Finite Group Databasebeta

← Group #13160240

Character table — Group #13160240

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size11222222222222244444444444444444444444666688888888888888899121212121212121212121212121212121616161616161616161616161818181818243636364848484854545454727272216
order1233333466666883333666612121212122424242424242424242416161616412121212121224242424242424244448484848484848484848484848484848121212121212121212121212288121246242412121212161616162662
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111-1-11111111111111111111111111111-1-1-1-1-11-1-1-11111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1111-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1111111111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111111111111111-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1111-1-1-1-1-1-1-1-1111-1
χ611111111111111111111111111111111111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-11
χ711111111111111111111111111111111111111-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-11
χ811111111111111111111111111111111111111-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-111111111111-1
χ92222222222222-2-22222222222222-2-2-2-2-2-2-2-2-2-200000002222-2-2-2-2-2-2-2-22200000000000000000000000000002-2-22202-2-2000000000000
χ102222222222222-2-22222222222222-2-2-2-2-2-2-2-2-2-200000002222-2-2-2-2-2-2-2-2-2-20000000000000000000000000000-222-2-20-222000000000000
χ112222222-2222220022222222-2-2-2-2-2000000000022−2−2000-2-2-2-2000000002222222222−2−2−2−2−2−2−2−2000000000000-200220-200000022−2−20000
χ122222222-2222220022222222-2-2-2-2-2000000000022−2−2000-2-2-2-200000000-2-222222222−2−2−2−2−2−2−2−2000000000000200-2-202000000−2−2220000
χ132222222-2222220022222222-2-2-2-2-20000000000−2−222000-2-2-2-20000000022−2−2−2−2−2−2−2−222222222000000000000-200220-2000000−2−2220000
χ142222222-2222220022222222-2-2-2-2-20000000000−2−222000-2-2-2-200000000-2-2−2−2−2−2−2−2−2−222222222000000000000200-2-20200000022−2−20000
χ15222222-12-1222222-1-1-1-1-1-1-1-12222-1-1-12222222200002-1-1-1-1-1-1-1-1-1-1-1-1-1-12200000000000000002222-1-1-1-1-1-1-1-1222-1-10-1-1-1000000002-1-10
χ16222222-12-1222222-1-1-1-1-1-1-1-12222-1-1-12222222200002-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-200000000000000002222-1-1-1-1-1-1-1-1-2-2-211011100000000-2110
χ17222222-12-1222222-1-1-1-1-1-1-1-12222-1-1-1222222220000-211-1-1-1-1-1-1-1-1-1-1-1-1220000000000000000-2-2-2-211111111222-1-10-1-1-100000000-2110
χ18222222-12-1222222-1-1-1-1-1-1-1-12222-1-1-1222222220000-211-1-1-1-1-1-1-1-1-1-1-1-1-2-20000000000000000-2-2-2-211111111-2-2-2110111000000002-1-10
χ19222222-12-12222-2-2-1-1-1-1-1-1-1-12222-111-2-2-2-2-2-2-2-200000−i3i3-1-1-1-1111111112200000000000000000000−i3−i3−i3−i3i3i3i3i32-2-2-1-10-111000000000−i3i30
χ20222222-12-12222-2-2-1-1-1-1-1-1-1-12222-111-2-2-2-2-2-2-2-200000−i3i3-1-1-1-111111111-2-200000000000000000000−i3−i3−i3−i3i3i3i3i3-2221101-1-1000000000i3−i30
χ21222222-12-12222-2-2-1-1-1-1-1-1-1-12222-111-2-2-2-2-2-2-2-200000i3−i3-1-1-1-1111111112200000000000000000000i3i3i3i3−i3−i3−i3−i32-2-2-1-10-111000000000i3−i30
χ22222222-12-12222-2-2-1-1-1-1-1-1-1-12222-111-2-2-2-2-2-2-2-200000i3−i3-1-1-1-111111111-2-200000000000000000000i3i3i3i3−i3−i3−i3−i3-2221101-1-1000000000−i3i30
χ23222-1-1-12222-1-1-1222-1-1-12-1-1-12-1-1-122222-1-1-1-1-1-122222222-1-1-122-1-1-1-1-1-10022-1-1-1-1-1-122-1-1-1-1-1-12-1-1-12-1-1-12-1-1-10000020002-1-1-100000000
