Finite Group Databasebeta

← Group #270621

Character table — Group #270621

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11112222222244444444444444488888888888888888888161616161616161616161616163232
order12222244444444444444444444424444444448888888888224444888888828
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-1-1-1-1-11-11-1-1-1111-1-1-1-1-1-1
χ31111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1
χ41111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-1-1-1111111
χ5111111111111111-1-1111-1-1111111-11-111-1-1-1-11111111111-1-1-1-1-1-11-1-11111-1-1
χ6111111111111111-1-1111-1-1111111-11-111-1-1-1-111-1-1-1-1-1-1-1-1-11-11111-1-1-1-1-1-111
χ7111111111111111-1-1111-1-1-1-1-1-111-11-1-1-11111-1-111111111-1-1-1-1-1-1-111-1-1-1-111
χ8111111111111111-1-1111-1-1-1-1-1-111-11-1-1-11111-1-1-1-1-1-1-1-1-1-1-11-1111-1111111-1-1
χ91111111111111-1-1111-1-11111111-11-11111111-1-11111-1-1-1-1-11-11-1-1-1-1-1-1-111-11
χ101111111111111-1-1111-1-11111111-11-11111111-1-1-1-1-1-11111-1-1-1-111-1-1-111-1-11-1
χ111111111111111-1-1111-1-111-1-1-1-11-11-11-1-1-1-1-1-1111111-1-1-1-1-11-11-1-111111-1-11-1
χ121111111111111-1-1111-1-111-1-1-1-11-11-11-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111-1-111-11
χ131111111111111-1-1-1-11-1-1-1-111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11-11-111-111-1-1111-1
χ141111111111111-1-1-1-11-1-1-1-111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-11111-1-1-11
χ151111111111111-1-1-1-11-1-1-1-1-1-1-1-11-1-1-1-1-1-11111111111-1-1-1-11-11-1111-1-111-1-1-11
χ161111111111111-1-1-1-11-1-1-1-1-1-1-1-11-1-1-1-1-1-1111111-1-1-1-111111111-1-11-1-1-1-1111-1
χ1722222222-222-2-22200-222002222-2-20-20-2-200002200000000000000-200000000
χ1822222222-222-2-22200-22200-2-2-2-2-2-20-20220000-2-200000000000000200000000
χ1922222222-222-2-2-2-200-2-2-2002222-22020-2-20000-2-200000000000000200000000
χ2022222222-222-2-2-2-200-2-2-200-2-2-2-2-220202200002200000000000000-200000000
χ21222222-2-22-2-22-20022200-2-20000-2020-200000000000022-2-200002-2000000000
χ22222222-2-22-2-22-20022200-2-20000-2020-2000000000000-2-2220000-22000000000
χ23222222-2-22-2-22-200-2-2200220000-20-20200000000000022-2-20000-22000000000
χ24222222-2-22-2-22-200-2-2200220000-20-202000000000000-2-22200002-2000000000
χ252222-2-22-222-22-22222-2-2-2-2-200002-2-222000000000000000020-2000000000000
χ262222-2-22-222-22-222-2-2-2-2-22200002-222-20000000000000000-202000000000000
χ272222-2-22-222-22-2-2-222-222-2-2000022-2-220000000000000000-202000000000000
χ282222-2-22-222-22-2-2-2-2-2-222220000222-2-2000000000000000020-2000000000000
χ292222-2-22-2-22-2-2222002-2-2000000-220-20002i2i−2i−2i000000000000000002i−2i000000
χ302222-2-22-2-22-2-2222002-2-2000000-220-2000−2i−2i2i2i00000000000000000−2i2i000000
χ312222-2-22-2-22-2-22-2-200222000000-2-2020002i2i−2i−2i00000000000000000−2i2i000000
χ322222-2-22-2-22-2-22-2-200222000000-2-202000−2i−2i2i2i000000000000000002i−2i000000
χ332222-2-2-222-22220022-200220000-20-20-20000000022-2-200000-20200000000000
χ342222-2-2-222-22220022-200220000-20-20-200000000-2-2220000020-200000000000
χ352222-2-2-222-222200-2-2-200-2-20000-202020000000022-2-20000020-200000000000
χ362222-2-2-222-222200-2-2-200-2-20000-2020200000000-2-22200000-20200000000000
χ372-22-2-22220-2-2002i−2i0002i−2i002i2i−2i−2i000000000002-2i2−i2i2−i22−22−2000000000i2−i22−200
χ382-22-2-22220-2-2002i−2i0002i−2i002i2i−2i−2i000000000002-2−i2i2−i2i2−22−22000000000−i2i2−2200
χ392-22-2-22220-2-2002i−2i0002i−2i00−2i−2i2i2i00000000000-22i2−i2i2−i22−22−2000000000−i2i2−2200
χ402-22-2-22220-2-2002i−2i0002i−2i00−2i−2i2i2i00000000000-22−i2i2−i2i2−22−22000000000i2−i22−200
χ412-22-2-22220-2-200−2i2i000−2i2i002i2i−2i−2i00000000000-22i2−i2i2−i2−22−22000000000−i2i22−200
χ422-22-2-22220-2-200−2i2i000−2i2i002i2i−2i−2i00000000000-22−i2i2−i2i22−22−2000000000i2−i2−2200
χ432-22-2-22220-2-200−2i2i000−2i2i00−2i−2i2i2i000000000002-2i2−i2i2−i2−22−22000000000i2−i2−2200
χ442-22-2-22220-2-200−2i2i000−2i2i00−2i−2i2i2i000000000002-2−i2i2−i2i22−22−2000000000−i2i22−200
χ45444444-4-4-4-4-4-440000-400000000400000000000000000000000000000000000
χ464444-4-4-44-4-44-4-40000400000000400000000000000000000000000000000000
χ474-44-44-44-40-44004i−4i000−4i4i000000000000000000000000000000000000000000
χ484-44-44-44-40-4400−4i4i0004i−4i000000000000000000000000000000000000000000
χ494-44-44-4-4404-400000000000000000000000000002i2−2i2−2i22i20000000000000000000
χ504-44-44-4-4404-40000000000000000000000000000−2i22i22i2−2i20000000000000000000
χ514-44-4-44-4-40440000000000000000000000000000000022−22−2222000000000000000
χ524-44-4-44-4-404400000000000000000000000000000000−222222−22000000000000000
χ534-4-440000400-40004i−4i000002-22-2000002-22i−2i2i−2i0000000000000000000000000
χ544-4-440000400-40004i−4i00000-22-2200000-22−2i2i−2i2i0000000000000000000000000
χ554-4-440000400-4000−4i4i000002-22-2000002-2−2i2i−2i2i0000000000000000000000000
χ564-4-440000400-4000−4i4i00000-22-2200000-222i−2i2i−2i0000000000000000000000000
χ574-4-440000-4004000000004-42-22-200000-222-2-220000000000000000000000000
χ584-4-440000-4004000000004-4-22-22000002-2-222-20000000000000000000000000
χ594-4-440000-400400000000-442-22-200000-22-222-20000000000000000000000000
χ604-4-440000-400400000000-44-22-22000002-22-2-220000000000000000000000000
χ6188-8-80000000000000000004i−4i−4i4i000000000000000000000000000000000000
χ6288-8-8000000000000000000−4i4i4i−4i000000000000000000000000000000000000

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