Finite Group Databasebeta

← Group #137321

Character table — Group #137321

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11111111222244444444444488888888888888888888161616161616161616161616161616161616
order12222222222244444444444422224444444444444444444444888888888888
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ5111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1111111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1
χ6111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111
χ7111111111111111-1-1-1-1-1-1-1-11-1-1-1-1111111-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-11111
χ8111111111111111-1-1-1-1-1-1-1-11-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1
χ91-1-111-1-111-11-111-1iiii−i−i−i−i-111-1-1ii−i−i1-111-1-1ii−i−i1-1i−i1-11-1ii−i−i11-1-1ii−i−i
χ101-1-111-1-111-11-111-1iiii−i−i−i−i-111-1-1ii−i−i1-111-1-1ii−i−i1-1i−i-11-11−i−iii-1-111−i−iii
χ111-1-111-1-111-11-111-1iiii−i−i−i−i-1-1-111−i−iii1-1-1-111−i−iii1-1i−i1-11-1ii−i−i-1-111−i−iii
χ121-1-111-1-111-11-111-1iiii−i−i−i−i-1-1-111−i−iii1-1-1-111−i−iii1-1i−i-11-11−i−iii11-1-1ii−i−i
χ131-1-111-1-111-11-111-1−i−i−i−iiiii-111-1-1−i−iii1-111-1-1−i−iii1-1−ii1-11-1−i−iii11-1-1−i−iii
χ141-1-111-1-111-11-111-1−i−i−i−iiiii-111-1-1−i−iii1-111-1-1−i−iii1-1−ii-11-11ii−i−i-1-111ii−i−i
χ151-1-111-1-111-11-111-1−i−i−i−iiiii-1-1-111ii−i−i1-1-1-111ii−i−i1-1−ii1-11-1−i−iii-1-111ii−i−i
χ161-1-111-1-111-11-111-1−i−i−i−iiiii-1-1-111ii−i−i1-1-1-111ii−i−i1-1−ii-11-11ii−i−i11-1-1−i−iii
χ1722222222222222222222222200000000-2-200000000-2-2-2-20000000000000000
χ18222222222222222-2-2-2-2-2-2-2-2200000000-2-200000000-2-2220000000000000000
χ19222222222222-2-2-200000000-2000022222-20000-2-2-2-2-22000000000000000000
χ20222222222222-2-2-200000000-20000-2-2-2-22-200002222-22000000000000000000
χ21222222222222-2-2-200000000-222220000-22-2-2-2-200002-2000000000000000000
χ22222222222222-2-2-200000000-2-2-2-2-20000-22222200002-2000000000000000000
χ2322-22-22-2-2-222-22-2-22i2i−2i−2i2i2i−2i−2i2000000000000000000000000000000i2−i2i2−i22−22−2
χ2422-22-22-2-2-222-22-2-22i2i−2i−2i2i2i−2i−2i2000000000000000000000000000000−i2i2−i2i2−22−22
χ2522-22-22-2-2-222-22-2-2−2i−2i2i2i−2i−2i2i2i2000000000000000000000000000000i2−i2i2−i2−22−22
χ2622-22-22-2-2-222-22-2-2−2i−2i2i2i−2i−2i2i2i2000000000000000000000000000000−i2i2−i2i22−22−2
χ272-222-2-22-2-2-2222-2222-2-2-2-222-2000000000000000000000000000000i2−i2−i2i2−i2i2i2−i2
χ282-222-2-22-2-2-2222-2222-2-2-2-222-2000000000000000000000000000000−i2i2i2−i2i2−i2−i2i2
χ292-222-2-22-2-2-2222-22-2-22222-2-2-2000000000000000000000000000000i2−i2−i2i2i2−i2−i2i2
χ302-222-2-22-2-2-2222-22-2-22222-2-2-2000000000000000000000000000000−i2i2i2−i2−i2i2i2−i2