χ24222-1-1-12222-1-1-1222-1-1-12-1-1-12-1-1-122222-1-1-1-1-1-12222-2-2-22-1-1-122-1-1-1-1-1-10022-1-1-1-1-1-122-1-1-1-1-1-1-2111-2111-211100000-2000-211100000000
χ25222-1-1-12222-1-1-1222-1-1-12-1-1-12-1-1-122222-1-1-1-1-1-1-2-2-2-22222-1-1-122-1-1-1-1-1-100-2-2111111-2-21111112-1-1-12-1-1-12-1-1-100000-2000-211100000000
χ26222-1-1-12222-1-1-1222-1-1-12-1-1-12-1-1-122222-1-1-1-1-1-1-2-2-2-2-2-2-22-1-1-122-1-1-1-1-1-100-2-2111111-2-2111111-2111-2111-21110000020002-1-1-100000000
χ2722-12-1-1222-12-1-122-12-1-1-12-1-1-12-1-1222-1-122-1-1-1-12222222-12-1-1-1-122-1-1-1-100-1-122-1-1-1-1-1-122-1-1-1-1-12-1-1-12-1-1-12-1-1000002000-12-1-100000000
χ2822-12-1-1222-12-1-122-12-1-1-12-1-1-12-1-1222-1-122-1-1-1-12222-2-2-2-12-1-1-1-122-1-1-1-100-1-122-1-1-1-1-1-122-1-1-1-11-2111-2111-21100000-20001-21100000000
χ2922-12-1-1222-12-1-122-12-1-1-12-1-1-12-1-1222-1-122-1-1-1-1-2-2-2-2222-12-1-1-1-122-1-1-1-10011-2-2111111-2-21111-12-1-1-12-1-1-12-1-100000-20001-21100000000
χ3022-12-1-1222-12-1-122-12-1-1-12-1-1-12-1-1222-1-122-1-1-1-1-2-2-2-2-2-2-2-12-1-1-1-122-1-1-1-10011-2-2111111-2-211111-2111-2111-211000002000-12-1-100000000
χ3122-1-12-1222-1-12-122-1-12-1-1-12-1-1-12-1222-1-1-1-122-1-12222222-1-12-1-1-1-1-122-1-100-1-1-1-122-1-1-1-1-1-122-1-1-1-12-1-1-12-1-1-12-1000002000-1-12-100000000
χ3222-1-12-1222-1-12-122-1-12-1-1-12-1-1-12-1222-1-1-1-122-1-12222-2-2-2-1-12-1-1-1-1-122-1-100-1-1-1-122-1-1-1-1-1-122-1-111-2111-2111-2100000-200011-2100000000
χ3322-1-12-1222-1-12-122-1-12-1-1-12-1-1-12-1222-1-1-1-122-1-1-2-2-2-2222-1-12-1-1-1-1-122-1-1001111-2-2111111-2-211-1-12-1-1-12-1-1-12-100000-200011-2100000000
χ3422-1-12-1222-1-12-122-1-12-1-1-12-1-1-12-1222-1-1-1-122-1-1-2-2-2-2-2-2-2-1-12-1-1-1-1-122-1-1001111-2-2111111-2-21111-2111-2111-21000002000-1-12-100000000
χ3522-1-1-12222-1-1-1222-1-1-12-1-1-12-1-1-12222-1-1-1-1-1-1222222222-1-1-12-1-1-1-1-1-12200-1-1-1-1-1-122-1-1-1-1-1-122-1-1-12-1-1-12-1-1-12000002000-1-1-1200000000
χ3622-1-1-12222-1-1-1222-1-1-12-1-1-12-1-1-12222-1-1-1-1-1-1222222-2-2-2-1-1-12-1-1-1-1-1-12200-1-1-1-1-1-122-1-1-1-1-1-122111-2111-2111-200000-2000111-200000000
χ3722-1-1-12222-1-1-1222-1-1-12-1-1-12-1-1-12222-1-1-1-1-1-122-2-2-2-2222-1-1-12-1-1-1-1-1-12200111111-2-2111111-2-2-1-1-12-1-1-12-1-1-1200000-2000111-200000000
χ3822-1-1-12222-1-1-1222-1-1-12-1-1-12-1-1-12222-1-1-1-1-1-122-2-2-2-2-2-2-2-1-1-12-1-1-1-1-1-12200111111-2-2111111-2-2111-2111-2111-2000002000-1-1-1200000000
χ392-2222220-2-2-2-2-22−22222-2-2-2-2000002−22−22−22−22−2−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ4300000002−22−22−22−22i−2i−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ430000000000000−i2i22i−2i00−i2i20000ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ470000
χ402-2222220-2-2-2-2-22−22222-2-2-2-2000002−22−22−22−22−2−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ4300000002−22−22−22−2−2i2i−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ430000000000000i2−i2−2i2i00i2−i20000−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ470000
χ412-2222220-2-2-2-2-22−22222-2-2-2-2000002−22−22−22−22−2ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ4300000002−22−22−22−22i−2iζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ430000000000000−i2i22i−2i00−i2i20000−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ470000
χ422-2222220-2-2-2-2-22−22222-2-2-2-2000002−22−22−22−22−2ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ4300000002−22−22−22−2−2i2iζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ430000000000000i2−i2−2i2i00i2−i20000ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ470000
