Finite Group Databasebeta

← Group #141325

Character table — Group #141325

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11112222222222222222222222444444444444444444448888888888888888161616161616161632323232
order1222444444444488888888888824888888888888888888888888888888888816161616161616164444
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ611111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ711111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ811111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ91111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-111111-1-111-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i1-11-1
χ101111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-111111-1-111-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii-11-11
χ111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-111111-1-111-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i-11-11
χ121111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-111111-1-111-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii1-11-1
χ131111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-111111-1-1-1-111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii1-1-11
χ141111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-111111-1-1-1-111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i-111-1
χ151111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-111111-1-1-1-111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii-111-1
χ161111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-111111-1-1-1-111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i1-1-11
χ172222222222222222222222-2-2-2-222-2-2-2-2-2-22222-2-2-2-2-2-2-2-20000000000000000000000000000
χ1822222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-2-2-2222222220000000000000000000000000000
χ1922222222-2-2-2-2-2-22222-2-2-2-200002-2000000-2-222000000000000000000000000i2−i2i2−i2i2−i2i2−i20000
χ2022222222-2-2-2-2-2-22222-2-2-2-200002-2000000-2-222000000000000000000000000−i2i2−i2i2−i2i2−i2i20000
χ2122222222-2-2-2-2-2-2-2-2-2-2222200002-200000022-2-2000000000000000000000000i2−i2i2−i2−i2i2−i2i20000
χ2222222222-2-2-2-2-2-2-2-2-2-2222200002-200000022-2-2000000000000000000000000−i2i2−i2i2i2−i2i2−i20000
χ23222222-2-22222-2-2000000002222-2-222-2-2-2-20000000000000000000022-2-222-2-2000000000000
χ24222222-2-22222-2-2000000002222-2-222-2-2-2-200000000000000000000-2-222-2-222000000000000
χ25222222-2-22222-2-200000000-2-2-2-2-2-2-2-222220000000000002i2i−2i−2i2i2i−2i−2i00000000000000000000
χ26222222-2-22222-2-200000000-2-2-2-2-2-2-2-22222000000000000−2i−2i2i2i−2i−2i2i2i00000000000000000000
χ272222-2-22222-2-2-2-22222-2-2-2-22222-22-2-2-2-22222-2-2-2-2-2-222220000000000000000000000000000
