Finite Group Databasebeta

← Group #131920

Character table — Group #131920

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11112222222222222244444444444444444444444488888888161616161616161616161616161616163232
order1222224444444488884488888816161616161616161616161616161616224444442244448888881616161688
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111
χ511111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1
χ91111-1-1-111-111-1-1-1-1-1-11-11111-1-1iiiiiiii−i−i−i−i−i−i−i−i1-11-111-1-11-11-11-11-1ii−i−iii−i−ii−i
χ101111-1-1-111-111-1-1-1-1-1-11-11111-1-1iiiiiiii−i−i−i−i−i−i−i−i1-11-1-1-111-11-11-111-1−i−iiiii−i−i−ii
χ111111-1-1-111-111-1-1-1-1-1-11-11111-1-1iiiiiiii−i−i−i−i−i−i−i−i-11-1111-1-11-1-11-11-11ii−i−i−i−iii−ii
χ121111-1-1-111-111-1-1-1-1-1-11-11111-1-1iiiiiiii−i−i−i−i−i−i−i−i-11-11-1-111-111-11-1-11−i−iii−i−iiii−i
χ131111-1-1-111-111-1-1-1-1-1-11-11111-1-1−i−i−i−i−i−i−i−iiiiiiiii1-11-111-1-11-11-11-11-1−i−iii−i−iii−ii
χ141111-1-1-111-111-1-1-1-1-1-11-11111-1-1−i−i−i−i−i−i−i−iiiiiiiii1-11-1-1-111-11-11-111-1ii−i−i−i−iiii−i
χ151111-1-1-111-111-1-1-1-1-1-11-11111-1-1−i−i−i−i−i−i−i−iiiiiiiii-11-1111-1-11-1-11-11-11−i−iiiii−i−ii−i
χ161111-1-1-111-111-1-1-1-1-1-11-11111-1-1−i−i−i−i−i−i−i−iiiiiiiii-11-11-1-111-111-11-1-11ii−i−iii−i−i−ii
χ1722222222222222-2-2-2-222-2-2-2-2-2-2000000000000000022220000000000-2-20000000000
χ1822222222222222-2-2-2-222-2-2-2-2-2-20000000000000000-2-2-2-20000000000220000000000
χ192222222-2-2-2222-22222-2-2-2-222-2-2000000000000000000002222-2-20000000000000000
χ202222222-2-2-2222-22222-2-2-2-222-2-200000000000000000000-2-2-2-2220000000000000000
χ212222222-2-2-2222-2-2-2-2-2-2-222-2-222000000000000000000000000002-2-22000000000000
χ222222222-2-2-2222-2-2-2-2-2-2-222-2-22200000000000000000000000000-222-2000000000000
χ23222222-2-2-2-2-2-2-2-2000022000000i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i22-2-220000000000000000i2−i2i2−i200
χ24222222-2-2-2-2-2-2-2-2000022000000i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2-222-20000000000000000−i2i2−i2i200
χ25222222-2-2-2-2-2-2-2-2000022000000−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i22-2-220000000000000000−i2i2−i2i200
χ26222222-2-2-2-2-2-2-2-2000022000000−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2-222-20000000000000000i2−i2i2−i200
χ272222-2-22-2-22-2-22200002-20000002222−2−2−2−2−2−2−2−2222222-2-200000000000000002−2−2200
χ282222-2-22-2-22-2-22200002-20000002222−2−2−2−2−2−2−2−22222-2-2220000000000000000−222−200
χ292222-2-22-2-22-2-22200002-2000000−2−2−2−222222222−2−2−2−222-2-20000000000000000−222−200
χ302222-2-22-2-22-2-22200002-2000000−2−2−2−222222222−2−2−2−2-2-22200000000000000002−2−2200
χ312222-2-2-222-222-2-222222-2-2-2-2-22200000000000000002-22-20000000000-220000000000
χ322222-2-2-222-222-2-222222-2-2-2-2-2220000000000000000-22-2200000000002-20000000000
χ332222-2-2-2-2-2222-222222-2222-2-2-2-20000000000000000000000000022-2-2000000000000
χ342222-2-2-2-2-2222-222222-2222-2-2-2-200000000000000000000000000-2-222000000000000
χ352222-2-2-2-2-2222-22-2-2-2-2-22-2-222220000000000000000000022-2-2-220000000000000000
χ362222-2-2-2-2-2222-22-2-2-2-2-22-2-2222200000000000000000000-2-2222-20000000000000000
χ3722-2-22-22000-22-20-2-22200002-20022−2−222−2−222−2−222−2−200002i−2i2i−2i00000000i2−i2i2−i2000000
χ3822-2-22-22000-22-20-2-22200002-20022−2−222−2−222−2−222−2−20000−2i2i−2i2i00000000−i2i2−i2i2000000
