Finite Group Databasebeta

← Group #135105

Character table — Group #135105

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11112222222222222222222222444444444444444444448888888888888888161616161616161632323232
order122222444444448888888888884488888888888888888816161616161616161616161616161616224488884444
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
χ5111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ6111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ7111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ8111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ91111-1-1-1-1-1-1111111111111-1-1-1-1-1111-1-111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1-11-111-1-1i−ii−i
χ101111-1-1-1-1-1-1111111111111-1-1-1-1-1111-1-111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-11-11-1-111−ii−ii
χ111111-1-1-1-1-1-1111111111111-1-1-1-1-1111-1-111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1-11-111-1-1−ii−ii
χ121111-1-1-1-1-1-1111111111111-1-1-1-1-1111-1-111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-11-11-1-111i−ii−i
χ131111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1111-1-1-1-11111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii1-11-1-1-111i−i−ii
χ141111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1111-1-1-1-11111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-11-1111-1-1−iii−i
χ151111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1111-1-1-1-11111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i1-11-1-1-111−iii−i
χ161111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1111-1-1-1-11111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-11-1111-1-1i−i−ii
χ1722222222222222-2-2-2-22222-2-2-2-222-2-2-2-2222222-2-2-2-2-2-2-2-20000000000000000000000000000
χ1822222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-2-2-2222222220000000000000000000000000000
χ19222222-2-222-2-222000022220000-2-20000-2-2-2-2220000000022−2−222−2−222−2−222−2−2000000000000
χ20222222-2-222-2-222000022220000-2-20000-2-2-2-22200000000−2−222−2−222−2−222−2−222000000000000
χ21222222-2-222-2-2220000-2-2-2-20000-2-200002222-2-20000000022−2−222−2−2−2−222−2−222000000000000
χ22222222-2-222-2-2220000-2-2-2-20000-2-200002222-2-200000000−2−222−2−22222−2−222−2−2000000000000
χ23222222-2-2-2-222-2-222220000-2-2-2-22-2-2-22200000000000000000000000000000000002i−2i2i−2i0000
χ24222222-2-2-2-222-2-222220000-2-2-2-22-2-2-2220000000000000000000000000000000000−2i2i−2i2i0000
χ25222222-2-2-2-222-2-2-2-2-2-2000022222-222-2-20000000000000000000000000000002-2-2200000000
χ26222222-2-2-2-222-2-2-2-2-2-2000022222-222-2-2000000000000000000000000000000-222-200000000
χ272222-2-2222222-2-2222200002222-2-2-2-2-2-200000000000000000000000000000000002i−2i−2i2i0000
χ282222-2-2222222-2-2222200002222-2-2-2-2-2-20000000000000000000000000000000000−2i2i2i−2i0000
χ292222-2-2222222-2-2-2-2-2-20000-2-2-2-2-2-2222200000000000000000000000000000022-2-200000000
χ302222-2-2222222-2-2-2-2-2-20000-2-2-2-2-2-22222000000000000000000000000000000-2-22200000000
χ312222-2-222-2-2-2-2220000222200002-20000-2-222-2-200000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2000000000000
χ322222-2-222-2-2-2-2220000222200002-20000-2-222-2-200000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2000000000000
χ332222-2-222-2-2-2-2220000-2-2-2-200002-2000022-2-22200000000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2000000000000
χ342222-2-222-2-2-2-2220000-2-2-2-200002-2000022-2-22200000000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2000000000000
χ352222-2-2-2-2-2-22222-2-2-2-222222222-22-2-22222-2-2-2-2-2-2-2-222220000000000000000000000000000
χ362222-2-2-2-2-2-22222-2-2-2-2-2-2-2-22222-22-2-222-2-222222222-2-2-2-20000000000000000000000000000
χ372-2-222-2002-200-2222−2−222-2-222−2−2002−22−200002-222−2−222−2−2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5000000000000
χ382-2-222-2002-200-2222−2−222-2-222−2−2002−22−200002-222−2−222−2−2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5000000000000
χ392-2-222-2002-200-2222−2−2-2-22222−2−2002−22−20000-22−2−222−2−222ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5000000000000