χ282222-2-22222-2-2-2-2-2-2-2-222222222-22-2-2-2-222-2-2222222-2-2-2-20000000000000000000000000000
χ292222-2-222-2-22222222222220000-2-2000000-2-2-2-20000000000000000000000002−2−222−2−220000
χ302222-2-222-2-22222222222220000-2-2000000-2-2-2-2000000000000000000000000−222−2−222−20000
χ312222-2-222-2-22222-2-2-2-2-2-2-2-20000-2-200000022220000000000000000000000002−2−22−222−20000
χ322222-2-222-2-22222-2-2-2-2-2-2-2-20000-2-20000002222000000000000000000000000−222−22−2−220000
χ332222-2-2-2-222-2-2220000000022222-2-2-222-2-200000000000022-2-2-2-22200000000000000000000
χ342222-2-2-2-222-2-2220000000022222-2-2-222-2-2000000000000-2-22222-2-200000000000000000000
χ352222-2-2-2-222-2-22200000000-2-2-2-22-222-2-222000000000000000000002i2i−2i−2i−2i−2i2i2i000000000000
χ362222-2-2-2-222-2-22200000000-2-2-2-22-222-2-22200000000000000000000−2i−2i2i2i2i2i−2i−2i000000000000
χ372-22-22i−2i002-22i−2i00i2i2−i2−i222−2−22i2i−2i−2i002-20000i2−i22−2i2i2−i2−i222−2−21+i−1−i1+i−1−i1−i−1+i1−i−1+i002ζ3−2ζ3002ζ−2ζ000000000000
χ382-22-22i−2i002-22i−2i00i2i2−i2−i222−2−22i2i−2i−2i002-20000i2−i22−2i2i2−i2−i222−2−2−1−i1+i−1−i1+i−1+i1−i−1+i1−i00−2ζ32ζ300−2ζ2ζ000000000000
χ392-22-22i−2i002-22i−2i00i2i2−i2−i222−2−2−2i−2i2i2i00-220000i2−i22−2−i2−i2i2i2−2−2221−i−1+i−1+i1−i−1−i1+i1+i−1−i2ζ−2ζ002ζ3−2ζ300000000000000
χ402-22-22i−2i002-22i−2i00i2i2−i2−i222−2−2−2i−2i2i2i00-220000i2−i22−2−i2−i2i2i2−2−222−1+i1−i1−i−1+i1+i−1−i−1−i1+i−2ζ2ζ00−2ζ32ζ300000000000000
χ412-22-22i−2i002-22i−2i00−i2−i2i2i2−2−2222i2i−2i−2i002-20000−i2i2−22−i2−i2i2i2−2−2221+i−1−i1+i−1−i1−i−1+i1−i−1+i00−2ζ32ζ300−2ζ2ζ000000000000
χ422-22-22i−2i002-22i−2i00−i2−i2i2i2−2−2222i2i−2i−2i002-20000−i2i2−22−i2−i2i2i2−2−222−1−i1+i−1−i1+i−1+i1−i−1+i1−i002ζ3−2ζ3002ζ−2ζ000000000000
χ432-22-22i−2i002-22i−2i00−i2−i2i2i2−2−222−2i−2i2i2i00-220000−i2i2−22i2i2−i2−i222−2−21−i−1+i−1+i1−i−1−i1+i1+i−1−i−2ζ2ζ00−2ζ32ζ300000000000000
χ442-22-22i−2i002-22i−2i00−i2−i2i2i2−2−222−2i−2i2i2i00-220000−i2i2−22i2i2−i2−i222−2−2−1+i1−i1−i−1+i1+i−1−i−1−i1+i2ζ−2ζ002ζ3−2ζ300000000000000
χ452-22-2−2i2i002-2−2i2i00i2i2−i2−i2−2−2222i2i−2i−2i00-220000i2−i2−22−i2−i2i2i222−2−21+i−1−i−1−i1+i−1+i1−i1−i−1+i2ζ3−2ζ3002ζ−2ζ00000000000000
χ462-22-2−2i2i002-2−2i2i00i2i2−i2−i2−2−2222i2i−2i−2i00-220000i2−i2−22−i2−i2i2i222−2−2−1−i1+i1+i−1−i1−i−1+i−1+i1−i−2ζ32ζ300−2ζ2ζ00000000000000
χ472-22-2−2i2i002-2−2i2i00i2i2−i2−i2−2−222−2i−2i2i2i002-20000i2−i2−22i2i2−i2−i2−2−2221−i−1+i1−i−1+i1+i−1−i1+i−1−i002ζ−2ζ002ζ3−2ζ3000000000000
χ482-22-2−2i2i002-2−2i2i00i2i2−i2−i2−2−222−2i−2i2i2i002-20000i2−i2−22i2i2−i2−i2−2−222−1+i1−i−1+i1−i−1−i1+i−1−i1+i00−2ζ2ζ00−2ζ32ζ3000000000000
χ492-22-2−2i2i002-2−2i2i00−i2−i2i2i222−2−22i2i−2i−2i00-220000−i2i22−2i2i2−i2−i2−2−2221+i−1−i−1−i1+i−1+i1−i1−i−1+i−2ζ32ζ300−2ζ2ζ00000000000000
χ502-22-2−2i2i002-2−2i2i00−i2−i2i2i222−2−22i2i−2i−2i00-220000−i2i22−2i2i2−i2−i2−2−222−1−i1+i1+i−1−i1−i−1+i−1+i1−i2ζ3−2ζ3002ζ−2ζ00000000000000
