Finite Group Databasebeta

← Group #117720

Character table — Group #117720

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444488888888888888888888888888888888161616161616161616161616
order12224444224444444444444422444488888888888888888888888888888888444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ5111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ91111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1111-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i11-1-1ii−i−i11-1-1
χ101111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1111-11111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-1-111ii−i−i-1-111
χ111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1111-11111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i-1-111−i−iii-1-111
χ121111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1111-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii11-1-1−i−iii11-1-1
χ131111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1111-1-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii11-1-1−i−iii-1-111
χ141111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1111-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-111−i−iii11-1-1
χ151111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1111-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii-1-111ii−i−i11-1-1
χ161111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1111-1-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i11-1-1ii−i−i-1-111
χ17222222222222-2-2-2-222-2-2-2-222-2-2-2-222000000000000000000000000000000002-22-200000000
χ18222222222222-2-2-2-222-2-2-2-222-2-2-2-22200000000000000000000000000000000-22-2200000000
χ192222222222-2-22222222222-2-2-2-2-2-2-2-222-2-222-2-2000000000000000000000000000000000000
χ202222222222-2-22222222222-2-2-2-2-2-2-2-2-2-222-2-222000000000000000000000000000000000000
χ212222222222-2-2-2-2-2-222-2-2-2-2-2-22222-2-200000000000000000000000000000000000000002i−2i2i−2i
χ222222222222-2-2-2-2-2-222-2-2-2-2-2-22222-2-20000000000000000000000000000000000000000−2i2i−2i2i
χ2322222222-2-22222-2-2-2-222-2-2222-22-2-2-200000000000000000000000022-2-222-2-2000000000000
χ2422222222-2-22222-2-2-2-222-2-2222-22-2-2-2000000000000000000000000-2-222-2-222000000000000
χ2522222222-2-222-2-222-2-2-2-22222-22-22-2-20000000000000000000000000000000000002-22-20000
χ2622222222-2-222-2-222-2-2-2-22222-22-22-2-2000000000000000000000000000000000000-22-220000
χ2722222222-2-2-2-222-2-2-2-222-2-2-2-2-22-222200000000000000002i2i−2i−2i2i2i−2i−2i00000000000000000000
χ2822222222-2-2-2-222-2-2-2-222-2-2-2-2-22-22220000000000000000−2i−2i2i2i−2i−2i2i2i00000000000000000000
χ2922222222-2-2-2-2-2-222-2-2-2-222-2-22-22-222000000002i2i−2i−2i2i2i−2i−2i0000000000000000000000000000
χ3022222222-2-2-2-2-2-222-2-2-2-222-2-22-22-22200000000−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000
χ312222-2-2-2-222222222-2-2-2-2-2-2-2-222-2-22-2000000000000000000000000000000002-2-2200000000
χ322222-2-2-2-222222222-2-2-2-2-2-2-2-222-2-22-200000000000000000000000000000000-222-200000000
χ332222-2-2-2-222-2-22222-2-2-2-2-2-222-2-222-2200000000000000000000000000000000000000002i−2i−2i2i
χ342222-2-2-2-222-2-22222-2-2-2-2-2-222-2-222-220000000000000000000000000000000000000000−2i2i2i−2i
χ352222-2-2-2-222-2-2-2-2-2-2-2-222222222-2-2-2222-2-2-2-222000000000000000000000000000000000000
χ362222-2-2-2-222-2-2-2-2-2-2-2-222222222-2-2-22-2-22222-2-2000000000000000000000000000000000000
χ372222-2-2-2-2-2-22222-2-222-2-222-2-22-2-22-220000000000000000000000000000000000002i−2i−2i2i0000
χ382222-2-2-2-2-2-22222-2-222-2-222-2-22-2-22-22000000000000000000000000000000000000−2i2i2i−2i0000
χ392222-2-2-2-2-2-222-2-2222222-2-2-2-2-222-2-220000000000000000000000002i2i−2i−2i−2i−2i2i2i000000000000
χ402222-2-2-2-2-2-222-2-2222222-2-2-2-2-222-2-22000000000000000000000000−2i−2i2i2i2i2i−2i−2i000000000000
χ412222-2-2-2-2-2-2-2-222-2-222-2-22222-222-22-20000000022-2-2-2-2220000000000000000000000000000
χ422222-2-2-2-2-2-2-2-222-2-222-2-22222-222-22-200000000-2-22222-2-20000000000000000000000000000