χ402-2-222-2002-200-2222−2−2-2-22222−2−2002−22−20000-22−2−222−2−222−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5000000000000
χ412-2-222-2002-200-22−2−22222-2-2−2−22200−22−2200002-2−2−222−2−222ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7000000000000
χ422-2-222-2002-200-22−2−22222-2-2−2−22200−22−2200002-2−2−222−2−222−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7000000000000
χ432-2-222-2002-200-22−2−222-2-222−2−22200−22−220000-2222−2−222−2−2ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7000000000000
χ442-2-222-2002-200-22−2−222-2-222−2−22200−22−220000-2222−2−222−2−2−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7000000000000
χ452-2-22-2200-2200-2222−2−222-2-2−2−222002−2−220000-2222−2−2−2−222ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7000000000000
χ462-2-22-2200-2200-2222−2−222-2-2−2−222002−2−220000-2222−2−2−2−222−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7000000000000
χ472-2-22-2200-2200-2222−2−2-2-222−2−222002−2−2200002-2−2−22222−2−2ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7000000000000
χ482-2-22-2200-2200-2222−2−2-2-222−2−222002−2−2200002-2−2−22222−2−2−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7000000000000
χ492-2-22-2200-2200-22−2−22222-2-222−2−200−222−20000-22−2−22222−2−2ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5000000000000
χ502-2-22-2200-2200-22−2−22222-2-222−2−200−222−20000-22−2−22222−2−2−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5000000000000
χ512-2-22-2200-2200-22−2−222-2-22222−2−200−222−200002-222−2−2−2−222ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5000000000000
χ522-2-22-2200-2200-22−2−222-2-22222−2−200−222−200002-222−2−2−2−222−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5000000000000
χ5344444444-4-4-4-4-4-4000000000000-440000000000000000000000000000000000000000000000
χ544444-4-4-4-444-4-4-4-4000000000000440000000000000000000000000000000000000000000000
χ5544-4-40000004-400000022−2222−224i−4i4i−4i00000022−22000000002i2−2i22i2−2i20000000000000000000000000000
χ5644-4-40000004-400000022−2222−22−4i4i−4i4i00000022−2200000000−2i22i2−2i22i20000000000000000000000000000
χ5744-4-40000004-4000000−2222−22224i−4i4i−4i000000−222200000000−2i22i2−2i22i20000000000000000000000000000
χ5844-4-40000004-4000000−2222−2222−4i4i−4i4i000000−2222000000002i2−2i22i2−2i20000000000000000000000000000
χ5944-4-4000000-44004i−4i4i−4i22−2222−220000000000−222200002i2−2i22i2−2i200000000000000000000000000000000
χ6044-4-4000000-44004i−4i4i−4i−2222−2222000000000022−220000−2i22i2−2i22i200000000000000000000000000000000
χ6144-4-4000000-4400−4i4i−4i4i22−2222−220000000000−22220000−2i22i2−2i22i200000000000000000000000000000000
χ6244-4-4000000-4400−4i4i−4i4i−2222−2222000000000022−2200002i2−2i22i2−2i200000000000000000000000000000000
χ634-44-4004-40000002i2−2i2−2i22i222−22−22222i2−2i2−2i22i20000000022−22002i−2i−2i2i2i−2i−2i2i0000000000000000000000000000
χ644-44-4004-40000002i2−2i2−2i22i2−222222−222i2−2i2−2i22i200000000−222200−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000
χ654-44-4004-4000000−2i22i22i2−2i222−22−2222−2i22i22i2−2i20000000022−2200−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000
χ664-44-4004-4000000−2i22i22i2−2i2−222222−22−2i22i22i2−2i200000000−2222002i−2i−2i2i2i−2i−2i2i0000000000000000000000000000
χ674-44-400-440000002i2−2i2−2i22i222−22−2222−2i22i22i2−2i200000000−2222002i−2i−2i2i−2i2i2i−2i0000000000000000000000000000
χ684-44-400-440000002i2−2i2−2i22i2−222222−22−2i22i22i2−2i20000000022−2200−2i2i2i−2i2i−2i−2i2i0000000000000000000000000000
χ694-44-400-44000000−2i22i22i2−2i222−22−22222i2−2i2−2i22i200000000−222200−2i2i2i−2i2i−2i−2i2i0000000000000000000000000000
χ704-44-400-44000000−2i22i22i2−2i2−222222−222i2−2i2−2i22i20000000022−22002i−2i−2i2i−2i2i2i−2i0000000000000000000000000000
χ714-4-444-400-44004-42222−22−220000−22−22222200−222222−22000000000000000000000000000000000000000000
χ724-4-444-400-44004-4−22−22222200002222−22−220022−22−2222000000000000000000000000000000000000000000
χ734-4-44-44004-4004-42222−22−2200002222−22−2200−2222−2222000000000000000000000000000000000000000000
χ744-4-44-44004-4004-4−22−2222220000−22−2222220022−2222−22000000000000000000000000000000000000000000

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