Finite Group Databasebeta

← Group #415610

Character table — Group #415610

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222444444444444888888888888888888888888888888161616161616161616161616
order12224444222222444444888888888888222244444444444488888888888888444444888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-11111
χ51111111111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1
χ61111111111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-111-1-1-1-111
χ71111111111111111111111111111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-111
χ81111111111111111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-111-1-1
χ911111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111
χ1011111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1
χ1111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-11111-1-1-1-1-1-1
χ1211111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1111111
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-111-1-1
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-111
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111-1-1
χ1722222222-2-22-2-222-2-22-2-22222-2-2-2-222220000000022-2-20000000000000000-2-2000000000000
χ1822222222-2-22-2-222-2-22-2-22222-2-2-2-2-2-2-2-200000000-2-222000000000000000022000000000000
χ1922222222-2-22-2-222-2-22-2-2-2-2-2-22222222200000000-2-2220000000000000000-2-2000000000000
χ2022222222-2-22-2-222-2-22-2-2-2-2-2-22222-2-2-2-20000000022-2-2000000000000000022000000000000
χ212222-2-2-2-2222222-2-2-2-2-2-22i2i−2i−2i2i2i−2i−2i000000000000000000002i2i−2i−2i00000000002-20000000000
χ222222-2-2-2-2222222-2-2-2-2-2-22i2i−2i−2i2i2i−2i−2i00000000000000000000−2i−2i2i2i0000000000-220000000000
χ232222-2-2-2-2222222-2-2-2-2-2-2−2i−2i2i2i−2i−2i2i2i000000000000000000002i2i−2i−2i0000000000-220000000000
χ242222-2-2-2-2222222-2-2-2-2-2-2−2i−2i2i2i−2i−2i2i2i00000000000000000000−2i−2i2i2i00000000002-20000000000
χ252222-2-2-2-222-2-2-2-22222-2-20000000022-2-22222-2-2-2-2000000000000000000002-2000000000000
χ262222-2-2-2-222-2-2-2-22222-2-20000000022-2-2-2-2-2-22222000000000000000000002-2000000000000
χ272222-2-2-2-222-2-2-2-22222-2-200000000-2-22222-2-2-2-22200000000000000000000-22000000000000
χ282222-2-2-2-222-2-2-2-22222-2-200000000-2-222-2-22222-2-200000000000000000000-22000000000000
χ292222-2-2-2-2-2-22-2-22-222-2222i2i−2i−2i−2i−2i2i2i000000000000000022-2-2000000000000000000002i−2i0000
χ302222-2-2-2-2-2-22-2-22-222-2222i2i−2i−2i−2i−2i2i2i0000000000000000-2-22200000000000000000000−2i2i0000
χ312222-2-2-2-2-2-22-2-22-222-222−2i−2i2i2i2i2i−2i−2i000000000000000022-2-200000000000000000000−2i2i0000
χ322222-2-2-2-2-2-22-2-22-222-222−2i−2i2i2i2i2i−2i−2i0000000000000000-2-222000000000000000000002i−2i0000
χ332222-2-2-2-2-2-2-222-22-2-22220000000022-2-2000000000000000000002i2i−2i−2i2i2i−2i−2i-22000000000000
χ342222-2-2-2-2-2-2-222-22-2-22220000000022-2-200000000000000000000−2i−2i2i2i−2i−2i2i2i-22000000000000
χ352222-2-2-2-2-2-2-222-22-2-222200000000-2-222000000000000000000002i2i−2i−2i−2i−2i2i2i2-2000000000000
χ362222-2-2-2-2-2-2-222-22-2-222200000000-2-22200000000000000000000−2i−2i2i2i2i2i−2i−2i2-2000000000000
χ372-2-2222-2-22-222-2-2-22-222-2000000000000002-2002-22i−2i2i−2i000000002i−2i2i−2i000000000000000000
χ382-2-2222-2-22-222-2-2-22-222-2000000000000002-2002-2−2i2i−2i2i00000000−2i2i−2i2i000000000000000000
χ392-2-2222-2-22-222-2-2-22-222-200000000000000-2200-222i−2i2i−2i00000000−2i2i−2i2i000000000000000000
χ402-2-2222-2-22-222-2-2-22-222-200000000000000-2200-22−2i2i−2i2i000000002i−2i2i−2i000000000000000000