χ432222-2-2-2-2-2-2-2-2-2-2222222-2-2222-2-222-2000000000000000022-2-2-2-22200000000000000000000
χ442222-2-2-2-2-2-2-2-2-2-2222222-2-2222-2-222-20000000000000000-2-22222-2-200000000000000000000
χ452-22-22i2i−2i−2i2-2002i−2i2i−2i2i−2i2-22-200000000002i−2i002-2000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000
χ462-22-22i2i−2i−2i2-2002i−2i2i−2i2i−2i2-22-200000000002i−2i002-200000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000
χ472-22-22i2i−2i−2i2-2002i−2i2i−2i2i−2i2-22-20000000000−2i2i00-22000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000
χ482-22-22i2i−2i−2i2-2002i−2i2i−2i2i−2i2-22-20000000000−2i2i00-2200000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000
χ492-22-22i2i−2i−2i-22002i−2i−2i2i−2i2i2-2-22000000002-2002i−2i00000000001−i−1+i−1+i1−i−1−i1+i1+i−1−i1−i−1+i−1+i1−i1+i−1−i−1−i1+i000000000000
χ502-22-22i2i−2i−2i-22002i−2i−2i2i−2i2i2-2-22000000002-2002i−2i0000000000−1+i1−i1−i−1+i1+i−1−i−1−i1+i−1+i1−i1−i−1+i−1−i1+i1+i−1−i000000000000
χ512-22-22i2i−2i−2i-22002i−2i−2i2i−2i2i2-2-2200000000-2200−2i2i00000000001−i−1+i−1+i1−i−1−i1+i1+i−1−i−1+i1−i1−i−1+i−1−i1+i1+i−1−i000000000000
χ522-22-22i2i−2i−2i-22002i−2i−2i2i−2i2i2-2-2200000000-2200−2i2i0000000000−1+i1−i1−i−1+i1+i−1−i−1−i1+i1−i−1+i−1+i1−i1+i−1−i−1−i1+i000000000000
χ532-22-2−2i−2i2i2i2-200−2i2i−2i2i−2i2i2-22-200000000002i−2i00-22000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000
χ542-22-2−2i−2i2i2i2-200−2i2i−2i2i−2i2i2-22-200000000002i−2i00-2200000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000
χ552-22-2−2i−2i2i2i2-200−2i2i−2i2i−2i2i2-22-20000000000−2i2i002-2000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000
χ562-22-2−2i−2i2i2i2-200−2i2i−2i2i−2i2i2-22-20000000000−2i2i002-200000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000
χ572-22-2−2i−2i2i2i-2200−2i2i2i−2i2i−2i2-2-22000000002-200−2i2i00000000001+i−1−i−1−i1+i−1+i1−i1−i−1+i1+i−1−i−1−i1+i1−i−1+i−1+i1−i000000000000
χ582-22-2−2i−2i2i2i-2200−2i2i2i−2i2i−2i2-2-22000000002-200−2i2i0000000000−1−i1+i1+i−1−i1−i−1+i−1+i1−i−1−i1+i1+i−1−i−1+i1−i1−i−1+i000000000000
χ592-22-2−2i−2i2i2i-2200−2i2i2i−2i2i−2i2-2-2200000000-22002i−2i00000000001+i−1−i−1−i1+i−1+i1−i1−i−1+i−1−i1+i1+i−1−i−1+i1−i1−i−1+i000000000000
χ602-22-2−2i−2i2i2i-2200−2i2i2i−2i2i−2i2-2-2200000000-22002i−2i0000000000−1−i1+i1+i−1−i1−i−1+i−1+i1−i1+i−1−i−1−i1+i1−i−1+i−1+i1−i000000000000
χ614-44-44i4i−4i−4i4-400−4i4i−4i4i4i−4i-44-440000000000000000000000000000000000000000000000000000
χ624-44-44i4i−4i−4i-4400−4i4i4i−4i−4i4i-444-40000000000000000000000000000000000000000000000000000
χ634-44-4−4i−4i4i4i4-4004i−4i4i−4i−4i4i-44-440000000000000000000000000000000000000000000000000000
χ644-44-4−4i−4i4i4i-44004i−4i−4i4i4i−4i-444-40000000000000000000000000000000000000000000000000000
χ654-4-444i−4i4i−4i004-400000000004i−4i000000000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ30000000000000000000000000000
χ664-4-444i−4i4i−4i004-400000000004i−4i00000000000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ30000000000000000000000000000
χ674-4-444i−4i4i−4i00-440000000000−4i4i000000000000002ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ0000000000000000000000000000
χ684-4-444i−4i4i−4i00-440000000000−4i4i00000000000000−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ0000000000000000000000000000
χ694-4-44−4i4i−4i4i004-40000000000−4i4i000000000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ0000000000000000000000000000
χ704-4-44−4i4i−4i4i004-40000000000−4i4i00000000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ0000000000000000000000000000
χ714-4-44−4i4i−4i4i00-4400000000004i−4i000000000000002ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ30000000000000000000000000000
χ724-4-44−4i4i−4i4i00-4400000000004i−4i00000000000000−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ30000000000000000000000000000
χ7388-8-88-8-88000000000000000000000000000000000000000000000000000000000000000000
χ7488-8-8-888-8000000000000000000000000000000000000000000000000000000000000000000

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