Finite Group Databasebeta

← Group #152511

Character table — Group #152511

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11112222222222222222222222444444444444444444448888888888888888161616161616161632323232
order12222222444444888816161616161616162488888816161616161616161616161632323232323232323232323232323232888888884444
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
χ5111111-1-111-1-111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ6111111-1-111-1-111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ7111111-1-111-1-111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ8111111-1-111-1-111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ91111-1-1111-1-1-11-11111-1-1-1-1-1-1-1-1-11-1-111-1-111111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i1-11-1
χ101111-1-1111-1-1-11-11111-1-1-1-1-1-1-1-1-11-1-111-1-111111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii-11-11
χ111111-1-1111-1-1-11-11111-1-1-1-1-1-1-1-1-11-1-111-1-111111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i-11-11
χ121111-1-1111-1-1-11-11111-1-1-1-1-1-1-1-1-11-1-111-1-111111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii1-11-1
χ131111-1-1-1-11-1111-11111-1-1-1-1-1-1-1-11-1-1-1-1-1111111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii1-1-11
χ141111-1-1-1-11-1111-11111-1-1-1-1-1-1-1-11-1-1-1-1-1111111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i-111-1
χ151111-1-1-1-11-1111-11111-1-1-1-1-1-1-1-11-1-1-1-1-1111111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii-111-1
χ161111-1-1-1-11-1111-11111-1-1-1-1-1-1-1-11-1-1-1-1-1111111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i1-1-11
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
χ2022222222-2-2-2-2-2-200002222−2−2−2−22-200000022−2−222−2−222−2−2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5000000000000
χ2122222222-2-2-2-2-2-200002222−2−2−2−22-200000022−2−222−2−222−2−2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5000000000000
χ2222222222-2-2-2-2-2-20000−2−2−2−222222-2000000−2−222−2−222−2−222ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7000000000000
χ2322222222-2-2-2-2-2-20000−2−2−2−222222-2000000−2−222−2−222−2−222−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7000000000000
χ24222222-2-222-2-2222222-2-2-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-2222222220000000000000000000000000000
χ25222222-2-222-2-222-2-2-2-200000000-2-2-2-2222200000000000022−2−222−2−2−2−222−2−222000000000000
χ26222222-2-222-2-222-2-2-2-200000000-2-2-2-22222000000000000−2−222−2−22222−2−222−2−2000000000000
χ27222222-2-2-2-222-2-200002222−2−2−2−2-2200000022−2−2−2−222−2−222ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5000000000000
χ28222222-2-2-2-222-2-200002222−2−2−2−2-2200000022−2−2−2−222−2−222−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5000000000000
χ29222222-2-2-2-222-2-20000−2−2−2−22222-22000000−2−22222−2−222−2−2ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7000000000000
χ30222222-2-2-2-222-2-20000−2−2−2−22222-22000000−2−22222−2−222−2−2−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7000000000000
χ312222-2-2222-2-2-22-2222222222222-22-2-222-2-2-2-2-2-2-2-2-2-222220000000000000000000000000000
χ322222-2-2222-2-2-22-2-2-2-2-200000000-2222-2-222000000000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2000000000000
χ332222-2-2222-2-2-22-2-2-2-2-200000000-2222-2-222000000000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2000000000000
χ342222-2-222-2222-2200002222−2−2−2−2-2-2000000−2−222−2−22222−2−2ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5000000000000
χ352222-2-222-2222-2200002222−2−2−2−2-2-2000000−2−222−2−22222−2−2−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5000000000000
χ362222-2-222-2222-220000−2−2−2−22222-2-200000022−2−222−2−2−2−222ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7000000000000
χ372222-2-222-2222-220000−2−2−2−22222-2-200000022−2−222−2−2−2−222−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7000000000000
χ382222-2-2-2-22-2222-22222222222222-2-2-2-2-222-2-2-2-22222-2-2-2-20000000000000000000000000000
χ392222-2-2-2-22-2222-2-2-2-2-2000000002-22222-2-2000000000000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2000000000000
χ402222-2-2-2-22-2222-2-2-2-2-2000000002-22222-2-2000000000000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2000000000000
χ412222-2-2-2-2-22-2-2-2200002222−2−2−2−222000000−2−22222−2−2−2−222ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5000000000000
χ422222-2-2-2-2-22-2-2-2200002222−2−2−2−222000000−2−22222−2−2−2−222−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5000000000000
