Finite Group Databasebeta

← Group #13144778

Character table — Group #13144778

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122
size111111111111222222222222222222666666666666666688888812121212121212121212121212121212121212121212121218181818181818181818181818181818181818181818181824242424242424242424242424242424727272727272
order12334466121212122466888812122424242424242424333366661212121212121212246612126666121212122424242424242424242424242424242416161616161616164848484848484848484848484848484866666666121212121212121224661212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111-1-111-1-1-1-1-11-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-11-111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-111-1-1
χ61111-1-111-1-1-1-1-11-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-11-111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-11-1-111
χ71111-1-111-1-1-1-1-11-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-11-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-1-111
χ81111-1-111-1-1-1-1-11-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-11-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111-111-1-1
χ92222222222222222222222222222222-1-1-12-1-1-122-1-1-1-1-1-12222222-1-1-12-1-1-122-1-1-1-1-1-122-1-1-1-1-1-100000000000000000000000022-1-1-1-1-1-122-1-1-1-1-1-1000000
χ102222222222222222222222222222222-1-1-12-1-1-122-1-1-1-1-1-1-2-2-2-2-2-22-1-1-12-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1000000000000000000000000-2-2111111-2-2111111000000
χ11222222222222222222222222222222-12-1-1-12-1-1-1-122-1-1-1-1222222-12-1-1-12-1-1-1-122-1-1-1-1-1-122-1-1-1-1000000000000000000000000-1-122-1-1-1-1-1-122-1-1-1-1000000
χ12222222222222222222222222222222-12-1-1-12-1-1-1-122-1-1-1-1-2-2-2-2-2-2-12-1-1-12-1-1-1-122-1-1-1-1-1-122-1-1-1-100000000000000000000000011-2-2111111-2-21111000000
χ13222222222222222222222222222222-1-12-1-1-12-1-1-1-1-122-1-1222222-1-12-1-1-12-1-1-1-1-122-1-1-1-1-1-122-1-1000000000000000000000000-1-1-1-122-1-1-1-1-1-122-1-1000000
χ14222222222222222222222222222222-1-12-1-1-12-1-1-1-1-122-1-1-2-2-2-2-2-2-1-12-1-1-12-1-1-1-1-122-1-1-1-1-1-122-1-10000000000000000000000001111-2-2111111-2-211000000
χ15222222222222222222222222222222-1-1-12-1-1-12-1-1-1-1-1-122222222-1-1-12-1-1-12-1-1-1-1-1-122-1-1-1-1-1-122000000000000000000000000-1-1-1-1-1-122-1-1-1-1-1-122000000
χ16222222222222222222222222222222-1-1-12-1-1-12-1-1-1-1-1-122-2-2-2-2-2-2-1-1-12-1-1-12-1-1-1-1-1-122-1-1-1-1-1-122000000000000000000000000111111-2-2111111-2-2000000
χ172222222222222222-2-2-2-222-2-2-2-2-2-2-2-2222222222222222200000022222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000000000000000000000
χ182222222222222222-2-2-2-222-2-2-2-2-2-2-2-22-1-1-12-1-1-122-1-1-1-1-1-10000002-1-1-12-1-1-1-2-2111111-2-211111100000000000000000000000000−i3i3−i3i3−i3i300−i3i3−i3i3−i3i3000000
χ192222222222222222-2-2-2-222-2-2-2-2-2-2-2-22-1-1-12-1-1-122-1-1-1-1-1-10000002-1-1-12-1-1-1-2-2111111-2-211111100000000000000000000000000i3−i3i3−i3i3−i300i3−i3i3−i3i3−i3000000
χ202222222222222222-2-2-2-222-2-2-2-2-2-2-2-2-12-1-1-12-1-1-1-122-1-1-1-1000000-12-1-1-12-1-111-2-2111111-2-21111000000000000000000000000−i3i300−i3i3i3−i3−i3i300−i3i3i3−i3000000
χ212222222222222222-2-2-2-222-2-2-2-2-2-2-2-2-12-1-1-12-1-1-1-122-1-1-1-1000000-12-1-1-12-1-111-2-2111111-2-21111000000000000000000000000i3−i300i3−i3−i3i3i3−i300i3−i3−i3i3000000
