Finite Group Databasebeta

← Group #131413

Character table — Group #131413

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111122222222444444444888888888888816161616161616161616161616161616161616161616
order12222222444424488888844448161616161616161622244444444488888816161616
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ311111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1
χ5111111111111111111111-1-1-1-111111111111-1-1-111-11111-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111-1-1-1-1111111111-1-1111-1-11-1-1-1-1-1-11111-1-1-1-1
χ7111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-111-1-1-1-1-1-1-111111111
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1111-1-111111-1-1-1-1-1-11111
χ91111-1-1-1-11-11-111-111-1-1-1-11-11-11iiii−i−i−i−i1-111-11-1-1ii−i−i1-1ii−i−iii−i−i
χ101111-1-1-1-11-11-111-111-1-1-1-11-11-11iiii−i−i−i−i-11-1-11-111−i−iii1-1−i−iiiii−i−i
χ111111-1-1-1-11-11-111-111-1-1-1-11-11-11−i−i−i−iiiii1-111-11-1-1−i−iii1-1−i−iii−i−iii
χ121111-1-1-1-11-11-111-111-1-1-1-11-11-11−i−i−i−iiiii-11-1-11-111ii−i−i1-1ii−i−i−i−iii
χ131111-1-1-1-11-11-111-111-1-1-1-1-11-111iiii−i−i−i−i1-1-1-111-11ii−i−i-11−i−iii−i−iii
χ141111-1-1-1-11-11-111-111-1-1-1-1-11-111iiii−i−i−i−i-1111-1-11-1−i−iii-11ii−i−i−i−iii
χ151111-1-1-1-11-11-111-111-1-1-1-1-11-111−i−i−i−iiiii1-1-1-111-11−i−iii-11ii−i−iii−i−i
χ161111-1-1-1-11-11-111-111-1-1-1-1-11-111−i−i−i−iiiii-1111-1-11-1ii−i−i-11−i−iiiii−i−i
χ17222222222222222-2-2-2-2-2-22222-200000000000000000000-2-200000000
χ18222222222222222-2-2-2-2-2-2-2-2-2-2-2000000000000000000002200000000
χ19222222-2-22222-2-2-22222-2-20000-200000000002-2200-200000000000000
χ20222222-2-22222-2-2-22222-2-20000-20000000000-22-200200000000000000
χ21222222-2-22222-2-2-2-2-2-2-222000020000000022000-2-2000000000000000
χ22222222-2-22222-2-2-2-2-2-2-2220000200000000-2-200022000000000000000
χ23222222-2-2-2-2-2-2-2220000002-2-220i2i2−i2−i2i2i2−i2−i2000000000000000000i2−i2i2−i2
χ24222222-2-2-2-2-2-2-2220000002-2-220−i2−i2i2i2−i2−i2i2i2000000000000000000−i2i2−i2i2
χ25222222-2-2-2-2-2-2-222000000-222-20i2i2−i2−i2i2i2−i2−i2000000000000000000−i2i2−i2i2
χ26222222-2-2-2-2-2-2-222000000-222-20−i2−i2i2i2−i2−i2i2i2000000000000000000i2−i2i2−i2
χ272222-2-2222-22-2-2-2222-2-2220000-200000000002-2-200200000000000000
χ282222-2-2222-22-2-2-2222-2-2220000-20000000000-22200-200000000000000
χ292222-2-2222-22-2-2-22-2-222-2-200002000000002-2000-22000000000000000
χ302222-2-2222-22-2-2-22-2-222-2-20000200000000-220002-2000000000000000
χ312222-2-222-22-22-22-200000022-2-2022−2−2−2−2220000000000000000002−2−22
χ322222-2-222-22-22-22-200000022-2-20−2−22222−2−2000000000000000000−222−2
χ332222-2-222-22-22-22-2000000-2-222022−2−2−2−222000000000000000000−222−2
χ342222-2-222-22-22-22-2000000-2-2220−2−22222−2−20000000000000000002−2−22
χ352222-2-2-2-22-22-222-2-2-222222-22-2-200000000000000000000-2200000000
χ362222-2-2-2-22-22-222-2-2-22222-22-22-2000000000000000000002-200000000
χ3744444444-4-4-4-44-4-400000000000000000000000000000000000000000
χ384444-4-4-4-4-44-444-4400000000000000000000000000000000000000000
χ3944-4-44-40044-4-40000000000000000000000000000002-22-20000000000
χ4044-4-44-40044-4-4000000000000000000000000000000-22-220000000000
χ4144-4-44-400-4-4440000000000000000000000000000000000002-22-20000
χ4244-4-44-400-4-444000000000000000000000000000000000000-22-220000
χ4344-4-4-44004-4-440000000000000000000000000000002i−2i−2i2i0000000000
χ4444-4-4-44004-4-44000000000000000000000000000000−2i2i2i−2i0000000000
χ4544-4-4-4400-444-40000000000000000000000000000000000002i−2i−2i2i0000
χ4644-4-4-4400-444-4000000000000000000000000000000000000−2i2i2i−2i0000
χ474-4-44004-4000000022−220022−2200000ζ+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−ζ70000000000000000000000
χ484-4-44004-4000000022−220022−2200000−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+ζ70000000000000000000000
χ494-4-44004-40000000−222200−222200000ζ−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−ζ70000000000000000000000
χ504-4-44004-40000000−222200−222200000−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+ζ70000000000000000000000
χ514-4-4400-44000000022−2200−222200000ζ+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−ζ70000000000000000000000
χ524-4-4400-44000000022−2200−222200000−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+ζ70000000000000000000000
χ534-4-4400-440000000−22220022−2200000ζ−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−ζ70000000000000000000000
χ544-4-4400-440000000−22220022−2200000−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+ζ70000000000000000000000
χ558-88-800000000000004i2−4i20000000000000000000000000000000000000
χ568-88-80000000000000−4i24i20000000000000000000000000000000000000

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