Finite Group Databasebeta

← Group #143907

Character table — Group #143907

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44
size111122224444444444488888888816161616161616163232323232323232
order12224444244448888888161616161616161624881616161622448888
χ111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1-11-11-111-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-11-11-1-111
χ511111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11-11-1-1-111
χ611111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-11-1111-1-1
χ711111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ811111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ92222222222222-2-2-2-2-2-2-20000000022-2-2000000000000
χ102222222222222-2-2-2-2-2-2-200000000-2-222000000000000
χ1122222222-2-22-2-222-222-2-2000000000000000000002-200
χ1222222222-2-22-2-222-222-2-200000000000000000000-2200
χ1322222222-2-22-2-2-2-22-2-2220000000000000000020-20000
χ1422222222-2-22-2-2-2-22-2-22200000000000000000-2020000
χ1522222-2-2222-2-2-222-2-2-2-222i2i2i2i−2i−2i−2i−2i0000000000000000
χ1622222-2-2222-2-2-222-2-2-2-22−2i−2i−2i−2i2i2i2i2i0000000000000000
χ1722222-2-2222-2-2-2-2-22222-200000000000022-2-200000000
χ1822222-2-2222-2-2-2-2-22222-2000000000000-2-22200000000
χ1922222-2-22-2-2-222222-2-22-2000000000000000020-200000
χ2022222-2-22-2-2-222222-2-22-20000000000000000-20200000
χ2122222-2-22-2-2-222-2-2-222-2200000000000000000000002-2
χ2222222-2-22-2-2-222-2-2-222-220000000000000000000000-22
χ232222-222-22-2-2-22000000022−2−222−2−22-2002−22−200000000
χ242222-222-22-2-2-22000000022−2−222−2−2-2200−22−2200000000
χ252222-222-22-2-2-220000000−2−222−2−2222-200−22−2200000000
χ262222-222-22-2-2-220000000−2−222−2−222-22002−22−200000000
χ272222-2-2-2-22-222-20000000i2i2−i2−i2−i2−i2i2i2002i−2i2−2−2200000000
χ282222-2-2-2-22-222-20000000i2i2−i2−i2−i2−i2i2i200−2i2i−222−200000000
χ292222-2-2-2-22-222-20000000−i2−i2i2i2i2i2−i2−i2002i−2i−222−200000000
χ302222-2-2-2-22-222-20000000−i2−i2i2i2i2i2−i2−i200−2i2i2−2−2200000000
χ314444-444-4-44-44-40000000000000000000000000000000
χ324444-4-4-4-4-444-440000000000000000000000000000000
χ3344-4-4400-4000000004i−4i002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ30000000000000000
χ3444-4-4400-4000000004i−4i00−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ30000000000000000
χ3544-4-4400-400000000−4i4i002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ0000000000000000
χ3644-4-4400-400000000−4i4i00−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ0000000000000000
χ3744-4-4-40040000000400-402i−2i−2i2i2i−2i−2i2i0000000000000000
χ3844-4-4-40040000000400-40−2i2i2i−2i−2i2i2i−2i0000000000000000
χ3944-4-4-40040000000-400402-2-22-222-20000000000000000
χ4044-4-4-40040000000-40040-222-22-2-220000000000000000
χ418-88-800000000042−4200000000000000000000000000000
χ428-88-8000000000−424200000000000000000000000000000
χ438-8-8808-80000000000000000000000000000000000000
χ448-8-880-880000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.