χ222222222222222222-2-2-2-222-2-2-2-2-2-2-2-2-1-12-1-1-12-1-1-1-1-122-1-1000000-1-12-1-1-12-11111-2-2111111-2-211000000000000000000000000−i3i3i3−i300−i3i3−i3i3i3−i300−i3i3000000
χ232222222222222222-2-2-2-222-2-2-2-2-2-2-2-2-1-12-1-1-12-1-1-1-1-122-1-1000000-1-12-1-1-12-11111-2-2111111-2-211000000000000000000000000i3−i3−i3i300i3−i3i3−i3−i3i300i3−i3000000
χ242222222222222222-2-2-2-222-2-2-2-2-2-2-2-2-1-1-12-1-1-12-1-1-1-1-1-122000000-1-1-12-1-1-12111111-2-2111111-2-2000000000000000000000000−i3i3−i3i3i3−i300−i3i3−i3i3i3−i300000000
χ252222222222222222-2-2-2-222-2-2-2-2-2-2-2-2-1-1-12-1-1-12-1-1-1-1-1-122000000-1-1-12-1-1-12111111-2-2111111-2-2000000000000000000000000i3−i3i3−i3−i3i300i3−i3i3−i3−i3i300000000
χ26222222222222-2-2-2-20000-2-2000000002222222222222222000000-2-2-2-2-2-2-2-2000000000000000022−2−222−2−22222−2−2−2−22222−2−2−2−20000000000000000000000
χ27222222222222-2-2-2-20000-2-2000000002222222222222222000000-2-2-2-2-2-2-2-20000000000000000−2−222−2−222−2−2−2−22222−2−2−2−222220000000000000000000000
χ282222-2-222-2-2-2-22-2220000-2-20000000022222222-2-2-2-2-2-2-2-20000002222-2-2-2-2000000000000000022−2−2−2−2222222−2−2−2−2−2−2−2−222220000000000000000000000
χ292222-2-222-2-2-2-22-2220000-2-20000000022222222-2-2-2-2-2-2-2-20000002222-2-2-2-20000000000000000−2−22222−2−2−2−2−2−222222222−2−2−2−20000000000000000000000
χ302222-2-222-2-2-2-2-22-2-222-2-2222222-2-2-2-222222222-2-2-2-2-2-2-2-2000000-2-2-2-22222-2-2-2-2-2-2-2-2222222220000000000000000000000000000000000000000000000
χ312222-2-222-2-2-2-2-22-2-222-2-2222222-2-2-2-22-1-1-12-1-1-1-2-2111111000000-21112-1-1-1-2-211111122-1-1-1-1-1-100000000000000000000000000−i3i3−i3i3−i3i300i3−i3i3−i3i3−i3000000
χ322222-2-222-2-2-2-2-22-2-222-2-2222222-2-2-2-22-1-1-12-1-1-1-2-2111111000000-21112-1-1-1-2-211111122-1-1-1-1-1-100000000000000000000000000i3−i3i3−i3i3−i300−i3i3−i3i3−i3i3000000
χ332222-2-222-2-2-2-2-22-2-222-2-2222222-2-2-2-2-12-1-1-12-1-111-2-211110000001-211-12-1-111-2-21111-1-122-1-1-1-1000000000000000000000000−i3i300−i3i3i3−i3i3−i300i3−i3−i3i3000000
χ342222-2-222-2-2-2-2-22-2-222-2-2222222-2-2-2-2-12-1-1-12-1-111-2-211110000001-211-12-1-111-2-21111-1-122-1-1-1-1000000000000000000000000i3−i300i3−i3−i3i3−i3i300−i3i3i3−i3000000
χ352222-2-222-2-2-2-2-22-2-222-2-2222222-2-2-2-2-1-12-1-1-12-11111-2-21100000011-21-1-12-11111-2-211-1-1-1-122-1-1000000000000000000000000−i3i3i3−i300−i3i3i3−i3−i3i300i3−i3000000
χ362222-2-222-2-2-2-2-22-2-222-2-2222222-2-2-2-2-1-12-1-1-12-11111-2-21100000011-21-1-12-11111-2-211-1-1-1-122-1-1000000000000000000000000i3−i3−i3i300i3−i3−i3i3i3−i300−i3i3000000
χ372222-2-222-2-2-2-2-22-2-222-2-2222222-2-2-2-2-1-1-12-1-1-12111111-2-2000000111-2-1-1-12111111-2-2-1-1-1-1-1-122000000000000000000000000−i3i3−i3i3i3−i300i3−i3i3−i3−i3i300000000
χ382222-2-222-2-2-2-2-22-2-222-2-2222222-2-2-2-2-1-1-12-1-1-12111111-2-2000000111-2-1-1-12111111-2-2-1-1-1-1-1-122000000000000000000000000i3−i3i3−i3−i3i300−i3i3−i3i3i3−i300000000
χ392222-2-222-2-2-2-2-22-2-2-2-22222-2-2-2-222222-1-1-12-1-1-1-2-21111112-222-2-2-21112-1-1-122-1-1-1-1-1-1-2-211111100000000000000000000000022-1-1-1-1-1-1-2-2111111000000
χ402222-2-222-2-2-2-2-22-2-2-2-22222-2-2-2-222222-1-1-12-1-1-1-2-2111111-22-2-222-21112-1-1-122-1-1-1-1-1-1-2-2111111000000000000000000000000-2-211111122-1-1-1-1-1-1000000