χ412-2-2222-2-22-2-2-2222-22-22-22i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000002i−2i00002-200
χ422-2-2222-2-22-2-2-2222-22-22-22i−2i2i−2i2i−2i2i−2i000000000000000000000000000000000000−2i2i0000-2200
χ432-2-2222-2-22-2-2-2222-22-22-2−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000000002i−2i0000-2200
χ442-2-2222-2-22-2-2-2222-22-22-2−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000000000−2i2i00002-200
χ452-2-2222-2-2-222-22-2-2-222-220000000000002-2002-2002i−2i−2i2i0000000000002i−2i2i−2i00000000000000
χ462-2-2222-2-2-222-22-2-2-222-220000000000002-2002-200−2i2i2i−2i000000000000−2i2i−2i2i00000000000000
χ472-2-2222-2-2-222-22-2-2-222-22000000000000-2200-22002i−2i−2i2i000000000000−2i2i−2i2i00000000000000
χ482-2-2222-2-2-222-22-2-2-222-22000000000000-2200-2200−2i2i2i−2i0000000000002i−2i2i−2i00000000000000
χ492-2-2222-2-2-22-22-2222-2-2-222i−2i2i−2i−2i2i−2i2i000000000000000000000000000000000000002i−2i00002-2
χ502-2-2222-2-2-22-22-2222-2-2-222i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000000000−2i2i0000-22
χ512-2-2222-2-2-22-22-2222-2-2-22−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000000000002i−2i0000-22
χ522-2-2222-2-2-22-22-2222-2-2-22−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000000000−2i2i00002-2
χ532-2-22-2-2222-2-2-222-22-22-222-2-222-2-220000002-200-2200000000000000002-2-2200000000000000
χ542-2-22-2-2222-2-2-222-22-22-222-2-222-2-22000000-22002-20000000000000000-222-200000000000000
χ552-2-22-2-2222-2-2-222-22-22-22-222-2-222-20000002-200-220000000000000000-222-200000000000000
χ562-2-22-2-2222-2-2-222-22-22-22-222-2-222-2000000-22002-200000000000000002-2-2200000000000000
χ572-2-22-2-222-22-22-22-2-2222-22-2-22-222-200002-200-22000000000000002-2-22000000000000000000
χ582-2-22-2-222-22-22-22-2-2222-22-2-22-222-20000-22002-200000000000000-222-2000000000000000000
χ592-2-22-2-222-22-22-22-2-2222-2-222-22-2-2200002-200-2200000000000000-222-2000000000000000000
χ602-2-22-2-222-22-22-22-2-2222-2-222-22-2-220000-22002-2000000000000002-2-22000000000000000000
χ614444444444-4-4-4-4-4-4-4-444000000000000000000000000000000000000000000000000000000
χ6244444444-4-4-444-4-444-4-4-4000000000000000000000000000000000000000000000000000000
χ6344-4-44i−4i4i−4i0000000000000000000022−222i2−2i20000000000002-22i−2i2ζ−2ζ2ζ3−2ζ30000000000000000000000
χ6444-4-44i−4i4i−4i0000000000000000000022−222i2−2i2000000000000-22−2i2i−2ζ2ζ−2ζ32ζ30000000000000000000000
χ6544-4-44i−4i4i−4i00000000000000000000−2222−2i22i20000000000002-22i−2i−2ζ2ζ−2ζ32ζ30000000000000000000000
χ6644-4-44i−4i4i−4i00000000000000000000−2222−2i22i2000000000000-22−2i2i2ζ−2ζ2ζ3−2ζ30000000000000000000000
χ6744-4-4−4i4i−4i4i0000000000000000000022−22−2i22i20000000000002-2−2i2i−2ζ32ζ3−2ζ2ζ0000000000000000000000
χ6844-4-4−4i4i−4i4i0000000000000000000022−22−2i22i2000000000000-222i−2i2ζ3−2ζ32ζ−2ζ0000000000000000000000
χ6944-4-4−4i4i−4i4i00000000000000000000−22222i2−2i20000000000002-2−2i2i2ζ3−2ζ32ζ−2ζ0000000000000000000000
χ7044-4-4−4i4i−4i4i00000000000000000000−22222i2−2i2000000000000-222i−2i−2ζ32ζ3−2ζ2ζ0000000000000000000000
χ714-4-44-4-4444-444-4-44-44-4-44000000000000000000000000000000000000000000000000000000
χ724-4-44-4-444-444-44-444-4-44-4000000000000000000000000000000000000000000000000000000
χ738-88-88i−8i−8i8i000000000000000000000000000000000000000000000000000000000000000000
χ748-88-8−8i8i8i−8i000000000000000000000000000000000000000000000000000000000000000000

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