Finite Group Databasebeta

← Group #135607

Character table — Group #135607

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size111122222244444444448888888888888888816161616161616161616161632323232
order12224444442224888888244488888161616161616161688888888161616168888
χ111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1
χ41111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111-1-1-1-11111111111111-1-111-1-1-1-1-1-1-1-111-1-1
χ611111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111
χ711111111111111111111-1-1-1-11-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111
χ811111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1
χ911111-1-11111-1-1-111-1-1-1-11-1-1111111iiii−i−i−i−i-11-1-111-1-1ii−i−ii−ii−i
χ1011111-1-11111-1-1-111-1-1-1-11-1-1111111−i−i−i−iiiii-11-1-111-1-1−i−iii−ii−ii
χ1111111-1-11111-1-1-111-1-1-1-11-1-111-1-1-1-1iiii−i−i−i−i-1111-1-111ii−i−i−ii−ii
χ1211111-1-11111-1-1-111-1-1-1-11-1-111-1-1-1-1−i−i−i−iiiii-1111-1-111−i−iiii−ii−i
χ1311111-1-11111-1-1-111-1-1-1-1-111-111111iiii−i−i−i−i1-1-1-1-1-111−i−iiii−i−ii
χ1411111-1-11111-1-1-111-1-1-1-1-111-111111−i−i−i−iiiii1-1-1-1-1-111ii−i−i−iii−i
χ1511111-1-11111-1-1-111-1-1-1-1-111-11-1-1-1-1iiii−i−i−i−i1-11111-1-1−i−iii−iii−i
χ1611111-1-11111-1-1-111-1-1-1-1-111-11-1-1-1-1−i−i−i−iiiii1-11111-1-1ii−i−ii−i−ii
χ1722222222222222-2-2-2-2-2-22222-2000000000000-2-200000000000000
χ1822222222222222-2-2-2-2-2-2-2-2-2-2-20000000000002200000000000000
χ1922222222-2-2-22-2-22222-2-20000-200000000000000002i−2i2i−2i00000000
χ2022222222-2-2-22-2-22222-2-20000-20000000000000000−2i2i−2i2i00000000
χ2122222222-2-2-22-2-2-2-2-2-222000022i2i−2i−2i00000000002i−2i000000000000
χ2222222222-2-2-22-2-2-2-2-2-22200002−2i−2i2i2i0000000000−2i2i000000000000
χ2322222-2-22222-2-2-2-2-222222-2-22-20000000000002-200000000000000
χ2422222-2-22222-2-2-2-2-22222-222-2-2000000000000-2200000000000000
χ2522222-2-22-2-2-2-22222-2-2220000-200000000000000002i−2i−2i2i00000000
χ2622222-2-22-2-2-2-22222-2-2220000-20000000000000000−2i2i2i−2i00000000
χ2722222-2-22-2-2-2-222-2-222-2-2000022i2i−2i−2i0000000000−2i2i000000000000
χ2822222-2-22-2-2-2-222-2-222-2-200002−2i−2i2i2i00000000002i−2i000000000000
χ292222-222-2-2-22-2-2200000022-2-200000i2i2−i2−i2i2i2−i2−i200000000i2−i2i2−i20000
χ302222-222-2-2-22-2-2200000022-2-200000−i2−i2i2i2−i2−i2i2i200000000−i2i2−i2i20000
χ312222-222-2-2-22-2-22000000-2-22200000i2i2−i2−i2i2i2−i2−i200000000−i2i2−i2i20000
χ322222-222-2-2-22-2-22000000-2-22200000−i2−i2i2i2−i2−i2i2i200000000i2−i2i2−i20000
χ332222-2-2-2-2-2-2222-20000002-22-20000022−2−2−2−222000000002−2−220000
χ342222-2-2-2-2-2-2222-20000002-22-200000−2−22222−2−200000000−222−20000
χ352222-2-2-2-2-2-2222-2000000-22-220000022−2−2−2−22200000000−222−20000
χ362222-2-2-2-2-2-2222-2000000-22-2200000−2−22222−2−2000000002−2−220000
χ374444-444-444-4-44-4000000000000000000000000000000000000000
χ384444-4-4-4-444-44-44000000000000000000000000000000000000000
χ3944-4-400004i−4i00000022−222i2−2i20000000002ζ−2ζ2ζ5−2ζ52ζ3−2ζ32ζ7−2ζ70000000000000000
χ4044-4-400004i−4i00000022−222i2−2i2000000000−2ζ2ζ−2ζ52ζ5−2ζ32ζ3−2ζ72ζ70000000000000000
χ4144-4-400004i−4i000000−2222−2i22i20000000002ζ5−2ζ5−2ζ2ζ−2ζ72ζ72ζ3−2ζ30000000000000000
χ4244-4-400004i−4i000000−2222−2i22i2000000000−2ζ52ζ52ζ−2ζ2ζ7−2ζ7−2ζ32ζ30000000000000000
χ4344-4-40000−4i4i00000022−22−2i22i20000000002ζ7−2ζ72ζ3−2ζ32ζ5−2ζ52ζ−2ζ0000000000000000
χ4444-4-40000−4i4i00000022−22−2i22i2000000000−2ζ72ζ7−2ζ32ζ3−2ζ52ζ5−2ζ2ζ0000000000000000
χ4544-4-40000−4i4i000000−22222i2−2i20000000002ζ3−2ζ3−2ζ72ζ7−2ζ2ζ2ζ5−2ζ50000000000000000
χ4644-4-40000−4i4i000000−22222i2−2i2000000000−2ζ32ζ32ζ7−2ζ72ζ−2ζ−2ζ52ζ50000000000000000
χ474-4-44400-40000004i−4i0000000002+2i−2−2i2−2i−2+2i000000000000000000000000
χ484-4-44400-40000004i−4i000000000−2−2i2+2i−2+2i2−2i000000000000000000000000
χ494-4-44400-4000000−4i4i0000000002−2i−2+2i2+2i−2−2i000000000000000000000000
χ504-4-44400-4000000−4i4i000000000−2+2i2−2i−2−2i2+2i000000000000000000000000
χ518-88-808i−8i0000000000000000000000000000000000000000000000
χ528-88-80−8i8i0000000000000000000000000000000000000000000000
χ538-8-88-8008000000000000000000000000000000000000000000000

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