Finite Group Databasebeta

← Group #135404

Character table — Group #135404

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11112222224444444444444444888888161616161616161616161616161616161616161616161616
order122222444444448888888888882444884444444416161616161616161616161616161616
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i
χ611111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii
χ711111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii
χ811111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−i
χ91111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ101111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1−i−iii−i−iii−i−iii−i−iii
χ111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111ii−i−iii−i−i−i−iii−i−iii
χ121111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111−i−iii−i−iiiii−i−iii−i−i
χ131111111111-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111
χ141111111111-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-111-1-11111-1-1-1-11111-1-1
χ151111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11111-1-111-1-1-1-111-1-11111-1-1
χ161111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-111
χ172222222222222222222222-2-2-2-2-2-2-2-2-2-2000000000000000000000000
χ1822222222222222-2-2-2-2-2-2-2-22222-2-2-2-222000000000000000000000000
χ192222222222-2-2-2-22222-2-2-2-2222222-2-2-2-2000000000000000000000000
χ202222222222-2-2-2-2-2-2-2-22222-2-2-2-222-2-222000000000000000000000000
χ212222-2-22-22-22i2i−2i−2i22-2-22i2i−2i−2i000000000000000000000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i
χ222222-2-22-22-22i2i−2i−2i22-2-22i2i−2i−2i00000000000000000000000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i
χ232222-2-22-22-22i2i−2i−2i-2-222−2i−2i2i2i000000000000000000000000001−i−1+i−1−i1+i−1+i1−i1+i−1−i
χ242222-2-22-22-22i2i−2i−2i-2-222−2i−2i2i2i00000000000000000000000000−1+i1−i1+i−1−i1−i−1+i−1−i1+i
χ252222-2-22-22-2−2i−2i2i2i22-2-2−2i−2i2i2i000000000000000000000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i
χ262222-2-22-22-2−2i−2i2i2i22-2-2−2i−2i2i2i00000000000000000000000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i
χ272222-2-22-22-2−2i−2i2i2i-2-2222i2i−2i−2i000000000000000000000000001+i−1−i−1+i1−i−1−i1+i1−i−1+i
χ282222-2-22-22-2−2i−2i2i2i-2-2222i2i−2i−2i00000000000000000000000000−1−i1+i1−i−1+i1+i−1−i−1+i1−i
χ292-22-22-2-2-222000000002-22-222-2-2002-200002i−2i2i−2i000000000000000000
χ302-22-22-2-2-222000000002-22-222-2-2002-20000−2i2i−2i2i000000000000000000
χ312-22-22-2-2-222000000002-22-2-2-22200-22002i−2i00002i−2i0000000000000000
χ322-22-22-2-2-222000000002-22-2-2-22200-2200−2i2i0000−2i2i0000000000000000
χ332-22-22-2-2-22200000000-22-2222-2-200-22002i−2i0000−2i2i0000000000000000
χ342-22-22-2-2-22200000000-22-2222-2-200-2200−2i2i00002i−2i0000000000000000
χ352-22-22-2-2-22200000000-22-22-2-222002-200002i−2i−2i2i000000000000000000
χ362-22-22-2-2-22200000000-22-22-2-222002-20000−2i2i2i−2i000000000000000000
χ372-22-2-222-2-222i−2i2i−2i000000002i−2i2i−2i00002-2000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i00000000
χ382-22-2-222-2-222i−2i2i−2i000000002i−2i2i−2i00002-200000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i00000000
χ392-22-2-222-2-222i−2i2i−2i00000000−2i2i−2i2i0000-22000000001−i−1+i−1−i1+i−1+i1−i1+i−1−i00000000
χ402-22-2-222-2-222i−2i2i−2i00000000−2i2i−2i2i0000-2200000000−1+i1−i1+i−1−i1−i−1+i−1−i1+i00000000
χ412-22-2-222-2-22−2i2i−2i2i000000002i−2i2i−2i0000-22000000001+i−1−i−1+i1−i−1−i1+i1−i−1+i00000000
χ422-22-2-222-2-22−2i2i−2i2i000000002i−2i2i−2i0000-2200000000−1−i1+i1−i−1+i1+i−1−i−1+i1−i00000000
χ432-22-2-222-2-22−2i2i−2i2i00000000−2i2i−2i2i00002-2000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i00000000
χ442-22-2-222-2-22−2i2i−2i2i00000000−2i2i−2i2i00002-200000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i00000000
χ45444444-4-4-4-400000000000000004-40000000000000000000000000000
χ46444444-4-4-4-40000000000000000-440000000000000000000000000000
χ474444-4-4-44-440000000000004i−4i−4i4i000000000000000000000000000000
χ484444-4-4-44-44000000000000−4i4i4i−4i000000000000000000000000000000
χ494-44-44-444-4-44-4-44000000000000000000000000000000000000000000
χ504-44-44-444-4-4-444-4000000000000000000000000000000000000000000
χ514-44-4-44-444-4000000004i−4i−4i4i0000000000000000000000000000000000
χ524-44-4-44-444-400000000−4i4i4i−4i0000000000000000000000000000000000
χ5388-8-800000000000042−4200000000000000000000000000000000000000
χ5488-8-8000000000000−424200000000000000000000000000000000000000
χ558-8-88000000000042−420000000000000000000000000000000000000000
χ568-8-880000000000−42420000000000000000000000000000000000000000

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