χ432222-2-2-2-2-22-2-2-220000−2−2−2−222222200000022−2−2−2−22222−2−2ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7000000000000
χ442222-2-2-2-2-22-2-2-220000−2−2−2−222222200000022−2−2−2−22222−2−2−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7000000000000
χ452-2-222-200-22002-2-2-22222-2-222-2-2002-200002-22-20000000000000000000000002i−2i2i−2i00000000
χ462-2-222-200-22002-2-2-22222-2-222-2-2002-200002-22-2000000000000000000000000−2i2i−2i2i00000000
χ472-2-222-200-22002-2-2-222-2-222-2-222002-20000-22-2200000000000000000000000000002i−2i2i−2i0000
χ482-2-222-200-22002-2-2-222-2-222-2-222002-20000-22-220000000000000000000000000000−2i2i−2i2i0000
χ492-2-22-2200-2-20022-2-22222-2-222-2-200-220000-22-2200000000000000000000000000002-2-220000
χ502-2-22-2200-2-20022-2-22222-2-222-2-200-220000-22-220000000000000000000000000000-222-20000
χ512-2-22-2200-2-20022-2-222-2-222-2-22200-2200002-22-20000000000000000000000002-2-2200000000
χ522-2-22-2200-2-20022-2-222-2-222-2-22200-2200002-22-2000000000000000000000000-222-200000000
χ5344-4-4004-400000022−2222−222ζ−2ζ7−2ζ+2ζ72ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ52ζ3−2ζ5−2ζ3+2ζ5000022−2200000000002ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ50000000000000000000000000000
χ5444-4-4004-400000022−2222−22−2ζ+2ζ72ζ−2ζ7−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ5−2ζ3+2ζ52ζ3−2ζ5000022−220000000000−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ50000000000000000000000000000
χ5544-4-4004-4000000−2222−22222ζ3−2ζ5−2ζ3+2ζ52ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ7−2ζ+2ζ72ζ−2ζ70000−222200000000002ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ70000000000000000000000000000
χ5644-4-4004-4000000−2222−2222−2ζ3+2ζ52ζ3−2ζ5−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ72ζ−2ζ7−2ζ+2ζ70000−22220000000000−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ70000000000000000000000000000
χ5744-4-400-4400000022−2222−222ζ−2ζ7−2ζ+2ζ72ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ52ζ3−2ζ5−2ζ3+2ζ50000−22220000000000−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ50000000000000000000000000000
χ5844-4-400-4400000022−2222−22−2ζ+2ζ72ζ−2ζ7−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ5−2ζ3+2ζ52ζ3−2ζ50000−222200000000002ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ50000000000000000000000000000
χ5944-4-400-44000000−2222−22222ζ3−2ζ5−2ζ3+2ζ52ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ7−2ζ+2ζ72ζ−2ζ7000022−220000000000−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ70000000000000000000000000000
χ6044-4-400-44000000−2222−2222−2ζ3+2ζ52ζ3−2ζ5−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ72ζ−2ζ7−2ζ+2ζ7000022−2200000000002ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ70000000000000000000000000000
χ614-44-40000004i−4i0022−22−22222ζ3−2ζ5−2ζ3+2ζ5−2ζ3+2ζ52ζ3−2ζ5−2ζ+2ζ72ζ−2ζ72ζ−2ζ7−2ζ+2ζ70000002i2−2i200002ζ3+2ζ5−2ζ3−2ζ52ζ+2ζ7−2ζ−2ζ700000000000000000000000000000000
χ624-44-40000004i−4i0022−22−2222−2ζ3+2ζ52ζ3−2ζ52ζ3−2ζ5−2ζ3+2ζ52ζ−2ζ7−2ζ+2ζ7−2ζ+2ζ72ζ−2ζ70000002i2−2i20000−2ζ3−2ζ52ζ3+2ζ5−2ζ−2ζ72ζ+2ζ700000000000000000000000000000000
χ634-44-40000004i−4i00−222222−222ζ−2ζ7−2ζ+2ζ7−2ζ+2ζ72ζ−2ζ72ζ3−2ζ5−2ζ3+2ζ5−2ζ3+2ζ52ζ3−2ζ5000000−2i22i20000−2ζ−2ζ72ζ+2ζ72ζ3+2ζ5−2ζ3−2ζ500000000000000000000000000000000
χ644-44-40000004i−4i00−222222−22−2ζ+2ζ72ζ−2ζ72ζ−2ζ7−2ζ+2ζ7−2ζ3+2ζ52ζ3−2ζ52ζ3−2ζ5−2ζ3+2ζ5000000−2i22i200002ζ+2ζ7−2ζ−2ζ7−2ζ3−2ζ52ζ3+2ζ500000000000000000000000000000000
χ654-44-4000000−4i4i0022−22−22222ζ3−2ζ5−2ζ3+2ζ5−2ζ3+2ζ52ζ3−2ζ5−2ζ+2ζ72ζ−2ζ72ζ−2ζ7−2ζ+2ζ7000000−2i22i20000−2ζ3−2ζ52ζ3+2ζ5−2ζ−2ζ72ζ+2ζ700000000000000000000000000000000
χ664-44-4000000−4i4i0022−22−2222−2ζ3+2ζ52ζ3−2ζ52ζ3−2ζ5−2ζ3+2ζ52ζ−2ζ7−2ζ+2ζ7−2ζ+2ζ72ζ−2ζ7000000−2i22i200002ζ3+2ζ5−2ζ3−2ζ52ζ+2ζ7−2ζ−2ζ700000000000000000000000000000000
χ674-44-4000000−4i4i00−222222−222ζ−2ζ7−2ζ+2ζ7−2ζ+2ζ72ζ−2ζ72ζ3−2ζ5−2ζ3+2ζ5−2ζ3+2ζ52ζ3−2ζ50000002i2−2i200002ζ+2ζ7−2ζ−2ζ7−2ζ3−2ζ52ζ3+2ζ500000000000000000000000000000000
χ684-44-4000000−4i4i00−222222−22−2ζ+2ζ72ζ−2ζ72ζ−2ζ7−2ζ+2ζ7−2ζ3+2ζ52ζ3−2ζ52ζ3−2ζ5−2ζ3+2ζ50000002i2−2i20000−2ζ−2ζ72ζ+2ζ72ζ3+2ζ5−2ζ3−2ζ500000000000000000000000000000000
χ694-4-444-4004-400-4400002222−22−22−22−2222220000000022−22−2222000000000000000000000000000000000000
χ704-4-444-4004-400-440000−22−2222222222−22−2200000000−222222−22000000000000000000000000000000000000
χ714-4-444-400-44004-444-4-40000000000-4400000000000000000000000000000000000000000000
χ724-4-44-44004400-4-400002222−22−22−22−22222200000000−222222−22000000000000000000000000000000000000
χ734-4-44-44004400-4-40000−22−2222222222−22−220000000022−22−2222000000000000000000000000000000000000
χ744-4-44-4400-4-4004444-4-400000000004-400000000000000000000000000000000000000000000

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