Finite Group Databasebeta

← Group #138017

Character table — Group #138017

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11112222222222444444444444448888888888888888888888161616161616161632323232
order122222444488882244444488888844888816161616161616161616161616161616444444444444
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
χ51111111111111111-1-111-1-111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ61111111111111111-1-111-1-111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ71111111111111111-1-111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ81111111111111111-1-111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ91111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i1-11-1
χ101111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii-11-11
χ111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i-11-11
χ121111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-11111−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
χ1722222222222222-2-222-2-222222222-2-2-2-2-2-20000000000000000000000000000
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
χ202222222222-2-2-2-222-2-222-2-2-2-22222-2-2-2-2220000000000000000000000000000
χ21222222-2-2-2-200002222-2-2-2-2000000-22000022−2−222−2−222−2−222−2−2000000000000
χ22222222-2-2-2-200002222-2-2-2-2000000-220000−2−222−2−222−2−222−2−222000000000000
χ23222222-2-2-2-2000022-2-2-2-2220000002-2000022−2−222−2−2−2−222−2−222000000000000
χ24222222-2-2-2-2000022-2-2-2-2220000002-20000−2−222−2−22222−2−222−2−2000000000000
χ25222222-2-2-2-20000-2-22222-2-20000002-20000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2000000000000
χ26222222-2-2-2-20000-2-22222-2-20000002-20000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2000000000000
χ27222222-2-2-2-20000-2-2-2-22222000000-220000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2000000000000
χ28222222-2-2-2-20000-2-2-2-22222000000-220000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2000000000000
χ292222-2-222-2-200002-2002-200002i2i−2i−2i00002i−2ii2−i2i2−i2i2−i2i2−i22−22−22−22−2000000000000
χ302222-2-222-2-200002-2002-200002i2i−2i−2i00002i−2i−i2i2−i2i2−i2i2−i2i2−22−22−22−22000000000000
χ312222-2-222-2-200002-2002-20000−2i−2i2i2i0000−2i2ii2−i2i2−i2i2−i2i2−i2−22−22−22−22000000000000
χ322222-2-222-2-200002-2002-20000−2i−2i2i2i0000−2i2i−i2i2−i2i2−i2i2−i2i22−22−22−22−2000000000000
χ332222-2-222-2-20000-2200-2200002i2i−2i−2i0000−2i2i2−22−2−22−22i2−i2i2−i2−i2i2−i2i2000000000000
χ342222-2-222-2-20000-2200-2200002i2i−2i−2i0000−2i2i−22−222−22−2−i2i2−i2i2i2−i2i2−i2000000000000
χ352222-2-222-2-20000-2200-220000−2i−2i2i2i00002i−2i2−22−2−22−22−i2i2−i2i2i2−i2i2−i2000000000000
χ362222-2-222-2-20000-2200-220000−2i−2i2i2i00002i−2i−22−222−22−2i2−i2i2−i2−i2i2−i2i2000000000000
χ372222-2-2-2-22222222-200-2200-2-20000002-200000000002-2-222-2-22000000000000
χ382222-2-2-2-22222222-200-2200-2-20000002-20000000000-222-2-222-2000000000000
χ392222-2-2-2-2222222-22002-200-2-2000000-22002-2-22-222-200000000000000000000
χ402222-2-2-2-2222222-22002-200-2-2000000-2200-222-22-2-2200000000000000000000
χ412222-2-2-2-222-2-2-2-22-200-220022000000-22002i−2i−2i2i2i−2i−2i2i00000000000000000000
χ422222-2-2-2-222-2-2-2-22-200-220022000000-2200−2i2i2i−2i−2i2i2i−2i00000000000000000000
χ432222-2-2-2-222-2-2-2-2-22002-200220000002-200000000002i−2i−2i2i−2i2i2i−2i000000000000
χ442222-2-2-2-222-2-2-2-2-22002-200220000002-20000000000−2i2i2i−2i2i−2i−2i2i000000000000
χ452-22-22-22-22-22i2i−2i−2i002i−2i002i−2i2i−2i2-22-200000000000000000000001+i−1−i1−i−1+i1−i−1+i1+i−1−i0000
χ462-22-22-22-22-22i2i−2i−2i002i−2i002i−2i2i−2i2-22-20000000000000000000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i0000
χ472-22-22-22-22-22i2i−2i−2i00−2i2i00−2i2i2i−2i-22-2200000000000000000000001+i−1−i1−i−1+i−1+i1−i−1−i1+i0000
χ482-22-22-22-22-22i2i−2i−2i00−2i2i00−2i2i2i−2i-22-220000000000000000000000−1−i1+i−1+i1−i1−i−1+i1+i−1−i0000
χ492-22-22-22-22-2−2i−2i2i2i002i−2i002i−2i−2i2i-22-2200000000000000000000001−i−1+i1+i−1−i−1−i1+i−1+i1−i0000
χ502-22-22-22-22-2−2i−2i2i2i002i−2i002i−2i−2i2i-22-220000000000000000000000−1+i1−i−1−i1+i1+i−1−i1−i−1+i0000
χ512-22-22-22-22-2−2i−2i2i2i00−2i2i00−2i2i−2i2i2-22-200000000000000000000001−i−1+i1+i−1−i1+i−1−i1−i−1+i0000
χ522-22-22-22-22-2−2i−2i2i2i00−2i2i00−2i2i−2i2i2-22-20000000000000000000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i0000
χ534-44-44-4-44-440000004i−4i00−4i4i0000000000000000000000000000000000000000
χ544-44-44-4-44-44000000−4i4i004i−4i0000000000000000000000000000000000000000
χ554-44-4-444-4-44000000000000004i−4i−4i4i0000000000000000000000000000000000
χ564-44-4-444-4-4400000000000000−4i4i4i−4i0000000000000000000000000000000000
χ574-44-4-44-444-44i4i−4i−4i00000000−4i4i00000000000000000000000000000000000000
χ584-44-4-44-444-4−4i−4i4i4i000000004i−4i00000000000000000000000000000000000000
χ5988-8-800000042−4242−42000000000000000000000000000000000000000000000000
χ6088-8-8000000−4242−4242000000000000000000000000000000000000000000000000
χ618-8-880000004i2−4i2−4i24i2000000000000000000000000000000000000000000000000
χ628-8-88000000−4i24i24i2−4i2000000000000000000000000000000000000000000000000

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