Finite Group Databasebeta

← Group #499678

Character table — Group #499678

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222222222222222244444444444444444444888888888888888816161616161616161616161616161616
order12222222444444444444888888888888161616161616161616161616161616164444888816161616161616162222444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111
χ511111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1
χ611111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-111-1-111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-111-1-1
χ911111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1111-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-1
χ1011111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-11111
χ1111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-111-1-1-111-1-1-1-111111111-1-111-1-1-1-1-1-111
χ1211111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-111-1-1-111-1-1-1-11111-1-1-1-111-1-1111111-1-1
χ1311111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1111-1-1-1-1-1-1111111-1-1-1-1-1-111-1-11111
χ1411111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1111-1-1-1-1-1-11111-1-1111111-1-111-1-1-1-1
χ1511111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-111-1-1-1111111-1-1-1-11111-1-1-1-1-1-11111-1-1
χ1611111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-111-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ1722222222222222222222-2-2-2-2-2-2-2-2-2-2-2-200000000000000002222-2-2-2-2000000000000000000000000
χ1822222222222222222222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000-2-2-2-22222000000000000000000000000
χ19222222222222-2-2-2-2-2-2-2-20000000000002222−2−2−2−22222−2−2−2−222-2-2000022−2−222−2−20000000000000000
χ20222222222222-2-2-2-2-2-2-2-20000000000002222−2−2−2−22222−2−2−2−2-2-2220000−2−222−2−2220000000000000000
χ21222222222222-2-2-2-2-2-2-2-2000000000000−2−2−2−22222−2−2−2−2222222-2-20000−2−222−2−2220000000000000000
χ22222222222222-2-2-2-2-2-2-2-2000000000000−2−2−2−22222−2−2−2−22222-2-222000022−2−222−2−20000000000000000
χ2322222222-2-2-2-22222-2-2-2-20000000000002222−2−2−2−2−2−2−2−222222-22-2000022−2−2−2−2220000000000000000
χ2422222222-2-2-2-22222-2-2-2-20000000000002222−2−2−2−2−2−2−2−22222-22-220000−2−22222−2−20000000000000000
χ2522222222-2-2-2-22222-2-2-2-2000000000000−2−2−2−222222222−2−2−2−22-22-20000−2−22222−2−20000000000000000
χ2622222222-2-2-2-22222-2-2-2-2000000000000−2−2−2−222222222−2−2−2−2-22-22000022−2−2−2−2220000000000000000
χ2722222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2222200000000000000002-2-22-2-222000000000000000000000000
χ2822222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-222220000000000000000-222-222-2-2000000000000000000000000
χ29222-2-2-2-222i2i−2i−2i2i2i−2i−2i22-2-22222-2-2-2-22i2i−2i−2i0000000000000000000000000000000000000000002i−2i002-2
χ30222-2-2-2-222i2i−2i−2i2i2i−2i−2i22-2-22222-2-2-2-22i2i−2i−2i000000000000000000000000000000000000000000−2i2i00-22
χ31222-2-2-2-222i2i−2i−2i2i2i−2i−2i22-2-2-2-2-2-22222−2i−2i2i2i000000000000000000000000000000000000002i−2i00002-200
χ32222-2-2-2-222i2i−2i−2i2i2i−2i−2i22-2-2-2-2-2-22222−2i−2i2i2i00000000000000000000000000000000000000−2i2i0000-2200