χ432-2222220-2-2-2-2-2−222222-2-2-2-200000−22−22−22−22−22ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ470000000−22−22−22−222i−2iζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ470000000000000i2−i22i−2i00i2−i20000−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ430000
χ442-2222220-2-2-2-2-2−222222-2-2-2-200000−22−22−22−22−22ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ470000000−22−22−22−22−2i2iζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ470000000000000−i2i2−2i2i00−i2i20000ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ430000
χ452-2222220-2-2-2-2-2−222222-2-2-2-200000−22−22−22−22−22−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ470000000−22−22−22−222i−2i−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ470000000000000i2−i22i−2i00i2−i20000ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ430000
χ462-2222220-2-2-2-2-2−222222-2-2-2-200000−22−22−22−22−22−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ470000000−22−22−22−22−2i2i−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ470000000000000−i2i2−2i2i00−i2i20000−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ430000
χ47444444-2-4-2444400-2-2-2-2-2-2-2-2-4-4-4-4200000000000000000222200000000440000000000000000000000000000-400-2-20200000000000000
χ48444444-2-4-2444400-2-2-2-2-2-2-2-2-4-4-4-4200000000000000000222200000000-4-40000000000000000000000000000400220-200000000000000
χ49444-2-2-24444-2-2-2-4-44-2-2-24-2-2-24-2-2-24-4-4-4-422222200000004-2-2-2-4-4222222000000000000000000000000000000000000000000000000000
χ50444-2-2-24-444-2-2-2004-2-2-24-2-2-2-4222-400000000002222−22−22000-422200000000002222−2−2−2−2−2−2−22−22222222000000000000000000000000000000000
χ51444-2-2-24-444-2-2-2004-2-2-24-2-2-2-4222-40000000000−22−222222000-42220000000000−22−222222222222−2−2−2−2−2−2000000000000000000000000000000000
χ52444-2-2-2-24-24-2-2-244-2111-21114-2-2-2-2-2-244-2-2-2-2-2-200004-2-2-2111-2-21111110000000000000000004-2-2-2-2111-2111000000000000000000000
χ53444-2-2-2-24-24-2-2-244-2111-21114-2-2-2-2-2-244-2-2-2-2-2-20000-422-2111-2-2111111000000000000000000-42222-1-1-12-1-1-1000000000000000000000
χ54444-2-2-2-24-24-2-2-2-4-4-2111-21114-2-2-2-222-4-422222200000−2i32i3-211122-1-1-1-1-1-10000000000000000000000−2i3i3i3i32i3−i3−i3−i3000000000000000000000
χ55444-2-2-2-24-24-2-2-2-4-4-2111-21114-2-2-2-222-4-4222222000002i3−2i3-211122-1-1-1-1-1-100000000000000000000002i3−i3−i3−i3−2i3i3i3i3000000000000000000000
χ5644-24-2-2444-24-2-2-4-4-24-2-2-24-2-2-24-2-24-4-422-4-422220000000-24-2-222-4-42222000000000000000000000000000000000000000000000000000
χ5744-24-2-24-44-24-2-200-24-2-2-24-2-22-422-400000000002222−22−220002-4220000000000−2−22222−2−2−2−222−22−222222000000000000000000000000000000000
χ5844-24-2-24-44-24-2-200-24-2-2-24-2-22-422-40000000000−22−2222220002-422000000000022−22−222222−2−22222−2−2−2−2000000000000000000000000000000000
χ5944-24-2-2-24-2-24-2-2441-2111-211-24-2-2-2-2-2-2-244-2-2-2-200004-2-21-21111-2-21111000000000000000000-24-2-21-2111-211000000000000000000000
χ6044-24-2-2-24-2-24-2-2441-2111-211-24-2-2-2-2-2-2-244-2-2-2-20000-4221-21111-2-211110000000000000000002-422-12-1-1-12-1-1000000000000000000000
χ6144-24-2-2-24-2-24-2-2-4-41-2111-211-24-2-2-22222-4-4222200000−2i32i31-211-1-122-1-1-1-10000000000000000000000i3−2i3i3i3−i32i3−i3−i3000000000000000000000
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Here ζ is a primitive root of unity of order 48 (ζ48 = 1); i = ζ12.