Finite Group Databasebeta

← Group #138484

Character table — Group #138484

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11112222222222444444444444448888888888888888888888161616161616161632323232
order122222444444442244448888888844888816161616161616161616161616161616888888884444
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111-1-111-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ611111111111111-1-111-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ711111111111111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ811111111111111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ9111111-1-1-1-1-111-1111-1-1-11111-1-1-1-11-111-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i1-11-1
χ10111111-1-1-1-1-111-1111-1-1-11111-1-1-1-11-111-1-1iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii-11-11
χ11111111-1-1-1-1-111-1111-1-1-11111-1-1-1-11-111-1-1−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i-11-11
χ12111111-1-1-1-1-111-1111-1-1-11111-1-1-1-11-111-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii1-11-1
χ13111111-1-1-1-1-111-1-1-11-1111111-1-1-1-1-11-1-111iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii1-1-11
χ14111111-1-1-1-1-111-1-1-11-1111111-1-1-1-1-11-1-111iiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i-111-1
χ15111111-1-1-1-1-111-1-1-11-1111111-1-1-1-1-11-1-111−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii-111-1
χ16111111-1-1-1-1-111-1-1-11-1111111-1-1-1-1-11-1-111−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i1-1-11
χ1722222222222222222222-2-2-2-2-2-2-2-222-2-2-2-20000000000000000000000000000
χ1822222222222222-2-222-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000000000000000
χ1922222222-2-2-2-2-2-222-22-2-200000000-220000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2000000000000
χ2022222222-2-2-2-2-2-222-22-2-200000000-220000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2000000000000
χ2122222222-2-2-2-2-2-2-2-2-2222000000002-20000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2000000000000
χ2222222222-2-2-2-2-2-2-2-2-2222000000002-20000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2000000000000
χ23222222-2-2222-2-2222-2-22200000000-2-2000022−2−2−2−22222−2−2−2−222000000000000
χ24222222-2-2222-2-2222-2-22200000000-2-20000−2−22222−2−2−2−22222−2−2000000000000
χ25222222-2-2222-2-22-2-2-2-2-2-20000000022000022−2−2−2−222−2−22222−2−2000000000000
χ26222222-2-2222-2-22-2-2-2-2-2-200000000220000−2−22222−2−222−2−2−2−222000000000000
χ27222222-2-2-2-2-222-2222-2-2-2-2-2-2-222222-2-2-2220000000000000000000000000000
χ28222222-2-2-2-2-222-2-2-22-222-2-2-2-22222-2222-2-20000000000000000000000000000
χ292222-2-22222-222-200-2-20022-2-222-2-2000000000000000000000000002i−2i2i−2i0000
χ302222-2-22222-222-200-2-20022-2-222-2-200000000000000000000000000−2i2i−2i2i0000
χ312222-2-22222-222-200-2-200-2-222-2-22200000000000000000000002i−2i2i−2i00000000
χ322222-2-22222-222-200-2-200-2-222-2-2220000000000000000000000−2i2i−2i2i00000000
χ332222-2-2-2-2-2-2222200-220022-2-2-2-222000000000000000000000000002-2-220000
χ342222-2-2-2-2-2-2222200-220022-2-2-2-22200000000000000000000000000-222-20000
χ352222-2-2-2-2-2-2222200-2200-2-22222-2-200000000000000000000002-2-2200000000
χ362222-2-2-2-2-2-2222200-2200-2-22222-2-20000000000000000000000-222-200000000
χ372-2-22-22002-2200-22-2002-22−22−22−22−2002−22−2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7000000000000
χ382-2-22-22002-2200-22-2002-22−22−22−22−2002−22−2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7000000000000
χ392-2-22-22002-2200-22-2002-2−22−22−22−2200−22−22ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5000000000000
χ402-2-22-22002-2200-22-2002-2−22−22−22−2200−22−22−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5000000000000
χ412-2-22-22002-2200-2-2200-222−22−22−22−200−22−22ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7000000000000
χ422-2-22-22002-2200-2-2200-222−22−22−22−200−22−22−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7000000000000
χ432-2-22-22002-2200-2-2200-22−22−22−22−22002−22−2ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5000000000000
χ442-2-22-22002-2200-2-2200-22−22−22−22−22002−22−2−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5000000000000
χ452-2-22-2200-22-20022-200-222−22−2−22−22002−2−22ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5000000000000
χ462-2-22-2200-22-20022-200-222−22−2−22−22002−2−22−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5000000000000
χ472-2-22-2200-22-20022-200-22−22−222−22−200−222−2ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7000000000000
χ482-2-22-2200-22-20022-200-22−22−222−22−200−222−2−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7000000000000
χ492-2-22-2200-22-2002-22002-22−22−2−22−2200−222−2ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5000000000000
χ502-2-22-2200-22-2002-22002-22−22−2−22−2200−222−2−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5000000000000
χ512-2-22-2200-22-2002-22002-2−22−222−22−2002−2−22ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7000000000000
χ522-2-22-2200-22-2002-22002-2−22−222−22−2002−2−22−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7000000000000
χ534444-4-444-4-44-4-44004-400000000000000000000000000000000000000000000
χ544444-4-4-4-444-4-4-4-4004400000000000000000000000000000000000000000000
χ554-4-444-4004-4-400400000022−22−222222−22−22220000000000000000000000000000000000
χ564-4-444-4004-4-4004000000−222222−22−222222−220000000000000000000000000000000000
χ574-4-444-400-44400-400000022−22−2222−222222−220000000000000000000000000000000000
χ584-4-444-400-44400-4000000−222222−2222−22−22220000000000000000000000000000000000
χ5988-8-800000008-80000000000000000000000000000000000000000000000000
χ6088-8-80000000-880000000000000000000000000000000000000000000000000
χ618-88-8008-8000000000000000000000000000000000000000000000000000000
χ628-88-800-88000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.