Finite Group Databasebeta

← Group #140239

Character table — Group #140239

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11112222222222444444444444448888888888888888888888161616161616161632323232
order1222224444444444888888888888444444448888888888888816161616161616162488
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ5111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ6111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ7111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-111
χ8111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1
χ91111-1-11-1-1-1111-11-11-1iiii−i−i−i−i1-1iiii−i−i−i−i1-11111-1-1-1-1ii−i−iii−i−i11-1-11-1i−i
χ101111-1-11-1-1-1111-11-11-1iiii−i−i−i−i1-1iiii−i−i−i−i1-11111-1-1-1-1ii−i−i−i−iii-1-111-11−ii
χ111111-1-11-1-1-1111-11-11-1iiii−i−i−i−i1-1−i−i−i−iiiii1-1-1-1-1-11111ii−i−iii−i−i11-1-1-11−ii
χ121111-1-11-1-1-1111-11-11-1iiii−i−i−i−i1-1−i−i−i−iiiii1-1-1-1-1-11111ii−i−i−i−iii-1-1111-1i−i
χ131111-1-11-1-1-1111-11-11-1−i−i−i−iiiii1-1iiii−i−i−i−i1-1-1-1-1-11111−i−iiiii−i−i-1-1111-1−ii
χ141111-1-11-1-1-1111-11-11-1−i−i−i−iiiii1-1iiii−i−i−i−i1-1-1-1-1-11111−i−iii−i−iii11-1-1-11i−i
χ151111-1-11-1-1-1111-11-11-1−i−i−i−iiiii1-1−i−i−i−iiiii1-11111-1-1-1-1−i−iiiii−i−i-1-111-11i−i
χ161111-1-11-1-1-1111-11-11-1−i−i−i−iiiii1-1−i−i−i−iiiii1-11111-1-1-1-1−i−iii−i−iii11-1-11-1−ii
χ172222222222222222-2-222222222-2-200000000-2-200000000-2-2-2-2000000000000
χ182222222222222222-2-2-2-2-2-2-2-2-2-2-2-200000000-2-2000000002222000000000000
χ19222222-22-2-222-22-2-222000000002222-2-222-2-2-2-2000000000000000000000000
χ20222222-22-2-222-22-2-2220000000022-2-222-2-222-2-2000000000000000000000000
χ21222222-22-2-222-22-2-2-2-200000000-2-200000000222i2i−2i−2i2i2i−2i−2i0000000000000000
χ22222222-22-2-222-22-2-2-2-200000000-2-20000000022−2i−2i2i2i−2i−2i2i2i0000000000000000
χ23222222-2-2-2-2-2-2-2-222002i2i−2i−2i2i2i−2i−2i0000000000000000000000002−22−2i2−i2i2−i20000
χ24222222-2-2-2-2-2-2-2-222002i2i−2i−2i2i2i−2i−2i000000000000000000000000−22−22−i2i2−i2i20000
χ25222222-2-2-2-2-2-2-2-22200−2i−2i2i2i−2i−2i2i2i0000000000000000000000002−22−2−i2i2−i2i20000
χ26222222-2-2-2-2-2-2-2-22200−2i−2i2i2i−2i−2i2i2i000000000000000000000000−22−22i2−i2i2−i20000
χ272222-2-22-2-2-2222-22-2-222i2i2i2i−2i−2i−2i−2i-2200000000-2200000000−2i−2i2i2i000000000000
χ282222-2-22-2-2-2222-22-2-22−2i−2i−2i−2i2i2i2i2i-2200000000-22000000002i2i−2i−2i000000000000
χ292222-2-2-2222-2-2-222-20022-2-2-2-222000000000000000000000000i2−i2−i2i2−i2i2i2−i20000
χ302222-2-2-2222-2-2-222-20022-2-2-2-222000000000000000000000000−i2i2i2−i2i2−i2−i2i20000
χ312222-2-2-2222-2-2-222-200-2-22222-2-2000000000000000000000000i2−i2−i2i2i2−i2−i2i20000
χ322222-2-2-2222-2-2-222-200-2-22222-2-2000000000000000000000000−i2i2i2−i2−i2i2i2−i20000
χ332222-2-2-2-22222-2-2-222-2000000002-22i2i−2i−2i−2i−2i2i2i-22000000000000000000000000
