Finite Group Databasebeta

← Group #272191

Character table — Group #272191

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size1111222222224444444444444888888888888888881616161616161616161616161616163232
order12222244444422224444488882444444888888888822444888888888828
χ111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1111111111-11-1-1-1-1-1-1-1111-1-1-1-1
χ3111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-111111-1-1111-1-1-1-1-1-1-1
χ4111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-1-1-1-1-11111
χ511111111111111-1-1111111111-11-1-111111-1-1111111-11-1-1-1111-1-1-1-1-111-1-1
χ611111111111111-1-1111111111-11-1-11-1-1-1-1-1-1111111-1-1-111-1-1-111-1-1-1-1-111
χ711111111111111-1-111111-1-1-1-1-11-1-11111111-1-1-1-1-1-1-11-1-1-1-1-11-1-1111-1-111
χ811111111111111-1-111111-1-1-1-1-11-1-11-1-1-1-111-1-1-1-1-1-1-1-1-11111-11111111-1-1
χ9111111111111-1-111-1-111111111-111-111-1-11111-1-1-1-1-11-11111-1-1-11-1-1-1-11-1
χ10111111111111-1-111-1-111111111-111-1-1-1111111-1-1-1-1-1-1-1-1-1-1-11111-1-111-11
χ11111111111111-1-111-1-1111-1-1-1-11-111-111-1-1-1-1-1-11111-11-111-1-1-1-1-1-11111-11
χ12111111111111-1-111-1-1111-1-1-1-11-111-1-1-111-1-1-1-11111-1-1-1-1-111111-111-1-11-1
χ13111111111111-1-1-1-1-1-11111111-1-1-1-1-111-1-1-1-111-1-1-1-1111-1-111-111-111-1-1-11
χ14111111111111-1-1-1-1-1-11111111-1-1-1-1-1-1-111-1-111-1-1-1-11-1111-1-11-1-1-111111-1
χ15111111111111-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-111-1-111-1-11111111-1-1-1-1-1111-1-1111-1
χ16111111111111-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-11111-1-111111-1111111-1-11-1-1-1-1-11
χ172222222-2-2222220022-2-2-200000-200-22222000000000-200000-2000000000
χ182222222-2-2222220022-2-2-200000-200-2-2-2-2-20000000002000002000000000
χ192222222-2-2222-2-200-2-2-2-2-200000200222-2-2000000000-2000002000000000
χ202222222-2-2222-2-200-2-2-2-2-2000002002-2-222000000000200000-2000000000
χ21222222-222-2-2-20022002-2-2000020-2-20000000002i2i−2i−2i000000000002i−2i0000
χ22222222-222-2-2-20022002-2-2000020-2-2000000000−2i−2i2i2i00000000000−2i2i0000
χ23222222-222-2-2-200-2-2002-2-20000-20220000000002i2i−2i−2i00000000000−2i2i0000
χ24222222-222-2-2-200-2-2002-2-20000-2022000000000−2i−2i2i2i000000000002i−2i0000
χ252222-2-2222-2-22002200-2-222222-202-20000022-2-200000000000000-2000000
χ262222-2-2222-2-22002200-2-22-2-2-2-2-202-200000-2-222000000000000002000000
χ272222-2-2222-2-2200-2-200-2-22222220-2200000-2-2-2-2000000000000002000000
χ282222-2-2222-2-2200-2-200-2-22-2-2-2-220-2200000222200000000000000-2000000
χ292222-2-2-22222-22222-2-2-22-20000-2-2-22200000000000020-200000000000000
χ302222-2-2-22222-222-2-2-2-2-22-200002-22-22000000000000-20200000000000000
χ312222-2-2-22222-2-2-22222-22-20000-22-22-2000000000000-20200000000000000
χ322222-2-2-22222-2-2-2-2-222-22-20000222-2-200000000000020-200000000000000
χ332222-2-2-2-2-222-22200-2-22-2200000200-20000000000000002-20002-20000000
χ342222-2-2-2-2-222-22200-2-22-2200000200-2000000000000000-22000-220000000
χ352222-2-2-2-2-222-2-2-200222-2200000-20020000000000000002-2000-220000000
χ362222-2-2-2-2-222-2-2-200222-2200000-2002000000000000000-220002-20000000
χ372-22-22-22002-2-22-2002-2000i2i2−i2−i2000002i−2i2i−2i00i2−i2i2−i2i2−i2000002−20000002−200
χ382-22-22-22002-2-22-2002-2000i2i2−i2−i200000−2i2i−2i2i00i2−i2i2−i2i2−i200000−22000000−2200
χ392-22-22-22002-2-22-2002-2000−i2−i2i2i2000002i−2i2i−2i00−i2i2−i2i2−i2i200000−22000000−2200
χ402-22-22-22002-2-22-2002-2000−i2−i2i2i200000−2i2i−2i2i00−i2i2−i2i2−i2i2000002−20000002−200
χ412-22-22-22002-2-2-2200-22000i2i2−i2−i2000002i−2i−2i2i00i2−i2−i2i2−i2i2000002−2000000−2200
χ422-22-22-22002-2-2-2200-22000i2i2−i2−i200000−2i2i2i−2i00i2−i2−i2i2−i2i200000−220000002−200
χ432-22-22-22002-2-2-2200-22000−i2−i2i2i2000002i−2i−2i2i00−i2i2i2−i2i2−i200000−220000002−200
χ442-22-22-22002-2-2-2200-22000−i2−i2i2i200000−2i2i2i−2i00−i2i2i2−i2i2−i2000002−2000000−2200
χ45444444-4-4-4-4-4-4000000-44400000000000000000000000000000000000000
χ464444-4-44-4-4-4-4400000044-400000000000000000000000000000000000000
χ474-44-44-4-400-4440000000000000000000000000022−22−222200000000000000000
χ484-44-44-4-400-44400000000000000000000000000−222222−2200000000000000000
χ494-44-4-44400-44-40000000002i22i2−2i2−2i200000000000−2i22i2000000000000000000000
χ504-44-4-44400-44-4000000000−2i2−2i22i22i2000000000002i2−2i2000000000000000000000
χ514-44-4-44-4004-444-400-4400000000000000000000000000000000000000000
χ524-44-4-44-4004-44-44004-400000000000000000000000000000000000000000
χ534-4-44000-44000004-40000022−2222−2200000000022−2200000000000000000000000
χ544-4-44000-44000004-400000−2222−2222000000000−222200000000000000000000000
χ554-4-44000-4400000-440000022−2222−22000000000−222200000000000000000000000
χ564-4-44000-4400000-4400000−2222−222200000000022−2200000000000000000000000
χ5788-8-8000000000000000004i−4i−4i4i0000000000000000000000000000000000
χ5888-8-800000000000000000−4i4i4i−4i0000000000000000000000000000000000
χ598-8-880008-800000000000000000000000000000000000000000000000000

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