Finite Group Databasebeta

← Group #251721

Character table — Group #251721

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11112222224444444444444444888888161616161616161616161616161616161616161616161616
order12222244442244444444444444444444224444444444888888888888
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-1
χ611111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-111-1-11111-1-1-1-11111
χ711111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-11111
χ811111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1
χ91111111111-1-1-1-11111-1-1-1-11111-1-111-1-1111-1111-1-1-1-1-111-1-111-1-111-1-1
χ101111111111-1-1-1-11111-1-1-1-11111-1-111-1-111-1111-11-1-1-1-1-1-111-1-111-1-111
χ111111111111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-11-1-1-11-1111111-1-1-1-111-1-111
χ121111111111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-11-1-1-111111-1-11111-1-111-1-1
χ131111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111-1-1-11-1-1-111-1-11111-1-1-1-111
χ141111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-11-1-1-11-1-11111-1-1-1-11111-1-1
χ151111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-11-1111-111-1-1-1-111-1-11111-1-1
χ161111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1111-1111-1-111-1-111-1-1-1-111
χ17222222222222222222-2-2-2-2-2-2-2-2-2-2-2-222000000000000000000000000
χ1822222222222222-2-2-2-22222-2-2-2-2-2-222-2-2000000000000000000000000
χ192222222222-2-2-2-222222222-2-2-2-222-2-2-2-2000000000000000000000000
χ202222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222000000000000000000000000
χ21222222-2-2-2-222-2-20000000022-2-2-22000000002-200002-2000000000000
χ22222222-2-2-2-222-2-20000000022-2-2-2200000000-220000-22000000000000
χ23222222-2-2-2-222-2-200000000-2-2222-200002-20000002-200000000000000
χ24222222-2-2-2-222-2-200000000-2-2222-20000-22000000-2200000000000000
χ25222222-2-2-2-2-2-2220000000022-2-22-2000000002-20000-22000000000000
χ26222222-2-2-2-2-2-2220000000022-2-22-200000000-2200002-2000000000000
χ27222222-2-2-2-2-2-22200000000-2-222-2200002-2000000-2200000000000000
χ28222222-2-2-2-2-2-22200000000-2-222-220000-220000002-200000000000000
χ292222-2-222-2-2000000002i2i−2i−2i2-22-200002i−2i0002000-200002i−2i0000000000
χ302222-2-222-2-2000000002i2i−2i−2i2-22-200002i−2i000-200020000−2i2i0000000000
χ312222-2-222-2-2000000002i2i−2i−2i-22-220000−2i2i002000-200000002i−2i00000000
χ322222-2-222-2-2000000002i2i−2i−2i-22-220000−2i2i00-200020000000−2i2i00000000
χ332222-2-222-2-200000000−2i−2i2i2i2-22-20000−2i2i0002000-20000−2i2i0000000000
χ342222-2-222-2-200000000−2i−2i2i2i2-22-20000−2i2i000-2000200002i−2i0000000000
χ352222-2-222-2-200000000−2i−2i2i2i-22-2200002i−2i002000-20000000−2i2i00000000
χ362222-2-222-2-200000000−2i−2i2i2i-22-2200002i−2i00-2000200000002i−2i00000000
χ3722-2-22-22-2-222-22-200002i−2i2i−2i0000002i−2i000000000000000000i2−i2i2−i22−22−2
χ3822-2-22-22-2-222-22-200002i−2i2i−2i0000002i−2i000000000000000000−i2i2−i2i2−22−22
χ3922-2-22-22-2-222-22-20000−2i2i−2i2i000000−2i2i000000000000000000i2−i2i2−i2−22−22
χ4022-2-22-22-2-222-22-20000−2i2i−2i2i000000−2i2i000000000000000000−i2i2−i2i22−22−2
χ4122-2-22-22-2-22-22-2200002i−2i2i−2i000000−2i2i000000000000000000i2−i2−i2i2−222−2
χ4222-2-22-22-2-22-22-2200002i−2i2i−2i000000−2i2i000000000000000000−i2i2i2−i22−2−22
χ4322-2-22-22-2-22-22-220000−2i2i−2i2i0000002i−2i000000000000000000i2−i2−i2i22−2−22
χ4422-2-22-22-2-22-22-220000−2i2i−2i2i0000002i−2i000000000000000000−i2i2i2−i2−222−2
χ454444-4-4-4-4440000000000004-4-44000000000000000000000000000000
χ464444-4-4-4-444000000000000-444-4000000000000000000000000000000
χ4744-4-44-4-444-44-4-44000000000000000000000000000000000000000000
χ4844-4-44-4-444-4-444-4000000000000000000000000000000000000000000
χ4944-4-4-444-44-4000000004-4-440000000000000000000000000000000000
χ5044-4-4-444-44-400000000-444-40000000000000000000000000000000000
χ5144-4-4-44-44-4400004i4i−4i−4i00000000000000000000000000000000000000
χ5244-4-4-44-44-440000−4i−4i4i4i00000000000000000000000000000000000000
χ538-88-800000000004i−4i4i−4i00000000000000000000000000000000000000
χ548-88-80000000000−4i4i−4i4i00000000000000000000000000000000000000
χ558-8-8800000000004-4-4400000000000000000000000000000000000000
χ568-8-880000000000-444-400000000000000000000000000000000000000

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