Finite Group Databasebeta

← Group #142151

Character table — Group #142151

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11112222222222444444444444448888888888888888888888161616161616161632323232
order1222224444888822448888888888444444444444888888888816161616161616164444
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1iiii−i−i−i−i11iiii−i−i−i−iiiii−i−i−i−i11-1-1
χ611111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1iiii−i−i−i−i11iiii−i−i−i−i−i−i−i−iiiii-1-111
χ711111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1−i−i−i−iiiii11−i−i−i−iiiiiiiii−i−i−i−i-1-111
χ811111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1−i−i−i−iiiii11−i−i−i−iiiii−i−i−i−iiiii11-1-1
χ91111111111-1-1-1-11111-1-111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-111-1-11-11-1
χ101111111111-1-1-1-11111-1-111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-111-11-11
χ111111111111-1-1-1-11111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-11-11
χ121111111111-1-1-1-11111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1111-11-1
χ131111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111iiii−i−i−i−i11−i−i−i−iiiiiii−i−i−i−iii1-1-11
χ141111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111iiii−i−i−i−i11−i−i−i−iiiii−i−iiiii−i−i-111-1
χ151111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111−i−i−i−iiiii11iiii−i−i−i−iii−i−i−i−iii-111-1
χ161111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111−i−i−i−iiiii11iiii−i−i−i−i−i−iiiii−i−i1-1-11
χ1722222222222222222222-2-22222-2-2-2-2-2-200000000-2-200000000000000000000
χ1822222222222222-2-2-2-22222-2-2-2-222-2-22200000000-2-200000000000000000000
χ192222222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2222200000000-2-200000000000000000000
χ202222222222-2-2-2-2-2-2-2-2-2-22222222222-2-200000000-2-200000000000000000000
χ212222-2-22-22-222220000-2-22i−2i00002i−2i002i−2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i001+i1+i−1−i−1−i1−i1−i−1+i−1+i000000000000
χ222222-2-22-22-222220000-2-22i−2i00002i−2i002i−2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i00−1−i−1−i1+i1+i−1+i−1+i1−i1−i000000000000
χ232222-2-22-22-222220000-2-2−2i2i0000−2i2i00−2i2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i001−i1−i−1+i−1+i1+i1+i−1−i−1−i000000000000
χ242222-2-22-22-222220000-2-2−2i2i0000−2i2i00−2i2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i00−1+i−1+i1−i1−i−1−i−1−i1+i1+i000000000000
χ252222-2-22-22-2-2-2-2-20000222i−2i00002i−2i00−2i2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i00−1−i−1−i1+i1+i−1+i−1+i1−i1−i000000000000
χ262222-2-22-22-2-2-2-2-20000222i−2i00002i−2i00−2i2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i001+i1+i−1−i−1−i1−i1−i−1+i−1+i000000000000
χ272222-2-22-22-2-2-2-2-2000022−2i2i0000−2i2i002i−2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i00−1+i−1+i1−i1−i−1−i−1−i1+i1+i000000000000
χ282222-2-22-22-2-2-2-2-2000022−2i2i0000−2i2i002i−2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i001−i1−i−1+i−1+i1+i1+i−1−i−1−i000000000000
χ292-22-22-22-2-2200002-2-2200220000-2-20000000000002-22-22-22-22-2000000000000
