Finite Group Databasebeta

← Group #142944

Character table — Group #142944

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41
size1111222244444888888881616161616161616161616161616323232323232
order12222244224442444888824444444888888248888
χ111111111111111111111111111111111111111111
χ21111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1
χ3111111111111111111111-1-1-1-1111111-1-1-1-111-1-1-1-1
χ4111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111
χ511111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1111-1-1
χ611111111111111111-1-1-1-11111-1-111-1-1-1-1-1-11-1-1-111
χ711111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-11-1-111
χ811111111111111111-1-1-1-1-1-1-1-1-1-111-1-111111-111-1-1
χ92222222222222-2-2-2-2222200000000-2-20000000000
χ102222222222222-2-2-2-2-2-2-2-200000000220000000000
χ1122222222-2-22-2-22-2-220000000022000000000-20000
χ1222222222-2-22-2-22-2-2200000000-2-200000000020000
χ1322222222-2-22-2-2-222-2000000000022000000-200000
χ1422222222-2-22-2-2-222-20000000000-2-2000000200000
χ15222222-2-222-2-2-222-2-2000000000000002i2i−2i−2i000000
χ16222222-2-222-2-2-222-2-200000000000000−2i−2i2i2i000000
χ17222222-2-222-2-2-2-2-222000022-2-20000000000000000
χ18222222-2-222-2-2-2-2-2220000-2-2220000000000000000
χ19222222-2-2-2-2-2222-22-200000000000000000000002-2
χ20222222-2-2-2-2-2222-22-20000000000000000000000-22
χ21222222-2-2-2-2-222-22-22000000000000000000002-200
χ22222222-2-2-2-2-222-22-2200000000000000000000-2200
χ234444-4-44400-400000000002-2-220000000000000000
χ244444-4-44400-40000000000-222-20000000000000000
χ254444-4-4-4-400400000000002-22-20000000000000000
χ264444-4-4-4-40040000000000-22-220000000000000000
χ2744-4-44-4000004i−4i0000000000000000002ζ−2ζ2ζ3−2ζ3000000
χ2844-4-44-4000004i−4i000000000000000000−2ζ2ζ−2ζ32ζ3000000
χ2944-4-44-400000−4i4i0000000000000000002ζ3−2ζ32ζ−2ζ000000
χ3044-4-44-400000−4i4i000000000000000000−2ζ32ζ3−2ζ2ζ000000
χ3144-4-4-44004-400000000000000000002i2−2i20000000000
χ3244-4-4-44004-40000000000000000000−2i22i20000000000
χ3344-4-4-4400-4400000002i22i2−2i2−2i200000000000000000000
χ3444-4-4-4400-440000000−2i2−2i22i22i200000000000000000000
χ354-4-4400-440000000002-22-200002-22-2000000000000
χ364-4-4400-440000000002-22-20000-22-22000000000000
χ374-4-4400-44000000000-22-2200002-2-22000000000000
χ384-4-4400-44000000000-22-220000-222-2000000000000
χ398-88-800000000000002i2−2i2−2i22i200000000000000000000
χ408-88-80000000000000−2i22i22i2−2i200000000000000000000
χ418-8-88008-8000000000000000000000000000000000

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