Finite Group Databasebeta

← Group #138331

Character table — Group #138331

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11111111222244444444444488888888161616161616161616161616161616161616161616161616
order12222222222244444444444422444444444444448888888888888888
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i
χ61111111111111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii
χ71111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii
χ81111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i
χ9111111111111-1-1-1-111111111-1-111-1-1-1-111-1-111-1-111-1-111-1-111-1-111-1-1
χ10111111111111-1-1-1-111111111-1-111-1-1-1-111-1-111-1-1-1-111-1-111-1-111-1-111
χ11111111111111-1-1-1-111111111-1-111-1-1-1-1-1-111-1-11111-1-111-1-1-1-111-1-111
χ12111111111111-1-1-1-111111111-1-111-1-1-1-1-1-111-1-111-1-111-1-11111-1-111-1-1
χ13111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii
χ14111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i
χ15111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ16111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii
χ17222222222222222222-2-2-2-22222-2-2-2-2-2-2000000000000000000000000
χ182222222222222222-2-22222-2-2-2-2-2-2-2-222000000000000000000000000
χ19222222222222-2-2-2-222-2-2-2-222-2-2-2-22222000000000000000000000000
χ20222222222222-2-2-2-2-2-22222-2-222-2-222-2-2000000000000000000000000
χ2122-2-222-2-22-22-200002-200002-200002i−2i2i−2i00000000i2−i22−2i2−i22−200000000
χ2222-2-222-2-22-22-200002-200002-200002i−2i2i−2i00000000−i2i2−22−i2i2−2200000000
χ2322-2-222-2-22-22-200002-200002-20000−2i2i−2i2i00000000i2−i2−22i2−i2−2200000000
χ2422-2-222-2-22-22-200002-200002-20000−2i2i−2i2i00000000−i2i22−2−i2i22−200000000
χ2522-2-222-2-22-22-20000-220000-2200002i−2i−2i2i000000002−2−i2i2−22i2−i200000000
χ2622-2-222-2-22-22-20000-220000-2200002i−2i−2i2i00000000−22i2−i22−2−i2i200000000
χ2722-2-222-2-22-22-20000-220000-220000−2i2i2i−2i000000002−2i2−i2−22−i2i200000000
χ2822-2-222-2-22-22-20000-220000-220000−2i2i2i−2i00000000−22−i2i22−2i2−i200000000
χ292-2-2-22-2222-2-2200002222-2-2-2-2002-2000000000000000000002i−2i002i−2i00
χ302-2-2-22-2222-2-2200002222-2-2-2-2002-200000000000000000000−2i2i00−2i2i00
χ312-2-2-22-2222-2-22000022-2-222-2-200-2200000000000000000000002i−2i002i−2i
χ322-2-2-22-2222-2-22000022-2-222-2-200-220000000000000000000000−2i2i00−2i2i
χ332-2-2-22-2222-2-220000-2-222-2-22200-2200000000000000000000002-200-22
χ342-2-2-22-2222-2-220000-2-222-2-22200-220000000000000000000000-22002-2
χ352-2-2-22-2222-2-220000-2-2-2-22222002-2000000000000000000002-200-2200
χ362-2-2-22-2222-2-220000-2-2-2-22222002-200000000000000000000-22002-200
χ3744444444-4-4-4-444-4-40000000000000000000000000000000000000000
χ3844444444-4-4-4-4-4-4440000000000000000000000000000000000000000
χ39444-4-4-4-440000004i−4i000000000000000000002-22i−2i0000000000000000
χ40444-4-4-4-440000004i−4i00000000000000000000-22−2i2i0000000000000000
χ41444-4-4-4-44000000−4i4i000000000000000000002-2−2i2i0000000000000000
χ42444-4-4-4-44000000−4i4i00000000000000000000-222i−2i0000000000000000
χ4344-4-444-4-4-44-440000004i−4i4i−4i0000000000000000000000000000000000
χ4444-4-444-4-4-44-44000000−4i4i−4i4i0000000000000000000000000000000000
χ454-4444-4-4-444-4-400004-40000-4400000000000000000000000000000000
χ464-4444-4-4-444-4-40000-4400004-400000000000000000000000000000000
χ474-4444-4-4-4-4-4440000004i−4i−4i4i0000000000000000000000000000000000
χ484-4444-4-4-4-4-444000000−4i4i4i−4i0000000000000000000000000000000000
χ494-44-4-444-400004i−4i0000000000000000002-22i−2i00000000000000000000
χ504-44-4-444-400004i−4i000000000000000000-22−2i2i00000000000000000000
χ514-44-4-444-40000−4i4i0000000000000000002-2−2i2i00000000000000000000
χ524-44-4-444-40000−4i4i000000000000000000-222i−2i00000000000000000000
χ534-4-4-44-444-444-40000000000004-4000000000000000000000000000000
χ544-4-4-44-444-444-4000000000000-44000000000000000000000000000000
χ5588-88-8-88-8000000000000000000000000000000000000000000000000
χ568-8-88-88-88000000000000000000000000000000000000000000000000

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