Finite Group Databasebeta

← Group #116289

Character table — Group #116289

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444488888888888888888888888888888888161616161616161616161616
order12224444222244444444444424444444444444444444448888888888888888244488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ5111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111
χ91111-1-1-1-111-1-1111111-1-1-1-1-1-1-111-1-11iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i1111-1-1-1-111-1-1ii−i−iii−i−i
χ101111-1-1-1-111-1-1111111-1-1-1-1-1-1-111-1-11iiii−i−i−i−i1111-1-1-1-1−i−i−i−iiiii-1-1-1-11111-1-111−i−iiiii−i−i
χ111111-1-1-1-111-1-1111111-1-1-1-1-1-1-111-1-11iiii−i−i−i−i-1-1-1-11111iiii−i−i−i−i1111-1-1-1-1-1-111−i−iii−i−iii
χ121111-1-1-1-111-1-1111111-1-1-1-1-1-1-111-1-11iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii-1-1-1-1111111-1-1ii−i−i−i−iii
χ131111-1-1-1-111-1-1111111-1-1-1-1-1-1-111-1-11−i−i−i−iiiii1111-1-1-1-1iiii−i−i−i−i-1-1-1-11111-1-111ii−i−i−i−iii
χ141111-1-1-1-111-1-1111111-1-1-1-1-1-1-111-1-11−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii1111-1-1-1-111-1-1−i−iii−i−iii
χ151111-1-1-1-111-1-1111111-1-1-1-1-1-1-111-1-11−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i-1-1-1-1111111-1-1−i−iiiii−i−i
χ161111-1-1-1-111-1-1111111-1-1-1-1-1-1-111-1-11−i−i−i−iiiii-1-1-1-11111−i−i−i−iiiii1111-1-1-1-1-1-111ii−i−iii−i−i
χ1722222222222222-2-2-2-222-2-2-2-222-2-2-2-20000000000000000000000000000000000002-22-20000
χ1822222222222222-2-2-2-222-2-2-2-222-2-2-2-2000000000000000000000000000000000000-22-220000
χ192222222222-2-2-2-22222222222-2-2-2-2-2-2000000000000000022-2-222-2-200000000000000000000
χ202222222222-2-2-2-22222222222-2-2-2-2-2-20000000000000000-2-222-2-22200000000000000000000
χ212222222222-2-2-2-2-2-2-2-222-2-2-2-2-2-222220000000022-2-222-2-20000000000000000000000000000
χ222222222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2222200000000-2-222-2-2220000000000000000000000000000
χ2322222222-2-2222222-2-2-2-222-2-2-2-2-22-2222-2-222-2-2000000000000000000000000000000000000
χ2422222222-2-2222222-2-2-2-222-2-2-2-2-22-22-2-222-2-222000000000000000000000000000000000000
χ2522222222-2-22222-2-222-2-2-2-222-2-22-22-2000000000000000000000000000000002-22-200000000
χ2622222222-2-22222-2-222-2-2-2-222-2-22-22-200000000000000000000000000000000-22-2200000000
χ2722222222-2-2-2-2-2-222-2-2-2-222-2-2222-22-20000000000000000000000002i2i−2i−2i2i2i−2i−2i000000000000
χ2822222222-2-2-2-2-2-222-2-2-2-222-2-2222-22-2000000000000000000000000−2i−2i2i2i−2i−2i2i2i000000000000
χ2922222222-2-2-2-2-2-2-2-222-2-2-2-22222-22-2200000000000000000000000000000000000000002-22-2
χ3022222222-2-2-2-2-2-2-2-222-2-2-2-22222-22-220000000000000000000000000000000000000000-22-22
χ312222-2-2-2-22222-2-22222-2-2-2-2-2-22-2-222-200000000000000002i2i−2i−2i−2i−2i2i2i00000000000000000000
χ322222-2-2-2-22222-2-22222-2-2-2-2-2-22-2-222-20000000000000000−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ332222-2-2-2-22222-2-2-2-2-2-2-2-222222-22-2-220000000022-2-2-2-2220000000000000000000000000000
χ342222-2-2-2-22222-2-2-2-2-2-2-2-222222-22-2-2200000000-2-22222-2-20000000000000000000000000000
χ352222-2-2-2-222-2-222-2-2-2-2-2-22222-22-222-20000000000000000000000000000000000002i−2i−2i2i0000
χ362222-2-2-2-222-2-222-2-2-2-2-2-22222-22-222-2000000000000000000000000000000000000−2i2i2i−2i0000
χ372222-2-2-2-2-2-222-2-222-2-222-2-222-2222-2-20000000000000000000000002i2i−2i−2i−2i−2i2i2i000000000000
χ382222-2-2-2-2-2-222-2-222-2-222-2-222-2222-2-2000000000000000000000000−2i−2i2i2i2i2i−2i−2i000000000000
χ392222-2-2-2-2-2-222-2-2-2-2222222-2-2-22-2-22200000000000000000000000000000000000000002i−2i−2i2i
χ402222-2-2-2-2-2-222-2-2-2-2222222-2-2-22-2-2220000000000000000000000000000000000000000−2i2i2i−2i
χ412222-2-2-2-2-2-2-2-22222-2-222-2-2222-2-2-2222i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000
