Finite Group Databasebeta

← Group #142146

Character table — Group #142146

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size1111222222444444444444888888881616161616161616161616161616161632323232
order1222224444444488888888444488888888888816161616161616164444
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
χ51111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1
χ61111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ91111111111-1-1-1-11111-1-1-1-111-1-111-1-1ii−i−iii−i−iii−i−iii−i−i1-11-1
χ101111111111-1-1-1-11111-1-1-1-111-1-111-1-1ii−i−iii−i−i−i−iii−i−iii-11-11
χ111111111111-1-1-1-11111-1-1-1-111-1-111-1-1−i−iii−i−iiiii−i−iii−i−i-11-11
χ121111111111-1-1-1-11111-1-1-1-111-1-111-1-1−i−iii−i−iii−i−iii−i−iii1-11-1
χ131111111111-1-1-1-11111-1-1-1-1-1-111-1-111ii−i−i−i−iiiii−i−i−i−iii1-1-11
χ141111111111-1-1-1-11111-1-1-1-1-1-111-1-111ii−i−i−i−iii−i−iiiii−i−i-111-1
χ151111111111-1-1-1-11111-1-1-1-1-1-111-1-111−i−iiiii−i−iii−i−i−i−iii-111-1
χ161111111111-1-1-1-11111-1-1-1-1-1-111-1-111−i−iiiii−i−i−i−iiiii−i−i1-1-11
χ1722222222222222-2-2-2-2-2-2-2-22222-2-2-2-200000000000000000000
χ1822222222222222-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000000000
χ192222222222-2-2-2-2-2-2-2-2222222-2-2-2-22200000000000000000000
χ202222222222-2-2-2-2-2-2-2-22222-2-22222-2-200000000000000000000
χ212222-2-222-2-222-2-222-2-22-22-2000000000000000000002-22-20000
χ222222-2-222-2-222-2-222-2-22-22-200000000000000000000-22-220000
χ232222-2-222-2-222-2-2-2-222-22-2200000000000000002-22-200000000
χ242222-2-222-2-222-2-2-2-222-22-220000000000000000-22-2200000000
χ252222-2-222-2-2-2-22222-2-2-22-22000000000000000000002i−2i−2i2i0000
χ262222-2-222-2-2-2-22222-2-2-22-2200000000000000000000−2i2i2i−2i0000
χ272222-2-222-2-2-2-222-2-2222-22-200000000000000002i−2i−2i2i00000000
χ282222-2-222-2-2-2-222-2-2222-22-20000000000000000−2i2i2i−2i00000000
χ2922-2-22-22-22-2000000002-2-22002i−2i2i−2i00i2−i2i2−i22−22−2000000000000
χ3022-2-22-22-22-2000000002-2-22002i−2i2i−2i00−i2i2−i2i2−22−22000000000000
χ3122-2-22-22-22-2000000002-2-2200−2i2i−2i2i00i2−i2i2−i2−22−22000000000000
χ3222-2-22-22-22-2000000002-2-2200−2i2i−2i2i00−i2i2−i2i22−22−2000000000000
χ3322-2-22-22-22-200000000-222-2002i−2i−2i2i002−2−22i2−i2−i2i2000000000000
χ3422-2-22-22-22-200000000-222-2002i−2i−2i2i00−222−2−i2i2i2−i2000000000000
χ3522-2-22-22-22-200000000-222-200−2i2i2i−2i002−2−22−i2i2i2−i2000000000000
χ3622-2-22-22-22-200000000-222-200−2i2i2i−2i00−222−2i2−i2−i2i2000000000000
χ37444444-4-4-4-44-44-4000000000000000000000000000000000000
χ38444444-4-4-4-4-44-44000000000000000000000000000000000000
χ394444-4-4-4-4444-4-44000000000000000000000000000000000000
χ404444-4-4-4-444-444-4000000000000000000000000000000000000
χ4144-4-44-4-44-440000000000000000004i−4i00000000000000000000
χ4244-4-44-4-44-44000000000000000000−4i4i00000000000000000000
χ4344-4-4-444-4-440000000044-4-40000000000000000000000000000
χ4444-4-4-444-4-4400000000-4-4440000000000000000000000000000
χ4544-4-4-44-444-40000000000004i−4i00000000000000000000000000
χ4644-4-4-44-444-4000000000000−4i4i00000000000000000000000000
χ478-88-80000000000004i2−4i200000000000000000000000000000000
χ488-88-8000000000000−4i24i200000000000000000000000000000000
χ498-8-8800000000004i2−4i20000000000000000000000000000000000
χ508-8-880000000000−4i24i20000000000000000000000000000000000

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