Finite Group Databasebeta

← Group #488685

Character table — Group #488685

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111222222222222444444444444488888888888888888888881616161616161616161616163232
order122222444444888822444448888882488881616161616161616161616161616161622444444444444
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
χ5111111111111111111-1-11-1-1111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-11-11-11-11111-1-1
χ6111111111111111111-1-11-1-1111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-11-11-11-1-1-1-111
χ7111111111111111111-1-11-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-11-11-1-1-1-1-111
χ8111111111111111111-1-11-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-11-11-111111-1-1
χ9111111-1-1-1-111-1-1-1-1-1-1111-1-1-1-11111-11-1-1111111-1-1-1-11111-1-1-1-111-1-111-1-111-1-11-1
χ10111111-1-1-1-111-1-1-1-1-1-1111-1-1-1-11111-11-1-1111111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111-11
χ11111111-1-1-1-111-1-1-1-1-1-1111-1-1-1-11111-11-1-111-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-111-11
χ12111111-1-1-1-111-1-1-1-1-1-1111-1-1-1-11111-11-1-111-1-1-1-11111-1-1-1-11111-1-111-1-11111-1-11-1
χ13111111-1-1-1-111-1-1-1-1-1-1-1-1111-1-111111-111-1-11111-1-1-1-1-1-1-1-111111-1-111-1-1111-1-1-11
χ14111111-1-1-1-111-1-1-1-1-1-1-1-1111-1-111111-111-1-11111-1-1-1-1-1-1-1-11111-111-1-111-1-1-1111-1
χ15111111-1-1-1-111-1-1-1-1-1-1-1-1111-1-111111-111-1-1-1-1-1-111111111-1-1-1-11-1-111-1-11-1-1111-1
χ16111111-1-1-1-111-1-1-1-1-1-1-1-1111-1-111111-111-1-1-1-1-1-111111111-1-1-1-1-111-1-111-111-1-1-11
χ17222222222222-2-2-2-22222222-2-2-2-2-2-222-2-2-2-2000000000000000000000000000000
χ18222222222222-2-2-2-222-2-22-2-2-2-2-2-2-2-2-2-22222000000000000000000000000000000
χ192222222222-2-20000-2-222-222000000-2-2000022−2−222−2−222−2−222−2−200000000000000
χ202222222222-2-20000-2-222-222000000-2-20000−2−222−2−222−2−222−2−22200000000000000
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
χ23222222-2-2-2-2222222-2-2222-2-222-2-2-2-2-2222-2-2000000000000000000000000000000
χ24222222-2-2-2-2222222-2-2-2-222222-2-2-2-22-2-2-222000000000000000000000000000000
χ25222222-2-2-2-2-2-200002222-2-2-20000002-2000022−2−2−2−22222−2−2−2−22200000000000000
χ26222222-2-2-2-2-2-200002222-2-2-20000002-20000−2−22222−2−2−2−22222−2−200000000000000
χ27222222-2-2-2-2-2-2000022-2-2-222000000-22000022−2−2−2−222−2−22222−2−200000000000000
χ28222222-2-2-2-2-2-2000022-2-2-222000000-220000−2−22222−2−222−2−2−2−22200000000000000
χ292222-2-222-2-22222222-200-200-2-222-2-2000000000000000000000002020-20-2000000
χ302222-2-222-2-22222222-200-200-2-222-2-200000000000000000000000-20-20202000000
χ312222-2-222-2-222-2-2-2-22-200-20022-2-222000000000000000000000020-20-2020000000
χ322222-2-222-2-222-2-2-2-22-200-20022-2-2220000000000000000000000-202020-20000000
χ332222-2-2-2-222222222-2200-200-2-2-2-22200000000000000000000002020-20-20000000
χ342222-2-2-2-222222222-2200-200-2-2-2-2220000000000000000000000-20-202020000000
χ352222-2-2-2-22222-2-2-2-2-2200-2002222-2-20000000000000000000000020-20-202000000
χ362222-2-2-2-22222-2-2-2-2-2200-2002222-2-200000000000000000000000-202020-2000000
χ372-22-22-22i−2i2i−2i00i2i2−i2−i2002-202i−2ii2−i22−22−200i2−i22−2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ700000000000000
