Finite Group Databasebeta

← Group #144362

Character table — Group #144362

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38
size112224444444488816161616161616161616161616161616323232323232
order12222222222444442224444444448888444444
χ111111111111111111111111111111111111111
χ2111111111111111111-111-11111-1-1-1-1-1-111-1-1-1-1
χ311111111111111111-111-1111-1-111-1-1-1-1-1-111-1-1
χ411111111111111111-1-11-1-111-1-1-1-11111-1-1-1-111
χ51111111111111111-111-111-1-11111-1-1-1-1-1-1-1-111
χ61111111111111111-11-1-11-1-1-111-1-11111-1-111-1-1
χ71111111111111111-1-11-1-11-1-1-1-111111111-1-1-1-1
χ81111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ9222222222-2-2-2-22-2-20020020000-2-20000000000
χ10222222222-2-2-2-22-2-200-200-20000220000000000
χ112222222-2-222-2-2-22-202002000-2-2000000000000
χ122222222-2-222-2-2-22-20-200-200022000000000000
χ132222222-2-2-2-222-2-22000000000000000000002-2
χ142222222-2-2-2-222-2-2200000000000000000000-22
χ1522222-2-22222-2-2-2-22200200-2-200000000000000
χ1622222-2-22222-2-2-2-22-200-2002200000000000000
χ1722222-2-222-2-222-22-20000000000000000002-200
χ1822222-2-222-2-222-22-2000000000000000000-2200
χ1922222-2-2-2-222222-2-200000000000000002-20000
χ2022222-2-2-2-222222-2-20000000000000000-220000
χ2122222-2-2-2-2-2-2-2-22220000000000002i2i−2i−2i000000
χ2222222-2-2-2-2-2-2-2-2222000000000000−2i−2i2i2i000000
χ23444-4-400004-40000000200-200002-20000000000
χ24444-4-400004-40000000-20020000-220000000000
χ25444-4-40000-440000000200-20000-220000000000
χ26444-4-40000-440000000-200200002-20000000000
χ2744-44-4004-400000000200-20002-2000000000000
χ2844-44-4004-400000000-2002000-22000000000000
χ2944-44-400-4400000000200-2000-22000000000000
χ3044-44-400-4400000000-20020002-2000000000000
χ3144-4-444-4000000000200-2002-200000000000000
χ3244-4-444-4000000000-200200-2200000000000000
χ3344-4-44-44000000000200-200-2200000000000000
χ3444-4-44-44000000000-2002002-200000000000000
χ358-80000000004i−4i0000000000000002ζ−2ζ2ζ3−2ζ3000000
χ368-80000000004i−4i000000000000000−2ζ2ζ−2ζ32ζ3000000
χ378-8000000000−4i4i0000000000000002ζ3−2ζ32ζ−2ζ000000
χ388-8000000000−4i4i000000000000000−2ζ32ζ3−2ζ2ζ000000

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