Finite Group Databasebeta

← Group #401798

Character table — Group #401798

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222222222222222244444444444444444444888888888888888816161616161616161616161616161616
order12224444222222444444444444444444888888888888888822224444444444444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111
χ511111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-111-1-111-1-11111-1-1-1-1
χ611111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-111-1-111-1-1-1-11111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-11111-1-1-1-11111-1-1
χ911111111111111111-1-1-1-1-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111
χ1011111111111111111-1-1-1-1-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ1111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-111-1-1
χ1211111111111111111-1-1-1-1-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11111-1-111
χ1311111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-111111111-1-111-1-111-1-1-1-1
χ1411111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-11111-1-1-1-111-1-111-1-11111
χ1511111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-111
χ1611111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-111111111-1-1
χ17222222222-22-2-2-22-2-200000000-22-200002222-2-2-2-200000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ18222222222-22-2-2-22-2-200000000-22-200002222-2-2-2-20000000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ19222222222-22-2-2-22-2-200000000-22-20000-2-2-2-2222200000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ20222222222-22-2-2-22-2-200000000-22-20000-2-2-2-222220000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ2122222222-22-2-2-22-22222222222-2-2-2-2-2-2-200000000000000000000000000000000002i−2i000000002i−2i00
χ2222222222-22-2-2-22-22222222222-2-2-2-2-2-2-20000000000000000000000000000000000−2i2i00000000−2i2i00
χ2322222222-22-2-2-22-222-2-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000000000002i−2i00000000−2i2i00
χ2422222222-22-2-2-22-222-2-2-2-2-2-2-2-2-2-2-222220000000000000000000000000000000000−2i2i000000002i−2i00
χ252222-2-2-2-22-22-2-2-2-2222i2i2i2i−2i−2i−2i−2i2-222i2i−2i−2i000000000000000000000000000000002-20000002i−2i000000
χ262222-2-2-2-22-22-2-2-2-2222i2i2i2i−2i−2i−2i−2i2-222i2i−2i−2i00000000000000000000000000000000-22000000−2i2i000000
χ272222-2-2-2-22-22-2-2-2-222−2i−2i−2i−2i2i2i2i2i2-22−2i−2i2i2i000000000000000000000000000000002-2000000−2i2i000000
χ282222-2-2-2-22-22-2-2-2-222−2i−2i−2i−2i2i2i2i2i2-22−2i−2i2i2i00000000000000000000000000000000-220000002i−2i000000
χ292222-2-2-2-2-22-2-2-222-2-200000000222000022-2-222-2-2000000002222-2-2-2-2000000000000000000000000
χ302222-2-2-2-2-22-2-2-222-2-200000000222000022-2-222-2-200000000-2-2-2-22222000000000000000000000000
χ312222-2-2-2-2-22-2-2-222-2-2000000002220000-2-222-2-2220000000022-2-2-2-222000000000000000000000000
χ322222-2-2-2-2-22-2-2-222-2-2000000002220000-2-222-2-22200000000-2-22222-2-2000000000000000000000000
χ332222-2-2-2-2-2-2-222-22222i2i2i2i−2i−2i−2i−2i-22-2−2i−2i2i2i22-2-2-2-2222i2i2i2i−2i−2i−2i−2i00000000000000000000000000000000
