Finite Group Databasebeta

← Group #135137

Character table — Group #135137

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11112222222222222222222222444444444444444444448888888888888888161616161616161632323232
order122222444444448888888888884488888888888888888816161616161616161616161616161616224488888888
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
χ511111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ611111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ711111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ811111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ91111-1-1-1-1111-1-111111-1-11111-1-1-1111-1-111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1-11-111-1-1i−ii−i
χ101111-1-1-1-1111-1-111111-1-11111-1-1-1111-1-111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-11-11-1-111−ii−ii
χ111111-1-1-1-1111-1-111111-1-11111-1-1-1111-1-111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1-11-111-1-1−ii−ii
χ121111-1-1-1-1111-1-111111-1-11111-1-1-1111-1-111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-11-11-1-111i−ii−i
χ131111-1-1-1-1111-1-111111-1-1-1-1-1-1-1-1-1111-1-1-1-11111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii1-11-1-1-111i−i−ii
χ141111-1-1-1-1111-1-111111-1-1-1-1-1-1-1-1-1111-1-1-1-11111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-11-1111-1-1−iii−i
χ151111-1-1-1-1111-1-111111-1-1-1-1-1-1-1-1-1111-1-1-1-11111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i1-11-1-1-111−iii−i
χ161111-1-1-1-1111-1-111111-1-1-1-1-1-1-1-1-1111-1-1-1-11111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-11-1111-1-1i−i−ii
χ1722222222222222-2-2-2-2-2-22222-2-222-2-2-2-2222222-2-2-2-2-2-2-2-20000000000000000000000000000
χ1822222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-2-2-2222222220000000000000000000000000000
χ192222222222-2-2-2-2222222000022-2-2-2-2-2-200000000000000000000000000000000002i−2i2i−2i0000
χ202222222222-2-2-2-2222222000022-2-2-2-2-2-20000000000000000000000000000000000−2i2i−2i2i0000
χ212222222222-2-2-2-2-2-2-2-2-2-20000-2-2-2-222220000000000000000000000000000002-2-2200000000
χ222222222222-2-2-2-2-2-2-2-2-2-20000-2-2-2-22222000000000000000000000000000000-222-200000000
χ23222222-2-2-2-22222000000222200-2-20000-2-2-2-2220000000022−2−222−2−222−2−222−2−2000000000000
χ24222222-2-2-2-22222000000222200-2-20000-2-2-2-22200000000−2−222−2−222−2−222−2−222000000000000
χ25222222-2-2-2-22222000000-2-2-2-200-2-200002222-2-20000000022−2−222−2−2−2−222−2−222000000000000
χ26222222-2-2-2-22222000000-2-2-2-200-2-200002222-2-200000000−2−222−2−22222−2−222−2−2000000000000
χ272222-2-222-2-22-2-220000002222002-20000-2-222-2-200000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2000000000000
χ282222-2-222-2-22-2-220000002222002-20000-2-222-2-200000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2000000000000
χ292222-2-222-2-22-2-22000000-2-2-2-2002-2000022-2-22200000000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2000000000000
χ302222-2-222-2-22-2-22000000-2-2-2-2002-2000022-2-22200000000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2000000000000
χ312222-2-2-2-2222-2-22-2-2-2-222222222-22-2-22222-2-2-2-2-2-2-2-222220000000000000000000000000000
χ322222-2-2-2-2222-2-22-2-2-2-222-2-2-2-222-22-2-222-2-222222222-2-2-2-20000000000000000000000000000
χ332222-2-2-2-222-222-22222-2-20000-2-22-2-2-22200000000000000000000000000000000002i−2i−2i2i0000
χ342222-2-2-2-222-222-22222-2-20000-2-22-2-2-2220000000000000000000000000000000000−2i2i2i−2i0000
χ352222-2-2-2-222-222-2-2-2-2-2220000222-222-2-200000000000000000000000000000022-2-200000000
χ362222-2-2-2-222-222-2-2-2-2-2220000222-222-2-2000000000000000000000000000000-2-22200000000
χ372-2-222-2000022-2-222−2−22−22i2i−2i−2i2−2002−22−200002i−2ii2i2−i2−i2i2i2−i2−i2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7000000000000
χ382-2-222-2000022-2-222−2−22−22i2i−2i−2i2−2002−22−200002i−2ii2i2−i2−i2i2i2−i2−i2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7000000000000
χ392-2-222-2000022-2-222−2−22−2−2i−2i2i2i2−2002−22−20000−2i2i−i2−i2i2i2−i2−i2i2i2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7000000000000
χ402-2-222-2000022-2-222−2−22−2−2i−2i2i2i2−2002−22−20000−2i2i−i2−i2i2i2−i2−i2i2i2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7000000000000
