Finite Group Databasebeta

← Group #501368

Character table — Group #501368

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size112222222224444444888888888888888888888816161616161616161616161616163232
order1222244448822448884444444488161616161616161616161616244444888888161644
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1
χ41111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-111-1-1-1-111-1-1
χ6111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111
χ7111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ8111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111-1-1111111-1-1
χ911111111111-1-1-1-1111111111-1-1-1-11111-1-1-1-11111-1-111-1-11-111-1-1-1-11-1
χ1011111111111-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-11-1-1-11111-11
χ1111111111111-1-1-1-11111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1111-1-111-11
χ1211111111111-1-1-1-11111111-1-111-1-1-1-1-1-111111111-1-1-1-111-11-1-111-1-11-1
χ1311111111111-1-1-1-1111-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1111-1-1-111-1-1-11
χ1411111111111-1-1-1-1111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1111-111-1-1111-1
χ1511111111111-1-1-1-1111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-11-1-111111-1
χ1611111111111-1-1-1-1111-1-1-1-1-1-111-1-1-1-1-1-1111111111111-1-1-1111-1-1-1-1-11
χ17222222222-2-22222-2-2-200002222-2-2000000000000000000-2-200000000
χ18222222222-2-22222-2-2-20000-2-2-2-2-2-20000000000000000002200000000
χ19222222222-2-2-2-2-2-2-2-2-2000022-2-222000000000000000000-2200000000
χ20222222222-2-2-2-2-2-2-2-2-20000-2-222220000000000000000002-200000000
χ21222-2-222-2-20022-2-200000002i−2i2i−2i00i2i2−i2−i2i2i2−i2−i222−2−20000000000002−200
χ22222-2-222-2-20022-2-200000002i−2i2i−2i00−i2−i2i2i2−i2−i2i2i2−2−222000000000000−2200
χ23222-2-222-2-20022-2-20000000−2i2i−2i2i00i2i2−i2−i2i2i2−i2−i2−2−222000000000000−2200
χ24222-2-222-2-20022-2-20000000−2i2i−2i2i00−i2−i2i2i2−i2−i2i2i222−2−20000000000002−200
χ25222-2-222-2-200-2-22200000002i−2i−2i2i00i2i2−i2−i2−i2−i2i2i222−2−2000000000000−2200
χ26222-2-222-2-200-2-22200000002i−2i−2i2i00−i2−i2i2i2i2i2−i2−i2−2−2220000000000002−200
χ27222-2-222-2-200-2-2220000000−2i2i2i−2i00i2i2−i2−i2−i2−i2i2i2−2−2220000000000002−200
χ28222-2-222-2-200-2-2220000000−2i2i2i−2i00−i2−i2i2i2i2i2−i2−i222−2−2000000000000−2200
χ29222-2-2-2-222222-22-2-2-2222-2-200002-20000000000002-200000000000000
χ30222-2-2-2-222222-22-2-2-22-2-22200002-2000000000000-2200000000000000
χ31222-2-2-2-22222-22-22-2-2222-2-20000-22000000000000-2200000000000000
χ32222-2-2-2-22222-22-22-2-22-2-2220000-220000000000002-200000000000000
χ33222-2-2-2-222-2-22-22-222-200000000-22000000000000002i−2i2i−2i0000000000
χ34222-2-2-2-222-2-22-22-222-200000000-2200000000000000−2i2i−2i2i0000000000
χ35222-2-2-2-222-2-2-22-2222-2000000002-2000000000000002i−2i−2i2i0000000000
χ36222-2-2-2-222-2-2-22-2222-2000000002-200000000000000−2i2i2i−2i0000000000
χ3722-22-22-22-2-2-200002-222-22-200000000002i−2i2i−2i000000000000002i−2i0000
χ3822-22-22-22-2-2-200002-222-22-20000000000−2i2i−2i2i00000000000000−2i2i0000
χ3922-22-22-22-2-2-200002-22-22-2200000000002i−2i2i−2i00000000000000−2i2i0000
χ4022-22-22-22-2-2-200002-22-22-220000000000−2i2i−2i2i000000000000002i−2i0000
χ4122-2-22-222-2-2-20000-2222-2-220000002i−2i2i−2i00000000000000002i−2i000000
χ4222-2-22-222-2-2-20000-2222-2-22000000−2i2i−2i2i0000000000000000−2i2i000000
χ4322-2-22-222-2-2-20000-222-222-20000002i−2i2i−2i0000000000000000−2i2i000000
χ4422-2-22-222-2-2-20000-222-222-2000000−2i2i−2i2i00000000000000002i−2i000000
χ4544444-4-4-4-4004-4-4400000000000000000000000000000000000000000
χ4644444-4-4-4-400-444-400000000000000000000000000000000000000000
χ4744-44-44-44-4440000-44-400000000000000000000000000000000000000
χ4844-44-4-44-44000000000000000000022−22−2222000000000000000000000000
χ4944-44-4-44-440000000000000000000−222222−22000000000000000000000000
χ5044-4-444-4-440000000000000000000000022−22−222200000000000000000000
χ5144-4-444-4-4400000000000000000000000−222222−2200000000000000000000
χ5244-4-44-444-44400004-4-400000000000000000000000000000000000000
χ538-8000000042−4200000000000000000000000002ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ50000000000000000
χ548-8000000042−420000000000000000000000000−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ50000000000000000
χ558-80000000−424200000000000000000000000002ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ70000000000000000
χ568-80000000−42420000000000000000000000000−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ70000000000000000

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