χ342222-2-2-2-2-2-2-222-22222i2i2i2i−2i−2i−2i−2i-22-2−2i−2i2i2i-2-22222-2-2−2i−2i−2i−2i2i2i2i2i00000000000000000000000000000000
χ352222-2-2-2-2-2-2-222-2222−2i−2i−2i−2i2i2i2i2i-22-22i2i−2i−2i22-2-2-2-222−2i−2i−2i−2i2i2i2i2i00000000000000000000000000000000
χ362222-2-2-2-2-2-2-222-2222−2i−2i−2i−2i2i2i2i2i-22-22i2i−2i−2i-2-22222-2-22i2i2i2i−2i−2i−2i−2i00000000000000000000000000000000
χ372-2-2222-2-22-2-22-2222-222-2-222-2-22-2-22-22-2000000000000000000000000000000000000002i−2i0000002i−2i
χ382-2-2222-2-22-2-22-2222-222-2-222-2-22-2-22-22-200000000000000000000000000000000000000−2i2i000000−2i2i
χ392-2-2222-2-22-2-22-2222-2-2-222-2-2222-2-2-22-22000000000000000000000000000000000000002i−2i000000−2i2i
χ402-2-2222-2-22-2-22-2222-2-2-222-2-2222-2-2-22-2200000000000000000000000000000000000000−2i2i0000002i−2i
χ412-2-2222-2-2-2222-2-2-2-220000000022-20000000000002i2i−2i−2i2i2i−2i−2i002-2002-22i−2i2i−2i00000000000000000000
χ422-2-2222-2-2-2222-2-2-2-220000000022-20000000000002i2i−2i−2i2i2i−2i−2i00-2200-22−2i2i−2i2i00000000000000000000
χ432-2-2222-2-2-2222-2-2-2-220000000022-2000000000000−2i−2i2i2i−2i−2i2i2i002-2002-2−2i2i−2i2i00000000000000000000
χ442-2-2222-2-2-2222-2-2-2-220000000022-2000000000000−2i−2i2i2i−2i−2i2i2i00-2200-222i−2i2i−2i00000000000000000000
χ452-2-2222-2-2-2-22-222-22-222-2-222-2-2-222-22-2200000000000000002-2002-2002-2-2200000000000000000000
χ462-2-2222-2-2-2-22-222-22-222-2-222-2-2-222-22-220000000000000000-2200-2200-222-200000000000000000000
χ472-2-2222-2-2-2-22-222-22-2-2-222-2-222-2222-22-200000000000000002-2002-200-222-200000000000000000000
χ482-2-2222-2-2-2-22-222-22-2-2-222-2-222-2222-22-20000000000000000-2200-22002-2-2200000000000000000000
χ492-2-22-2-22222-2-22-2-22-22i2i−2i−2i−2i−2i2i2i22-22i−2i−2i2i0000000000000000002-200-2200002i−2i2i−2i0000000000000000
χ502-2-22-2-22222-2-22-2-22-22i2i−2i−2i−2i−2i2i2i22-22i−2i−2i2i000000000000000000-22002-20000−2i2i−2i2i0000000000000000
χ512-2-22-2-22222-2-22-2-22-2−2i−2i2i2i2i2i−2i−2i22-2−2i2i2i−2i0000000000000000002-200-220000−2i2i−2i2i0000000000000000
χ522-2-22-2-22222-2-22-2-22-2−2i−2i2i2i2i2i−2i−2i22-2−2i2i2i−2i000000000000000000-22002-200002i−2i2i−2i0000000000000000
χ532-2-22-2-2222-2-22-22-2-2200000000-22200000000000022-2-2-2-2222-200-220000002-2-220000000000000000
χ542-2-22-2-2222-2-22-22-2-2200000000-22200000000000022-2-2-2-222-22002-2000000-222-20000000000000000
χ552-2-22-2-2222-2-22-22-2-2200000000-222000000000000-2-22222-2-22-200-22000000-222-20000000000000000
χ562-2-22-2-2222-2-22-22-2-2200000000-222000000000000-2-22222-2-2-22002-20000002-2-220000000000000000
χ572-2-22-2-222-2222-2-222-22i2i−2i−2i−2i−2i2i2i-2-22−2i2i2i−2i0000000000000000000000000000000000002-200002i−2i0000
χ582-2-22-2-222-2222-2-222-22i2i−2i−2i−2i−2i2i2i-2-22−2i2i2i−2i000000000000000000000000000000000000-220000−2i2i0000
χ592-2-22-2-222-2222-2-222-2−2i−2i2i2i2i2i−2i−2i-2-222i−2i−2i2i0000000000000000000000000000000000002-20000−2i2i0000
χ602-2-22-2-222-2222-2-222-2−2i−2i2i2i2i2i−2i−2i-2-222i−2i−2i2i000000000000000000000000000000000000-2200002i−2i0000
χ6144444444-4-4-444-4-4-4-4000000004-440000000000000000000000000000000000000000000000000000
