Finite Group Databasebeta

← Group #102702

Character table — Group #102702

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41
size111111114444444488816161616161616161616161616161616323232323232
order12222222444444444448888888888888888444444
χ111111111111111111111111111111111111111111
χ21111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1
χ411111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111-1-1-1-11111-1-1-1-11111-1-11-11-1
χ61111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-11-11
χ71111111111111111111-1-1-1-1-1-1-1-111111111-1-1-11-11
χ81111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111-11-1
χ9222222222222-2-2-2-22-2-2000000000000000000020-2
χ10222222222222-2-2-2-22-2-20000000000000000000-202
χ112222222222-2-222-2-2-22-2000022-2-200000000000000
χ122222222222-2-222-2-2-22-20000-2-22200000000000000
χ132222222222-2-2-2-222-2-2200000000000000002-20000
χ142222222222-2-2-2-222-2-220000000000000000-220000
χ1522222222-2-22222-2-2-2-2222-2-2000000000000000000
χ1622222222-2-22222-2-2-2-22-2-222000000000000000000
χ1722222222-2-222-2-222-22-200000000000000000020-20
χ1822222222-2-222-2-222-22-2000000000000000000-2020
χ1922222222-2-2-2-222222-2-20000000022-2-20000000000
χ2022222222-2-2-2-222222-2-200000000-2-2220000000000
χ2122222222-2-2-2-2-2-2-2-22220000000000002i2i−2i−2i000000
χ2222222222-2-2-2-2-2-2-2-2222000000000000−2i−2i2i2i000000
χ234444-4-4-4-44-40000000002-22-2000000000000000000
χ244444-4-4-4-44-4000000000-22-22000000000000000000
χ254444-4-4-4-4-440000000002-2-22000000000000000000
χ264444-4-4-4-4-44000000000-222-2000000000000000000
χ2744-4-44-4-440000004-400000002i−2i2i−2i00000000000000
χ2844-4-44-4-440000004-40000000−2i2i−2i2i00000000000000
χ2944-4-44-4-44000000-4400000002i−2i−2i2i00000000000000
χ3044-4-44-4-44000000-440000000−2i2i2i−2i00000000000000
χ314-44-4-44-44004-40000000000000002i−2i2i−2i0000000000
χ324-44-4-44-44004-4000000000000000−2i2i−2i2i0000000000
χ334-44-4-44-4400-440000000000000002i−2i−2i2i0000000000
χ344-44-4-44-4400-44000000000000000−2i2i2i−2i0000000000
χ354-4-4444-4-400004i−4i000000000000000002ζ−2ζ2ζ3−2ζ3000000
χ364-4-4444-4-400004i−4i00000000000000000−2ζ2ζ−2ζ32ζ3000000
χ374-4-4444-4-40000−4i4i000000000000000002ζ3−2ζ32ζ−2ζ000000
χ384-4-4444-4-40000−4i4i00000000000000000−2ζ32ζ3−2ζ2ζ000000
χ3988-8-8-888-8000000000000000000000000000000000
χ408-88-88-88-8000000000000000000000000000000000
χ418-8-88-8-888000000000000000000000000000000000

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