Finite Group Databasebeta

← Group #138161

Character table — Group #138161

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11112222222222444444444444448888888888888888888888161616161616161632323232
order122222444488882244444488888844888816161616161616161616161616161616888888882444
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111-1-111-1-11111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ611111111111111-1-111-1-11111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ711111111111111-1-111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ811111111111111-1-111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ91111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i1-11-1
χ101111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii-11-11
χ111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i-11-11
χ121111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii1-11-1
χ131111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii1-1-11
χ141111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1iiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i-111-1
χ151111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii-111-1
χ161111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i1-1-11
χ172222222222222222-2-222-2-2222222-2-2-2-2-2-20000000000000000000000000000
χ1822222222222222-2-2-2-2-2-2-2-222-2-2-2-222-2-2220000000000000000000000000000
χ192222222222-2-2-2-222222222-2-2-2-2-2-222-2-2-2-20000000000000000000000000000
χ202222222222-2-2-2-2-2-222-2-222-2-22222-2-2-2-2220000000000000000000000000000
χ21222222-2-2-2-200002222-2-2-2-20000002-20000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2000000000000
χ22222222-2-2-2-200002222-2-2-2-20000002-20000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2000000000000
χ23222222-2-2-2-2000022-2-2-2-222000000-22000022−2−2−2−22222−2−2−2−222000000000000
χ24222222-2-2-2-2000022-2-2-2-222000000-220000−2−22222−2−2−2−22222−2−2000000000000
χ25222222-2-2-2-20000-2-22222-2-2000000-220000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2000000000000
χ26222222-2-2-2-20000-2-22222-2-2000000-220000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2000000000000
χ27222222-2-2-2-20000-2-2-2-222220000002-2000022−2−2−2−222−2−22222−2−2000000000000
χ28222222-2-2-2-20000-2-2-2-222220000002-20000−2−22222−2−222−2−2−2−222000000000000
χ292222-2-222-2-20000002-2002-2002i2i−2i−2i00002i−2ii2−i2i2−i2i2−i2i2−i22−22−22−22−2000000000000
χ302222-2-222-2-20000002-2002-2002i2i−2i−2i00002i−2i−i2i2−i2i2−i2i2−i2i2−22−22−22−22000000000000
χ312222-2-222-2-20000002-2002-200−2i−2i2i2i0000−2i2ii2−i2i2−i2i2−i2i2−i2−22−22−22−22000000000000
χ322222-2-222-2-20000002-2002-200−2i−2i2i2i0000−2i2i−i2i2−i2i2−i2i2−i2i22−22−22−22−2000000000000
χ332222-2-222-2-2000000-2200-22002i2i−2i−2i0000−2i2i2−22−2−22−22i2−i2i2−i2−i2i2−i2i2000000000000
χ342222-2-222-2-2000000-2200-22002i2i−2i−2i0000−2i2i−22−222−22−2−i2i2−i2i2i2−i2i2−i2000000000000
χ352222-2-222-2-2000000-2200-2200−2i−2i2i2i00002i−2i2−22−2−22−22−i2i2−i2i2i2−i2i2−i2000000000000
χ362222-2-222-2-2000000-2200-2200−2i−2i2i2i00002i−2i−22−222−22−2i2−i2i2−i2−i2i2−i2i2000000000000
χ372222-2-2-2-2222222002-200-22-2-20000002-2002-2-222-2-2200000000000000000000
χ382222-2-2-2-2222222002-200-22-2-20000002-200-222-2-222-200000000000000000000
χ392222-2-2-2-222222200-22002-2-2-2000000-2200000000002-2-22-222-2000000000000
χ402222-2-2-2-222222200-22002-2-2-2000000-220000000000-222-22-2-22000000000000
χ412222-2-2-2-222-2-2-2-2002-200-2222000000-2200000000002i−2i−2i2i2i−2i−2i2i000000000000
χ422222-2-2-2-222-2-2-2-2002-200-2222000000-220000000000−2i2i2i−2i−2i2i2i−2i000000000000
χ432222-2-2-2-222-2-2-2-200-22002-2220000002-2002i−2i−2i2i−2i2i2i−2i00000000000000000000
χ442222-2-2-2-222-2-2-2-200-22002-2220000002-200−2i2i2i−2i2i−2i−2i2i00000000000000000000
χ452-2-22-222-22-222-2-22-2002-2002-22-22-20000000000000000000000i2−i2i2−i2i2−i2i2−i20000
χ462-2-22-222-22-222-2-22-2002-2002-22-22-20000000000000000000000−i2i2−i2i2−i2i2−i2i20000
χ472-2-22-222-22-222-2-2-2200-22002-2-22-220000000000000000000000i2−i2i2−i2−i2i2−i2i20000
χ482-2-22-222-22-222-2-2-2200-22002-2-22-220000000000000000000000−i2i2−i2i2i2−i2i2−i20000
χ492-2-22-222-22-2-2-2222-2002-200-22-22-2200000000000000000000002−2−222−2−220000
χ502-2-22-222-22-2-2-2222-2002-200-22-22-220000000000000000000000−222−2−222−20000
χ512-2-22-222-22-2-2-222-2200-2200-222-22-200000000000000000000002−2−22−222−20000
χ522-2-22-222-22-2-2-222-2200-2200-222-22-20000000000000000000000−222−22−2−220000
χ534-4-444-44-4-44000000000000004i−4i−4i4i0000000000000000000000000000000000
χ544-4-444-44-4-4400000000000000−4i4i4i−4i0000000000000000000000000000000000
χ554-4-444-4-444-444-4-400000000-4400000000000000000000000000000000000000
χ564-4-444-4-444-4-4-444000000004-400000000000000000000000000000000000000
χ574-4-44-44-44-4400004-400-44000000000000000000000000000000000000000000
χ584-4-44-44-44-440000-44004-4000000000000000000000000000000000000000000
χ5988-8-80000004i2−4i24i2−4i2000000000000000000000000000000000000000000000000
χ6088-8-8000000−4i24i2−4i24i2000000000000000000000000000000000000000000000000
χ618-88-80000004i2−4i2−4i24i2000000000000000000000000000000000000000000000000
χ628-88-8000000−4i24i24i2−4i2000000000000000000000000000000000000000000000000

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