i2−2i22i20000000000000000000000000000000000000000
χ674-444-4-4-440000400-4-44004i−4i−4i4i4i−4i−4i4i0000000000000000000000000000000000000000000000000000
χ684-444-4-4-440000400-4-4400−4i4i4i−4i−4i4i4i−4i0000000000000000000000000000000000000000000000000000
χ694-444-4-4-440000-40044-4000000000000000000000000004i−4i4i−4i00000000000000000000000000000000
χ704-444-4-4-440000-40044-400000000000000000000000000−4i4i−4i4i00000000000000000000000000000000
χ714-44-4-444-40000000000002i2−2i2−2i22i2−2i22i22i2−2i20000004-4000000002i2−2i2−2i22i200000000000000000000000000000000
χ724-44-4-444-40000000000002i2−2i2−2i22i2−2i22i22i2−2i2000000-4400000000−2i22i22i2−2i200000000000000000000000000000000
χ734-44-4-444-4000000000000−2i22i22i2−2i22i2−2i2−2i22i20000004-400000000−2i22i22i2−2i200000000000000000000000000000000
χ744-44-4-444-4000000000000−2i22i22i2−2i22i2−2i2−2i22i2000000-44000000002i2−2i2−2i22i200000000000000000000000000000000
χ754-4-4444-4-4000044-44-4-44-40000000000-44000000000000000000000000000000000000000000000000
χ764-4-4444-4-400004-444-4-4-4400000000004-4000000000000000000000000000000000000000000000000
χ774-4-4-44-444000004-4000-4422−2222−22−2222−222200000000000022−22−2222000000000000000000000000000000000000
χ784-4-4-44-444000004-4000-44−2222−222222−2222−22000000000000−222222−22000000000000000000000000000000000000
χ794-4-4-44-44400000-440004-422−2222−22−2222−2222000000000000−222222−22000000000000000000000000000000000000
χ804-4-4-44-44400000-440004-4−2222−222222−2222−2200000000000022−22−2222000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).