Finite Group Databasebeta

← Group #138921

Character table — Group #138921

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size111122222244444444448888888888888888816161616161616161616161632323232
order12222222442444888888444444448161616161616161644444488161616162488
χ111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-111-1-1
χ4111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-111
χ511111111111111111111-1-1-1-11111111111111-1-1-1-1-1-1111111-1-1-1-1
χ611111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ711111111111111111111-1-1-1-1-1-1-1-1111111111-1-11111-1-1-1-1-1-1-1-111
χ811111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1
χ9111111-1-111-11-1-11111-1-111-1-1ii−i−i-11111-1-1-1-11-1ii−i−ii−iii−i−i1-1i−i
χ10111111-1-111-11-1-11111-1-111-1-1ii−i−i-1-1-1-1-111111-1ii−i−ii−i−i−iii-11−ii
χ11111111-1-111-11-1-11111-1-111-1-1−i−iii-11111-1-1-1-11-1−i−iii−ii−i−iii1-1−ii
χ12111111-1-111-11-1-11111-1-111-1-1−i−iii-1-1-1-1-111111-1−i−iii−iiii−i−i-11i−i
χ13111111-1-111-11-1-11111-1-1-1-111ii−i−i-11111-1-1-1-1-11−i−iiii−iii−i−i-11−ii
χ14111111-1-111-11-1-11111-1-1-1-111ii−i−i-1-1-1-1-11111-11−i−iiii−i−i−iii1-1i−i
χ15111111-1-111-11-1-11111-1-1-1-111−i−iii-11111-1-1-1-1-11ii−i−i−ii−i−iii-11i−i
χ16111111-1-111-11-1-11111-1-1-1-111−i−iii-1-1-1-1-11111-11ii−i−i−iiii−i−i1-1−ii
χ1722222222222222-2-2-2-2-2-200002222-200000000000000-2-200000000
χ1822222222222222-2-2-2-2-2-20000-2-2-2-2-2000000000000002200000000
χ19222222-2-222-22-2-2-2-2-2-22200002i2i−2i−2i200000000000000−2i2i00000000
χ20222222-2-222-22-2-2-2-2-2-2220000−2i−2i2i2i2000000000000002i−2i00000000
χ212222-2-22222-2-22-222-2-22200000000-200000000002-22-20000000000
χ222222-2-22222-2-22-222-2-22200000000-20000000000-22-220000000000
χ232222-2-22222-2-22-2-2-222-2-222220000200000000-2-200000000000000
χ242222-2-22222-2-22-2-2-222-2-2-2-2-2-200002000000002200000000000000
χ252222-2-222-2-2-22-2200000000002-22-2022−2−222−2−2000000002−22−20000
χ262222-2-222-2-2-22-2200000000002-22-20−2−222−2−22200000000−22−220000
χ272222-2-222-2-2-22-220000000000-22-22022−2−222−2−200000000−22−220000
χ282222-2-222-2-2-22-220000000000-22-220−2−222−2−222000000002−22−20000
χ292222-2-2-2-2222-2-2222-2-2-2-200000000200000000002i−2i−2i2i0000000000
χ302222-2-2-2-2222-2-2222-2-2-2-20000000020000000000−2i2i2i−2i0000000000
χ312222-2-2-2-2222-2-22-2-2222222-2-20000-200000000-2200000000000000
χ322222-2-2-2-2222-2-22-2-22222-2-2220000-2000000002-200000000000000
χ332222-2-2-2-2-2-2222-200000000002i−2i−2i2i022−2−2−2−22200000000i2−i2−i2i20000
χ342222-2-2-2-2-2-2222-200000000002i−2i−2i2i0−2−22222−2−200000000−i2i2i2−i20000
χ352222-2-2-2-2-2-2222-20000000000−2i2i2i−2i022−2−2−2−22200000000−i2i2i2−i20000
χ362222-2-2-2-2-2-2222-20000000000−2i2i2i−2i0−2−22222−2−200000000i2−i2−i2i20000
χ3744444444-4-44-4-4-4000000000000000000000000000000000000000
χ38444444-4-4-4-4-4-444000000000000000000000000000000000000000
χ394-44-4004-400000022−220022−22000000000ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ70000000000000000
χ404-44-4004-400000022−220022−22000000000−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ70000000000000000
χ414-44-4004-4000000−222200−2222000000000ζ−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+ζ70000000000000000
χ424-44-4004-4000000−222200−2222000000000−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−ζ70000000000000000
χ434-44-400-4400000022−2200−2222000000000ζ+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+ζ70000000000000000
χ444-44-400-4400000022−2200−2222000000000−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−ζ70000000000000000
χ454-44-400-44000000−22220022−22000000000ζ−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−ζ70000000000000000
χ464-44-400-44000000−22220022−22000000000−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+ζ70000000000000000
χ474-4-440000-440000004-400004-400000000000000000000000000000
χ484-4-440000-440000004-40000-4400000000000000000000000000000
χ494-4-440000-44000000-44004-40000000000000000000000000000000
χ504-4-440000-44000000-4400-440000000000000000000000000000000
χ5188-8-88-800000000000000000000000000000000000000000000000
χ5288-8-8-8800000000000000000000000000000000000000000000000
χ538-8-8800008-80000000000000000000000000000000000000000000

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