Finite Group Databasebeta

← Group #150139

Character table — Group #150139

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11112222222222222222222222444444444444444444448888888888888888161616161616161632323232
order12222244444444888816161616161616164488888816161616161616161616161632323232323232323232323232323232444444448888
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
χ5111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11-111-1-1-1-111111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1ii−i−i
χ6111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11-111-1-1-1-111111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11111−i−iii
χ7111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11-111-1-1-1-111111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1−i−iii
χ8111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11-111-1-1-1-111111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11111ii−i−i
χ91111-1-111-1-11111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-11-11-1
χ101111-1-111-1-11111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-11-11
χ111111-1-111-1-11111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-11-11
χ121111-1-111-1-11111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1111-11-1
χ131111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-11-1-1-1-1111111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111i−i−ii
χ141111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-11-1-1-1-1111111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1−iii−i
χ151111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-11-1-1-1-1111111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111−iii−i
χ161111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-11-1-1-1-1111111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1i−i−ii
χ17222222222222222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000
χ1822222222222222-2-2-2-20000000022-2-2-2-2-2-200000000000022−2−222−2−222−2−222−2−2000000000000
χ1922222222222222-2-2-2-20000000022-2-2-2-2-2-2000000000000−2−222−2−222−2−222−2−222000000000000
χ202222222222-2-2-2-200002222−2−2−2−2-2-200000022−2−222−2−222−2−2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5000000000000
χ212222222222-2-2-2-200002222−2−2−2−2-2-200000022−2−222−2−222−2−2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5000000000000
χ222222222222-2-2-2-20000−2−2−2−22222-2-2000000−2−222−2−222−2−222ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7000000000000
χ232222222222-2-2-2-20000−2−2−2−22222-2-2000000−2−222−2−222−2−222−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7000000000000
χ24222222-2-2-2-222-2-22222222222222-222-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000000000000000
χ25222222-2-2-2-222-2-2-2-2-2-2000000002-2-2-22222000000000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2000000000000
χ26222222-2-2-2-222-2-2-2-2-2-2000000002-2-2-22222000000000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2000000000000
χ27222222-2-2-2-2-2-22200002222−2−2−2−2-22000000−2−222−2−22222−2−2ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5000000000000
χ28222222-2-2-2-2-2-22200002222−2−2−2−2-22000000−2−222−2−22222−2−2−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5000000000000
χ29222222-2-2-2-2-2-2220000−2−2−2−22222-2200000022−2−222−2−2−2−222ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7000000000000
χ30222222-2-2-2-2-2-2220000−2−2−2−22222-2200000022−2−222−2−2−2−222−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7000000000000
χ312222-2-222-2-222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-2-2-2222222220000000000000000000000000000
χ322222-2-222-2-22222-2-2-2-200000000-2-222-2-22200000000000022−2−2−2−22222−2−2−2−222000000000000
χ332222-2-222-2-22222-2-2-2-200000000-2-222-2-222000000000000−2−22222−2−2−2−22222−2−2000000000000
χ342222-2-222-2-2-2-2-2-200002222−2−2−2−22200000022−2−2−2−222−2−222ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5000000000000
χ352222-2-222-2-2-2-2-2-200002222−2−2−2−22200000022−2−2−2−222−2−222−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5000000000000
χ362222-2-222-2-2-2-2-2-20000−2−2−2−2222222000000−2−22222−2−222−2−2ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7000000000000
χ372222-2-222-2-2-2-2-2-20000−2−2−2−2222222000000−2−22222−2−222−2−2−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7000000000000
χ382222-2-2-2-22222-2-2222222222222-22-2-2-2-222-2-2-2-22222-2-2-2-20000000000000000000000000000
χ392222-2-2-2-22222-2-2-2-2-2-200000000-222222-2-2000000000000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2000000000000
χ402222-2-2-2-22222-2-2-2-2-2-200000000-222222-2-2000000000000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2000000000000
χ412222-2-2-2-222-2-22200002222−2−2−2−22-2000000−2−22222−2−2−2−222ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5000000000000
χ422222-2-2-2-222-2-22200002222−2−2−2−22-2000000−2−22222−2−2−2−222−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5000000000000
