Finite Group Databasebeta

← Group #488728

Character table — Group #488728

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111222222222222444444444444488888888888888888888881616161616161616161616163232
order122222444444888822224448888884488881616161616161616161616161616161622224444444422
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ411111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111-1-1-1-1111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1
χ61111111111111111-1-1-1-1111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111
χ71111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-111
χ81111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1
χ9111111-1-1-1-111-1-1-1-111-1-1-1-11-1-111111-111-1-11111-1-1-1-11111-1-1-1-11-11-11-11-111-1-11-1
χ10111111-1-1-1-111-1-1-1-111-1-1-1-11-1-111111-111-1-11111-1-1-1-11111-1-1-1-1-11-11-11-11-1-111-11
χ11111111-1-1-1-111-1-1-1-111-1-1-1-11-1-111111-111-1-1-1-1-1-11111-1-1-1-111111-11-11-11-1-1-111-11
χ12111111-1-1-1-111-1-1-1-111-1-1-1-11-1-111111-111-1-1-1-1-1-11111-1-1-1-11111-11-11-11-1111-1-11-1
χ13111111-1-1-1-111-1-1-1-1-1-111-1-11-1-11111-11-1-1111111-1-1-1-1-1-1-1-111111-1-111-1-1111-1-1-11
χ14111111-1-1-1-111-1-1-1-1-1-111-1-11-1-11111-11-1-1111111-1-1-1-1-1-1-1-11111-111-1-111-1-1-1111-1
χ15111111-1-1-1-111-1-1-1-1-1-111-1-11-1-11111-11-1-111-1-1-1-111111111-1-1-1-11-1-111-1-11-1-1111-1
χ16111111-1-1-1-111-1-1-1-1-1-111-1-11-1-11111-11-1-111-1-1-1-111111111-1-1-1-1-111-1-111-111-1-1-11
χ17222222222222-2-2-2-22222222-2-2-2-2-2-222-2-2-2-2000000000000000000000000000000
χ18222222222222-2-2-2-2-2-2-2-2222-2-2-2-2-2-2-2-22222000000000000000000000000000000
χ192222222222-2-200002222-2-2-2000000-2-2000022−2−222−2−222−2−222−2−200000000000000
χ202222222222-2-200002222-2-2-2000000-2-20000−2−222−2−222−2−222−2−22200000000000000
χ212222222222-2-20000-2-2-2-2-2-2-200000022000022−2−222−2−2−2−222−2−22200000000000000
χ222222222222-2-20000-2-2-2-2-2-2-2000000220000−2−222−2−22222−2−222−2−200000000000000
χ23222222-2-2-2-222222222-2-2-2-2222-2-2-2-22-2-2-222000000000000000000000000000000
χ24222222-2-2-2-2222222-2-222-2-2222-2-2-2-2-2222-2-2000000000000000000000000000000
χ25222222-2-2-2-2-2-2000022-2-222-2000000-22000022−2−2−2−22222−2−2−2−22200000000000000
χ26222222-2-2-2-2-2-2000022-2-222-2000000-220000−2−22222−2−2−2−22222−2−200000000000000
χ27222222-2-2-2-2-2-20000-2-22222-20000002-2000022−2−2−2−222−2−22222−2−200000000000000
χ28222222-2-2-2-2-2-20000-2-22222-20000002-20000−2−22222−2−222−2−2−2−22200000000000000
χ292222-2-222-2-222222200002-2-2-2-222-2-20000000000000000000000002200-2-2000000
χ302222-2-222-2-222222200002-2-2-2-222-2-2000000000000000000000000-2-20022000000
χ312222-2-222-2-222-2-2-2-200002-2-222-2-22200000000000000000000002-200-2200000000
χ322222-2-222-2-222-2-2-2-200002-2-222-2-2220000000000000000000000-22002-200000000
χ332222-2-2-2-2222222220000-22-2-2-2-2-22200000000000000000000002200-2-200000000
χ342222-2-2-2-2222222220000-22-2-2-2-2-2220000000000000000000000-2-2002200000000
χ352222-2-2-2-22222-2-2-2-20000-22-22222-2-20000000000000000000000002-200-22000000
χ362222-2-2-2-22222-2-2-2-20000-22-22222-2-2000000000000000000000000-22002-2000000
χ372-2-22-222-22-20022−2−22-22-20002−22−22−2002−22−2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ500000000000000
χ382-2-22-222-22-20022−2−22-22-20002−22−22−2002−22−2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ500000000000000
χ392-2-22-222-22-20022−2−2-22-220002−22−22−200−22−22ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ500000000000000
χ402-2-22-222-22-20022−2−2-22-220002−22−22−200−22−22−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ500000000000000
χ412-2-22-222-22-200−2−2222-22-2000−22−22−2200−22−22ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ700000000000000
χ422-2-22-222-22-200−2−2222-22-2000−22−22−2200−22−22−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ700000000000000
χ432-2-22-222-22-200−2−222-22-22000−22−22−22002−22−2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ700000000000000
χ442-2-22-222-22-200−2−222-22-22000−22−22−22002−22−2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ700000000000000
χ452-2-22-22-22-220022−2−22-2-220002−2−22−2200−222−2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ700000000000000
χ462-2-22-22-22-220022−2−22-2-220002−2−22−2200−222−2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ700000000000000
χ472-2-22-22-22-220022−2−2-222-20002−2−22−22002−2−22ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ700000000000000
χ482-2-22-22-22-220022−2−2-222-20002−2−22−22002−2−22−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ700000000000000
χ492-2-22-22-22-2200−2−2222-2-22000−222−22−2002−2−22ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ500000000000000
χ502-2-22-22-22-2200−2−2222-2-22000−222−22−2002−2−22−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ500000000000000
χ512-2-22-22-22-2200−2−222-222-2000−222−22−200−222−2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ500000000000000
χ522-2-22-22-22-2200−2−222-222-2000−222−22−200−222−2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ500000000000000
χ534444-4-444-4-4-4-400000000-444000000000000000000000000000000000000000000
χ544444-4-4-4-444-4-4000000004-44000000000000000000000000000000000000000000
χ554-44-4000000-444-44-400000000000000000000000000000000000000000002-22-200
χ564-44-4000000-444-44-40000000000000000000000000000000000000000000-22-2200
χ574-44-4000000-44-44-4400000000000000000000000000000000000000000002-2-2200
χ584-44-4000000-44-44-440000000000000000000000000000000000000000000-222-200
χ594-4-444-44-4-44002222−22−220000000−222222−22−2222000000000000000000000000000000000000
χ604-4-444-44-4-4400−22−222222000000022−22−222222−22000000000000000000000000000000000000
χ614-4-444-4-444-4002222−22−220000000−2222−222222−22000000000000000000000000000000000000
χ624-4-444-4-444-400−22−222222000000022−2222−22−2222000000000000000000000000000000000000
χ6388-8-80000000042−42−42420000000000000000000000000000000000000000000000000
χ6488-8-800000000−424242−420000000000000000000000000000000000000000000000000
χ658-88-80000008-800000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 16 (ζ16 = 1).