χ382-22-22-22i−2i2i−2i00i2i2−i2−i2002-202i−2ii2−i22−22−200i2−i22−2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ700000000000000
χ392-22-22-22i−2i2i−2i00i2i2−i2−i200-220−2i2ii2−i22−22−200−i2i2−22ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ700000000000000
χ402-22-22-22i−2i2i−2i00i2i2−i2−i200-220−2i2ii2−i22−22−200−i2i2−22−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ700000000000000
χ412-22-22-22i−2i2i−2i00−i2−i2i2i2002-202i−2i−i2i2−22−2200−i2i2−22ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ500000000000000
χ422-22-22-22i−2i2i−2i00−i2−i2i2i2002-202i−2i−i2i2−22−2200−i2i2−22−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ500000000000000
χ432-22-22-22i−2i2i−2i00−i2−i2i2i200-220−2i2i−i2i2−22−2200i2−i22−2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ500000000000000
χ442-22-22-22i−2i2i−2i00−i2−i2i2i200-220−2i2i−i2i2−22−2200i2−i22−2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ500000000000000
χ452-22-22-2−2i2i−2i2i00i2i2−i2−i2002-20−2i2ii2−i2−22−2200i2−i2−22ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ500000000000000
χ462-22-22-2−2i2i−2i2i00i2i2−i2−i2002-20−2i2ii2−i2−22−2200i2−i2−22−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ500000000000000
χ472-22-22-2−2i2i−2i2i00i2i2−i2−i200-2202i−2ii2−i2−22−2200−i2i22−2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ500000000000000
χ482-22-22-2−2i2i−2i2i00i2i2−i2−i200-2202i−2ii2−i2−22−2200−i2i22−2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ500000000000000
χ492-22-22-2−2i2i−2i2i00−i2−i2i2i2002-20−2i2i−i2i22−22−200−i2i22−2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ700000000000000
χ502-22-22-2−2i2i−2i2i00−i2−i2i2i2002-20−2i2i−i2i22−22−200−i2i22−2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ700000000000000
χ512-22-22-2−2i2i−2i2i00−i2−i2i2i200-2202i−2i−i2i22−22−200i2−i2−22ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ700000000000000
χ522-22-22-2−2i2i−2i2i00−i2−i2i2i200-2202i−2i−i2i22−22−200i2−i2−22−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ700000000000000
χ534444-4-444-4-4-4-40000-4400400000000000000000000000000000000000000000000
χ544444-4-4-4-444-4-400004-400400000000000000000000000000000000000000000000
χ554-44-4-444i−4i−4i4i002i22i2−2i2−2i20000000−2i22i222−22−2222000000000000000000000000000000000000
χ564-44-4-444i−4i−4i4i00−2i2−2i22i22i200000002i2−2i2−222222−22000000000000000000000000000000000000
χ574-44-4-44−4i4i4i−4i002i22i2−2i2−2i20000000−2i22i2−222222−22000000000000000000000000000000000000
χ584-44-4-44−4i4i4i−4i00−2i2−2i22i22i200000002i2−2i222−22−2222000000000000000000000000000000000000
χ594-4-440000004-44i−4i4i−4i00000000000000000000000000000000000000000002-22i−2i00
χ604-4-440000004-44i−4i4i−4i0000000000000000000000000000000000000000000-22−2i2i00
χ614-4-440000004-4−4i4i−4i4i00000000000000000000000000000000000000000002-2−2i2i00
χ624-4-440000004-4−4i4i−4i4i0000000000000000000000000000000000000000000-222i−2i00
χ6388-8-80000000042−42−42420000000000000000000000000000000000000000000000000
χ6488-8-800000000−424242−420000000000000000000000000000000000000000000000000
χ658-8-88000000-8800000000000000000000000000000000000000000000000000000

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