χ432222-2-2-2-222-2-2220000−2−2−2−222222-200000022−2−2−2−22222−2−2ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7000000000000
χ442222-2-2-2-222-2-2220000−2−2−2−222222-200000022−2−2−2−22222−2−2−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7000000000000
χ452-22-2002i−2i002-22i−2i22-2-22i2i−2i−2i2i2i−2i−2i00002i−2i002-22-2000000000000000000000000002-2002i−2i0000
χ462-22-2002i−2i002-22i−2i22-2-22i2i−2i−2i2i2i−2i−2i00002i−2i002-22-200000000000000000000000000-2200−2i2i0000
χ472-22-2002i−2i002-22i−2i22-2-2−2i−2i2i2i−2i−2i2i2i00002i−2i00-22-220000000000000000000000002-2002i−2i000000
χ482-22-2002i−2i002-22i−2i22-2-2−2i−2i2i2i−2i−2i2i2i00002i−2i00-22-22000000000000000000000000-2200−2i2i000000
χ492-22-200−2i2i002-2−2i2i22-2-22i2i−2i−2i2i2i−2i−2i0000−2i2i00-22-220000000000000000000000002-200−2i2i000000
χ502-22-200−2i2i002-2−2i2i22-2-22i2i−2i−2i2i2i−2i−2i0000−2i2i00-22-22000000000000000000000000-22002i−2i000000
χ512-22-200−2i2i002-2−2i2i22-2-2−2i−2i2i2i−2i−2i2i2i0000−2i2i002-22-2000000000000000000000000002-200−2i2i0000
χ522-22-200−2i2i002-2−2i2i22-2-2−2i−2i2i2i−2i−2i2i2i0000−2i2i002-22-200000000000000000000000000-22002i−2i0000
χ5344-4-400004-4000022−2222−222ζ−2ζ7−2ζ+2ζ72ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ52ζ3−2ζ5−2ζ3+2ζ500000022−2200002ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ500000000000000000000000000000000
χ5444-4-400004-4000022−2222−22−2ζ+2ζ72ζ−2ζ7−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ5−2ζ3+2ζ52ζ3−2ζ500000022−220000−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ500000000000000000000000000000000
χ5544-4-400004-40000−2222−22222ζ3−2ζ5−2ζ3+2ζ52ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ7−2ζ+2ζ72ζ−2ζ7000000−222200002ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ700000000000000000000000000000000
χ5644-4-400004-40000−2222−2222−2ζ3+2ζ52ζ3−2ζ5−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ72ζ−2ζ7−2ζ+2ζ7000000−22220000−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ700000000000000000000000000000000
χ5744-4-40000-44000022−2222−222ζ−2ζ7−2ζ+2ζ72ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ52ζ3−2ζ5−2ζ3+2ζ5000000−22220000−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ500000000000000000000000000000000
χ5844-4-40000-44000022−2222−22−2ζ+2ζ72ζ−2ζ7−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ5−2ζ3+2ζ52ζ3−2ζ5000000−222200002ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ500000000000000000000000000000000
χ5944-4-40000-440000−2222−22222ζ3−2ζ5−2ζ3+2ζ52ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ7−2ζ+2ζ72ζ−2ζ700000022−220000−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ700000000000000000000000000000000
χ6044-4-40000-440000−2222−2222−2ζ3+2ζ52ζ3−2ζ5−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ72ζ−2ζ7−2ζ+2ζ700000022−2200002ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ700000000000000000000000000000000
χ614-44-4004i−4i004-44i−4i-4-444000000000000−4i4i000000000000000000000000000000000000000000
χ624-44-4004i−4i00-44−4i4i00002i22i2−2i2−2i2−2i2−2i22i22i20000000022−22−2222000000000000000000000000000000000000
χ634-44-4004i−4i00-44−4i4i0000−2i2−2i22i22i22i22i2−2i2−2i200000000−222222−22000000000000000000000000000000000000
χ644-44-400−4i4i004-4−4i4i-4-4440000000000004i−4i000000000000000000000000000000000000000000
χ654-44-400−4i4i00-444i−4i00002i22i2−2i2−2i2−2i2−2i22i22i200000000−222222−22000000000000000000000000000000000000
χ664-44-400−4i4i00-444i−4i0000−2i2−2i22i22i22i22i2−2i2−2i20000000022−22−2222000000000000000000000000000000000000
χ674-4-444-40000000022−22−22222ζ3+2ζ5−2ζ3−2ζ5−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ7−2ζ−2ζ72ζ+2ζ70022−220000000000002ζ3+2ζ5−2ζ3−2ζ52ζ+2ζ7−2ζ−2ζ70000000000000000000000000000
χ684-4-444-40000000022−22−2222−2ζ3−2ζ52ζ3+2ζ52ζ3+2ζ5−2ζ3−2ζ5−2ζ−2ζ72ζ+2ζ72ζ+2ζ7−2ζ−2ζ70022−22000000000000−2ζ3−2ζ52ζ3+2ζ5−2ζ−2ζ72ζ+2ζ70000000000000000000000000000
χ694-4-444-400000000−222222−222ζ+2ζ7−2ζ−2ζ7−2ζ−2ζ72ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ52ζ3+2ζ5−2ζ3−2ζ500−22220000000000002ζ+2ζ7−2ζ−2ζ7−2ζ3−2ζ52ζ3+2ζ50000000000000000000000000000
χ704-4-444-400000000−222222−22−2ζ−2ζ72ζ+2ζ72ζ+2ζ7−2ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ5−2ζ3−2ζ52ζ3+2ζ500−2222000000000000−2ζ−2ζ72ζ+2ζ72ζ3+2ζ5−2ζ3−2ζ50000000000000000000000000000
χ714-4-44-440000000022−22−22222ζ3+2ζ5−2ζ3−2ζ5−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ7−2ζ−2ζ72ζ+2ζ700−2222000000000000−2ζ3−2ζ52ζ3+2ζ5−2ζ−2ζ72ζ+2ζ70000000000000000000000000000
χ724-4-44-440000000022−22−2222−2ζ3−2ζ52ζ3+2ζ52ζ3+2ζ5−2ζ3−2ζ5−2ζ−2ζ72ζ+2ζ72ζ+2ζ7−2ζ−2ζ700−22220000000000002ζ3+2ζ5−2ζ3−2ζ52ζ+2ζ7−2ζ−2ζ70000000000000000000000000000
χ734-4-44-4400000000−222222−222ζ+2ζ7−2ζ−2ζ7−2ζ−2ζ72ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ52ζ3+2ζ5−2ζ3−2ζ50022−22000000000000−2ζ−2ζ72ζ+2ζ72ζ3+2ζ5−2ζ3−2ζ50000000000000000000000000000
χ744-4-44-4400000000−222222−22−2ζ−2ζ72ζ+2ζ72ζ+2ζ7−2ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ5−2ζ3−2ζ52ζ3+2ζ50022−220000000000002ζ+2ζ7−2ζ−2ζ7−2ζ3−2ζ52ζ3+2ζ50000000000000000000000000000

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