χ412222-2-222-2-2-2-2-22-2-2-2-22222-2-2-2-22222-12-1-1-12-1-111-2-211112-222-2-21-211-12-1-1-1-122-1-1-1-111-2-21111000000000000000000000000-1-122-1-1-1-111-2-21111000000
χ422222-2-222-2-2-2-2-22-2-2-2-22222-2-2-2-22222-12-1-1-12-1-111-2-21111-22-2-2221-211-12-1-1-1-122-1-1-1-111-2-2111100000000000000000000000011-2-21111-1-122-1-1-1-1000000
χ432222-2-222-2-2-2-2-22-2-2-2-22222-2-2-2-22222-1-12-1-1-12-11111-2-2112-222-2-211-21-1-12-1-1-1-1-122-1-11111-2-211000000000000000000000000-1-1-1-122-1-11111-2-211000000
χ442222-2-222-2-2-2-2-22-2-2-2-22222-2-2-2-22222-1-12-1-1-12-11111-2-211-22-2-22211-21-1-12-1-1-1-1-122-1-11111-2-2110000000000000000000000001111-2-211-1-1-1-122-1-1000000
χ452222-2-222-2-2-2-2-22-2-2-2-22222-2-2-2-22222-1-1-12-1-1-12111111-2-22-222-2-2111-2-1-1-12-1-1-1-1-1-122111111-2-2000000000000000000000000-1-1-1-1-1-122111111-2-2000000
χ462222-2-222-2-2-2-2-22-2-2-2-22222-2-2-2-22222-1-1-12-1-1-12111111-2-2-22-2-222111-2-1-1-12-1-1-1-1-1-122111111-2-2000000000000000000000000111111-2-2-1-1-1-1-1-122000000
χ472-2222i−2i-2-22i2i−2i−2i0000−i2i22−200−i2−i2i2i222−2−22222-2-2-2-22i−2i2i−2i2i−2i2i−2i000000000000002−22−22−22−2−i2i2−i2i2−i2i2−i2i2−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47−ζ25+ζ31−ζ41+ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43−ζ11+ζ13+ζ29−ζ43ζ11+ζ13+ζ29+ζ43ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−ζ11−ζ13−ζ29−ζ43−ζ25−ζ31−ζ41−ζ47−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ25+ζ31+ζ41+ζ470000000000000000000000
χ482-2222i−2i-2-22i2i−2i−2i0000−i2i22−200−i2−i2i2i222−2−22222-2-2-2-22i−2i2i−2i2i−2i2i−2i000000000000002−22−22−22−2−i2i2−i2i2−i2i2−i2i2ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ25−ζ31+ζ41−ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43ζ11−ζ13−ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43ζ11+ζ13+ζ29+ζ43ζ25+ζ31+ζ41+ζ47ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47−ζ25−ζ31−ζ41−ζ470000000000000000000000
χ492-2222i−2i-2-22i2i−2i−2i0000i2−i2−2200i2i2−i2−i2−2−2222222-2-2-2-22i−2i2i−2i2i−2i2i−2i00000000000000−22−22−22−22i2−i2i2−i2i2−i2i2−i2ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43ζ11−ζ13−ζ29+ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ25+ζ31−ζ41+ζ47−ζ25−ζ31−ζ41−ζ47−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ25+ζ31+ζ41+ζ47−ζ11−ζ13−ζ29−ζ43−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43ζ11+ζ13+ζ29+ζ430000000000000000000000
χ502-2222i−2i-2-22i2i−2i−2i0000i2−i2−2200i2i2−i2−i2−2−2222222-2-2-2-22i−2i2i−2i2i−2i2i−2i00000000000000−22−22−22−22i2−i2i2−i2i2−i2i2−i2−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−ζ11+ζ13+ζ29−ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ25−ζ31+ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47−ζ25−ζ31−ζ41−ζ47ζ11+ζ13+ζ29+ζ43ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−ζ11−ζ13−ζ29−ζ430000000000000000000000
χ512-222−2i2i-2-2−2i−2i2i2i0000−i2i2−2200−i2−i2i2i2−2−2222222-2-2-2-2−2i2i−2i2i−2i2i−2i2i00000000000000−22−22−22−22−i2i2−i2i2−i2i2−i2i2ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ11−ζ13−ζ29+ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ25+ζ31−ζ41+ζ47ζ25+ζ31+ζ41+ζ47ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47−ζ25−ζ31−ζ41−ζ47ζ11+ζ13+ζ29+ζ43ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−ζ11−ζ13−ζ29−ζ430000000000000000000000
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Here ζ is a primitive root of unity of order 48 (ζ48 = 1); i = ζ12.