Finite Group Databasebeta

← Group #141140

Character table — Group #141140

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11112222222222444444444444448888888888888888888888161616161616161632323232
order12222244448888224444448888884444444444888888888888888888884444
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111-1-1-1-1-1-1-1-111-1-1-1-111iiii−i−i−i−i11-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-1
χ611111111111111-1-1-1-1-1-1-1-111-1-1-1-111iiii−i−i−i−i11-1-1iiii−i−i−i−i−i−i−i−iiiii-1-111
χ711111111111111-1-1-1-1-1-1-1-111-1-1-1-111−i−i−i−iiiii11-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-111
χ811111111111111-1-1-1-1-1-1-1-111-1-1-1-111−i−i−i−iiiii11-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-1
χ91111111111-1-1-1-111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11-11-1
χ101111111111-1-1-1-111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-11-11
χ111111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-11-11
χ121111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111-11-1
χ131111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111iiii−i−i−i−i-1-111−i−i−i−iiiiiii−i−i−i−iii1-1-11
χ141111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111iiii−i−i−i−i-1-111−i−i−i−iiiii−i−iiiii−i−i-111-1
χ151111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111−i−i−i−iiiii-1-111iiii−i−i−i−iii−i−i−i−iii-111-1
χ161111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111−i−i−i−iiiii-1-111iiii−i−i−i−i−i−iiiii−i−i1-1-11
χ172222222222222222-2-22-2-22222222-2-200000000-2-2-2-200000000000000000000
χ1822222222222222-2-222-222-222-2-2-2-2-2-200000000-2-22200000000000000000000
χ192222222222-2-2-2-222-2-22-2-22-2-2-2-2-2-2-2-200000000222200000000000000000000
χ202222222222-2-2-2-2-2-222-222-2-2-22222-2-20000000022-2-200000000000000000000
χ21222222-2-2-2-200002222-2-2-2-20000002-20000000000002i2i−2i−2i2i2i−2i−2i000000000000
χ22222222-2-2-2-200002222-2-2-2-20000002-2000000000000−2i−2i2i2i−2i−2i2i2i000000000000
χ23222222-2-2-2-2000022-2-2-222-2000000-2222-2-222-2-2000000000000000000000000
χ24222222-2-2-2-2000022-2-2-222-2000000-22-2-222-2-222000000000000000000000000
χ25222222-2-2-2-20000-2-2222-2-22000000-222i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ26222222-2-2-2-20000-2-2222-2-22000000-22−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ27222222-2-2-2-20000-2-2-2-222220000002-200000000000022-2-2-2-222000000000000
χ28222222-2-2-2-20000-2-2-2-222220000002-2000000000000-2-22222-2-2000000000000
χ292-2-222-22-22-20000002i−2i02i−2i0002i2i−2i−2i001+i−1−i1+i−1−i1−i−1+i1−i−1+i2-2001+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000
χ302-2-222-22-22-20000002i−2i02i−2i0002i2i−2i−2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i2-200−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000
χ312-2-222-22-22-20000002i−2i02i−2i000−2i−2i2i2i001+i−1−i1+i−1−i1−i−1+i1−i−1+i-2200−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000
χ322-2-222-22-22-20000002i−2i02i−2i000−2i−2i2i2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i-22001+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000
χ332-2-222-22-22-2000000−2i2i0−2i2i0002i2i−2i−2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i-2200−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000
χ342-2-222-22-22-2000000−2i2i0−2i2i0002i2i−2i−2i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i-22001−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000
χ352-2-222-22-22-2000000−2i2i0−2i2i000−2i−2i2i2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i2-2001−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000
χ362-2-222-22-22-2000000−2i2i0−2i2i000−2i−2i2i2i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i2-200−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000
χ372-2-222-2-22-2222-2-2002i−2i0−2i2i02-20000001−i−1+i−1+i1−i1+i−1−i−1−i1+i002i−2i1−i−1+i−1+i1−i−1−i1+i1+i−1−i000000000000
χ382-2-222-2-22-2222-2-2002i−2i0−2i2i02-2000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i002i−2i−1+i1−i1−i−1+i1+i−1−i−1−i1+i000000000000
χ392-2-222-2-22-2222-2-200−2i2i02i−2i02-20000001+i−1−i−1−i1+i1−i−1+i−1+i1−i00−2i2i1+i−1−i−1−i1+i−1+i1−i1−i−1+i000000000000
χ402-2-222-2-22-2222-2-200−2i2i02i−2i02-2000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i00−2i2i−1−i1+i1+i−1−i1−i−1+i−1+i1−i000000000000
χ412-2-222-2-22-22-2-222002i−2i0−2i2i0-220000001−i−1+i−1+i1−i1+i−1−i−1−i1+i00−2i2i−1+i1−i1−i−1+i1+i−1−i−1−i1+i000000000000
χ422-2-222-2-22-22-2-222002i−2i0−2i2i0-22000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i00−2i2i1−i−1+i−1+i1−i−1−i1+i1+i−1−i000000000000
χ432-2-222-2-22-22-2-22200−2i2i02i−2i0-220000001+i−1−i−1−i1+i1−i−1+i−1+i1−i002i−2i−1−i1+i1+i−1−i1−i−1+i−1+i1−i000000000000
χ442-2-222-2-22-22-2-22200−2i2i02i−2i0-22000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i002i−2i1+i−1−i−1−i1+i−1+i1−i1−i−1+i000000000000
χ452-2-22-222-2-2222-2-22-200200-2-222-22-20000000000000000000000i2−i2i2−i2i2−i2i2−i20000
χ462-2-22-222-2-2222-2-22-200200-2-222-22-20000000000000000000000−i2i2−i2i2−i2i2−i2i20000
χ472-2-22-222-2-2222-2-2-2200-2002-22-22-2200000000000000000000002−22−2−22−220000
χ482-2-22-222-2-2222-2-2-2200-2002-22-22-220000000000000000000000−22−222−22−20000
χ492-2-22-222-2-22-2-2222-200200-22-2-22-220000000000000000000000i2−i2−i2i2i2−i2−i2i20000
χ502-2-22-222-2-22-2-2222-200200-22-2-22-220000000000000000000000−i2i2i2−i2−i2i2i2−i20000
χ512-2-22-222-2-22-2-222-2200-20022-22-22-200000000000000000000002−2−22−222−20000
χ522-2-22-222-2-22-2-222-2200-20022-22-22-20000000000000000000000−222−22−2−220000
χ534444-4-444-4-4000000000000004i−4i−4i4i0000000000000000000000000000000000
χ544444-4-444-4-400000000000000−4i4i4i−4i0000000000000000000000000000000000
χ554444-4-4-4-444444400000000-4-400000000000000000000000000000000000000
χ564444-4-4-4-444-4-4-4-4000000004400000000000000000000000000000000000000
χ574-4-44-44-444-400004-400-40040000000000000000000000000000000000000000
χ584-4-44-44-444-40000-4400400-40000000000000000000000000000000000000000
χ5988-8-800000042−4242−42000000000000000000000000000000000000000000000000
χ6088-8-8000000−4242−4242000000000000000000000000000000000000000000000000
χ618-88-800000042−42−4242000000000000000000000000000000000000000000000000
χ628-88-8000000−424242−42000000000000000000000000000000000000000000000000

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