Finite Group Databasebeta

← Group #492012

Character table — Group #492012

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111122222222444444444448888888888888888888816161616161616163232323232
order122244448888224888816161616444448888816161616161616161616244888161644448
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111-1-11111111111111111-1-1-11-1-111-1-1-1-1-1
χ31111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11-1-1111-1-111-1-1-1
χ41111111111111111111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1111
χ5111111111111111-1-1111111-1-1111-111-1-1111111-1-1-1-1111-1-1-1-1-11-11-1-1
χ6111111111111111-1-1111111-1-1-1-11-111-1-1111111-1-1-1-1-1-1-1-111-1-1-11-111
χ7111111111111111-1-111-1-1-1-1-1-1111-111-1-1-1-1-1-1-1-111111-1-1-1-1-1111-1-111
χ8111111111111111-1-111-1-1-1-1-1-1-1-11-111-1-1-1-1-1-1-1-11111-111-11111-111-1-1
χ9111111111111-1-1111111111-1-111-11-1-11111-1-1-1-11111111-111-1-1-1-1-1-11
χ10111111111111-1-1111111111-1-1-1-1-11-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1
χ11111111111111-1-111111-1-1-1-1-1-111-11-1-111-1-11111-1-1-1-11-1-1-11111-1-111-1
χ12111111111111-1-111111-1-1-1-1-1-1-1-1-11-1-111-1-11111-1-1-1-1-111-1-1-11111-1-11
χ13111111111111-1-11-1-11111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-11-11-1
χ14111111111111-1-11-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1111111-11-11
χ15111111111111-1-11-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111111111-1-11-1-1-1-1-111-11
χ16111111111111-1-11-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-111111-1-11-1-11-1
χ1722222222-2-2-2-222222-2-20000220022-2-2-2-20000000000000-2000000000
χ1822222222-2-2-2-2222-2-2-2-20000-2-2002-2-2-22200000000000002000000000
χ1922222222-2-2-2-2-2-2222-2-20000-2-200-2222-2-200000000000002000000000
χ2022222222-2-2-2-2-2-22-2-2-2-200002200-2-222220000000000000-2000000000
χ2122222-2-22000022-2220022−2−22-200-2-200002−222−2−222−2−20000002−200000
χ2222222-2-22000022-22200−2−2222-200-2-20000−22−2−222−2−222000000−2200000
χ2322222-2-22000022-2-2-20022−2−2-2200-2200002−222−2−2−2−222000000−2200000
χ2422222-2-22000022-2-2-200−2−222-2200-220000−22−2−22222−2−20000002−200000
χ2522222-2-220000-2-2-2220022−2−2-22002-200002−2−2−22222−2−2000000−2200000
χ2622222-2-220000-2-2-22200−2−222-22002-20000−2222−2−2−2−2220000002−200000
χ2722222-2-220000-2-2-2-2-20022−2−22-2002200002−2−2−222−2−2220000002−200000
χ2822222-2-220000-2-2-2-2-200−2−2222-200220000−2222−2−222−2−2000000−2200000
χ292222-222-2222200-200-2-222220022000000-2-200000000-2-220000000000
χ302222-222-2222200-200-2-2222200-2-2000000-2-20000000022-20000000000
χ312222-222-2222200-200-2-2-2-2-2-200220000002200000000-22-20000000000
χ322222-222-2222200-200-2-2-2-2-2-200-2-200000022000000002-220000000000
χ334444-444-4-4-4-4-400-400440000000000000000000000000000000000000
χ344444-4-4-4-4000000400002222−22−220000000000−2222000000000000000000000
χ354444-4-4-4-400000040000−22−222222000000000022−22000000000000000000000
χ3644-4-4000022−2222−2200022−22002ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ5000000002-2000000ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ70000000000000
χ3744-4-4000022−2222−2200022−2200−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ5000000002-2000000−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ70000000000000
χ3844-4-4000022−2222−22000−2222002ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ500000000-22000000−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ70000000000000
χ3944-4-4000022−2222−22000−222200−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ500000000-22000000ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ70000000000000
χ4044-4-40000−2222−222200022−22002ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ700000000-22000000ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ70000000000000
χ4144-4-40000−2222−222200022−2200−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ700000000-22000000−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ70000000000000
χ4244-4-40000−2222−2222000−2222002ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ7000000002-2000000−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ70000000000000
χ4344-4-40000−2222−2222000−222200−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ7000000002-2000000ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ70000000000000
χ444-44-4400-422−22−22224-400022−22000000000022−220000000000000000000000000
χ454-44-4400-422−22−2222-4400022−220000000000−22220000000000000000000000000
χ464-44-4400-4−222222−224-4000−22220000000000−22220000000000000000000000000
χ474-44-4400-4−222222−22-44000−2222000000000022−220000000000000000000000000
χ484-44-4-400422−22−222200000−222200000000000000002ζ3+2ζ5−2ζ3−2ζ52ζ+2ζ7−2ζ−2ζ700000000000000000
χ494-44-4-400422−22−222200000−22220000000000000000−2ζ3−2ζ52ζ3+2ζ5−2ζ−2ζ72ζ+2ζ700000000000000000
χ504-44-4-4004−222222−220000022−2200000000000000002ζ+2ζ7−2ζ−2ζ7−2ζ3−2ζ52ζ3+2ζ500000000000000000
χ514-44-4-4004−222222−220000022−220000000000000000−2ζ−2ζ72ζ+2ζ72ζ3+2ζ5−2ζ3−2ζ500000000000000000
χ524-4-4404-4044-4-400000000000004i−4i00000000000000000000000000000
χ534-4-4404-4044-4-40000000000000−4i4i00000000000000000000000000000
χ544-4-4404-40-4-4440000000000000000000000000000000000022−220000000
χ554-4-4404-40-4-44400000000000000000000000000000000000−22220000000
χ568-8-880-880000000000000000000000000000000000000000000000000

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