χ312-2-222-2-222-22-222-22i2i2i2i−2i−2i−2i−2i-200000000-2200000000-22−2i2i0000000000000000
χ322-2-222-2-222-22-222-2−2i−2i−2i−2i2i2i2i2i-200000000-2200000000-222i−2i0000000000000000
χ332-2-222-2-222-22-2-2-2200000000200002i2i−2i−2i220000−2i−2i2i2i-2-2000000000000000000
χ342-2-222-2-222-22-2-2-220000000020000−2i−2i2i2i2200002i2i−2i−2i-2-2000000000000000000
χ352-2-222-2-222-22-2-2-2200000000222-2-20000-2-2-2-222000022000000000000000000
χ362-2-222-2-222-22-2-2-22000000002-2-2220000-2-222-2-2000022000000000000000000
χ3744444444-4-4-4-4000000000000000000000000000000000022-2-2000000000000
χ3844444444-4-4-4-40000000000000000000000000000000000-2-222000000000000
χ39444-4-4-4-4400000002i−2i2i−2i2i−2i2i−2i02-22-22i−2i2i−2i000000000000000000000000000000
χ40444-4-4-4-4400000002i−2i2i−2i2i−2i2i−2i0-22-22−2i2i−2i2i000000000000000000000000000000
χ41444-4-4-4-440000000−2i2i−2i2i−2i2i−2i2i02-22-2−2i2i−2i2i000000000000000000000000000000
χ42444-4-4-4-440000000−2i2i−2i2i−2i2i−2i2i0-22-222i−2i2i−2i000000000000000000000000000000
χ4344-44-44-4-44-4-44000000000000000000000000000000000000002i−2i2i−2i00000000
χ4444-44-44-4-44-4-4400000000000000000000000000000000000000−2i2i−2i2i00000000
χ4544-44-44-4-4-444-4-44400000000-400000000000000000000000000000000000000
χ4644-4-44-44-400000002-2-222-2-22000000000002i−2i2i−2i2i−2i2i−2i00000000000000000000
χ4744-4-44-44-400000002-2-222-2-2200000000000−2i2i−2i2i−2i2i−2i2i00000000000000000000
χ4844-4-44-44-40000000-222-2-222-2000000000002i−2i2i−2i−2i2i−2i2i00000000000000000000
χ4944-4-44-44-40000000-222-2-222-200000000000−2i2i−2i2i2i−2i2i−2i00000000000000000000
χ504-444-4-44-444-4-4000000000000000000000000000000000000002-2-2200000000
χ514-444-4-44-444-4-400000000000000000000000000000000000000-222-200000000
χ524-444-4-44-4-4-444-44-400000000400000000000000000000000000000000000000
χ534-44-444-4-400000002i−2i−2i2i−2i2i2i−2i000000000002i−2i−2i2i-222-200000000000000000000
χ544-44-444-4-400000002i−2i−2i2i−2i2i2i−2i00000000000−2i2i2i−2i2-2-2200000000000000000000
χ554-44-444-4-40000000−2i2i2i−2i2i−2i−2i2i000000000002i−2i−2i2i2-2-2200000000000000000000
χ564-44-444-4-40000000−2i2i2i−2i2i−2i−2i2i00000000000−2i2i2i−2i-222-200000000000000000000
χ574-4-444-4-44-44-4400000000000000000000000000000000002-2-22000000000000
χ584-4-444-4-44-44-440000000000000000000000000000000000-222-2000000000000
χ594-4-4-4-444400000002-22-2-22-2202-2-222-2-22000000000000000000000000000000
χ604-4-4-4-444400000002-22-2-22-220-222-2-222-2000000000000000000000000000000
χ614-4-4-4-44440000000-22-222-22-202-2-22-222-2000000000000000000000000000000
χ624-4-4-4-44440000000-22-222-22-20-222-22-2-22000000000000000000000000000000

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