Finite Group Databasebeta

← Group #317170

Character table — Group #317170

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11112222222222444444444488888888161616161616161616161616161616161616161616161616
order12222244448888444444448844888888444444444444888888888888
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
χ51111111111111111-1-1-1-11111-1-1-1-1-1-111111-1111-1-1-1-1-111-1-11111-1-1-1-1
χ61111111111111111-1-1-1-11111-1-1-1-1-1-11111-1111-11-1-1-1-1-1-111-1-1-1-11111
χ71111111111111111-1-1-1-11111-1-1-1-1-1-111-1-11-1-1-11-1111111-1-1-1-1-1-11111
χ81111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-11-1-1-111111-1-1111111-1-1-1-1
χ91111111111-1-1-1-111111111-1-111-1-1-1-1-1-1111-1-1-11-111-1-1-1-11111-1-111-1-1
χ101111111111-1-1-1-111111111-1-111-1-1-1-1-1-111-11-1-1-1111-1-111-1-1-1-111-1-111
χ111111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-11-1111-1-1-111-1-111-1-111-1-111
χ121111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1111-11-1-11111-1-111-1-111-1-1
χ131111111111-1-1-1-111-1-1-1-111-1-1-1-11111-1-11111-1-111-1-111-1-1-1-111-1-1-1-111
χ141111111111-1-1-1-111-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1111111-1-11111-1-1
χ151111111111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1
χ161111111111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-111-1-111-1-1111111-1-1-1-111
χ1722222222222222-2-22222-2-222-2-222-2-2-2-2000000000000000000000000
χ1822222222222222-2-2-2-2-2-2-2-22222-2-222-2-2000000000000000000000000
χ192222222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-22222000000000000000000000000
χ202222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-222000000000000000000000000
χ212222-2-222-2-200002-22i2i−2i−2i-22002i−2i0000000002000-200002i−2i0000000000
χ222222-2-222-2-200002-22i2i−2i−2i-22002i−2i000000000-200020000−2i2i0000000000
χ232222-2-222-2-200002-2−2i−2i2i2i-2200−2i2i0000000002000-20000−2i2i0000000000
χ242222-2-222-2-200002-2−2i−2i2i2i-2200−2i2i000000000-2000200002i−2i0000000000
χ252222-2-222-2-20000-222i2i−2i−2i2-200−2i2i000000002000-200000002i−2i00000000
χ262222-2-222-2-20000-222i2i−2i−2i2-200−2i2i00000000-200020000000−2i2i00000000
χ272222-2-222-2-20000-22−2i−2i2i2i2-2002i−2i000000002000-20000000−2i2i00000000
χ282222-2-222-2-20000-22−2i−2i2i2i2-2002i−2i00000000-2000200000002i−2i00000000
χ292222-2-2-2-2222222220000-2-2-2-20000002-2000000002i−2i2i−2i000000000000
χ302222-2-2-2-2222222220000-2-2-2-20000002-200000000−2i2i−2i2i000000000000
χ312222-2-2-2-2222222-2-2000022-2-2000000-222-2002-2000000000000000000
χ322222-2-2-2-2222222-2-2000022-2-2000000-22-2200-22000000000000000000
χ332222-2-2-2-222-2-2-2-2220000-2-222000000-22000000002i−2i−2i2i000000000000
χ342222-2-2-2-222-2-2-2-2220000-2-222000000-2200000000−2i2i2i−2i000000000000
χ352222-2-2-2-222-2-2-2-2-2-2000022220000002-22-200-22000000000000000000
χ362222-2-2-2-222-2-2-2-2-2-2000022220000002-2-22002-2000000000000000000
χ3722-2-22-22-2-222i2i−2i−2i002i−2i2i−2i002i−2i002-200000000000000000000i2−i22−22−2i2−i2
χ3822-2-22-22-2-222i2i−2i−2i002i−2i2i−2i002i−2i002-200000000000000000000−i2i2−22−22−i2i2
χ3922-2-22-22-2-222i2i−2i−2i00−2i2i−2i2i002i−2i00-2200000000000000000000i2−i22−2−22−i2i2
χ4022-2-22-22-2-222i2i−2i−2i00−2i2i−2i2i002i−2i00-2200000000000000000000−i2i2−222−2i2−i2
χ4122-2-22-22-2-22−2i−2i2i2i002i−2i2i−2i00−2i2i00-2200000000000000000000i2−i2−222−2−i2i2
χ4222-2-22-22-2-22−2i−2i2i2i002i−2i2i−2i00−2i2i00-2200000000000000000000−i2i22−2−22i2−i2
χ4322-2-22-22-2-22−2i−2i2i2i00−2i2i−2i2i00−2i2i002-200000000000000000000i2−i2−22−22i2−i2
χ4422-2-22-22-2-22−2i−2i2i2i00−2i2i−2i2i00−2i2i002-200000000000000000000−i2i22−22−2−i2i2
χ45444444-4-4-4-400004-400004-40000000000000000000000000000000000
χ46444444-4-4-4-40000-440000-440000000000000000000000000000000000
χ4744-4-44-4-444-40000000000000000004-400000000000000000000000000
χ4844-4-44-4-444-4000000000000000000-4400000000000000000000000000
χ4944-4-4-444-44-40000004-4-44000000000000000000000000000000000000
χ5044-4-4-444-44-4000000-444-4000000000000000000000000000000000000
χ5144-4-4-44-44-444i4i−4i−4i00000000−4i4i00000000000000000000000000000000
χ5244-4-4-44-44-44−4i−4i4i4i000000004i−4i00000000000000000000000000000000
χ538-88-800000042−4242−42000000000000000000000000000000000000000000
χ548-88-8000000−4242−4242000000000000000000000000000000000000000000
χ558-8-880000004i2−4i2−4i24i2000000000000000000000000000000000000000000
χ568-8-88000000−4i24i24i2−4i2000000000000000000000000000000000000000000

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