Finite Group Databasebeta

← Group #72285535

Character table — Group #72285535

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55
size112224444448888881616161616161616161616161616161616161616161616161616161616323232646464646464
order1222222222222444422444444444444444444444444444444448888
χ11111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1
χ31111111111111111111111-1-11111111111111111111111-1-1-1-1-1-1-1-1-1
χ41111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111-1-11-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1111-1-111-1-1
χ611111111111111111-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-111
χ711111111111111111-1-11-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-111-1-111
χ811111111111111111-1-11-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-11111-1-1
χ91111111-1-1-1-111-1-1-1-11-1-11-1111111-1-1iiii−i−i−i−iiiii−i−i−i−i1-1-11-1i−ii−i
χ101111111-1-1-1-111-1-1-1-11-1-11-1111111-1-1−i−i−i−iiiii−i−i−i−iiiii1-1-11-1−ii−ii
χ111111111-1-1-1-111-1-1-1-11-1-11-1-1-11111-1-1iiii−i−i−i−iiiii−i−i−i−i-111-11−ii−ii
χ121111111-1-1-1-111-1-1-1-11-1-11-1-1-11111-1-1−i−i−i−iiiii−i−i−i−iiiii-111-11i−ii−i
χ131111111-1-1-1-111-1-1-1-1-11-1-111111-1-111iiii−i−i−i−i−i−i−i−iiiii1-1-1-11i−i−ii
χ141111111-1-1-1-111-1-1-1-1-11-1-111111-1-111−i−i−i−iiiiiiiii−i−i−i−i1-1-1-11−iii−i
χ151111111-1-1-1-111-1-1-1-1-11-1-11-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii-1111-1−iii−i
χ161111111-1-1-1-111-1-1-1-1-11-1-11-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−i-1111-1i−i−ii
χ172222222222222-2-2-2-22222200-2-2-2-2-2-20000000000000000000000000
χ182222222222222-2-2-2-2-2-22-2-200-2-222220000000000000000000000000
χ1922222222222-2-222-2-200-200002-200000000000022-2-222-2-2000000000
χ2022222222222-2-222-2-200-200002-2000000000000-2-222-2-222000000000
χ2122222222222-2-2-2-22200-20000-22000022-2-222-2-200000000000000000
χ2222222222222-2-2-2-22200-20000-220000-2-222-2-22200000000000000000
χ232222222-2-2-2-22222222-2-22-200-2-2-2-2220000000000000000000000000
χ242222222-2-2-2-2222222-22-2-2200-2-222-2-20000000000000000000000000
χ252222222-2-2-2-2-2-222-2-20020000-2200002i2i−2i−2i−2i−2i2i2i00000000000000000
χ262222222-2-2-2-2-2-222-2-20020000-220000−2i−2i2i2i2i2i−2i−2i00000000000000000
χ272222222-2-2-2-2-2-2-2-22200200002-20000000000002i2i−2i−2i−2i−2i2i2i000000000
χ282222222-2-2-2-2-2-2-2-22200200002-2000000000000−2i−2i2i2i2i2i−2i−2i000000000
χ29222-2-22-200002-22i−2i2i−2i0200-200002i−2i001+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000
χ30222-2-22-200002-22i−2i2i−2i0200-200002i−2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000
χ31222-2-22-200002-22i−2i2i−2i0-20020000−2i2i001+i−1−i1+i−1−i1−i−1+i1−i−1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000
χ32222-2-22-200002-22i−2i2i−2i0-20020000−2i2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000
χ33222-2-22-200002-2−2i2i−2i2i0200-20000−2i2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000
χ34222-2-22-200002-2−2i2i−2i2i0200-20000−2i2i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000
χ35222-2-22-200002-2−2i2i−2i2i0-200200002i−2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000
χ36222-2-22-200002-2−2i2i−2i2i0-200200002i−2i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000
χ37222-2-22-20000-222i−2i−2i2i200-200000002i−2i1−i−1+i−1+i1−i1+i−1−i−1−i1+i1−i−1+i−1+i1−i1+i−1−i−1−i1+i000000000
χ38222-2-22-20000-222i−2i−2i2i200-200000002i−2i−1+i1−i1−i−1+i−1−i1+i1+i−1−i−1+i1−i1−i−1+i−1−i1+i1+i−1−i000000000
χ39222-2-22-20000-222i−2i−2i2i-20020000000−2i2i1−i−1+i−1+i1−i1+i−1−i−1−i1+i−1+i1−i1−i−1+i−1−i1+i1+i−1−i000000000
χ40222-2-22-20000-222i−2i−2i2i-20020000000−2i2i−1+i1−i1−i−1+i−1−i1+i1+i−1−i1−i−1+i−1+i1−i1+i−1−i−1−i1+i000000000
χ41222-2-22-20000-22−2i2i2i−2i200-20000000−2i2i1+i−1−i−1−i1+i1−i−1+i−1+i1−i1+i−1−i−1−i1+i1−i−1+i−1+i1−i000000000
χ42222-2-22-20000-22−2i2i2i−2i200-20000000−2i2i−1−i1+i1+i−1−i−1+i1−i1−i−1+i−1−i1+i1+i−1−i−1+i1−i1−i−1+i000000000
χ43222-2-22-20000-22−2i2i2i−2i-200200000002i−2i1+i−1−i−1−i1+i1−i−1+i−1+i1−i−1−i1+i1+i−1−i−1+i1−i1−i−1+i000000000
χ44222-2-22-20000-22−2i2i2i−2i-200200000002i−2i−1−i1+i1+i−1−i−1+i1−i1−i−1+i1+i−1−i−1−i1+i1−i−1+i−1+i1−i000000000
χ4544444-4-444-4-400000000000220000000000000000000000-22-2000000
χ4644444-4-444-4-400000000000-2-200000000000000000000002-22000000
χ4744444-4-4-4-44400000000000220000000000000000000000-2-22000000
χ4844444-4-4-4-44400000000000-2-2000000000000000000000022-2000000
χ49888-8-8-88000000000000000000000000000000000000000000000000
χ5088-88-800008-800000000000000000000000000000000000000000000
χ5188-88-80000-8800000000000000000000000000000000000000000000
χ5288-8-88008-80000000000000000000000000000000000000000000000
χ5388-8-8800-880000000000000000000000000000000000000000000000
χ5416-16000000000000000000004i−4i0000000000000000000000000000000
χ5516-1600000000000000000000−4i4i0000000000000000000000000000000

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