Finite Group Databasebeta

← Group #142144

Character table — Group #142144

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size1111222222222244444488888888881616161616161616161616161616161632323232
order122222444488888888884444448888161616161616161616161616161616164444
χ111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1
χ611111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111
χ711111111111111111111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111
χ811111111111111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ91111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i1-11-1
χ101111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1ii−i−iii−i−i−i−iii−i−iii-11-11
χ111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1−i−iii−i−iiiii−i−iii−i−i-11-11
χ121111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1−i−iii−i−iii−i−iii−i−iii1-11-1
χ131111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111ii−i−i−i−iiiii−i−i−i−iii1-1-11
χ141111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111ii−i−i−i−iii−i−iiiii−i−i-111-1
χ151111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111−i−iiiii−i−iii−i−i−i−iii-111-1
χ161111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111−i−iiiii−i−i−i−iiiii−i−i1-1-11
χ172222222222222222-2-2-2-222-2-2-2-222-2-200000000000000000000
χ182222222222222222-2-2-2-2-2-2-2-222-2-22200000000000000000000
χ192222222222-2-2-2-2-2-2222222-2-2-2-2-2-22200000000000000000000
χ202222222222-2-2-2-2-2-22222-2-2-2-22222-2-200000000000000000000
χ212222-2-222-2-20000002-22-200002i−2i2i−2i00i2−i2i2−i22−22−2000000000000
χ222222-2-222-2-20000002-22-200002i−2i2i−2i00−i2i2−i2i2−22−22000000000000
χ232222-2-222-2-20000002-22-20000−2i2i−2i2i00i2−i2i2−i2−22−22000000000000
χ242222-2-222-2-20000002-22-20000−2i2i−2i2i00−i2i2−i2i22−22−2000000000000
χ252222-2-222-2-2000000-22-2200002i−2i−2i2i002−2−22−i2i2i2−i2000000000000
χ262222-2-222-2-2000000-22-2200002i−2i−2i2i00−222−2i2−i2−i2i2000000000000
χ272222-2-222-2-2000000-22-220000−2i2i2i−2i002−2−22i2−i2−i2i2000000000000
χ282222-2-222-2-2000000-22-220000−2i2i2i−2i00−222−2−i2i2i2−i2000000000000
χ2922-2-22-22-22-222-2-22-22-2-22002-2000000000000002-22-200000000
χ3022-2-22-22-22-222-2-22-22-2-22002-200000000000000-22-2200000000
χ3122-2-22-22-22-222-2-22-2-222-200-220000000000000000002-22-20000
χ3222-2-22-22-22-222-2-22-2-222-200-22000000000000000000-22-220000
χ3322-2-22-22-22-2-2-222-222-2-2200-220000000000000000002i−2i−2i2i0000
χ3422-2-22-22-22-2-2-222-222-2-2200-22000000000000000000−2i2i2i−2i0000
χ3522-2-22-22-22-2-2-222-22-222-2002-2000000000000002i−2i−2i2i00000000
χ3622-2-22-22-22-2-2-222-22-222-2002-200000000000000−2i2i2i−2i00000000
χ37444444-4-4-4-400000000004-40000000000000000000000000000
χ38444444-4-4-4-40000000000-440000000000000000000000000000
χ394444-4-4-4-4444444-4-40000000000000000000000000000000000
χ404444-4-4-4-444-4-4-4-4440000000000000000000000000000000000
χ4144-4-44-4-44-440000000000000000004-400000000000000000000
χ4244-4-44-4-44-44000000000000000000-4400000000000000000000
χ4344-4-4-444-4-4400000044-4-4000000000000000000000000000000
χ4444-4-4-444-4-44000000-4-444000000000000000000000000000000
χ4544-4-4-44-444-444-4-4-440000000000000000000000000000000000
χ4644-4-4-44-444-4-4-4444-40000000000000000000000000000000000
χ478-88-800000042−4242−42000000000000000000000000000000000000
χ488-88-8000000−4242−4242000000000000000000000000000000000000
χ498-8-8800000042−42−4242000000000000000000000000000000000000
χ508-8-88000000−424242−42000000000000000000000000000000000000

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