χ342222-2-2-2-22222-2-2-222-2000000002-2−2i−2i2i2i2i2i−2i−2i-22000000000000000000000000
χ352222-2-2-2-22222-2-2-22-2200000000-22000000002-22i2i−2i−2i−2i−2i2i2i0000000000000000
χ362222-2-2-2-22222-2-2-22-2200000000-22000000002-2−2i−2i2i2i2i2i−2i−2i0000000000000000
χ372-2-222-202002-20-2002-2i2−i2i2−i2i2−i2i2−i2-22002-2002-200i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000000000
χ382-2-222-202002-20-2002-2i2−i2i2−i2i2−i2i2−i2-2200-2200-2200−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2000000000000
χ392-2-222-202002-20-2002-2−i2i2−i2i2−i2i2−i2i2-22002-2002-200−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000000000
χ402-2-222-202002-20-2002-2−i2i2−i2i2−i2i2−i2i2-2200-2200-2200i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2000000000000
χ412-2-222-202002-20-200-22i2−i2i2−i2i2−i2i2−i22-22i−2i002i−2i00002−2−222−2−22−i2i2−i2i2000000000000
χ422-2-222-202002-20-200-22i2−i2i2−i2i2−i2i2−i22-2−2i2i00−2i2i0000−222−2−222−2−i2i2−i2i2000000000000
χ432-2-222-202002-20-200-22−i2i2−i2i2−i2i2−i2i22-22i−2i002i−2i0000−222−2−222−2i2−i2i2−i2000000000000
χ442-2-222-202002-20-200-22−i2i2−i2i2−i2i2−i2i22-2−2i2i00−2i2i00002−2−222−2−22i2−i2i2−i2000000000000
χ452-2-22-220-2002-20200222−22−2−22−22-2-2002i−2i00−2i2i00−i2i2−i2i2i2−i2i2−i22−2−22000000000000
χ462-2-22-220-2002-20200222−22−2−22−22-2-200−2i2i002i−2i00i2−i2i2−i2−i2i2−i2i22−2−22000000000000
χ472-2-22-220-2002-2020022−22−222−22−2-2-2002i−2i00−2i2i00i2−i2i2−i2−i2i2−i2i2−222−2000000000000
χ482-2-22-220-2002-2020022−22−222−22−2-2-200−2i2i002i−2i00−i2i2−i2i2i2−i2i2−i2−222−2000000000000
χ492-2-22-220-2002-20200-2-22−22−2−22−22222-200-2200002−2−22−222−2−222−2000000000000
χ502-2-22-220-2002-20200-2-22−22−2−22−2222-22002-20000−222−22−2−22−222−2000000000000
χ512-2-22-220-2002-20200-2-2−22−222−22−2222-200-220000−222−22−2−222−2−22000000000000
χ522-2-22-220-2002-20200-2-2−22−222−22−222-22002-200002−2−22−222−22−2−22000000000000
χ534444444-444-4-44-4-4-40000000000000000000000000000000000000000000000
χ544444-4-444-4-4-4-444-440000000000000000000000000000000000000000000000
χ554-4-444-40-400-4404000022−22−222222−22−2222000000000000000000000000000000000000
χ564-4-444-40-400-44040000−222222−22−222222−22000000000000000000000000000000000000
χ574-4-44-440400-440-400002i2−2i2−2i22i2−2i22i22i2−2i2000000000000000000000000000000000000
χ584-4-44-440400-440-40000−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000000000000000000000
χ5988-8-800008i−8i0000000000000000000000000000000000000000000000000000
χ6088-8-80000−8i8i0000000000000000000000000000000000000000000000000000
χ618-88-800800000-80000000000000000000000000000000000000000000000000
χ628-88-800-80000080000000000000000000000000000000000000000000000000

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