Finite Group Databasebeta

← Group #488705

Character table — Group #488705

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size1111222222444444444488888888888881616161616161616161616161616161616163232
order12222244442244888888244481616161616161616222444444444881616161644
χ111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ31111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1
χ41111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111
χ511111111111111111111-1-1-1-111111111111-111-1-1-1-1-1-1-1-1-1-1-1-1-111
χ611111111111111111111-1-1-1-1111111111-1-11-1-11111111-1-1-1-1-1-1-1-1
χ711111111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-111-1-1-11111-1-11111-1-1
χ811111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-11-1-1111-1-1-1-1-1-1111111
χ9111111-1-111-1-11-1-1-111111-1-11-11111-1-1-1-11-111-11-1-111-1-11-111-1-11-1
χ10111111-1-111-1-11-1-1-111111-1-11-11111-1-1-1-1-11-1-11-111-1-1111-111-1-1-11
χ11111111-1-111-1-11-1-1-111111-1-11-1-1-1-1-111111-111-11-1-1-1-1111-1-1-111-11
χ12111111-1-111-1-11-1-1-111111-1-11-1-1-1-1-11111-11-1-11-11111-1-11-1-1-1111-1
χ13111111-1-111-1-11-1-1-11111-111-1-11111-1-1-1-11-1-11-1-111-1-111-11-1-1111-1
χ14111111-1-111-1-11-1-1-11111-111-1-11111-1-1-1-1-111-111-1-111-1-1-11-1-111-11
χ15111111-1-111-1-11-1-1-11111-111-1-1-1-1-1-111111-1-11-1-11111-1-1-1111-1-1-11
χ16111111-1-111-1-11-1-1-11111-111-1-1-1-1-1-11111-111-111-1-1-1-111-1111-1-11-1
χ1722222222222222-2-2-2-2-2-22222-200000000000000000000-2-2000000
χ1822222222222222-2-2-2-2-2-2-2-2-2-2-20000000000000000000022000000
χ1922222222-2-2-2-2-2200000022-2-2022−2−222−2−2000000000000002−22−200
χ2022222222-2-2-2-2-2200000022-2-20−2−222−2−22200000000000000−22−2200
χ2122222222-2-2-2-2-22000000-2-222022−2−222−2−200000000000000−22−2200
χ2222222222-2-2-2-2-22000000-2-2220−2−222−2−222000000000000002−22−200
χ23222222-2-222-2-22-222-2-2-2-22-2-22200000000000000000000-22000000
χ24222222-2-222-2-22-222-2-2-2-2-222-22000000000000000000002-2000000
χ25222222-2-2-2-222-2-20000002-22-2022−2−2−2−222000000000000002−2−2200
χ26222222-2-2-2-222-2-20000002-22-20−2−22222−2−200000000000000−222−200
χ27222222-2-2-2-222-2-2000000-22-22022−2−2−2−22200000000000000−222−200
χ28222222-2-2-2-222-2-2000000-22-220−2−22222−2−2000000000000002−2−2200
χ292222-2-222222-2-2-22222-2-20000-2000000002-20-22000000000000000
χ302222-2-222222-2-2-22222-2-20000-200000000-2202-2000000000000000
χ312222-2-222222-2-2-2-2-2-2-222000020000000000200-2-22000000000000
χ322222-2-222222-2-2-2-2-2-2-222000020000000000-20022-2000000000000
χ332222-2-2-2-222-22-2222-2-2220000-20000000000200-22-2000000000000
χ342222-2-2-2-222-22-2222-2-2220000-20000000000-2002-22000000000000
χ352222-2-2-2-222-22-22-2-222-2-20000200000000220-2-2000000000000000
χ362222-2-2-2-222-22-22-2-222-2-20000200000000-2-2022000000000000000
χ374444-4-444-4-4-444-4000000000000000000000000000000000000000
χ384444-4-4-4-4-4-44-444000000000000000000000000000000000000000
χ3944-4-44-4000000000022−2222−220000000002ζ3+2ζ5−2ζ3−2ζ52ζ+2ζ7−2ζ−2ζ700000000000000000000
χ4044-4-44-4000000000022−2222−22000000000−2ζ3−2ζ52ζ3+2ζ5−2ζ−2ζ72ζ+2ζ700000000000000000000
χ4144-4-44-40000000000−2222−22220000000002ζ+2ζ7−2ζ−2ζ7−2ζ3−2ζ52ζ3+2ζ500000000000000000000
χ4244-4-44-40000000000−2222−2222000000000−2ζ−2ζ72ζ+2ζ72ζ3+2ζ5−2ζ3−2ζ500000000000000000000
χ4344-4-4-44000000000022−22−2222000002ζ+2ζ7−2ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ5000000000000000000000000
χ4444-4-4-44000000000022−22−222200000−2ζ−2ζ72ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ5000000000000000000000000
χ4544-4-4-440000000000−222222−22000002ζ3+2ζ5−2ζ3−2ζ5−2ζ−2ζ72ζ+2ζ7000000000000000000000000
χ4644-4-4-440000000000−222222−2200000−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ7000000000000000000000000
χ474-4-4400004-400004i−4i00000000000000000000000002i−2i2-200000000
χ484-4-4400004-400004i−4i0000000000000000000000000−2i2i-2200000000
χ494-4-4400004-40000−4i4i00000000000000000000000002i−2i-2200000000
χ504-4-4400004-40000−4i4i0000000000000000000000000−2i2i2-200000000
χ518-88-8008i−8i000000000000000000000000000000000000000000000
χ528-88-800−8i8i000000000000000000000000000000000000000000000
χ538-8-880000-880000000000000000000000000000000000000000000

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