χ624444-4-4-4-4444444-4-4-400000000-4-4-40000000000000000000000000000000000000000000000000000
χ6344-4-44i−4i4i−4i0000000002+2i−2−2i2+2i−2−2i2−2i−2+2i2−2i−2+2i0000000000022−222i2−2i22ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ00000000000000000000000000000000
χ6444-4-44i−4i4i−4i0000000002+2i−2−2i2+2i−2−2i2−2i−2+2i2−2i−2+2i00000000000−2222−2i22i2−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ00000000000000000000000000000000
χ6544-4-44i−4i4i−4i000000000−2−2i2+2i−2−2i2+2i−2+2i2−2i−2+2i2−2i0000000000022−222i2−2i2−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ00000000000000000000000000000000
χ6644-4-44i−4i4i−4i000000000−2−2i2+2i−2−2i2+2i−2+2i2−2i−2+2i2−2i00000000000−2222−2i22i22ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ00000000000000000000000000000000
χ6744-4-4−4i4i−4i4i0000000002−2i−2+2i2−2i−2+2i2+2i−2−2i2+2i−2−2i0000000000022−22−2i22i2−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ300000000000000000000000000000000
χ6844-4-4−4i4i−4i4i0000000002−2i−2+2i2−2i−2+2i2+2i−2−2i2+2i−2−2i00000000000−22222i2−2i22ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ300000000000000000000000000000000
χ6944-4-4−4i4i−4i4i000000000−2+2i2−2i−2+2i2−2i−2−2i2+2i−2−2i2+2i0000000000022−22−2i22i22ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ300000000000000000000000000000000
χ7044-4-4−4i4i−4i4i000000000−2+2i2−2i−2+2i2−2i−2−2i2+2i−2−2i2+2i00000000000−22222i2−2i2−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ300000000000000000000000000000000
χ714-44-44i−4i−4i4i0000000002+2i−2−2i−2−2i2+2i2−2i−2+2i−2+2i2−2i000000022−222i2−2i200002ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ300000000000000000000000000000000
χ724-44-44i−4i−4i4i0000000002+2i−2−2i−2−2i2+2i2−2i−2+2i−2+2i2−2i0000000−2222−2i22i20000−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ300000000000000000000000000000000
χ734-44-44i−4i−4i4i000000000−2−2i2+2i2+2i−2−2i−2+2i2−2i2−2i−2+2i000000022−222i2−2i20000−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ300000000000000000000000000000000
χ744-44-44i−4i−4i4i000000000−2−2i2+2i2+2i−2−2i−2+2i2−2i2−2i−2+2i0000000−2222−2i22i200002ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ300000000000000000000000000000000
χ754-44-4−4i4i4i−4i0000000002−2i−2+2i−2+2i2−2i2+2i−2−2i−2−2i2+2i000000022−22−2i22i20000−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ00000000000000000000000000000000
χ764-44-4−4i4i4i−4i0000000002−2i−2+2i−2+2i2−2i2+2i−2−2i−2−2i2+2i0000000−22222i2−2i200002ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ00000000000000000000000000000000
χ774-44-4−4i4i4i−4i000000000−2+2i2−2i2−2i−2+2i−2−2i2+2i2+2i−2−2i000000022−22−2i22i200002ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ00000000000000000000000000000000
χ784-44-4−4i4i4i−4i000000000−2+2i2−2i2−2i−2+2i−2−2i2+2i2+2i−2−2i0000000−22222i2−2i20000−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ00000000000000000000000000000000
χ794-4-4444-4-444-4-44-44-4400000000-4-440000000000000000000000000000000000000000000000000000
χ804-4-44-4-444-4-44-4444-44000000004-4-40000000000000000000000000000000000000000000000000000

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