χ412-2-222-2000022-2-2−2−222−222i2i−2i−2i−2200−22−2200002i−2i−i2−i2i2i2−i2−i2i2i2ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5000000000000
χ422-2-222-2000022-2-2−2−222−222i2i−2i−2i−2200−22−2200002i−2i−i2−i2i2i2−i2−i2i2i2−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5000000000000
χ432-2-222-2000022-2-2−2−222−22−2i−2i2i2i−2200−22−220000−2i2ii2i2−i2−i2i2i2−i2−i2ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5000000000000
χ442-2-222-2000022-2-2−2−222−22−2i−2i2i2i−2200−22−220000−2i2ii2i2−i2−i2i2i2−i2−i2−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5000000000000
χ452-2-22-2200002-22-222−2−2−222i2i−2i−2i−22002−2−220000−2i2ii2i2−i2−i2−i2−i2i2i2ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5000000000000
χ462-2-22-2200002-22-222−2−2−222i2i−2i−2i−22002−2−220000−2i2ii2i2−i2−i2−i2−i2i2i2−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5000000000000
χ472-2-22-2200002-22-222−2−2−22−2i−2i2i2i−22002−2−2200002i−2i−i2−i2i2i2i2i2−i2−i2ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5000000000000
χ482-2-22-2200002-22-222−2−2−22−2i−2i2i2i−22002−2−2200002i−2i−i2−i2i2i2i2i2−i2−i2−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5000000000000
χ492-2-22-2200002-22-2−2−2222−22i2i−2i−2i2−200−222−20000−2i2i−i2−i2i2i2i2i2−i2−i2ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7000000000000
χ502-2-22-2200002-22-2−2−2222−22i2i−2i−2i2−200−222−20000−2i2i−i2−i2i2i2i2i2−i2−i2−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7000000000000
χ512-2-22-2200002-22-2−2−2222−2−2i−2i2i2i2−200−222−200002i−2ii2i2−i2−i2−i2−i2i2i2ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7000000000000
χ522-2-22-2200002-22-2−2−2222−2−2i−2i2i2i2−200−222−200002i−2ii2i2−i2−i2−i2−i2i2i2−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7000000000000
χ53444444-4-4-4-4-4-4-4-4000000000000440000000000000000000000000000000000000000000000
χ544444-4-444-4-4-444-4000000000000-440000000000000000000000000000000000000000000000
χ5544-4-400004-4000000004422−2222−22-4-400000022−220000000022−2222−220000000000000000000000000000
χ5644-4-400004-40000000044−2222−2222-4-4000000−222200000000−2222−22220000000000000000000000000000
χ5744-4-400004-400000000-4-422−2222−224400000022−2200000000−2222−22220000000000000000000000000000
χ5844-4-400004-400000000-4-4−2222−222244000000−22220000000022−2222−220000000000000000000000000000
χ5944-4-40000-4400004i−4i4i−4i0022−2222−2200000000−222200002i2−2i22i2−2i200000000000000000000000000000000
χ6044-4-40000-4400004i−4i4i−4i00−2222−22220000000022−220000−2i22i2−2i22i200000000000000000000000000000000
χ6144-4-40000-440000−4i4i−4i4i0022−2222−2200000000−22220000−2i22i2−2i22i200000000000000000000000000000000
χ6244-4-40000-440000−4i4i−4i4i00−2222−22220000000022−2200002i2−2i22i2−2i200000000000000000000000000000000
χ634-44-4004i−4i0000002i2−2i2−2i22i222−222i2−2i2−2i22i2−22220000000022−2200-222-22i−2i−2i2i0000000000000000000000000000
χ644-44-4004i−4i0000002i2−2i2−2i22i222−22−2i22i22i2−2i2−222200000000−2222002-2-22−2i2i2i−2i0000000000000000000000000000
χ654-44-4004i−4i000000−2i22i22i2−2i2−22222i2−2i2−2i22i222−220000000022−22002-2-22−2i2i2i−2i0000000000000000000000000000
χ664-44-4004i−4i000000−2i22i22i2−2i2−2222−2i22i22i2−2i222−2200000000−222200-222-22i−2i−2i2i0000000000000000000000000000
χ674-44-400−4i4i0000002i2−2i2−2i22i2−22222i2−2i2−2i22i222−2200000000−222200-222-2−2i2i2i−2i0000000000000000000000000000
χ684-44-400−4i4i0000002i2−2i2−2i22i2−2222−2i22i22i2−2i222−220000000022−22002-2-222i−2i−2i2i0000000000000000000000000000
χ694-44-400−4i4i000000−2i22i22i2−2i222−222i2−2i2−2i22i2−222200000000−2222002-2-222i−2i−2i2i0000000000000000000000000000
χ704-44-400−4i4i000000−2i22i22i2−2i222−22−2i22i22i2−2i2−22220000000022−2200-222-2−2i2i2i−2i0000000000000000000000000000
χ714-4-444-40000-4-4442222−22−2222−22000022−2200−2222−2222000000000000000000000000000000000000000000
χ724-4-444-40000-4-444−22−222222−22220000−22220022−2222−22000000000000000000000000000000000000000000
χ734-4-44-440000-44-442222−22−22−22220000−222200−222222−22000000000000000000000000000000000000000000
χ744-4-44-440000-44-44−22−22222222−22000022−220022−22−2222000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.