χ3922-2-22-22000-22-20-2-22200002-200−2−222−2−222−2−222−2−22200002i−2i2i−2i00000000−i2i2−i2i2000000
χ4022-2-22-22000-22-20-2-22200002-200−2−222−2−222−2−222−2−2220000−2i2i−2i2i00000000i2−i2i2−i2000000
χ4122-2-2-22-2000-222022-2-200002-200i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i200002i−2i−2i2i00000000−222−2000000
χ4222-2-2-22-2000-222022-2-200002-200i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i20000−2i2i2i−2i000000002−2−22000000
χ4322-2-2-22-2000-222022-2-200002-200−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i200002i−2i−2i2i000000002−2−22000000
χ4422-2-2-22-2000-222022-2-200002-200−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i20000−2i2i2i−2i00000000−222−2000000
χ45444444-4444-4-4-440000-4-4000000000000000000000000000000000000000000000000
χ464444-4-4444-4-4-44-40000-44000000000000000000000000000000000000000000000000
χ4744-4-44-44000-44-4044-4-40000-4400000000000000000000000000000000000000000000
χ4844-4-44-4-40004-4400000000000002i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i00000000000000000000000000
χ4944-4-44-4-40004-440000000000000−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i00000000000000000000000000
χ5044-4-4-4440004-4-4000000000000022-2-2-2-222-2-22222-2-200000000000000000000000000
χ5144-4-4-4440004-4-40000000000000-2-22222-2-222-2-2-2-22200000000000000000000000000
χ5244-4-4-44-4000-4440-4-4440000-4400000000000000000000000000000000000000000000
χ534-44-40004i−4i0000022−2222−220000002i2−2i22ζ−2ζ2ζ−2ζ2ζ5−2ζ52ζ5−2ζ52ζ3−2ζ32ζ3−2ζ32ζ7−2ζ72ζ7−2ζ700000000000000000000000000
χ544-44-40004i−4i0000022−2222−220000002i2−2i2−2ζ2ζ−2ζ2ζ−2ζ52ζ5−2ζ52ζ5−2ζ32ζ3−2ζ32ζ3−2ζ72ζ7−2ζ72ζ700000000000000000000000000
χ554-44-40004i−4i00000−2222−2222000000−2i22i22ζ5−2ζ52ζ5−2ζ5−2ζ2ζ−2ζ2ζ−2ζ72ζ7−2ζ72ζ72ζ3−2ζ32ζ3−2ζ300000000000000000000000000
χ564-44-40004i−4i00000−2222−2222000000−2i22i2−2ζ52ζ5−2ζ52ζ52ζ−2ζ2ζ−2ζ2ζ7−2ζ72ζ7−2ζ7−2ζ32ζ3−2ζ32ζ300000000000000000000000000
χ574-44-4000−4i4i0000022−2222−22000000−2i22i22ζ7−2ζ72ζ7−2ζ72ζ3−2ζ32ζ3−2ζ32ζ5−2ζ52ζ5−2ζ52ζ−2ζ2ζ−2ζ00000000000000000000000000
χ584-44-4000−4i4i0000022−2222−22000000−2i22i2−2ζ72ζ7−2ζ72ζ7−2ζ32ζ3−2ζ32ζ3−2ζ52ζ5−2ζ52ζ5−2ζ2ζ−2ζ2ζ00000000000000000000000000
χ594-44-4000−4i4i00000−2222−22220000002i2−2i22ζ3−2ζ32ζ3−2ζ3−2ζ72ζ7−2ζ72ζ7−2ζ2ζ−2ζ2ζ2ζ5−2ζ52ζ5−2ζ500000000000000000000000000
χ604-44-4000−4i4i00000−2222−22220000002i2−2i2−2ζ32ζ3−2ζ32ζ32ζ7−2ζ72ζ7−2ζ72ζ−2ζ2ζ−2ζ−2ζ52ζ5−2ζ52ζ500000000000000000000000000
χ614-4-44000004000-422−22−22220022−220000ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ700000000000000000000000000
χ624-4-44000004000-422−22−22220022−220000−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ700000000000000000000000000
χ634-4-44000004000-4−222222−2200−22220000ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ700000000000000000000000000
χ644-4-44000004000-4−222222−2200−22220000−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ700000000000000000000000000
χ654-4-4400000-4000422−22−222200−22220000ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ700000000000000000000000000
χ664-4-4400000-4000422−22−222200−22220000−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ700000000000000000000000000
χ674-4-4400000-40004−222222−220022−220000ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ700000000000000000000000000
χ684-4-4400000-40004−222222−220022−220000−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ700000000000000000000000000

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