χ422222-2-2-2-2-2-2-2-22222-2-222-2-2222-2-2-222−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000
χ432222-2-2-2-2-2-2-2-222-2-2222222-2-22-222-2-2000000000000000000000000000000002-2-2200000000
χ442222-2-2-2-2-2-2-2-222-2-2222222-2-22-222-2-200000000000000000000000000000000-222-200000000
χ4522-2-22i2i−2i−2i2-200002-22-22i−2i2i−2i2i−2i0000001+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000002ζ−2ζ002ζ3−2ζ32−22−2i2−i2i2−i2000000000000
χ4622-2-22i2i−2i−2i2-200002-22-22i−2i2i−2i2i−2i0000001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000−2ζ2ζ00−2ζ32ζ3−22−22−i2i2−i2i2000000000000
χ4722-2-22i2i−2i−2i2-200002-22-22i−2i2i−2i2i−2i000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000002ζ−2ζ002ζ3−2ζ3−22−22−i2i2−i2i2000000000000
χ4822-2-22i2i−2i−2i2-200002-22-22i−2i2i−2i2i−2i000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000−2ζ2ζ00−2ζ32ζ32−22−2i2−i2i2−i2000000000000
χ4922-2-22i2i−2i−2i-2200002-2-22−2i2i2i−2i−2i2i0000001+i−1−i−1−i1+i1−i−1+i−1+i1−i000000002ζ3−2ζ3002ζ−2ζ00i2−i2−i2i2−222−2000000000000
χ5022-2-22i2i−2i−2i-2200002-2-22−2i2i2i−2i−2i2i0000001+i−1−i−1−i1+i1−i−1+i−1+i1−i00000000−2ζ32ζ300−2ζ2ζ00−i2i2i2−i22−2−22000000000000
χ5122-2-22i2i−2i−2i-2200002-2-22−2i2i2i−2i−2i2i000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i000000002ζ3−2ζ3002ζ−2ζ00−i2i2i2−i22−2−22000000000000
χ5222-2-22i2i−2i−2i-2200002-2-22−2i2i2i−2i−2i2i000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i00000000−2ζ32ζ300−2ζ2ζ00i2−i2−i2i2−222−2000000000000
χ5322-2-2−2i−2i2i2i2-200002-22-2−2i2i−2i2i−2i2i0000001−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000002ζ3−2ζ3002ζ−2ζ−22−22i2−i2i2−i2000000000000
χ5422-2-2−2i−2i2i2i2-200002-22-2−2i2i−2i2i−2i2i0000001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000−2ζ32ζ300−2ζ2ζ2−22−2−i2i2−i2i2000000000000
χ5522-2-2−2i−2i2i2i2-200002-22-2−2i2i−2i2i−2i2i000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000002ζ3−2ζ3002ζ−2ζ2−22−2−i2i2−i2i2000000000000
χ5622-2-2−2i−2i2i2i2-200002-22-2−2i2i−2i2i−2i2i000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000−2ζ32ζ300−2ζ2ζ−22−22i2−i2i2−i2000000000000
χ5722-2-2−2i−2i2i2i-2200002-2-222i−2i−2i2i2i−2i0000001−i−1+i−1+i1−i1+i−1−i−1−i1+i000000002ζ−2ζ002ζ3−2ζ300i2−i2−i2i22−2−22000000000000
χ5822-2-2−2i−2i2i2i-2200002-2-222i−2i−2i2i2i−2i0000001−i−1+i−1+i1−i1+i−1−i−1−i1+i00000000−2ζ2ζ00−2ζ32ζ300−i2i2i2−i2−222−2000000000000
χ5922-2-2−2i−2i2i2i-2200002-2-222i−2i−2i2i2i−2i000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i000000002ζ−2ζ002ζ3−2ζ300−i2i2i2−i2−222−2000000000000
χ6022-2-2−2i−2i2i2i-2200002-2-222i−2i−2i2i2i−2i000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i00000000−2ζ2ζ00−2ζ32ζ300i2−i2−i2i22−2−22000000000000
χ6144-4-44i4i−4i−4i4-40000-44-444i−4i−4i4i−4i4i00000000000000000000000000000000000000000000000000
χ6244-4-44i4i−4i−4i-440000-444-4−4i4i−4i4i4i−4i00000000000000000000000000000000000000000000000000
χ6344-4-4−4i−4i4i4i4-40000-44-44−4i4i4i−4i4i−4i00000000000000000000000000000000000000000000000000
χ6444-4-4−4i−4i4i4i-440000-444-44i−4i4i−4i−4i4i00000000000000000000000000000000000000000000000000
χ654-44-44-44-4004-44-40000000000000000000000002i−2i2i−2i2i−2i2i−2i0000000000000000000000000000
χ664-44-44-44-4004-44-4000000000000000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000
χ674-44-44-44-400-44-440000000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000000000000000
χ684-44-44-44-400-44-44000000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000
χ694-44-4-44-44004-4-440000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000000000000000
χ704-44-4-44-44004-4-44000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000000000000000
χ714-44-4-44-4400-444-40000000000000000000000002i−2i2i−2i−2i2i−2i2i0000000000000000000000000000
χ724-44-4-44-4400-444-4000000000000000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000
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.