Finite Group Databasebeta

← Group #400435

Character table — Group #400435

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222444444444444888888888888888888888888888888161616161616161616161616
order12224444222222444444444444448888222244444444444444448888888888448888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111111111-1-1
χ51111111111111111111111111111-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ71111111111111111111111111111-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1
χ81111111111111111111111111111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111
χ911111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-111-1-1-1-1
χ1011111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-11111
χ1111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-111-1-1-1-111-1-111-1-1
χ1211111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-111
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-1-1-11111
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-111-1-11111-1-1-1-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-111
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-111-1-1
χ17222222222-2-2-2-222-2-2-2-222222-2-2-2-2222200000000000000000000000022-2-2-2-2000000000000
χ18222222222-2-2-2-222-2-2-2-222222-2-2-2-2-2-2-2-2000000000000000000000000-2-22222000000000000
χ19222222222-2-2-2-222-2-2-2-22-2-2-2-222222222000000000000000000000000-2-222-2-2000000000000
χ20222222222-2-2-2-222-2-2-2-22-2-2-2-22222-2-2-2-200000000000000000000000022-2-222000000000000
χ212222-2-2-2-2222222-2-2-2-2-2-222-2-222-2-20000000000000000000000002i2i−2i−2i00000000000000002i−2i
χ222222-2-2-2-2222222-2-2-2-2-2-222-2-222-2-2000000000000000000000000−2i−2i2i2i0000000000000000−2i2i
χ232222-2-2-2-2222222-2-2-2-2-2-2-2-222-2-2220000000000000000000000002i2i−2i−2i0000000000000000−2i2i
χ242222-2-2-2-2222222-2-2-2-2-2-2-2-222-2-222000000000000000000000000−2i−2i2i2i00000000000000002i−2i
χ252222-2-2-2-22-2-2-2-22-22222-222-2-2-2-2220000000000000000000022-2-200000000002-20000000000
χ262222-2-2-2-22-2-2-2-22-22222-222-2-2-2-22200000000000000000000-2-2220000000000-220000000000
χ272222-2-2-2-22-2-2-2-22-22222-2-2-22222-2-20000000000000000000022-2-20000000000-220000000000
χ282222-2-2-2-22-2-2-2-22-22222-2-2-22222-2-200000000000000000000-2-22200000000002-20000000000
χ292222-2-2-2-2-222-2-2-2222-2-220000000022-2-20000000022-2-222-2-20000000000002-2000000000000
χ302222-2-2-2-2-222-2-2-2222-2-220000000022-2-200000000-2-222-2-2220000000000002-2000000000000
χ312222-2-2-2-2-222-2-2-2222-2-2200000000-2-2220000000022-2-2-2-222000000000000-22000000000000
χ322222-2-2-2-2-222-2-2-2222-2-2200000000-2-22200000000-2-22222-2-2000000000000-22000000000000
χ332222-2-2-2-2-2-2-222-22-2-22220000000022-2-22222-2-2-2-200000000000000000000-22000000000000
χ342222-2-2-2-2-2-2-222-22-2-22220000000022-2-2-2-2-2-2222200000000000000000000-22000000000000
χ352222-2-2-2-2-2-2-222-22-2-222200000000-2-22222-2-2-2-222000000000000000000002-2000000000000
χ362222-2-2-2-2-2-2-222-22-2-222200000000-2-222-2-22222-2-2000000000000000000002-2000000000000
χ3722-2-222-2-2-22-22-22-22-22-222i−2i2i−2i2i−2i2i−2i0000002-2002-200002i−2i2i−2i00000000000000000000000000
χ3822-2-222-2-2-22-22-22-22-22-222i−2i2i−2i2i−2i2i−2i000000-2200-220000−2i2i−2i2i00000000000000000000000000
χ3922-2-222-2-2-22-22-22-22-22-22−2i2i−2i2i−2i2i−2i2i0000002-2002-20000−2i2i−2i2i00000000000000000000000000
χ4022-2-222-2-2-22-22-22-22-22-22−2i2i−2i2i−2i2i−2i2i000000-2200-2200002i−2i2i−2i00000000000000000000000000