χ33222-2-2-2-22−2i−2i2i2i−2i−2i2i2i22-2-22222-2-2-2-2−2i−2i2i2i0000000000000000000000000000000000000000002i−2i00-22
χ34222-2-2-2-22−2i−2i2i2i−2i−2i2i2i22-2-22222-2-2-2-2−2i−2i2i2i000000000000000000000000000000000000000000−2i2i002-2
χ35222-2-2-2-22−2i−2i2i2i−2i−2i2i2i22-2-2-2-2-2-222222i2i−2i−2i000000000000000000000000000000000000002i−2i0000-2200
χ36222-2-2-2-22−2i−2i2i2i−2i−2i2i2i22-2-2-2-2-2-222222i2i−2i−2i00000000000000000000000000000000000000−2i2i00002-200
χ3722-222-2-2-22-22-22-22-22-22-2000000000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200002-22-2i2−i2i2−i2i2−i2i2−i20000000000000000
χ3822-222-2-2-22-22-22-22-22-22-2000000000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000-22-22−i2i2−i2i2−i2i2−i2i20000000000000000
χ3922-222-2-2-22-22-22-22-22-22-2000000000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200002-22-2−i2i2−i2i2−i2i2−i2i20000000000000000
χ4022-222-2-2-22-22-22-22-22-22-2000000000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000-22-22i2−i2i2−i2i2−i2i2−i20000000000000000
χ4122-222-2-2-22-22-2-22-22-22-2222-2-222-2-22-22-20000000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ4222-222-2-2-22-22-2-22-22-22-2222-2-222-2-22-22-2000000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ4322-222-2-2-22-22-2-22-22-22-22-2-222-2-222-22-222i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ4422-222-2-2-22-22-2-22-22-22-22-2-222-2-222-22-22−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ4522-222-2-2-2-22-222-22-2-22-2222-2-222-2-2-22-220000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ4622-222-2-2-2-22-222-22-2-22-2222-2-222-2-2-22-22000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ4722-222-2-2-2-22-222-22-2-22-22-2-222-2-2222-22-22i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ4822-222-2-2-2-22-222-22-2-22-22-2-222-2-2222-22-2−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ4922-222-2-2-2-22-22-22-222-22-2000000000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i200002-2-22i2−i2i2−i2−i2i2−i2i20000000000000000
χ5022-222-2-2-2-22-22-22-222-22-2000000000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i20000-222-2−i2i2−i2i2i2−i2i2−i20000000000000000
χ5122-222-2-2-2-22-22-22-222-22-2000000000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i200002-2-22−i2i2−i2i2i2−i2i2−i20000000000000000
χ5222-222-2-2-2-22-22-22-222-22-2000000000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i20000-222-2i2−i2i2−i2−i2i2−i2i20000000000000000
χ5322-2-2-222-22i−2i−2i2i−2i2i2i−2i-222-222-2-2-2-2222i−2i−2i2i000000000000000000000000000000002-2002i−2i0000000000
χ5422-2-2-222-22i−2i−2i2i−2i2i2i−2i-222-222-2-2-2-2222i−2i−2i2i00000000000000000000000000000000-2200−2i2i0000000000
χ5522-2-2-222-22i−2i−2i2i−2i2i2i−2i-222-2-2-22222-2-2−2i2i2i−2i00000000000000000000000000000000002-200002i−2i000000
χ5622-2-2-222-22i−2i−2i2i−2i2i2i−2i-222-2-2-22222-2-2−2i2i2i−2i0000000000000000000000000000000000-220000−2i2i000000
χ5722-2-2-222-2−2i2i2i−2i2i−2i−2i2i-222-222-2-2-2-222−2i2i2i−2i000000000000000000000000000000002-200−2i2i0000000000
χ5822-2-2-222-2−2i2i2i−2i2i−2i−2i2i-222-222-2-2-2-222−2i2i2i−2i00000000000000000000000000000000-22002i−2i0000000000