χ512-22-2−2i2i002-2−2i2i00−i2−i2i2i222−2−2−2i−2i2i2i002-20000−i2i22−2−i2−i2i2i222−2−21−i−1+i1−i−1+i1+i−1−i1+i−1−i00−2ζ2ζ00−2ζ32ζ3000000000000
χ522-22-2−2i2i002-2−2i2i00−i2−i2i2i222−2−2−2i−2i2i2i002-20000−i2i22−2−i2−i2i2i222−2−2−1+i1−i−1+i1−i−1−i1+i−1−i1+i002ζ−2ζ002ζ3−2ζ3000000000000
χ53444444-4-4-4-4-4-444000000000000-440000000000000000000000000000000000000000000000
χ544444-4-4-4-4-4-444-4-4000000000000440000000000000000000000000000000000000000000000
χ5544-4-4004-400000000004-44-422−2222−2200000022−22000022−2222−2200000000000000000000000000000000
χ5644-4-4004-400000000004-44-4−2222−2222000000−22220000−2222−222200000000000000000000000000000000
χ5744-4-4004-40000000000-44-4422−2222−2200000022−220000−2222−222200000000000000000000000000000000
χ5844-4-4004-40000000000-44-44−2222−2222000000−2222000022−2222−2200000000000000000000000000000000
χ5944-4-400-440000004-44-4000022−2222−22000000−22220000000022−2222−220000000000000000000000000000
χ6044-4-400-440000004-44-40000−2222−222200000022−2200000000−2222−22220000000000000000000000000000
χ6144-4-400-44000000-44-44000022−2222−22000000−222200000000−2222−22220000000000000000000000000000
χ6244-4-400-44000000-44-440000−2222−222200000022−220000000022−2222−220000000000000000000000000000
χ634-44-44i−4i00-44−4i4i002i22i2−2i2−2i2−22−222222000000000000−2i22i222−22000000000000000000000000000000000000
χ644-44-44i−4i00-44−4i4i00−2i2−2i22i22i22222−22−220000000000002i2−2i2−2222000000000000000000000000000000000000
χ654-44-4−4i4i00-444i−4i002i22i2−2i2−2i22222−22−22000000000000−2i22i2−2222000000000000000000000000000000000000
χ664-44-4−4i4i00-444i−4i00−2i2−2i22i22i2−22−2222220000000000002i2−2i222−22000000000000000000000000000000000000
χ674-4-44000000004i−4i2i2−2i2−2i22i222−22−22222i2−2i2−2i22i2000022−220000002i−2i−2i2i2-2-220000000000000000000000000000
χ684-4-44000000004i−4i2i2−2i2−2i22i222−22−2222−2i22i22i2−2i20000−2222000000−2i2i2i−2i-222-20000000000000000000000000000
χ694-4-44000000004i−4i−2i22i22i2−2i2−222222−222i2−2i2−2i22i2000022−22000000−2i2i2i−2i-222-20000000000000000000000000000
χ704-4-44000000004i−4i−2i22i22i2−2i2−222222−22−2i22i22i2−2i20000−22220000002i−2i−2i2i2-2-220000000000000000000000000000
χ714-4-4400000000−4i4i2i2−2i2−2i22i2−222222−222i2−2i2−2i22i20000−2222000000−2i2i2i−2i2-2-220000000000000000000000000000
χ724-4-4400000000−4i4i2i2−2i2−2i22i2−222222−22−2i22i22i2−2i2000022−220000002i−2i−2i2i-222-20000000000000000000000000000
χ734-4-4400000000−4i4i−2i22i22i2−2i222−22−22222i2−2i2−2i22i20000−22220000002i−2i−2i2i-222-20000000000000000000000000000
χ744-4-4400000000−4i4i−2i22i22i2−2i222−22−2222−2i22i22i2−2i2000022−22000000−2i2i2i−2i2-2-220000000000000000000000000000

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