χ4122-2-222-2-2-2-22-222-2-22-2222i−2i2i−2i−2i2i−2i2i00002-2002-2002i−2i2i−2i000000000000000000000000000000
χ4222-2-222-2-2-2-22-222-2-22-2222i−2i2i−2i−2i2i−2i2i0000-2200-2200−2i2i−2i2i000000000000000000000000000000
χ4322-2-222-2-2-2-22-222-2-22-222−2i2i−2i2i2i−2i2i−2i00002-2002-200−2i2i−2i2i000000000000000000000000000000
χ4422-2-222-2-2-2-22-222-2-22-222−2i2i−2i2i2i−2i2i−2i0000-2200-22002i−2i2i−2i000000000000000000000000000000
χ4522-2-2-2-22222-2-22-2-22-2-2220000000000002-200-220000002i−2i−2i2i000000002i−2i2i−2i00000000000000
χ4622-2-2-2-22222-2-22-2-22-2-2220000000000002-200-22000000−2i2i2i−2i00000000−2i2i−2i2i00000000000000
χ4722-2-2-2-22222-2-22-2-22-2-222000000000000-22002-20000002i−2i−2i2i00000000−2i2i−2i2i00000000000000
χ4822-2-2-2-22222-2-22-2-22-2-222000000000000-22002-2000000−2i2i2i−2i000000002i−2i2i−2i00000000000000
χ4922-2-2-2-2222-222-2-2-2-222-22000000000000002-200-222i−2i−2i2i0000000000002i−2i−2i2i00000000000000
χ5022-2-2-2-2222-222-2-2-2-222-22000000000000002-200-22−2i2i2i−2i000000000000−2i2i2i−2i00000000000000
χ5122-2-2-2-2222-222-2-2-2-222-2200000000000000-22002-22i−2i−2i2i000000000000−2i2i2i−2i00000000000000
χ5222-2-2-2-2222-222-2-2-2-222-2200000000000000-22002-2−2i2i2i−2i0000000000002i−2i−2i2i00000000000000
χ5322-2-2-2-222-22-22-222-22-22-22i−2i−2i2i2i−2i−2i2i0000000000000000000000000000000000002-22i−2i000000
χ5422-2-2-2-222-22-22-222-22-22-22i−2i−2i2i2i−2i−2i2i000000000000000000000000000000000000-22−2i2i000000
χ5522-2-2-2-222-22-22-222-22-22-2−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000000000002-2−2i2i000000
χ5622-2-2-2-222-22-22-222-22-22-2−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000000000-222i−2i000000
χ5722-2-2-2-222-2-22-22222-22-2-22i−2i−2i2i−2i2i2i−2i00000000000000000000000000000000000000002-22i−2i00
χ5822-2-2-2-222-2-22-22222-22-2-22i−2i−2i2i−2i2i2i−2i0000000000000000000000000000000000000000-22−2i2i00
χ5922-2-2-2-222-2-22-22222-22-2-2−2i2i2i−2i2i−2i−2i2i00000000000000000000000000000000000000002-2−2i2i00
χ6022-2-2-2-222-2-22-22222-22-2-2−2i2i2i−2i2i−2i−2i2i0000000000000000000000000000000000000000-222i−2i00
χ6144444444-444-4-4-4-4-4-444-4000000000000000000000000000000000000000000000000000000
χ6244444444-4-4-444-4-444-4-4-4000000000000000000000000000000000000000000000000000000
χ6344-4-444-4-444-4-44-44-444-4-4000000000000000000000000000000000000000000000000000000
χ6444-4-444-4-44-444-4-444-4-44-4000000000000000000000000000000000000000000000000000000
χ654-44-44i−4i4i−4i0000000000000000000022−222i2−2i200000000000000002-22i−2i2ζ−2ζ2ζ3−2ζ3000000000000000000
χ664-44-44i−4i4i−4i0000000000000000000022−222i2−2i20000000000000000-22−2i2i−2ζ2ζ−2ζ32ζ3000000000000000000
χ674-44-44i−4i4i−4i00000000000000000000−2222−2i22i200000000000000002-22i−2i−2ζ2ζ−2ζ32ζ3000000000000000000
χ684-44-44i−4i4i−4i00000000000000000000−2222−2i22i20000000000000000-22−2i2i2ζ−2ζ2ζ3−2ζ3000000000000000000
χ694-44-4−4i4i−4i4i0000000000000000000022−22−2i22i200000000000000002-2−2i2i−2ζ32ζ3−2ζ2ζ000000000000000000
χ704-44-4−4i4i−4i4i0000000000000000000022−22−2i22i20000000000000000-222i−2i2ζ3−2ζ32ζ−2ζ000000000000000000
χ714-44-4−4i4i−4i4i00000000000000000000−22222i2−2i200000000000000002-2−2i2i2ζ3−2ζ32ζ−2ζ000000000000000000
χ724-44-4−4i4i−4i4i00000000000000000000−22222i2−2i20000000000000000-222i−2i−2ζ32ζ3−2ζ2ζ000000000000000000
χ738-8-888i−8i−8i8i000000000000000000000000000000000000000000000000000000000000000000
χ748-8-88−8i8i8i−8i000000000000000000000000000000000000000000000000000000000000000000

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