χ302-22-22-22-2-2200002-2-2200220000-2-20000000000002-2-22-22-22-22000000000000
χ312-22-22-22-2-2200002-2-2200-2-200002200002i−2i2i−2i2i−2i2i−2i-2200000000000000000000
χ322-22-22-22-2-2200002-2-2200-2-20000220000−2i2i−2i2i−2i2i−2i2i-2200000000000000000000
χ332-22-22-22-2-220000-222-200220000-2-200002-22-2-22-22-2200000000000000000000
χ342-22-22-22-2-220000-222-200220000-2-20000-22-222-22-2-2200000000000000000000
χ352-22-22-22-2-220000-222-200-2-20000220000000000002-22i−2i2i−2i−2i2i−2i2i000000000000
χ362-22-22-22-2-220000-222-200-2-20000220000000000002-2−2i2i−2i2i2i−2i2i−2i000000000000
χ372-22-22-2-222-222-2-22-22-22-20022-2-20000000000000000000000002−22−22−22−20000
χ382-22-22-2-222-222-2-22-22-22-20022-2-2000000000000000000000000−22−22−22−220000
χ392-22-22-2-222-222-2-2-22-222-200-2-222000000000000000000000000i2−i2i2−i2−i2i2−i2i20000
χ402-22-22-2-222-222-2-2-22-222-200-2-222000000000000000000000000−i2i2−i2i2i2−i2i2−i20000
χ412-22-22-2-222-2-2-2222-22-2-2200-2-2220000000000000000000000002−2−222−2−220000
χ422-22-22-2-222-2-2-2222-22-2-2200-2-222000000000000000000000000−222−2−222−20000
χ432-22-22-2-222-2-2-222-22-22-220022-2-2000000000000000000000000i2−i2−i2i2−i2i2i2−i20000
χ442-22-22-2-222-2-2-222-22-22-220022-2-2000000000000000000000000−i2i2i2−i2i2−i2−i2i20000
χ452-22-2-2222-2-200000000002i−2i2i−2i2i−2i−2i2i2-2001+i−1−i−1−i1+i−1+i1−i1−i−1+i001+i−1−i−1−i1+i1−i−1+i−1+i1−i000000000000
χ462-22-2-2222-2-200000000002i−2i2i−2i2i−2i−2i2i2-200−1−i1+i1+i−1−i1−i−1+i−1+i1−i00−1−i1+i1+i−1−i−1+i1−i1−i−1+i000000000000
χ472-22-2-2222-2-200000000002i−2i−2i2i−2i2i−2i2i-22001+i−1−i−1−i1+i−1+i1−i1−i−1+i00−1−i1+i1+i−1−i−1+i1−i1−i−1+i000000000000
χ482-22-2-2222-2-200000000002i−2i−2i2i−2i2i−2i2i-2200−1−i1+i1+i−1−i1−i−1+i−1+i1−i001+i−1−i−1−i1+i1−i−1+i−1+i1−i000000000000
χ492-22-2-2222-2-20000000000−2i2i2i−2i2i−2i2i−2i-22001−i−1+i−1+i1−i−1−i1+i1+i−1−i00−1+i1−i1−i−1+i−1−i1+i1+i−1−i000000000000
χ502-22-2-2222-2-20000000000−2i2i2i−2i2i−2i2i−2i-2200−1+i1−i1−i−1+i1+i−1−i−1−i1+i001−i−1+i−1+i1−i1+i−1−i−1−i1+i000000000000
χ512-22-2-2222-2-20000000000−2i2i−2i2i−2i2i2i−2i2-2001−i−1+i−1+i1−i−1−i1+i1+i−1−i001−i−1+i−1+i1−i1+i−1−i−1−i1+i000000000000
χ522-22-2-2222-2-20000000000−2i2i−2i2i−2i2i2i−2i2-200−1+i1−i1−i−1+i1+i−1−i−1−i1+i00−1+i1−i1−i−1+i−1−i1+i1+i−1−i000000000000
χ53444444-4-4-4-4000044-4-400000000000000000000000000000000000000000000
χ54444444-4-4-4-40000-4-44400000000000000000000000000000000000000000000
χ554444-4-4-44-440000000000004i−4i−4i4i000000000000000000000000000000000000
χ564444-4-4-44-44000000000000−4i4i4i−4i000000000000000000000000000000000000
χ574-44-4-44-4-44444-4-40000-44000000000000000000000000000000000000000000
χ584-44-4-44-4-444-4-44400004-4000000000000000000000000000000000000000000
χ5988-8-800000042−4242−42000000000000000000000000000000000000000000000000
χ6088-8-8000000−4242−4242000000000000000000000000000000000000000000000000
χ618-8-8800000042−42−4242000000000000000000000000000000000000000000000000
χ628-8-88000000−424242−42000000000000000000000000000000000000000000000000

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