χ5922-2-2-222-2−2i2i2i−2i2i−2i−2i2i-222-2-2-22222-2-22i−2i−2i2i00000000000000000000000000000000002-20000−2i2i000000
χ6022-2-2-222-2−2i2i2i−2i2i−2i−2i2i-222-2-2-22222-2-22i−2i−2i2i0000000000000000000000000000000000-2200002i−2i000000
χ61444-4-4-4-444i4i−4i−4i−4i−4i4i4i-4-444000000000000000000000000000000000000000000000000000000000000
χ62444-4-4-4-44−4i−4i4i4i4i4i−4i−4i-4-444000000000000000000000000000000000000000000000000000000000000
χ6344-4-4-444-44i−4i−4i4i4i−4i−4i4i4-4-44000000000000000000000000000000000000000000000000000000000000
χ6444-4-4-444-4−4i4i4i−4i−4i4i4i−4i4-4-44000000000000000000000000000000000000000000000000000000000000
χ654-444-44-4-400000000000022−2222−2222−2222−220000000000002ζ+2ζ7−2ζ−2ζ72ζ+2ζ7−2ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ52ζ3+2ζ5−2ζ3−2ζ500000000000000000000000000000000
χ664-444-44-4-400000000000022−2222−2222−2222−22000000000000−2ζ−2ζ72ζ+2ζ7−2ζ−2ζ72ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ5−2ζ3−2ζ52ζ3+2ζ500000000000000000000000000000000
χ674-444-44-4-4000000000000−2222−2222−2222−22220000000000002ζ3+2ζ5−2ζ3−2ζ52ζ3+2ζ5−2ζ3−2ζ5−2ζ−2ζ72ζ+2ζ7−2ζ−2ζ72ζ+2ζ700000000000000000000000000000000
χ684-444-44-4-4000000000000−2222−2222−2222−2222000000000000−2ζ3−2ζ52ζ3+2ζ5−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ72ζ+2ζ7−2ζ−2ζ700000000000000000000000000000000
χ694-44-44-44-400000000000022−2222−22−2222−222200002ζ+2ζ7−2ζ−2ζ72ζ+2ζ7−2ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ52ζ3+2ζ5−2ζ3−2ζ50000000000000000000000000000000000000000
χ704-44-44-44-400000000000022−2222−22−2222−22220000−2ζ−2ζ72ζ+2ζ7−2ζ−2ζ72ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ5−2ζ3−2ζ52ζ3+2ζ50000000000000000000000000000000000000000
χ714-44-44-44-4000000000000−2222−222222−2222−2200002ζ3+2ζ5−2ζ3−2ζ52ζ3+2ζ5−2ζ3−2ζ5−2ζ−2ζ72ζ+2ζ7−2ζ−2ζ72ζ+2ζ70000000000000000000000000000000000000000
χ724-44-44-44-4000000000000−2222−222222−2222−220000−2ζ3−2ζ52ζ3+2ζ5−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ72ζ+2ζ7−2ζ−2ζ70000000000000000000000000000000000000000
χ734-4-44-4-44400000000000022−22−222222−22−22220000000000002ζ−2ζ7−2ζ+2ζ7−2ζ+2ζ72ζ−2ζ72ζ3−2ζ5−2ζ3+2ζ5−2ζ3+2ζ52ζ3−2ζ500000000000000000000000000000000
χ744-4-44-4-44400000000000022−22−222222−22−2222000000000000−2ζ+2ζ72ζ−2ζ72ζ−2ζ7−2ζ+2ζ7−2ζ3+2ζ52ζ3−2ζ52ζ3−2ζ5−2ζ3+2ζ500000000000000000000000000000000
χ754-4-44-4-444000000000000−222222−22−222222−220000000000002ζ3−2ζ5−2ζ3+2ζ5−2ζ3+2ζ52ζ3−2ζ5−2ζ+2ζ72ζ−2ζ72ζ−2ζ7−2ζ+2ζ700000000000000000000000000000000
χ764-4-44-4-444000000000000−222222−22−222222−22000000000000−2ζ3+2ζ52ζ3−2ζ52ζ3−2ζ5−2ζ3+2ζ52ζ−2ζ7−2ζ+2ζ7−2ζ+2ζ72ζ−2ζ700000000000000000000000000000000
χ774-4-4-444-4400000000000022−22−2222−222222−2200002ζ−2ζ7−2ζ+2ζ7−2ζ+2ζ72ζ−2ζ72ζ3−2ζ5−2ζ3+2ζ5−2ζ3+2ζ52ζ3−2ζ50000000000000000000000000000000000000000
χ784-4-4-444-4400000000000022−22−2222−222222−220000−2ζ+2ζ72ζ−2ζ72ζ−2ζ7−2ζ+2ζ7−2ζ3+2ζ52ζ3−2ζ52ζ3−2ζ5−2ζ3+2ζ50000000000000000000000000000000000000000
χ794-4-4-444-44000000000000−222222−2222−22−222200002ζ3−2ζ5−2ζ3+2ζ5−2ζ3+2ζ52ζ3−2ζ5−2ζ+2ζ72ζ−2ζ72ζ−2ζ7−2ζ+2ζ70000000000000000000000000000000000000000
χ804-4-4-444-44000000000000−222222−2222−22−22220000−2ζ3+2ζ52ζ3−2ζ52ζ3−2ζ5−2ζ3+2ζ52ζ−2ζ7−2ζ+2ζ7−2ζ+2ζ72ζ−2ζ70000000000000000000000000000000000000000

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